HANDBOOK of MAGNETIC MATERIALS
VOLUME 14 EDITED BY
K.H.J. BUSCHOW Van der Waals-Zeeman Institute University of Amsterdam Amsterdam The Netherlands
I
2002
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First edition 2002 Library of Congress Cataloging in Publication Data A catalog record from the Library of Congress has been applied for. British Library Cataloguing in Publication Data Handbook of magnetic materials Vol. 14 edited by K.H.J. Buschow 1. Magnetic materials 2. Magnetism I. Buschow, K. H. J. 538.4'4
ISBN: ISBN:
044451144X(VoI.14) 0444 85313 8 (Series)
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PREFACE TO VOLUME 14
The Handbook series Magnetic Materials is a continuation of the Handbook series Ferromagnetic Materials. When Peter Wohlfarth started the latter series, his original aim was to combine new developments in magnetism with the achievements of earlier compilations of monographs, producing a worthy successor to Bozorth's classical and monumental book Ferromagnetism. This is the main reason that Ferromagnetic Materials was initially chosen as title for the Handbook series, although the latter aimed at giving a more complete cross-section of magnetism than Bozorth's book. In the last few decades magnetism has seen an enormous expansion into a variety of different areas of research, comprising the magnetism of several classes of novel materials that share with truly ferromagnetic materials only the presence of magnetic moments. For this reason the Editor and Publisher of this Handbook series have carefully reconsidered the title of the Handbook series and changed it into Magnetic Materials. It is with much pleasure that I can introduce to you now Volume 14 of this Handbook series Magnetoelectronics is a novel and rapidly developing field, where new functionalities are created by combining and utilizing simultaneously two degrees of freedom, the charge and the spin of the carriers. This new field is frequently referred to as spinelectronics or spintronics. It includes spin-utilizing devices that need neither a magnetic field nor magnetic materials. In semiconductor devices, the spin of the carriers has only played a very modest role so far because well established semiconductor devices are non-magnetic and show only negligible effects of spin. However, interesting enhanced spin-related phenomena were observed in magnetic semiconductors and diluted magnetic semiconductors already many years ago. A review of diluted magnetic semiconductors has been presented by Kossut and Dobrowolski in Volume 7. In a way compatible with the present-day electronic materials, diluted magnetic semiconductors can be prepared by introducing high concentrations of magnetic ions into the parent non-magnetic semiconductors. Semiconductors based on III-V compound are widely used for highspeed electronic devices as well as for optoelectronic devices. Moreover, heterostructures based on the GaAs/(Al,Ga)As systems have proven to be a convenient testing ground for novel physical concepts and devices. The introduction of magnetism into 111-V compounds therefore, opens up the possibility of using a variety of magnetic and/or spin-dependent phenomena. not present in the conventional non-magnetic parent compounds. Preparation and properties of ferromagnetic III-V based semiconductors are reviewed in Chapter 1, including heterostructures. Nanoscale thin films and multilayers, nanocrystalline magnetic materials, granular films, and amorphous alloys have attracted much attention in the last few decades, in the field of basic research as well as in the broader field of materials science. Such v
vi
PREFACE TO VOLUME 14
heterogeneous materials display uncommon magnetic properties that virtually do not occur in bulk materials. This is true, in particular with respect to surface (interface) magnetic anisotropy and surface (interface) magnetostrictive strains and giant magnetoresistance. The local atomic arrangement at the interface differs strongly from that in the bulk. The local symmetry is lowered, so that some interactions are changed or are missing altogether. The interface atoms may be envisaged as forming a new phase and some properties characteristic of this phase may become predominant for the entire system. This becomes particularly evident in the case of interfacial magnetostriction which can lead to a decrease (almost to zero) or to an increase (over the bulk value) of the resulting magnetostriction of the nanoscale system. In Chapter 2 of the present Volume, the magnetoelasticity of heterogeneous materials is treated in much details. Generally, the dimensions of a magnetostrictive material change when the material is subjected to a change in magnetic field. Hence, magnetostrictive materials can be applied in transducers, which directly convert electrical energy into mechanical energy. They are useful in the manufacture of sensors, actuators, controllers, force and displacement as well as other electro-acoustic devices. For these applications, transducer materials in the form of thin films are of special interest because cost-effective mass production is possible, compatible to microsystem processing technologies. In addition, magnetostrictive thin films are particularly promising as microactuator elements like cantilevers or membranes, since they combine high-energy output, high-frequency and remote-control operation. Due to this potential, interest in such giant magnetostrictive thin films has rapidly grown over the past few years and results are reviewed in this Chapter 2. This chapter is a logical extension of previous wok on magneto-elastic effects published in this handbook series over the years. Bulk giant magnetostrictive materials based on rare-earth compounds were reviewed by Clark (Volume I), quadrupolar interactions and magneto-elastic effects in rare-earth intermetallics were treated by Morin and Schmitt (Volume 5) and thermal expansion anomalies and spontaneous magnetostriction of these compounds were reviewed by Andreev (Volume 8). There are various forms of the interplay of magnetism and superconductivity, which can be divided into competition and coexistence phenomena. For instance, a strong competition is found in high- T e cuprates. In these materials, depending on the doping rate, either Neel-type antiferromagnetism or superconductivity may occur, both based on the copper d-electrons. A coexistence of localized magnetic moments (e.g. from 4f-elements) with superconductivity is known to occur in systems where the concentration of these moments is sufficiently small or where they are antiferromagnetically ordered and only weakly coupled to the conduction electrons. A review on the interplay of magnetism and superconductivity in various types of intermetallic compounds has been presented by Fischer in Volume 5 of the Handbook. An extensive review on the normal state magnetic properties of cuprate high-temperature superconductors and related materials has been presented by Johnston in Volume 10. A striking feature distinguishing the superconducting RT2B2C compounds from other superconductors is the following: For certain combinations of the Rand T elements superconductivity and antiferromagnetic order have been found to coexist and more importantly, the values of the magnetic ordering temperature TN are comparable in magnitude with the values of the superconducting transition temperatures T e . This means that the magnetic energy is comparable with the
PREFACE TO VOLUME 14
vii
superconducting condensation energy. Therefore the investigation of these compounds is expected to result in new insights into the interplay between superconductivity and magnetism. The high values of T~ demand that in the quaternary borocarbides, different from the situation in high- T c cuprates and the classical magnetic superconductors, the exchange coupling between the rare-earth magnetic moments is the dominant magnetic interaction rather than magnetostatic interaction. Obviously the exchange coupling is mediated by the conduction electrons, Consequently also the interaction between the magnetic moments and the conduction electrons must be relatively strong in the quaternary borocarbides. A comprehensive review on the current status of research of the quaternary borocarbide superconductors, starting from their discovery, is presented in Chapter 3 of this Volume. For the reasons mentioned, the magnetic and as well as the superconducting properties of this interesting class of materials is discussed together. During the years, intermetallic gadolinium compounds have adopted a special position in the study of 4f electron magnetism. The reason for this is the fact that the gadolinium moment consists only of a pure spin moment, orbital contributions to the moment being absent. As a consequence, gadolinium compounds have been regarded as ideal test benches for studying exchange interactions, free from complications due to crystal field effects. Large spontaneous magnetoelastic effects are frequently associated with rare earth compounds in which crystal fields are operative and in which the rare earth moments also have an orbital contribution. Surprisingly, equally large spontaneous magnetoelastic effects have been observed in some Gd compounds, showing that the contribution of the exchange interaction to spontaneous magnetoelastic effects can become of equal importance as the crystal field contribution. In several of the Gd compounds so-called magnetostructural transitions occur where giant spontaneous as well as forced magnetoelastic effects can be correlated with structural transitions. In Chapter 4 a review is given of experimental studies of spontaneous magnetoelastic effects in Gd compounds, offering the possibility to estimate the relative contribution of exchange striction to the total spontaneous magnetoelastic effects in materials where also crystal field related contributions are present. Volume 14 of the Handbook on the Properties of Magnetic Materials, as the preceding volumes, has a dual purpose. As a textbook it is intended to be of assistance to those who wish to be introduced to a given topic in the field of magnetism without the need to read the vast amount of literature published. As a work of reference it is intended for scientists active in magnetism research. To this dual purpose, Volume 14 of the Handbook is composed of topical review articles written by leading authorities. In each of these articles an extensive description is given in graphical as well as in tabular form, much emphasis being placed on the discussion of the experimental material in the framework of physics, chemistry and material science. The task to provide the readership with novel trends and achievements in magnetism would have been extremely difficult without the professionalism of the North Holland Physics Division of Elsevier Science B.Y., and I wish to thank Paul Penman for his great help and expertise. K.H.J. Buschow Van der Waals-Zeeman Institute University of Amsterdam
CONTENTS
Preface to Volume 14
v
Contents
ix
Contents of Volumes 1-13
xi
List of Contributors
xv
1. III-V Ferromagnetic Semiconductors F. MATSUKURA, H. OHNO and T. DIETL 2. Magnetoelasticity in Nanoscale Heterogeneous Magnetic Materials N.H. DUC and P.E. BROMMER 3. Magnetic and Superconducting Properties of Rare Earth Borocarbides of the Type RNi 2 B 2 C K.-H. MULLER, G. FUCHS, S.-L. DRECHSLER and V.N. NAROZHNYI . . . 4. Spontaneous Magnetoelastic Effects in Gadolinium Compounds A. LINDBAUM and M. ROTTER
307
Author Index
363
Subject Index
405
Materials Index
413
ix
1 89
199
CONTENTS OF VOLUMES 1-13 Volume 1 1. 2. 3. 4. 5. 6. 7.
Iron, Cobalt and Nickel, by E. P. Wohlfarth Dilute Transition Metal Alloys: Spin Glasses, by J. A. Mydosh and G.J. Nieuwenhuys Rare Earth Metals and Alloys, by S. Legvold Rare Earth Compounds, by K. H. J. Buscfum Actinide Elements and Compounds, by W. Trzebiatowski Amorphous Ferromagnets. by F E. Luborsky Magnetostrictive Rare Earth-Fe^ Compounds, by A. E. Clark
1 71 183 297 415 451 531
Volume 2 1. 2. 3. 4. 5. 6. 7. 8.
Ferromagnetic Insulators: Garnets, by M. A. Giileo Soft Magnetic Metallic Materials. byG.Y.Chin and J. H. Wernick Ferrites for Non-Microwave Applications, by P. I. Slick Microwave Ferrites, by J. Nicolas Crystalline Films for Bubbles, by A.M. Eschenfelder Amorphous Films for Bubbles, by A. H. Eschenfelder Recording Materials, by G. Bate Ferromagnetic Liquids, by S. W. Charles and J. Popplewell
I 55 189 243 297 345 381 . 509
Volume 3 1. Magnetism and Magnetic Materials: Historical Developments and Present Role in Industry and Technology, by U, Enz 2. Permanent Magnets; Theory, by H. Zijlstra 3. The Structure and Properties of Alnico Permanent Magnet Alloys, by R. A. McCurrie 4. Oxide Spinels, by S. Krupitka and P. Novak 5. Fundamental Properties of Hexagonal Ferrites with Magnetoplumbite Structure. byH.Kojima 6. Properties of Ferroxplana-Type Hexagonal Ferrites, by M. Sugimota 7. Hard Ferrites and Plastoferrites. by H. Stablein 8. Sulphospinels. by R. P. van Stapelt 9. Transport Properties of Ferromagnets. by I. A. Campbell and A. Fert
I 37 107 189 305 393 441 603 747
Volume 4 1. Permanent Magnet Materials Based on 3d-rich Ternary Compounds, by K. H. J. Buschaw . . . . 2. Rare Earth-Cobalt Permanent Magnets, by A J. Srrnai . 3. Ferromagnetic Transition Metal Intermeiallic Compounds, by J. G. Booth XI
1 131 211
xii
CONTENTS O F VOLUMES 1-13
4. Intermetallic Compounds of Actmides. by V. Sechmsky and L Havela
309
5. Magneto-Optical Properties of Alloys and Intermetallic Compounds, by K. H. J. Buschow
.
.
.
493
Volume 5 1. Quadrupolar Interactions and Magneto-Elastic Effects in Rare-Earth Intermetallic Compounds. by P Morin and D. Schmitt
I
2. Magneto-Optical Spectroscopy of f-Electron Systems, by W. Reim and J. Schitenes
133
3. INVAR: Moment-Volume Instabilities in Transition Metals and Alloys, by E.F. Wassermtm
.
.
.
4. Strongly Enhanced Itinerant Intermelallics and Alloys, by P. E. Bmmmerand
.
.
.
J.J. M. Franse
237 323
5. First-Order Magnetic Processes, by C Asti
397
6. Magnetic Superconductors, by 0. Fischer
465
Volume 6 1. Magnetic Properties of Ternary Rare-Earth TransUion-Metal Compounds, by H.-S. Li and J.M.D.Coey 2. Magnetic Properties of Ternary Intermetallic Rare-Earth Compounds, by A. Szylula
1 85
3. Compounds of Transition Elements with Nonmetals. by O. Bechnan and L. Lundgren
181
4. Magnetic Amorphous Alloys, by P. Hansen
289
5. Magnetism and Ouasicrystals. byR. C. O'Hundley. R.A. Dunlap andM. E McHenry
453
6. Magnetism of Hydrides, by G. Wiesinger and G. Hilscher
511
Volume 7 1. Magnetism in Ultrathin Transition Metal Films, by II. Gradmann 2. Energy Band Theory of Metallic Magnetism in the Elements, by V.L Moruzzi and P.M.Man-us 3. Density Functional Theory of the Ground State Magnetic Properties of Rare Earths and Actinides. by M. S. S. BrtH>ks and B. Johansson
1 97 139
4. Diluted Magnetic Semiconductors, by J. Kossut and W. Dobrmvolski
231
5. Magnetic Properties of Binary Rare-Earth 3d-Transition-Metal Intermetallic Compounds, by J.J. M. Franse and R.J'. Radv.an.ski
307
6. Neutron Scattering on Heavy Fermion and Valence Fluctuation 4f-systems. by M. Ldoewenhaupl and K. H. Fischer
503
Volume 8 1. Magnetism in Artificial Metallic Superlattices of Rare Earth Metals, by J.J. Rhyne and R. W. En* in 2. Thermal Expansion Anomalies and Spontaneous Magnetostriction in Rare-Earth Intermetallics with Cobalt and Iron, by A. V. Andreev 3. Progress in Spinel Ferrite Research, hy V. A. M. Brabers
1 59 189
4. Anisotropy in Iron-Based Soft Magnetic Materials, by M. Soinski and A. J. Moses
325
5. Magnetic Properties of Rare Earth-Cui Compounds, hy Nguyen Hoang Luang and J.J.M. Franse
415
Volume 9 1. Heavy Fermions and Related Compounds, hy G.J. Nieuwenliuys 2. Magnetic Materials Studied by Muon Spin Rotation Spectroscopy, hy A. Schenck and F.N. Gygax
1 57
CONTENTS OF VOL UMES 1-43
xiii
3. Interstitially Modified Intermetallics of Rare Earth and 3d Elements, by H. Fujii and H. Sun
.
.
.
4. Field Induced Phase Transitions in Ferrimagnels. by A. K. Zvezdin 5. Photon Beam Studies of Magnetic Materials, by S. W. Lmesey
.¾).¾
4()5 545
Volume 10 1. Normal-State Magnetic Properties of Single-Layer Cuprate High-Temperature Superconductors and Related Materials, by D.C. Johnston 1 2. Magnetism of Compounds of Rare Earths with Non-Magnetic Metals, by D. Gignoux and D. Schmitt 239 3. Nanocrystalline Soft Magnetic Alloys, by G. Herzer 415 4. Magnetism and Processing of Permanent Magnet Materials, by K.H.J. Buschow 463
Volume 11 1. Magnetism of Ternary Intermetallic Compounds of Uranium, by V. Sechovsky and L. Have la . . 1 2. Magnetic Recording Hard Disk Thin Film Media. byJ.C. Ladder 291 3. Magnetism of Permanent Magnet Materials and Related Compounds as Studied by NMR. by Cz. Kapu.ua. PC. Riedi and G.J. Tomka 407 4. Crystal Field Effects in Intermetallic Compounds Studied by Inelastic Neutron Scattering, by O. Maze 493
Volume 12 1. Giant Magnetoresistance in Magnetic Multilayers, by A. Barthe'lemy, A. Fertand F. Petrvff . . . 2. NMR of Thin Magneiic Films and Superlattices. by P.C. Riedi. T. Thomson and G.J. Tomka . . . 3. Formation of 3d-Moinents and Spin Fluctuations in Some Rare-Earth-Cobalt Compounds. by N.H. Due and P.E. Brtmmer 4. Magnetocaloric Effect in the Vicinity of Phase Transitions, by A.M. Ttshin
I 97 259 395
Volume 13 1. Interlayer Exchange Coupling in Layered Magnetic Structures, by D.E. Biirgler. P. Grtinberg, S.O. Demokritpx-andM.T. Johnson 2. Density Functional Theory Applied to 4f and 5f Elements and Metallic Compounds, by M. Richter 3. Magneto-Optical Kerr Spectra, by P.M. Oppeneer 4. Geometrical Frustration, by A. P. Ramirez
1 87 229 423
Material chroniony prawem autorskim
LIST OF CONTRIBUTORS
P.E. Brommer, Van der Waals-Zeeman Instituut, Universiteit van Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam, The Netherlands T. Dietl, Research Institute of Electrical Communication, Tohoku University, Sendai, Japan S.-L. Drechsler, Leibniz-Institut filr Festkorper- und Werkstofforschung Dresden, P.O. Box 270116, D-O1171, Dresden, Germany N.H. Due. Cryogenic Laboratory, Faculty of Physics. National University of Hanoi, 334 Nguyen Trai, Thanh xuan, Hanoi, Vietnam G. Fuchs. Leibniz-Institut fur Festkorper- und Werkstofforschung Dresden, P.O. Box 270116, D-O1171, Dresden, Germany A. Lindbaum, Institut fur Festkorperphysik, Technische Universitat Wien, Wiedner Hauptstrasse 8-10/138, A-I040 Wien, Austria
F. Matsukura, Laboratory for Electronic Intelligent Systems, Research Institute of Electrical Communication, Tohoku University, Sendai, Japan K.-H. Muller, Leibniz-Institut fur Festkorper- und Werkstofforschung Dresden, P.O. Box 270116, D-O1171, Dresden, Germany V.N. Narozhnyi, Leibniz-Institut fUr Festkorper- und Werkstofforschung Dresden, P.O. Box 270116, D-O1171, Dresden, Germany H. Ohno, Laboratory for Electronic Intelligent Systems, Research Institute of Electrical Communication, Tohoku University, Sendai, Japan M. Rotter, Institut fur Angewandte Physik, Technische Universitlit Dresden, D-01062, Dresden, Germany
chapter 1 III-V FERROMAGNETIC SEMICONDUCTORS
F. MATSUKURA Laboratory for Electronic Intelligent Systems Research Institute of Electrical Communication, Tohoku University Sendai Japan
H.OHNO Laboratory for Electronic Intelligent Systems Research Institute of Electrical Communication, Tohoku University Sendai Japan
T. DIETL
Institute of Physics, Polish Academy of Sciences Warszawa Poland
Handbook of Magnetic Materials, Vol. 14 Edited by K.H.J. Buschow © 2002 Elsevier Science B.V. All rights reserved
CONTENTS I. Introduction
.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2. Preparation of III-V magnetic semiconductors by molecular beam epitaxy 2.1. (Ga,Mn)As
.
4
6 6
2.2. (In,Mn)As grown on GaAs
10
2.3. (In,Mn)As grown on (AI,Ga)Sb
II
2.4. Other Ill-V magnetic semiconductors .
12
.
15
3.1. Lattice constants . . . . . . . . . . .
15
3.2. Local lattice configuration (EXAFS)
17
3.3. Atomic-scale observations by scanning tunneling microscopy (STM)
18
3. Lattice properties
4. Spin and charge states of Mn in III-V magnetic semiconductors.
18
4.1. Electron spin resonance (ESR)
.
4.2. Optical spectroscopy . . . . . . .
.
19
4.3. X-ray magnetic circular dichroism (XMCD)
20
4.4. Photoemission
21
19
5. Magnetic properties .
21
5.1. Magnetization.
21
5.2. Magnetic anisotropy
24
5.3. Magnetic domains .
26
5.4. Cantilever magnetometry
26 27
6. Magnetotransport properties 6.1. (Ga,Mn)As
27
6.2. (In,Mn)As .
34
6.3. Infrared and far infrared optical conductivity .
37
6.4. Cyclotron resonance
37
7. Magneto-optical properties
38
7.1. Faraday rotation
39
..
40
7.2. Magnetic circular dichroism (MCD) 8. Origin of ferromagnetism 8.1. First-principles studies
.
41
.
41
8.2. Parameterized Hamiltonians . .
45
8.3. Hole states and hole mediated exchange interactions
47
8.4. Mean-field Zener model and its application to (Ga,Mn)As
50
8.5. Comparison of theoretical and experimental results
55
2
III-V FERROMAGNETIC SEMICONDUCTORS 8.6. Limitations and refinements of the mean-field Zener model ..
3 59
9. Heterostructures . . . . . . . . . . . . . .
61
9.1. Basic properties of heterostructures
61
9.2. Spin-dependent scattering. interlayer coupling. and tunnel magnetoresistance in trilayer structures
64
9.3. Resonant tunneling diodes (RTDs) .. . . . . . . . . . . . . . . .
67
9.4. Spin-injection in ferromagnetic semiconductor heterostructures
70
9.5. Photo-induced ferromagnetism in (In.Mn)AslGaSb . . . . .
72
9.6. Electric-field control of ferromagnetism in gated structures .
73
9.7. Ferromagnetic imprinting .. . . . . . . . . .
75
10. Ferromagnetic semiconductors at room temperature
75
10.1. Theoretical suggestions
75
10.2. Cautionary remarks.
77
10.3. Experimental results
77
11. Summary and outlook . Acknowledgements References
.
79 79 79
1. Introduction Modem information technology utilizes the charge degree of freedom of electrons in semiconductors to process the information and the spin degree of freedom in magnetic materials to store the information. Magnetoelectronics is a new fastly developing field, where the two degrees of freedom, the charge and the spin of the carriers, are utilized simultaneously to create new functionalities. In more general terms, this new field is referred to as spin-electronics or spintronics to include those spin-utilizing devices that need neither the magnetic field nor magnetic materials. The magnetoresistance (MR) sensors made of multilayers containing metal ferromagnets, showing giant magnetoresistance (GMR) or tunneling magnetoresistance (TMR), are today's best known successful magnetoeloectronics devices based on the interplay between the two degrees of freedom (Prinz 1998; De Boeck and Borghs 1999; Wolf 2000; Ball 2000; Ziese and Thornton 200 I; Wolf et al. 2001). In semiconductor devices, the spin of carriers has played a minor role so far because the most-well established semiconductor devices based on Si and GaAs are non-magnetic and show only negligible effects of spin. On the other hand, from the physical points of view, the enhanced spin-related phenomena due to the coexistence of the magnetism and semiconductor properties have been recognized in magnetic semiconductors and diluted magnetic semiconductors (DMS) (or semimagnetic semiconductors; SMSC) since the 60s. The family of magnetic semiconductors encompasses europium and chromium chalcogenides (rock-salt type: EuSe, EuO and spinels: CdCr2S4, CdCr2Se4), which show ferromagnetic order at low temperatures with the Curie temperature Tc :::; 100 K. They have been extensively studied, because of their peculiar properties resulting from the exchange interaction between itinerant electrons and localized magnetic spins (s-f and s-d exchange interactions) (Kasuya and Yanase 1968; Methfessel and Mattis 1968; Mauger and Gotard 1986). Owing to these interactions, magnetic semiconductors exhibit a rich variety of striking optical and transport phenomena, which are strongly affected by the magnetic field and the magnetic order, particularly near the metal-to-insulator transition (MIT). However, difficulties in material preparation and in fabrication of heterostructures make this family of compounds less attractive from the application point of view. Manganites (perovskite: (La,Sr)Mn03 and related materials), which show colossal magnetoresistance (CMR), are magnetic semiconductors, whose studies have been particularly active over the recent years. Their ferromagnetic order, beginning at "" 350 K, originates from the doubleexchange interaction. Properties of manganites and their epitaxial heterostructures are currently studied aggressively (Coey et al. 1999; Tokura and Tomioka 1999; Tokura 2000). Their compatibility to the well-established electronic devices is an open issue because of the differences in both crystal structure and constituting elements. 4
III-V FERROMAGNETIC SEMICONDUCTORS
5
DMS are based on non-magnetic semiconductors, and are obtained by alloying them with a sizable amount (a few percents or more) of magnetic elements, such as Mn. The studies of DMS and their heterostructures have offered a wide variety of materials and structures, making it possible to explore further the effect of the exchange interaction in semiconductors. Most of the work had been centered around II-VI based materials such as (Cd,Mn)Te, (Zn,Co)S, (Hg,Fe)Se, where the valence of group II cations is identical to that of most magnetic transition metals (Furdyna and Kossut 1988; Kossut and Dobrowolski 1993; Dietl 1994). Although this made them relatively easy to prepare, difficulties in doping of II-VI-based DMS to either p- or n-type as well as relatively weak bonds made these materials less attractive for applications. The magnetic properties of II-VI DMS are dominated by the antiferromagnetic super-exchange interactions among the localized spins, which result in paramagnetic, spinglass or antiferromagnetic behavior depending on the concentration of the magnetic ions and temperature. Recent progress in doping of II-VI materials is gradually changing this situation (Shibata et at. 1988; Baron et at. 1994), for example, hole mediated ferromagnetism was found in p-type II-VI DMS with Tc < 10 K (Haury et at. 1997; Ferrand et at. 2001; Hansen et a1. 200 1). Understanding of the carriermediated ferromagnetism in semiconductors was put forward by a study of ferromagnetism in IV-VI DMS such as (Pb.Sn.Mnj'Ie (Story et al. 1986). However, IV-VI DMS and their heterostructures are again rather difficult to prepare. An approach compatible with the present-day electronic materials is to make nonmagnetic semiconductors magnetic, and even ferromagnetic, by introducing a high concentration of magnetic ions. III-V compound semiconductors are widely used for highspeed electronic devices as well as for optoelectronic devices. Moreover, heterostructures based on the GaAs/(Al,Ga)As systems have proven to be a convenient test bench for new physics and device concepts. Introduction of magnetic III-V compounds opens, therefore, up the possibility of using a variety of magnetic and/or spin-dependent phenomena, not present in the conventional non-magnetic III-Vs, in the optical and electrical devices already established (fig. 1). The proposal of III-V based magnetic semiconductors with various sets of host materials and transition metals was put forward in 1970s (Galazka 1977), and some experimental studies were then initiated. At that time, however, III-V materials with a sizable concentration of uniformly distributed magnetic elements were not obtained due to the low solubility of transition metals in III-V semiconductors (Aliyev et a1. 1980). The application of non-equilibrium methods to grow III-V-based DMS was rewarded by successful molecular beam epitaxy (MBE) of uniform (In,Mn)As films on GaAs substrates (Munekata et at. 1989). Subsequent discovery of the hole-induced ferromagnetic order in p-type (In,Mn)As (Ohno et a1. 1992) encouraged researchers to investigate GaAs-based system (De Boeck et at. 1996) and led to the successful growth of ferromagnetic (Ga,Mn)As (Ohno et a1. 1996a). Currently, a number of groups is working on the MBE growth of (Ga,Mn)As and related heterostructures to advance the understanding of this new class of materials (Ohno et a1. 1996a; Ohno 1999; Hayashi et a1. 1997a; Nishikawa et a1. 1997; Van Esch et a1. 1997; Sadowski et at. 1998; Kawakami et at. 2000; Potashnik et a1. 200 1; Schott et a1. 200 1; Liu et a1. 200 1). This chapter reviews the properties of ferromagnetic III-Vs, and is organized in the following way. Section 2 describes the preparation of ferromagnetic III-Vs, and is followed by the presentation of lattice properties in section 3. In section 4, spin and charge states of
6
F. MATSUKURA et aI.
Fig. I. Concept of spin-electronics (spintronics). In semiconductor spin-electronics spin properties as well as electronic and optical properties are utilized at the same time.
magnetic ions in III-V DMS are discussed. The magnetic and magnetotransport properties are presented in sections 5 and 6. respectively. Section 7 summarizes optical and magnetooptical properties. Possible origin of ferromagnetism in III-V-based DMS is discussed in section 8. Properties of heterostructures are presented in section 9 and recent developments of room-temperature ferromagnetic semiconductors are introduced in section 10. Summary and outlook is given in section II. 2. Preparation of 111-V magnetic semiconductors by molecular beam epitaxy In order to observe magnetic cooperative phenomena in diluted magnetic systems. one needs to introduce a sizable amount of magnetic elements (a few percents or more). which is beyond their solubility limit in III-V semiconductors. Although non-equilibrium epitaxial growth methods such as molecular beam epitaxy (MBE) could offer doping in excess of the thermodynamic solubility limit. segregation of impurities during MBE growth was an obstacle in obtaining high concentrations of magnetic elements (DeSimone 1982). It was demonstrated that low temperature MBE (LT-MBE. growth temperature Ts < 300°C) can lead to successful epitaxy of (In.Mn)As with a few percents of Mn, in which the solubility limit is overcome as well as the segregation phenomena. and the formation of unwanted second phases is suppressed (Munekata et al. 1989). InAs was chosen as a host compound because it was thought to be a suitable material for low temperature growth due to its relatively small bond energy. 2.1. (Ga,Mn)As
Typical MBE growth of (Ga,Mn)As is carried out by using solid source MBE with elemental sources Ga. Mn, In. Al and As, usually without intentional doping. Mn provides both localized spins and holes due to its acceptor nature. Epitaxial films of (Ga.Mn)As are grown on semi-insulating GaAs (00 I) substrates at a typical growth rate of 0.60.8 JLmlhour under As-stabilized conditions. Normally. either a GaAs buffer layer or an
III-V FERROMAGNETIC SEMICONDUcrORS
7
(Al,Ga)As buffer layer is grown before epitaxy of (Ga,Mn)As. To control strain in the film, strain-relaxed thick (In,Ga)As ('" 1 jlm) with the lattice constant Q o greater than the subsequent (Ga,Mn)As layer can be employed. The Mn composition x in the Ga I-x Mn, As films can be determined from measurements of Q o by x-ray diffraction (XRD), once the dependence Qo(x)is calibrated by other means, such as electron probe micro-analysis (EPMA) or secondary ion mass spectroscopy (SIMS). The growth of (Ga,Mn)As can be initiated by simply commencing the Mn flow during the LT-GaAs growth and keeping the substrate temperature Ts constant at 250°C. No special precautions are needed at the start of (Ga,Mn)As growth. However, properties of (Ga,Mn)As films do depend on the growth parameters such as As overpressure and Ts (Matsukura et al. 1998a; Shimizu et al. 1999; Schott et al. 200 1). This may stem from the influence of these parameters on the degree of compensation of the Mn acceptors by deep donors, primarily As antisites which are known to be present with a high concentration in LT-GaAs (Look 1991; Luysberg et al. 1998). However, as long as the established growth procedure is followed, the properties of (Ga,Mn)As films are reproducible; for example, for a given Mn composition x, the ferromagnetic transition temperature Tc can always be maintained in the range of 2000x ± 10 K (Matsukura et al. 1998b). Reflection high-energy electron diffraction (RHEED) patterns are used to monitor the surface reconstruction during the growth. RHEED of GaAs [or (AI,Ga)As] buffer layer grown at Ts '" 570°C shows the well-known (2 x 4) pattern, which changes to the c(4x4) pattern when Ts is lowered to 48D-520°C, and remains c(4x4) below. Whereas the RHEED pattern of GaAs layers grown at Ts = 250°C shows a (I x I) pattern (no reconstruction) (fig. 2a), that of (Ga,Mn)As is (I x2) during and after the growth (fig. 2b). The origin of this difference is not yet clear. When the Mn flux and/or Ts are too high, the RHEED pattern indicates the appearance of a second phase on the surface, which is MnAs in the hexagonal NiAs-structure (fig. 2d). When Ts is too low, spotty RHEED pattern appears showing that the growth mode changes from the two-dimensional (2D) to threedimensional (3D), resulting in a polycrystalline material (fig. 2c). The maximum value of x obtained so far is about 0.07 at 250°C, and increases up to '" 0.10 at Ts = 200°C (Takamura et al. 200 1). Attempts to increase x even further have so far been unsuccessful because of the surface segregation that occurs even at low growth temperatures. At a fixed value of x = 0.035, epitaxial (Ga,Mn)As films can be grown at Ts varying from 160 to 320°C (Shen et al. 1997a). Clear RHEED oscillations are observed at the initial growth stage (also without Mn) under the conditions appropriate for (Ga,Mn)As epitaxy. Thus, the growth is twodimensional, and its rate can be determined from the oscillation period (fig. 3) (Shen et al. 1997a, 1997b). Monte Carlo simulations of RHEED oscillations have been carried out for LT-GaAs employing the cubic solid-on-solid model (Yasuda and Ohno 1999). The results show that the RHEED oscillations are related to an enhancement in migration of Ga adatoms caused by a surfactant effect of the excess As overlayer. The surfactant effect of As is demonstrated also by the surface visualization (Guo et al. 2000; Tazima et al. 2001a). Scanning tunneling microscopy (STM) study of LT-GaAs shows that the step density on the surface increases monotonically with the decrease of Ts, indicating the monotonous decrease of Ga migration length. This result suggests that the origin of RHEED oscillation may also relate to the decrease of the Schwoebel barrier height due to the formation of
8
F. MATSUKURA et a1.
Fig. 2. Reflection high energy electron diffraction (RHEED) patterns taken from [110] azimuth. (a) Low-temperature grown GaAs at 250o e. (b) (Ga,Mn)As at 250 o e. (c) 170o e. and (d) 320 0 e (Shen et a1. I997a).
tshu er openingGaAs T=600°C
t ~
~
GaAs
~500C
W
IZ
(Ga,Mn)As T=250°C s
2s
......
TIMEFig. 3. Temporal evolution of RHEED specular beam intensity (along [110] azimuth) for GaAs at 6OOo e. GaAs at 250o e. and (Ga.Mn)As at 250 0 e from top to bottom (Shen et at. I997a).
III-V FERROMAGNETIC SEMICONDUCTORS
....
.
..... .....
300
\
--
200
,-
\
\ \
. ...CIl
~
.
Growth inhibited, ..... ..... formation of MnAs ..... ..... • ..... ..... ..... ..... ~ Metallic (Ga,Mn)As
~\
p
.
9
,
I /
,
/Insulating· ......... _ .... ", (Ga,Mn)As Roughening
Polycrystal 100 "'--_......_-"""'--_......._ _... 0.02 0.04 0.06 0.08 0.00 Mn composition x in Ga 1_xMnxAs
.
.
Fig. 4. Schematic diagram of properties of {Ga,Mn)As films in relation to the growth parameters. Lines provide a rough guide (Ohno 1998; Shen et aI. 1999).
small growth islands (Tazima et al. 200 Ib). The enhancement of the RHEED oscillation of (Ga,Mn)As is observed, when the lattice-relaxed (In,Ga)As is used as a buffer layer (Matsukura 1997) or (Ga,Mn)As contains a few percents of In (Katsumoto 1999). In these cases, it is considered that In atoms act as additional surfactant. A schematic phase diagram of MBE growth is depicted in fig. 4 (Ohno 1998; Shen et al. 1999). Recently it was shown that metallic (Ga,Mn)As with x = 0.1 can be obtained by the use of a modified MBE growth technique at Ts = 150°C, migration-enhanced epitaxy (MEE), where the beam fluxes of source materials are precisely controlled (Sadowski et al.
zoois.zoouo. The surface morphology investigated by atomic-force microscopy (AFM) shows that (Ga,Mn)As with 2D growth mode has a flat surface being comparable with a GaAs surface [root-mean-square (RMS) of the roughness < 0.5 nm]. On the other hand, (Ga,Mn)As with segregated RHEED pattern has a rather rough surface, characterized by about 10 times larger RMS, which is probably due to small MnAs clusters (Yang et al. 2000). The homogeneity of as-grown (Ga,Mn)As and the precipitation of MnAs clusters after annealing at around 600°C are confirmed by transmission electron microscopy (TEM) (De Boeck et al. 1996). The disappearance of the (Ga,Mn)As phase by annealing at temperatures above 400°C is also confirmed by the disappearance of x-ray diffraction peaks of (Ga,Mn)As (Shen et a1. 1997a). Low-temperature annealing at '" 300°C changes lattice constant, magnetic, and electrical properties of (Ga,Mn)As, which is thought to result from the evaporation of excess As atoms that form complexes with Mn acceptors (Hayashi et a1. 200 I; Potashnik et al, 200 I). By additional doping of high concentration of Sn, n-type (Ga,Mn)As can be also grown (Satoh et a1. 1997,2001).
10
F. MATSUKURA er aI.
It has been shown that digital alloys. multilayer structures consisting of GaAs and less-than 1 monolayer (ML)-thick MnAs. which exhibit the ferromagnetic order at low temperatures. can be grown by atomic-layer epitaxy (ALE) (Chen et al. 2000; Kawakami et al, 2(00). The growth of (Ga.Mn)As with nominal Mn composition up to 0.04 by metal-organic vapor-phase epitaxy (MOVPE) has also been carried out. MOVPE-grown (Ga.Mn)As includes MnAs microclusters due to the high-growth temperature of 400600°C. which is necessary for the decomposing of precursor compounds (Hartmann et a1. 2000; Heimbrodt et a1. 2001). MBE growth of (Ga.Mnjas on GaAs (41l)A and Si (00l) substrates and (In.Ga.MnjAs on InP (001) substrates and the observation of their ferromagnetism also have been carried out (Omiya et al. 200 1; Zhao et al. 2002; Ohya et a1. 200 I; Siupinski et al. 2002a).
2.2. (In.Mn)As grown on GaAs The overall trend in the properties of (In.Mn)As grown by MBE can be summarized in terms of x and Ts (Munekata et al. 1989. 1990. 1991; Ohno et a1. 1991). When (In.Mn)As layers are grown directly on the GaAs substrate. either Il'- or p-type conduction is observed depending on x and Ts. At Ts of 200°C. thick (In.Mn)As layers (> I JLm) grown on GaAs (00l) substrates are n-type. The anomalous Hall effect. which is proportional to the perpendicular component of the magnetization of the film. has not been observed in n-type films. Donor-type defect formation in the InAs host lattice at growth temperature is most probably responsible for the n-type conduction in such (In.Mn)As layers. Defect formation may also be enhanced by the high density of mismatch dislocations in the (In.Mn)As layers; the lattice mismatch in question is about 7%. When Ts < 200°C. polycrystalline growth occurs. At higher Ts of 400°C. the layers are p-type at low x « 0.03). MnAs ferromagnetic clusters start to form above x = 0.03. and the films become eventually n-type at high x values of 0.18. The hole concentration is identical to the Mn concentration up to x = 0.004 (p = 7 X 10 19 cm'). at which the hole concentration peaks and then rolls off with the increase of x. Thus. in the low x region of thick p-type layers grown at 300°C. Mn behaves as a shallow acceptor. At x = 0.026 the hole concentration is 3 x 10 18 cm >'. No epitaxy is observed at Ts > 400°C. The phase diagram showing the relation between film properties and growth parameters is shown in fig. 5 (Ohno et al. 1991). Low-temperature annealing of (In.Mn)As results in an increase of p and Te. similar to (Ga.Mnj.As (Endo et al, 2001; Hashimoto et al. 2002). The homogeneity of (In.Mn)As films grown at '" 200°C and the existence of MnAs clusters in the samples grown at '" 300°C are confirmed by TEM observation. The annealing at 450°C modifies the size of the clusters (Guha and Munekata 1993; Van Esch et a1. 1995). InAs quantum dots (QDs) fabricated by the self-organized growth mode (StrankiKrastanov mode) have attracted a great deal of interest. The interplay between dimensional confinement and magnetism is certainly an interesting topic to pursue. The formation of self-organized (In.Mnjas dots was demonstrated by growing (In.Mn)As on (00l), (211)B. (311)B GaAs substrates by MBE at Ts = 350°C (Guo et al. 1998, 1999). In order to obtain uniform structures. the growth temperature should be kept as high as possible. close to the point of the phase separation. Photoluminescence from (In.MmAs QDs has been observed (Sadowski et al. 200lc).
11
III-V FERROMAGNETIC SEMICONDUcrORS ( (
Growth Inhibited
400
p-lnMnAs
p-lnMnAs+MnAs
6300-
.
'?..-
CIl
x-O.03
t-
200
.
n-lnMnAs (x s 0.24)
Polycrystal l\
I
100 ' - - - - - - - - - - - - , 'r--~ IJ 0.25 0.00 Mn composition x in In,."Mn"As Fig. 5. Schematic diagram of properties of (In,Mn)As films grown directly on GaAs (001) substrate in relation to the growth parameters (Ohno et al. 1991).
2.3. (In,Mn)As grown on (Al,Ga)Sb Contrary to the results of thick layers directly grown on GaAs substrate, thin (In,Mn)As layers « 30 nm) grown at 200°C pseudomorphically on thick (Al,Ga)Sb buffer layers (200-500 nm grown on (001) GaAs substrates) are p-type (Ohno et al. 1992; Munekata et al. 1992). A schematic phase diagram of thin (In,Mn)As layers on (Al,Ga)Sb buffer layer is shown in fig. 6 (Munekata 1995). The p-type conduction results, most probably, from the acceptor nature of Mn and low dislocation density in the pseudomorphic thin layers. Although the lattice mismatch between the (In,Mn)As layers and the (AI,Ga)Sb buffer layers is small, depending on the growth procedure different initial growth modes have been observed (Shen et al. 1997c). Careful minimization of As flux is required to obtain 2D growth at the initial stage of (In,Mn)As epitaxy (x = 0.02-0.04) on (Al,Ga)Sb, otherwise 3D growth takes place, as witnessed by RHEED patterns. It is interesting to note that despite streaky RHEED patterns that appear after 10-20 nm growth of (In,Mn)As, the magnetic properties, probed by the anomalous Hall effect, show a correlation with the initial growth mode. In particular, the 3D nucleation results in superparamagnetism, whereas the 2D nucleation leads to ferromagnetism with square hysteresis (Shen et al. 1997c). The tensile strain associated with the lattice mismatch between (In,Mn)As and (Al,Ga)Sb (0.6-1.3%) makes the easy axis to be perpendicular to the film plane (Munekata et al. 1993). The increase of the thickness beyond the critical value (about 55 nm for (In,Mn)As/AlSb) causes lattice relaxation, which affects magnetic anisotropy. The thickness of the (In,Al)As spacer layer (AI composition r - 0.15) between (In,Mn)As layer and AISb buffer also influences the magnetic properties of (In,Mn)As (Munekata et al. 1992).
12
F. MATSUKURA et al.
,
x= x . I
300
I \
.
C
p-lnMnAs + MnAs
.. - - - - - - - -T=TC
p-lnMnAs on (AI,Ga)Sb I GaAs(001
200 ~ 0.0
.
.
0.1
0.2
Mn composition
x in In 1•xMn xAs
Fig. 6. Schematic diagram of properties of (In,Mn)As films grown on GaAs substrate with thick (AI,Ga)Sb buffer layer between the two in relation to the growth parameters (Munekata 1995).
2.4. Other III-V magnetic semiconductors
With the advances of the non-equilibrium crystal growth techniques, other III-V magnetic semiconductors than (Ga,Mn)As and (In,Mn)As with different host semiconductors and different transition metals have appeared and the investigation of properties of these new materials are underway. • (Ga,Fe)As: The growth of (Ga,Fe)As with Fe compositions up to ~ 0.1 was carried out by LT-MBE at Ts = 260-350°C on GaAs substrate (Haneda et al. 2000a). The lattice constant of (Ga,Fe)As becomes smaller with the increase of Fe composition, reflecting the shorter bond length of Fe-As than that of Ga-As. The elevation of Ts leads to the precipitation of Fe-related clusters. The extended x-ray absorption fine structure (EXAFS) analysis revealed that Fe atoms in (Ga,Fe)As grown at low Ts substitute into Ga sites in the zinc-blende structure. whereas that Fe atoms in high- Ts grown samples form Fe clusters and/or Fe-As complexes (Soo et al. 200la). Van-Vleck type paramagnetism occurs in (Ga.FefAs, as the temperature dependence of magnetization is rather weak at low temperatures « 10 K). The conduction type is n-type and a photoinduced MR effect is observed below 100 K. In GaAs-Fe composite structures (GaAs including Fe clusters), photo-induced magnetization as well as MR effect is observed even at room temperature (Haneda et al. 2000b, 200 I), The properties of (Ga.Fe.Mnj.As with transition metal compositions up to 0.04 have been investigated. The results show that (Ga,Fe,Mn)As becomes insulating with the increase of Fe content, and that there are contributions of ferromagnetic and paramagnetic terms to the film magnetization. The ratio of paramagnetic part to ferromagnetic part increases with the increase of Fe content (Moriya et al. 2002).
III-V FERROMAGNETIC SEMICONDUcrORS
13
• (Ga,Cr)As: (Ga,Cr)As layers with Cr compositions up to 0.1 were grown by LT-MBE at Ts = 250°C on GaAs substrates (Saito et al. 2001). The magnetization measurements show that (Ga.CrjAs is superparamagnetic and the Curie-Weiss plot has a positive Curie temperature, indicating that the dominant interactions between the Cr ions are ferromagnetic. The value of the effective magnetic moment of the Cr ions is consistent with that of the divalence state of Cr, suggesting that the Cr atoms act as acceptors. Whereas there is a report of p-type conduction of (Ga,Cr)As (Okazawa et al. 1999, 2001), the determination of the conduction type by Hall measurements is rather difficult due to a small Hall voltage, suggesting that the conduction is dominated by hopping. Ferromagnetism below r - 45 K of (Ga,Cr)As with higher Cr composition (0.14) is also observed. From photoemission spectroscopy, (Ga,Cr)As with Cr compositions larger than 0.25 is metallic (Yamada et al. 2(01). Ferromagnetic properties of (Ga,Cr,Mn)As grown by MBE are reported (Akinaga et al. 2000a). However, Tc is lower than that of (Ga,Mn)As with the same Mn composition, which may be due to the compensation effect. • (Ga,Mn)N: bulk crystals with x up to 0.02 were grown by a resublimation method (Gebicki et al. 2(00), and microcrystals with x up to 0.005 were obtained by an ammonthermal method (Zajac et al. 200 Ia). Both compounds show extra Raman peaks induced by disorder stemming from Mn incorporation. Magnetization measurements reveal that these compounds are paramagnetic and from its temperature dependence antiferromagnetic nearest-neighbor interaction coupling v- -2 K) is obtained (Zajac et al. 200lb). Structural properties of MBE-grown (Ga,Mn)N with x up to 0.09 on AIN buffer onto Ah03 substrate grown at Ts = 650-750°C by MBE using RF-nitrogen plasma source have been investigated (Kuwabara et al. 200 Ia, 200 Ib). Both cross-sectional TEM and plane-view scanning electron microscopy (SEM) images show no visible second phase. Extended x-ray absorption fine structure (EXAFS) analysis indicates that the Mn atoms are incorporated in the Ga sites. Magnetization measurement revealed that there exist contributions from both ferromagnetic (even at room temperature) and paramagnetic phases. Kuwabara et al. suppose that the ferromagnetic part may originate from the presence of ferromagnetic or ferrimagnetic second phases of Ga-Mn and/or Mn-N, since the samples are highly resistive and thus no carrier-induced ferromagnetism is expected. According to the Curie-Weiss analysis of the paramagnetic part, the paramagnetic Curie-Weiss temperature 9p is negative in the very dilute Mn composition regime (9p '" -8 K with S'" 2.5 for [Mn] = 7 x 10 19 cm- 3), and changes into positive when the Mn composition is increased (9p '" 20 K with S '" 2.5 for [Mn] = 8 x 1020 cm >'). The EXAFS and near-edge x-ray absorption fine structure (NRXAFS) analyses on the samples prepared by the same authors indicate that the most part of Mn substitutes into the Ga sites, the valency of Mn is 2+, and that there is a possible formation of Mn clusters (Soo et al. 2001b). An n-type (Ga,Mn)N film with x = 0.07 on Al203 substrate was grown by MBE at 865°C using a nitrogen plasma source (Overberg et al. 2(01). The magnetization at 10 K is nonlinear as a function of the magnetic field and small hysteresis are visible, indicating that the film is ferromagnetic. Negative magnetoresistance and nonlinear dependence of the Hall resistance are assigned to spin effects, though the negative magnetoresistance is reminiscent of a weak localization effect.
14
F. MATSUKURA et at.
MBE-grown (Ga,Mn)N films with x = 0.06 and 0.09 were prepared using NH3 as nitrogen source (Sonoda et al. 2002). The results of magnetization measurements are similar to those of Kuwabara et al. However, Sonoda et al. claim that their (Ga,Mn)N films show the ferromagnetic behavior even at room temperature. Indeed, the estimation of Tc from temperature dependence of magnetization is 940 K, and no Mn-Ga and Mn-N compounds with such high Tc have previously been found. (One should note that rather high Tc ('" 750 K) has been observed in Mn-Ga alloys (Bither and Cloud 1965). Very recently, the room temperature ferromagnetism in (Ga,Cr)N (Hashimoto et al. 2(02) and (Ga,Mn)P:C (Theodoropoulou et al. 2(02) has also been reported.) The magnetic properties of p-GaN implanted with high doses (3-5%) of Mn (annealed at 700-1000°C after doses) have been investigated. The result shows that the sample is ferromagnetic with Tc '" 250 K (Theodoropoulou et al. 200 1a). (Ga,Mn)N film prepared by post growth Mn doping using solid state diffusion shows ferromagnetic behavior at room temperature, which is confirmed by the observation of an anomalous Hall effect (Reed et al. 2(01). It seems that a considerable amount of work is needed to clarify the structural and magnetic properties of (Ga,Mn)N. • (Ga,Fe)N: GaN films doped with Fe, with concentrations up to '" 3 x 10 19 cm- 3 were grown by MBE at several Ts from 380 to 520°C directly on sapphire (0001) substrates. Ferromagnetic behavior with Tc '" 100 K is observed only in the sample grown at '" 400°C, in spite of quite a low concentration of Fe (Akinaga et al. 2000b). GaN:Fe films (Fe up to 6 X 102 1 cm >') grown by MBE at Ts = 500-8OO°C show a superparamagnetic behavior (Kuwabara et al. 200 Ia, 200 1b) together with superparamagnetic contributions of possible Ga-Fe and/or Fe-N inclusions. The EXAFS analysis suggests that the decrease of Ts leads to a structural transition from wurtzite to zinc-blende structure, and this transition may be related to the origin of ferromagnetism in the GaN film with Fe (Ofuchi et al. 2oola). The emission channeling result on annealed Fe implanted GaN (Fe concentration 10 17_10 18 cmr') shows that the majority of Fe (80%) occupies substitutional Ga sites (Wahl et al. 200 I). p-GaN implanted with a high dose of Fe (3-5%) shows ferromagnetic behavior, Tc '" 250 K (Theodoropoulou et al. 200lb). • (Ga,Mn)Sb and (Ga.CrjSb: The growth of bulk GaSb crystals heavily doped by Mn was reported earlier, but whether an alloy between GaSb and Mn is formed remains unclear (Aliyev et al. 1980; Adhikari and Basu 1984). GaSb films with a few percent of Mn or Cr were also grown by MBE at Ts = 250-560°C (Abe et al. 2000,2001). The surface morphology of MBE-grown samples observed by atomic force microscopy (AFM) shows that these films contain clusters, which may be transition-metal-antimonide compounds. The size of the clusters becomes smaller with the decrease of Ts. For GaSb with Mn, magnetization measurements show a ferromagnetic behavior even at room temperature, indicating the existence of ferromagnetic Mn-Sb clusters. The larger coercive force for higher Ts may reflect the larger size of these clusters. The increase of the magnetization at low-temperatures suggests the formation of ferromagnetic zinc-blende (Ga,Mn)Sb. According to the saturation value of the magnetization, only about 10% of the nominal Mn concentration contributes to the formation of (Ga,Mn)Sb grown at Ts = 560°C, but 30% of Mn contributes to (Ga,Mn)Sb
m-v FERROMAGNETIC SEMICONDUCTORS
15
if Ts = 250°C. Magnetotransport measurements determine the properties of (Ga,Mn)Sb without the influence of Mn-Sb clusters, and the data show a ferromagnetic behavior with Tc ,.... 10 K and r - 30 K for Ts = 560°C and 250°C, respectively (Abe et a1. 2(00). In the case of GaSb with Cr, both antiferromagnetic and ferromagnetic contributions are detected. Due to an antiferromagnetic nature of Cr-Sb compounds, the magnitude of the magnetization decreases with the increase of Cr content, whereas ferromagnetic hysteresis persist even at room temperature. The result of magnetotransport measurements shows that (Ga,Cr)Sb grown at Ts = 550°C is antiferromagnetic at 1.5 K. (Ga,Cr)Sb grown at 250°C is highly resistive at low temperatures « 100 K), which may be due to the compensation of intrinsic holes in epitaxial GaSb films by the Cr ions (Abe et a1. 2001). • Mn doped InSb: The properties ofInSb:Mn single crystals with [Mn] < 3.5 x 10 17 cm- 3 grown by the Czochralski method have been investigated extensively (Obukhov and Pepic 1989; Obukhov 1993, 1996; Henriques et a1. 1999). Mn in InSb behaves as a shallow acceptor (activation energy E a = 7 meV), and a metal-insulator transition (MIT) occurs at low Mn concentrations (2x 10 17 cm- 3) due to a relatively large Bohr radius of the bound holes. The interactions between the Mn spins are predominately antiferromagnetic. A strong spin-dependent coupling between the Mn spins and holes gives rise to large magnetoresistance effects, leading to the field-induced insulator-tometal transition in InSb:Mn at low temperatures (Obukhov 1996; Henriques et a1. 1999). An anomalous Hall effect, whose coefficient is larger for lower Mn concentrations (2 x 10 16 < [Mn] < 3 x 10 17 cm- 3) , has been observed (Obukhov and Pepic 1989).
3. Lattice properties 3.1. Lattice constants X-ray diffraction (XRD) measurements show that (Ga,Mn)As has the zinc-blende structure without detectable second phase. The results for the (004) reflection using Cu- Ko radiation show that the lattice constant a of (Ga,Mn)As increases with the increase of x as shown in fig. 7a (Ohno et a1. 1996a). Asymmetric double-crystal XRD on (224) or (115) reflection demonstrates that the (Ga,Mn)As films are fully strained at least up to 2 JLm (fig. 7c) (Shen et a1. 1999). The reciprocal space mapping on the (004) plane confirms also that the (Ga,Mn)As layers are fully strained (Sadowski et a1. 2000). This rather high critical thickness is probably due to the low growth temperature, which prevents dislocations from nucleating (Price 1991). The direction of the strain can be controlled by using a thick lattice-relaxed (In,Ga)As buffer layer, which has a larger lattice constant than that of (Ga,Mn)As as shown in fig. 7b (Ohno et a1. 1996b ). The peak corresponding to (Ga,Mn)As on (In,Ga)As is located at the higher angle side of GaAs, indicating that the film is now under a tensile strain. In order to calculate the relaxed lattice constant Qo, it is assumed that elastic constants of (Ga,Mn)As are the same as in GaAs (Poisson ratio: v = 0.311). On the other hand, since thick (In,Mn)As films on GaAs are fully relaxed, a o of (In,Mn)As can be directly determined from the positions of the diffraction peaks. The dependencies ao(x) for (Ga,Mn)As and (In,Mn)As, as determined by XRD, are summarized in fig. 8. In both materials, ao depends linearly on x following Vegard's
F. MATSUKURA et aI.
16
(a) (Ga,Mn)As x=0.015 x=0.035 =0.07~ \, .'
I \
... •I
•
f
(b)
~ 'fi)
c:
65
66 2(} (deg)
~
c:
- (c)
(224) reflection " , \
-
-
high incident angle low incident angle
, l-(Ga,Mn)As_
'I I
,
-1500
2IJ.m
(AI,Ga)As
I
-1000
-500 to (arcsec)
, GaAs o
500
Fig. 7. X-ray diffraction curves for (Ga,Mn)As films obtained with Cu Ka radiation. (a) Mn concentration dependence of peak positions [(004) reflection] of 150-nm thick (Ga,Mn)As grown on GaAs with compressive strain (Ohno et aI. 1996a). (b) (Ga.Mn)As grown on (In,Ga)As buffer layer with tensile strain. (c) Double-crystal x-ray diffraction curves for a 2 /lm-thick (Ga.Mn)As showing the asymmetric (224) reflection with high- and low-incident angle (Shen et aI. 1999).
law, which for (Ga,Mn)As assumes the form a o = 0.566(1 - x) + 0.598x (nm) (Ohno et at. 1996a). The lattice constant is known to depend on the growth conditions such as As pressure and/or growth temperature due to the corresponding excess of As (Shimizu et at. 1999; Haneda et at. 2000a). A growth of (Ga,Mn)As under other conditions gives a o = 0.5654(1 - x) + 0.5901x (nm) (Sadowski et at. 2001a). It is shown that the lattice constant of (Ga,Mn)As depends on the growth condition, probably due to the excess As incorporation and the formation of a Mn-As complex (Schott et at. 2(01). The extrapolated values of ao(x) for x ~ 0 are in good agreement with the actual GaAs and InAs lattice constants, respectively. The extrapolated lattice constants for hypothetical zinc-blende
17
III-V FERROMAGNETIC SEMICONDUCTORS
0.61 r--.....-
..,.-.-oIIIIIIr--.,
......--,........
(In,Mn}As
..-..
E 0.60 c:
'-'
C
~c: o o
0.59
0.58
Q)
o
Eto
-.J
E s
0.57
•
0.566 nm
0567 0566 0 5 6 5 ' - - - - -.... 000 0~4 008
0.56 .........._ .....- -......_ ....._ -...._ .....
0.0
0.2
0.4
0.6
0.8
1.0
Mn Composition x Fig. 8. Cubic lattice constant ao versus Mn composition x in Gal_xMnxAs and Inl_xMnxAs films. Inset shows the magnified view of the results for (Ga,Mn)As films (Munekata et al. 1989; Ohno et aI. I996a).
MnAs determined from (Ga,Mn)As and (In,Mn)As data show a good correspondence. This suggests that virtually all Mn atoms occupy the substitutional sites. The lattice constant of hypothetical zincblende MnAs in the ferromagnetic state has been predicted to be 0.59 nm by first-principle calculations (Shirai et al. 1998; Ogawa et al. 1999). 3.2. Local lattice configuration (EXAFS) An extended x-ray absorption fine structure (EXAFS) study, carried out using the Mn K-edge, of thick (~ 111m) (In,Mn)As reveals that Mn is incorporated substitutionally into the In sites. This is especially true for low x (,..., 0.0 I) samples grown at low Ts (200°C). Although the substitutional signal is still dominant, either increasing of x above 0.1 or raising Ts to 300°C results in a modification of the local structure. In the case of greater x or higher Ts, the local structure shows that Mn is incorporated in the form of hexagonal MnAs (NtAs-structure) (Krol et al. 1993; Soo et al. 1996). Fluorescence EXAFS studies of a (In,Mn)As thin layer (10 nm) grown on a GaSb buffer layer and of (In,Mn)As quantum dots (QDs) on GaAs were also performed. The results show that in the thin (In,Mn)As layer, the In-site substitutional Mn and the NiAs-type MnAs coexist, whereas the majority of Mn atoms are substituted into the In-sites of InAs in (In,Mn)As QDs. It is argued that the difference of the strain deformation between the thin layer (with strain) and thick layer and QDs (strain relaxed) is responsible for the differences in the local structure of the Mn atoms (Ofuchi et al. 200 Ib).
18
F. MATSUKURA et al.
EXAFS measurements of (Ga,Mn)As (x = 0.005 and 0.074) also indicate that Mn atoms are substitutionally incorporated into the Ga sublattice (Shioda et al. 1998). The Mn-As bond length is found to be 0.249-0.250 nm, longer than the host Ga-As bond length (0.244 nm) and shorter than the expected bond length of Mn-As in the hypothetical zincblende MnAs (0.259 nm). 3.3. Atomic-scale observations by scanning tunneling microscopy (STM)
Cross-sectional scanning tunneling microscopy (XSTM) measurements were carried out for a cleaved (110) surface of GaAs doped with Mn. The samples were cleaved in an ultrahigh vacuum (UHV) chamber in order to expose the atomically flat (110) surface. The measurements have been done in the UHV chamber at room temperature. The defects and impurities of Mn-doped GaAs (Mn composition < 0.001) layers grown at 400°C are identified in the XSTM images. The results show that Mn impurities have negative charge, indicating that Mn acts as an acceptor. The Mn acceptor concentration deduced from the XSTM images is in a good agreement with the hole concentration determined by Hall measurements at room temperature. As-vacancy defects are also observed. Since the number of the vacancies increases with time, they are presumably formed after the cleavage due to the desorption of As atoms from the surface. No Asantisite related defects are detected in the samples grown at 400°C (Tsuruoka et al. 2000, 2002). XSTM images for Mn-doped GaAs (Mn composition = 0.005) grown at 255°C show that there are numerous As-antisites, the concentration of which is '" 1 x 1020 em -3, similar to LT-GaAs. The Mn concentration determined from the images is 7 x 1019 em -3, which is consistent with the nominal Mn concentration, '" 1 x 1020 em -3. The tunneling spectrum reveals the presence of a state in the midgap region caused by the As-antisite donors and a shift of the Fermi energy brought about by the incorporation of Mn because of its acceptor nature (Grandidier et al. 2000). 4. Spin and charge states of Mn in 111-V magnetic semiconductors Various properties of Mn impurity centers have been investigated by many methods, such as magnetic resonance and magnetization measurements, for a long time. It is expected that there are three possible electronic states of the Mn impurity substituting a trivalent cation: AO(d4 ) and AO(d 5+h) for Mn 3+ , and A-(d5 ) for Mn 2+ . AO denotes the neutral center, A - is the negatively charged center, and the notation in parentheses is the electronic configuration of the d electrons. There have been no reports on the observation of AO(d4 ) neutral centers in GaAs. In contrast, the anisotropy of some of electron spin resonance (ESR) lines in the illuminated n-type GaP:Mn can be explained in terms of AO(d4 ) centers (Kreisel et al. 1996) that undergo a Jahn-Teller distortion, as observed for Cr(3d 4 ) in GaAs (Krebs and Stauss 1977). In the case of the AO(d4 ) center the hole resides in the 3d shell. However, strong Hund's intra-site exchange interaction may favor a state having five d electrons and a loosely bound hole. This is the case of the AO(d5+h) configuration, where the A 0(d 4 ) center traps tightly an electron in the 3d shell forming the high spin, S = 5/2, 3d5 configuration, and this
III-V FERROMAGNETIC SEMICONDUCTORS
19
negatively charged Mn ion binds the hole in an effective mass state. Experimental results discussed below indicate that the ground state of the Mn impurity in III-V compounds corresponds to such AO(d 5+h) configuration. 4.1. Electron spin resonance (ESR)
The result of ESR measurements for bulk Mn doped GaAs (GaAs:Mn) with a Mn concentration of ~~ I x 1017 cm- 3 is interpreted in terms of the AO(d 5+h) acceptor state. Owing to the antiferromagnetic exchange coupling between the d-electrons and the p-like hole, the total angular momentum is J = I (Schneider et aJ. 1987; Masterov et aJ. 1988). The ESR spectra for bulk GaAs:Mn with a Mn concentration of 10 17 '" 10 18 cm- 3 show resonance with unresolved hyperfine structure even at 4 K, which can be attributed to the existence of A- (d 5 ) centers (Almelsh and Goldstein 1962). Results of low-temperature magnetization measurements on GaAs:Mn with a hole concentration of 5 x 10 18 cm- 3 at 300 K are consistent with the coexistence of AO(d 5+h) and A-(d 5 ) centers (Mac et aJ. 1994). Electron spin resonance (ESR) spectra for (Ga,Mn)As grown by LT-MBE show usually only one resonance corresponding to g = 2.0 (Nojiri et aJ. 1998; Szczytko et aJ. 1999a). This resonance can be attributed to A - (d5 ) centers. The ESR intensity becomes weak around the Curie temperature; i.e., the observed signal is due to the ferromagnetic resonance (FMR). The description of the observed signal in terms of the standard FMR formula, in which the magnetic crystaJline anisotropy is neglected, indicates that the magnitude of magnetization is smaller than that expected for the given x value. This suggests that only a part of the Mn spins contributes to the ferromagnetic order in (Ga,Mn)As. The conclusion is consistent with results of other studies that will be discussed below. From the fine structure of the ESR spectrum of (Ga,Mn)As with x < 1.5 x 10-3 , the single-ion crystal-field anisotropy of the Mn spin energy was determined (Fedorych et aJ. 200 I). No signal of AO(d 5+h) centers is usually detected in (Ga,Mn)As grown by LT-MBE (Nojiri et aJ. 1998; Szczytko et aJ. 1999a). The reason can be either the compensation by the antisite donors in the low x limit or the high hole concentration for larger x values, which leads to screening of the Coulomb potentials of the A- (d5 ) centers, resulting in a low ionization energy of the holes and eventually to the insulator-to-metal transition. A similar situation occurs in the case of (In.Mn)As layers (Szczytko et aJ. 2oola). A negligible contribution of the centers other than A - (d5 ) suggests that the double-exchange mechanism of the coupling between the Mn spins is ineffective. as this mechanism requires the coexistence of the Mn ions with a different valence. 4.2. Optical spectroscopy
The results of infrared absorption measurements on GaAs:Mn prepared by the solidstate diffusion method are also in good agreement with the AO(d 5+h) center model (Linnarsson et aJ. 1997). According to infrared spectroscopy and photoluminescence (PL) measurements for GaAs:Mn with a Mn concentration of '" 1018 cmr'. this acceptor level is located 113 meV above the top of the valence band (Chapman and Hutchinson 1967; Ilegems et aJ. 1975). Two photoluminescence (PL) lines observed by Liu et aJ. (1995) in
20
F. MATSUKURA et al,
magnetic fields up to 30 T were identified as radiative recombination of the hole bound to Mn with the conduction band and donor electrons, respectively. From the field-induced PL line splittings, an effective Lande factor of the neutral acceptor g = 2.47 was determined, confirming qualitatively the ESR results discussed above. This work corroborated also an earlier conclusion (Schairer and Schmidt 1974) about the absence of transitions involving excitons bound to neutral Mn acceptors in GaAs:Mn. This surprising result was explained by Bhattacharjee and Benoit a la Guillaume (2000) taking into account the presence of a strong exchange interaction between the holes and Mn ions. In contrast, Sapega et al. (200 I) assigned a weak line in their PL spectrum to such a transition. At the same time, this transition energy corresponds to a resonant enhancement of spin-flip Raman scattering studied in detail by Sapega et al. (200 I). However, to interpret their Raman spectra, a coupling of bound excitons to more than one Mn ion had to be invoked by Sapega et al. (2001). It appears probable, therefore, that the PL line and spin-flip Raman scattering in question originate from complexes involving the hole interacting with a pair of nearest neighbor Mn ions or with other types of Mn clusters. Isolated neutral acceptors, in tum, being unable to bind any exciton, are invisible in spin-flip Raman spectroscopy. This would explain why the p-d exchange energy determined by Sapega et al. (200 I) is much smaller than those imply by other experiments. 4.3. X-ray magnetic circular dichroism (XMCD)
X-ray absorption spectroscopy (XAS) provides direct information of the 3d electronic structure of Mn, since the 2p electron is ensured to be excited into 3d state because of the dipole selection rule. The x-ray magnetic-circular dichroism (XMCD) spectrum obtained for 150-nm thick (Ga,Mn)As with x = 0.02 in the photon energy region 630660 eV shows the two groups of rich peak structures associated with 2p3/2 and 2PI/2 final state holes. The rich structures are caused by the spin-orbit interaction of the holes and the Coulomb and exchange interactions between the 2p core and 3d shell (Ohldag et al. 2000). The temperature dependence of XMCD at 642.2 eV, at which the 2p3/2-related signal has maximum intensity, can be well fit by a mean-field model with Tc of 37 K, which is consistent with Tc: of (Ga,Mn)As with x = 0.02. Comparison of measured and calculated XMCD spectra shows that a linear combination of Mn 3d5 (80%) and Mn 3d6 (20%) configurations gives the best agreement. This configuration appears to occur for all Mn atoms whose spins are, therefore, highly localized and the magnetic moment is about 4.5 /-LB. From the ratio of the observed MCD to the calculated MCD, only 13% of Mn in (Ga,Mn)As contributes to the ferromagnetic order. This is consistent with the magnetization measurement for (Ga,Mn)As with x = 0.023, where considerable amounts of Mn spins behave as paramagnetic spins (Oiwa et al. I998a). For as-grown samples, XAS shows two-component contributions of Mn to the spectrum. Since one of them disappears after low-temperature heat-treatment « 300°C), it may be related to Mn-As complexes (Katsumoto et al. 2001). The analysis of XAS and XMCD based on the cluster model shows that the orbital momentum of Mn electrons is small and that the sign of the p-d interaction is antiferromagnetic (Veda et al. 200 I). The result shows that the 3d electron count ofMn is '" 5 (Ao(d 5+h) or A -(d5 which is consistent with the lack of the AO(d4 ) centers in the ESR signals.
»,
II1-V FERROMAGNETIC SEMICONDUCTORS
21
4.4. Photoemission
The core-level x-ray photoemission spectrum of the Mn 2p core level for (Ga,Mn)As with x = 0.074 was measured and was analyzed by a configuration interaction (CI) cluster-model assuming a Mn 2+ and Mn3+ ground state (Okabayashi et al. 1998). For the d 5 configuration, the p-d exchange energy (which is conventionally referred to as NoP for DMS) should be negative and NoP "" -1.2 eV is obtained for A-(d5 ) centers with an optimized parameter set. The resonant photoemission technique was used for several (Ga,Mn)As layers to elucidate the nature of the Mn 3d partial density of states (DOS) (Okabayashi et al. 1999, 2001a, 200lb). The main structure of Mn partial DOS extends from the Fermi energy EF down to -4.5 eV below it. The configuration interaction (CI) model calculation indicates an enhanced Mn 3d electron count of 5.3. The largest contribution to the DOS at EF comes from As 4p states. However, the Mn partial DOS extends up to the top of the valence band, suggesting partial d character of the conducting holes. On the other hand, in-situ measurement on an as-grown sample shows a suppression of the d character of the holes at Fermi level, suggesting that the observed d-character of the conducting holes may be related to the experimental error due to the surface condition (Okabayashi et al. 200lc). In the region extending from the Fermi energy EF down to 0.5 eV below it, an increase in emission intensity due to Mn-induced states is observed in Gal-xMnxAs with x = 0.035 and 0.069 (Okabayashi et al. 200la, 200lb). Since an insulator-to-metal transition occurs in the vicinity of this Mn concentration (Oiwa et al. 1997; Matsukura et al. 1998b), it is tempting to assign this DOS to Mn acceptor states merging with the valence band. No clear Fermi edge is observed, which may be due to a relatively low hole concentration and poor metallic conduction.
5. Magnetic properties 5. J. Magnetization Magnetic properties of III-V DMSs can be measured by direct magnetization measurements as well as magnetotransport measurements. In this chapter, we focus on the magnetic properties of (Ga,Mn)As obtained by direct magnetization measurements. For (In,Mn)As, since there are only limited magnetization measurements, we will describe magnetic and magnetotransport properties together in the next chapter. Direct measurements of the magnetization M of (Ga,Mn)As layers as a function of magnetic field B and temperature T have been done using a commercially available superconducting quantum interference device (SQUID) magnetometer. The temperatureindependent diamagnetic response of the thick GaAs substrate (which could occasionally show a slight temperature dependence of unknown origin) can be determined from a separate measurement of only the same GaAs substrate used for the epitaxial growth. It can be also determined from the low-temperature high-filed magnetization measurements, where the magnetization of the (Ga,Mn)As layer should saturate, or from high-temperature measurements, where the magnetization of the (Ga,Mn)As of the epitaxial layer on the substrate should be negligible. The diamagnetic component is then subtracted from the total response to obtain the magnetization of the magnetic layer.
22
F. MATSUKURA et a1.
x =0.035, 150 nm 0.04 r-........-...-............-
................
B /I plane 003 r - - - - = ~ " '~", o o - o - <
5K
~ooo E
1
i 0
LJ
-003. >-0-<>0 -002
0.03r--------,
~ ~o 0
l:;. ~~
0000
b
b 6 ~
100
200
T(K)
-0.04 ...........--t..............._
-0.5
0.0 B (T)
................
0.5
Fig. 9. Magnetic field dependence of the magnetization at selected temperatures for a 150-nm thick Gal_xMnxAs film with a Mn composition x = 0.035. The magnetic field is applied parallel to the sample surface (direction of magnetic easy axis) except for the closed circles at 5 K taken in perpendicular geometry. The solid line for 5 K shows the magnetization determined from transport measurements. The upper left inset shows a magnified view of the magnetization in the parallel field at 5 K. The lower right inset shows the temperature dependence of the remanent magnetization (Ohno et al. I996a).
Figure 9 shows magnetization curves at several temperatures of a ISO-nm thick (Gao.96sMnO.03S)As layer grown on GaAs. where B is applied parallel and perpendicular to the plane. As shown in the inset. when B is applied parallel to the plane. the M-B curve shows a clear hysteresis as in the upper right inset. which indicates the presence of ferromagnetic order. A paramagnetic response is often observed after closure of the hysteresis in the magnetization curves. as seen in the 5 K curve of fig. 9 and shown for (Ga.Mnjas with several Mn compositions in fig. 10. This paramagnetic response is correlated with the transport properties of the film, the more metallic sample (in terms of the metal-insulator transition (MIT» the less the portion of paramagnetic response (Oiwa et aI. 1998a. 1999). Shown in the lower left inset of fig. 9 is the temperature dependence of remanence of M after switch off of the parallel B. which reveals that the Tc of the film is '" 60 K. Note also that there is no indication of inclusion of MnAs with NiAs-structure (Tc '" 310 K) in the trace. as only a negligible M is present above the Tc of (Ga.Mnjxs. This. however. is not always the case. and a small non-zero M up to 300 K is occasionally observed. especially in samples grown at higher Ts or having large x.
23
III-V FERROMAGNETIC SEMICONDUcrORS
0.10 _ - - _ - - . . - - - _ - - " ' "
(Ga,Mn)As I LT-GaAs
x = 0.071
••••<;)••••
2K
<}o.'.~
.~ sa··...., ,."., -..-.~"v x = 0.053 ••••A-
. ..
.·0 .. ~....
~
0.05
#j:.-..,_·' i}_·' i}_·~;;:' cM· ~ t::..
x=0.035 x= 0.022
_O-_O-J::>--~x· 0.015
0.00 fIIII:; _ _...._ _.a... o 2
B (T)
... 4
Fig. 10. Magnetization for six samples of Ga I-x Mn, AslGaAs with Mn compositions x ranging from 0.015 to 0.071 at 2 K. The magnetic field is perpendicular to the sample surface for x = 0.035-0.071 and parallel to it for x = 0.015 and 0.022. The dashed lines show fit to the mean-field Brillouin function and the solid line for x = 0.015 (paramagnetic sample) a fit to the Brillouin function (Oiwa et al, 1998a).
The solid line in fig. 9 shows M determined by the transport measurements, where the Hall resistance is almost proportional to the perpendicular component of M, as described in the next section. The good agreement between M determined by SQUID and transport measurements indicates that one can correctly determine M of (Ga,Mn)As by magnetotransport measurements. The saturation magnetization MSal (M at T 5 K and B > 5 T) of the samples shown in figs 9-11 indicates that S = 2.0-2.5 when calculated using MSat = x Nog /LaS and nominal x as well as neglecting the hole contribution (Dietl et al. 200lc). Although S is related to the valence of Mn and thus to the mechanism of ferromagnetism, a more accurate determination of S from magnetization measurements is not possible because of the error involved in the determination of the x value (±IO%). Figure Ila presents magnetization determined for a 200-nm thick film of Gao.947MnO.053As. Here almost no hysteresis is observed because B is applied perpendicular to the sample plane along the magnetic hard axis. The inset displays the temperature dependence of the remanent magnetization for B II plane, showing that Tc is above lOOK. Using Arrott plots to minimize the effect of magnetic anisotropy and domain rotation (Arrott 1957), the spontaneous magnetization Ms at each temperature is determined from the curves in fig. lla and plotted in fig. lib. The Tc of this sample is about 110 K. The non-standard temperature dependence of Ms shows a rather steep increase at low T. The temperature dependence of the inverse susceptibility 1/ X shown in the same figure gives a paramagnetic transition temperature () consistent with the Tc determined from Ms. For the extrapolation of 1/ x, data points above 150 K were used.
=
24
F. MATSUKURA et al.
5K 25K 55K 100 K 125 K 250K
(a) 0.03
x= 0.053 B 1.. plane
E ::e 0.00 B /I plan
-0.03 200 --
-5
5 J
(x10 ) 1.5
0 1.0
E
::e'"
..... ~
0.0 .5
0.000
100
200
3~0
T (K) Fig. II. (a) Temperature dependence of the magnetization for 200-nm thick Gal_xMnxAs with x = 0.053. The magnetic field is applied perpendicular to the sample surface (hard axis). The inset shows the temperature dependence of the remanent magnetization (0 T) and the magnetization at I T in a field parallel to the film surface. (b) Temperature dependence of the saturation magnetization MS determined from the data shown in (a) by using Arroll plots (closed circles). Open circles show inverse magnetic susceptibility and the Curie-Weiss fit is depicted by the solid straight line (Ohno and Matsukura 2(01).
The Curie constant C = g2J1.~xNoS(S + 1)/3kBT, determined from l/X-T curve shown in fig. l lb gives a spin of S ~ 3, when the nominal value of the Mn concentration, x = 0.053, is used. Here No is the cation density, g (= 2.0) the Lande factor of the Mn ions, J1.B is the Bohr magneton, kB is the Boltzmann constant. Judging from this value of S, some ferromagnetic clusters exist already above Tc ; Magnetization measurements on semi-insulating (Ga,Mn)As:Sn, in which the holes are compensated by Sn donors, point to a paramagnetic behavior. The Curie-Weiss (l/X-T) plot gives TAF '" 2 K, indicating that the "intrinsic" mechanism of the interaction between the Mn spins is the antiferromagnetic superexchange (Satoh et al. 1997,2001). This means that the ferromagnetic coupling in (Ga,Mn)As is induced by the presence of the holes. 5.2. Magnetic anisotropy As shown in fig. 9 for the magnetization at 5 K, the magnetic easy axis is in the plane of the film, and shows a weak four-fold symmetry within the plane. The anisotropy energy
25
III-V FERROMAGNETIC SEMICONDUCTORS
0.15 .....
0.05
r
0.00
~
e _ 00 0
-0.05
-
-0.10
••• 300 _. -600
I
0.02
-15
....+-.....-t
--; 0.031====+=+~..-.oll--
a::
~
.,
0.10
-
......_ ..........
1.5 urn (Gao 9BSMnO o3s)As Irr~=ro=:=-==,=:: !II LT-GaAs
T= 2.3 K
0.01 0.00 compressive slraln
-0.01
;I
-0.02
-0.03 .........................l........................._
-0.5
0.0
......
0.5
B (T) Fig. 12. Hall resistance RHall of (a) (Ga,Mn)As/(In,Ga)As and (b) (Ga,Mn)As/GaAs as a function of the magnetic field for various angles between the field and the sample surface normal. (Ga,Mn)As films in (a) and (b) are under tensile and compressive strain. respectively. Clear hysteresis and angle independent heights of the hysteresis in (a) show that magnetic easy axis is perpendicular to the sample surface. whereas the easy axis in (b) is in-plane (Shen et al. 1997a).
K calculated from the difference between the two magnetization curves at 5 K with B.l.. plane and B II plane is K = 2.9 x 103 J/m3 • This anisotropy energy of (Ga,Mn)As is strain dependent (Ohno et a1. 1996b; Shen et a1. 1997a) and is also expected to depend on the hole concentration (Abolfath et a1. 2001; Dietl et a1. 2oo1c). The strain in the film shown in fig. 9 is -0.24%. The magnetic easy axis can be made perpendicular to the plane by the reversing the sign of strain in the film. Figure 12 shows clearly the different directions of the magnetic easy axis for the different buffer layers. Figure 12a shows the direction of the B dependence of the Hall resistance RHall for (Ga,Mn)As with tensile strain on a thick lattice-relaxed (Ino.16Gao.84)As buffer layer and fig. 12b for (Ga,Mn)As with compressive strain on a GaAs buffer layer. Only the (Ga,Mn)As with tensile strain shows a clear hysteresis which suggests a change of the direction of the magnetic easy axis. The height of the hysteresis is almost independent
26
F. MATSUKURA et al.
of the direction of the magnetic field, which shows that the direction of the easy axis is perpendicular to the plane. On the other hand, (Ga.MnjAs with compressive strain shows only a small hysteresis and no perpendicular component of the remanent magnetization. The result confirms that the direction of the magnetic easy axis of (Ga,Mn)As with compressive strain is in-plane (Ohno et al. I996b). The significant increase of coercive force and Ti; of (Ga.Mn)As with spinglass (Zn,Mn)Se overlayer on it are observed. The observed effects are technological important to control the hardness of ferromagnetism. Although the origin of which is not clear yet, it is most probably related to the exchange coupling between (Ga,Mn)As and (Zn,Mn)Se (Liu et al. 2(01). 5.3. Magnetic domains
Using a scanning Hall microscope, a stripe-shaped domain structure has been observed in a (Ga,Mn)As sample with tensile strain and perpendicular easy axis (Shono et al. 2000; Fukumura et al. 2(01). The Baukhausen noise due to the scattering from the domain wall movement has also been observed in magnetotransport measurements (Hayashi et al. 2(00). Ac-susceptibility measurements on (Ga,Mn)As with x = 0.042 have been performed in alternating B from 0.1-4 mT. In the temperature dependence of susceptibility, there is a sharp peak at about 48 K at 0.1 mT, which suggests a ferromagnetic phase transition. The temperature and magnetic field dependence is rather complicated and an increase of B involves additional peaks (the number of which up to 4), which may be due to domain formation and domain wall movement (Sadowski et al. 2(00). There is also a report about ac-susceptibility measurements on (Ga,Mn)As with x = 0.07, which shows that there is no difference between the field-cooled and zero-field cooled ac-susceptibilities measured with B = 10 mT (Van Esch et al. 1997). 5.4. Cantilever magnetometry
Torsional magnetometry using submicron GaAs micromechanical cantilevers is useful for measuring the magnetic properties of small samples over a wide range of applied magnetic fields and temperatures. Since (Ga,Mn)As can be grown epitaxially on GaAs, it can be incorporated in a GaAs cantilever using photolithography. l5-lLm-radius disk-shape mesas of (Gao.962MnO.03S)As samples with 6 nm and 20 nm of thickness have been fabricated at the end of the cantilevers and their magnetic properties have been investigated (Harris et al. 1999). The cantilevers are 50 ILm wide and 100 nm thick and the longest lever is '" 400 ILm long. The cantilever with (Ga,Mn)As shows a twist of several degrees in the last 50 ILm due to the lattice mismatch between GaAs and (Ga,Mn)As. From the measurement, it is found that the torsional magnetometers have quite a high sensitivity of 3 x 106 ILB at 0.1 T. The obtained magnetization curves for 20-nm thick (Ga,Mn)As shows ferromagnetic behavior with an in-plane easy axis, being consistent with the results obtained with a SQUID magnetometer for much larger samples. From the temperature dependence of the remanent moment, Te is determined as 39 K. Illumination of the sample with a blue light-emitting diode (LED) has no measurable effect on the magnetization of (Ga,Mn)As either above or below Te. Measurement on 6-nm thick (Ga,Mn)As shows no ferromagnetism down to 350 mK, which is consistent with SQUID results (Tanaka 1998).
III-V FERROMAGNETIC SEMICONDUCTORS
27
6. Magnetotransport properties Due to the presence of the anomalous Hall effect (known also as the extraordinary or spin Hall effect), magnetotransport measurements provide valuable information on the magnetism of thin films. The Hall resistance RHall is empirically known to be a sum of ordinary and anomalous Hall terms, (1)
Here, Ro and Rs are the ordinary and anomalous Hall coefficients, respectively; d is the thickness of the conducting channel; Ml. is the component of magnetization perpendicular to the sample surface (Chien and Westgate 1980), and Rs is proportional with temperature-independent proportionality constant, where Rsheel is the sheet to R~heel resistance. Usually, y is either 1 or 2 depending on the origin of the effect; the skewscattering mechanism results in y = I, whereas for the side-jump mechanism y = 2. The proportionality constant, which determines the overall magnitude of the anomalous Hall effect, scales with the strength of the spin-orbit coupling for the carriers at the Fermi level as well as with the exchange energy describing the ratio of carrier spin polarization to magnetization M«. Accordingly, at given Ml.' the effect is expected to be much stronger for the holes than for the electrons in the tetrahedrally coordinated semiconductors. Furthermore, since its magnitude depends on the degree of spin polarization of the carrier liquid, it ceases to be proportional to the magnetization when the carrier spin-splitting becomes comparable to the Fermi energy. Because of the high sensitivity, the determination of the magnetization by magnetotransport studies is the important technique for thin films of diluted magnets, in which the magnitude of the total magnetic moment is rather small. Accordingly, recent years have witnessed a renewed interest in the theory of the anomalous Hall effect (Hirsch 1999; Ye et al. 1999; Zhang 2000; Ferrand et al. 2000; Crepieux and Bruno 2001; Jungwirth et al. 2002). Theoretical calculations for p-type OMS, based on the side-jump mechanism, suggests an increase of the Hall conductivity with the decrease of the carrier concentration (Jungwirth et al. 2002). Experimental results discussed below: (i) demonstrate the critical importance of the Hall effect in the assessment of the magnetic properties of III-V ferromagnetic semiconductors; (ii) suggest that both side-jump and skew-scattering mechanisms operate (iii) point to various effects that can lead to differences between magnetizations determined by standard and Hall magnetometry. Furthermore, the accumulated magnetoresistance data indicate a significance of the spin-disorder scattering as well as reveal various effects associated with the interplay between spin and localization phenomena, specific to doped OMS in the vicinity of the metal-insulator transition (Dietl 1994). 6.1. (Ga,Mn)As 6.1.1. The Hall effect
Figure 13a presents the Hall resistance RHall at various temperatures plotted as a function of the magnetic field for the same sample, for which magnetization data were collected in fig. I I (200-nm thick Gao.947Mno.o53As). The inset shows the temperature
28
F. MATSUKURA et al.
0.03
-c ---
o::I
2K 25 K / 55 K
B ..L plane
. ,..........................'1'-: .
0.00
",0"
..........
..~.. . ~ •. ~ •. ~
.,~' ..•.•
-0.03
: -: -. -: . -: . ~
:..:.:..'~:..:.;...:.:;,,;.~
/ ............. 1b~~~~ ~
1 ,
~
( ij
....
;-
(a) x =0.053
/
_/ ,J
g I
..~. 125 K 300 K
'05'" •• , •••.•:: .•••••••••• ~
-r.;.... ~ ~ O O K
0.4 .•.•.•._'~ . . . .
~2.5.~5~
~.~
•• ""
····2K, ....25K ...• ll:. ..::""", _
./
03
• . . • . .
30CK
-5
o
-5
.. ~.
~
_
t
.~
8?n
5
5
B (T) 0.08
...... o::lIls: ............ I III
-..,
Qj Q)
l1)
0.04
0-
(ij
-0::
C ::J ;::;:
0.02
---en
0.0
200
300
T (K) 120
(c)
----
80 ~
~
40
~
8.00
0.04
0.08
X Fig. 13. (a) Temperature dependence of the Hall resistance RHaJl for the same sample as in fig. II. The inset shows the temperature dependence of the sheet resistance Rsheet. (b) Temperature dependence of the saturation magnetization [RHaJlI RsheedS obtained using Arrott plots (closed circles) and inverse susceptibility I/XHaJl (open circles), both from the transport data shown in (a). Solid lines depict [RHaJl 1Rsheells and II XHaJl calculated assuming the mean-field Brillouin behavior for the Mn spin S = 5/2 and the Curie-Weiss law, respectively. (c) Mn composition dependence of the magnetic transition temperature Te. as determined from transport data (Ohno and Matsukura 2001).
III-V FERROMAGNETIC SEMICONDUcrORS
29
dependence of Rshcct- A close similarity between the results of figs 13a and lla indicates that the contribution from the ordinary Hall term is rather small in the displayed field and temperature range. Thus, if skew-scattering is assumed, RHall :=:= c RSheetM, where c is a temperature-independent constant. Actually, a comparison of magnetization and magnetotransport data suggests the value of the exponent y to be between 1 and 2 at low temperatures, and that the assumption of either mechanism leads to virtually identical conclusions about the magnetic properties. In particular, since RHall/ Rshcct ex M, Arrott's plots can be employed to determine the temperature dependence of spontaneous magnetization Ms. The outcome of transport measurements is summarized in figs 13b and 13c. The values of Tc are in good agreement with those determined from the direct magnetization measurements. As shown in fig. 13c, the value of the Curie temperature is almost proportional to x up to x of about 5% according to Tc :=:= 2000x ± 10 K. However, a further increase of x decreases Te. The origin of this behavior is unclear; it may result from the compensation by interstitial Mn donors (Yamamoto and Katayama-Yoshida 1999; Masek and Maka 200 1) and/or from changes in the local spin configurations (van Schifgaarde and Mryasov 2(01). The temperature dependence of Ms determined by the magnetotransport measurements can be fitted rather well by the mean-field Brillouin function, as shown by the solid line in fig. 13b (Matsukura et a1. 1998b). Owing to a moderate temperature and magnetic field dependence of Rsheeh this conclusion remains valid assuming RHall :=:= c'R;heetM. However, a rather different temperature dependence stems from the direct magnetization measurements (fig. l lb). To conjecture about the origin of this difference one should note that the anomalous Hall effect scales with the spin polarization of the carrier liquid. This polarization is proportional to the magnetization only if (i) the spin-splitting is much smaller than the Fermi energy and (ii) the contribution of the carriers to the total magnetization can be disregarded. Furthermore, the anomalous Hall effect does not provide information about the magnetization of the whole samples but only about its value in regions visited by the carriers. Just in these regions the carrier-mediated ferromagnetic interactions are strong. Thus, since near the metal-insulator boundary the carrier distribution is highly non-uniform, magnetotransport and direct magnetic measurements may provide different magnetization values (Dietl et al. 2000). Parenthetically, no clear indication of the presence of MnAs clusters has been observed in the transport results, even in the cases where direct magnetization measurements detect their presence. One of possibilities is that the Schottky barrier formation around the MnAs clusters prevents their interaction with the carriers. 6.1.2. Temperature and magnetic field dependence of resistivity The temperature dependencies of the resistivity p in 200-nm thick layers of Ga I-x Mn, As with different Mn content x are displayed in fig. 14. In terms of the metal-insulator transition (MIT), these films can be cost into two categories. Low- and high-Mn composition samples (x < 0.03, x > 0.06) are on the insulator side of the MIT, whereas the layers containing intermediate Mn concentrations (0.03 ~ x ~ 0.06) are metallic. All samples exhibit a negative magnetoresistance (MR) at low temperatures. Quite generally, the MIT occurs
30
F. MATSUKURA et aI.
200-nm (Ga,Mn)As / (AI,Ga)As
1
10
2
1.0 x 10'
E o
c
x 0.015 0.022
......... 10.1 ~
~:-::--..r-L,~0.071
~
0.035 0.043 ..........__...a...._ _.....................__..z0.053
o
100
200
300
T(K) Fig. 14. Temperature dependence of the resistivity p at zero magnetic field for Gal_xMnxAs films with x = 0.015~.071. Samples with x = 0.035~.053 exhibit metallic behavior. The inset shows an expanded view for the sample with x = 0.053 together with the dependence on the magnetic field (Matsukura et aI. 1999b).
if the kinetic energy of holes at the Fermi level is high enough to prevent localization by disorder associated with the presence of Mn acceptors and compensating donors. The temperature dependence of p in the metallic (Ga.Mn)As samples show a maximum around Tc (the inset to fig. 14). where the negative magnetoresistance also peaks; p decreases by 20% in B = 7 T (at 100 K) (see the insets to figs 13a and 14). Such behavior suggests the presence of spin disorder scattering by thermodynamic fluctuations of the magnetization. In particular. the peak around Tc can be interpreted in terms of a critical scattering by packets of ferromagnetic ally coupled spins. whose correlation length is comparable to the wavelength of the carriers at the Fermi level (Matsukura et al. 1998b; Omiya et al. 2000). Such spin-disorder scattering may also perturb the position of the mobility edge, affecting the temperature dependence of the conductivity (Van Esch et al. 1997). The negative MR occurs because the field-induced spin-alignment reduces the spindisorder scattering. The effect of critical scattering on the resistance was evaluated assuming that the holes reside in a simple parabolic band (Omiya et al. 2000). The corresponding contribution to the resistivity has to take into account the presence of correlation between neighboring spins. (SiSj) #- (S;)Oij (Dietl 1994). PS =
2iT
2
kF m 2 fJ2 kBT - 2 -3-2"2[2x.d T • B) pe
h
g /-LB
+ XII(T. B)].
(2)
31
III-V FERROMAGNETIC SEMICONDUcrORS
. 1.00
~
.
•
•
T
I
iT -
E
0.90 ~
P
xT
(J
-IT
-.T-'T1'
0
c:
.
~~£T
~ 0.80
~~2
~~TTT
~.IIl.T
0.70
~
. 150
200
~
.
.
250
300
T(K) Fig. 15. Temperature dependence of the resistivity for a 200-nm thick film of Gal_xMnxAs with x = 0.053 in the high-temperature paramagnetic region. Solid squares and open circles show experimental data and the fitting using eq. (2), respectively (Omiya et aI. 2000).
Here kF is the Fermi wave vector determined from the value of the hole concentration p assuming a spherical Fermi surface, m is the hole effective mass taken as 0.5mo (mo is the free electron mass), fJ is the exchange integral between the holes and the Mn spins, and h is Planck's constant. The transverse and longitudinal magnetic susceptibilities are determined from the magnetotransport data according to Xl. = aM / aB and X" = M/ B. As shown in fig. IS, eq. (2) reproduces the high-temperature part of the temperature dependence of p (Omiya et al. 2000); the data can be fitted by XT, the temperature dependence characteristic for critical scattering. On approaching Tc; however, the XT fit deviates from the experimental points. This is, presumably, because no dependence of the magnetic susceptibility X on the wave vector q is taken into account. Since X (q) is a decreasing function of q in ferromagnetic materials, eq. (2) overestimates the critical scattering, particularly near Tc, where X (q = 0) diverges. As shown in fig. 16, the negative MR can be explained by a reduction of spin-dependent scattering in the magnetic field, according to eq. (2). From the fit of eq. (2) to the temperature and field dependencies of p, the exchange energy INofJ I was evaluated by Omiya et al. (2000). Both T and B fits yield INofJ I of 1.5 ± 0.2 eY. Though this value of the exchange energy compares favorably with that determined by photoemission experiments on (Ga,Mn)As, 1.0-1.2 eV (Okabayashi et al. 1998), it should be stressed that it has been obtained disregarding effects of localization. Another possible source of ambiguity is the complex valence band structure, not accounted for in eq. (2). A rather large negative MR, with a substantial anisotropy, has been observed in 'reentrant' insulating samples with high x (Oiwa et al. 1998b; Katsumoto et at. 1998). A destruction of bound magnetic polarons, as invoked in an earlier work on (In,Mn)As
F. MATSUKURA et al.
32
x10-3 8.0 r"-P~f-r-T""""
d=200nm
__T""'I"""T'"""""""""'....-r-.......__'P-o
x = 0.053
'J
-c: E o
-
exp
--fit
B -l plane
200K
7.5
c:.. .-.
7.0 -10
-5
~-
.,
....."".,.. 250 K
... ''';
o
5
....... 10
B (T) Fig. 16. Magnetic field dependence of the resistivity for a 200-nm thick film of Ga I _ .r Mn x As with x = 0.053 in the high-temperature paramagnetic region. The solid lines show the fitting using eq. (2) (Omiya et al. 2000).
(Ohno et al. 1992), and an increase in the hole kinetic energy due to giant spin-splitting, are suggested as mechanisms leading to the enhanced conductivity in the magnetic field. The latter can be particularly strong in p-type materials, in which the exchange splitting mixes heavy and light hole subbands (Wojtowicz et al. 1986). The theoretical model describes transport properties of (Ga.MnjAs (T and B dependence) by using Zubarev's double-time Green's function rather well (Kuivalainen 2001). The results show that the spin scattering (spin disorder scattering and critical scattering) as well as ionized impurity scattering have significant contributions to the total carrier mobility. For better understanding, an improvement of the theory is necessary, which includes the effect of disorder, the formation of polarons, etc. Anisotropic magnetoresistance has also been observed in metallic (Ga,Mn)As, which depends on the relative direction between the magnetic field and the current. For (Ga,Mn)As with compressive strain grown on a GaAs buffer layer, the resistance is higher when the magnetic field is perpendicular to the measuring current than when the two are mutually parallel (Baxter et al. 2(02). On the other hand, for (Ga,Mn)As with tensile strain grown on an (In,Ga)As buffer layer, the resistance is lower when a magnetic field perpendicular to the current (Sugawara et al. 1997). The origin of the anisotropic magnetoresistance is not clear yet. Because of the dominance of the anomalous Hall term in wide temperature and field ranges, it is not straightforward to determine the carrier type and concentration in ferromagnetic semiconductors. Only at low temperatures and in very high fields, the anomalous Hall term saturates, so that the ordinary Hall coefficient can be determined from the remaining linear change of the Hall resistance in the magnetic field. Note that although M saturates in relatively low magnetic fields, the negative MR usually persists, and generates the field dependence of the anomalous Hall coefficient.
33
III-V FERROMAGNETIC SEMICONDUCTORS
30 30.5
-.a..... z"iii
rr.
-9.
20
'ii
50mK 30.0 exp --linear fit
:I:
0::
10
29.5 22
24
26
an
(a) 0 0.0
28
-e
l-0.1
-0.2 L L . _...._
o
...... _ ~ _
10
................- - '
20
30
B (T) Fig. 17. Magnetotransport properties of a 2oo-nm thick film of Ga I-x Mnx As with x = 0.053 at 50 m K in high magnetic fields. (a) Hall resistance. which is a linear function of the magnetic field in the high-field region (inset). (b) Sheet resistance; negative magnetoresistance tends to saturate in the high-field region (Omiya et aI. 2000).
Measurement of RHall at 50 mK in the field range of 22-27 T on the sample with x = 0.053 revealed that the conduction is of p-type, consistent with the acceptor character of Mn. The determined hole concentration was p = 3.5 x 1020 em -3, about 30% of the nominal concentration of Mn (fig. 17) (Omiya et al. 2000). A similar value of the hole concentration. which is almost independent of x, has been obtained from the Seebeck coefficient assuming a simple model of the valence band (Osinniy et al. 2001). If all Mn centers are acting as acceptors in the metallic sample described above, 70% of them must have been compensated by donors. The most natural candidates for these donors are As antisite defects, which act as deep donors in GaAs. Accordingly, (Ga,Mn)As should become insulating at room temperature when the density of As anti sites exceeds the density of shallow acceptors. Because the magnitudes of these densities are comparable and moreover fluctuate from run to run depending on subtleties of the growth conditions, we expect the overcompensation to occur occasionally. However, no such 'overcompensated' sample has been obtained so far. This seems to call for mechanisms controlling the upper limit of the excess As concentration (Luysberg et al. 1998) and/or leading to autocompensation of Mn but not to overcompensation (Walukiewicz 1988). One candidate for the latter might be the Mn interstitial, which is a donor according to first principles calculation (Yamamoto and Katayama-Yoshida 1999; Masek and Maka 2001). Another
34
F. MATSUKURA et at
candidate is the formation of disordered sixfold-coordinated centers with As, which would act as a donor (Van Esch et al. 1997). Since the As antisite is anyway one of the most important defects acting as the compensating donor, the excess As influences substantially the magnetic and transport properties of (Ga,Mn)As. The increase of substrate temperature and the decrease of the As pressure reduces the density of excess As, which result in a decrease of the lattice constant and an increase in both the hole concentration and conductivity. Importantly, this generates a raise of Tc (Shimizu et al. 1999), confirming the critical role of band holes in the ferromagnetism of (Ga,Mn)As. The annealing of (Ga,Mn)As at relatively low temperatures (~ 300 K) leads to similar results due to the evaporation of excess As (Hayashi et al. 200 1; Potashnik et al. 200 I). 6.2. (/n,Mn)As 6.2./. n-type (/n,Mn)As Magnetization measurements reveal that n-type (In,Mn)As layers with x = 0.046-0.18 grown at 200°C are paramagnetic. The analysis in terms of the Curie-Weiss law shows that the interaction between the Mn ions is antiferromagnetic with the nearest-neighbor exchange inn = -1.9 K (von Molnar et al. 1991). The effective magnetic moment ofMn is determined as Peff (= gJS(S + 1)) = 5.49 for x = 0.046, indicating that the Mn electrons are mostly in the high spin d 5 configuration. Magnetotransport measurements on n-type samples show no evidence for carrier-Mn spin interactions (Ohno et al. 1991). In particular, no magnetization-dependent anomalous Hall effect is observed within the experimental error. 6.2.2. p-type (/n,Mn)As p-type (In,Mn)As shows ferromagnetism at low temperatures. Magnetotransport measurements of thick p-type (In,Mn)As films grown on (00 I) semi-insulating GaAs reveals that the temperature dependence of the Hall coefficient, RH, can be expressed, as is the case of (Ga,Mn)As, by eq. (1) (Ohno et al. 1992). Since M = XH, B = ILoH, X = C/ (T - ()) in the paramagnetic temperature region, and assuming Rs = cp one obtains the Hall coefficient as,
(3) where the Hall resistivity PH all = dRHall. Equation (3) can describe the temperature dependence of RH of a 1.3-Jlm thick (In,Mn)As sample (x = 0.013) grown directly on a GaAs substrate at 275°C, especially from 20 to 200 K, as shown in fig. 18. The fit carried out by adopting the calculated value of the Curie constant (using x = 0.013 and assuming Mn spin S = 5/2) yields Ro, c and (), which are p = 2.2 x 10 19 cm- 3 (determined from Ro), c = 5.6, and () = 3.8 K. The sign of () demonstrates that the interaction between the Mn spins is ferromagnetic. A ferromagnetic Mn-Mn interaction has only been observed in p-type samples so far, proving that this interaction is induced by the presence of the holes. Equation (1) is shown to be valid at low temperatures also, where hysteresis appears in the field dependence of PHall, as shown in the inset to fig. 19. This points to the presence of ferromagnetic order. By comparing the remanent magnetization determined
35
III-V FERROMAGNETIC SEMICONDUCTORS
10.7
10.2 \1 V P ...... -:...\1 \1 \1 \1
.........
E c 10.4
-
\1 \1\1
...
~
.........
t: E c
-
10-6 ~
Q:l:
a
_
••••••••
_
.....
RO
10.9
--- .!-... .
:-..:
3
10. 11 . ......
.... .
.
.
-......... I
.
/----CpxllJ o
10.6 10
10. 13 300
100
T (K) Fig. 18. Temperature dependence of the Hall coefficient RH and resistivity p of a 1.3-JLrn thick film of Inl_xMnxAs with x = 0.013. RH can be modeled over a wide range of temperatures as Ro + cPX/JLo, which is shown by the solid line assuming C = 5.6. The susceptibility X (depicted by the dashed line) is calculated assuming the Curie-Weiss law with x = 0.013, Mn spin S = 5/2, and the Curie-Weiss temperature 8 = 3.8 K (Ohno et al, 1992).
0.015....
-...--,....""1"""".....- . . . - - , , - -_ _... 6
2.8 K
4
E
3.5 K
~
:l· 0.005 0
0.000 .....
o
0
'tl
3 3
:0
-100
0
-
2 0
0
20
60
40
-
80
0 BdmT) o 0
----1...--.. . ---'1...--.. 2
6
4
8
0 10
B (T) Fig. 19. Magnetic field dependence of the diagonal resistivity P (open circles) and magnetization MHall (close circles) determined from the ratio of the Hall and diagonal resistivities. MHall = PHali/CP, where C = 6.3, for a 1.3-llm thick film ofInl_xMnxAs with x = 0.013. The solid line is a fit by the modified Brillouin function BS(y). where S = 5/2 and y = SgIlBB/(T + To) with To = 1.5 K. The inset shows the hysteresis observed in the Hall resistivity at 3.5 K (Ohno et al, 1992).
36
F. MATSUKURA et aI.
from the SQUID measurements at low temperatures with the temperature dependence of the remanent part of PHalliP (PHall ~ RsM = cpM) as shown in fig. 19, one can again evaluate the proportionality constant c as 6.3, in good agreement with c = 5.6 obtained from the paramagnetic temperature region. This indicates that the mechanism responsible for the anomalous Hall effect does not change between the two temperature ranges. The magnetic field dependence of MHall (= PHalli Rs) (i.e., magnetization measured by the anomalous Hall effect) can be expressed as a sum of ferromagnetic and paramagnetic terms. The latter can be described by a modified Brillouin function (Gaj et a1. 1979), as shown in fig. 19. The magnitude of saturation magnetization (the sum of the two responses at B = 0.015 Tat T = 3.5 K) is 0.014 T,just the value expected for x = 0.013 and S = 5/2. 6.2.3. Pseudomorphic p-type (In,Mn)As
The (In,Mn)As layers grown on quasi-lattice matched buffer layer (GaSb or (AI,Ga)Sb) films are either superparamagnetic or ferromagnetic at low temperatures depending on the initial growth mode (Shen et a1. 1997c). They have rather high Tc (= 50 K) with 19 x ~ 0.07 and relatively low p (~2-3 X 10 cm >', determined from the Hall coefficient at room temperature) (Slupinski et a1. 2002b). The magnetotransport properties show no clear evidence for partial ferromagnetism, that is for the co-existence of ferromagnetism and paramagnetism in the same films. A comparison of transport and magnetization measurements revealed that the anomalous Hall coefficient Rs is rather proportional to p 2 than to P in the low-temperature regime (Oiwa et a1. 1999). Surprisingly, in contrast to the case of (Ga,Mn)As and (In,Mn)As with high hole concentrations, the sign of the anomalous Hall effect was found to be negative in (In,Mn)As films with low hole concentrations (Munekata et a1. 1997). Such a sign reversal appears to be possible if skew-scattering by compensating impurities dominates (Leroux-Hugon and Ghazali 1972; Chazalviel 1975; Dorleijn 1976). The magnetic anisotropy in (In,Mn)As has been investigated for various strains in the film, by means of varying the lattice constant of the buffer layer (Munekata et a1. 1993). To increase the tensile strain, (AI,Ga)Sb with high Al composition was employed, whereas to decrease its magnitude, AI(Sb,As) was used as a buffer layer. The corresponding reduction of the tensile strain diminishes the perpendicular magnetic anisotropy, which demonstrates that strain is indeed responsible for the magnetic anisotropy. At the same time, no changes in Tc are observed upon changing the strain (Fumagalli and Munekata 1996). The thickness of the (In,Mn)As film affects also the magnitude of the magnetic anisotropy. For thick samples there is no magnetic anisotropy due to the relaxation of the lattice mismatch, whereas for very thin samples there is no ferromagnetic order due to the depletion of the holes. The thick (In,Mn)As films without anisotropy exhibit long-term magnetization relaxation at low temperatures, which suggests that a cluster-glass state is formed (Oiwa et a1. 1999). The magnetic properties of structures consisting of an (In,Mn)As layer grown onto an (In,AI)As with an composition of Al '" 0.15 and an AISb buffer layer were examined by means of the anomalous Hall effect. The weakening of hysteresis with the increase of the intermediary (In,AI)As layer thickness was observed. This may result from a decrease of overlap between the Mn spins in the (In,Mn)As layer and the holes accumulated at the (In,AI)AsIAISb heterointerface (Munekata et a1. 1992).
111-V FERROMAGNETIC SEMICONDUCTORS
37
6.3. Infrared and far infrared optical conductivity
Infrared (IR) and far infrared (FIR) transmission spectra were collected between 10 and 12000 em -I for two (Ga,Mn)As samples with metallic de conductivity (Nagai et al. 200 I). The thickness and Mn concentration of these two films were 2 ILm, x = 0.034 and 0.4 ILm, x = 0.050, respectively. In the whole spectral region studied, the absorption coefficient is larger for the sample with the higher Mn composition. In the absorption spectrum of the sample with x = 0.034, a broad peak is observed around 1600 em"! (200 meV). Most probably, this peak reflects both photo-ionization transitions between Mn impurity states and the valence band as well as inter-valence band transitions, which have been also observed in the IR absorption spectrum of bulk GaAs:Mn with a Mn concentration of 4 x 10 17 cm- 3 (Chapman and Hutchinson 1967). There exists also quite a different interpretation, which assigns the peak to the formation of polarons (Katsumoto et al. 200 I). This peak is less visible in the sample with x = 0.050, presumably because of a greater degree of overlap among the Mn impurity states, which leads to hole delocalization. In the FIR region, the absorption increases monotonously with the photon energy, and no clear Drude conductivity is observed down to 10 em -I. This behavior may reflect the influence of quantum localization effects on the Drude conductivity as well as the coexistence of the hopping and Drude terms in the vicinity of the MIT (Liu et al. 1993; Gaymann et al. 1996). The dependence of the absorption coefficient on temperature and the magnetic field in the FIR region is consistent with the corresponding behavior of the d.c. conductivity. In particular, the optical density shows both a minimum around Te and an increase in the magnetic field. When the absorption spectrum at Te is subtracted from the spectra below Tc, a Drude-like absorption is obtained below 400 meV, whose magnitude increases as temperature decreases. The Drude-like absorption and localization-induced effects are observed also in (In,Mn)As (Hirakawa et al. 2001). A detected shift of the spectral density towards higher energies was taken as an evidence for the double exchange spin-spin interaction mechanisms (Hirakawa et al. 200 I). This conclusion awaits a verification by considering the behavior of the sum rule in the case of the narrow-gap and complex valence band structure, specific to p-type (In,Mn)As. Theoretical simulations for the optical spectra were also been performed (Sakai et al. 200 I; Sakai and Suzuki 200 I). 6.4. Cyclotron resonance
Magneto-transmission spectra of GaAs:Mn with Mn a concentration of '" 9 x 10 17 cm- 3 grown by MBE were taken at several temperatures in magnetic fields up to 110 T by the use of a FIR laser line of 119 ILm (10.4 meV) and 70.5 ILm (17.6 meV) (Matsuda et al. 1998). It was found that the carrier mobility is too low above 270 K to observe the cyclotron resonance (CR) and that carrier freeze-out occurs below 140 K. In the intermediate temperature region a CR peak was observed in '" 40 T at 119 ILm. The mobility determined from the CR linewidth at 220 K is 780 cm 2/Vs. The cyclotron mass is 0.42mo and r - 0.47mo at 119ILm and 70.5 ILm, respectively. On the other hand, 150-nm thick (Ga,Mn)As with x = 0.053 (Te = 88 K) shows no CR up to 150 T at 119 ILm, which may result from too a low mobility value. In the investigated temperature range from 20 to 150 K, the transmission decreases with the magnetic field, '"v
38
F. MATSUKURA et al,
this behavior being consistent with a negative magnetoresistance observed in such samples. The spin origin of the effect is corroborated by the fact that the magnetic field at which the transmission ceases to change corresponds with to the saturation field of the magnetization (Matsuda et al. 1998). The CR of n-type (In,Mn)As layers with x = 0, 0.08, and 0.12 was observed at 5.5 J.l.m (224 meV) and 10.6 J.l.m (117 meV). The cyclotron mass at 224 meV decreases from 0.054mo to 0.048mo for x increasing from 0 to 0.12. The conduction-band effective mass depends also on temperature. For example, for the x = 0.08 sample, it decreases from 0.051mo at room temperature to 0.045mo at 18 K. For l-um thick (In,Mn)As with p""" 1019 cm'. the CR of the light-hole was detected (Matsuda et al. 2001).
7. Magneto-optical properties Magneto-optical properties of (In,Mn)As and (Ga,Mn)As have been studied in order to elucidate the origin of ferromagnetism as well as to explore the possibility of using these materials as Faraday isolators, suitable for monolithic integration with the existing semiconductor lasers. The absorption edge of (Ga,Mn)As is not sharp, as shown in fig. 20 (Kuroiwa et al. 1998; Szczytko et al. 1999b). This is probably due to impurity band formation caused by the high concentration of ionized Mn and compensating donors (Kuroiwa et al. 1998). Even below the fundamental absorption edge, the absorption coefficient is rather large due to free-carrier (Casey et al. 1975) and intra-Mn absorption. There is no report on the observation of exciton states or photoluminescence, which is probably due to non-radiative recombination, carrier screening, and the formation of an impurity band (Ando et al. 1999).
- - (Ga,Mn)As, - - - LT-GaAs
x = 0.043
o
c ro ~
E (/) c
.-~ 1.3
1.4
1.5
1.6
1.7
Energy (eV) Fig. 20. Optical transmission spectra of 2-llm thick films of Ga J -x Mnx As with x = 0.043 and low-temperature grown GaAs at - 10 K (Kuroiwa et al, 1998).
39
III-V FERROMAGNETIC SEMICONDUCTORS
7.1. Faraday rotation
Figure 21a shows Faraday rotation spectra of (Ga,Mn)As (2 J-Lm, x = 0.043) at 10 and 300 K in the vicinity of the band gap energy (Kuroiwa et al. 1998). Compared to GaAs, the magnitude of the Faraday rotation in (Ga,Mn)As is very large and proportional to magnetization, as shown in fig. 21b. The observed value of the Faraday rotation is 6 x 104 0 fcm in 0.1 Tat 10 K, and the room temperature Verdet constant is 9 x 10- 2 0 fG cm. Oscillations seen in the low-energy region at 10 K are caused by interference originating from internal multiple reflections. The Faraday rotation angle eF can be expressed as, eF~
Ed an --!:lE 2hc aE '
(4)
where E is the photon energy, c is the light velocity, n is the refractive index, and !:lE is the energy difference of the transitions for the two circular light polarizations. The value
(a) (Ga,Mn)As x 0.043
15
=
.- 10
6T
~
"C
-~
5 300 K
o
1.4
1.6
1.8
Energy (eV)
. ~:::A:=&=t5=~ r--..,..-......
15 10 ~ (b)
.- 5 ~ C>
Q)
"C ~
{I'J~~~
o e;..,:,..,:,..,:,..,;,,"-,-._ -5
~
-10
~
300K 1.49 eV
(Ga,Mn)As x= 0.043
I
__-tJ-e-~-t~!t"_.-D:-.H~_B~
-10 K _ _ (.J-magnetization 1.55 eV _ ~. (from transport)
-3
,;
.
0
3
6
B (T) Fig. 21. Faraday rotation for a 2-JLm thick film of Gal_xMnxAs with x = 0.043 measured as a function of the photon energy in a magnetic field of 6 T at - 10 and 300 K (a) and as a function of the magnetic field at - 10K, 1.55 eV and at 300 K. 1.49 eV (b). Solid lines show the magnetization determined from magnetotransport measurements at the given temperatures (scaled to match the open symbols) (Kuroiwa et al. 1998).
40
F. MATSUKURA et aI.
of !:i.E inferred from eq. (4), using experimentally determined anjaE, is about 35 meV, fairly independent of E between 1.25 and 1.6 eV. If one uses !:i.E = (Nof3 - Noa)x(Sz), which is valid only at the band edge, then (Nof3 - Noa) ~ 1 eV is obtained. Here Noa is the exchange integral for the conduction band, and (Sz) the thermal average of the Mn spins in the direction of B, determined by an independent magnetization measurement. The positive value of (Nof3 - Noa) reflects the positive sense of the Faraday rotation, which is opposite to that of II-VI DMSs like undoped (Cd,Mn)Te. This surprising result is explained if a large Burstein-Moss shift due to the high hole concentration specific to III-V DMS is taken into consideration (Szczytko et al. 1999b; Dietl et al. 200 lc). The magnetic field dependence of the Kerr-rotation in (Ga,Mn)As at low-temperature shows clear hysteresis reflecting the ferromagnetic order (Sadowski et al. 200Id). A study on reflectivity and polar Kerr-rotation of thin (In,Mn)As films grown on (Al,Ga)Sb buffer layers showed that the squareness (the ratio of the Kerr-rotation angle at remanence to that at saturation) can be as high as 100% (Fumagalli and Munekata 1996).
7.2. Magnetic circular dichroism (MeD) Magnetic circular dichroism (MCD) is caused by the difference in the magnitude of photon absorption for left-polarized (0"-) and right-polarized (0"+) light,
(5) where a+ (T+) and a- (T-) are the absorption (transmission) coefficients for right and left circularly polarized light, respectively. The incorporation of Mn enhances the MCD signal at optical critical points as shown in fig. 22 (Ando et al. 1998). According to MCD
(a)
Eo
GaAs (x10) E,
x= 0
E , +/l 1
(Ga 1• xMn)As x = 0.005
0 0 ~
(c)
5K 1T 0
2
4
E (eV) Fig. 22. Magnetic circular dichroism (MeD) spectra of (a) undoped semi-insulating GaAs substrate and (b), (c) of epitaxial Gal_xMnxAs films at T = 55 K and B = I T. The spectrum ofGaAs is magnified ten times because the signal is weaker than that of Ga I-x Mn, As (Ando et al. 1998).
III-V FERROMAGNETIC SEMICONDUCTORS
41
studies of (Ga,Mn)As in the reflectivity mode near the Eo critical point, the splitting of the valence band points to a negative Nof3 value, similarly to the case of II-VI DMS. On the other hand, a positive value of MCD deduced from absorption measurements appears to suggest that Nof3 is positive (Szczytko et at. 1996; Shimizu et aI. 1998; Beschoten et at. 1999). As already mentioned, a larger absorption coefficient for the left light polarization can be reconciled with the negative value of Nof3 by taking into account the Moss-Burstein shift (Szczytko et at. 1999b; Dietl et at. 200lc). This mechanism operates also on the insulator side of the MIT, that is in the case of samples with small Mn concentrations, provided that the intra-center correlation energy U of Mn acceptors is smaller than the Fermi energy in the impurity band. In addition to the positive MCD, a negative contribution of magnitude that increases with decreasing temperature, was observed in ferromagnetic (Ga,Mn)As (Beschoten et at. 1999). This peculiar temperature dependence can be explained in the framework of the standard model of interband transitions in doped DMS. It results from a non-linear dependence of MCD on magnetization at the Moss-Burstein edge (Dietl et at. 2001c). In order to describe the experimental data more quantitatively, a model taking into account the effect of disorder on the transition probability was also proposed (Szczytko et a1. 200lb).
8. Origin of ferromagnetism Despite a considerable effort aiming at elucidating the nature of ferromagnetism in III-V magnetic semiconductors, the form of the relevant minimal Hamiltonian and its universality for all III-V compounds are still under an active debate. Such a situation reflects the multifaceted environment, in which the ferromagnetism appears. Indeed, conceptual and technical difficulties inherent to theory of strongly correlated and disordered transition metal compounds are combined - in III-V magnetic semiconductors - with the intricate physics of Anderson-Mott localization that is specific to heavily doped semiconductors. Moreover, low-temperature epitaxy, by which most of the materials is obtained, results in a large concentration of native defects such as antisites, which act as compensating donors. Another possible source of local bond reconstructions is the mechanism of self-compensation, occurring in heavily doped semiconductors once the Fermi level reaches the energy triggering defect reactions. Structural faults may form with neighbor transition metal impurities defect complexes exhibiting hitherto unexplored magnetic characteristics. At the same time, strong compensation by donor-like defects enhances the electrostatic disorder substantially, leading to deep and long-range potential fluctuations that result in significant band tailing. In this section, we first discuss predictions of ab initio computations in comparison to photoemission and x-ray magnetic-circular dichroism data, discussed already in the previous sections. Theoretical models employing parameterized Hamiltonians are presented next emphasizing their successes and shortcomings in the description of magnetic phenomena. 8. J. First-principles studies Ab initio computations of the band structure in zinc-blende ferromagnetic semiconductors were initiated by Shirai et at. (1998), who employed the full potential augmented plane
42
F. MATSUKURA et al.
wave (FLAPW) method within the local-spin density approximation (LSDA) for MnAs and for a supercell structure of Gal-xMnxAs with x = 1/2. The total energy calculation demonstrated that the ferromagnetic ground state has indeed lower energy comparing to competing magnetic states and led to the correct value of the lattice constant. This points to the usefulness of LDSA for the determination of the ground state properties of the compounds in question. Later. the same group (Ogawa et al. 1999) adopted the linear muffin-tin orbital (LMTO) atomic sphere approximation (ASA) and essentially reproduced the results for x = I as well as extended the previous computations to ordered alloys with x = 1/8 and 1/4. It has been noted that the band structure is half-metallic for the ferromagnetic state, i.e., the Fermi level lies in-between the densities of states corresponding to the majority spin-down and minority spin-up states. Furthermore, owing to the p-d hybridization there appears a magnetic moment on the As sites. The As and Mn moments are antiparallel. which confirms that the coupling between the carriers residing on the anion orbitals and the Mn spins is antiferromagnetic, Nof3 < O. At the same time. the magnetic moment within the Mn muffin-tin radius is reduced to about 4/LB. This may suggest that the Mn ion is in d4 state, i.e., that the holes have largely d-like character. This is not the case. however. according to the population analysis carried out by Sanvito et al. (2000. who employed the linear combination of atomic orbitals (LeAO) within LSDA for ab initio studies ofGat-xMnxAs. The results of Sanvito et al. (2001) imply that the charge accumulated on the Mn d-shell is about 5.5 in the electron charge units. This demonstrates that a transfer of electrons from the 3d Mn shell to sp bonds is actually outweighed by a transfer in the opposite sense. resulting in a partial occupation of the 3d6-like state and a corresponding reduction of the Mn magnetic moment. The supercell sizes adopted by Sanvito et al. (200 I) corresponded to a wide range of Mn concentrations in Gal-xMnxAs. for which Nof3 was evaluated. A surprising result is that the apparent value of the p-d exchange energy Nof3* , determined from the computed spin splitting of the valence band at the r point of the Brillouin zone, increases from -5.5 eV for x = 0.06 to -8.2 eV for x = 0.02. This dependence Sanvito et al. (2001) interpret in terms of the model put forward by Benoit a la Guillaume et al. (1992). who considered the case of strong and attractive "chemical" and exchange potentials introduced by the Mn atoms in II-VI DMS. It has been found that since in such a case the hole wave function tends to concentrate around the Mn ions. the virtual-crystal and molecularfield approximations cease to be valid. As a result, a bowing of the energy gap and an enhancement of the spin splitting is expected, particularly in the range of small Mn concentrations x. In an extreme case, the Mn can localize a hole, like Cu ions in underdoped cuprate superconductors (Zhang and Rice 1988). By fitting the computed valenceband splitting to the model of Benoit a la Guillaume et al. (1992). Sanvito et al. (200 I). evaluated the bare value of the exchange energy Nof3 = -4.5 ± 0.3 eV and the "chemical" (spin-independent) part of the total Mn potential to be close to zero. For these parameters, the holes are not yet localized in the Zhang-Rice states but certainly the local potential will significantly contribute to the binding energy of the Mn acceptor state. As discussed in section 4. the experimental values of INof31 are smaller, Nof3 ~ -1 e V. More recently. Zhao et al. (2001a) employed the FLAPW method within the generalized gradient approximation (GGA) to investigate further electronic and magnetic properties of ordered Gal-xMnxAs alloys with low and high Mn concentrations, 0.031 ~ x ~ 0.5.
III-V FERROMAGNETIC SEMICONDUCTORS
43
The determined Mn moment in the muffin tin (MT) sphere at given x was found to be in a good agreement with the results of Ogawa et al. (1999). This indicates that LSDA and GGA agree with each other very well in the description of magnetic properties for a given Gal-xMnxAs structure. At the same time, the occupancy analysis indicates that the charge accumulated on the d-shell in the MT sphere is 5.2, again greater than 5, although slightly smaller than that obtained by Sanvito et al. (2001), as quoted above. Furthermore, the difference in total energies of antiferromagnetic and ferromagnetic ground states, normalized to one Mn atom, was found to increase from 0.12 eV for x = 0.0625 to 0.24 eV for x = 0.5. This confirms that enlargement of Mn content in III-V compounds might constitute a road towards higher Curie temperatures Tc: The question about the performance of other transition metals in synthesizing functional ferromagnetic III-V semiconductors was addressed by Shirai (200 1), who extended FLAPW computation within LSDA to zinc blende arsenides, MAs, where M = Ti, V, Cr, Mn, Fe, Co and Ni. It was found that the ferromagnetic order is more stable than the antiferromagnetic state for VAs, CrAs, and MnAs, the greatest energy gain being predicted for CrAs. Another interesting question concerns ground state properties of hosts other than GaAs. Kato and Katayama-Yoshida (1999) carried out first principles studies of ordered Gao.75MnO.25N, Gao.75MnO.25NO.7500.25, and Gao.75Feo.25N alloys within the LAPWLSDA scheme. The hole-mediated ferromagnetic ordering is favored in (Ga,Mn)N, as confirmed in the later work by Sato and Katayama-Yoshida (2001c), but for the remaining two alloys, in which there are no carriers, an antiferromagnetic ground state is predicted. Ordered alloys of Gal-xMnxN with several Mn concentrations were studied by Kulatov et al. (2001) employing the tight binding LMTO-ASA-LSDA approach. The Mn 3d band was found to reside inside the band gap and to hybridize rather weakly with the band states. Nevertheless, the ground state appears to be ferromagnetic, and its stability in contradiction to results of Kato and Katayama-Yoshida (1999) mentioned above increases with n-type doping but decreases with p-type doping. The first principles studies referred to above have stimulated interesting discussions about the accuracy of the adopted approximations. In particular, a question arises to what extend supercell models as well as the LSD and scalar-relativistic approximations are valid in the case of magnetic alloys in question. Akai (1998), by using the KorringaKohn-Rostoker (KKR) within LSDA approximation and describing chemical disorder in the cation sublattice by the coherent-potential approximation (CPA), obtained information about the ground state energy ofthe random Inl-xMnxAs alloy with x = 0.06. Again, the ferromagnetic phase was found to have lower energy than the local-moment disordered state. Similarly to the results of the supercell LSDA calculations discussed above, the ferromagnetic state is half metallic, and the states near the Fermi energy contain a d-like component. On this ground, Akai (1998) assigns the ferromagnetism to the double exchange mechanism (Zener 1951b). Another important aspect of Akai's work is the direct demonstration that ferromagnetism is unstable once holes introduced by the Mn acceptors become compensated by electrons originating from As antisites or Sn donors. Here, as in most magnetic materials, antiferromagnetic superexchange dominates in the absence of the carriers. Surprisingly, however, the Mn magnetic moment increases only slightly as a function of compensation, from 4.2 to 4.3J.LB. This appears to constitute an additional hint that the holes reside rather on p than on d shells.
44
F. MATSUKURA et al.
A destructive influence of antisites on the ferromagnetic phase in ordered GaJ-xMnxAs alloys has been demonstrated also by Sanvito and Hill (200 I). In another work devoted to effects of disorder, Schulthess and Butler (2001) compare results for a GaJ-xMnxAs supercell, x = 0.0625, computed employing the Vienna ab initio simulation package (VASP), with the outcome of CPA computations for an equivalent random alloy with x = 0.05. According to the VASPdata, the difference in total energies of antiferromagnetic and ferromagnetic ground states, normalized to one Mn atom, is !:i.E = 0.076 eV. For unspecified reason, this stability energy is appreciably smaller than the values of 0.15 and 0.12 eV determined for the same Mn content by Sanvito and Hill (2001) and Zhao et al. (2oo1a), respectively. According to the CPA results, the disorder does not qualitatively affect the density of states but reduces !:i.E to 0.045 eV (Schulthess and Butler 2001). Exchange energies of various molecular clusters of Cr, Mn, and Fe embedded in zinc blende GaAs, GaN, and AIN have been computed within the LSDA by van Schlifgaarde and Mryasov (2001). According to this work, magnetic energy leads to a strong short-range attractive force between the magnetic dopants but whether the corresponding clustering is kinetically allowed at growth temperatures has not been assessed. In all works referred to above LSDA or GGA have been employed. These approximations are known (Kotani 2000) to underestimate the on-site correlation effects for 3d electrons in non-metallic solids. This means, according to the Anderson model of magnetic impurities, that magnitudes of p-d hybridization and related interactions will be overestimated. For instance, the values of Neel temperatures in zinc blende Mn chalcogenides, evaluated within LSDA (Wei and Zunger 1993), are about two times larger than those determined experimentally. This discrepancy is removed in a computation scheme, known as LSDA+U, in which an external parametric potential is added, whose role is to displace the d band, hence change the p-d coupling (Wei and Zunger 1993). Figure 23 compares the partial density-of-states (DOS) for Mn d-electrons in an ordered Gal_xMnxAs alloy with x = 0.0625 computed by Park et al. (2000) within LMTO-LSDA and LMTO-LSDA+U, respectively. In agreement with the Parmenter (1973) model, the parametric potential is characterized by two adjustable parameters, the correlation energy U and Hund's intra-site exchange energy J. As expected, DOS from the LSDA+U model is sharper and located further off the Fermi energy than the LSDA d bands. Another interesting aspect of the theoretical results (Park et aI. 2000) is the observation that the coupling of two Mn spins changes from ferromagnetic to antiferromagnetic when the distance between the pair increases, a behavior reminiscent of the Ruderman-Kittel-Kasuya-Yosida oscillations. It would be interesting to check the stability of the ferromagnetic phase and the magnitude ofNof3 within the LSDA+U model. It is tempting to compare the computed DOS with photoemission spectra. Certainly, DOS obtained within the LSDA+U model agrees better with photoemission results (Okabayashi et al. 1998,1999, 2001a, 2001b), though a direct comparison is hampered by the influence of electron-hole correlation and multiplet effects on the form of excitation spectra (Mizokawa and Fujimori 1993). According to the LSDA+U model, the Mn occupancy increases to 5.4, and the participation of d states in the wave function of holes near the Fermi energy is reduced compared to the LSDA results (Park et al. 2000). The occupation number in excess of 5 is directly corroborated by x-ray magnetic circular dichroism (XMCD) studies (Ohldag et al. 2000; Ueda et aI. 2001), and also, in a model
45
III- V FERROMAGNETIC SEMICONDUCTORS
--> Q)
en
4
+-'
ro 1i> en Q) +-' ro 1i>
--
-
- - -LSDA --LSDA+U
,
Q)
\
2
", ,~ l1 J
0
J
"
,
I ",", I
,
"" ,"
.
0
>- -2 +-' '00 c Q) 0 -4 -8
-4
o
4
8
Energy (eV) Fig. 23. The spin polarized Mn 3d partial density of states of Gao.93SMno.063As from the LSDA and the LSDA+U (Park et al. 2(00).
dependent way, by photoemission experiments of Okabayashi et al. (1998, 1999), which lead to the value 5.3 ± 0.1, as discussed in section 4. At the same time, the local magnetic moment, which amounts 4.1J1.B in LSDA, increases to 4.4J1.B in LSDA+U (Park et al. 2(00). The latter compares favorably with the value 4.6J1.B determined by fitting XMCD spectra (Ohldag et al. 2(00). According to results presented in section 5, the saturation values of the magnetization point to a magnitude of the magnetic moment between 4 and 5J1.B, its more accurate determination being precluded by difficulties in the evaluation of the Mn content x. 8.2. Parameterized Hamiltonians
Experimental and theoretical results presented in the previous sections make it possible to sketch a picture of interplay between electronic and magnetic properties in (Ga,Mn)As. This magnetic semiconductor can be classified as a charge transfer insulator, in which the high spin state, S = 5/2, is stabilized by positive values of energies required to transfer an electron either from the Mn 3d shell to the Fermi level or vice versa. Since Mn atoms are divalent in the S = 5/2 configuration, they act as effective mass acceptors when they substitute for trivalent Ga. The corresponding energy level should not be confused with the Mn 3d shells. At the same time, it is important to realize that the quasi-atomic Woodbury-Ludwig description of magnetic d orbitals is by no means valid in the case of doping by 3d transition metals. Actually, the position and origin of both band and 3d-like local states are determined - to a large extend - by their strong hybridization (Zunger 1986). In particular, the hybridization accounts for a large splitting between tZg and eg components. Moreover, it leads to an admixture of the d 6 configuration to the
46
F. MATSUKURA et al.
wave function of the occupied states visible in XMCD and x-ray photoemission spectra (XPS), as discussed above. Furthermore, the p-d interaction tends to renormalize the energy of anion p-type orbitals adjacent to Mn atoms. This will contribute to the "chemical shift" of Mn acceptors ionization energy in GaAs:Mn, and to the valence band off-set in (Ga.Mn)As. Importantly. a part of the p-d interaction is spin-dependent. which according to the Schrieffer-Wolf transformation, leads to a Kondo-like coupling between effective mass carriers and localized spins (Kacman 200 1). In view of the above discussion. the one-carrier effective mass Hamiltonian describing the interaction with a Mn atom located at R, assumes the form,
(6) where Ho(p) is the k . p Hamiltonian for the crystal structure in question, Vc and v:~ describe the Coulomb and short-range "chemical" part of the potential introduced by the Mn ion, respectively. and I is the short-range exchange operator. It appears that as long as magnetic ion occupies the tetrahedral position (so that there is no. e.g. static Jahn-Teller distortion), the Kondo form of the spin dependent interaction is valid even for magnetic ions with non-zero orbital momentum (Kacman 200 1). However. the orbital momentum. and the associated spin-orbit interaction will affect the relation between magnetization M and expectation value of spin operator S. At the same time. in order to describe correctly the influence of the exchange interaction on the effective mass states, it is essential to take the spin-orbit interaction into account in the k . p Hamiltonian Ho(p). It is convenient to replace. in the spirit of the Kohn-Luttinger effective mass theory for the valence subbands, short range potentials by appropriate matrix elements Wand fJ according to W = (XlVsIX) and fJ = (XllIX). where X denotes a py-like component of the Bloch wave functions for the rg point of the Brillouin zone. The parameter fJ is the familiar exchange integral. whereas W describes the valence band off set disregarding long-range Coulomb effects. Such a parameterized Hamiltonian (6) and its variants constitute a starting point for a number of ferromagnetism models, which will be outlined in this section. First. however, available information on the values of Wand fJ is summarized. As already mentioned. theoretical results of Sanvito et aI. (200 I) lead to NofJ ~ -4.5 eV and W close to zero. Experimental sources of information on fJ and W are parameters serving to describe photoemission and XMCD results. Both XPS (Okabayashi et al. 1998). and resonant photoemission spectra (Okabayashi et al. 1999) can be described with the same set of charge transfer energies in the cluster model (Mizokawa and Fujimori 1993). which result in NofJ = -1.2 ±0.2 eV for Gal-xMnxAs with x = 0.074 (Okabayashi et al. 1998). At the same time. the values of the transfer energies inserted into the formula of Hass (1991) imply that the contribution of the p-d interaction to INoW I is below leV. However. the application of the model of Mizokawa and Fujimori (1993) to XMCD data leads to somewhat different values of the charge transfer energies. from which NofJ ~ -0.34 eV and Wpd > 0 in Gal-xMnxAs with x = 0.025 (Ueda et al. 2001). Bhattacharjee and Benoit a la Guillaume (2000) adopted the Hamiltonian (6) in order to describe experimental values of spin-flip and ionization energies of holes localized on Mn acceptors in the case of weak doping. x < 0.1 %. Their results, obtained by employing
III-V FERROMAGNETIC SEMICONDUCTORS
47
the Baldereschi-Lipari effective mass theory, lead to NoP ~ -0.9 eY. However, for the assumed shape of the acceptor wave function, the magnitude of INoPI would, presumably, be about two times smaller when taking a more recent value of the spin flip energy, as determined by Sapega et aI. (2000, 2001). According to Bhattacharjee and Benoit a la Guillaume (2000), a positive value of No W having a magnitude larger than INoP I is necessary in order to explain the "chemical shift" of the Mn acceptor. The positive sign of W is consistent with the existence of a barrier for the hole injection from (Ga,Mn)As to GaAs in p-i-n diodes (Arata et aI. 2001). It has been concluded, by comparing results for three kinds of p-i heterojunctions: (Ga,Mn)AslGaAs, GaAs:Be/GaAs, and GaAs:Be/(Al,Ga)As that the barrier height in (Ga,Mn)AslGaAs is too large to be entirely assigned to band gap narrowing by many body effects within the carrier liquid. A barrier height of 100 meV for x = 0.05, would imply NoW = 2 eV in the virtual crystal approximation. Such a band off-set is consistent with a reduction of the energy gap in (Ga,Mn)As comparing to GaAs, noted by Dietl et al. (2oo1c) and Szczytko et al. (2oo1b) when analyzing optical transmission data of Szczytko et al. (1999b) and Beschoten et al. (1999). Importantly, assuming a value of NoP = -1.2 eV, a consistent account of the MCD spectra of Beschoten et al. (1999) is possible within the k . P model of the valence band (Dietl et aI. 2oo1c). More recently, Szczytko et aI. (2oo1b) by taking the effect of disorder on selection rules into account obtained an accurate description of their magnetotransmission results (Szczytko et al. 1999b) with NoP = -1.0 eV. Finally, we recall that a description of the temperature and field dependence of the resistance in terms of spin-disorder scattering yielded INoPI of 1.5 ± 0.2 eV (Omiya et al. 2(00), assuming a simple structure of the valence band and neglecting the q-dependence of the magnetic susceptibility. The body of findings presented above demonstrates that owing to the p-d hybridization there exists an antiferromagnetic coupling between the hole and Mn spins in (Ga,Mn)As. If described in terms of the Kondo Hamiltonian, the magnitude of the corresponding exchange energy is, presumably, of the order of -I eV, NoP ~ -1.0 eV. Furthermore, in the GaAs/(Ga,Mn)As heterojunction, the valence band edge of (Ga,Mn)As resides higher than in GaAs, No W > 0, so that the potential Vs in eq. (6) is attractive for the holes. However, to what extent this band offset is controlled by the p-d hybridization and what is its exact magnitude is unknown at present. 8.3. Hole states and hole mediated exchange interactions It is now well established that in the absence of free carriers the dominant exchange mechanism is the superexchange in zinc blende magnetic semiconductors. This mechanism leads to antiferromagnetic interactions, except perhaps for some Cr-based compounds, for which a ferromagnetic coupling is theoretically predicted (Blinowski et al. 1996). Remarkably, owing to the large exchange energy INoPI and the high density of states, the hole-mediated ferromagnetic exchange interaction can overcome antiferromagnetic superexchange (Dietl et ai. 1997). Indeed, as already emphasized, the presence of holes is essential for the existence of the ferromagnetic order in Mn-based semiconductors. The case of III-V magnetic semiconductors is particularly fortunate as Mn atoms act as acceptors. It should be recalled at this point that electronic states in doped semiconductors undergo dramatic changes as a function of the impurity concentration (Belitz and
48
F. MATSUKURA et aI.
Kirkpatrick 1994; Edwards and Rao 1995). Hence, the hole states, and possibly holemediated exchange mechanisms, maya priori undergo dramatic changes as function of the Mn content x and the concentration of compensating donors, ND in III-V magnetic semiconductors. The evolution of electronic states in doped semiconductors is governed by the ratio of the average distance between the carriers 'c to the effective impurity Bohr radius aB, determined by both Coulomb and short-range potentials of eq. (6). In the case of the holes in (Ga,Mn)As, r c = (3j4rrp) 1/3, p = x N« - ND, and aB ~ 0.78 nm (Bhatt and Berciu 2(01). In the range of small impurity concentrations, 'c »aB, the holes are tightly bound to acceptors. Hence, the conductivity vanishes in the limit of zero temperature. At non-zero temperatures, the charge transport proceeds either via phonon-assisted hopping between occupied and empty acceptors or by means of thermal activation from the acceptor levels to the valence band. In a pioneering work Pashitskii and Ryabchenko (1979) evaluated the strength of exchange interactions between localized spins mediated by band carriers thermally activated from impurity levels. More recently, Wolff et al. (1996) considered carriers localized on impurities and forming bound magnetic polarons (BMP). It was found that there exists a range of parameters, in which the coupling between the BMP is ferromagnetic. This idea was further explored by Bhatt and Wan (1999), who examined by Monte Carlo simulations properties of a ferromagnetic phase transition driven by the interactions between BMP. Two other groups noted that a long-range exchange interaction between Mn spins can be mediated by holes undergoing quantum hoping from the Mn-derived impurity states to the extended valence band states. Inoue et al. (2000) adopted the Slater-Koster approach, well known in the physics of resonant states, for the case of two magnetic impurities. It has been found, by a model calculation, that the pairs of Mn spins coupled to the valence band states have a lower energy in the ferromagnetic than in the antiferromagnetic configuration. Litvinov and Dugajev (2001) suggested than the ferromagnetic spin-spin interaction can originate from virtual excitations between the acceptor-like impurity level and the valence band, a variant of the Bloembergen-Rowland indirect exchange mechanism. They evaluated Curie temperatures by using a formula, derived originally for excitations between valence and conduction bands, without proving its correctness for the case in question. With the increase of the net acceptor concentration, the impurity band merges with the valence band. For r; «aB, the holes reside in the band, and their quasi-free propagation is only occasionally perturbed by scattering of Mn (eq. (6» and other defect potentials, whose long-range Coulomb part is screened by the carrier liquid. Here, the celebrated RudermanKittel-Kasuya-Yosida (RKKY) mechanism, driven by intraband virtual excitations, is expected to dominate. In the context of III-V magnetic semiconductors, this mechanism was discussed by Gummich and da Cunha Lima (1990) and Matsukura et al. (I 998b). At the same time, Dietl et al. (1997) demonstrated the equivalence of the RKKY and Zener (l951a, 1951c) models, at least on the level of the mean-field and continuous medium approximations. However, with no doubts, beyond those approximations such equivalence can be questioned (Semenov and Stepanovich 200 I). Within the Zener approach, and its nuclear spin variant (Frohlich and Nabarro 1940), the degree of spin ordering, Mq , at given temperature T is found by minimizing the total free energy of the spin and carrier subsystems, F[Mq ]. Here M q denotes the Fourier
III-V FERROMAGNETIC SEMICONDUCTORS
49
components of localized spin magnetization M(r), so that the minimum of F[Mq ] for M q=O # 0 implies the ferromagnetic order. In general, however, other ground states, such as non-collinear structures or spin-density waves, described by M q",O have to be considered (Dietl et al. 1999). This is a rather versatile scheme, to which carrier correlation and confinement (Dietl et al. 1997,1999; Haury et al. 1997; Jungwirth et al. 1999; Lee et al. 2000; Fernandez-Rossler and Sham 2001), k- P and spin-orbit couplings (Dietl et al. 2000, 2oo1c; Abolfath et al. 2001; Femandez-Rossier and Sham 2001) as well as disorder and antiferromagnetic interactions (Dietl et al. 1997; Kossacki et al. 2000) can be introduced in a controlled way, and within which a quantitative comparison of experimental and theoretical results is possible (Dietl et al. 2oo1a, 2oo1c; Ferrand et al. 2001). In view of the above discussion the question arises whether the hole-mediated ferromagnetism appears in the insulator or in the metallic phase. It is well established that the metal-insulator transition (MIT) occurs at re ~ 2.4aB in doped non-magnetic semiconductors (Edwards and Sienko 1978). According to this criterion one gets the critical hole concentration Pc = 4 X 10 19 cm- 3 for aB = 0.78 nm. Experimentally, the MIT occurs at about 3.5% of Mn in (Ga,Mn)As, i.e., for Nox = 7 x 1020 cm- 3 (Oiwa et al. 1997; Matsukura et al. 1998b; Katsumoto et al. 1998). A large difference between these two values is presumably caused by the compensation (discussed above) as well as by the enhancement of localization by the sp-d exchange scattering (Dietl 1994). The latter is documented in (Ga,Mn)As by the presence of negative magnetoresistance and associated insulator-to-metal transition driven by the magnetic field (Katsumoto et al. 1998). In addition to the MIT at x ~ 0.035, the reentrant insulator phase is observed for x > 0.06 (Matsukura et al. 1998b), as discussed in section 6. Presumably, a selfcompensation mechanism is involved but no microscopic model has been proposed so far. Perhaps, the most intriguing property of the materials in question is that the ferromagnetism is observed on the both sides of MIT (Oiwa et al. 1997; Matsukura et al. 1998b). It is, therefore, interesting to contemplate the nature of electronic states in the vicinity of the MIT in doped semiconductors. Obviously, the random spatial distribution of acceptor and donor centers gives rise to strong spatial fluctuations in the carrier density and states characteristics. According to the phenomenological two-fluid model there exist two kinds of relevant states (Paalanen and Bhatt 1991). The first are strongly localized and thus singly occupied states associated with the attractive potential of a single majority impurity. The strongly localized carriers barely contribute to the conduction process. However, they produce a Curie-like component in the magnetic susceptibility and give rise to the presence of BMP in magnetic semiconductors. Obviously, the impurity-like states dominate deeply in the insulating phase but their presence is noticeable also in the metallic phase (Paalanen and Bhatt 1991; Glod et al. 1994). The second pool of states determines the conductivity, so that properties of these states are described by the scaling theory of MIT. Accordingly, the corresponding localization radius ~ is rather controlled by interference of multi-scattering processes than by the attractive potential of a single impurity. Thus, ~ of these weakly localized states is significantly larger than aB, and diverges on approaching the MIT from the insulator side. It is worth noting that such a two-fluid model is consistent with a.c. conductivity studies (Nagai et al. 2001), which show the coexistence of weakly and strongly localized states near the MIT in (Ga,Mn)As. Furthermore, the merging of impurity and
50
F. MATSUKURA et aI.
band states in this range is substantiated by angle-resolved photoemission spectra in the same system (Okabayashi et al. 2001a, 2oolb). In order to tell the dominant mechanism accounting for the existence of long-range spin order in ferromagnetic semiconductors it is instructive to trace the evolution of their magnetic properties on crossing the MIT. Remarkably, in contrast to rather strong changes of resistivity, the evolution of magnetic properties is gradual. This substantiates the notion that thermodynamic properties do not exhibit any critical behavior at MIT as they are insensitive to large-scale characteristics of the wave functions. Importantly, the values of the Curie temperature are found to grow with the degree of the material metallicity (Matsukura et al. 1998b; Katsumoto et al. 200 1; Potashnik et al. 200 1). Moreover, the examination of the magnetization as a function of temperature and magnetic field indicates that virtually all Mn spins contribute to ferromagnetic order in the most metallic samples (Oiwa et al. 1997; Matsukura et a1. 1998b; Potashnik et al. 2(01). However, on crossing the MIT (by lowering x), the relative concentration of ferromagnetic ally coupled spins decreases substantially. According to XMCD results of Ohldag et al. (2000), about 10% of the Mn spins is involved in ferromagnetism of Gal-xMnxAs with x = 2%. Also ferromagnetic resonance studies (Szczytko et al. 1999b) and direct magnetization measurements demonstrate that only a part of the spins contribute to spontaneous magnetization, while the alignment process of the remaining moments occurs according to a Brillouin function for a weakly interacting spin system (Oiwa et al. 1997). Remarkably, the anomalous Hall effect reveals clearly the presence of the first component but hardly points to the existence of any loose spins (Matsukura et al. 1998b). The above findings indicate that Mn spins in the regions visited by itinerant holes are coupled ferromagnetically. These holes set long-range ferromagnetic correlations between the Mn spins, including those contributing to BMP that are formed around singly occupied local states. Obviously, the ferromagnetic portion of the material, and thus the magnitude of the spontaneous magnetization, grows with the dopant concentration, attaining 100% in the metallic phase. Such a trend is confirmed by the available data, as discussed above. Thus, the delocalized or weakly localized holes are responsible for ferromagnetic correlation in (Ga,Mn)As (Dietl et al. 2(00). At the same time, mechanisms that involve strongly localized states, such as excitations from impurity levels or a direct coupling between BMP, appear to be of lesser importance. 8.4. Mean-field Zener model and its application to (Ga,Mn)As
In this section, theoretical foundations and application of the mean-field Zener model to III-V magnetic semiconductors are discussed in some detail. The capabilities of the model to describe various magnetic properties of (Ga,Mn)As are presented, too. In the final part, limitations of the model and its numerous refinements put recently forward are discussed. As already mentioned, it is convenient to apply the Zener model (Zener 1951a, 1951c) by introducing the Ginzburg-Landau functional F[M(r») of the free energy density (Ma 1976), where M (r) denotes local magnetization of the Mn spins. The choice of M (r) as the order parameter means that the spins are treated as classical vectors, and that spatial disorder inherent to magnetic alloys is neglected. In the case of magnetic semiconductors F[M(r») consists of two terms, F[M(r») = Fs[M(r») + FclM(r»), which describe, for a given magnetization profile M(r), the free energy densities of the Mn spins in the
III-V FERROMAGNETIC SEMICONDUCTORS
51
absence of any carriers and of the carriers in the presence of the Mn spins, respectively (Leroux-Hugon 1973; Dietl 1994). A visible asymmetry in the treatment of the carries and of the spins corresponds to an adiabatic approximation, the dynamics of the spins in the absence of the carriers being assumed to be much slower than that of the carriers. Furthermore, in the spirit of the virtual-crystal model molecular-field approximations, the classical continuous field M(r) controls the effect of the spins upon the carriers. Now, the system thermodynamics is described by the partition function Z, which can be obtained by a functional integral of the Boltzmann factor exp( - f dr F[ M (r)]/ kBT) over all magnetization profiles. In the mean-field approximation (MFA), a term corresponding to the minimum of F[M(r)] is assumed to determine Z with a sufficient accuracy. If energetics is dominated by a spatially uniform magnetization M, the spin part of the free energy density in the magnetic field H can be written in the form
(7)
Here, h(Mo) denotes the inverse function to Mo(h), where M o is the macroscopic magnetization of the spins in the absence of carriers at a field h and temperature T. It is usually possible to parameterize Mo(h) by the Brillouin function Bs according to
(8) where two empirical parameters, the effective spin concentration XeffNO < xNo and the temperature Teff > T, take the presence of the short-range superexchange antiferromagnetic interactions into account (Gaj et al. 1979). The dependencies Xeff(X) and TAF(X) are known for II-VI DMS compounds. However, as argued by Dietl et al. (2000, 2001c), the antiferromagnetic short-range interaction is overcompensated by the ferromagnetic double exchange coupling in the case of III-V DMS. According to the two fluids model introduced in section 8.3, a part of the carriers is trapped on strongly localized impurity states, and thus forms BMP. To gain the Coulomb energy, the singly occupied local states are preferentially formed around close pairs of ionized acceptors. In the case of III-V materials, one hole localized at two Mn ions generates, via Zener's (Zener 1951b) double exchange, a strong ferromagnetic coupling that overcompensates the intrinsic antiferromagnetic interaction (Blinowski et al. 1997). Accordingly, Xeff ~ x and Teff ~ T. By contrast, in II-VI compounds in which acceptor cores do not carry any spin, and the degree of compensation is low, BMP are not preferentially formed around Mn pairs, so that the close pairs remain antiferromagnetically aligned. The presence of a competition between the ferromagnetic and antiferromagnetic interactions in p-type II-VI DMS, and its absence in Mnbased III-V materials, constitutes the important difference between those two families of magnetic semiconductors. It is clear from eqs (7) and (8) that Fs[M] monotonously increases with IMI, so thatas expected - the minimum of Fs[M] corresponds to M = 0, for which the spin entropy attains the highest value. It is convenient to introduce the spin susceptibility is related to
52
F. MATSUKURA et a1.
INoIi1 = 1.2 eV _ _--1
;.;.0;.;;5_~"-~~_~ 0.0 LX~-_-~0. r
:> Q)
>~
-0.2
Q)
c
W
-0.4
-2
-1
0
2
- - k (10 7 cm') _ _ k-LM
kllM
Fig. 24. The computed valence band dispersion E(k) computed from the 6 x 6 Luttinger model for the wave vector parallel and perpendicular to the Mn spin magnetization in (Ga,Mn)As. assuming that the spin splitting of the heavy-hole band at the r point is 0.15 e V.
the magnetic susceptibility XO of the spins according to is = (gf..LB)2 XO. In the limit, where Mo(T, h)
= Xo(T)h,
(9) which shows that the increase of Fs with M slows down with lowering temperature. In contrast to Fs[Ml, owing to Zeeman splitting of the bands imposed by the sp-d exchange interaction, the energy of the carriers, and thus Fc£Ml, decreases with IMI. Accordingly, a minimum of F[Ml at non-zero M may develop in H = 0 at sufficiently low temperatures. In order to take into account the complex structure of the valence band, Dietl et al. (2000, 2oo1c) and Abolfath et al. (2001) have computed hole energies by diagonalizing the 6 x 6 k . p Luttinger matrix together with the p-d exchange contribution taken in the virtual crystal and molecular field approximation, Hpd
= {3sM/gf..LB.
(10)
This tenn leads to spin splittings of the valence subbands, whose magnitudes - owing to the spin-orbit coupling - depends on the hole wave vectors in a complex way even for spatially uniform magnetization, as shown in fig. 24. It would be technically difficult to incorporate such effects into the RKKY model, as the spin-orbit coupling leads to non-scalar terms in the spin-spin Hamiltonian. At the same time, the indirect exchange associated with the virtual spin excitations between the valence subbands, the Bloembergen-Rowland mechanism (Dietl 1994; Kacman 200 1), is automatically included. The model allows for biaxial strain (Dietl et al. 2000, 2oo1c; Abolfath et al. 2001),
III-V FERROMAGNETIC SEMICONDUCTORS
53
confinement (Fernandez-Rossier and Sham 2001), and is developed for both zinc blende and wurtzite materials (Dietl et al. 2000, 2oolc). Furthermore, Dietl et aI. (2oo1c) take into consideration the direct influence of the magnetic field on the hole spectrum. The carriercarrier spin correlation is described by introducing a Fenni-liquid-like parameter AF, which enlarges the Pauli susceptibility of the hole liquid (Altshuler and Aronov 1985; Dietl et al. 1997). No disorder effects are taken into account on the grounds that their influence on thermodynamic properties is relatively weak. Having the hole energies, the Helmholtz free energy density FC£M] can be evaluated according to the standard procedure for the Fermi gas. By minimizing F[M] = Fs[M] + Fc[M] with respect to M at given T, H, and hole concentration p, one obtains M(T, H) as a solution of the mean-field equation,
where peculiarities of the valence band structure, such as the presence of various hole subbands, anisotropy, and spin-orbit coupling, are hidden in FC£M]. Near the Curie temperature Tc and at H = 0, where M is small, we expect FC£M] - FC£O] ,..., M 2 • It is convenient to parameterize this dependence by a generalized carrier spin susceptibility Xc, which is related to the magnetic susceptibility of the carrier liquid according to X = AF(g* ILB)2XC. In terms of Xc, (12)
By expanding Bs(M) one arrives at the well-known form for the mean-field value of Tc (Dietl et al. 1997; Jungwirth et al. 1999) (13)
For a strongly degenerate carrier liquid lSFI/ kBT » 1, as well as neglecting the spinorbit interaction, Xc = p/4, where p is the total density-of-states for intra-band charge excitations, which in the 3D case is given by p = mOoskF/rr2h2. In general, however, Xc has to be determined numerically by computing FdM). Large magnitudes of both density of states and exchange integral specific to the valence band make Tc much higher in p-type than in n-type materials with a comparable carrier concentration. The above reasoning can easily be generalized to the case of a phase transition to a spatially modulated ground state, characterized by non-zero magnetization M q • The corresponding mean-field value of the ordering temperature Tc(q) is given by the solution of the equation (Dietl et al. 1999) (14)
where the carrier spin susceptibility can be determined from the standard linear-response expression,
(15)
54
F. MATSUKURA et aI.
ui
tl
Ei
tl
Here ), fin), and ) are the periodic part of the Bloch function, energy and Fermi-Dirac distribution functions for the n-th carrier spin subband. In the case of cubic symmetry, the susceptibility tensor is isotropic, X~ij) = Xe8;j. It has been checked within the 4 x 4 Luttinger model that the values of Tc, determined from eqs (13) and (12), which and from eqs (14) and (15) in the limit q ~ 0, are identical do not involve explicitly (Ferrand et al. 200 1). Such a comparison demonstrates that almost 30% of the contribution to Te originates from interband polarization, i.e. from virtual transitions between heavy and light hole subbands. It is possible to extend the above approach to the case of low dimensional structures (Dietl et al. 1997, 1999; Haury et al. 1997; Lee et al. 2000; Femandez-Rossier and Sham 200 1). If the carriers occupy one electric subband, the mean-field value of ordering temperature Te(q) is given by the formula that generalizes eq. (13) (Dietl et al. 1999)
-t:
(16) where qJo(~) is the envelope function of the occupied subband in the confining potential, ~ and q are vectors in the 3 - d and d dimensional space, respectively. We now tum to the ferromagnetic phase, T < Te. Here, in addition to M(T, H), the evaluation of FdM] makes it possible to determine the energy density of magnetic anisotropy. K (Dietl et al. 2000. 2oo1c; Abolfath et al. 2001) as well as the hole spin polarization P = 2gJ1.B(aFdM)/aM)/({3p) and magnetic moment Me = -aFdM]/aH (Dietl et al. 2oolc). Another important characteristic of any ferromagnetic system is the magnetic stiffness A. which describes the energy penalty associated with a local twisting of the direction of magnetization. Actually, in the experimentally important case of a uniaxial ferromagnet. the energy functional is entirely described by K u , A, and the value of magnetization M according to, (17)
where ii (i) is the unit vector that specifies the local Mn spin orientation. and 9 is its angle with respect to the easy axis. The latter is controlled by biaxial strain in epilayers (Ohno et al. 1996b; Shen et al. 1997a. 1997b, 1997c. 1997d) and by confinement in quantum wells (Dietl et al. 1997; Haury et al. 1997). Konig et al. (2000, 2001) have developed a theory of magnetic stiffness A in III-V ferromagnetic semiconductors. Remarkably, A determines the magnitude and character of thermodynamic fluctuations of magnetization. the width and energy of domain walls as well as the spectrum of spin excitations. In particular, the quantized energies of long-wavelength spin waves are given by (18) It is clear from eq. (17) that A describes how the Ginzburg-Landau functional F[8Mq ] varies with q. Here, 8Mq are the Fourier components of the difference between local and macroscopic magnetization M(T, H). In the long-wave limit. in which eq. (17) is valid,
III-V FERROMAGNETIC SEMICONDUCTORS
55
the magnitude of A is expected to be primarily determined by the magnetic stiffness of the carrier subsystem, that is by Fd8Mq] and thus by X~ii)(q). Indeed, the distance between the spins is smaller that that between the carriers, and the intrinsic spin-spin interactions are short-range. It is seen, by comparing eqs (12) and (17), that X~ii) (q, T) for the direction i perpendicular to M(T, H) is relevant, and its numerical evaluation from eq. (15) for a given M(T, H) will provide A(T, H). By parametrizing X~(q) = X~(q = 0) - Cl.q2 one gets (19) As long as the valence band splitting t::. = AFfJM/gJLB is much smaller than the Fermi energy one expects the spin susceptibility, and thus C to be independent of M, and isotropic for the cubic symmetry Cl. ~ clI' An important observation of Konig et al. (2001) is that the magnetic stiffness computed within the 6 x 6 Luttinger model is almost by a factor of 10 greater than that expected for a simple doubly degenerate band with the heave-hole band-edge mass. This enhancement, which stabilizes strongly the ferromagnetic order, stems presumably from p-like symmetry of the valence band wave functions as well as from interband q-dependent polarization. 8.5. Comparison oftheoretical and experimental results
In this section, the mean-field Zener model discussed above is employed to describe experimental values of Curie temperature, spontaneous magnetization, anisotropy field, and domain stripe width. Standard values of band-structure parameters, elastic constants, and share deformation potentials of GaAs are adopted (Abolfath et aI. 2001; Dietl et al. 2oolc). The Mn spins are assumed to be in the d 5 configuration, so that S = 5/2 and the Mn Lande factor g = 2.0. For the pod exchange energy NofJ = -1.2 eV is taken (Okayabashi et al. 1998), which for the cation concentration of GaAs, No = 2.21 x 1022 cm- 3 , corresponds to Jpd == -fJ = 0.054 eVnm 3. The Fermi liquid parameter AF = 1.2 (Jungwirth et al. 1999) enters the enhancement of Te and of the valence band pod exchange splitting t::. = AFfJM/(gJLB) at magnetization M of the Mn spins (Dietl et al. 200Ic). The most interesting property of Gal-xMnxAs epilayers is the large magnitude of Te, up to 110 K for the Mn concentration x = 5.3% (Ohno et al. 1996b; Matsukura et al. 1998b). Because of this high Te, the spin-dependent extraordinary contribution to the Hall resistance RH persists up to 300 K, making an accurate determination of the hole density difficult (Oiwa et al. 1997; Van Esch et aI. 1997; Matsukura et aI. 1998b; Shimizu et al. 1999). However, the recent measurement (Omiya et al. 2000) of RH up to 27 T and at 50 mK yielded an unambiguous value of p = 3.5 x 1020 cm- 3 for the metallic Gao.947MnO.053As sample, in which Tc 110 K is observed (Matsukura et aI. 1998b). The above value of p is about three times smaller than x No, confirming the importance of compensation in Gal_xMnxAs. As shown in fig. 25, the numerical results lead to Tc = 120 K for x = 0.05, and thus, Tc: = 128 K for x = 0.053 and p = 3.5 x 1020 cm- 3. It seems therefore that the mean-field Zener model, with no adjustable parameters, can explain the high values of Tc found in
=
S6
F. MATSUKURA et al.
Ga'_xMnxAs
-
Q'100
x =0.05
l,aNa l = 1.2 eV AF
=1.2
mOOS
..............................
.. '
10
1 .....-"'----....................."---.......-.--.......~ .......-
0.01
0.1
Hole Concentration (10
.......................
1 20
ern")
Fig.2S. Curie temperature as a function of the hole concentration for Gao.9SMnO.osAs computed from the 6 x 6 Luttinger model (solid line). Straight dashed lines represent results obtained assuming large and small values of the spin-orbit splitting !J.o , respectively. The dotted line is calculated neglecting the effect of the spin-orbit interaction on the hole spin susceptibility (Dietl et al. 200lc).
Gal-xMnxAs. Furthermore, the scaling theory of electronic states near the MIT, discussed in the previous sections, makes it possible to explain the presence of the ferromagnetism on the both sides of the MIT, and a non-critical evolution of Te across the critical point (Matsukura et a1. 1998b). A comparison between theoretical and experimental data in a wider range of Mn and hole concentrations requires reliable information on the hole density in particular samples, which is not presently available. In appears, however, that in the case of both Gal-xMnxAs and Inl_xMnxAs on the insulator side of the MIT, the experimental values of Te are systematically higher than those expected from the Zener model. Turning to the temperature dependence of the spontaneous magnetization in the ferromagnetic phase one should note that the total magnetic moment consists of spin and hole contributions. The hole part was found (Dietl et a1. 2oo1c) to be negative and to attain only a few percent of the total magnetization values, as the hole polarization is incomplete, the hole concentration is smaller than that of the spins, and because of a partial cancellation between the Pauli and Landau terms. If the hole liquid is only partially spin polarized (i.e. 161 < IEFD, which is usually the case in Gal_xMnxAs, M(T) is expected to grow at T ~ 0 according to the Brillouin function (Dietl et a1. 2oo1c), in agreement with the experimental results (Matsukura et a1. 1998b), shown in fig. 13. For lower hole concentrations or higher Mn content, M(T) will tend to its saturation value M; somewhat slower (Dietl et a1. 2oo1c). This, together with a lowering of M (T) by spin wave excitations, may account for the dependence M(T)/ M s = 1- AT 3/ 2 , detected experimentally for T ~ 0 (Potashnik et a1. 2001). Both hydrostatic and axial strain affect the valence band, and thus alter the magnitude of the density of states and Tc : Quantitatively, however, the effect is evaluated to be small
III-V FERROMAGNETIC SEMICONDUCTORS
57
(Dietl et al. 2001c). There exists another mechanism by which strain may affect Tc· It is presently well known that the upper limit of the achievable carrier concentration is controlled by pinning of the Fermi level by impurity or defect states in virtually all compound semiconductors. Since the energies of such states in respect to bands vary strongly with the bond length, the hole concentration and thus Tc will depend on strain. Apart from Tc and Ms , it is interesting to consider means making it possible to tailor magnetic anisotropy, and thus the direction of the spontaneous magnetization, the coercive force, the switching field, the domain structure. Already early studies of the ferromagnetic phase in Int-xMnxAs (Munekata et al. 1993) and Gat-xMnxAs (Ohno et al. 1996b; Shen et al. I997a) demonstrated the existence of a sizable magnetic anisotropy. Magnetic anisotropy is usually associated with the interaction between spin and orbital degrees of freedom of the d-electrons, According to the model advocated here, these electrons are in the d 5 configuration. For such a case the orbital momentum L = 0, so that effects stemming from the spin-orbit coupling are expected to be rather weak. It has, however, been noted that the interaction between the localized spins is mediated by the holes that have a non-zero orbital momentum (Dietl et al. 2(00). An important aspect of the Zener model is that it does take into account the anisotropy of the carrier-mediated exchange interaction associated with the spin-orbit coupling in the host material (Dietl et al. 2000, 2001c; Abolfath et al. 2(01), an effect difficult to include within the standard approach to the RKKY interaction. A detail numerical analysis of anisotropy energies has been carried out for a number of experimentally important cases (Dietl et al. 2000, 2001c; Abolfath et al. 2(01). In particular, the cubic anisotropy as well as uniaxial anisotropy under biaxial strain have been studied as a function of the hole concentration p. The computation indicates that for the parameters of Gal-xMnxAs films grown along the [001] direction, the spontaneous magnetization M lies in the (001) plane, and the easy axis is directed along the [100] or along the [110] (or equivalent) crystal axis depending on the degree of the occupation the hole subbands as well as on their mixing by the k . p interactions. As a result, the easy axis fluctuates between [100] and [110] as a function of p, the preferred direction for typical hole concentrations being [110]. The magnitude of the external magnetic field Heu that aligns M along the hard direction in the (001) plane is evaluated to be up to 0.2 T (Dietl et al. 200 Ic). However, the orientation of the easy axis changes rapidly with p and M. Therefore disorder, which leads to broadening of hole subbands, will presumably diminish the actual magnitude of magnetic anisotropy. The field /-Lo H eu determines also the magnitude of the switching field, which could be observed in microstructures containing only a single domain. In macroscopic films, however, smaller values of the coercive field /-LoHe are expected as actually observed: typically /-LoHe = 4 mT for the magnetic field along the easy axis in the (001) plane in Gat-xMnxAs (Shen et al. 1997a). It can be expected that strain engineering can efficiently control magnetic properties resulting from the hole-mediated exchange. Indeed, sizable lattice-mismatch driven by biaxial strain is known to exist in semiconductor layers. In some cases, particularly if epitaxy occurs at appropriately low temperatures, such strain can persist even beyond the critical thickness due to relatively high barriers for the formation of misfit dislocations. It has been found that the biaxial strain leads to uniaxial anisotropy, whose magnitude can be much greater than that resulting from either cubic anisotropy or stray fields. As shown
58
F. MATSUKURA et al.
1.2
.......
I-
x =0.05
IfJNol =1.2 eV
1.0
AF
c:
::x:::>
e
"U (1)
u::
0.8 20
3.5x10 em"
0.6
/
>.
a. 0.4 0
...... 0 0
U)
=1.2
0.2
'2
-c
0.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
Biaxial Strain exx (%) Fig. 26. Computed minimum value of the magnetic field Hun necessary to align the saturation value of magnetization M s along the hard axis as a function of biaxial strain component €x. for two values of the hole concentrations in Gao.95Mno.05As. The symbol [100]-> [0011 means that the easy axis is along [100]. so that Hun is applied along [(01) (Dietl et al. 200lc).
in fig. 26 for the experimentally relevant values of p and M. the easy axis is predicted to be oriented along the [00 I] direction for tensile strain, whereas it should reside in the (001) plane for the case of unstrained or compressively strained films (Dietl et al. 2000, 200lc; Abolfath et al. 2(01). This is corroborated by the experimental study (Ohno et al. I996b), in which either (In,Ga)As or GaAs substrate was employed to impose tensile or compressive strain in Gai-xMnxAs, respectively. In particular, for the Gao.965Mno.035As film on GaAs, for which t:x x = -0.24%, the anisotropy field /-LoHun = 0.4 ± 0.1 T is observed (Ohno et al. 1996b; Shen et al. I997a, I997b, 1997c, 1997d), in quantitative agreement with the theoretical results of fig. 26. This field is about two orders of magnitude greater than that evaluated from the extrapolation of ESR data on single-ion anisotropy at low x (Fedorych et al. 200 I), a result confirming the dominant contribution of the holes to the magnitude of Hun. Though no theoretical computations have been performed for Inl_xMnxAs, a qualitatively similar effect of biaxial strain is expected, in agreement with results of Munekata et al. (1993), who tailored the easy axis direction by employing (AI,Ga)Sb or AI(Sb,As) substrates with various Ga contents or As contents. Recently, the structure of magnetic domains in Gal_xMnxAs under tensile strain has been determined by micro-Hall probe imaging (Shono et al. 20(0). The regions with magnetization oriented along the [00 I] and [00 i) easy axis form alternating stripes extending in the [110] direction. This indicates, for either Bloch or Neel domain walls, that the in-plane easy axis is rather along [110] than along [100] directions, a conclusion consistent with the theoretical expectation for in-plane (cubic) magnetic anisotropy presented above. As shown in fig. 27, the experimentally determined stripe width is
59
III-V FERROMAGNETIC SEMICONDUCTORS
.
.
10 r-----r--..--"""T"-....... --,----T""""'--., • •
E
-::1.
.c :2 ~ c:
'm
6 •
-- ----
o
....
,-
·
......•.
"
"
•
4~
E o
_........
-- -- _ --
- - - ---"
·
..........................................rfJ 2
."
·
0'--_ _......._ ....._ . & -......_ 0.2 0.4 0.0
.
......._
.
....._ . & -......
0.6
0.8
-'
1.0
Relative Temperature Tffc Fig. 27. Temperature dependence of the width of domain stripes as measured by SOOno et al. (2000) for the Gao.957Mll().043As film with the easy axis along the growth direction (fun squares). Computed domain width is shown by the solid line. The dashed line is computed assuming that the parameter Ac (eq. (20» is by a factor of 1.8 greater (Dietl et al. 200la).
W = 1.5 JLm at 5 K for a 0.2 JLm film of Gao.957MnO.043As on Gao.SdnO.16As, for which a tensile strain of cxx = 0.9% is expected. According to the micromagnetic theory, W is determined by the dimensionless parameter Ac, which is given by the ratio of the domain wall and stray field energies,
(20) where d is the film thickness. Figure 27 presents values of W(T) calculated by Dietl et aI. (200la) in comparison to the experimental data of Shono et al. (2000). Furthermore, in order to establish the sensitivity of the theoretical results to the parameter values, the results calculated for a value of Ac that is 1.8 times larger are included as well. The computed value for low temperatures, W = I. I JLm, compares favorably with the experimental finding, W = 1.5 JLm. However, the model predicts a much weaker temperature dependence of W than observed experimentally, which Dietl et al. (200la) link to critical fluctuations, disregarded in the mean-field approach. 8.6. Limitations and refinements ofthe mean-field Zener model
It is obvious that the role of randomness in the distribution of Mn acceptors and extrinsic defects, which is neglected in the model in question, will grow with approaching the localized regime. According to the two fluid model discussed previously, there is a
60
F. MATSUKURA et aI.
coexistence of weakly localized carriers and bound magnetic polarons in this regime. In this context particularly interesting are results of Bhatt and Berciu (200 I), whose starting point is the impurity band of holes localized by the Mn acceptors. Interestingly, according to their numerical mean-field treatment, positional disorder enhances Te. A further study along the same lines (Kennett et al. 200 1) supports the two fluid picture, demonstrating the presence of "strongly" and "weakly" coupled spins. It worth noting that the itinerant carriers may set long-range ferromagnetic correlation between magnetic polarons. Since Te is proportional to the square of the relevant spin vectors, the weight of the BMP contribution may greatly exceed their relative concentration. The latter, together with the disorder enhancement of Te mentioned above, may account for higher values of Tc on the insulator side of the MIT than those expected from the Zener model. Another important issue requiring further studies is the role of carrier-carrier correlation. It is known that the effect of disorder on carrier-carrier interactions controls the localization and enhances the spin susceptibility (Altshuler and Aronov 1985), and thus the tendency towards ferromagnetism. However, spin-disorder scattering may limit the efficiency of this process (Altshuler and Aronov 1985). If this is the case, LSDA (Jungwirth et al. 1999; Lee et al. 2(00) can provide a reasonable evaluation of the relevant Fermi-liquid parameter. There are three other experimentally important situations, for which the mean-field Zener model, as introduced above, ceases to be valid. The first one corresponds to the case when an average time of carrier tunneling between typical Mn pairs (Vx~~3)-1 becomes 1 significantly longer than the inverse exchange energy INoPI- • Here V is the width of the carrier band, and its magnitude, not the Fermi energy as sometimes suggested, constitutes the relevant energy scale. For long tunneling times, the virtual-crystal approximations break down, an effect detected in Cdl-xMnxS (Benoit a la Guillaume et al. 1992). A modified double-exchange model will constitute an appropriate description of the carriermediated exchange interaction in the strong coupling limit V < INoPI, where the holes are bound in Zhang-Rice (Zhang and Rice 1988) states, and only occasionally hop between the Mn ions. Here, a strong sensitivity of Te to the concentration of compensating donors is expected. Dynamic mean-field theory, as developed for III-V magnetic semiconductors by Chattopadhyay et al. (2001), can constitute an appropriate approach in this regime. Another regime, in which the mean-field Zener model may cease to be valid, is that of large carrier concentrations n > XeffNO. In the limit when the continuous-medium approximation is obeyed, n « x No, the mean-field value of the ordering temperature T(q) deduced from the RKKY model are identical, independently of microscopic spin arrangement. If, however, n > XeffNO, important changes in the carrier response function occur at the length scale of a mean distance between the localized spins. Accordingly, the description of spin magnetization by the continuous-medium approximation, which constitutes the basis of the Zener model, ceases to be valid. In contrast, the RKKY model is a good starting point in this regime (Ferrand et al. 200 1), as it provides the dependence of the interaction energy of particular spin pairs as a function of their distance. This makes it possible to evaluate the system energy for a given distribution of the localized spins. Here, randomness associated with the competition of ferromagnetic and antiferromagnetic interactions can drive the system towards a spin-glass phase (Eggenkamp et al. 1995). In the extreme case, n »XeffNO, the Kondo effect that is dynamic screening of the localized
II1-V FERROMAGNETIC SEMICONDUcrORS
61
spins by the sea of the carriers may preclude both ferromagnetic and spin-glass magnetic ordering. Finally, the accuracy ofthe mean field approximation (MFA) ought to be addressed. It is well known that the MFA results are exact if the range of spin-spin interactions is infinite (Fisher et al. 1972). The decay of the strength of the carrier-mediated exchange interaction with the distance r between two Mn spins is described by the RKKY function. At small r, the interaction is ferromagnetic, and then changes sign at r = 1.2rc , where rc is an average distance between the carriers that mediate spin-spin coupling. This means that the MFA is valid quantitatively at n «xeffNo, a conclusion consistent with the estimate of Tc taking the spin wave excitations into account (Konig et al. 2000). Actually, however, the range of validity of the MFA is significantly larger than that initially found (Konig et al. 2(00), as the magnitudes of spin stiffness evaluated within the 6 x 6 Luttinger model are much greater (Konig et al. 2001) than those obtained for a simple parabolic band (Konig et a1. 2000). Recently, Monte-Carlo studies of carrier-mediated ferromagnetism in semiconductors have been initiated (Sakai et al. 2001; Sakai and Suzuki 2001; Bosselli et al. 2000; Schliemann et al. 200la, 200lb). Such an approach has a potential to test the accuracy of the approximations mentioned above and to determine the actual spin configuration corresponding to the ground state. Preliminary results appear to confirm the validity of the MFA (Sakai et al. 200 I; Bosselli et al. 2(00), and indicate a possibility of the existence of non-collinear magnetic structures in low-dimensional systems (Bosselli et al. 2(00). More recent comprehensive simulations of Schliemann et al. (200 Ib) carried out within the hybrid Monte Carlo scheme, identify the parameter space, in which the mean-field Zener model may break down. It would be interesting to check separately the regions of validity of particular approximations involved: MFA, virtual crystal approximation (VCA), and molecular-field approximation, as well as to elucidate the role of electrostatic disorder.
9. Heterostructures New physics such as the fractional quantum Hall effect has emerged from non-magnetic semiconductor heterostructures. These systems have also been a test bench for a number of new device concepts, among which are quantum well lasers and high electron mobility transistors. Ferromagnetic III-Vs can add a new dimension to the III-V heterostructure systems because they can introduce magnetic cooperative phenomena that were not present in the conventional Ill-V materials. 9.1. Basic properties of heterostructures 9.1.1. Structural properties ofmultilayer structures Figure 28 shows a typical double-crystal x-ray diffraction pattern of the (004) reflection of a GaAsI(Ga,Mn)As superlattice grown on GaAs (001) substrate, taken by employing CuKa( radiation (Shen et al. 1997d). The sample consists of 20 periods of nominally 11.4-nm thick GaAs and 12.l-nm thick (Ga,Mn)As with x = 0.054. Satellite peaks witnessing the periodicity of the structure are clearly visible. Theoretical simulations of the rocking curve were carried out by adding background noise of 10 cps. The values of
62
F. MATSUKURA et al.
d~I=11.79
d(Ga.Mn~1=11.
nm 74 n
- - experimental - - - simulated
xMn=0.056
10' 10° ......WooI. ...._ .....................WooI. ...._ ..........- . . -1500 -1000 -500 0 500 1000 1500
Relative Angle (arcsec) Fig. 28. X-ray diffraction rocking curve of (Ga,Mn)AslGaAs superlattices with 20 periods (solid line). The nominal thicknesses of the GaAs and (Ga,Mn)As layers and the Mn composition x are 11.4 nrn, 12.1 nm, and 0.054, respectively. The dashed line shows the simulated rocking curve. The fit to the experimental curve is obtained with GaAs and (Ga,Mn)As thicknesses and x of 11.14 nm, 11.79 nm, and 0.056, respectively (Shen et al. 1997d).
the elastic constants and the Debye-Waller factor determined for GaAs were adopted for zinc-blende MnAs. The best fit shown in fig. 28 reveals that x = 0.056 as well as that the thicknesses of the GaAs and (Ga,Mn)As layers are 11.4 nm and 11.70 nrn, respectively, in good agreement with the nominal values. The fact that almost the same line width is obtained for the experimental and the simulated satellite peaks suggests a high quality of the films and the interfaces. The high perfection of the structure is also confirmed by the observation of thickness fringes due to perfect crystal diffraction from thin films. 9.1.2. Magnetic properties ofsuperlattices, thin films. and quantum wells
Transport measurements on multilayer structures demonstrate that the ferromagnetism can be retained down to a (Ga,Mn)As layer thickness of 5 nm, below which the structure becomes paramagnetic. On the other hand, there was a report on the persistence of ferromagnetic properties in short-period superlattices consisting of m (Ga,Mn)As and n GaAs monolayers, with 8:::; m :::; 12 and 4 :::; n :::; 8 (Sadowski et al. 200le). The reason for these diverging conclusions is not clearly understood; it may be related to the Mn segregation at the initial stage of growth, which leads to a depletion of Mn and/or the distribution of the spin-polarized carrier (Louriero da Silva et al. 2001; Vurgaftman and Meyer 2(01). Multiple (Ga,Mn)As quantum wells (QWs) were also fabricated and studied by means of magnetization, magneto-optical and magneto-transport phenomena (Hayashi et a1. 1997b, 1998). No ferromagnetic order in (Ga,Mn)As QWs with thickness less than 5 nm is observed. MCD results show clear evidence of the quantum confinement and the formation of subband.
63
III-V FERROMAGNETIC SEMICONDUCTORS
(Gs o965MnO 035)AslL T-GaAs 1 J.lm ~
r
180 nm
_ .~ ..~ .., :-_-;.IO~~---'I
•• -
,. :
,
• .
I .
..
10 nm
I
. '
I'
10 K
I I
--- --
....u
0 0
500
n 0.0
0.5
1.0
B (T) Fig. 29. Thickness dependence of the ratio of Hall resistance and sheet resistance RHall/ Rsheet, which is proportional to magnetization perpendicular to the film plane, as a function of the magnetic field at 10 K. The inset shows the thickness dependence of TC (Matsukura et aI. 1998a).
Figure 29 shows the thickness dependence of magnetization in (Ga,Mn)As films, as determined by the Hall effect (note that RHaU/ Rsheet oc M) (Matsukura et al. 1998a). The inset presents the values of Tc in these films. Apart from an increase in anisotropy and a gradual growth of Tc, no significant changes are observed when the film thickness is reduced from I /Lm to 10 nm. Below 5 nm, however, the (Ga,Mn)As films become insulating. At the same time, Tc drops significantly, often below the lowest studied temperature of 2 K. Similarly, the ferromagnetism disappears in (Ga,Mn)As QWs, if their width is below 5 nm (Hayashi et al. 1997b). No systematic differences in the behavior of superlattices, thin films or quantum wells have been detected. In contrast, the ferromagnetism was observed in GaAs samples to which a submonolayer of MnAs was inserted (Kawakami et al. 2000). Further studies are apparently necessary to understand the thickness dependence of magnetic properties in these materials. 9.1.3. Band offset between (Ga,Mn)As and GaAs A heterojunction is primarily characterized by the band alignment. This most fundamental property of any heterojunction is not well established in the case of Mn-doped III-V's. The difficulty in determining the band offset arises from a number of reasons, such as a high doping level in Mn-doped I1I-V's and a relatively small values of Mn concentrations, which results in a tiny magnitude of the band offset. The close examination of currentvoltage (I-V) characteristics of p-i-n and p-p diodes made of (Ga,Mn)As and GaAs shows that thermoionic emission at temperatures higher than Tc is the dominant mechanism of the current transport (Ohno et al. 2000; Ohno et al. 2001; Arata et al. 2001). By analyzing the temperature dependence of the I-V characteristics, one can deduce the barrier
64
F. MATSUKURA et aI.
200
2
>
.
E
- -• • "::l
•
.I::.
0) '0) 100
.I::.
.... ....
.;::
0
CO .0
00
0
E i-GaAs v
1
~
);'
-
0
0 0.00
0.04
0 0.08
X Fig. 30. Barrier height [). measured by current-voltage (I-V) characteristics of (Ga,Mn)As/GaAs diodes. [). shown by closed circles is the barrier height between the Fermi energy of (Ga.Mn)As and the valence band top of GaAs as shown in the inset. Open circles depict the effective Richardson constants. (Ohno et aI. 2001).
height between (Ga,Mn)As and GaAs measured from the Fermi level of (Ga,Mn)As. Results of such an analysis are depicted in fig. 30 (Ohno et al. 200 I), which presents the measured barrier height t:.. as a function of x , together with the associated effective Richardson constant (A* / A). Inset shows the band structure of the measured samples. The findings demonstrate that the holes flowing from the (Ga,Mn)As side have to overcome a barrier of about 100 meV, the value being virtually independent of x. However, the interpretation of this number and the determination of the bare offset t:.. E v between (Ga.Mn )As and GaAs valence band edges is by no means straightforward. In particular, the Fermi energy of (Ga,Mn)As (usually of the order of 100 meV) has to be taken into account, which will result in t:..Ev :::::: 200 meV. At the same time, however, band gap renormalization caused by the hole-hole interactions, the hole coupling to the system of ionized impurities, and the impurity band formation will shift the (Ga,Mn)As valence band edge towards higher energies, reducing t:..Ev . 9.2. Spin-dependent scattering, interlayer coupling. and tunnel magnetoresistance in
trilayer structures
Ferromagnetlnonmagnetlferromagnet trilayer structures constitute the most fundamental building block of modem magnetic sensors and storage elements, and are useful for the examination of various magnetotransport processes. Especially important is spindependent scattering in such structures, as this is the basic process that gives rise to the effect of giant magnetoresistance (GMR). Equally important is the effect of tunneling magnetoresistance (TMR) in structures containing a thin insulator as the nonmagnetic layer. In order to investigate the nature of spin-dependent transport in systems made of semiconductors only, various (Ga,Mn)As/(AI,Ga)As/(Ga,Mn)As structures have been
III-V FERROMAGNETIC SEMICONDUcrORS
65
0.3 r - -....T""',.......-r---....,......_.., 2.50
.. --
-- .
0.2
!
ct
0.1
00
2.48
1-A...._I.0001....._I.0001..................... ~
~
-4
o B (mT)
4
8
Fig. 31. Hall resistance RHall (circles) and sheet resistance Rsheel (triangles) versus magnetic field B at 25 K for a (Gao.9sMno.os)As/(Alo.14Gao.86)As/(Gao.97Mno.03)As trilayer structure. Closed and open symbols show the major and minor loops, respectively. Dashed arrows indicate sweep directions of the magnetic field. The minor loop of RHall is skewed by the presence of a ferromagnetic coupling between the two (Ga,Mn)As layers (Chiba et al. 2000).
prepared and studied (Akiba et al. 1998a, 1998b, 2000a; Hayashi et al. 1999; Chiba et al. 2000; Higo et al. 2001a, 2001b). Figure 31 presents the field dependence of the Hall resistance and the magnetoresistance at 25 K for a Hall bar pattern of a trilayer structure (Chiba et al. 2(00). The device consists of two 30 nm Gal-xMnxAs layers separated by a 2.8 nm nonmagnetic Alo.14Gao.86As layer, acting as a barrier for holes, whose height depends on the AI concentration. The layers are grown onto a 50 nm Alo.30Gao.70As buffer and a I ILm relaxed InO.15Gao.85As film. The Mn content x = 0.05 and 0.03 ofthe two (Ga,Mn)As layers results in a difference of their coercive forces. The (Ino./SGao.8S)As film introduces a tensile strain, which makes the magnetic easy axis to be perpendicular to the structure plane. With this easy axis direction, the Hall effect can be used to monitor magnetization. Parallel transport in trilayer structures is characterized by the MR ratio (Rsheet - Ro)/ Ro, where Ro is the layer resistance in the absence of the external magnetic field, Rsheet(B = 0), and for parallel magnetizations M of the two (Ga,Mn)As layers. A plateau seen in the Hall resistance data collected in fig. 31, indicates that magnetizations of the two (Ga,Mn)As layers are anti-parallel (note that RHall is proportional to a weighted average of M of the two (Ga,Mn)As layers). A clear increase of the MR ratio is observed in the plateau region between 3 and 6 mT. This demonstrates the presence of spin-dependent scattering in the trilayer structures made of semiconductors only. The MR ratio decreases with the increase of AI composition in the barrier, which reduces the number of holes traveling across it. In the minor loop measurements, when the direction of magnetization of one of the two layers is fixed, the hysteresis loops of RHall and the MR ratio show a good correspondence (open symbols in fig. 31). This confirms that the observed MR effect
66
F. MATSUKURA et 31.
60 (a)
--E -
20K
30
l-
0
~
-,
-30 6
--
(b)
-
-...
•
0:::0 3
-
~
•
.% #:
:\
0~
• !
+
0
0 T (K)
5
43
--6'
::tl
t
42
I
-
-
44
+
~
0:::
,,
0 41 -50
0
50
100
B (mT) Fig. 32. (a) Magnetization M and (b) tunneling magnetoresistance of 30 nm (Gao.95MnO.os)As/2.8 nm AIAs/30 nm (Gao.97MnO.03)As tunnel junction at 20 K. Inset shows the temperature dependence of tunneling magnetoresistance ratio (Chiba et 31. 2000).
is indeed due to spin-dependent scattering. The minor loop is shifted away from B = 0, which indicates that there is a ferromagnetic interlayer coupling between the two (Ga,Mn)As layers. The magnitude of this coupling estimated from this shift is quite small « I l.d/m 2 ) . The coupling is always ferromagnetic. although theory predicts an antiferromagnetic interaction under certain sets of parameters (Jungwirth et al. 1999). The magnitude of the coupling increases with the lowering of the Al composition in the (AI.Ga)As barrier. This suggests that the interlayer coupling is mediated by holes. Elastic neutron scattering and polarized neutron reflectivity measurements on short-period (Ga.Mn)AslGaAs superlattices show also the presence of a ferromagnetic interlayer coupling (Szuszkiewicz et al. 200 I; Kepa et al. 200 I). An interlayer coupling between two (In,Mn)As layers separated by InAs has also been observed (Yanagi et al. 2(02). Vertical transport measurements of trilayer structures reveal the presence of TMR. Figure 32a shows findings obtained at 20 K for a device containing a 2.8 nm AlAs barrier (Chiba et al. 2000). The structure was grown on a (In,Ga)As film to fix the magnetization direction perpendicular to the plane. For TMR measurements. the electrodes were formed on the top and bottom (Ga.Mn)As layers. The temperature dependence of the MR ratio is shown in the inset to fig. 32. The difference in the coercive forces produces a plateau visible in fig. 32a, in the region, where magnetizations of the two ferromagnetic layers
67
IIl-V FERROMAGNETIC SEMICONDUcrORS
-
N
-a
4>
0
c
-
25 (a)
E 0
8K
20
. 60
'I
Ir ~
-l
I,
40
"
I II
II
JJ
20
II
'ii)
-
15 -20
II
~
4>
0:::
~ II
minor loop
-10
, I I I
0
3:
-~
::0
.o
10
20
B 1/ [100] (mT) 100
I
(b)
/---\
~
0
0
:0::
~
50
0:::
•
~ ~
0
I
I
81/[100]
8K
/-----,., --I 81/[110]"
..
1.4
1.6
1.8
~-.-
2.0
2.2
Barrier thickness (nm) Fig. 33. (a) TMRcurves at 8 Kof a Gaj __ xMnxAs(x =4.0%.50 nm)/AiAs (1.6 nm)/Gal_xMnxAs (x = 3.3%. 50 nm) tunnel junction 200 J./-m in diameter. Bold solid and dashed curves were obtained by sweeping the magnetic field from positive to negative and negative to positive. respectively. A minor loop is shown by a thin solid curve. The magnetic field was applied along the (100) axis in the plane. (b) Barrier thickness dependence of TMR values with the magnetic field applied along the [100] and [110] axes at 8 K (Tanaka and Higo 2001).
are antiparallel. A resistance increase is observed between 8 mT and 16 mT, in the field region corresponding to an antiparallel configuration of magnetizations. The MR ratio is about 5.5% at 20 K. This is TMR, because the barrier produced by AlAs is high (0.55 eV), so that the hole transport across the AlAs layer proceeds by tunneling. The TMR ratio decreases with temperature most probably due to a corresponding drop of spontaneous magnetization in (Ga,Mn)As layers. A TMR ratio over 70% was observed in a (Ga,Mn)AsIAIAs/(Ga,Mn)As structure with an AlAs thickness of 5 monolayers (1.6 nm) as shown in fig. 33. Such a high value indicates that spin polarization of carriers in (Ga,Mn)As is quite high (Higo et al. 2oo1a, 2oo1b; Tanaka and Higo 2001). A theoretical calculation ofTMR with ferromagnetic DMS electrodes shows how the TMR ratio depends on the Mn and hole concentrations (Lyu and Moon 2001).
9.3. Resonant tunneling diodes (RTDs) Spontaneous magnetization in ferromagnetic semiconductors gives rise to spin splitting of the conduction and valence bands due to the presence of exchange interaction. This spin
68
F. MATSUKURA et aI.
•••• HH
---- LH2 •••• HH3
GaAs
(Ga.Mn)As
•... HH .... LH1 GaAs:Be •••• HH11.-......... _
I,
GaAs AlAs
I
o
AlAs
GaAs 5 nm
v
Fig. 34. Schematic valence band diagram of resonant tunneling diode structures. simplified diagram of energy versus wave vector parallel to the interface. and resulting 1-V curve by spin-splitting of the valence band of (Ga,Mn)As emitter.
splitting can be observed in current-voltage (l- V) characteristics of resonant-tunneling diodes (RTDs) having a ferromagnetic emitter as shown in fig. 34. Nonmagnetic double barrier AIAslGaAslAIAs RIDs with a (Ga,Mn)As emitter reveal spontaneous splitting of resonant peaks below Tc of (Ga,Mn)As, even in the absence of an external magnetic field (Ohno et al. 1998; Akiba et al. 1998a, 1998b). Figure 35a shows the temperature dependence of dl /d V versus V of an RTD having a (Ga,Mn)As emitter. Clear spontaneous splitting of resonant peaks labeled HH2 and LHI is observed below Tc of 60 K. The structure in question was grown onto a p+ GaAs substrate and consists of several layers (from top): 150 nm (Gao.965MnO.035)As/15 nm undoped GaAs spacer/5 nm undoped AlAs barrier/5 nm undoped GaAs QW/5 nm undoped AlAs barrier/5 nm undoped GaAs spacer/150 nm Be doped GaAs (p = 5 x 10 17 cm- 3)/150 nm Be doped GaAs (p = 5 x 10 18 cm"). Each label in fig. 35 indicates the resonant state in the GaAs well, where in total six states occur. Akiba et al. (2000b) performed a calculation of the corresponding dl /dV-V characteristics, taking into account a strong k-dependent mixing and the presence of the exchange
III-V FERROMAGNETIC SEMICONDUCTORS
69
(a) T (I<) - - - - - - -.......---~ .....-...-......... 300 - ........--...------":j250
2
3
4
5
M 1/(110), x = 0.05, p = 1x1Uo em",compressive strain 1 %
(b) H1 /\ ..·....lH1 / ,'·.~H2.~.~
..
HH3 lI.t2 .•....
..··P.....'"_../_\. .,",.\.. , '"~\ '".HH4 -. ,' ~\.".:. ~_ - "
NrfJ(eV) 0
..... , -0.2 .... , .'\ ... ~ - , .... -,. .,', \' .-.. ., .• -.---0.5 ...... ,r=.\;11- "-. ' •• _..... 7 -._ . •' " ....._._.-._. ._.-0. oo. -1-. -1.0 .. . . . . .. \ . , ..... __ .... _ ~ .... ~ \. " _ _ _ _ _ -1.2
.
..--
IIIIlIIooo
..
~
0.0
0.2
0.4
""---
," ,.".,----""'---..f -1 .5 0.6
0.8
1.0
1.2
V(V) Fig. 35. Temperature dependence of the differential conductance dJjdV versus bias voltage V of a resonant tunneling diode with a (Ga,Mn)As emitter. No magnetic field is applied (Ohno et al, 1998). (b) Calculated resonant tunneling spectra as a function of the exchange energy Nof3 (Akiba et aI. 2000b).
interaction. Previous theoretical approaches to p-type RTD's (Chao and Chuang 1991; Rodrigues Bittemcourt et at. 1998) were supplemented by incorporating the p-d exchange interaction into the 6 x 6 Luttinger-Kohn Hamiltonian. The resonant states in the GaAs well were calculated by using the 4 x 4 Hamiltonian. The current density Jz for a given hole concentration and voltage was then calculated as, 4
Jz=~
(2Jr)
L .
'/_1 I,J, -
ff'(J
E(EF
d 3k.(aE).T*Tij'[J(E)-f(E-eV)],ciI. ak z (21)
70
F. MATSUKURA et al.
Here. T* Tij is the transmission coefficient from the heavy or light hole state in the emitter to the heavy and light hole states in the collector. f(E) the Fermi-Dirac distribution function. Cit is the probability amplitude of the jth hole state in the lth band. Figure 35b shows the calculated dl/dV-V characteristics with JNoPI as a parameter. which corresponds to various values of magnetization in the present case. A I nm AlAs barrier is assumed to avoid numerical instability. A 5% compressive strain is included in the (Ga.Mn)As (x = 0.05) layer containing I x 1020 holes per em". The magnetization is assumed to be in plane along the [110] direction. As can be seen in fig. 35b. the HH2 resonant peaks shows a clear splitting as NoP (magnetization) increases. whereas other peaks (except probably LHl) do not show such pronounced splitting. the conclusions being in accord with the findings. The splitting of the HH2 peak is so pronounced because the dispersion of the HH2 resonance is similar to that of the dominant valence band state in the emitter. Other resonant states either show a very different dispersion and/or lie high in energy. where transmission maxima become broad. Note that no clear cut-off of the current is observed neither in the experiment nor in theory because of a rather high hole concentration. The present results indicate that because of a complex interplay between the k . p and exchange interactions. it is necessary to go through a rather elaborate calculation to understand the origin of the peaks and their splitting. Similar calculations were performed for different structures with a DMS QW and adopting Keldysh formalism (Petukhov et al. 2000; Inoue et al. 2000; Nonoyama and Inoue 2001; Kuivalainen and Hovinen 2002).
9.4. Spin-injection inferromagnetic semiconductor heterostructures Spontaneous magnetization in ferromagnetic semiconductors introduces an imbalance in the spin population of the carries. Thus. these materials can be used as a source of spin polarized carriers. which can be injected into non-magnetic structures. In spite of the common belief that very fast hole spin relaxation precludes the effect. hole spin injection from (Ga.Mn)As into GaAs was demonstrated (Ohno et al. 1999). Figure 36a shows a schematic diagram of a light emitting diode employed to demonstrate the spin injection. Partly spin polarized holes are injected from a p-type (Ga.MnjAs layer through an intrinsic GaAs spacer into an (In.GajAs QW. where they recombine with unpolarized electrons injected from nonmagnetic n-type GaAs substrate. The spin polarization of the recombining holes and hence spin injection is demonstrated by the observation of electroluminescence (EL) polarization. Figure 36b shows the relative polarization change !l P as a function of the magnetic field at various temperatures. Two polarization states are clearly observed at B = 0 at low temperatures. A series of experiments was done to exclude effects of both fringing fields and magnetic circular dichroism from the adjacent (Ga.Mn)As. Because the easy direction is in-plane for (Ga.Mn)As grown on GaAs. EL was collected along the direction parallel to the QW plane. Since the selection rule at the very bottom of the band in QW does not allow emission of circularly polarized light in this direction. the effect of band filling (Le. nonzero k) needs to be taken into account to fully understand the results. Injection of electron spins is preferable from the application point of view as electrons usually exhibit longer spin lifetime. Spin-injection experiments using n-type II-VI DMS in the magnetic field were performed by Fiederling et al. (1999) and Jonker et al. (2000). An appealing scheme for electrical electron spin injection from a ferromagnetic material
71
III-V FERROMAGNETIC SEMICONDUcrORS
(a) GaAs spacer (il (In,Ga)As (i) GaAs (i)
GaAs spacer (i)I--------i GaAs substrate (n)b:::::::::!!j!Zl:::::::::::::J
(b)
-"#.
.. ~
1
c: 0
cu
.~
CU
0Q. .5
0
E = 1.34eV d= 140 nrn 1= 2.8 rnA --+-sweepup -It-sweepdown - . - 6K -e- 16 K -£-31 K ... 5 2 K "
, "
r-
I.
~oof.
~ily' "./ ;.",:,..___",d-"
c: CU
-fi \I)
.....:::cu
-1
.;: :~.,. ~
:~ .
:. - :: '
~
--
\I) C)
I»
~
'i1-
..•. ,=-
c:
0..
~
if
<3
-t~~\
0 100
I
,_.rr .
~ -15
-10
-5
0
5
10
15
B (mT) Fig. 36. (a) The structure of a light emitting diode for detection of electrical spin-injection. (b) Relative change in light polarization t>.P as a function of the magnetic field at four different temperatures. Inset compares the remanent magnetization as determined by SQUID magnetomery with the remanent t>.P (Ohno et al. 1999).
is the use of a broken gap heterojunction system such as InAsiGaSb, in which the valence band edge of GaSb is energetically higher than the conduction band edge of InAs. The successful growth of ferromagnetic (Ga,Mn)Sb should make it possible to inject spin polarized electrons into nonmagnetic InAs (Abe et al. 2(00). Another way is to use an Esaki tunnel diode, a method successfully developed by Koda et al. (2001) and by JohnstonHalperin et al. (2002), who employed p-(Ga,Mn)Asln-GaAs diodes. By solving the drift-diffusion equation for a GaAs-based pn junction, it has been shown theoretically that the spin-polarization in the p region can be transferred into the n region with high efficiency through the depletion layer (Zutic et al. 200 I). In this structure the spin polarization in the n region can be controlled by the external applied electronic bias; i.e., an increase of forward bias results in a decrease of the spin polarization.
72
F. MATSUKURA et aI.
9.5. Photo-inducedferromagnetism in (In,Mn)As/GaSb
The relationship between Tc and the hole concentration indicates the possibility of control of magnetic properties isothermally by light irradiation, electric field, carrier injection, and all other means that change the carrier concentration in semiconductors. The concept of such devices was proposed already in 1960s in the context of work on rare-earth magnetic semiconductors (Methfessel 1965; Methfessel and Holtzberg 1966). (In,Mn)As (12 nm, x = 0.06)/GaSb heterostructure was found to exhibit photo-induced ferromagnetism as shown in fig. 37 (Koshihara et al. 1997). The illumination by photons with the energy larger than the bandgap of GaSb (""' 0.8 eV) turns the paramagnetic sample without remanent magnetization to a ferromagnetic state with a clear hysteresis at 5 K. which is documented by both magnetization and magnetotransport measurements. 3
X
.... 2
'"'
Eci
hole GaSb
(In,Mn)As
....-
8
EF Ev
0.2 T
1
~ 00
= 0.06
0°," 0 °00
10 20 30 40 50
T(K)
(c)
5K
4
N
b
~
0
X
~ -4
-....'i -
-8 1
0
';;
et -1 -2
- - •before irradiation - - after irradiation L - _......__......---JL....'---.....J
-0.3
0.0
0.3
Fig. 37. Band edge profile of a (In,Mn)AslGaSb heterostructure. EC. Ev , and EF denote band edges of conduction band. valence band, and Fermi level, respectively. (b) Temperature dependence of the magnetization observed during cooldown in the dark (open circles) and warmup (solid circles) under a fixed magnetic field of 0.02 T. The effect of light irradiation at 5 K is also shown by an arrow. (c) Magnetization curves at 5 K observed before (open circles) and after (solid circles) light irradiation. Solid line shows a theoretical curve. (d) Hall resistivity PH.II observed at 5 K before (dashed line) and after (solid line) light irradiation (Koshihara et aI. 1997).
III-V FERROMAGNETIC SEMICONDUcrORS
73
The ferromagnetic state persists even after switching the light off and, at the same time, a persistent conductivity is observed. If the sample is heated up to '" 45 K, the initial state is recovered. It appears that the interface electric field separates photo-holes and photo-electrons, the former being accumulated in the (In,Mn)As layer, which triggers the ferromagnetism. According to the Hall measurements up to 15 T, a critical holeconcentration that generates the ferromagnetic order is '" 3.8 x 1019 cm- 3 , whereas the change of the hole concentration after illumination is as low as 1.4 x 1018 cm- 3. Further studies are necessary in order to clarify the reason why there is a threshold hole concentration and why only a slight increase of the hole concentration leads to such a dramatic effect. A similar persistent light-enhanced magnetization is observed in (lno.9sMno.os)(Aso.sSbo.2)lInSb heterostructure (Kanamura et al. 2(02). Reflecting the small band-gap of InSb, a lower photon energy is more efficient than that for the (In,Mn)As case. On the other hand, it is difficult to observe irradiation effects in (lno.9sMno.os)(Aso.2Sbo.s)lInSb, which may be related to the small built-in electric field in the structure. Ferromagnetic (In,Mn)AslGaSb heterostructures with rectangular hysteresis show also peculiar light-irradiation effects. In particular, the coercive force is drastically reduced by the illumination, which suggests a reduction of the domain wall pining energy (Oiwa et aI. 2(01). A magnetization enhancement of (Ga,Mn)As by circularly polarized light illumination has been also observed (Oiwa et aI. 2(02). These effects open up the possibility of novel magneto-optical memory devices. 9.6. Electric-field control offerromagnetism in gated structures
The modification of ferromagnetism was demonstrated also in a structure consisting of an insulating-gate field-effect transistor (FET) with an (In,Mn)As channel (Ohno et aI. 2(00). The 5-nm thick channel layer (x = 0.03) was grown on a 10 nm InAsl500 nm (Al,Ga)Sb buffer and a GaAs substrate. A 0.8 /Lm gate insulator and a metal electrode completed the device. The hole concentration in the channel was estimated to be 5-8 x 1013 cm- 2 from the resistance changes with the gate voltage and Hall effect at room temperature. Figure 38 shows magnetization deduced from the Hall resistance at 22.5 K for three different values of the gate voltage VG, +125, 0, and -125 V. The bias of VG = 125 V changes the sheet-hole concentration by '" 3 x 1012 cm- 2. At zero gate bias, the channel is weakly ferromagnetic as can be seen from the presence of a small hysteresis. The application of a positive gate voltage depletes the channel and, thus, reduces the ferromagnetic interaction mediated by the holes, which results in a paramagnetic behavior of the magnetization without hysteresis. When the holes are accumulated by applying a negative gate voltage, a clear hysteresis appears. The magnetization curve resumes its original values as the gate voltage returns to 0 V. The 125 V swing give rise to ±6% change in the hole concentration and results in a Tc change of ±4% (±l K). The value of Tc calculated form the mean-field theory for three-dimensional (3D) case (Dietl et aI. 2000, 2001c) is '" 18 K for (In,Mn)As with x = 0.03 and the hole density 1 x 1020 cm- 3 , which corresponds to p = 5 x 1013 cm- 3 in a 5 nm-thick film. For this calculation the Luttinger-Kohn parameters given in by Wiley (1975), the energy of the exchange interaction between the holes and Mn spins NofJ = -0.98 eV (Dietl et aI.
74
F. MATSUKURA et al.
0.04 1
(
-c -
iii
a::
. 20
-1
~
fJ
~
-0.5
0.0
O.
B (T)
0.00 ,,~
-0.02 .~-
-0.04 -1.0
( ~(
." ~.Q~
~_L
~
~
J:
1.5K 5K
.~o, .. .:::t'.... , ~
0.02
....
...:-
r
~
.~
.......
... J"-' I.,.' ", / ' ,
.
~--
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.
- ""'---.... 22.5 K
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...
-'.~ ,....
....
) 0.0 B (mT)
VG
.
OV +125 V --125V _.- OV
--
• 0.5
1.0
Fig. 38. Hall resistance RHali of an insulated gate (In,Mn)As field-effect transistor at 22.5 K as a function of the magnetic field for three different gate voltages. RHali is proportional to the magnetization of the (In,Mn)As channel. Upper right inset shows the temperature dependence of RHali' Left inset shows schematically the gate voltage control of the hole concentration and the corresponding change of the magnetic phase (Ohno et al. 2(00).
200lc), as well as the enhancement factor AF = 1.2 describing carrier-carrier interactions (Jungwirth et a1. 1999) are adopted. The calculation also shows that a modulation of I::!..p = 3 X 1012 cm- 2 gives a change of Tc of r - I K. These evaluations show. therefore. a rather good correspondence with the experimental findings. On the other hand, the thickness of the (In,Mn)As channel in the examined FET structures may suggest that the system is two-dimensional (2D). For 2D systems. the mean-field theory predicts no carrier concentration dependence of Tt; as long as the 2D density-of-states (DOS) that determines Tc is energy-independent (Dietl et a1. 1997). For the hole concentrations in question, several 2D subbands are occupied and the valence band DOS is a complex function of energy, so that we expect a modulation of Tc through a modulation of p. Moreover, since the mean free path is comparable to the quantum well width. the disorder-induced mixing of electric subbands turns DOS towards the 3D value (Kossacki et a1. 2000). An additional contribution to the modulation of Tc may come from the particular design of the FET device: a nonmagnetic InAs is placed beneath the magnetic (In,Mn)As layer. Application of positive (negative) bias displaces the hole wavefunctions away from (towards) the magnetic layer, resulting in a reduction (increase) of the interaction between the holes and magnetic spins and hence in a reduction (increase) of Tc (Lee et a1. 2000). Control of ferromagnetism in gated structure has also been observed in a group VI ferromagnetic semiconductor Mn.Ge I-x (Park et a1. 2(02).
III-V FERROMAGNETIC SEMICONDUCTORS
75
9.7. Ferromagnetic imprinting The manipulation of spin coherence of electron spins and nuclear spins in semiconductor materials is one of the most important issues to pursue in spintronics for spin-based qubits in future quantum computing. A proximity effect on spin coherence in nonmagnetic semiconductors in ferromagnet/semiconductor heterostructures has been observed (Kawakami et a1. 200 1). The spin dynamics in GaAs on which a ferromagnetic layer, (Ga,Mn)As or MnAs, is grown, is investigated using time resolved Faraday rotation (TRFR). The results at 5 K show that the presence of a ferromagnetic layer strongly modifies the spin coherence of electrons. The dependence of TRFR on applied magnetic fields shows hysteresis behavior, and the effective field extracted from the data suggests that there is a nuclei-mediated effective field. The results derived from all-optical nuclear magnetic resonance (Kikkawa and Awshalom 2(00) on the samples also support the existence of the "imprinting" on nuclear spins by the neighboring ferromagnetic layer.
10. Ferromagnetic semiconductors at room temperature For the application of magnetic semiconductors, a Tc above room temperature is required. Room-temperature ferromagnetic sulphospinels have been found in 1960's (Goodenough 1969; Van Stapele 1982), but the application of these ferromagnetic semiconductors has been hampered by difficulties in their fabrication. Recent experimental as well as theoretical progress in material science allows one to design and synthesize new ferromagnetic semiconductors with Tc above room temperature. 10.J. Theoretical suggestions
The mean-field Zener model described in section 8 predicts Tc to lie above room temperature for DMS containing large amounts of magnetic ions and carriers. Thus, the elaboration of methods enabling a simultaneous increase of the magnetic ion and carrier concentrations in DMS is one of the ways to be pursued (Dietl et a1. 2000, 2001c). Furthermore, a chemical trend was theoretically established, suggesting that the highest values of Tc can be achieved in materials containing light anions (Dietl et ai. 2000, 2001c). The tendency for higher Tc values in the case of lighter elements stems from the corresponding increase in the p-d hybridization and the reduction of the spin-orbit coupling. It can be expected that this tendency is not altered by the uncertainties in the values of the parameters employed for the computation. In particular, if one could introduce 5% ofMn and 3.5 x 1020 cm- 3 of holes into wide-gap semiconductors, such as GaN, ZnO, and C, these materials should be ferromagnetic at room temperature. The first-principle calculation also predicts a rather stable ferromagnetism for these materials. The results show that V, Cr, Fe, Co, or Ni doped ZnO is a half-metallic double-exchange ferromagnet, Mn doped ZnO is an antiferromagnetic insulator which changes to a ferromagnet by additional doping of holes, whereas Ti or Cu doped ZnO remains paramagnetic (Sato and Katayama- Yoshida 2000). It is also predicted from the first-principle calculation that V-, Cr-, or Mn-doped GaN is ferromagnetic without additional doping (Sato and KatayamaYoshida 200lc).
76
F. MATSUKURA et aI.
In order to solve the problems of the low solubility of magnetic ions in III-V semiconductors and the difficulty of the carrier control in II-VI semiconductors, modulation-doped III-VIII-VI superlattice structures have been proposed (Kamatani and Akai 200 Ia). Here, a II-VI layer serves as the magnetic layer, which can contain a large concentration of Mn, and III-V barrier layers. where impurities are incorporated. provide carriers to II-VI magnetic layers. The results of the first principle calculation for a AIAs:C/(Cd.Mn)Te superlattice shows that the ferromagnetic state is indeed stable for high concentrations of C. The highest spin and the associated large magnitude of the on-site correlation energy U account for the divalent character of the Mn atoms in a large variety of environments. This results. in particular. in a large solubility of Mn in II-VI materials and its acceptor character in a number of III-V compounds. A question arises about ferromagnetic properties of semiconductors containing other magnetic components. One should recall in this context the existence of. e.g., ferromagnetic europium chalcogenides and chromium spinels. In those compounds, the ferromagnetism is not driven by free carriers. With no doubt, the availability of intrinsic and n-type tetrahedrally-coordinated ferromagnetic compounds would enlarge considerably the impact of semiconductor electronics. Actually, a theoretical suggestion was made that superexchange in Cr-based II-VI compounds can lead to a ferromagnetic order (Blinowski et al. 1996). High composition (I(}-25%) of V or Cr doped ZnS, ZnSe. and ZnTe have been predicted by first-principle calculations to exhibit the ferromagnetism at room temperature even without p- or n-type doping (Sato and Katayama-Yoshida 2(01). Desirable material properties. such as divergent magnetic susceptibility and spontaneous magnetization, can also be achieved in the case of a strong antiferromagnetic super-exchange interaction. The idea here (Dietl 1994) is to synthesize a ferrimagnetic system that would consist of antiferromagnetically coupled alternating layers containing different magnetic cations, e.g., Mn and Co. In general terms. the transition metals (TM) other than Mn are no longer always divalent, they lead to the presence of magnetic levels in the gap, and they are characterized by a non-zero orbital momentum. These will considerably modify transport and optical properties as well as enhance the sensitivity to co-doping and illumination. Furthermore, an increase in magnetic anisotropy as well as an enlargement of the coupling to phonons and thus a shortening of spin-lattice relaxation time are expected, too. Recent ab initio calculations of Sato and Katayama-Yoshida (2000) suggest that V. Cr. Fe, Co, and Ni in ZnO should provide carriers, which owing to the double exchange mechanism generate the ferromagnetic order. We note that in the case of wide gap II-VI compounds studied so far, neither of these transition metals (TM) introduces free carriers. However. for sufficiently high TM concentrations a Mott-Hubbard transition is expected, leading to a transport through the gap d-states. A co-doping with either shallow acceptors or donors could make such transport. and the associated exchange interaction. more efficient. Since the TMs act as deep donors and acceptors, the co-doping of such compounds with shallow impurities (e.g.• by 0 for Mn in III-V compounds) constitutes a natural way to control the ferromagnetic couplings (Katayama-Yoshida et al. 2001). Indeed, according to Sato and Katayama-Yoshida (200 Ib). for Fe. Co, or Ni doped ZnO. the ferromagnetic state is stabilized by the doping of shallow donors.
III-V FERROMAGNETIC SEMICONDUcrORS
77
10.2. Cautionary remarks
Before discussing experimental results, it is appropriate to enlist difficulties encountered in assessing properties of new ferromagnetic semiconductors. The well-known difficulty is the multi-phase character of materials grown by non-equilibrium techniques, such as MBE. In particular, some phases may consist of ferromagnetic and/or ferromagnetic precipitations, such as metallic and ferromagnetic MnAs. These precipitations, even if too small to be detected by x-ray diffraction, can give the dominant contribution to the total magnetic moment of the sample, particularly at high temperatures. Importantly, the Curie temperature of the precipitations may not be identical to the tabulated values, and may depend on their size and the host material. Another source of undesirable magnetic signals originates often from magnetic impurities residing outside the studied layer, for instance in the substrate. Since ferromagnetic semiconductors are characterized by colossal magnetotransport and magnetooptical phenomena, a correlation between semiconductor and magnetic properties allows one usually to rule out parasitic effects. However, stray magnetic fields produced by ferromagnetic inclusions or their contribution to charge transport may constitute a source of ambiguity. Additionally, multi-layer and/or multicarrier transport of semiconductor structures, together with localization, surface, and interface phenomena, may generate strong magnetoresistance effects, usually hard to separate from spin-related phenomena in the examined material. 10.3. Experimental results 10.3.1. (Ga,Mn)As As mentioned above, the mean-field Zener model suggests that Tc values above 300 K could be achieved in, e.g., Gao.9MnO.1 As, if such a large value of x would be accompanied by a corresponding increase of the hole concentration. The elaboration of an annealing procedure that increases Tc (Katsumoto et al. 1999; Poshtanik et al. 2001) as well as a successful implementation of low-temperature atomic layer epitaxy to increase the Mn composition x (Sadowski et al. 2oo1a) constitute examples of recent encouraging developments in this direction. 10.3.2. (Ga,Mn)N As discussed in section 2.4, indications of high temperature ferromagnetism in (Ga,Mn)N have been reported by Sonoda et al. (2002) and Reed et al. (2001), whose layers grown by ammonia-MBE or prepared by solid state diffusion show ferromagnetism well above room temperature. Work is under way to rule out the influence of precipitations as well as to establish how Tc depends on the Mn and carrier concentration. Possible mechanisms accounting for the experimental observations have been put forward (Dietl et al. 2oo1b). 10.3.3. (Cd,Mn)GeP2 Il-VI-V2 chalcopyrite OMS, (Cdl_xMnx)GeP2 was prepared by the solid phase chemical reaction. Mn vacuum deposition (30 nm) on a single crystal of CdGeP2 and the reacting process (500°C, 30 min) was carried out in an MBE chamber (Medvedkin et al. 2000). The Mn/Cd composition ratio decreases rapidly with the depth. The average
78
F. MATSUKURA et al.
MnlCd ratio was determined as 20% for an effective thickness 0.5 JLm by energy dispersive x-ray analysis. The value Tc: ,...., 320 K of (Cdl-xMn x )GePz was determined by magnetization measurements. Clear hysteresis in the field dependence of magnetization and the stripe magnetic domain pattern were observed by magnetic force microscopy (MFM) even at room temperature. A large Faraday rotation of 5.7 x 104 deg/cm at an energy gap of CdGePz (1.83 eV) was estimated from the magneto-optical Kerr effect at room temperature. The energy gap of (Cd,Mn)GePz is two times larger than that of CdGePz. Photoluminescence indicates also that the introduction of Mn enlarges the energy gap. Results of a first principles calculation shows that the antiferromagnetic state is more stable than the ferromagnetic state, and that the energy gap decreases with the Mn composition (Zhao, Y.-J.et al. 200 Ib). The reason for the discrepancies between theoretical expectations and experimental results is not clear; it may stem from the substitution of Ge for Mn in surface-doped samples. More recent plane-wave pseudopotential and KKRCPA calculations show that the intrinsic defects are responsible for the stabilization of the ferromagnetic state (Mahadevan and Zunger 2002; Kamatani and Akai 200 Ib). 10.3.4. Co doped no, It has been shown by means of magnetization measurements that anatase and rutile (two forms of TiOz) doped with several percents of Co are ferromagnetic at room temperature (Matsumoto et al. 200 I, 200 I). Co doped TiOz has been synthesized by laser ablation MBE employing a combinatorial method, in which a series of thin films with different compositions can be grown on a single substrate while keeping other growth parameters virtually unchanged (Ohno 2001). No ferromagnetic order has been found for other form of TiOz (blookite) and for other transition metals. 10.3.5. Co doped zoo The magnetic properties of n-type transition-metal doped ZnO have been investigated (Veda, K. et al. 200 I). The material is synthesized by the pulsed laser deposition, and 1% of Al is added to produce n-type conduction. Co, Ni, Cr, or Mn serves as a source of the magnetic spins. ZnO with 5% of Mn, Ni, or Co shows an antiferromagnetic behavior with Neel temperatures of 310, 350, and 270 K, respectively. On the other hand ZnO with 525% of Co exhibits ferromagnetic (or weak-ferromagnetic) behavior, which is confirmed by magnetization measurements. The magnetic properties depend on carrier concentration and mobility. Samples with higher carrier concentrations and mobilities show a stable ferromagnetism, otherwise spin-glass behavior is observed. V doped ZnO (V composition 0.05-0.15) with higher conductivity shows ferromagnetic behavior at room temperature, whereas that with lower conductivity is nonmagnetic (Saeki et al. 200 1). 10.3.6. Zinc-blende CrAs and CrSb Thin epitaxial films (less than 3 nm) of CrAs and CrSb with zinc-blende structure can be grown on GaAs substrates by MBE. Their Tc exceeds 400 K (Akinaga et al. 2000c; Zhao et al. 200 1b). A zinc-blende structure is confirmed by in-situ RHEED collected during the growth and ex-situ cross-sectional transmission electron microscopy (TEM). The
III-V FERROMAGNETIC SEMICONDUCTORS
79
preparation and properties of zinc-blende MnAs have also been investigated (Okabayashi et al. 2001d; Hazama et al. 2(01). According to first-principle calculations (Shirai 2(01) such materials possess a half-metallic electronic structure. Hence. being compatible with the existing semiconductor electronics. these systems appear to be promising spin injectors. 11. Summary and outlook Ferromagnetic semiconductors based on III-V compounds can be incorporated into IIIV based epitaxial structures allowing one to explore spin-dependent phenomena. not available in structures made of nonmagnetic semiconductors alone. There are two major directions for the exploration of spin-dependent phenomena in magnetic semiconductors. One concerns with new functionalities and materials for classical devices. such as optical isolators and modulators, magnetic sensors and memories. This direction requires systems with Tc above room temperature. The other direction is quantum related: new developments in magnetic III-V heterostructures combined with recent progress in coherent manipulation of carriers (Kikkawa and Awschalom 1999; Malajovich et al. 2000. 200 1; Salis et al. 200 Ib) and nuclear spins (Kikkawa and Awschalom 2000; Salis et al. 2001a) pave the way for future quantum information technologies that will utilize spins in semiconductors (Kane 1998; Loss and DiVincenzo 1998; Das Sarma et al. 2000; Vrijen et al. 2(00). Ferromagnetic III-V heterostructures are excellent media to explore this new field of semiconductor physics and technology. where both charge and spins play critical roles. With no doubt. however. there is plenty of room for new ideas how to explore outstanding properties of magnetic semiconductors. which have not yet been exploited. Acknowledgements The authors thank many collaborators for fruitful discussion. especially colleagues at Tohoku University. The work at Tohoku University was supported partly by the Japan Society for the Promotion and Ministry of Education. Culture. Sports. Science and Technology. Japan. and the work at Polish Academy of Sciences was supported partly by Foundation for Polish Science. References Abe, E.. F. Matsukura, H. Yasuda, Y. Ohno and H. Ohno, 2000, Physica E 7, 981. Abe, E., K. Sato, F. Matsukura, Y. Ohno and H. Ohno, 2001, Extend Abstracts (The 48th Spring Meeting, The Japan Society of Applied Physics) p. 1322. Abolfath, M., T. Jungwirth, J. Brum and A.H. MacDonald, 2001, Phys. Rev. B 63, 054418. Adhikari, T., and S. Basu, 1984, Jpn. J Appl. Phys., Part I, 33, 4581. Akai, H., 1998, Phys, Rev. Lett. 81, 3002.
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c..
chapter 2
MAGNETOELASTICITY IN NANOSCALE HETEROGENEOUS MAGNETIC MATERIALS
NGUYEN HUU Due Cryogenic Labotatory, Faculty of Physics, National University of Hanoi 334 Nguyen Ttai, Thanh xuan, Hanoi Vietnam
p.E. BROMMER Van der Waals-Zeeman Instituut, Universiteit van Amsterdam Valckeniersttaat 65, 1018 XE Amsterdam The Netherlands
Handbook of Magnetic Materials, Vol. 14 Edited by K.H.J. Buschow 2002 Elsevier Science B.V. All rights reserved
e
89
CONTENTS Abbreviations . .
91
List of symbols .
91
I. Introduction
93
2. Magnetoelastic effects.
95
2.1. Physical background of magnetoelasticity
95
2.2. Symmetry considerations ..
97
2.3. Surface and interface effects
105
3. Determination of magnetostriction of thin films.
106
3.1. The magnetoelastic cantilever method
106
3.2. The strain induced anisotropy method
108
3.3. Magnetostriction in spin valves . . . .
110
3.4. The strain modulated ferromagnetic resonance (SMFMR) method .
III
3.5. The secondary electron spin-polarisation spectroscopy (SESPS) .
112
3.6. The strain-induced anisotropy due to the spontaneous strains
..
113
4. Giant magnetostriction in rare-earth-transition metal thin films . . . .
114
4.1. General consideration of magnetism in rare-earth-transition metal alloys .
114
4.2. Magnetostriction of amorphous rare earth based thin films ..
116
4.3. Magnetostriction of nanocrystalline rare earth based thin films.
132
5. Magnetostrictive multilayers . . . . . . . . . . . . . . . . . . . . 5.1. Nanocrystalline TbDyFe + ZrlNb multilayers
.
5.2. Magnetostrictive spring magnet type multilayers (MSMM)
139 139 140
151
5.3. Interface magnetostriction of multilayers .
158
7. Magnetostriction of R-T sandwich films . . . .
163
6. Magnetoelasticity of rare-earth superlattices
8. Magnetostriction in nanocrystalline and granular magnetic materials 9. Huge magnetostriction in perovskites
.
168 174
10. Potential applications of magnetostrictive materials
185
11. Summary and concluding remarks
190
Acknowledgements
192
References . . . . .
192
90
Abbreviations a-
AF AFM AFI
c
CEF CEMS CG CL
CMR CO DE EDW
EMD FM FMM GMR GMS IT
MEMS MOKE
MSMM n p
PMI R HR
LR SAMR SESPS SMFMR T
amorphous anti ferromagnetic anti ferromagnetic metal antiferromagnetic insulator crystalline crystalline electric-field conversion electron Mossbauer spectra cluster glass (state) charge localisation colossal magnetoresistance charge-ordered (state) double exchange extended domain wall easy magnetisation direction ferromagnetic ferromagnetic metal giant magnetoresistance giant magnetostriction Jahn-Teller rnicroelectromechanical system magneto-optic Kerr effect magnetostrictive spring magnet type multilayer nanocrystalline polycrysta1line paramagnetic insulator rare-earth heavy rare-earth light rare-earth small-angle magnetisation rotation secondary electron spin-polarisation spectroscopy strain modulated ferromagnetic resonance transition metal
List of symbols X A
magnetic susceptibility magnetostriction 91
92
N.H. DUe and P.E.BROMMER
v w
a X)..
Aam Xb
Acr
Aeff
Pi aj
(i=x,y,z) (i=x,y,z)
a]
AS AS At
AV A Aij
b
B B bu1k , By,2 Be~ch
Bhf
bsurf bv d e E
gR J
1R K MY Mj
MR MT
Ms P t
TA
Tc Ts Zij
r 6
Poisson's ratio spontaneous volume magnetostriction stress magnetostrictive susceptibility magnetostriction of amorphous matrix magnetoelastic susceptibility magnetostriction of nanocrystalline grains effective magnetostriction direction cosines of the measured magnetostriction direction cosines of the magnetisation Stevens factor saturation magnetostriction surface/interface magnetostriction anisotropic (Joule) magnetostriction volume magnetostriction divalent alkaline ions spin-spin coupling parameter elastic coefficient in thin films external magnetic field (/-LoH) magnetoelastic coefficient in bulk materials exchange field hyperfine field surface/interface magnetoelastic coefficient in thin films volume magnetoelastic coefficient in thin films grain diameter volume dilatation Young's modulus Lande factor quantum number of the total angular momentum the total angular momentum for the 4f ions anisotropy constant magnetoelastic tensor sublattice magnetisation magnetisation of the R sub lattice magnetisation of the T sublattice spontaneous magnetisation volume fraction film thickness annealing temperature Curie temperature substrate temperature number of nearest neighbours exchange integral sperimagnetic cone angle
MAGNETOELASTICITY IN NANOSCALE HETEROGENEOUS MAGNETIC MATERIALS
93
1. Introduction The origin of magnetoelasticity is the interplay of the elastic properties of a material and its magnetic state. The magnetoelastic coupling terms in the free energy give rise to (extra) strains in a magnetic substance, i.e. the volume magnetostriction and the Joule magnetostriction (anisotropic changes in linear dimensions). The concurring change of the magnetic state can be induced either by a temperature variation (spontaneous magnetostriction) or by application of a magnetic field (forced magnetostriction). The magnetostriction varies from nearly 1% in rare-earth based intermetallic compounds to almost zero for iron based amorphous and nanocrystalline alloys. Also the elastic moduli, can be affected, e.g. the !l E effect. Conversely, an imposed strain may cause extra magnetic anisotropy. Apart from these magnetoelastic coupling effects, a magnetised body may gain magnetostatic energy by macroscopic, rather small (~I 0- 6 ) , deformations, i.e. the form effect. Nanoscale thin films and multilayers, nanocrystalline magnetic materials, granular films, and amorphous materials have been and still are most attractive topics in the field of basic and applied magnetic research. The local properties of these nanoscale heterogeneous magnetic systems do vary in the scale of nanometers, for amorphous materials down to an atomic scale. One is able to produce nanocrystals with a narrow size distribution, embedded in an amorphous matrix at approximately constant distance between them. Granular solids composed of magnetic particles diluted in a non-magnetic matrix are also heterogeneous systems. Going down to an atomic scale, amorphous magnets can be considered as (on nanoscale uniform) heterogeneous magnetic systems. The local anisotropy is assumed to vary in strength and orientation with a uniform correlation length of only a few angstroms. The exchange coupling between the adjacent magnetic moments shows an analogous variation. Heterogeneous materials exhibit unusual magnetic properties which do not occur, or are negligible, in bulk materials: e.g. surface (interface) magnetic anisotropy and surface (interface) magnetostrictive strains, giant magnetoresistance and so on. An important key to understanding such effects is the knowledge of the magnetic behaviour at the interfaces, where questions concerning the magnetic moments, the type of magnetic exchange coupling and the spin orientation may be answered. The local atomic arrangement at the interface differs strongly from that in the bulk. The local symmetry is lowered, some interactions are changed or are missing. Indeed, the interface atoms may be considered to form a new phase and any property characteristic of this phase may become a dominant one for the whole system. It becomes particularly evident in the case of interfacial magnetostriction which can lead to a decrease (almost to zero) or to an increase (over the bulk value) of the resulting magnetostriction of the nanoscale system. In this handbook series, magnetism in ultrathin transition metal films and muItilayers (Gradmann 1993) and magnetism in artificial metallic superlattices (Rhyne and Erwin 1995) was presented in the volumes 7 and 8, respectively. Herzer (1997) reviewed nanocrystalline soft magnetic alloys in volume 10. Giant magnetoresistance in multilayers was presented in volume 12 by Barthelemy et al. (1999), and NMR in multilayers by Riedi et al. (1999). The present chapter deals with the magnetoelasticity of heterogeneous materials. Generally, the dimensions of a magnetostrictive material change when the material is
94
N.H. Due and P.E. BROMMER
subjected to a change in magnetic field. Hence. magnetostrictive materials can be applied in transducers (as well as piezoelectric and shape memory ones). which directly convert electrical energy into mechanical energy. They are useful in the manufacture of sensors. actuators. controllers. force and displacement as well as other electro-acoustic devices. For these applications. transducer materials in the form of thin films are of special interest because cost-effective mass production is possible. compatible to microsystem processing technologies. In addition. magnetostrictive thin films are particularly promising as microactuator elements like cantilevers or membranes, since they combine high-energy output. high-frequency and remote-control operation. Due to this potential, interest in such giant magnetostrictive thin films has rapidly grown over the past few years. Owing to the specifications related with applications in microelectromechanical systems (MEMS). materials research has been focused on thin-film materials showing giant magnetostriction (GMS) in combination with soft magnetic properties. Here, the rare-earth metals and rare-earth-iron intermetallic compounds have been shown to generate very interesting systems. In 1971. A.E. Clark at the Naval Ordnance Laboratory (NOL). now Naval Surface Warfare Center discovered that bulk TbFe2 (Terfenol: Ter for Tb, fe for Fe. nol for NOL as above) has the highest room-temperature magnetostriction, and his Terfenol-D (D for Dy: TbxDYJ-xFe2. where x ~ 0.3) is still the best known, exploiting the huge magnetostriction in combination with reduced magnetocrystalline anisotropy (Clark and Belson 1972a, 1972b. 1972c). Wang et al. (2000) studied the magnetostriction and the magnetisation process in a TbO.27DYO.73Fe2 single crystal. Indeed. as a tradition, research on giant magnetostrictive thin films was focused on iron based rare-earth alloys. Later. however, important progress has been made with the development of rare-earth-cobalt alloys at the 'Laboratoire Louis Neel' in Grenoble (Betz et al. 1999). Due et al. (2001b) proposed to name the amorphous Tb-Co compounds (with composition near to TbC02) as 'a-TerCoNeeI', by an obvious analogy to the name TerFeNol above. Still better results were obtained by combining Fe and Co. Due et al. (1996) achieved a record magnetostriction of 1020 x 10-6 on 'a-Terfeconeel', i.e. an amorphous Tb-(Fe,Co h thin film. whereas Due et al. (2oooa) extended the study to 'a-Terfeconeel-D', i.e. amorphous (Tb,Dy)(Fe,Coh films. In Vietnam's capital Hanoi. as a variant, the amorphous compound with composition Tb(FeO.55C00.45) 1.5. to be named 'a-Terfecohan', was developed (Danh et al. 2000; Due et al. 2ooob). Composite materials are known to exhibit sometimes outstanding properties, which cannot be predicted simply from the behaviour of the constituents. Actually, a very high magnetostrictive susceptibility has been observed in TbCo/FeCo and TbFe/Fe multilayers (Quandt et al. 1997a, 1997b). The tlE effect (the change in the value of Young's modulus E) is perhaps the best known example of a change of the elastic moduli caused by magnetoelasticity (Du Tremolet de Lacheisserie 1993). The tl E effect plays an important role in various practical applications (Hernando et al. 1988; Gibbs 1992; Gibbs et al. 1996, 1997) including such spectacular MEMS as micromachines and actuators using thin film and multilayer magnetostrictive materials (Gibbs et al. 1996, 1997). For more insight on this effect and its applications, however, we refer to the above-mentioned publications. In this handbook series, previous work on giant magnetostriction (which was mainly focused on rare-earth compounds) is excellently reviewed by Clark (1980) on "Magnetostrictive Rare-Earth-Fer Compounds", by Morin and Schmitt (1990) on "Quadrupolar
MAGNETOELASTICITY IN NANOSCALE HETEROGENEOUS MAGNETIC MATERIALS
95
Interactions and Magneto-Elastic Effects in Rare-Earth Intennetallic Compounds" and by Andreev on "Thermal Expansion Anomalies and Spontaneous Magnetostriction in RareEarth Intennetallics with Cobalt and Iron" (Andreev 1996). Noteworthy are also the more recent review papers by Szymczak (1997) on "Mechanisms responsible for magnetostriction in heterogeneous magnetic systems" and on "From almost zero magnetostriction to giant magnetostrictive effects: recent results" (Szymczak 1999). We mention also the review report by Sander (1999) on 'The correlation between mechanical stress and magnetic anisotropy in ultrathin films". Szymczak (2000) focuses attention on "Giant magnetostrictive effects in magnetic oxides". Much detailed practical information can be found in the "Handbook of Giant Magnetostrictive Materials" by Engdahl (1999). The review of Due (2001) "Giant magnetostriction in lanthanide-transition metal thin films" deals with amorphous thin films. Therefore, in the present chapter, this subject is treated concisely, focussing attention on more recent results. The present chapter is organised as follows. After this introduction, section 2 is devoted to the description of magnetoelastic phenomena. Problems in the determination of the magnetostrictive coefficients of thin films are presented in section 3. In secttion 4, magnetism and magnetostriction in amorphous rare earth-transition metal alloys are summarised, and the possibilities to develop giant magnetostriction in nanocrystalline thin films are discussed. Sections from 5 to 8 deal with an overview of the research of magnetostriction in artificially structured materials, such as multilayers, rare-earth superlattices, R-T sandwich films, nanocrystalline soft magnetic materials and granular solids. Doped manganese oxides RI-xAxMn03, (RI-xAxhMn207, and cobaltates RI-xAxC003 have been shown to exhibit colossal magnetoresistance. Their magnetostriction is presented in section 9. Some actual and potential applications of magnetostrictive films in MEMS are briefly discussed in section 10. Finally, a summary and concluding remarks are presented in section 11. 2. Magnetoelastic effects 2.1. Physical background of magnetoelasticity Usually, a discussion of magnetoelastic effects is based on the minimisation of a free energy expression, which is the sum of the magnetostatic energy and the 'internal' free energy. The magnetostatic energy originates from the (long-range) dipolar interactions, giving rise to demagnetising fields, shape anisotropy and 'magnetic forces'. The minimisation of this energy leads to deformations, which depend on the geometry of the sample (hence the name form effect). These deformations can be inhomogeneous even when the magnetisation is uniform, and can contribute volume changes as well as anisotropic strains. This effect exists in all magnetic materials even in the case of vanishing magnetoelastic coupling. Its magnitude, however, is always small ( ~ 10-6 ). As shown in the next subsection, the 'internal' magnetoelastic effects are described by expanding the free energy as a sum of the elastic free energy, the magnetic free energy and the magnetoelastic coupling terms. Symmetry considerations restrict the number of possible terms (see e.g. Becker and Doring 1939). It is necessary, however, to consider the underlying physical mechanisms too. The isotropic Heisenberg exchange interaction for localised spins, for example, can be written as E j »i (-2AijSiSj), where the interaction
96
N.H. Due and P.E. BROMMER
parameters A;j may be assumed to be functions of the interatomic distance vector rij. Taking into account the variation of r;j with a certain strain component e, one finds magnetoelastic coupling terms like (1) Such a contribution can be expected not only for the volume magnetostriction but also in eq. (4) for other strain components (see e.g. the magnetostriction contribution "-'A~'O below). The temperature (and field) dependence of the magnetoelastic coupling parameter b is mainly determined by the correlation function (S;Sj). Analogously, the anisotropic Joule magnetostriction may originate from crystal field effects (also responsible for the magnetic anisotropy, if the symmetry is low enough; see introduction) and from the pseudo-dipolar exchange interactions, which are anisotropic and vary rapidly with the interatomic distance (see e.g. Du Tremolet de Lacheisserie (1999) for explicit expressions). The angular dependence is determined by the corresponding correlation function, and so is the temperature dependence of the magnetostriction and that of the magnetic anisotropy. Notice, however, that, by cancellation of terms due to symmetry, the (local or total) magnetic anisotropy may vanish, where the magnetostriction does not. For itinerantelectron systems, in addition, the band splitting may cause large deformations too. For instance, in Re02 based compounds, the (volume) magnetostriction can reach values up to "-'10- 2 , see Due and Goto (1999), Due and Brommer (1999). An important physical origin of the magnetostriction in rare-earth-transition metal based materials is indicated in fig. I. Here, the deformations are thought to be due to the anisotropy in the orbital part. For 3d-atoms, the large extension of the 3d-wave function invokes a strong interaction with the crystalline electric field, leading to (partly) quenching of the orbital moment. The spin-orbit coupling is relatively weak ("-'0.015 eV per atom), and, helped by the stronger exchange interactions ("-'0.1 eV), the spin moments can easily be rotated into the applied-field direction, leaving the orbitals almost unaffected (fig. la). The anisotropy and then the magnetostriction is small. For rare-earth ions, the spin-orbit coupling LS is strong and a rotation of the total moment L + S = J forces simultaneously a rotation of the orbitals. This results in not only a large magnetocrystalline anisotropy but also in a deformation of the crystal lattice. This magnetostriction happens to be negative when the distribution of the 4f-charge distribution is prolate, whereas the magnetostriction is positive when the charge distribution is oblate. As illustrated in fig. l(b, c), one may imagine that the surrounding positively charged neighbours are drawn to the negative charge cloud (see also section 4, and fig. 8). In the actual thin-film materials, large local strains and large variations in local atomic arrangement may occur, possibly leading to large magnetic anisotropy's and large magnetoelastic effects in the as-deposited materials. Nevertheless, even in amorphous thin films, the local atomic arrangements appear to resemble those of the crystalline materials, the more so after suitable annealing. Some relaxation may occur, however. Moreover, one should take into account the possibility that anisotropic pair ordering is induced or originates from the fabrication (e.g. sputtering) process. Models were worked out, for example, by Mergel et al. (1993) and Huang et al. (1995). Anyhow, such considerations do support the idea to look upon the whole range of materials, from crystalline down to amorphous, as being governed by basically the same physical interactions.
MAGNETOELASTICITY IN NANOSCALE HETEROGENEOUS MAGNETIC MATERIALS
97
ED
ED
1,1tfi\ ~, ED
ED
(a) weak spin-orbit coupling
(b) negative Joule magnetostriction
(c:)
positive Joule magnetostriction
Fig. I. Schematic representation of the phenomena of magnetostriction. The surrounding atoms, schematisc:d as positive charges. are displaced from their initial symmetrical position (open circles) to their final strained positions (black circles) due to the electrostatic interactions with the:aspherical electron distribution.
2.2. Symmetry considerations With respect to a (fictitious) non-magnetic, unstrained state, the free energy is written as the sum of an elastic contribution, a magnetic contribution and the magnetoelastic interaction. The elastic free energy is minimal for vanishing strains, and here, for simplicity, its expansion is restricted to terms of second order in the (six) different elements of the (symmetrized) strain tensor: exx. eyy. ezz, exy. eyz. exz. The magnetic contribution is described by an expansion in terms of a; (i = 1,2.3, corresponding to x, y, Z, respectively), i.e. the direction cosines of the magnetisation direction. For simplicity, we restrict the detailed discussion to the (first-order) magnetoelastic coupling terms, which are linear in the strains and are of up to second order in {a;}. Taking into account some underlying quantummechanical mechanisms, Callen and Callen (1963, 1965) have presented an instructive group-theoretical analysis, thereby establishing a notation, which has been used by many authors (many of them adding their own flavour, mostly adapting the normalisation; see e.g. Du Trernolet de Lacheisserie (1993, 1995». A brief outline of
98
N.H. Due and P.E. BROMMER
the reasoning may establish and clarify the notation. Let us start by recalling that, for given strains, the linear expansion, measured in the direction fJ = (f3I, f32, f33) is given by !:i.f./f. = Exxf3t
+ 2Exyf31 f32 + eye!.
(2)
This expression must be independent of the choice of the co-ordinate system. In line with the general usage to look upon the 6 independent elements of the symmetric strain (stress) tensor as components of a vector, we may elucidate this independence of co-ordinate system by writing eq. (2) as the scalar product of the vectors [E xx, Eyy, Ezz, exy.j2, eyz.j2, ezx.j2] and [f3t, f3i, f3j, f31f32.j2, f32f33.j2, f33f31.j2]. The components of these vectors transform like [x 2, y2, z2, xy.j2, yz.j2, xz.j2], and, hence, the scalar products transform as:
evidently invariant. This property remains intact, when one applies an orthogonal change of basis vectors (in the 6-dimensional space). So, introducing the 'volume dilatation' e = !:i. V/ V = (exx
+ eyl' + e:J,
we can replace the 'diagonal elements' {(exx + eyy + ed/.j3
{E xx , E yy , e:zl
= e] .j3, (2ez: -
by
exx - eyy)/.j6 = (e:: - e/3).j(3/2),
(exx - Eyy)/ .j2},
and analogously e.g. {f3r, f3i, f3jl by {I/ .j3, (f3j - 1/3).j(3/2), (f3? - f3i)/ .j21, and so on. Now, again forming the scalar product yields !:i.f./f. = e/3 + (3/2)(e:: - e/3)(f3j - 1/3) + O/2)(E xx - Eyy)(f3t - f3i)
+ [2exyf3If32 + eye!.],
(3a)
which also can be written as !:i.f./f. = e /3 + [(e:: - e!3)(f3] - 1/3) + 2exyf31 f32
+ cycl.].
(3b)
For a material strained in one direction, one may check that !:i.f./f. equals ez:, the only nonzero strain component, when the z-direction and the measuring direction are chosen along the strain direction. Next, we consider the symmetry operations of the system. The free energy is expanded as a function of the strains (as defined above) and the corresponding 'harmonic polynomials' h(uj). The resulting expression must be invariant under the symmetry transformations. If the symmetry is low enough, one can reduce further the vector space(s) introduced above, by choosing a suitable basis. The resulting irreducible subspaces are indicated
MAGNETOELASTICITY IN NANOSCALE HETEROGENEOUS MAGNETIC MATERIALS
99
by the superscript a when one-dimensional, and by superscripts y, ... , when moredimensional. A one-dimensional subspace yields an invariant strain and a corresponding harmonic polynomial (possibly isotropic), directly. Any product of these invariants (possibly originating from different irreducible subspaces) forms also an allowed invariant. For a more-dimensional subspace, e.g. spanned by functions {hi}, one knows from a fundamental group-theoretical theorem, that the only (second-order) invariant is I;j(hj)2. The only invariant (bilinear) magnetoelastic coupling terms are I;jeihi ' where lei} (the strains) and {h must transform according to the same irreducible representation y. Then, the magnetostrictive strains follow from the minimisation of the free energy part Y2CYI;j(ei)2 + BYI;jeihj, i.e. ei = -(BY /CY)hi, governed by the (first-order)
j}
'coefficient of magnetostriction' .AX = -(BY / CY), for the 'y combination' Hei}, {hi}].
The free-energy contribution can be written as -Y2(By2/CY)I;jhi2, showing explicitly the well-known magnetoelastic contribution to the magnetic anisotropy. As we have seen above, there is always at least one one-dimensional irreducible subspace, i.e. the invariant trace of the strain tensor, e = exx + e xy + ezz (analogously x 2 + y2 + Z2 = r 2 and + a~ + a~ = 1). For an isotropic material, the space spanned by the five remaining strain components cannot be reduced further. Consequently, there are only two magnetostriction modes. The energy density can be written down directly, in principle for either irreducible representation separately:
ar
F
= Y2C ae 2/3 +
B a,oe/3 +Y2CY[(e zz -e/3)2 +2e;y +cycl.]
+ By,2[(e zz - e/3)(a~
- 1/3)
+ 2e xya\a2 + cycl.],
(4)
For the magnetoelastic coupling parameters (Ba,o, BY,2), the first superscript indicates the irreducible representation, the second one the degree of the harmonic polynomial in {ai}. Notice that the bracketed expressions in eq. (4) can be rewritten in a form analogous to that in eq. (3a): (e z: - e/3)2 + cycl. = (3/2)(e zz - e/3)2 + (l/2)(e xx - e yy)2, (e zz - e/3)(a~
- 1/3) + cycl.
= (3/2)(e zz -
e/3)(a~
(Sa)
- 1/3)
+ (l/2)(e xx - eyy)(ar - aD.
(5b)
Moreover, still another fashionable way to write such expressions follows from e.g.: (3/2)(e zz - e/3)2 = (2/3){e zz - (exx
+ e yy)/2}2.
(5c)
The coupling gives rise to 'magnetic stresses', i.e. the magnetic pressure pmag = Ba,o /3, the diagonal traceless stress tensor elements (Tx~ag = -BY,2(ar - 1/3) (cycl.) and the off-diagonal stresses (Txymag = -By·2 a 1a 2 (cycl.). In response to these stresses, the equilibrium strains can be found by minimising the free energy contributions, resulting
100
N.H. Due and P.E.BROMMER
z A,cx,O
/i
1.,>0
~Ms=O
H=O
Fig. 2. The two principle modes of observable magnetostriction for an isotropic magnetic substance.
in e = Aa,O = _Ba,o [c" and {(e u - e/3) = ).Y.2(a~ - 1/3), e xy = Ay·2 a 1a 2 (cycl.j}, with )'y,2 = _BY'o IcY . Plugging in these results in eq. (3b), we find
Lli/i
=A
f1
•
/3 + )"Y.2[{ (a~
O
- 1/3)(pj - 1/3)
+ cycl.] + {2a,a2PI P2 + cycl.I], (6)
Starting from a perfectly demagnetised state (with (af) = (a~) = (a~) = 1/3, (ala2) = 0, and so on), the ideal 'saturated' relative change of length measured along the field direction (common to the magnetisation direction: a3 = P3 = 1) would be ).,11 = (Lli/i)"at - Aa,o/3 = 2Ay,2/3 = AS (by definition; subscript S indicates 'saturation'). The relative change in the plane perpendicular to the field would be (Lli/fh = )".1 = - ~).,s. As the materials always present an anisotropic demagnetised state, it is necessary to apply the field in two perpendicular directions and determine ).,y,2 = (All - A.1), and As = 2/3(AII - A.1), independent of the demagnetised state of the magnetic materials. The two principle modes of the magnetostriction ().,a.O and X, or ).,Y,2) introduced above are illustrated in fig. 2. With respect to the non-magnetic fictitious state, a spherical, isotropic sample exhibits a relative volume change LlV / V = Aa.O, when it becomes magnetic. In addition, when one forces the moments to be directed along an applied magnetic field B, an anisotropic deformation is induced, which transfers the sphere into an ellipsoid with the same volume. For a lattice with cubic symmetry, the 6 strain components are grouped into the one-dimensional representation a: basis e/.,/3, a two-dimensional representation y: basis {(e zz - e /3).,/(3/2), (e xx - eyy)/ .,/2}, and a three-dimensional one s: basis {exy.,/2. eyz.,/2, ezx.,/2}. The modes of deformation can be described as follows. The isotropic mode e/.,/3 '" (exx + eyy + ezz) gives a volume change and does not reduce the symmetry. The anisotropic y-modes reduce the cubic symmetry by varying the lattice parameters without modifying either the volume or the angles. Finally, the s-modes reduce the symmetry by shearing without changing either the volume or the lattice parameters (see fig. 3). Notice that, in this notation, the co-ordinate system should coincide now with the cubic axes.
MAGNETOELASTICITY IN NANOSCALE HETEROGENEOUS MAGNETIC MATERIALS
---
TJ LT'
_..1
I I I
,< ---
Ala
A24
101
I
I
I I I
I
I
I
I
I
I
At
'A'
Fig. 3. The normal modes of deformation and the corresponding magnetostriction modes for cubic and uniaxial symmetry.
The different contributions to the free energy can be written down immediately, by analogy to the procedure followed above. Here, we give the contribution of the magnetoelastic coupling to the energy density in the notation of Du Tremolet de Lacheisserie (J 993, 1995): FmetlV
= ( B;'O) (Exx + f yy + Ell) + By,z[23( Ezz + ~(ExX + 2B
E'Z(E
YZaz a3
Exx + EYY ) (z 2 a3 -
ar +2 a~)
- Eyy)(ar - aD]
+ Ezxa3a) + Exya)az),
(7a)
Notice the "splitting" of the (isotropic) BY'z in the two parts BY'z and Bd. A similar splitting occurs for the elastic energy density, of course:
102
N.H. Due and P.E. BROMMER
1
2
3
--
I + 2c
y[2( 3" czz -
cxx+cyy)2 1 2 + 2(c X X
-
cyy)
2] (7b)
The group-theoretical stiffness parameters can be expressed in the conventional (cubic) elastic stiffness coefficients:
The material is (elastically) isotropic when c" = cY • The magnetostriction in the cubic symmetry can be described as A
= ~Aa.o
y + A .2
G(a~
+ 2At:.2(a2a3~2~3
- a
f;
a~)(~~
+a3al~3~1
-
~r; ~i)
+ala2~1~2)
+
~(af
-
a~)(~r
-
~i) ] (8)
+....
Here {~;} represent the direction cosines of the measurement direction (of A = respect to the crystal axes. The first-order coefficients ofmagnetostriction of cubic materials are then
~l/l)
with
Now, the anisotropic Joule magnetostriction is essentially described by the two coefficients p.2 and A£,2. The familiar magnetostriction constants AIOO and Alii represent the relative
change in length measured in the [100] and [Ill] direction, respectively, when the magnetisation is directed along the named measuring direction. They are related to the coefficients given above by: AIOO = (2/3)A y •2
and
Alii = (2/3)A£,2
(see also fig. 3).
For uniaxial (hexagonal) symmetry the 6 strain components are subdivided in two (invariant) one-dimensional subsets (indicated by the superscript a, and subscripts 1 and 2 for the volume dilatation and the axial deformation, respectively), and two different two-dimensional subsets, indicated by y for deformations in the (hexagonal) plane, and by e for 'skew' deformations. These modes are also depicted in fig. 3. In this case, the magnetostriction can be expressed as A=
~A
+A
).Y'2[~(~r
+ 2)..t:.2(a2a3~2~3
-
_~)3
~i)(ar
+
[~A
I
+
~A
- aD + 2ala2~1 + a3 al ~3~d.
"'3
_ ~)](a2 3
3
_~) 3
~2 ] (9)
MAGNETOELASTICITY IN NANOSCALE HETEROGENEOUS MAGNETIC MATERIALS
103
Notice here the uniaxial deformation, A;'O, independent of the direction of the magnetisation, and the contribution to the volume magnetostriction, A~,2, which does depend on the magnetisation direction. Experimentally, one often tries to measure the magnetoelastic coupling parameters by measuring the anisotropy induced by a tensile stress, say, applied to an isotropic 'ribbon' (Villari effect). Choosing the x-axis along the direction of the applied stress a , we have only one non-zero component of the stress tensor: U x x = o . In the notation established above, we write the extra energy terms as -UxxE xx = -UExx = -ue/3 - (uj3){2(Exx ej3) - (Ezz - ej3) - (Eyy - ej3)}, whence the extra strains e =ujc" ,and (exx - ej3) = 2u j3c Y, (Eyy - ej3) = (ezz - ej3) = -u j3c Y, giving rise to the magnetoelastic coupling contributions [B U,Oej3 = ]B,,·ouj3c U = -AU,Ouj3, and [BY,2(e x x - ej3)(ar - Ij3) + cycl. = (3j2)By,2(E xx - ej3)(ar - Ij3) = ] By,2(u jcY)(af - Ij3) = -Ay,2u (a r Ij3) = -(3A suj2)(af - Ij3). In other words, the tensile stress induces a uniaxial anisotropy (10)
In performing such experiments on isotropic materials, one is accustomed to express the elastic stiffness parameters in the experimentally more readily accessible 'technical' parameters E (Young's modulus) and v (Poisson ratio). The relative change in length, in the direction of the tensile stress a is, by definition, given by (6.1jl)1I = a j E, whereas v = I(1:11jlhj(1:11jl) I I· For several magnetostrictive films and substrates, E and v values are listed in table I. Some useful relations are:
+ v) = (1 + v)c Y = 3c"c Yj(2c" + c Y) = c"(1 - 2v), v = cl2j(CII + Cl2) = (c" - c Y)j(2c" + c Y ) ; I - v = (c" + 2c Y)j(2c" + c"),
E = (CII - cl2)(1
Since thin magnetic films are deposited on a non-magnetic substrate, the actual strains, and thus the induced anisotropy, depend on the magnetoelastic coupling coefficients of TABLE I Young's modulus (E) and Poisson's ratio (v) for several magnetostrietive films and different substrates Material
E (GPa)
a-R-Fe a-R-Fe n-R-Fe a-R-Co TbFeJFe W Ta Other metals Glass Si [1(0) Si (110)
40 50 80 80 80-260 345 186 ~200
72 130.19 169.16
v 0.4 0.3 0.3 0.31 0.28 0.3 0.31 0.21 0.278 0.037
References Wada et aI. (l997e) Quandt (997) Quandt (997) Due et aI. (1996) Quandt and Ludwig (1999) Wada et aI. (l997e) Wada et aI. (l997e) Betz (1997) Due et al, (1996) Betz (1997) Betz (1997)
\04
N.H. Due and P.E. BROMMER
the film, and on the elastic properties of the substrate as well as on those of the film. Choosing the z-axis to be normal to the planar surface of the film (and substrate), the strains exx, eyy , and exy in the magnetic thin film are imposed by the corresponding strains in the substrate (more precisely: the equality of the strains is imposed as boundary condition). This situation is treated for instance by Du Tremolet de Lacheisserie (1995). Notice also the treatment of the case of hexagonal symmetry by Gutjahr-Loser et al. (2000). In the experiment discussed above, for instance, the tensile stress a is applied (along the x-direction) to the substrate. For an amorphous (not extremely thin) film neglecting surface effects, one finds then two contributions to the induced anisotropy:
3/2(e xx +eyy)(a~
- 1/3){-By·2c" J(c" +2cY ) }
+ By,2{Y2(e xx - eyy)(a? - aD
+ 2exyala2}.
(lla)
Neglecting the influence of the film, we find for the strains in the substrate (and thus also in the film): exy = 0, and
(exx + eyy) = a(l - vs ) / E s, (exx - e yy) = a(l
+ vs ) / E s
(subscript s means 'substrate'). Recalling )"y,2 = -By,2/c Y , 3c Y c" [tc" (subscript f means 'film'), one finds
+ 2c Y ) = Er/(l
- vr) and c Y
= ErI(I + vr)
I
Find(a) = 2aAy·2(Er/Es){(a5 - 1/3)(1- 1.1,)/0- vr) - (a? - aDO
+ vs)/O + vr)}.
(lIb)
For E r = E sand vr = v.. eq. (II b) is reduced to eq. (0). In case the magnetisation vector is confined to the film plane we have
and in case the magnetisation vector is confined to the xz-plane (a2 = 0)
Find(a) = Kind(a)(a5 - const) =aA y,2(Er/ Es){[(l - vsvr)/(I - v?)]a5 - const].
(lId)
The elastic properties of the substrate can be determined more accurately than those of the film. Hence, in principle, the magnetoelastic coupling parameter By,2 can be determined more accurately than the magnetostriction coefficient Ay •2 • An analogous conclusion can be drawn with respect to 'bending' experiments (see e.g. section 3.1: the magnetoelastic cantilever method). One may note that the relation between the actual surface layer (a few atomic layers, see next subsection) and the 'film' is quite analogous to the relation between the 'film' and the 'substrate'. Thus, the above derivations can be applied in that case too.
MAGNETOELASTICITY IN NANOSCALE HETEROGENEOUS MAGNETIC MATERIALS
105
Finally, we remark that for the higher-order coupling terms, i.e. non-linear in the strains, analogous symmetry considerations lead to the correct 'group-theoretical' invariant magnetoelastic energy contributions (see e.g. Du Tremolet de Lacheisserie (1993». In fact, it has been demonstrated (see e.g. Sander (1999» that, in accordance with the suggestion of O'Handley and Sun (1992) for epitaxially grown films, second-order magnetoelastic coupling parameters must be taken into account because of the large 'epitaxial' strains due to the mismatch between substrate and film. Fiihnle and Komelj (2000; see also references therein) proposed a way to determine these second-order parameters separately by measuring magnetostrictive stress and magnetic anisotropy in combination.
2.3. Surface and interface effects The discussion up to now is satisfactory for bulk magnetic materials, even when ribbonshaped, having a thickness of some micrometers, still very substantial as compared with the interatomic distances. For nanoscale thin films and multilayers, however, surface and interface effects are important. Neel (1953, 1954) recognised that at the surface, the breaking of the symmetry (leading to lower co-ordination numbers and 'missing' pair interactions) would give rise to surface magnetic anisotropy. Within localised-spin models, the surface magnetic anisotropy is associated with effects occurring only at the surface planes. Within itinerant-electron models, the changes in magnetic anisotropy due to the surface are related to electronic states extending into the interior of the magnetic materials. In an analogous way, the (magneto)elastic coefficients can be affected. Moreover, as pointed out by Du Tremolet de Lacheisserie (1995), the lower symmetry at the surfaces may necessitate extra (magneto)elastic coupling coefficients. Up to now, most theoretical models for surface magnetostriction are still rather phenomenological, although Freeman's group appears to have developed a promising simplification such that 'ab initio' calculations of the surface or interface magnetostriction become feasible (see references in Szymczak 1997; Shick et al. 1998; Wu et al. 1998; Wu and Freeman 1999 and Freeman et al. 1999). Otherwise, the problem of surface magnetostriction can be developed in the spirit of the Neel model of the surface anisotropy (Zuberek et al. 1994). Detailed theoretical calculations of the surface contribution to the magnetoelastic energy have been performed in the framework of the (pseudo- )dipolar pair model (Szumiata et al. 1993, 1999). Du Tremolet de Lacheisserie and McGrath (1995) have shown that single-ion terms can also be incorporated in such an approach. The relative influence of the surface (or interface) effects, of course, must decrease with increasing thickness t of the layer(s). Since the surface effects contribute 'per unit surface area', one defines, for the layer, effective parameters such that Beff , or beff, equals Bbulk + 2b surf / t, Here, the factor 2 is put in, because a layer has two surfaces. In practice, this simple 1/ t dependence works satisfactorily. For nanocrystallites, both the volume fraction and the 'volume to surface ratio' of the crystallites (i.e. their radius) must be taken into account (see also section 8). In connection to these effects, (non-linear) contributions to the magnetoelastic coefficients due to surface strains and surface roughness are expected to be considerable.
106
N.H. Due and P.E.BROMMER
3. Determination of magnetostriction of thin films For bulk ferromagnetic materials, the magnetostriction can be determined directly by measuring the relative deformation in one direction as a function of the magnetic field: "A(H) = !!..l/l. Thin magnetic films, however, are deposited on the planar surface of a non-magnetic substrate. As discussed in the preceding section, in such bimorphs, the observed strains depend on the magnetoelastic coupling coefficients of the film, as well as on the elastic properties of the substrate and those of the film. Moreover, in case surface or interface contributions become important, a larger number of coefficients is needed to describe the magnetoelastic effects because of the symmetry lowering (see preceding section). The experimental methods treated below do not permit to determine all of the magnetoelastic-coupling coefficients. Nevertheless, quantities relevant for technical applications can be determined experimentally, of course. Various experimental methods have been developed for investigating the magnetoelastic properties of thin films and nanoscale magnetic systems. In the following subsections, we discuss the most important ones: (i) the magnetoelastic cantilever, (ii) strain induced anisotropy, (iii) magnetostriction in spin valves, (iv) strain modulated ferromagnetic resonance, (v) secondary-electron spin-polarisation, and (vi) strain-induced anisotropy due to the spontaneous strains. For technical applications (sensors), Hristoforou et al. (1998) have developed an interesting method to determine the field-dependence of the magnetostrictive strain, based on measuring the delay due to Bloch-wall motion. 3.1. The magnetoelastic cantilever method
In this method a magnetic film deposited on one side of a cantilevered substrate is magnetised. The resulting 'magnetic stresses' will, for example, tend to lengthen the magnetic film. Hence, the substrate will be bent (fig. 4b), with anticlastic deformation (i.e, in saddle form, see fig. 4a, where the field is taken to be directed along the x-direction). Obviously, the bending will depend on the elastic properties of both the film and the substrate, as pointed out by Du Tremolet de Lacheisserie and Peuzin (1994, 1996), Van de Riet (1994), and Weber et al. (1994). Notice that some errors in the older literature were amended in these works. See also the debate in Klokholm and Jahnes (1996). The theory of bending of plates was applied to obtain precise results, e.g. for non-isotropic substrates (Ciria et al. 1995), see also the review of Sander (1999). Szymczak (1999) (see also references therein) stresses the importance of the boundary conditions due to the clamping of the cantilever, and concludes that often 'finite-element' calculations are necessary. Also Iannotti and Lanotte (1999) treat the effect of clamping. The cantilever bending-technique requires a sensitive displacement detection such as a capacitance probe (Klokholm 1976, 1977), optical interferometry (Sontag and Tam 1986), a tunnelling tip (Wandass et al. 1988) or angular detection (e.g. laser beam deflection, Sontag and Tam 1986; Trippel 1977; Tam and Schroeder 1988; Betz 1997; Sanderet al. 1998). Using the laser beam deflection method, one determines the bending angle "', and subsequently the displacement D(~ L . ."/2) at the end of the film (x = L; fig. 4b). Then,
MAGNETOELASTICITY IN NANOSCALE HETEROGENEOUS MAGNETIC MATERIALS
z
107
L
x Fllm",ltb thickness tf Substrate with ~ thickness t• .Holder
(a) Fig. 4. (a) Anticlastic deformation of a bimorph in a magnetic field (saddle fonn). (b) Fixation of a bimorph on its sample holder and measurement principle of the defonnation of any magnetostrictive bimorph using the deflection of a laser beam.
an (effective) magnetoelastic coupling coefficient, or rather an 'effective magnetic stress' b(H) is calculated as Es
b(H)
= 3(1 + vs)
D(H)
L2
t; e, ts L\(I/R ) r; = 6(1 + v ) ts 2
s
L .
(12)
Here, t is the thickness, E is the Young modulus, v is the Poisson ratio; the subscripts f and s stand for film and substrate, respectively (see also preceding section). In the second equality (applied, for instance, by Sander et aI. 1999), RL is the (longitudinal) radius of curvature (signs should be chosen in such a way that positive b corresponds to negative magnetostriction, since e.g. ).,y.2 = -By·2/c Y). Assuming that the magnetic film is thin in comparison to the substrate, but that surface effects can be neglected, and ignoring an isotropic contribution, Du Trernolet de Lacheisserie (1995, 1999) has shown that, for an isotropic film magnetised to saturation in the direction a, the magnetoelastic parameter b(a) measures the bulk value By·2 as (13) In practice, one determines bn(H) with the field directed along the film direction (x axis), and b1. (H) with the applied field along the y-direction (still inside the film plane). At saturation, one has at = I and az I, respectively. When applied to cases where surface (interface) effects are important, it turns out that, with these field orientations, only
=
108
N.H. Due and P.E. BROMMER
the effective parameter b y · 2 (corresponding to By·2 in bulk material) can be determined (Du Tremolet de Lacheisserie and Peuzin 1994; Du Tremolet de Lacheisserie 1995). The difference between the saturated b sat values just yields the (effective) magnetoelastic coupling coefficient b y · 2 = bll sat - b.l sat [= By·2 for relatively thick films]. In order to facilitate comparison with other data, it is common practice to express these results as 'coefficients of magnetostriction' All, A.l and Ay·2 by: (14a) (l4b) In general, it is difficult to determine correctly the elastic parameters E f and Vf of thin films. Hence, this translation (eq. (l4a), (l4b» may introduce a large uncertainty in the A values.
3.2. The strain induced anisotropy method This method is based on the Villari effect: applying a uniaxial stress to a ferromagnetic substance induces a magnetoelastic anisotropy which may modify all the parameters of its magnetisation curve, e.g. magnetic susceptibility, coercive force, and so on. Some experimental techniques to measure the strain-induced anisotropy are discussed shortly below. An original technique was developed by Konishi et al. (1969) and extended later on by Narita et al. (1980). This method is known as the small-angle magnetisation rotation (SAMR) method: a static bias field HII and a tensile stress (a) are applied in the direction of the film; a small-amplitude ac driven field H.l = H.l max sin(wt) is applied perpendicular to HII' It is this ac magnetic field that induces a magnetisation rotation, which can be detected as an induced voltage in a sensor coil wound around the film axis. This response is measured as a function of the applied stress. i.e. of the strain-induced anisotropy. An experimental SAMR set-up is illustrated in fig. 5. The sensitivity of this method was 2 x 10-7 (Narita et al. 1980) and even much higher. namely 10-9 (Hernando et al. 1983).
Glassy Ribbon
Fig. 5. Experimental SAMR set-up. After Du Tremolet de Lacheisserie (1993).
MAGNETOELASTICITY IN NANOSCALE HETEROGENEOUS MAGNETIC MATERIALS
109
O'Handley et al. (1993) presented a method which allows magnetoelastic coefficients to be determined from arbitrarily shaped M -H curves taken at different strains, by calculating the area between them over a conveniently chosen magnetisation range. This reduces error in the magnetoelastic coefficients by avoiding hysteretic effects at low fields and ambiguity about saturation at high fields. These authors illustrated how the magnetic and magnetoelastic coefficients can be determined from the M-H loops using the magnetooptic Kerr effect (MOKE). For thin films with a perpendicular anisotropy (easy axis normal to the film plane), Huang et a1. (1995) determined magnetostriction (As) and anisotropy (K) values, by using the so-called 'initial-susceptibility method'. An ac magnetic field was applied in the film direction, and the induced magnetisation component in the field direction was measured. These authors deduced K and AS from the X -I vs. a plots, using:
X=
110 M 2 s 2K - 3Asa
(15)
Here, M s is the saturation magnetisation. Notice, that apparently, the stress transfer from the kapton substrate to the deposited film was ignored (compare eq. (15) with eq. (11d». A consistent result was obtained by determining the anisotropy from the hysteresis loops measured in the hard and easy magnetisation directions, using a vibrating sample magnetometer. Experiments using a standard electromagnet can be performed by measuring the strain modulated biased transverse susceptibility (Kraus 1989). In this measurement, a static bias field is applied in the film plane, now perpendicular to the film axis, while the ac driving field is parallel to that axis. The susceptibility (transverse to the bias field) is detected by the pick-up coils and its reciprocal value is then a linear function of both the de bias field (H de) and the magnetoelastic field (Hu = 3Asa/ Ms; see also eq. (l lcj): I I X;; = -(Hde - H a
Ms
-
Hs).
(16)
Here, Hs is the anisotropy field (Ny - Nx)M s • An increasingly important tool to determine the strain-induced anisotropy is MOKE (magneto-optical Kerr effect). In section 2 we mentioned already the calculations by Freeman et a1. (1999). Experimentally, e.g. Ali and Watts (1999); (see also references therein) apply a bending device to induce strains in a controlled way, and determine the (local) curvature and the strains by optical interferometry or by direct measurement (stylus). The properties of the substrate are incorporated in a finite-element modelling calculation, thus allowing an absolute determination of the film properties. Compare also Stobiecki et al. (2000), who studied the strain induced anisotropy in FeB/CulFeB trilayers, using Kerr magnetometry (MOKE). Other methods based on the Villari effect can be found in the paper by Lachovicz and Szymczak (1984).
N.H. Due and P.E. BROMMER
110
3.3. Magnetostriction in spin valves
An alternative to the cantilever beam method, called the bending method, was introduced by Baril et al. (1999), who measured the strain-induced magnetoelastic energy for spin valve structures. A spin valve consists of two thin conducting ferromagnetic layers, separated by a non-magnetic layer, which is thick enough to reduce the magnetic coupling between the two magnetic layers. The upper layer is coupled to the top antiferromagnetic layer. The lower one is deposited on the substrate (see Dieny et al. 1991b). The samples are strained by means of the bending device shown in fig. 6. The strain in the film is tensile, and as the bending is small, it is considered to remain in the film plane. The M-H loop is directly determined from the deduced resistance (R) versus magnetic field curve M= 2M s (
R(a ) - R(O) ~RGMR
I)
- - .
(17)
2
Here, a is the angle between the magnetisation directions of the two ferromagnetic layers which form the spin-valve. Assuming that the magnetic moment of the upper layer is rigidly fixed, and taking into account the (weak) coupling of the two ferromagnetic layers (coupling field Hi), the magnetostriction can be calculated from the area between the curves obtained without and with strain (subscripts u and s, respectively):
In this measurement, the hysteresis problem was solved by applying a constant transverse field. In eq. (18), this transverse field does not occur due to cancelling of terms. The same holds for the (in-plane) anisotropy and the shape anisotropy. Baril et al. (loc. cit.) claim that this is a reliable method, giving results consistent with the cantilever method and with a sensitivity better than 1 x 10- 7 . It is perhaps worthwhile, however, to consider all
~ x
substrate
~Vp
1
it
Fig. 6. Bending tool for the measurements of magnetostriction in spin valves. After Baril et al. (1999).
MAGNETOELASTICITY IN NANOSCALE HETEROGENEOUS MAGNETIC MATERIALS
III
assumptions critically, taking into account the weak coupling of the ferromagnetic layers and also the elastic properties of the substrate.
3.4. The strain modulatedferromagnetic resonance (SMFMR) method Magnetic resonance has been recognised as a powerful technique to study the magnetocrystalline anisotropy energy of ferro magnets (ferromagnetic resonance FMR) and crystalline electric fields in paramagnets (electron paramagnetic resonance, also named electron spin resonance ESR). The technique of ferromagnetic resonance under stress was firstly developed by Smith and Jones (1963) (see also Smith 1968) in order to derive magnetostriction coefficients from the shift in the resonant field caused by the application of a known static stress to a magnetostrictive thin film. The shift arises due to the Villari effect. Using a dynamic stress instead of the static one, Henning and den Boef (1978) have improved the performance of the strain modulatedferromagnetic resonance (SMFMR). This technique has been applied to measure the magnetostriction of amorphous wire (Kraus and Schneidner 1977) and multilayer films (Zuberek et al. 1987, 1988, 1995,2000). Apparently, the SMFMR method has some specific advantages, the most conspicuous one being the high sensitivity (magnetostrictive strains as small as 10-9 can be detected) and a possibility to measure several magnetoelastic tensor components. The resonance equation for a thin film, which is subject to an uniaxial stress, and which exhibits an intrinsic uniaxial perpendicular anisotropy field, may be expressed as (Bushnell and Vittoria 1993)
(~)
2=
[Hr + Ms - Hal-
+ 3UAs/M] X [Hr + 3UAs/Ms]'
(19)
where H r is the resonant field, M s is the saturation magnetisation, Hal- is the anisotropy field (= 2Kl-/ M«; Ks. is the perpendicular uniaxial magnetic anisotropy constant), y is the gyromagnetic ratio and the equilibrium position of M 5 is assumed to be collinear with Hr. Since the microwave frequency and gyro magnetic ratio are constant, changes in the applied stress will result in a shift in the resonant magnetic field. Indeed, the 'shift' equation is flHr -3A5 --=-flu Ms
(20)
Clearly, this equation allows to determine AS through the values of the stress a , the resonant-field shift flH r and the saturation magnetisation Ms. Details of the experimental set-up may be found in the review papers by Bushnell et al. (1992), Le Gall etal. (1989) and in Vukadinovic's thesis (Vukadinovic 1988). Unfortunately, up to now the measurements are limited to room temperature. In traditional discussions based on eq. (20), the resonance conditions have been expressed in terms of the magnetostriction coefficients. However, Du Tremolet de Lacheisserie (1995) has found that the elastic coefficients of the substrate (SIll and SI2 S ) have entered his formulas of the resonance frequency. He showed that in the SMFMR method only the b y •2 and ba •2 coefficients can be determined.
112
N.H. Due and P.E. BROMMER
3.5. The secondary electron spin-polarisation spectroscopy (SESPS)
The surface of a bulk solid is generally subject to relaxation strains (mainly normal to the surface) that can be as great as 10%. These arise from the lower symmetry and different electronic charge distribution there relative to the bulk. The surface of a cubic solid is generally tetragonally distorted relative to the bulk. The surface of a thin film is subject to the same relaxation effect as is the surface of a bulk sample. The surface of a material has an electronic structure that reflects lower symmetry and reduced co-ordination numbers relative to the interior, say, deeper than a few atomic layers. The secondary electrons, whose spin polarisation is measured as a probe of the magnetisation, come just from these outermost few layers. Thus, the spin-polarisation of secondary electrons, detected from the asymmetric spin-orbit scattering, can be used to monitor selectively and directly the surface magnetisation. Subsequently, by straining the sample (surface), the surface magnetoelastic coupling can be determined by measuring the strain dependence of the surface magnetisation. An experiment to measure the asymmetry as a function of applied magnetic field at different values of strain was set up by Sun and O'Handley (1991). It is shown in fig. 7. From the measured asymmetric spin-orbit scattering, A, the surface magnetisation, M surf is determined as (21)
Here, N is the number of magnetic atoms per unit volume, n is the total number of valence electrons (n = n+ +n-), nB is the valence-band magneton number (nB = n+ -n-), and S
MANIPULATOR
FIELD WINDINGS
Fig. 7. Experimental SESPS set-up. After Sun and O'Handley (1991).
MAGNETOELASTICITY IN NANOSCALE HETEROGENEOUS MAGNETIC MATERIALS
113
the asymmetric scattering efficiency of the detector. Then, from the strain dependence of the magnetisation curves, the surface magnetoelastic coefficient B surf is derived from (22)
=
=
with e t:x x , and where m 2(H) (af(H») in our notation. The value of the Poisson ratio of the bulk (ribbon) material, v, was taken equal to 1/3. Notice, that here B surf is considered as energy density, so analogous to the bulk quantity By·2, evidently now for the 'surface layers' only. The authors derived this expression by assuming isotropic magnetoelastic behaviour. One may, however, look upon the relation between the 'surface layers' and the 'bulk ribbon', as equivalent to the relation between a thin film and the substrate. Eq. (22) should then be compared with (the exx-derivative of) eq. (IIa). Taking (a~) = (a~) = (1 - {af)/2, one may deduce that, actually, the authors did apply the (almost equivalent) approximation [1 - vv surf + (v - vsurf )j 2]f[(1 - vsurf )] = 4/3, instead of (1 + v) = 4/3: indeed. again the elastic properties of the 'carrier' (here the ribbon) and the 'thin layer' (here the surface layers) do enter into the expressions. In this experiment, B surf was found to be (6.0 ± 0.2) x 105 J/m3 for the amorphous C076Cr4B20 alloy, approximately 3 times the bulk value [+ 1.8 x lOS J/m3 ], and to be -(1.6 ± 0.2) x lOS J/m3 for the amorphous Fe77Cr6B17 alloy, about half the bulk value [-3.0 x 105 J/m3 ]. The 'surface magnetisation', was found to be 92% and 63% of the bulk values for the Co-based and the Fe-based amorphous alloy, respectively.
3.6. The strain-induced anisotropy due to the spontaneous strains Bochi et aI. (1994) proposed a phenomenological equation that describes the film thickness dependence of the total effective magnetic anisotropy energy density of an epitaxial sandwich fcc (111 )Co/Cu. They showed that by fitting the measured effective anisotropy energy density with their equation, one can extract the surface magnetic anisotropy as well as the surface magnetoelastic coupling coefficients. A surprising result was obtained for fcc (l1I)Co/Cu superlattices (grown, on GaAs (110) substrates, by Lee et aI. 1990): the Neel surface magnetic anisotropy energy is KS sin 2(9), with KS = 0.47 erglcm 2, whereas the surface magnetoelastic coefficient BS is found to be BS = -25.5 erg/em", In this method, instead of artificially created strains (as in the preceding subsection 3.3) the strain induced anisotropy arises in the process of sample preparation, due to the Co-Cu misfit m = 1.9%. In fact, the strain e was taken to follow e = mtcu/(tco + tcu). The actual strain e was determined by X-ray scattering. Of course, the different methods are often combined. (Clamped) cantilevers (section 3.1) and bending devices (section 3.2) have also been used to determine the 'spontaneous' strains during the depositing process, or those caused by different thermal-expansion coefficients. As an example, we refer to Sander et aI. (1999), who determined the magnetoelastic coupling parameters as well as the epitaxial misfit stress in ultrathin Fe(100)-films on W(100) substrates. The change of sign of the magnetostriction constant, positive for Fe films thicker than 20 nm, and negative for thinner films, is ascribed to the strain dependence of the magnetoelastic coupling (higher order terms, see remarks in the
114
N.H. Due and P.E. BROMMER
final part of section 2.2), in combination with the fact that the strains are much larger in the thinner films. Gutjahr-Loser et al. (2000) performed a similar study on (ultra)thin Colayers, grown on W(OO 1). These authors suggest that a description with higher-order terms only may be too simple, because of the structural changes in the (ultra)thin layer forced by the epitaxial strains. Notice also that for such ultrathin layers, magnetic-anisotropy oscillations and quantum well states were observed (Weber et al. 1995, 1996a, 1996b).
4. Giant magnetostriction in rare-earth-transition metal thin films 4.1. General consideration ofmagnetism in rare-earth-transition metal alloys The rare earth-transition metal compounds are considered to be formed by the association of the relatively narrow 3d band with a wider 5d band with higher energy. The electronegativity difference between the constituents gives rise to a transfer of 5d electrons towards the unfilled 3d band. Since the screening of the nuclear potentials by the electrons is modified, the two bands draw together, leading to 3d-5d hybridisation states at the top of the 3d band and at the bottom of the 5d one. This strong 3d-5d hybridisation does not only result in the formation of the rare-earth intermetallics, but also determines the physical properties of the existing compounds. In the compounds based on rare-earth and transition metals, it is found, as a general rule that, due to the hybridisation between the 3d and 5d states, the 4f-3d spin-spin coupling is always antiferromagnetic (Campbell 1972; Due 1997). Taking into account the coupling between the spin and orbital moments of the 4f electrons, one can explain the parallel and antiparallel alignments of the 3d (Fe.Co.Ni)- and 4f-moments in the light- (J = IL - 51) and heavy- (J = L + 5) rare-earth compounds. The rare-earth elements can be separated into two groups, as already mentioned, of the light elements consisting of Ce, Pr, Nd, Pm, Srn, Eu and the heavy ones consisting of Gd, Tb, Dy, Ho, Er, Tm and Yb. Each of these groups can be subdivided into two subgroups according to the sign of the Stevens factor CX). This division takes into account the angular distribution of the charge density of the 4f electrons, which is in the oblate (CX) < 0) or prolate (CX) > 0) form (fig. 8). As mentioned in section 2 (fig. I), with the oblate distribution (CX) < 0), the magnetic moment is perpendicular to the plane as in Nd and Tb, for example. In this case, the magnetostriction is positive. For the case where CX) > 0, i.e. the electronic density distribution in the prolate form, the magnetic moment is aligned along the axis of the "rugby" and the magnetostriction is negative. Huge magnetostriction is expected to occur in those compounds, which combine a high rare-earth concentration with a high ordering temperature. This is the case for the Laves phase RFe2 compounds. The corresponding crystalline RC02 compounds, however, show a much lower Curie temperature (Tc) due to the metamagnetic behaviour of the 3d(Co) electrons (Due and Goto 1999; Due and Brommer 1999). They exhibit huge volume as well as Joule magnetostriction, but at low temperatures only. For this reason, these compounds are not particularly interesting for applications. Amorphous alloys are characterised by a structural disorder where each atom constitutes a structural unit. In this state, the low mass density and the loss of the periodicity enhance the localisation of the 3d electrons in the rare earth-transition metal alloys. In
MAGNETOELASTICITY IN NANOSCALE HETEROGENEOUS MAGNETIC MATERIALS
115
Light-lanthanide elements J= IL-si
<XJ>O
<XJ
~ Ce
e: Pr
ro Nd
~Pm
(D 8m
Eo
Heavy-lanthanide elements J=L+S
<XJ>O
<XJ
([)
ro
(l)
([)
Tb
Dy
Do
Er
~Tm
(l) Yb
Fig. 8. Angular distribution of the 4f charge density of lanthanide atoms for Jr = J (effective moment parallel to the z-axis). After Thole in Coehoom (1990). In Ceo Pr, Nd, Tb, Dy, Ho the charge density is oblate (aJ < 0). in Pm, Srn, Br, Tm, Yb it is prolate (aJ > 0). In Gd, Lu (L = 0). the charge density has spherical symmetry.
amorphous alloys. at a certain concentration, the 3d magnetic moment is higher, but the 4f3d exchange interactions are somewhat weaker in comparison with the crystalline alloys. These parameters, however, follow the same tendencies with varying the concentration (Due and Givord 1996). These results confirm again the systematic variation of the 3d5d hybridisation and its influence on the magnetism of the rare earth-transition metal compounds. The decrease of the transfer and of the associated hybridisation allow to maintain the strongly ferromagnetic character over a large range of concentrations, i.e. there exists a large value for the critical rare-earth concentration where the magnetism disappears in the amorphous alloys. These effects lead to an enhancement of the Curie temperature when going from the crystalline state to the amorphous state: for the R-Co alloys, e.g. the ordering temperature of c-TbC02 equals 230 K (Due and Brommer 1999), whereas Tc of a-TbC02 is comparable with that of a-TbFe2 (Tc > 400 K) (Hansen et al. 1989; Hansen 1991). For the a-RFe compounds. however, the magnetic properties are not improved by the amorphisation, but just the opposite. Due to the amorphous structure,
N.H. DUC and P.E. BROMMER
116
f
Tb Co
~c. (b)
(a)
Tb
~ (c)
Fe
~
Fe
(d)
Fig. 9. Sperimagnetic structures in amorphous Sm-Co (a), Tb-Co (b), Srn-Fe (c) and Tb-Fe (d).
the Fe-Fe interatomic distance is distributed and the Fe-Fe exchange interactions can be sometimes positive or negative. This leads to frustration and freezing of the Fe moments, and to the occurrence of asperomagnetism (M s > 0) or speromagnetism (M s = 0). The latter is observed for Y l-xFex (Coey 1978; Chappert et al. 1981). Sperimagnetism occurs in two-subsystem structures like rare-earth-transition metal alloys of composition RI-x T x where the 4f-3d exchange interactions are not modified (Due and Givord 1996; Danh et al. 1998), but the large spin-orbit coupling of the non-S-state rare-earth gives rise to large local anisotropy (local easy magnetisation axis). Taking into account the sign of the RT-coupling for the light rare earth and the heavy ones. we can again divide the amorphous R-T alloys into four groups of sperimagnetic structures as illustrated in fig. 9: a) b) c) d)
asperomagnetic LR. with collinear T (like Sm-Co), asperomagnetic HR. with collinear T (like Tb-Co), asperomagnetic LR, with non-collinearT (like Sm-Fe), asperomagnetic HR, with non-coIlinearT (like Tb-Fe),
In these sperimagnetic structures, the subsystem magnetisations are reduced with respect to the collinear magnetic structure in the crystalline compounds. As a consequence, the saturation magnetostriction As is decreased.
4.2. Magnetostriction ofamorphous rare earth based thin films The common approach to amorphous magnetostrictive thin films is to reduce the macroscopic anisotropy to achieve saturation of the magnetostriction in low magnetic fields. As a tradition. the R-Fe based alloys were thought to be the best candidates. giving a giant magnetostriction in bulk as well as in film materials. The magnetic and magnetostrictive properties and magnetic anisotropy of the amorphous binary TbI-xFex
MAGNETOELASTICITY IN NANOSCALE HETEROGENEOUS MAGNETIC MATERIALS
117
400
300
-e 200
100
o
o
0.2
0.4
0.6
lJoH (T) Fig. 10. Room-temperature magnetostriction for TbI_xFex films. After Miyazaki et a1. (1997).
films as a function of the Th concentration have been the subject of many investigations (Forester et al. 1978; Hansen et al. 1989; Hayashi et al. 1993; Quandt et al. 1994a; Grundy et al. 1994; Huang et al. 1995; Hernando et al. 1996 and Miyazaki et al. 1997). Jerems and Greenough (1999) studied amorphous melt-spun (ThFe2)t-xBx alloys. Magnetostriction curves measured in magnetic fields up to 0.7 T applied parallel to the film plane for several a-Tht-xFex thin films are presented in fig. 10 (after Miyazaki et al. 1997). For all samples, except for the x = 0.944 sample, which has the bee-Fe structure, the field dependence of the magnetostriction shows a relatively large random anisotropy. The values of the magnetostriction in the as deposited a-ThI-xFex thin films collected from different sources are summarised in fig. 11. Although there is some scatter they show a compositional variation of the magnetostriction, which is very similar to that observed for polycrystalline Tb-Fe compounds. A magnetostriction maximum occurs around 0.55 ~ x ~ 0.67. In fact, at JLoH = 0.7 T, the largest magnetostriction of about 480 x 10-6 was found at x = 0.67 which corresponds to an alloy of the ThFe2 composition (Miyazaki et al. 1997, see fig. 11). Note that, for these systems, Tc shows its maximum at the same composition range. Thus, the giant magnetostriction could be an optimal combination of the lanthanide concentration and the magnetic ordering temperature. The magnetostriction maximum shifts to higher Th contents with decreasing applied magnetic field, and a magnetostriction maximum of 220 x 10-6 was obtained at x = 0.58 in JLoH = 0.1 T. Indeed, Danh et al. (2000) and Due et al. (2ooob) have succeeded to enhance the magnetostriction even at lower fields PI.U = 340 x 10-6 at
118
N.H. Due and P.E. BROMMER
Tbtel7 Tbte:u TbFe3 TbF~.
Tb1_.Fe. 300 200
• .o.eTp.dlll84) • .o.44Tputdyol.0I.1t194) • .1.5T".....0I. .. 1I7III . . . 1.8T....".ot.ot.ll1l13)
100
0.1
0.2
0.3
I-x
• 0.4
0.5
Tb1.•Fe. o 0.7 T
400
0.3T
o 0.1 T
300 200
til
100
o
o
0.2
0.4
0.6
I-x Fig. 11. Magnetostriction as a function of Tb concentration for Tbl_xFex films. After Quandt (1997) (upper panel) and Miyazaki et aI. (1997) (lower panel).
l-toH = 20 mT in TbI_AFe,Coh with x = 0.6 (fig. 12). The saturation magnetostriction depends strongly upon the preparation condition. Films with a perpendicular magnetic anisotropy show a higher magneto striction, however, one needs higher applied fields to rotate the magnetisation into the film plane and then to attain saturation (see fig. 12) (Schatz et aI. 1994; Due et al. 2000b). This perpendicular anisotropy is usually thought to be induced during the deposition process. Heat treatments at temperatures up to T A = 450°C are often performed to relieve any stress. Heat treatments do cause a number of clear differences in the magnetic properties, such as the magnetic anisotropy change from perpendicular to parallel (Riedi et al. 1998; Danh et aI. 2000; Due et al. 2000b), the reduction of the magnetic coercive fields and the development of magnetostriction at low fields (see e.g. fig. 12). In order to obtain a soft magnetostrictive behaviour for Tb-Fe alloys, other attempts to reduce the magnetic anisotropy have been undertaken. Altering the deposition conditions, e.g. by applying a r.f. bias voltage (Quandt 1994), the tensile stress obtained can lead to an in-plane magnetic easy axis and to dramatically improved magnetostriction at low fields. Miyazaki et al. (1997) and Wada et al. (I997a, 1997b)
MAGNETOELASTICITY IN NANOSCALE HETEROGENEOUS MAGNETIC MATERIALS
119
600 500
-r = .'-'..
400 300
~
«
200 100 0 -0.8
-0.4
0
0.4
0.8
l10H (T) Fig. 12. Parallel magnetostrietive hysteresis loops for Tb(Feo.55COO.45) 1.5 films: (I) as-deposited film and (2) after annealing at 350°C and (3) at 450°C. After Due et aI. (2000b).
have also succeeded to enhance the low-field magnetostriction, however, by varying the substrate temperature and the heat treatments. Magnetic-field annealing (Due et al. 1996; Betz 1997) created a well-defined in-plane uniaxial anisotropy. Pasquale et aI. (2000) studied stress-induced anisotropy in ThFe thin films. At the composition Th54Fe46 these authors found optimal properties for sensor applications requiring magnetic softness and stress sensitivity. It is interesting to compare these results with those obtained by Jiang et al. (2000) on amorphous TbDyFe sputtered films. Notice also that for a-DYI-xFex films, the magnetostriction has a maximum at x = 0.7 (Williams et aI. 1994). Speliotis et aI. (1998) added Nb and Zr to ThDyFe-films in order to influence the (nano)crystallisation. For nanocrystalline (Tho.3DYo.7)4o(Feo.95Nbo.OS)60 films, deposited at 470°C, a roomtemperature magnetostriction of 500 ppm at 4 kOe and a coercivity lower than 30 Oe were observed. A negative magnetostriction was actually observed in amorphous Sm-Fe thin films in accordance with the positive sign of the Stevens factor (see section 4.1) (Hayashi et al. 1993; Honda et al. 1993, 1994). For these films, the room-temperature magnetostriction increases rapidly in low fields due to the in-plane anisotropy. The maximum absolute 1values of about 250-300 x 10-6 at 0.1 T and 300-400 x 10-6 at 1.6 T were obtained on films with 30-40 at% Sm. Honda et al. (1994) have used these magnetostrictive films for the fabrication of trimorph ThFelpolyimide/SmFe cantilevers (see fig. 86a, in section 12). Applying a bias voltage, it was again possible to alter the stress state to tensile stress, which resulted in a perpendicular anisotropy due to the negative but increased saturation magnetostriction (Quandt and Ludwig 1997). In contrast to Tb-Fe films, crystallisation of Sm-Fe films does not result in a higher saturation magnetostriction. The hysteresis, however, was found to be significantly increased. Boron added to the SmFe2 alloy improves the possibility to form the amorphous
N.H. DUC and P.E. BROMMER
120
20
320 Tbt_xCo x
-
15
240
10
160 C
\Ill ~
~
'-'
.c'"
-
~
c
.s
0.62
5
80 0.53
0
0
0.5
1.0
1.5
0 2.0
~H(T) Fig. 13. Room temperature magnetostriclion for several a-Tbj
c,
Cox alloys. After Givord et al. (1995).
state, reduces the local magnetic anisotropy energy (Polk 1972) and, thus, can enhance the low-field magnetostriction. This was examined by Kim (1993) on the de-sputtered (SmFez)lOo-xBx system with a thickness of 0.3 mm. In these alloys, the saturation magnetisation decreases with increasing x, whereas the saturation magnetostriction significantly increases. The highest saturation magnetostriction, of -670 x 10-6 at 1.0 T with an effective magnetostriction of -490 x 10-6 at 0.03 T has been obtained for a(SmFez)99.Z6BO.74. A similar result was reported for amorphous bulk alloys (Fujimori et a1. 1993; Shima et a1. 1997). Batt et a1. (2000) observed decreasing (absolute) magnetostriction values upon substituting Co for Fe in melt-spun Sm(Fe,Co)z ribbons and hot-pressed compacts. The magnetostriction of a-Thu.j Co, (0.78 ~ x ~ 0.38) thin films was studied intensively by Betz et a1. (1999) (see also Givord et a1. 1995; Betz 1997). Their reasons for expecting a larger magnetostriction in a-Tb-Co than in a-Tb-Fe is that effectively (see fig. 9(b and d)), the Tb-Co exchange interaction in the Tb-Co films are expected to be higher, and consequently, (i) the Tb-sperimagnetic cone-angle will be reduced, and (ii) the ordering temperature in a-Tb-Co will be raised. Indeed, it was shown that these alloys are ferrimagnets above room temperature for x ~ 0.62. For x ~ 0.67, T C reaches approximately 500 K, which is already higher than that of a-TbFez. Room-temperature magnetostriction is shown in fig. 13 for several a-Tb l-xCOx films. The magnetostriction is always positive. The compositional variation of magnetostriction is shown in fig. 14. It is clearly seen that the room temperature magnetostriction increases rapidly with increasing Co content as soon as the films become magnetic at that temperature, and reaches a maximum around x = 0.71 (bll = -20 MPa, b Y ' z = -24 MPa under JLoH = 1.9 T which corresponds to All = 320 x 10- 6 , AY' Z = 400 x 10-6 assuming Er = 80 GPa and Vr = 0.3). For comparison, the magnetostriction results for a-TbFe measured in a field of 1.6 T by Hayashi et a1. (1993) are also included in the same fig. 14. These earlier published results were corrected by multiplying with a correction-term (1 - vs)/(l + vs) for the use of
MAGNETOELASTICITY IN NANOSCALE HETEROGENEOUS MAGNETIC MATERIALS
25
Tb
1'1
...••••
FeI
(Hayashi et al.)
20
-,. "
~/
400
... ,
.-. ~
~
::g
15
350
,
~
~
300
.
250
»;c
200
.-.
,
'-'
...
121
N
;. 10
.... ~
•
150 J 100
5 50
I
0
0 0.4
0.5
0.6
0,7
0.8
0.9
1
X Fig. 14. Magnetostriction as a function of Tb concentration for a-TbI_xCOx thin films (after Betz 1997) and for a-TbI_xFex ones (after Hayashi et al, 1993).
0
0 \
.-.
\
-5
,\......
~
~
'-'
0
-5
\\
~
...~'!.a-:
-10
U
~ ~
I
+ ...r:r
g
-10
~::t"r~~
~
i
... -15
-IS
-:P
-20
·20 0
0.5
1
I.S
2
~O H (T) Fig. 15. Magnetostriction of SmO.37CoO.63 and TbO.36COO.64. After Betz (1997).
the former Klokholm's formula (Betz 1997; Betz et al. 1999; see also the discussion in section 2.2). It is also meaningful to consider the magnetostrictive susceptibility obloH (and/or 0).,10 H), which is of significance for applications. For the films under consideration, at low applied magnetic field, the magnetostrictive susceptibility is maximal for x = 0.65. Betz et al. (1999), thus, have succeeded to show the similarity of the compositional variation of the magnetostriction in both a-ThFe and a-ThCo alloys and opened up a promising series of magnetostrictive alloys for potential applications. A comparison of the magnetostriction of Sm-Co and Tb-Co systems is shown in fig. 15 for SmO.37CoO.63 and Tb0.36COO.64. The Sm-Co alloy shows a behaviour, which
122
N.H. Due and P.E. BROMMER
is comparable to that of the Tb-Co one, but with the opposite sign and a somewhat smaller magnetostriction in absolute value. In addition, the Sm-Co alloy is magnetically harder than Tb-Co: its magnetostriction saturates around 0.3 T and the coercive field is about 0.03 T. The high-field magnetostrictive susceptibility, however, is smaller in the case of Sm-Co. Since crystal field effects are supposed to be proportional to a)(O~}«r4r/ao)2) (see e.g. the review by Franse and Radwariski 1993, table 2.4), it is particularly interesting to compare these factors and the observed magnetostriction for these two alloys. The values are +40.2 x 10- 2 and -54.8 x 10-2 and the values of by·2 at 300 K of a) (O~}«r4f/ao)2) are + 11.0 and -18.3 MPa for the corresponding Sm-Co and Tb-Co films, respectively. One finds that the ratio between the operators is comparable with that between the two magnetoelastic coefficients: la)(O~}«r4r/ao)2)TbCo
/aJ(O~}«r4r/ao)2)SmCol
= 1.37
and
\bIlTbCo/bnSmCol = 1.67. A few amorphous Sm-Co alloys have also studied been by Quandt et al. (1994). A (negative) magnetostriction has been confirmed, somewhat smaller (by 30%-50%) than that of Tb-based alloys. The maximum magnetostriction found in the amorphous state for both Tb-Fe and Tb-Co alloys is much lower than in the crystalline state. There are three reasons to be considered for this difference. (i) The structure is not the same in the crystalline and the amorphous state. Nevertheless, it is often argued that the local environment in the amorphous state is reminiscent of that found in the crystalline one (see e.g. Hernando et al. 1997). As a starting point for the discussion, differences in the local environment can be neglected. The measured differences in magnetostriction between the crystalline and amorphous states might then be attributed to the facts that (ii) some compositions have a lower ordering temperature in the amorphous state which means that the magnetocrystalline anisotropy and so the magnetoelastic coefficient is lower and (iii) the sperimagnetic arrangement of the Tb-moment in the amorphous case gives rise to a distribution of the Tb-moments which lower the projected magnetisation and thus the magnetostriction.ln order to verify the latter argument, Betz (1997) has compared the mean Tb-magnetic moment in a-TbI-xCox and c-Tb I _ x Co x alloys and determined the variation of the low-temperature Tb-sperimagnetic cone angle 0. The results show that 0 decreases from 75 degrees to 40 degrees when x increases from 0.5 to 0.75. This result is comparable with that published in the literature (Cochrane et al. 1978; Danh et al. 1998). By assuming that the local environment in the amorphous state is similar to the crystalline one, a further approach to lower the remaining anisotropy is by eliminating the fourth-order anisotropy by substitution of Dy for Tb (Williams et al. 1994; Wada et al. 1996, 1997a, 1997b, 1997c, 1997d; Miyazaki et al. 1997). The well-known composition of the bulk Terfenol-D alloy is TbO.3DYO.7Fe2. For a-(Tb,DY)0.42FeO.58 thin films, Miyazaki et al. (1997) found that compensation of the magnetic anisotropy also occurs at the Tb:Dy ratio 3:7. Room temperature magnetostriction curves for a-(TbI-xDYx)0.42FeO.58 thin films are presented in fig. 16. Note that with increasing x the value of A decreases and tends to saturate with smaller magnetic field. In addition, the magnetostriction data
MAGNETOELASTlCITY IN NANOSCALE HETEROGENEOUS MAGNETIC MATERIALS
400
-= -
~
123
x=O.O
300
..-.I
-e
200 0.5
100
0
0.89 1.0
0
0.2
0.4
0.6
0.8
J.1oH (T) Fig. 16. Room-temperature magnetostriction for (Tbl-xDYx)0.42Feo.58 films. After Miyazaki et aI. (1997).
measured at J-LoH = 0.008, 0.05 and 0.07 T are plotted as a function of x in fig. 17a. At J-LoH = 0.05 T and J-LoH = 0.7 T, A does not decrease monotonically with x, but exhibits a broad peak around x = 0.7. This concentration dependence of A is rather similar to that of bulk polycrystalline (TbI-xDYx)Fe2 compounds (see fig. 17b). It indicates the near-zero magnetic anisotropy in a film of the Terfenol-D composition. The atomic short-range order of sputtered amorphous films, thus, can be considered as quite similar to that of crystalline bulk samples, and the same origin of the magnetic anisotropy as well as magnetostriction can be expected for both film and bulk alloys. We will come back to this aspect in the discussion for the a-(Tb,Dy)(Fe,Co) films below. As mentioned above, one of the ways to obtain a larger magnetostriction at room temperature, is to enhance the lanthanide magnetisation by increasing the ordering temperature and by diminishing the sperimagnetic cone angle. Due et al. (1996) have successfully substituted Co for Fe in a-R-(Fe,Co) alloys. The T-T interactions tend to be stronger in (Fe.Co)- than in either Fe- or Co-based alloys (Gavigan et al. 1988). This results in an increase of T c for a given R:T ratio. In general, however, R-Fe exchange interactions are larger than the equivalent R-Co interaction energies (Liu et al. 1994; Due 1997). This arises from the fact that the Fe moment is significantly larger than the Co one, while the R-T intersublattice exchange constant is approximately the same for T Fe and Co. Moreover, at the optimum concentration, the stronger R-FeCo exchange energies should then lead to a closing of the sperimagnetic cone angle and thus
=
124
N.H. Due and P.E.BROMMER
400 a-(Tb 1-.Dy.)O.41Feo .S8
-
300
(a)
~
~
200
-e
100 0
0
0.2
0.4
0.6
0.8 1.0
X
2000
-=
(Tb 1•• Dy.)O.41 Feo .S8 (bulk) (b)
~
-
1000
~
500 0
0.1 T
0
0.2
0.4
0.6
0.8
1.0
X Fig. 17. Magnetostriction as a function of Dy content for a-(TbI-xDYx)O.42Feo.58 films (a) and bulk (TbI_xDyx )0.42FeO.58 alloys (b). After Miyazaki et al. (1997) and refs therein.
to an enhancement of the magnetostriction. Due et a1. (2oooa, 2000c) have studied the (TbO.27DYo.73)(Fel-xCoxh system, in which the Tb:Dy ratio of I : 2.7 was fixed as the same as that of Terfenol-D. At low temperature, all these as-deposited compounds of the composition (Tbo.27Dyo.73)(Fel-xCoxh are magnetically rather hard. The coercive field starts, at x = 0, with the highest value of 3.4 T, and then decreases rapidly with increasing Co concentration down to about 0.5 T for 0.67 ~ x ~ 1.0. At 4.2 K, the saturation magnetisation, M». exhibits a maximum at x = 0.47 (see fig. 18). This compositional variation of M s is in contrast to the behaviour observed for the corresponding crystalline alloys where M s always shows a minimum in the middle of the composition range due to the enhancement of the (opposite) 3d(Fe,Co) magnetic moment. In the amorphous case, however, an increase in M 3d will close the sperimagnetic cone of the rare-earth moments. The maximum observed at x = 0.47 reflects that, at low temperatures, the enhancement of M3d is smaller than the associated increase in (MTb.Dy)' At room temperature, the films
MAGNETOELASTICITY IN NANOSCALE HETEROGENEOUS MAGNETIC MATERIALS
125
1000
800 ....- - - -
-1
..
400
..·..·r······......•...........•............•..-...-.-300- K
.
200
oL......<~--l.~--'--'--'-...J-..L-..L-J.--JL-.l--l.--'--'--'--'-...&.....J
o
0.6
0.4
0.2
0.8
x Fig. 18. Variation of spontaneous magnensation as a function of x at 4.2 K and 300 K for ThO.27DYO.73(CoxFel-x h thin films.After Duc et al. (2000a, 2000c).
30
500
25
400
.-. 20 ell
300
~
6
15 __-:::IIV
~ ~: ....~: ~ ....~ ~: ..· ~.'· o
-::...... 10
A" •••••••.•:&.,
-,). ... 0- •..••.•... 0-
o 0.0
200
-
J
•... .2 •
.,.9..
{:~·:~·:H:: : : : :·e'· ·I'1· · \
5
..
~
.-. o
100 .
o 0.2
0,4
x
0.6
0.8
1.0
Fig. 19. Magnetostriction measured at 0.06 T for ThO.27DYO.73(CoxFel-x h thin films: (I & I') as-deposited; (2 & 2') annealed at 150°C; (3 & 3') annealed at 250°C. Solid lines represent by •20. y · 2 ). dashed lines: bll ()'II)' The measuringdirectionalong the sample length is indicated. After Duc et al. (2QOOa, 2000c).
become magnetically rather soft. The strongest coercive field (of 15 mT only) is found at x = 0.63. The room-temperature spontaneous magnetisation M s. however, is almost independent of the Co-concentration (see fig. 18). Different field-annealing effects on the magnetostriction are evident across the whole composition range, as summarised in fig. 19. For the Co-rich alloys, b U increases
126
N.H. DUC and P.E. BROMMER
5.0
2.0
4.8
1.8
A.6
1.6
--. ....
-•
.:::,fI:l
--.
1\
';i' V
...":~
-....
.J=
4.4
1.4
4.2
~
'-"
1.2 a·(Tb0.21Dy0.13)(Fe1-"Co) II 2
4.0 0
0.2
0.4
0.6
0.8
1.0 1.0
X
Fig. 20. Variation of (MR) and M3d(Fe,Co) calculated from magnetostriction data as a function of x for ThO.27DYo.73(CoxFel-x)z thin films. After Due et aI. (2000a. 2000c).
significantly after annealing (dashed lines), whereas b y ,2 remains virtually unchanged. For the Fe-rich alloys, we see the opposite effect in that b y ,2 increases significantly after annealing while bll remains virtually unchanged. The increase in b y · 2 may be associated to the decrease of the saturation field after annealing. In fact, the largest magnetostriction of Ay ,2 = 480 X 10-6 and All = 250 x 10-6 is found in the middle of the composition range (at x = 0.47) and it can be obtained in the rather low applied magnetic field of 0.06 T. Note that, due to the substitution of Co for Fe, the ordering temperature in c-Tb(Fe l-xCOx h is increased. but without enhancement of the magnetostriction (Dwight and Kimball 1974; Belov et aI. 1975). At present, the magnetostriction increase is considered to be caused by the closing of the sperimagnetic cone angle due to the enhancement in M 3d in the substituted a-R(Fe,Coh alloys. A detailed analysis was performed by Due et al. (2000a), yielding values between 48° and 53° for the R-sperimagnetic cone-angle 0, in accordance with some literature values (Coey et aI. 1981; Hansen 1991; Danh et al. 1998). The variation in e also implies a variation in the average (Tb.Dy) moment as a function of x (see fig. 20). From the measured magnetisation data (fig. 18), M3d can be determined as a function of x (see also fig. 20). Clearly, a similar composition dependence of M 3d as observed in the crystalline R-(Fe,Co) alloys is found and a maximum is reached for x = 0.47 where there is sufficient Co to ensure good ferromagnetic T-T coupling as well as sufficient Fe giving the larger magnetic moment. This 3d magnetic moment enhancement caused by Co substitution was confirmed by Mossbauer studies (Danh et aI. 2000; Due et aI. 2000b): for a-Tb(Feo.55C00.45)1.5, a hyperfine-field value Bhf = 24.5 T was reported, whereas it equals only 21 T for a-Tbfe-. It is well known that the substitution of Dy for Tb gives rise to an increase of the magnetostriction at low magnetic fields, through the reduction of the saturation field. It is, however, also accompanied by a reduction of the saturation magnetostriction. The Co substitution in the R-(Fe,Co) alloys, in combination with the effects of field annealing,
MAGNETOELASTICITY IN NANOSCALE HETEROGENEOUS MAGNETIC MATERIALS
60
:
3
/;:::-
50 40
-.. ~
: ... I• ;•
30
800
2 --~:---
600
1
/I
~20 ..,..
f / , ~
400
., ;
10
'f--
--
8
-e
~
,.Q
127
200
~
o
3
2
.l..
J
o
-10
0.0
0.5
1.0
1.5
2.0
JloH (T) Fig. 21. Room temperature magnetostrietion for Tb(Feo.4SC00.5Sh.l: as-deposited (l), annealed at 150°C (2) and 250°C (3). After Due et aI. (1996).
results in an enhancement of both the low-field and the saturation magnetostriction. Thus, it shows a possibility to enhance the magnetostriction in this type of alloys by increasing the Tb concentration. Indeed, Duc et al. (1996) found a record giant magnetostriction of AY,2 = 1020 x 10-6 at l-toH = 1.8 T, with All = 585 x 10-6 at l-toH = 0.1 T, in a-Tb(Fe0.45CoO.55 h.l. The field dependence of the magnetostriction for these alloys is presented in fig. 21. Here we see that a magnetostriction of Ay,2 (= All - A.d = 800 x 10-6 at 1.8 T is already observed for the as-deposited film. The comparison between bl! (AU) and b1.(A.d indicates clearly the anisotropy of the sample. If the zero-field state is fully isotropic, then bU = -2b1. and if it is isotropic in the plane, then bU = -b1.. For the results presented in fig. 21, b1. = - ibll' indicating a certain initial anisotropy. After field annealing, bll increases, and bs. is significantly reduced (in absolute magnitude) in agreement with the fact that the easy axis becomes better defined. In addition, it is important to note that b y ,2 actually increases after annealing at 250°C, leading to the very large magnetoelastic coefficient of -60 MPa (i.e. AY.2 = 1020 x 10-6) at saturation. This result is particularly interesting as the magnetostriction was almost completely developed at only 0.3 T. In comparison, the magnetostriction of TbO.32(Feo.45C00.55)O.68 and TbO.32COO.68, prepared in the same condition, is presented in fig. 22. Clearly, the Fe for Co substitution increases the magnetostriction by a factor of 2. The temperature dependence of the magnetostriction is shown in fig. 23 for a TbO.36(FeO.5C00.5)O.64 film. The magnetostriction decreases linearly with increasing temperature up to the ordering temperature of about 423 K. Figure 24 illustrates five normalised magnetostriction loops of an amorphous Tb40Fe60 film. This film shows a T C of about 100°C (373 K). The measurement reveals not only the variation of the saturation magnetoelastic coupling constant and the Curie temperature of the investigated film, but also gives information on the change of the hysteresis curve with temperature.
128
N.H. DUC and P.E. BROMMER
40
Tb:M
= 1:2
600 500
30
400
.......
If
:E '-'
~
....... 300 ;,
20
..
200 '-'
.Q
10
100
0.61
0
0
-100 -10
0.5
0
I
1.S
2
~O H (T)
Fig. 22. Room temperature magnetostriction for as-deposited Tb(Feo.45COO.5512.I and TbC02.1. After Betz (1997).
-:....
30
Tb
..~
25
:E I
10
5
o
H
0.5
Co)
o
50
-
400
- 320 ~
...
....
240 ....... "Cl "Cl
'........
f-
0.5 0.64
=1.9 T
-,•.......
IS
~
~o
(Fe
.........
~
-
0.36
.
. . 20
N
480
I
160
!
80
150
Fig. 23. Magnetostriction of Tb(Feo.5CoO.512. I as a function of temperature. After Betz (1997).
Figure 25 presents low-field magnetostriction data for a-(TbI-xDYx)(Feo.45CoO.55h.l thin films with different TblDy ratios, after annealing at 250°C. It exhibits obviously a decrease in the magnetostriction and saturation field with increasing Dy content, but with a maximum in the initial magnetostrictive susceptibility for x = 0.73 as observed in other Terfenol-D based alloys. Here, we see a partial anisotropy compensation for x = 0.73 as found for crystalline (TbO.27Dyo.73)Fe2. As shown in fig. 26, the anisotropy constant K deduced from the magnetisation measurements has also a minimum for this composition.
MAGNETOELASTICITY IN NANOSCALE HETEROGENEOUS MAGNETIC MATERIALS
129
1.O1-_~
Q.8
CUSr-_~~ SJ=
...
0.4
Q.8
Fig. 24. Normalised magnetostriction as a function of the applied field, at different temperatures, for a Tb(},4Feo.6 thin film (d = 3 ILm). After LUdwig and Quandt (2000».
,..--.,..---r----r--.,.--.,..--...., 800
40
600
0.5
-
&1-
0.73
20
200
1.0
10
o
o
-.&.._---''--_...I-_.....J,_ _-L-_--'
0.1
0.2
0
0.3
~ H (T) o
Fig. 25. Room temperature parallel magnetostriction for (Tbl-x Dy, )(Feo.45COO.55 h.1 measured along the hard axis after annealing at 250°C. After Due et al. (1996).
This indicates that even in amorphous samples. in which the uniaxial K2 terms are expected to dominate due to the local distortions from cubic symmetry, there is stilI a significant contribution from the K4 cubic anisotropy terms. It is interesting to contrast this with the numerical simulations for a-TbFe2 which have shown that the fourth-order anisotropy energy per atom was an order of magnitude smaller than the second-order anisotropy energy per atom, albeit that the fourth-order term was of the same order of magnitude
130
N.H. DUC and P.E. BROMMER
16 14
...,......
12
'-'
10
...:.:...e ~
-
8
.c ""'
6
.c":::
4 2
0 0
0.2
0.6
0.4
0.8
1
x Fig. 26. Variation of the ratio bll/ b.1 and the anisotropy constant K as a function of x for (TbI-xDYx)(Feo.4sCo0.5S)2. After Due et al. (\996).
as in the crystalline TbFe2 Laves phase (Kaneyoshi 1984). The present result implies that K4 tends to be larger than expected and that the local environment is reminiscent of that in the cubic Laves phase. In the same figure, the ratio Ibll/bl.l shows a minimum at the same composition, implying that at this concentration the anisotropy is then less well defined by field annealing. The field dependence of the magnetostriction is usually associated with different types of magnetisation processes. For a system of randomly oriented spins and random distribution of domain walls, the magnetisation process takes place in two steps (Chikazumi 1964): first, the motion of 1800 domain walls leads to a magnetisation of Mo without any contribution to the magnetostriction. In the second step, the spins rotate into the direction of the applied magnetic field, leading to the change of both magnetisation and magnetostriction. For amorphous alloys of random three-dimensional spin orientation and of a random distribution of domain walls, Mo is expected to equal M max/2. In this case, the relation between magnetostriction and magnetisation is given as (Schatz et at. 1994): A(H)/A max = [2M(H)/M max - 1]3/2.
(23)
For the rotation of the magnetisation out of the easy axis into the field direction, the magnetostriction is related to the magnetisation as (Chikazumi 1964): A(H)/A max = [M(H)/Mmaxf.
(24)
The normalised magnetostriction as a function of normalised magnetisation for films with perpendicular and parallel anisotropy is plotted in fig. 27(a, b) for (TbO.27DYO.73)O.42FeO.58 (Schatz et at. 1994). The films with in-plane anisotropy appear to show high magnetostriction and magnetisation at low fields (the coercivity is less than 0.01 T), due to the easy rotation of the spins in the isotropic plane. The motion of 180 0
MAGNETOELASTICITY IN NANOSCALE HETEROGENEOUS MAGNETIC MATERIALS
1
0.8
I
f-
<, -< 0.4 8 0.6
=
I
f-
0.8
-
0.6
Theory -
0.4
-
0.2
.,
,,
,<
0.2
, • , , -
I
I
Perpendicular anisotropy (a)
,,
.-r-· 0.2 0.4
,
"
, .. '
, ,,
131
1
","
a
I
I
0.6
0.8
I
a
1
a
M/Mmax
1
0.8 0.6 -<8= <, -< 0.4 0.2
a
I
f-
I
I
I
In-plane anisotropy (b)
•
f-
," ,,. -
-
Theory,.
,,
a
,,-•
I
I
0.2
0.4
:~
0.6
I
0.8
1
1
0.8 0.6 0.4 0.2
a
M/Mm a x Fig. 27. Normalised magnetostriction as a function of normalised magnetisation for (ThO.27DYO.73)O.42Fe0.58 films with perpendicular (a) and parallel (b) anisotropies. Dashed curves are calculated with eqs (24) and (23). respectively. After Schatz et aI. (1994).
domain walls does not contribute to the magnetostriction, and eq. (23) can be applied. For the films with perpendicular anisotropy, the magnetisation is governed by rotations out of the EMD into the plane, requiring larger external fields. Here, eq. (24) holds. An analogous presentation is made for Tbo.4(Feo.ssCoo.4S)O.6 (Terfecohan; Due et aI. 2000b). In this case, the sample with perpendicular anisotropy shows again a similar variation as described in eq. (24). For the sample with parallel anisotropy, however, the onset of 'AJ'A max occurs at a M value which is even higher than M max/2(see fig. 28). It is possible that the spins are pulled into the plane by the shape anisotropy and only the random in-plane (two-dimensional) oriented spin structure is formed. This would lead to a magnetisation remanence, which is appreciably higher than in the case of the random three-dimensional spin orientation.
132
N.H. DUe and P.E. BROMMER
1.0 0.8
-e 0.4
0.2 0.0 0.0
0.5
1.0
Fig. 28. Experimental and theoretical relations between normalised magnetostriction and magnetisation for amorphous Terfecohan [Tb(Fe0.55eOO.45) 1.51 films. (1) and (2): theoretical curves described by eqs (23) and (24), respectively. (_) as-deposited, (e) T A = 250oe, (A) 350 0 e and (0) 450 oe. After Due et al. (2000b).
Finally, in view of possible applications, the interesting values of the magnetoelasticity and its magnetostrictive susceptibility (Xb = db/d(lLoH) (and/or XJ.. = dA/d(lLoH» are summarised in table 2. Although the results are not so good as for the multilayers to be discussed in the next section, the best results obtained for the single-layer films are good enough for rnicroactuator applications. We mention here, for example, for Th(Fe,Co)1.5 films, the suitable values Ay · 2 = 1020 x 10-6, 1L0H e = 6 mT and XJ..II = 1.8 x 10- 2 T- 1• As will be presented later in this chapter (section 10), many magnetostrictive devices have been designed and manufactured, using rare earth based amorphous thin films like those discussed here.
4.3. Magnetostriction ofnanocrystalline rare earth based thin films A great disadvantage of the amorphous R-Fe thin films, from the point of view of application in MEMS, is the comparatively low Curie temperature (T c ~ 400 K for amorphous Terfenol-D films). Polycrystalline Terfenol-D films exhibit a room temperature magnetostriction of As ~ 1500 X 10-6 and T c = 650 K. These films, however, are not suitable for micro-mechanical applications due to their comparatively high coercive fields. Material designs require always a synthesis between the advantage of the crystalline films (giant magnetostriction and high T c) and good magnetic softness of the amorphous films (low coercivity). In this context, the nanocrystalline structure is expected to be a reasonable compromise. Most of the work on nanocrystalline ThDyFe alloys was started with rapidly quenched ribbons (Kikuchi et al. 1993; Tanaka et al. 1995; Lim et al. 1994; Ooike et al. 1993). Addition of 5 to 8 at% B yields a fine grain structure with average diameter d ~ 10 nm. The best results {coercive field 1L0He 20 mT, magnetostriction A ~ 400 X 10-6, in an applied field lLoH 1.0 T} have been obtained for (ThO.3DYO.7 )0.3 Feo.62 BO.08 ribbons (Tanaka et al. 1995). Using different preparation conditions, a nanocrystalline structure with d 10 to 20 nm can be achieved directly
=
=
=
MAGNETOELASTICITY IN NANOSCALE HETEROGENEOUS MAGNETIC MATERIALS
133
TABLE 2 Comparison of the magnetoelastie data for magnetostrietive bulk and thin-film materiaIs MateriaIs
b
y•2
(MPa)
Bulk crystalline Terfenol-D 11>o.27DYO.73Fe2 Single layer films a-Th Fe2 a-11>0.27Dyo.73Fe2 n-Tho.27Dyo.73Fe2 a- ThC o2 a-ThO.27 Dyo.73CO2 a-Th(Feo.45 Coo.55 h a-Th(Feo.55 Coo.45) 1.5 a-Tho.27DYO.73 (Feo.45Coo.55h a-SmFel.6 a-( SmFe2>w.26 BO.74 a-SmCo2 a-Sm(Feo.5S Coo.42) 1.54
-101 -19.4 -17.2 -49.0 -24.5 -15.1 -63.5 -65.9 -20.15 25.9 45.6 11.0 27.4
Multi/ayers Tho.4 Feo.6/Fe Tho.27DYO.73Fe2 /Fe Tho.27Dyo.73Fe2/Finemel Th(Feo.55 Coo.45) 1.5/ Fe Tho.4 Feo.6/Feo.5Coo.5 Tho.37 Feo.63/ Feo.65Coo.35 Tho..27Feo.73/ Feo.75Coo.25 Tho.. I sFeo.S2/Feo. 75COO. 25 1b(Feo.55C oo.45)1.5/ Feo.85Coo.15
-39 -28 -31.1 -27 -44.5 -32
Sandwich system Ndo.25Coo. 75/Tho.28 Coo. 72/Ndo.25 Coo.75 Tho.28Coo.n/Ndo.25Coo.75/Tho.28Coo.n
-15.2 -16.5
-20 -12
A,y.2
(10- 6)
ilbli/ilB (Mpaff)
2400
568
321 300 800 400 260 1040 1080 330 -380 -670 -161 -320
20 50 155 190 300 1100 430
40 76
300
410
650 300 3040 1000
600
4000
348 890 530
4800 7850
248 270
560 117
Refs
[IJ [2J [3] [4J [5J [3J [6,7J [8] [6,7J [9J [I 0] [7J [IIJ
[I2J [13] [l3J [14J [12] [12J [12J [I2J [IS]
[8] £7,8,I6J
[IJ Clark (1980), [2J Hayashi et aI. (1993), [3J Due et aI. (2000a), [4] Riedi et aI. (1998), [5J Betz et aI. (1999), [6J Due et aI. (1996), [7J Betz (1997), [8J Due et aI. (2000b), [9J Honda et aI. (1994), [IOJ Kim (1993), [I I] S. David, unpublished data, [12] Quandt and Ludwig (1997), [I3] Farber and KronmUller (2000b), [l4J Due et aI. (2oola), [15] Due et aI. (2oo1b), [I6J Givord et aI. (1996).
by melt spinning of DYO.3FeO.56BO.14 ribbons, without further annealing treatment (Lim et aI. 1994). The influence of several additive elements on the magnetic and crystallisation behaviour of these materials was investigated with Mo (Kikuchi et a1. 1993) and Mn (Ooike et a1. 1993). Schatz et a1. (1993, 1994), Williams et aI. (1994), Miyazaki et al. (1997) and Wada et a1. (1997c, 1997d) reported investigations on the magnetic and magnetostrictive properties of amorphous and crystalline Tb-Dy-Fe thin films. Effects of the substrate temperature, of the annealing treatment on the microstructure, on the magnetic domains and then on the magnetic and magnetostrictive properties of the 'hot grown' Terfenol-D films have been investigated by Wada et aI. (1997c, 1997d). The changes in the in-plane
N.H. Due and P.E. BROMMER
134
1200 700
600
r
s S.OxlO-# I PG s "m·1 b. ... M/I,_"_cc"'
•
0
•
o
2.5
.l,,_',JIIfI
1000
HelkOe
06<>: IttllUl-eryrbllJlud
,
9""
u 500 u ~
800 r> S,ld,-4 tr.. _"'
E Q)
-a
2.0
..... : cry6llllJlud
o :-M,"S11Oo',.." cc·,
E
Q,
~o,,"-Uu
400
e,
It)
::::
~
600 ....
300
.'
~
.....II
a
.IC 9""
CD
1.50
~/
2
.IC
... ::::
111
, I
...
111
400 -e
1.0~
200
0,5
I
.,. I
200
I
I
I I
[J
100
I I I I I
[J
.------------~-----_cr-----~ 0
400
450
[J
500
550
600
0 650
0.0
Substrate temperature I K Fig. 29. The changes of the in-plane magnetisation, coercivity and magnetostriction as a function of substrate temperature Ts in TbO.27DYO.73Fe2 films. After Wada et al. (1997c).
magnetisation, coercivity and magnetostriction as a function of substrate temperature (T s) are summarised in fig. 29. The sharp increases in the magnetisation and magnetostriction at T s from 405 K to 410 K were associated with the formation of very fine nanocrystalline grains (smaller than 5 nm). The small change of coercivity confirmed the non-drastic structure change in this temperature range. At temperatures T s between 410 K and 600 K, the magnetisation, coercivity and magnetostriction remain almost constant. In accordance with microstructure studies, these results indicate a release of the internal stresses induced during the depositions. At T s over 600 K, the development of grain sizes from 10-20 nm to 40-100 nm was observed. This recrystallisation causes the second step of the sharp increase of the magnetisation, coercivity and magnetostriction as illustrated in fig. 29. For these films, it is worth to mention that surface oxidation with a thickness of 50 nm was observed. For films formed at T s below 405 (i.e. with grains below 5 nrn) the measured hysteresis loops and the observations of the magnetic domains in applied magnetic fields seem to
MAGNETOELASTICITY IN NANOSCALE HETEROGENEOUS MAGNETIC MATERIALS
135
0.8 )C
III
e O.6
~:::
~:: :'0.4
0.2
0.2
0.4
0.6
0.8
1.0
M"I M"max Fig. 30. Normalised magnetostriction as a function of normalised magnetisation for the nanocrystalline (n) and polycrystalline (p) (ThO.27DYO.73)Fe2 films. After Wada et al. (I997c).
indicate a preferential perpendicular magnetisation by spin rotations with low anisotropy in these nanocrystalline films (denoted as n-films). The magnetisation of the polycrystalline films formed at Ts between 610 K to 625 K (p-films), however. was suggested to be governed by the motion of domain walls at low magnetic fields. The change in the normalised in-plane magnetostriction AU/As as a function of the normalised magnetisation of these films is plotted in fig. 30. At low magnetic fields. the n-film shows a much higher magnetostrictive response to the magnetisation than the grown p-film. The parabolic dependence of the in-plane magnetostriction on in-plane magnetisation, observed for the nfilm, is in good agreement with the arguments mentioned above. and with the experimental results for the motion of 90° domain walls, i.e. the rotation of spins with perpendicular anisotropy into the plane (see also eq. (24) and fig. 27a). For the p-film, almost no magnetostriction takes place up to M/ M max = 0.2. This behaviour seems to be appropriate for random distributions of spins. as described by Schatz et a1. (1994) (see also eq. (23». Additional annealing of these 'hot grown' nanocrystalline Terfenol-D films at 630 K for 10 h increased the nanograins of below 5 nm to around 50 nm. An enhancement of the magnetostriction (up to 1500 x 10-6). however. occurs only for annealing during 2 h. Further annealing causes the magnetostriction to decrease due to the oxidation (Wada et a1. 1997d). No appreciable increase in grain size was observed in a similar annealing for a film with d = 10-20 nm. In addition, Riedi et a1. (1998) showed that annealing 'hot grown' films is not advantageous because of the formation of iron-rich phases like RFe3 and R6Fe23 which exhibit even less magnetostriction and higher magnetic coercivity. These authors. however. reported their results of annealing the 'cold grown' (Tho.3Dyo.7) I-x Fex (with x ~ 0.3) films as in fig. 31. The best magnetic properties were obtained for the sample
136
N.H. DUC and P.E. BROMMER
2°
800
03
i' 0
600
'<,
=
-e
t.
400 200
t. t.
t.
t.
0
0 4
I
0
E J: :::t
0
0.4
t. amorphous
0.3
o intermediate
0
0.2
0
I
•
0
3
• 3 20
600 ....U
40
20
0.0
SZ
-
o crystalline
0.1
~
0
0 0
4
0
500 400 Ii
t.
t. t. 0I
300 as-spat.
400
600
Fig. 31. The saturation values of the in-plane magnetostriction All, the in-plane coercivity ItOHq and the Curie temperature Tc as a function of the annealing temperature T A for (TbO.3DYO.7)O.3Feo.7: (0) amorphous, (0) intermediate and (t» crystalline states. (I. 2 and 3. 4 serve to distinguish different samples.) After Riedi et aI. (1998).
annealed at T A = 600°C for 10 minutes with a grain size around 10 nm, a saturation magnetostriction A = 860 x 10-6 but /-LO He = 120 mT. The appearance of a perpendicular anisotropy in the mixed state of both amorphous and crystalline structure was reported by Miyazaki et al. (1997) for (TbO.3DYO.7 )O.33FeO.67 films fabricated above 673 K (4{)()°C) (see fig. 32). The thermal stability and the reproducibility of those films were studied also. For films prepared with substrate temperatures above 673 K (400°C), the magnetostriction changes remarkably after 3 months. This is due to ageing effects, related to the formation of the Laves phase (Tb,Dy)Fe2. According to the random anisotropy model (Herzer 1990; Hofmann et al. 1992), a further reduction of the crystal size will reduce the coercive field, if the exchange length is larger than the average grain size. Hence, technologies which, on the one hand. can enhance the nucleation of grains, but, on the other hand, may limit the grain growth, must be applied to achieve a fine nanocrystalline structure. For this purpose Zr and Mo have been chosen as additives. In the binary system Fe-Zr the most stable intermetallic compound is
MAGNETOELASTICITY IN NANOSCALE HETEROGENEOUS MAGNETIC MATERIALS
137
~
Amorphous in plane
out of plane in plane
200 ,-..
...
150
-e
100
'i'
Q
'-'
O.7T O.lT .OST
SO t r - - - - - - - - - ,
o '-=:=i:==::::C==~---.:t:...--.J 100
200
300
400
SOO
600
Substrate temperature (0C) Fig. 3Z. Magnetostriction as a function of substrate temperature for (TbO.3DYO.7 )Fe2' The anisotropy type and the structural morphology is indicated too. After Miyazaki et al. (1997).
(Tbo.1l DY•.") •., ,Fe ..
-
- - «(Tb01lDYol,)."Fe )Zr•."
100
-0.8
-0.4
0.0
0.4
0.8
J.LoH'J:I [T] Fig.
33. Room-temperature parallel magnetostncuon loops for (Tbo.27DYO.73)O.32Feo.68 [(TbO.27DYO.73)O.32Feo.681Zro.03 films after annealing at 973 K. After Winzek et al. (1999).
and
the cubic Laves phase ZrFez. So the solubility of Zr in Fe is negligible, and it can be assumed that Zr is substituted for (Tb,Dy) in (Tb,DY)I-xFeZZrx alloys. In comparison to (Tb,Dy)Fez, ZrFez exhibits a more negative enthalpy of formation, and therefore the addition of Zr may enhance the nucleation of grains. Mo, however, has a much higher melting point, and intermetallic compounds containing Fe show a much lower stability. The existence of the Laves phase MoFez is still questionable. Moreover, the large Mo atoms reduce the diffusion, and therefore the addition of Mo was thought to limit the grain
138
N.H. Due and P.E. BROMMER 800 700
- 6 - «Tho.nDyo.Z7).,lFeo.61)Zr. Ol
600
-..
~,. . .,
0
......
~
o
- / 0 - (Tb•.71DYo.;n)Q.lZFe•.61
~
6
«Tho.."DYo.Z7).,!eo.61)Mo...
o
•
500
400 300
t:.
~6A..-..
200
~
o
~-t:>.
(a)
100 0 t... [minI 10 60 360
Tit [K]
300 250
E='
E ...... ::x::"
10 60 360
10 60 360
10
10
803
833
873
973
773
- 4 - (Th•.nOY•.27)•.11Fe•.61 - 6 - «Th•.nOy.1I).nFe•.61)Zr001 - 0 - «Th•.71DY027)•.lZFe•.61)MoDJ)<
crystallized
200
0
0-0
150
::t" 100
SO
X-ray amorphous
(b)
-4~
!_6-t:.
0 t... [min]
10 60360
10 60 360
10
10
TA [K]
773
833
873
973
Fig. 34. Magnetostriction (Asl, measured in I T (a), and coercivity (IJ,OHc) (b) of (TbO.27 DYO.73 lO.32 FeO.68, [(Tho.27DYO.73lo.32Feo.68IZro.03 and [(TbO.27DYO.73lo.32Feo.68IMoo.04 films, after different heat treatments at temperatures TA and annealing times IA. After Winzek et al. (1999). growth. Practically, the influence of the additives Zr and Mo on the crystallisation and on the magnetic properties was studied by Winzek et al. (1999). Typical magnetostriction loops are presented in fig. 33 for two films crystallised at 973 K for 10 minutes, one without additive and the other with 3 at% Zr. It is clearly seen that the Zr-substituted film shows All 430 x 10-6 at /-LOH 1.0 T and /-LoHe = 120 mT, a strong improvement with respect to the starting alloys: All = 230 x 10- 6 and /-LoHe = 300 mT. The saturation magnetostriction and the corresponding coercivity of all annealed films, without and with additives, are summarised in fig. 34(a, b). These additives were considered as causing an
=
=
MAGNETOELASTICITY IN NANOSCALE HETEROGENEOUS MAGNETIC MATERIALS
139
enhancement of the growth of RFe2 grains and to hinder the formation of RFe3 ones. It is assumed that the latter was responsible for the high coercivity values above 150 mT. Farber and Kronmiiller (2000a) reported also a reduction of the coercivity by 30% by the addition of 2 at% of Zr. In general. it should be noted that a reduction of the average grain size of the cubic Laves phases below 10 nm (and consequently coercivity values below 100 mT) could not be achieved in single-layer films. The grain growth, however. can be controlled in nanometer-scaled multilayers with interlayers of Nb. This will be presented in the next section. S. Magnetostrictive multilayers 5.1. Nanocrystalline TbDyFe + Zr/Nb multi/ayers Nanocrystalline structures combine the advantages of a crystalline film and the soft magnetic properties of an amorphous structure. These properties. however. can be achieved when the grain sizes (d) are smaller than the Bloch wall width of the crystalline material. For R-Fe alloys. the critical grain size has been estimated to be de ,...., 10-15 nm and a grain diameter below 5 nm is desirable to reduce coercivity significantly. The results of magnetostrictive single-layer films presented in the preceding section show that grain growth can be affected by several factors. but that it is rather difficult to reduce the average grain size below 5 nm. Fischer et al. (1999) and Winzek et al. (1999) have applied a method to inhibit grain growth by constructing multilayers in a special way. They fabricated a multilayer system containing TbDyFe + Zr layers with thickness of 5 nm, separated by Nb-layers with an average thickness of 0.25 nm. Their microstructure investigations have shown that this multilayer structure shifts the crystallisation temperature (for 10 minute annealing) from between 773 and 873 K (for single layers) up to about 923 K. At this annealing temperature, nanocrystallites of less than 5-10 nm were formed. After such a heat treatment, the corresponding single-layer film exhibits a polycrystalline structure with average grain sizes much larger than 20 nm (see section 4.3). This remarkable influence of the Nb spacer layers is thought to be due to reduced dimensions and an increase of interfacial surface area. Magnetic and magnetostriction data of the as-deposited and annealed TbDyFe + ZrlNb multilayers are summarised in fig. 35. After 10 min annealing at temperatures from 873 K to 973 K, the transition temperature increased from T c = 333 K to 592 K, accompanied by an increase of the parallel magnetostriction from 265 x 10-6 to 520 x 10-6 • while the coercive fields (increasing from #LoBe = 5 to 75 mT) stay distinctively below 100 mT. The variation of the magnetostriction, the ordering temperatures and the coercive fields are strongly correlated to the formation of the highly magnetostrictive RFe2 Laves phases. As mentioned above, the Nb spacer layers do inhibit the grain growth. and also increase the crystallisation temperature. Because of its strong affinity to iron. the additive Zr enhances local formation of the highly stable ZrFe2 Laves phases, which then act as nuclei for the similar, but less stable. RFe2 Laves phase. The difference of 34 K in the transition temperatures of single-layer TbDyFe + Zr (T c = 626 K, see also section 4.3) and multilayer films may result from differing average grain sizes and/or chemical composition. In the as-deposited multilayer the chemical composition is periodically varying spatially. In the annealed multilayer, however, due to the interdiffusion
N.H. DUC and P.E. BROMMER
140
600 , - - - - - - - - - - - - - - : - . . 100 multilayer
... - ..... .. .: - ,. .-~.
,.,'
[500
- -.~.
.::
a'
E-
oc
~400 as
..<
-
..
~300
\-.u
.....
---"- ----' ._._.-._--
200 u -
873
75 F
:::::
Tc [K]-..... / ... ~_c·
...
~-
f /
50
,
3'
.:j
,4'
25 _.
-A
-' ""__OJ
~
898
923
948
973
o
T.~[KI
Fig. 35. The in-plane magnetostriction All_ coercivity J.l.oHc and Curie temperature TC as a function of the annealing temperature T A for ThDyFe + ZrlNb multilayers. Open square symbols indicate the phase transition temperature of an amorphous rest phase. After Fischer et al. (1999).
of atoms between layers, modification of the layers must be taken into account. Due et aI. (2000d) have observed that an annealing at 350°C for 1 hour can extend the interfacial spacing with I nm. Farber and Kronmtiller (2000b) observed that the multilayer structure was destroyed at T A = 800 K (see also section 5.3 and fig. 56).
5.2. Magnetostrictive spring magnet type multi/ayers (MSMM) Originally, the research on giant magnetostriction was based on homogeneous R-Talloys. As described in section 4, attempts to reduce the driving fields required for giant magnetostriction are concentrated around techniques for reducing the macroscopic anisotropy, e.g., to control the Tb:Dy ratio in order to achieve compensation of fourthorder anisotropy, to use amorphous or nanocrystalline materials to reduce anisotropy, etc. Furthermore, the saturation field H s actually is determined by the anisotropy field K 12M sand thus can be reduced by increasing the saturation magnetisation M s, instead of by decreasing the anisotropy constant K. For a given Rvconcentration, which is optimised with respect to giant magnetostriction, e.g. at the 1:2 R:T ratio, an increase of the 'I'-sublattice magnetisation by substitution, for instance, will increase the total magnetisation in the RT alloys with R = light lanthanide, but will reduce the total magnetisation in the alloys with a heavy lanthanide (due to the ferrimagnetic nature, when the R-moment exceeds the T-moment). An increase in the R concentration, then, can increase M s- but also results in a lowering of the ordering temperature with the opposite effect. Thus, it is difficult to see how M s can be notably increased using homogeneous R- T alloys. Nevertheless, one has found this possibility by combining two different magnetic materials using an approach similar to those developed for the permanent "spring magnets". For the spring magnets, one matches a material which has a high magnetisation with another one which possesses a strong coercive field. These two materials are coupled magnetically. Here, multilayers are fabricated by combining also two different materials, one having a large room-temperature
MAGNETOELASTICITY IN NANOSCALE HETEROGENEOUS MAGNETIC MATERIALS
141
Fig. 36. Schematic view of a magnetostrictive "spring magnet" multilayer (MSMM).
magnetostriction (like, e.g., a-Tb-tfe.Co) alloys) and the other being magnetically soft and having a high magnetisation (like, for example, (Fe.Co) alloys). The structure of this spring-magnet type multilayer is illustrated in fig. 36. The thickness of these layers must be enough for magnetic coupling but they must be thinner than the magnetic exchange length, for which domain walls cannot be formed at the interfaces, i.e., the thickness should range between I nm to 20 nm (Givord et al. 1993, 1996; Wtichner et al. 1995, see also section 7). In this state, the 3d-3d exchange interactions ensure that parallel coupling of the transitionmetal magnetic moments persists throughout all multilayers. Without creation of domain walls at the interfaces, the multilayer behaves as one piece of material. Then, magnetisation processes result from the average of the magnetic characteristics of each individual layer. Assuming that the 3d-3d exchange interactions are infinite and the interfacial magnetic anisotropy is negligible, one can calculate the magnetisation, the magnetic anisotropy and the magnetostriction of the multi layers from the corresponding values of the simple alloys and the (average) thickness tTb and tT of the individual Tb-(Fe,Co) layers and the (Fe.Co) layer, respectively (Betz 1997): _ MTtT - MTbtTb ) ( MtT tTb
,
+ (K) = KTtT + KTbtTb, tT + tTb (b y •2htT + (b y ,2)Tb tTb (b y ,2) = - - - - - - tT
+1Tb
(25a) (25b) (25c)
In the as-deposited composite multilayers, the Tb-based layers were amorphous, while the transition metal layers were found to be nanocrystalline with a mean grain size being equal to the layer thickness (Quandt and Ludwig 1997). In spite of the compressive stress, these multilayers exhibit an in-plane EMD. The magnetisation of a TbFelFe and TbFeIFeCo multilayer series is presented as a function of the transition metal layerthickness in fig. 37 (Quandt and Ludwig 1997; Quandtet al. 1997a, 1997b). Comparison of the experimental data with theoretical calculations based on either parallel or antiparallel coupling between the Tb-Fe and the T layers strongly supports the antiparallel coupling, i.e. the (Fe.Co)- and Fe-magnetic moments are coupled ferromagnetically throughout the entire multilayer and are coupled antiferromagnetically to the magnetisation of the
142
N.H. DUC and P.E. BROMMER
1.5
.-----...--,...--.--y---.--,...-....,......--.",_--.~_.....,
1.0
....,..,. 0.5
•/ ••••• •••• •
.... ... ...
• lbFe(4.5 nm)/Fe(x nm) expo -lbFe/Fe parallel coupling lbl'e/Fe ontiparallel coupling •
lbFe(7 nm)/FeCo(x nm) expo
-1bFe/FeCo parallel coupling - - lbl'e/FeCo antiparallel coupling
0.0 '--........L-.--'-_"""'-_"'----'_--'-_........_ " ' - -........._ 4 6 2 8 o
..............
10
X (om) Fig. 37. Saturation magnetisation of the TbFelFe and TbFelFeCo multilayers as a function of the transition-metal sublayer-thickness, in comparison to a simple model for exchange coupled layers considering either parallel or anti parallel coupling of the TbFe and the transition metal layers. After Quandt and Ludwig (1997).
ferrimagnetic TbFe layers due to the dominating Tb moments in these layers. This behaviour is confirmed for TbFelFeCoBSi multilayers (Quandt and Ludwig 1999). The in-plane magnetisation loop of the as-deposited Tb(Feo.ssCo0.4s)1.5(7.5 nm)! Fe(5 nm) multilayer is plotted in fig. 38a together with the corresponding loop of a giant-magnetostrictive Terfecohan Tb(Feo.SSCoO.4S) 1.5 single-layer film (Due et al. 2000d. 200la). It reveals the reduced (but non-negligible) hysteresis and saturation field for the multilayer. This behaviour is confirmed in the magnetostriction loops (fig. 38b). Figures 39a and 39b show the magnetostrictive hysteresis loops of a TbFeIFe and a TbFelFeCo multilayer. respectively. For both multilayer systems. high saturated values were obtained for the magnetoelastic coefficient b y · 2 = (b ll -b1.): -28 MPa (TbFelFe) and -41 MPa (TbFelFeCo) in a field as low as 20 mT (corresponding to the Ay ,2 = (All - A1.) values 580 ppm and 850 ppm. respectively). These values. however. are still lower than those of the best TbFeCo single-layer films and also the uniaxial easy axis does not seem to be well established in these systems. The magnetostriction improvement in TbFeIFeCo compared to TbFelFe multilayers is due to the (extra) magnetostrictive contribution of the FeCo layers. which exhibit a saturation magnetostriction exceeding 100 x 10-6 (Quandt and Ludwig 1997; Betz 1997). In fig. 40a, the saturation magnetoelastic coupling coefficient b; = (3/2)b y ,2 of an annealed (Tb4oFe6o)/(FesoCoso) multilayer is compared with that of single films of Tb40Fe60 (with sputtering conditions optimised for attaining the large saturated b s value of about 41 MPa. see Quandt 1997) and of (Sm.Fe.B) (optimised for low-field performance. at the cost of the saturated value. which for the (Sm.Fe.B) system can be doubled, for a Sm content of 36.8%. see Lim et al. 1998). In fig. 40b a comparison is presented between the magnetoelastic coupling coefficient bll of the same multilayer and values for some other multilayers:
MAGNETOELASTICITY IN NANOSCALE HETEROGENEOUS MAGNETIC MATERIALS
143
1.0 0.5
~
0.0 -0.5 (a)
-1.0 -0.8
-0.4
0.0
0.8
0.4
floR (T)
700 600
SOO .-..
-
"=
400
~
300
-«
200
A,
100 0 -0.8
-0.4
0 l10B (1)
0.4
(b)
0.8
Fig. 38. In-plane magnetisation (a) and magnetostriction (b) of a Terfecohan Tb(Feo.55COO.45>t.5 single layer and a TerfecohanJFe multilayer film. Definitions of the magnetostriction remanence (A.r) and the coercive field (AHe> are illustrated for the Terfecohan film. After Due et a1. (200la).
Sm(TbI SFeS2)/(Fe75C025), (TbDyFe)/(FeSiCuNbB) and (Tb33Fe67)/(FesoB20). Ludwig and Quandt (2000) reported the possibility to control the orientation of the magnetic easy axis by magnetic annealing and, thus, to enhance the magnetostriction in the considered direction (see figs 41(a, bj). A uniaxially anisotropic multilayer TbFelFe can also be created by depositing under a magnetic field H def (Le Gall et al. 2(00). Typical field dependence of the magnetoelastic coefficient bY' of an isotropic TbFelFe multilayer deposited without a bias field (H dep = 0) is presented in fig. 42a. The symmetry of b" and as. with almost the same saturated values (""-"2 MPa) demonstrates the quasi-isotropic character of the magnetoelastic properties of the multilayer (see also eq. (13) in section 3). When deposited under a bias field in the x-direction (H dx = H dep I- 0), the multilayer presents the original magnetic (fig. 43) and magnetoelastic (fig. 42b) behaviour associated with strong uniaxial anisotropy. After saturation along the easy axis, the moments remain aligned along that axis, in a single domain, when the applied field H" is lowered down to zero (MriMs = 1). In reverse fields, the magnetisation is switched in a short field range.
N.H. DUC and P.E. BROMMER
144
200
(8)
IIIl
=~
-
0
-
-
'T'
c
-e
.Q
10
0
20 -0.05
\ -Tbo.JeG.6(4.5 om/Fe(6.5 om) -200 \ -Tbo.J~.6
~
...
-
0.00
0.05
-400 0.15
0.10
JJoH (T) 600
(b) _
-10
ClIl
=-
~
400
200
II 0
0
.Q
10
20 -0.05
--
b
TbFe(7nm)/FeCo(8nm)
-
-e
l-200
0.00
0.05
0.10
-400 0.15
JJeH (T) Fig. 39. Magnetostrictive hysteresis loops of a TbFelFe (a), compared with a TbFe single film, and of a TbFelFeCo (b) multilayer. After Quandt and Ludwig (1997).
Apparently, 'in field' depositing reduces also slightly the coercivity (from 6 mT to 4 mT). High-amplitude flexural and torsional-oscillation modes were observed for these films. In the absence of a long-range anisotropy in amorphous TbFeCo layers, along with negligible magneto-crystalline anisotropy in FeCo layers, the coercivity (between 4.5 mT and 7 mT) of MSMM is usually determined by stress-induced anisotropy. Chopra et a1. (2000) showed that the magnetoelastic constraints at the TbFeIFeCo interfaces (due to different values of the magnetostriction in adjacent layers) lead to biaxial stresses. They developed a model, which expresses the magnetic coercivity as follows (26)
Here, E is Young's modulus of TbFeCo.
MAGNETOELASTICITY IN NANOSCALE HETEROGENEOUS MAGNETIC MATERIALS
145
30 (7nn~/'''~
I
25 III Q.
~ ,Q-
10 5 (a)
0
•
~
.4)
20
IJaH.
4D
8D
8D
mT
45
:.
-15
,Q=
-10
:IE
o
20
IJoH-
40
60
mT
Fig. 40. A comparison of the magnetoelastic coupling coefficient of an annealed (Th40Fe60)/(FesOCoso) multilayer with the optimised Th40Fe60. SmFeB (a) and (ThISFeS2)/(Fe7SCOZS), (ThDyFe)/(FeSiCuNbB), (Th33Fe67)/(FesoB20) (b) ones. After Ludwig and Quandt (2000).
This model succeeds in predicting the correct order of magnitude of the experimental coercivity values in these MSMM. In attempts to improve the soft-magnetic properties of the highly magnetostrictive nanocrystalline layers (see above, and see section 5.l) by preparing MSMM's with soft magnetic interlayers, Farber and Kronmuller (2000b) have studied ThDyFelFinemet multilayers (Finemet is a nanocrystalline FeSiBNbCu soft magnetic alloy; see Herzer 1997). After production, the deposited ThDyFe as well as the Finemet are amorphous. Subsequent annealing leads to relaxation of the amorphous phases and to crystallisation in the (soft magnetic) Finemet layers. The properties of the multilayer can be described by eqs (25a-25c), i.e. by the mixture rule of two perfectly coupled components. Applying eq. (25c), the contribution of the individual layers to the magnetoelastic coupling
146
N.H. DUC and P.E. BROMMER
0.12....--.....---,----.--,.--.........--,----....------,
II
..
0.06
0.00 ~-------~
.L
41
0.1
Q.2
ClO6 r-----.---..-----.---~-__.-:--_,._---.,....---...,
aea II
(b)
.L
-4.1
0.1
Q.2
Fig. 41. Magnetostriction loops (parallel and perpendicular measurement direction) of an as-deposited (open symbols) and a magnetic-field annealed TbO.4FeO.6(7 nm)lFeo.5COO.5(9 om) multilayer (closed symbols): (a) annealing field aligned perpendicular to the long axis of the cantilever (parallel measurement direction), (b) annealing field aligned parallel to the long axis of the cantilever. Magnetostriction in arbitrary units, field in tesla. After Ludwig and Quandt (2000).
was deduced from their magnetoelastic data presented in fig. 44. Deviations from a linear behaviour are ascribed to the compensation of the magnetic moments. For these multilayers, the TbDyFe (amorphous Terfenol-D) contribution (b y ,2 = -15 to -18 MPa) and the Finemet contribution (b y •2 = 15 MPa) have opposite signs. whereas the Fe contribution (b y ,2 = 2 MPa) is small. with the same sign. For the bulk materials.
MAGNETOELASTICITY IN NANOSCALE HETEROGENEOUS MAGNETIC MATERIALS
147
(a)
Htl
o IV
a..
~ .1
.....
':a
-2 -3
y& ~x
(IbFC'JFe)x40 ~=O'
as-sput.
Ht,
-4
2
1
tJ;;• a.. X
8"
fL,
.
...
••• •
~:r
•"0•i .
'
.'.Ii
-2
. .-
~.
. .:
-3
iI
~
..• "" '
.. 0 '
:
~
",
~.'
~
(IbFeJFe)x40
*
Hd• p 0 as-sput
.' -4 L---''''''-.......I_--'-_--L_........ _-Lo -so so ·100
. .
"
••
~ ~
". " ,,~~
",
---J
100
J.1oH (mT) Fig. 42. Magnetoelastic coefficient versus magnetic field applied parallel and perpendicular to the long axis of the cantilever (parallel measurement direction) of an as-sputtered TbFelFe multilayer deposited (a) without a de field (Hdep = 0) and (b) with Hdep #- O.After Le Gall et aI. (2000).
Farber and Kronmuller (2ooob) quote the b y •2 values -22 MPa. 6 MPa and -6 MPa for a-Terfenol-D, Fe and Finemet, respectively. As regards the temperature dependence of the magnetoelastic-coupling coefficient. multilayers show a great advantage with respect to single films. Measurements by Ludwig and Quandt (2000) are presented in fig. 45 for a (Tb40Fe60)/(FesoCoso) multilayer. Note that. upon increasing the temperature. the slope of the magnetoelastic loop as well as the coercive force remain relatively constant. whereas the saturation field and the saturation value of the magnetoelastic-coupling coefficient are reduced. At 225°C. the saturation magnetostriction is still 20% of that at room temperature.
148
N.H. Due and P.E. BROMMER
1.0 0.5
f
(TbFelFe)x40 Hdep :# 0
. ~:
~
.
as-spur,
IL,-+;': 0.0
Y
~.~
fiJ.
~~
-1.0P==::::::.._--'"··::..··-,.; -100
L.::::+. a,
o
-50
I
100
50
J1JI (mT) Fig. 43. Easy-axis and hard-axis hysteresis loops of an anisotropic. as-sputtered ThFelFe multilayer. deposited under a dc field (Hdep # 0). After Le Gall et al. (2000).
.-.. 20 =:I
=.. :; '-' :::::
.Q .-.. ~
J
0
15
,!::
\; 10 J
-
........
.............
+
'-' I
5 0 0.0
0.2
0.4
0.6
0.8
1.0
tsoj/tnrlc Fig. 44. Plot of the weighted magnetostriction. -(I + tsof!ltstric)bll' of (D) Terfenol-DlFe and ('il) Terfenol-DlFinemet multilayers, as a function of the thickness ratio. t",ftltstric. of the soft magnetic layers (Fe and Finemet, respectively) and the magnetostrictive ones (Terfenol-D), After Farber and Kronmiiller (2oooa. 2ooob).
The large magnetostrictive susceptibility in Tb-FeCo/FeCo multilayers and its technical character were reported and discussed in detail by Due et al. (2001a) in a study of Terfecohan/Fe and Terfecohan/(Feo.sCoo.s) multilayers. Like in magnetic hysteresis loops, there is a so-called magnetostriction remanence (Ar) and a coercive field J...Hc, where A = 0 in the magnetostrictive hysteresis loop (see definitions in fig. 38). Note that, experimentally, J... He is observed to be equal to M He. Due to this magnetostriction remanence, the possible change of the magnetostriction in (re)magnetising fields (i.e. in H > 0), 6A = AS - Ar. is smaller than that in demagnetising (reverse) fields (i.e. in H < 0), where
MAGNETOELASTICITY IN NANOSCALE HETEROGENEOUS MAGNETIC MATERIALS
25
50
149
75
Fig.45. Normalised magnetoelastic coupling coefficient of a Tb0.4Feo.6(7 nm)/Feo.5CoO.5(9 nm) multilayer. as a function of external field at different temperatures. After Ludwig and Quandt (2000).
/),.).., = )..,S - )..,(>.. H c) = )..,s. The low-field dependence of the magnetostrictive susceptibility is presented in figs 46(a, b) for the TerfecohanlFe and Terfecohan/(Feo.sCoo.s) multilayers, respectively. As can be seen from these figures, the field direction dependence mentioned above may not be so clear for the case of the as-deposited films (see curves I in figs 46(a, bj), but certainly becomes rather important for the annealed films (see curves 2 in figs 46(a, bj), For the annealed TerfecohanlFe multilayer, X>"II shows a maximum (of 1.3 x 10- 2 T-I) in low magnetising fields. A sharp and larger maximum (of 3.5 x 10- 2 T- 1) , however, is exhibited in demagnetising fields just above >..Hc. The as-deposited Terfecohan/(Feo.sCOO.s) multilayer shows even a rather small and broad magnetostrictive susceptibility maximum (X>"II.max = 0.7 x 10- 2 T- 1 only) in magnetising fields. In demagnetising fields, X>"II.max reaches a value of 5.0 x 10- 2 T- 1, which strongly exceeds that of 2.0 x 10-2 T- 1 required for the application in magnetostrictive devices (Du Tremolet de Lacheisserie 1993). This magnetostrictive susceptibility maximum in demagnetising fields could be considered as a good working point for the magnetostrictive films in MEMS. For the samples under investigation, the working point is at JLoH dc ~ 6 mT. By applying a bias magnetic field at this magnetic field, a magnetostriction change /),.).., ~ 10- 4 can be obtained in an a.c. field of the magnitude of 2 mT. Attempts to reduce JLoHc also imply the possibility to shift the working point to lower fields. For this purpose, Quandt and Ludwig (1999) have prepared TbFeJFeCoBSi multilayers. It was shown that the FeCoBSi layers have improved the magnetic softness of the multilayer. Due (2002) and co-workers have succeeded to prepare Terfecohan/(Yo.zfeo.s) multilayers with JLoH c = 0.5 mT (see fig. 47b). Initially, this multilayer consists of amorphous TbFeCo layers and not-well crystallised (Y, Fe) layers. In this state, the multilayer exhibits already a soft magnetic and magnetostrictive character with a coercivity JLoH c = 3 mT and a parallel magnetostrictivesusceptibility X>"II.max = 3.8 x 10-2 T- 1 (see
N.H. DUC and P.E.BROMMER
150
0.04 9 9
(8) 0.03
1.-
0.02
~ 0.01 0
0 -0.1
-0.05
0.05
0 I
" "
~
0.02
I
j ~ "" 2 .'"
.'
0.03
0.1
": '":
(b)
0.04
1.-
0.05
-, " "
':" :'" " " " " ~
"
" ""
::
q q;
~~4
o.<;fl',0 t
0.01 ~
0.00 -0.1
-0.05
-:e%
~
Q:.
0 Il DU (I)
--
0.05
0.1
Fig, 46. Low-field dependence of the absolute value of the parallel magnetostrictive susceptibility for TerfecohanlFe (a) and Terfecohan/(Feo.5COO.5) (b) multilayers: curves (I) as-deposited, curves (2) annealed multilayers. After Due et al. (200la).
figs 47 and 48(a. bj), This magnetostrictive softness has been strongly improved by heat treatments: ll-oHc = 0.3 mT and X}"II = 13 x to- 2 T- 1 in a field of 1.8 mT (fig. 48(a. bj). These novel properties are associated with the development of a nanostructure in the (Y. Fe) layers. As indicated by the XRD results (fig. 49), the as-deposited 'Ierfecohan/(Y, Fe) multilayer shows no clear Bragg peaks. but only a rather broad contribution located around 20 = 45° (i.e. the (110) reflection of bee-Fe). Along with the results of the Mossbauer studies (see fig, 50). this could imply that the (Y, Fe) layers are amorphous, The (Ito) Bragg reflection of the bee-Fe structure is enhanced for the samples annealed at T A = 250°C. Finally, they are visible in the sample annealed at 350°C (fig. 49), This transformation from the initially not-well crystallised phase into the bee-phase in the (Y. Fe) layers is confirmed by the characteristic value of the hyperfine field (Bhf = 33 T) observed from the Mossbauer spectrum (see fig. SOc). Aside from the hE effect which is an interesting feature for designing resonant mechanical devices. MSMM show a GMR (hR) effect (Quandt and Ludwig 1999.2(00). Thus, as already introduced in section 3.3. the bending of a magnetostrictive bimorph
MAGNETOELASTICITY IN NANOSCALE HETEROGENEOUS MAGNETIC MATERIALS
lSI
Fig. 47. Magnetic hysteresis loops for Terfecohan/(YO.2FeO.g)multilayers: (a) as-deposited. (b) after annealing at 350°C. After Due (2002).
can be monitored by measuring the magnetoresistance. A comparison of the normalised magnetoresistance and the magnetostriction effect for an annealed (Tb4oFe60)/(FesoC050) multilayer is shown in fig. 51. The figure exhibits that both loops are nearly identical. This allows combining actuator and sensor functions at the same time. 5.3. Interface magnetostriction ofmultilayers
The magnetostriction of multilayers is found to change as the thickness t of the magnetic layer is changed (Zuberek et al. 1987. 1988; Awano et al. 1988; Dime and Denisson 1989; Nagi et al. 1988). These changes in the magnetoelastic properties have been attributed to magnetostrictive strains. which are localised at the interface. Such magnetostrictive effects are called "surface magnetostriction" (Szymczak et aI. 1988). Similar effects are observed for the surface magnetic anisotropy (Gradmann 1993). Surface and interface effects were already discussed in section 2.3. It is often claimed that the changes in elastic and magnetoelastic properties of multilayers are due to the presence
152
N.H. Due and P.E. BROMMER
200
ISO ,,~
-= '-"
'" .<
100
SO (a) 0
-IS
-10
-5
0
IlJl (mT)
5
10
IS
5
10
15
0.15
--
-'E-
(b) 2
0.10
:::::
..:
~
0.05
0.00 -15 -10
-5
o
J.LoH (ml) Fig. 48. Low field dependence of the parallel magnetostriction (a) and the magnetostrictive susceptibility (b) for Terfecohan/(Yo.zFeo.s) multilayers: (I) as-deposited, (2) annealed at 350°C. After Due (2002).
of interdiffusion layers. which are formed at the interfaces. Nowadays, however, one can fabricate multilayers, which have negligible interface diffusion. Nevertheless, their surface anisotropy and magnetostriction are considerable. Independent experimental evidence for the intrinsic character of the surface magnetoelastic coupling has been given by Sun and O'Handley (1991), who used the spin-polarisation of secondary electrons, detected from the asymmetric spin-orbit scattering, to monitor selectively and directly the surface magnetisation (see section 3.5). These measurements were performed using amorphous ribbons and therefore interdiffusion processes had no effect. Szymczak (1997, 1999) has stressed the possibility to distinguish between pure interface effects, i.e. surface magnetostriction, and the effects of an interface diffusion layer. Since magnetic anisotropy and magnetostriction have the same origin, the surface magnetostriction is expected to have an intrinsic character. In Szymczak's notation (Voigt
MAGNETOELASTICITY IN NANOSCALE HETEROGENEOUS MAGNETIC MATERIALS
153
~10)(Fe,CO)
--"-.a
T A =350°C
of
T A =250 °C
:I
•
'-'
-
As-dePCIsited
35
45
40
50
55
2 theta (degrees) Fig. 49. X-ray diffraction patterns of a Terfecohan/(Feo.85Coo.15) multilayer. After Due (2002).
Velocity (mm/s)
o
=
e
.-
1.00
(b)
Gf)
0
10
20
30
40
0
10
20
30
40
c.
1.02
';1
"--1 :il;zsJ ::1::2\1 +12
"":::l.
e
.&I
S
~
~
1.00
1.02
20
(c)
15 10 5 0 0
10
Fig. 50. Mossbauer spectra (CEMS) and hyperfine-field distributions of a Terfecohan/(YO.2Feo.8) multilayer: (a) the as-deposited film, (b) after annealing at 250°C and (c) 350°C. After Due (2002).
154
N.H. DUC and P.E. BROMMER
1.0
II
-
o.s
-0-
"IIII'*" "
iCI!
~1i'Y"'idiai
.<
is u 45 l.
-1..0 -1GD
-75
-25
2i
0
PaH..
50
75
100
mT
Fig. 5 I. Comparison between the normalised magnetostriction and the normalised magnetoresistance of a ThOAFeo.6(8 nm)lFeO.5CoO.5(9 nm) multilayer annealed at 250°C. After Ludwig and Quandt (2000).
notation), it means that the magnetoelastic tensor [M] in artificially structured materials should consist of two parts: (27) where [M]bulk describes the bulk magnetoelastic coupling and where [M]surf describes surface magnetoelastic coupling and/or the contribution to [M] due to the interdiffusion layers. This relation should be compared with the relation in our notation, discussed in section 2: BelT = B bu1k + 2b surfjt, where the factor 2 is put in, because a layer has two surfaces. The components Mil and MI2 are related to V· 2 = -By·2jc Y and A£,2 = - Bd j c", respectively, in such a way that, for (bulk) isotropic material, one has MIl = As and the 'isotropy condition' Mil = -2MI2. The intrinsic surface magnetoelastic tensor is expected to be strongly anisotropic, while magnetoelastic interactions in interdiffusion layers lead usually to an isotropic form of [M]surf. Information about the symmetry of [M]surf, therefore, is of great importance to determine the intrinsic nature of magnetic interactions in the interfaces. As an example, we give here some results obtained by Szymczak and co-workers (see e.g. Szymczak 1997) applying the SMFMR technique (see section 3.4). Experimental data obtained for several Ni-based multilayers are presented in fig. 52(a, b). The fitting parameters for the magnetoelastic tensor components Mij are listed in table 3. In isotropic approximation, (Mil )bulk should be equal to the magnetostriction constant for polycrystalline material As. The difference between As (= -35 X JO-6) of polycrystalline nickel and (Mil )bulk was attributed, for Ni/Ti, with (Mldbulk = -45 x 10- 6 , to the texture of the magnetic sublayers, and for Ni/Pb, with (Mil )bulk = -19.5 X JO- 6, to the strong reduction of the magnetisation (Zuberek et aJ. 1991). The strongest surface-tensor anisotropy, i.e. the ratio (MI dsurf/(MI2)surf, was observed for Nil Ag multilayers. This is taken as clear evidence for the existence of intrinsic surface magnetostriction. The SMFMR technique has also applied to study the magnetostriction in Co-based multilayers (see Szymczak 1997). In these cases,
MAGNETOELASTICITY IN NANOSCALE HETEROGENEOUS MAGNETIC MATERIALS
155
20-r--------------,
....
-..
~
-
*
.-
I~ 0
-•
' -'
i
~
MIJ
-20- - ;
.--.
!'P--0.1
0.0
--'&
Jt--
(a)
0.2
0.4
0.3
0.5
l/tNl (am") 15
.,=
-..
0
'-'
i i
-1
-3
-4
, ""
""
,At
.- .0.0
.- .-"
*" " ""
-." "
.
"
.-" .-.-
.- "
.-
...."
.- "
.-"
"...... Mil (b)
0.1
0.2
l/tNl (nm-
0.3 I
)
Fig. 52. Dependence of the magnetoelastic tensor components Mil and MI2 on the inverse Ni layer thickness for several Ni-based multilayers. (a) (.&) NiIPb and (*) NilAg. (b) (.&) NilTi and (*) NilC multilayers. After Szymczak (1997) and refs therein.
however, no indication of surface magnetoelastic coupling was observed (e.g. in Co/Ag multilayers). GdlFe multilayers fabricated by rf-sputterring exhibit clearly a magnetostriction contribution due to interdiffusion layers. Samples deposited by de-sputtering, however, have sharp interfaces. The variation of their effective (saturation) magnetostriction O'eff) is described as a function of the inverse of the iron sublayer thickness, tFe -I, (see fig. 53). In this case, the magnitude of the bulk (Abulk) and surface magnetostriction (Asurf) can also be deduced assuming the following relation: Aeff
= Abulk + 2tie' Asurf.
(28)
156
N.H. DUC and P.E. BROMMER TABLE 3 Values of M II and M 12 tensor components and their ratio MIl / M 12 for several multi layers Samples
Bulk Mil
Niffi NilC NilAg NilPb
Surface
MI2
(10-6 )
(10- 6)
-45 -32 -36 -19.5
21 17 17 8
MII/MI2
Mil
MI2
(10- 6 )
(10- 6 )
67 SI
-31 -45 -7 -6
-2.14 -1.88 -2.12 -2.44
II
14
MII/MI2
-2.16 -I.S0 -1.57 -2.33
After Szymczak (1997).
-1,---------------, GdlFe multilayers -2
,,
,,
-5--
, ,,
, ,,
,
, ,,
,
"
,•
,"
* 0.0
0.1
0.2
0.3
0.4
0.5
lItF e (nm") Fig. 53. Magnetostriction as a function of the inverse Fe-layer thickness for GdlFe multilayers. After Szymczak (1997) and refs therein.
It turns out that (= 6.5 x
10-6 )
Asurf
(= 10.2 x 10- 6 ) exceeds the observed bulk magnetostriction Abulk
(Szumiata et al. 1993; Zuberek et al. 1995). An excellent agreement with relation (28) was obtained for the magnetostriction data of FeCo/Au multilayers (fig. 54) (Zuberek et al. 2000), from which the values 6 6 Abulk = 57.8 x 10- and Asurf = -18.2 x 10- were deduced. Note that the obtained value of Abulk corresponds to that of polycrystalline FesoCoso alloys (Bozorth 1951). Lafford et al. (1995) reported a similar analysis for the magnetostriction of C032Pd6S!Ag multilayers (see fig. 55). Unfortunately, since only one magnetoelastic tensor component (or saturation magnetostriction) is determined, definite conclusions cannot be drawn from such experiments. Investigations on SmFeBffbFeB multilayers have shown that strain and stress are transferred effectively at the interface (Shima et al. 1997). In these SmFeBffbFeB multilayers, the thickness of the layers was varied, and it was found that the magnetostriction is sensitively affected by Young's modulus, the Poisson ratio and the thickness of the constituent layers.
MAGNETOELASTICITY IN NANOSCALE HETEROGENEOUS MAGNETIC MATERIALS
157
FeCo/Au multilayers
•
•
• 35+-~-r----.....,.---r-~-,--""'---r-..---i
0.1
0.0
0.3
0.2
0.8
0.5
0.4
Fig. 54. Magnetostriction as a function of the inverse Fe-layer thickness for FeCoiAu multilayers. After Zuberek et al. (2000).
0
C0 32Pd68!'Ag multilayers
...... 'f
-
= .... a~ )
.&JO
-
!
.1000
·1500
·2000 0
2
4
,
10
12
14
teoN (om) Fig. 55. Aeff· tCoPd as a function of tCoPd for CoPdlAg multilayers. After Szymczak (1999) and refs therein.
The changes in magnetic and magnetostrictive properties of multilayers which are due to the presence of interdiffusion layers formed at the interfaces, were studied by Quandt et al. (I 997a, 1997b) and Due et a1. (2000<1), for TbFeCoIFe multilayers. In these multilayers, the amorphous state was formed in the giant magnetostrictive TbFeColayers, while the Fe-layers were crystallised. This is confirmed by XRD investigations. Annealing at temperatures T A from 150°C to 350°C made the interface spacers to expand and the core of the individual layers to shrink. Assuming the same value of magnetisation for the TbFeCo-layers and the TbFeCoIFe interfaces, Due et al. (2000d) have estimated the thickness of the extended interface spacer due to the interdiffusion (t x ) by applying expression (25a) in the following form: (M TbFeCo/Fe ) =
MFe(tFe - tx) - MThFeCo(tThFeCo
+ tTbFeCo tFe
+ tx)
.
(29)
158
N.H. Due and P.E. BROMMER
rI'
... ..-;~~
1.......... ..
- .....
"' :.~
..
. .te':,....
"'''' ...
E
:r:"
.
..., ...
•
-
~
>
.\
I I I I I I
300
200
;...
-.
T crysl (single: film)
1:
~100
I I I
700
750
800 T.[K]
850
Fig. 56. The coercive field of different Terfenol-DlFe multi layers with Terfenollayer thickness Istric = 10 nm, and Fe layer thickness: Isoft = 2 nm (e), 6 nm (TSB) and 8 nm (.). The dashed line shows the crystallisation temperature of a 2-/Lm thick Terfenol-D film. After Farber and Kronmiiller (2000a, 2000b).
At T A = 350°C, Ix was found to be about 1 nm. Auger electron spectroscopy (AES) depth profiling showed that the interdiffusion was not found after annealing at 280°C, but that the layer structure was almost destroyed after annealing at 480°C (Quandt et al. 1997b). Annealing at temperatures above 820 K destroys the multilayer structure and then the film loses its soft-magnetic character. This is clearly seen from the microstructure graph illustrated in fig. 56. Annealing at medium temperature leads to an increase of the magnetostrictive susceptibility and a decrease of the saturation field (as well as coercive field), while annealing at higher temperatures usually reduces dramatically saturation magnetisation and then the saturation magnetostriction due to the expansion of the interface spacers. This is due to the formation of the so-called 'magnetostriction dead layers' (Farber and Kronmiiller 2000a). In case, however, a perpendicular magnetic anisotropy is created, associated with the modification of the structure and/or composition in the interface, the magnetostriction can be enhanced slightly. This phenomenon is observed in TbFeCoIFe multilayers annealed at 350°C (Duc et al. 2000d).
6. Magnetoelasticity of rare-earth superlattices Magnetic rare-earth superlattices RIM (M = Y, Lu) behave in a variety of ways. Two remarkable features in these artificial structures are: (i) helical magnetic order is found to
MAGNETOELASTICITY IN NANOSCALE HETEROGENEOUS MAGNETIC MATERIALS
159
propagate through non-magnetic layers and (ii) different magnetic phases are identified in the superlattices when comparing to bulk elements. The first feature has been explained in the framework of the RKKY interactions through a spin density wave and the discreteness of the interleaving material, which produces an increase of the magnetic period. The strain induced in the crystalline structure by the mismatch between layers of different elements was thought to be responsible for the second magnetic feature. The strain can couple to the magnetisation either by modifying the indirect exchange as was suggested to explain the suppression of the conical c-axis ferromagnetic phase transition in ErfY (Borchers et al. 1991), or by altering the energy balance between the exchange and magnetoelastic contributions. The latter mechanism accounts for magnetic changes in Dy-based supersublattices. Bulk Dy has a ferro-helix first-order transition at 85 K. It is suppressed or enhanced up to 100% depending on whether the Dy lattice was expanded (in DylY) (Erwin et al. 1987) or compressed (in DylLu) (Beach et al. 1993), respectively. O'Donovan et al. (1998) performed low-temperature X-ray measurements on a DylLu superlattice and found that the spontaneous ferromagnetic transition is accomplished by (continuous) formation of orthorhombic domains which preserve the area of the unit cell in the basal plane. The importance of epitaxial clamping in this system was emphasized. Similarly, the c-axis cone phase was observed to be suppressed in HolY (Jehan et al. 1993), while ferromagnetic order existed below 30 K in HolLu superlattices with less than 20 Ho-atomic planes (Swaddling et al. 1992). As regards the stress due to the misfit of lattice parameters, magnetoelastic studies of superlattices were carried out by Ciria et al. (1995), Del Moral et al. (1996, 1998) and Amaudas et al. (1996), applying a low-temperature cantilever technique. Their results have elucidated the role of epitaxial strains. The magnetoelastic coefficient By·2 (corresponding to the distortion of the cylindrical symmetry of the superlattice basal plane; see section 2, eq. (9» was determined from the magnetoelastic stress measurements (fig. 57). The thermal variation of BY measured in a field of 12 T is plotted in fig. 58 for the {H06fY6}100 and the {H0311Lu 19 }50superlattices. (The subscripts denote the number of atomic planes per layer, and the number oflayers in the superlattice, respectively. Alternatively: [H031 /Lu 19] x 50.) The BY values for the {H06/Y61100 sample are much larger than those for bulk Ho. Moreover, its thermal variation deviates from Callen and Callen's law of the cubic power variation of the reduced magnetisation (m 3 ) at low temperature for bulk rare earths. For the HolLu superlattices with thick Ho and thin Lu layers (e.g. {H03t1LuI9}) the BY(T) variation approaches that of bulk Ho at high temperatures, but below 50 K it shows a deviation. This was attributed to an opposite-sign surface magnetostriction which scales as m4 at low temperatures and as m 2 at high temperatures. At low temperatures, BY (T) is simply expressed as (30) with BVol Y (0) = + 1.43 GPa and B~urf(O) = -1.38 GPa. The surface magnetostriction is masked in {H06/Y6} I()() due to the large epitaxial effect. Magnetoelastic stress isotherms (T a and (Tb of the {H040/Lu 15 }50 superlattice, clamped along the a and b axes of the hcp structure, respectively, and with the applied magnetic field along the easy b axis are presented in fig. 59 (Del Moral et al. 1998). The sudden
160
N.H. Due and P.E. BROMMER
o
0
l
9-
,
--4.05
1O
e
4
·z
~.I
o
o
2
4
6
•
10
12
Appliedfield (T) Fig. 57. Magnetoelastic stress isotherms for a (H06fY61100 superlattice: 0"0 and O"b correspond to clamping along Q- and b-superlaltice axes, respectively. Inset: magnetic phase diagram «0) from magnetoelastic stress and (e) from magnetisation measurements; FM- ferromagnetic. F - fan and H - helical phases). After Del Moral et al. (1996).
0.5
•• • • •
0.4
• • • •
'2 0.3
tS........ ~
...........
0.2
~o\ ;~.~
I:Q
0.1
0
~ ~.
•• ••
b.
{HoJ-lI6l!lO
•
..
., ~.
0
50 100 Temperature (K)
150
Fig. 58. Thermal variation of the magnetoelastic coupling parameter BY for the superIattices (H06fY61100 (e) and (H031 fLu 19150 (6), and for bulk Ho (dashed - - -). The dash-dotted and continuous lines are calculated (see main text). After Amaudas et al. (1996).
onset of stress and saturation at low temperatures is interpreted as a direct transition from a helical to a ferromagnetic state. As the temperature is raised, the strain increases less abruptly, indicating the transition to a fan structure. The variation of the magnetoelastic coupling coefficient BY (T), or MY (= 2(0' a - O'b» in the notation of Del Moral et al.
MAGNETOELASTICITY IN NANOSCALE HETEROGENEOUS MAGNETIC MATERIALS
161
o [Ho.JLuu1x.SO
~I
-0.1-
\
I"--"~-.:~=:::====~1.cac: ::
fJ .e
110<
---------==
IlOK
~ r,-------------1OK
-0.2
0
-
m~~==========o4OK
~
eel
Q..
0....-
.. II:)
-0.04 &oK
-0.08
o
246 8 W Applied field (T)
~
Fig. 59. Magnetoelastic stress isotherms for a IH040/Lu IS150 superlattice: Ua and Ub correspond to clamping along the Q- and b-superlattice axis, respectively. After Del Moral et al, (1998).
(1998), as a function of the number of Ho-atomic planes at T = 10K is presented in fig. 60 for {HonlLu15}50 superlattices. MY was expressed as: (31)
Here, the first term describes the volume (bulk) value of MY, the second term is the interface contribution and the third term is determined by the lattice misfit. It turned out from this analysis that M~ol = 0.275 GPa. M:Urf/(c/2) -7.0 GPa and D~ol = -116 GPa, where c is the c-axis lattice parameter for Ho. This leads to the following conclusions: (i) M~ol equals the bulk value for Ho, (ii) the interface magnetoelastic stress is very strong compared with the volume one. up to 6.4 times larger for nHo = 8 and of opposite sign and (iii) the misfit stress is of the same order of magnitude as the interface magnetoelastic stress. In the spirit of the description of eq. (30) and assuming 'single-ion' CEF contributions for the rare-earth ion, the expression for M~ol can be generalised as
=
(32)
Here, i 5/2 is the reduced Bessel function, and its argument L -I (m) is the inverse Langevin function (see Callen and Callen 1963, 1965). Using the values given above for
162
N.H. Due and P.E. BROMMER
---.
103
~
103
c,
0
[Hon I LUIS]
'-'
---.
X 50
>
1()2
::s
1()2 ~-. .c!
...J
3: ::s
C
::t
+0
0
::t 10'
c::
10 ' ---.
t
'-'
0
"tl
ci.
~
~:l
'-'
::E
10°
10° 102
10'
nHo
104
103
Fig. 60. The variation of the basal plane cylindrical symmetry breaking magnetoelastic stress, M[xp. at 10K and at an applied magnetic field of 12 T, multiplied by (nHo + nLu). as a function of nHo (where nHo and nLu are the number of atomic planes in the Ho and Lu blocks. respectively) for IHo,.f[..u I S I so superlattices. The line indicates the fitting by the theoretical model. After Del Moral et al. (1998).
0.7 0.6
---.0.5
{;.
~
p..
o
'-'
::E
X
HO,.ILu,~
{;.
HolOlLuu
•
Ho",ILu,~
Ho./'-u ,S
0.4
0.3 0.2 0.1 O'--_.l-_-'--_-'--_...J-_~_
o
20
40
60
80
100
......- - L . . - - - J 120 140
Temperature (K) Fig. 61. The variation with temperature of the magnetoelastic stress, MY (IZ T) multiplied by (nHo + nLu)/nHo for IHolIlLuls lso superlattices. The lines are obtained by adapting reduced-magnetisation power laws. see Del Moral et al. (1998).
M~ol' M:urr/ (c / 2) and D~ol' and taking ex = 4 below a certain temperature and ex = 2 above that temperature, the fitting obtained for {HolIlLuI5}s0 superlattices with n = nHo = 14, 30,40 and 45 (fig. 61) is reasonably satisfactory. This, once more, confirms the relevance of the interfacial stress contribution to the magnetoelastic stress. In addition, it does suggest strongly that both volume and interface magnetoelastic coupling originate from single-ion crystal-field terms. Using X-ray spectrometry, De la Fuente et aL (1999) measured the thermal dependence of the a and c lattice parameters in a {Er3ZlLu IO}40 superlattice. Again, strong single-ion CEF contributions, originating from the ErlLu interfaces, were observed in the volume and tetragonal distortions. Their analysis reveals also important contributions caused by epitaxial misfit.
MAGNETOELASTICITY IN NANOSCALE HETEROGENEOUS MAGNETIC MATERIALS
163
7. Magnetostriction of R·T sandwich films Sandwich films of the type RTIR'TIRT made by stacking coupled layers with typical thicknesses of 100 nm have been intensively studied in the last decade (Dieny et al. 1990, 1991a, 1991b; Givord et al. 1993, 1996; Wiichner et al. 1995). Because properties such as magnetisation or anisotropy differ from one layer to the next, the reversal of the magnetisation occurs at a different value of the coercive field for each layer. When the reversal takes place in a given layer but not in the adjacent one, a domain wall will be formed at the interface between the layers, in order to minimise the exchange energy. Such a domain wall has the particular feature of extending over the whole film surface and therefore is referred to as an extended domain wall (EDW). In these systems, the magnetostriction, which is fundamentally different from that observed in the multilayers discussed in the preceding section, is associated with the creation of this domain wall. Magnetostriction associated with domain wall formation has been known for a long time as being due to the progressive rotation of magnetic moments making up the domain wall. Normally, this effect is small since the volume occupied by the domain wall is always quite small. In the systems with EDWs, however, the domain wall can occupy an extremely large fraction of the total volume of the sample. The effects ofEDW formation were investigated on sandwiches consisting of Nd-CofIbColNd-Co (system 1) and Tb-Co/Nd-Co/Tb-Co (system 2), in which a well defined easy axis was created by annealing at 150aC in a field of 2 T. The Tb magnetic moment is dominant in the Tb-Co layers at room temperature (Givord et al. 1996; Betz 1997). In order to better understand the magnetisation process, the coupling between one pair of layers was suppressed by a thin oxide layer at the interface. The configuration of magnetisation and of the magnetic moments in zero-magnetic field is illustrated in fig. 62a for the sandwich system 2 (layer thicknesses 57/67/57 nm). The magnetisation loop at room temperature is shown in fig. 63. Starting from the high-field state, where the magnetisation of the system is well saturated in the applied-field direction, we see that the Co moments between layers are antiparallelly coupled and an EDW is formed at the coupled interface (fig. 62b). As the field decreases, a (positive) critical field (of 8.5 mT) is reached, where the EDW at the Nd-CofIb-Co coupled interface is suppressed by the reversal of the moment in the Nd-Co layer (fig. 62c). Note that magnetisation reversal in the (coupled) Tb-CO layer is prohibited by the large coercivity (associated with the sperimagnetic Tb moments). The reversal of the uncoupled TbCo layer occurs at -46 mT, and, finally, for the coupled TbCo at a higher field of -96 mT due to the interlayer Co-Co exchange coupling and the (re)creation of the EDW (fig. 62(d, ej). The magnetostriction is shown in fig. 64. While the high-field magnetostriction exhibits a behaviour similar to that observed in single layer Tb-Co films, the low-field magnetostriction measured along the easy axis shows a rather complex field dependence with magnetostriction anomalies and, in particular, extremely large magnetostrictive susceptibilities. In the Nd-CofIb-ColNdCo sandwich system, a magnetostrictive susceptibility (ob/o#LoR) of 556 MPa/f was observed even at #LoR = 2 mT (Betz 1997). This field dependence can be understood on the basis of the magnetisation process depicted above. At saturation, the magnetostriction (which can be either positive or negative) is maximum. As the field is reduced, the magnetostriction decreases as the EDW becomes larger (and the Tb sperimagnetic cone
164
N.H. DUC and P.E. BROMMER
(a)
magnetic moment
zero-field un-coupled interface
Tb ~
Nd coupled interface
~
Tb
........ Co • ........ Co • ........ Co •
, '..•.
~.',
''''''''~
'.n ..·.·.:. _
.~.
"
,-'.t.
magnetisation
.> ••. ,,,,..:.,-- .•_."'"
•
.-
Tb-Co Nd-Co Tb-Co
(b)
positive high-field
Tb - -•• +-- Co
- . Tb-Co
Nd • ........ Co EDW-.j{~1~UF.~;~~ Tb • +-- Co
(c) positive low-field
Tb ..,
~,
Nd
+-- Co
• +-- Co
Tb Nd
•
+-- Co
• +--
Tb
(e)
negative high-field
Tb
-. Tb-Co
•
Nd-Co
-. Tb-Co
.-
........ Co
•
•
• " " ',.... -<~
Co
••- - ........ Co
+-- Co
Nd.
,I.'r. ~
Tb·
~tl{~.~);~
.,;~u..:.'f'1.:
~:1:"""-~)J~t·:~,,c;,··~
• • _" _~!';llr:<61'",
........ Co
Nd-Co
- . Tb-Co
Co
;..-"
•
Tb
(d) negative low-field
• +-..
•
',~,"
Tb-Co
.,
Nd-Co
-.
Tb-Co
. - Tb-Co •
Nd-Co ••;lI;'!!V":(R~.".~
. - Tb-Co
Fig. 62. Configuration of magnetisation and magnetic moment in the sandwich TbCoINdCofIbCo film in zero magnetic field (a) and during the (de)magnetisation processes (b-e).
MAGNETOELASTIClTY IN NANOSCALE HETEROGENEOUS MAGNETIC MATERIALS
165
0.015
Tb-Co/Nd-Co/Tb·Co
300K
0.010
......
N
eu
':3
e
0.005 0.000
II)
-
:E
-0.005 -0.010 -0.0 15
o
·0.11
- 0.2
~H
0.2
0.1
(T)
Fig. 63. Magnetisation versus applied field measured on the sandwich Tb-CoINd-CoITb-Co system at 300 K. After Givord et aI. (1995).
0.0
IS
Tb·Co/Nd·Cofl·b-Co
300K
hord 8xl.
...... -0.5
"'
0..
:::E
m -1.0
-1.5
·0.3
- 0.15
0 0.15 lloH (T)
0.3
Fig. 64. Magnetostriction versus applied field measured on the sandwich lb-CoINd-CoITb-Co system at 300 K. After Givord et aI. (1995).
opens up a little bit). At around 8.5 mT, the EDW is destroyed. All Tb moments contribute now to the magnetostriction, and thus a large change is observed. When the external field decreases and changes its direction, the cone of Tb moments opens up further, leading to the observed decrease of the magnetostriction. At the coercive field for reversal of the magnetisation in the uncoupled TbCo layer (-46 mT), a discontinuity in the magnetostriction takes place, since these Tb moments become more aligned along the applied field. Further variation of the field opens the cone in the coupled TbCo layer still more (evidently exceeding the closing of the cone in the uncoupled layer). Finally, at -95 mT the EDW is re-created with a sudden increase of the disorder in the magnetic
166
N.H. Due and P.E. BROMMER
0.4
(a)
0.2 (25nm TbFei 8nm FeCoBSI)
0.0 t---------i+t--------~ -0.2
-0.4
-0.6
·6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.4
0.6
(b)
-4
-2 O~-----__1f_-----,.tt_-~+_----__r":I
2 4
81....--..._.L.-......._.L.--..._......~_.L____'__....L..___'___' -0.2 0.2 -0.4 -0.6
Fig. 65. Magnetisation and magnetostriction versus applied field measured on a TbFe(25 nrn)/FeCoBSi(8 nm) multilayer. After Quandt and Ludwig (1999).
configuration giving rise to a large transition in the magnetostriction. Still further increase of the field does narrow the EDW and closes the Tb cone gradually, in both Tb-Co layers. Quandt and Ludwig (1999) studied the influence of domain wall formation on the magnetic and magnetostrictive behaviour of multilayers TbFelFeCoBSi(8 nm) with various
MAGNETOELASTICITY IN NANOSCALE HETEROGENEOUS MAGNETIC MATERIALS
167
700 600 500 ~ 400
= - 300 ~
«:
200 100
o -0.8
-0.4
o
0.4
0.8
Ii.H (1) Fig. 66. Magnetostriction hysteresis loops of a ThFeCo single-layer film and a FetrbFeCoIFe sandwich films. After Due et al, (200lc).
thickness of the TbFe-layer (see section 5.2). For a TbFe thickness of 25 nm, domain walls (EDW) can be formed at the interfaces. and the magnetisation process is comparable to that in the sandwich systems under consideration. In this case. the transition (rotation of the TbFe moments into the field direction) occurred in a rather wide field range (say. from 0.05 T to 0.3 T; fig. 65a). because of the high number of layers. which are not absolutely identical. Like above. the field dependence of the magnetostriction (fig. 65b) was explained in terms of the local orientation of the magnetisation vectors. For positive magnetostriction materials (b < 0). a magnetisation orientation parallel or antiparallel to the measurement direction results in a positive strain, while a perpendicular orientation leads to a negative strain. In low fields. the layers are still exchange coupled and thus the magnetostriction is similar to those of thinner layer thicknesses. When the (TbFe) magnetic moments are rotated into the field direction. the domain wall is formed, and some TbFe moments rotate out of the external field direction. The negative magnetostrictive susceptibility is associated with this process. At higher (parallel) fields, the domain wall width is reduced. and the (positive) magnetostriction is recovered. The sandwich system discussed above is a composite material. which gives evidence for the existence of the domain wall and of its influence on the magnetostriction. These systems are not optimised with respect to magnetostriction. Nevertheless. their high magnetostrictive susceptibility is interesting. For applications. it may be worthwhile to mention here (fig. 66) the magnetostriction data of a Fe(25 nm)!fbFeCo(5000 nm)/Fe(25 nm) sandwich (Due et al. 200lc). In comparison with the corresponding magnetostrictive TbFeCo single-layer film. the magnetic softness was strongly improved for this sandwich right after depositing. The (not so high: All = 180 x 10-6) saturation magnetostriction is already well developed at /LoR ~ 20 mT.
168
N.H. Due and P.E. BROMMER
8. Magnetostriction in nanocrystalline and granular magnetic materials Nanocrystalline materials obtained by controlled crystallisation of Fe-rich amorphous alloys are composed of crystalline grains embedded in a residual amorphous matrix. These materials belong to a wide class of heterogeneous structures, including organo-metallic complexes or metallic clusters deposited on graphite or build in polymers on a molecular scale (see e.g. Gubin et al. 2000; Koksharov et al. 2000), and composites consisting of nanoscale up to microscale grains embedded in either a metallic binder (see e.g. Herbst et al. 1997; Pinkerton et al. 1998) or in some resin or polymer (see e.g. Duenas and Carman 2000). Granular solids consisting of magnetic particles embedded in an immiscible medium have been intensively studied in the last decade, because of the interest of their physical properties as well as of their technological applications. Indeed, these materials exhibit novel phenomena such as superparamagnetism, giant magnetoresistance and giant magnetic coercivity (Chien 1991; Hernando et al. 1997; Due et al. 2001d and references therein). In this subsection we start by continuing, in a way, the discussion in section 4.3 on the attempts to control the nanocrystallisation process. There, attention was focused on the possibility to manipulate the magnetic anisotropy. In section 5.1, it was shown that the crystal growth can also be limited by the layer thickness in multilayer structures In the present section, we discuss in particular the magnetostrictive properties. Originally, the excellent soft magnetic properties of these materials have been associated with the absence of magnetostriction in order to minimise magneto-elastic energies. In the amorphous state, however, the material reveals a (high) positive magnetostriction of As ~ +23 X 10-6 . In the nanocrystalline composite material, this positive magnetostriction is compensated by the negative magnetostriction of the crystalline material. The effective magnetostriction of nanocrystalline alloys at different stages of crystallisation is illustrated in figs 67(a, b) for (Fe,Cu,Nb,Si,B) alloys (see Herzer 1997 and references therein). This effective magnetostriction Aeff is usually interpreted as the simple volume average of the positive contribution from the amorphous matrix (Aam) and the negative one from the grains (Acr) (Herzer 1991): (33) where p is the crystalline volume fraction. As an example, fig. 68 shows the decrease of Aeff with increasing crystalline volume fraction. Clearly, in order to attain near zero magnetostriction in nanocrystalline Fe-based alloys it is necessary to have a large crystalline volume fraction with negative magnetostriction. It was reported that Acr ~ -6 x 10-6 for a-Fe8oSi20 grains in the (Fe,Cu,Nb,Si,B) system and that Acr ~ -4 x 10-6 for a-Fe grains in the (Fe,Zr,B) system (Suzuki et al. 1991). Tejedor et al. (1998) report a change of sign of the magnetostriction upon annealing Fe 73.5 Cu I Nb3Si 16.5B6 ribbons. With respect to nanocrystalline Fe 73.5 Cu I Nb3Si 13.5B9 rapidly solidified ribbons, Chiriac et al. (1999) stressed the importance of the 'inheritance' of the short range order in the melt. Holzer et al. (1999) found that the low-temperature temperature dependence of the magnetostriction in such ribbons follows a Bloch T 3/ 2 law. See also the low-temperature studies of Skorvanek et al. (2000) on the crystalline-fraction
MAGNETOELASTICITY IN NANOSCALE HETEROGENEOUS MAGNETIC MATERIALS
-
30
I
-.e 0
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(a)
Fe73.5Cu1N~SixB22.S.x
as cast
\ : \ \ \ \
0
....III
-
annealed 1h at T.
,-:. :a--_I._, ... ··········'··0 \ . 20 \ :
C
15 'C
: : : :
Si = 16.5\ 0.13.5 at%
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.'
•
• l>..
'. e-....o'
Q)
C)
.,<>-
e :
10
0
c:
169
0
0·'
O.
-·- ___ e
-5
I.
700
600
500
400
0
Annealing Temperature,
T« (DC)
15
(b)
to I
-
0
T"""
o ./"'0-' o;
10 0
f/l
-e
C 0
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-.... Q)
I
I
SI+B(.\~)
o :18.5 0 20.5 • 22.5 0 23.5
,e,
I
"'0...
, I
bn.
5 6'
~=t-Fe·Cu,SixNb5.7B13
8'8-
I
III
0
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0
c:
~Fe84Nb789
b,'Q--
):::Fe-CUO_1Zr6-782.0
'<>
C)
m
::!
-5
0
5
10
Si-Content,
15 X
20
(at%)
Fig. 67. The saturation magnetostriction, AS. of Fe-Cu-Nb-Si-B alloys: (a) influence of the annealing temperature and (b) influence of the Si content in the nanocrystalline state. The figure includes the data for Fe-Nb-B (A.) and Fe-(Cu)-Zr-B (6) alloys. After Herzer (1997) and refs therein.
dependence of the magnetostriction of Nanoperm-like (Fe,Nb,B) alloys. Upon increasing the annealing temperature, and thus increasing the (nano)crystalline fraction, Chiriac et aI. (2000a, 2000b) observed a change of sign of the magnetostriction in nanocrystalline Fe90Hf7B3 ribbons. In a study of annealed nanocrystalline (Fe,Zr,Nb,B) melt-spun ribbons, Makino et aI. (2000) found minimal core losses in a Fes5.5Zr2Nb4BS.5 alloy, which exhibited zero nagnetostriction. In many cases, however, the above simple model did not fit the experimental results even though the changes in ).am with the evolution of crystallisation were considered (SlawskaWaniewska et aI. 1994; Herzer 1993). In this case, an additional surface contribution was introduced. Indeed, nanocrystals usually have a diameter of 10-15 nm and hence a
170
N.H. DUC and P.E. BROMMER <0
6
20
C 10 .Q
U
I '1:
0+----------=__._----1
c
Cl CIl
::i: -10 +-.....--.--.--.--..---,-~__r_~---l
0.0
0.2
0.4
0.6
0.8
1.0
Crystalline Fraction Fig. 68. Dependence of the saturation magnetostriction, As, on the fraction of the precipitated bee Fe-Si grains for samples annealed at different temperatures and times. After 1'warowski et al, (1995). TABLE 4 The fitted parameters (see text) of the saturation magnetostriction for several nanocrystalline alloys and multilayers Samples
FeSSZr7B6Cu2 alloys Fe73.SCul Nb3Sil3.sB9 alloys FelC multilayers FeCoiAu FelGd
Acr
Aam
(10- 6 )
(10- 6 )
AS(S/V) (10- 6 )
2.2 25
6.55 3.37
-4 -6 58.6 -6.5
AS
k
(10- 6 nm)
(10- 6 )
10.9 5.57 45.7 -18.2 I
12.1 -11.5
Refs
[1,2] [2,3,4] [5] [6] [2]
[I] Slawska-Waniewska et al. (1996), [2] Szymczak (1999), [3] Slawska-Waniewska et al, (1997), [4] Gutierrez et al, (1995), [5] Zuberek et al, (1994), [6] Zuberek et al. (2000).
large fraction of their atoms are surface atoms. Moreover, it was found from Mossbauer measurements that the Fes5Zr7B6Cu2 nanocrystalline sample, annealed at 540°C, consists of three components: crystalline, amorphous and interfacial phases with the volume fractions 52.5%, 31.3% and 16.2%, respectively (Slawska-Waniewska et a1. 1997). The hyperfine field Bhf is 33 T for the crystalline phase, distributes below 25 T for the amorphous phase, and ranges from 20 to 35 T for the interfacial phase. Assuming that the grains are spherical and 10 nm in diameter, the thickness of the interfacial layer was estimated to be about 0.6 nm. Taking into account the different contributions, the effective magnetostriction of the nanocrystalline materials has been approximated by Aeff = pAcr + (1 - p)(A am + kp)
+ p(3A surf )1R.
(34)
Here, the parameter k expresses the changes of the magnetostriction due to the change in composition of the residual amorphous matrix with the evolution of crystallisation. In fact, a linear approximation Aam(p) = Aam(0) + kp is applied. The last term describes the surface effects in which R is the effective radius of the grains, i.e, 3/ R is the surface to volume ratio for the spherical grains (SI V in table 4). Figure 69a shows the
MAGNETOELASTICITY IN NANOSCALE HETEROGENEOUS MAGNETIC MATERIALS
'9 0
..... ..!' l:
0
•
25
" ...
I
20
•
10
'1ii
5
~l:
0
III
-5
Ol
~
'9
(a)
...
15
ts 'i::
171
experimental
p," (b)
4
0
..... ..<." l:
0
ts 'i::
Ul
-2
0
-4
l: Ol
-6
Gi III
~
• 0
experimental
40 20 60 Crystalline Fraction p [ % ]
Fig.69. Saturation magnetostriction, AS, versus crystalline fraction, p. in (a) FeS9Zr7B4 and (b) FeSSZr7B6Cu2 nanocrystalline alloys. After Slawska-Waniewska et al. (1996).
magnetostriction for Fes9Zr7B4, observed by SMFMR (see section 3.4). In a first fitting attempt, Slawska-Waniewska et al. (1996) did apply eq. (34), with Aam(o) + kp replaced again by Aam (p), because the linear approximation mentioned above could not be applied. Actual Aam(p) values were estimated from magnetostriction data obtained on a series of amorphous Fe93-xZr7Bx alloys. Further deviations were ascribed to the 'snowflake-like' crystallites (with high SN values). Figure 69b shows the same attempt for FeS5Zr7B6CU2, where almost spherical grains with a diameter of 10 nm were observed. pm(p) values were now deduced from magnetostriction data obtained on amorphous Fe91-xZr7BxCu2 alloys. The indicated linear contribution of the 'surface term' was deduced then. Since for this series, a linear approximation for Aam(p) appears to work well, in later studies eq. (34) was applied (at the same time replacing the value Acr = -7 x 10-6 by the more common value for a-Fe grains Acr = -4 x 10-6 ) . Figure 70 shows the observed saturation magnetostriction of Fe73.5Cu,Nb3SiI3.5B9 nanocrystalline alloys as a function of the volume fraction of the crystalline phase p. Here, eq. (34) has been applied too. The fitted parameters used to describe the experimental data are listed in table 4. The positive value of k in the case of Fes5Zr7B6CU2 indicates that the magnetostriction of the amorphous phase increases with a decrease of Fe content. This is in agreement with the experimental results of Slawska-Waniewska et al. (1996) mentioned above. In the case of Fe73.5CU I Nb3Si I3.5B9, the negative value of k reflects the decrease of the magnetostriction of the residual, Band Nb enriched, amorphous matrix with increasing crystalline fraction. The important feature of the results discussed is the difference of
172
N.H. DUC and P.E. BROMMER
15
-,-,
'1/
0
.....
10
~
5
~
..................~"." =:~,
0
_·_~
•••••O·· _<;4·· · ~.O
a
•.... Q •••• 1
-5 0.0
0.2
0.4
0.6
0.8
1.0
crystalline fraction Fig. 70. Saturation magnetostriction, AS. versus nanocrystalline fraction in Fe73.SCul Nb3Sil3B9 alloys. The numbers 1.2.3 denote the different contributions according to eq. (34). After Szymczak (\999) and refs therein.
the signs for the bulk and surface magnetostriction. It seems to be a general rule as similar observations were found in multilayers and superlattices, see also sections 5 and 7. Notice, however, that Areas et a1. (1998) found that, at applying transverse fields to nanocrystalline Fe73.sSilS.5B7Nb3CUJ samples, for low fields the total elongation is negative whereas it shifts to positive values for increasing transverse applied fields. This behaviour was explained as a consequence of spatial fluctuations of the average magnetostriction, correlated in length to the domain width. Obviously, the problem of surface/interface magnetoelasticity requires further studies, in particular, magnetostriction measurements above the Curie temperature of the amorphous phase, where only the ferromagnetic grains should give a magnetic contribution, simplifying separation between bulk and surface effects. Alves et a1. (2000) have studied stress-induced anisotropy in Finemet- and Nanopermtype nanocrystalline materials, like Fe74.3Nb2.7CuISils.5B6.5 and Fes4Nb3.5Zr3.5BgCul, applying flash stress-annealing. In Finemet a strong transverse anisotropy was induced, for example 2600 J/m3 after annealing at 610°C for 30 sunder 400 MPa, higher than by field-annealing (about 10 J/m3 ) . These effects are assumed to be located within the grains in magneto-elastic form due to tensile back stress exerted by the amorphous phase. In Nanoperm type nanocrystalline alloys, the authors observed a low longitudinal anisotropy (around 20 J/m3 ) , in spite of a negative magnetostriction of the Fe crystallites (around -4.1 ppm). This observation was also interpreted by the correlation between the sign of the induced anisotropy and grain size due to the contribution of interface properties. The existence of the surface contribution to the effective magnetostriction of nanocrystalline alloys has been confirmed theoretically in terms of the dipolar model (Szumiata et al. 1999). These authors showed that, due to the limited radius of the nanopartides, additional magnetostrictive stresses are localised at the interfaces. The evaluation of the influence of the dipolar interaction on the magnetostriction in crystalline grains of perfect spherical shape surrounded by a magnetic environment of about 0.5 nm with either crystalline or amorphous structure has been calculated. A similar method was previously used to obtain the surface and volume anisotropy (Draaisma and de Jonge 1988) and to
MAGNETOELASTICITY IN NANOSCALE HETEROGENEOUS MAGNETIC MATERIALS
173
deduce the surface magnetostriction and the volume magnetostriction in ultrathin films (Szumiata et a1. 1993), and nanoparticles (Zuberek et a1. 1998). The effective magnetostriction of a system consisting of highly magnetostrictive spherical grains embedded in a non- (or low-)magnetostrictive matrix has been studied by Herbst et a1. (1997). In this case the magnetostriction of the system can be described as Aeff= Acr
p
1 - 1.25v
(1.l5-1.26v-0.2 Ip 2/ 3) ,
(35)
where v is the Poisson ratio for the low-magnetostriction component. This model gives a satisfactory description of the fill factor dependence of the effective magnetostriction observed on composites consisting of SmFe2 particles (obtained by ball milling) in an Al or Fe matrix. See also Pinkerton et a1. (1998), who reported on the trade-off between high magnetostriction and desirable mechanical properties (hardness, density). For hot-pressed SmFe2lFe, in an applied field of 1.9 T, the saturation magnetostriction varies from 100 ppm for mechanically robust high-density material, up to 900 ppm for low-density material. In an attempt to reduce the anisotropy, Pinkerton et a1. (1998) substituted Nd for Sm in meltspun Smt-xNdxFe2 ribbons, which are transformed into Sml-xNdxFe2lFe composites by (optimal) annealing. The intrinsic coercivity H ci of the melt-spun ribbons decreases from 2.0 kOe for SmFe2 to 0.5 kOe for Srno.5Ndo.5Fe2. As x increases from 0 to 0.5, A of the composites decreases roughly linearly with x from 430 to 80 ppm. Duenas and Carman (2000) have optimised the magnetostrictive properties of composites containing up to 50% (microscale) Terfenol-D grains in a non-metallic binder (epoxy). During preparation, the elongated grains are oriented in a magnetic field, and are thought to form a fiber-like structure. Such composites are durable and are easily machined or otherwise manufactured into complex shapes, but usually their magnetostrictive response is comparatively low. By choosing an optimal Terfenol-D volume fraction, related to the selected non-metallic matrix, a composite can be obtained of which the magnetostrictive response is comparable to that of Terfenol-D itself. Nan and Weng (1999) have developed a Green function method to determine selfconsistently the effective magnetostrictive properties of composites. The authors claim that their method, in principle, can be used to study the effects of material constants and microstructure, such as anisotropy, particle shape and orientation relative to the applied magnetic field. Armstrong (2000a, 2000b) calculated the nonlinear multiaxial magnetostriction versus applied magnetic-field curves of oriented Terfenol-D magnetostrictive particulate composites for very general conditions of magnetic field orientation, multiaxial applied stress, particulate volume fraction, and particulate aspect ratio. The applied curing field does preferentially align individual magnetic particles along easy magnetisation directions and promotes the formation of particle chains parallel to the field. Applying an optical cantilever method, Ohnuma et al. (1999) performed magnetostriction studies on the (Col-xFex)-AI-O granular system. They found a composition dependence of the magnetostriction which was almost the same as that of bulk Co-Fe alloys (Bozorth 1951), although somewhat smaller (see fig. 71). In fact, zero magnetostriction was found for as-deposited Fe-AI-O and (Coo.94Feo.06)-AI-O films, and, after annealing
174
N.H. DUC and P.E. BROMMER
100
Co-Fe (",,(from Bozorth) : ....... _.... . .~ '"
80
..r .=..
60
-e
40
'-'
I
.
I I
"..
-,
",
I
"
'
! 0----
""'"
20
·20 0.0
,,
0.2
0.4
0.6
0.8
1.0
Fig. 71. Composition dependence of the magnetostriction, A. of (Col_xFex )-AI-O soft magnetic films. After Ohnuma et al. (1999).
at 300°C. also for (CoO.92Feo.og)-AI-O. The latter composition exhibits optimum properties for use as core material of an inductor (see section 12). because it combines the zero magnetostriction with high resistivity (as the other films. about 200 /LQcm) and acceptable saturation magnetisation (induction about 1.2 T. somewhat lower than the other compositions) with a large anisotropy field (which vanishes for Fe-AI-O). The random anisotropy model describes the magnetostriction in amorphous alloys (Szymczak and Zuberek 1982. 1983). and explains also the suppression of the local magnetocrystalline anisotropy in nanocrystalline alloys (Herzer 1997). This model has also been adapted to the case of granular systems (Szymczak et al. 1999). Finally. the interaction between small metallic spheres is of the RKKY type. Its anisotropic part is thought to be responsible for the oscillations of the magnetic anisotropy in nanoscale magnetic films (Back et al. 1997). According to Szymczak et al. (1999). this anisotropic part should also contribute to the magnetostriction in heterogeneous magnetic systems. 9. Huge magnetostriction in perovskites In the preceding sections. magnetostriction has been associated mostly with the properties of rare-earth ions and 3d itinerant-electrons. In this section. we discuss the huge magnetostriction occurring in another kind of material. i.e. in perovskites and some related manganese oxides exhibiting colossal magnetoresistance. Although much experimental work has been performed on bulk samples. thin films of these ceramics can be produced by (pulsed) laser ablation deposition. Consequently. these materials are regarded as possible alternatives for the more conventional epitaxially grown thin films. Among the perovskite oxides. only manganites RI-xAxMn03 and cobaltates Rl-xAxC003 (R: trivalent rare-earth; A: divalent alkaline ion) show colossal magnetoresistance. The most attractive feature of their magnetic behaviour is the co-existence of metallic conductivity and ferromagnetism. Hole-doping (substituting A 2+ for R3+ ) in the parent compounds LaMn03 and LaCo03 creates mixed valence in Mn and Co
MAGNETOELASTICITY IN NANOSCALE HETEROGENEOUS MAGNETIC MATERIALS
175
•
-- t·s
-
b
)oC
0
'0 U
.....
lOll
Ol U
'§
....,
S
ISO
200
250 300 350 400 TEMPERATURE (K)
450
500
Fig. 72. Linear thermal expansion of Lao.6YO.07Cao.33Mn03' Inset: anomalous thermal expansion contribution (61/ l)p. After Ibarra et al. (1995).
ions (Mn3+, Co 3+ and Mn 4 + , Co4 + ) and produces a ferromagnetic metallic state for x ~ 0.25. Notice also that Mathieu et al. (2000) produced doping by adding monovalent K in Lao.96-yNdyKo.04Mn03. Doped manganites and cobaltates show not only colossal magnetoresistance but also various magnetic-field induced phenomena such as magnetic structural, ferromagnetic metal (FMM)-paramagnetic insulator (PMI) phase transitions, collapse of charge-ordered states under fields and many others. Extensive studies have revealed that the observed features can be attributed to double-exchange (DE) interactions (Zener 1951; De Gennes 1960), in competition with other mechanisms such as antiferromagnetic (AFM) superexchange, Jahn-Teller (JT) effect, charge-orbital ordering, etc. A detailed (spin-orbit coupling) model was presented by Feiner and Oles (2000). The magnetic properties of these doped perovskite manganites are reviewed by Ramirez (1997), Ibarra and de Teresa (1998), Coey et al. (1999) and Szymczak (2000). Alejandro et al. (2000) presented ESR-studies of the relation between the magnetic properties and IT-distortions. Calculations performed by Nakano et al. (2000) revealed that IT distortions work co-operatively to enhance the optical-response incoherence caused by orbital (eg ) fluctuations. First observations of large magnetostrictive effects in manganites have been reported in 1995 by Ibarra et al. (1995). The measurement was performed on doped LaO.60Y0.lJ7Cao.33Mn03 perovskite. Colossal magnetoresistance has been observed in this polycrystalline sample, where t::.RjR ~ 10000% just below T c (i.e. at 140 K, at B = 6 T; Jin et al. 1995). The thermal-expansion (fig. 72) shows an extra contribution (with respect to the phonon contribution) for temperatures above Tc (= 160 K, the temperature of the FMM-PMI transition) up to a temperature T» (~ 320 K). In this temperature range, T C < T < T p, a large negative volume magnetostriction (of order of 1.0 x 10- 3) was observed (see fig. 73), ascribed to the change from a charge localised PMI high-volume state to a FMM low-volume one, upon application of a magnetic field (or when the long-range magnetic order sets in). Similar effects were observed
176
N.H. DUC and P.E. BROMMER
a
3
§
0
J.
:i
lot
..... 'y•. I7C... H MDOl
,...,........... ~
e
---...;;;......
-3
' ...<,-,"
~-6
Cl
~
~'12 CS > -IS
~'-.
"'
·9
0
.................
~-
......--..~
_-- ....- ....---.,.
IS K 348.5 K 130K
200K
~
5 10 APPUED MAGNETIC FIElD H, (Teala)
170K IS
Fig. 73. Volume magnetostriction isotherms of Lao.6YO.07Cao.33Mn03 at selected temperatures. After Ibarra et aI. (1995) .
.
,--..,.--,.--,..-..,.--,.--.,
~
,......, l"l
-
b
~
~ :it
! s
<1
.
. SO
0
. . '.
100 T(K)
'
.-,.. , ....' .'
----_ .. -. ' 100 o
200
300
400
500
600
T(K) Fig. 74. Linear !hennal expansion of Gdo.5Sro.sMn03 in zero field and under applied fields of 6 T and 12 T. The dashed curve represents a fit of the high-temperature linear thermal expansion using a Griineisen law and a Debye temperature eD = 500 K. After Garcia-Landa et aI. (1998a. 1998b).
in Lao.62Tbo.o5Ca0.35Mn03 (De Teresa et al. 1996). Wang et al. (1998) ascribe the shift of the transition temperature upon applying a magnetic field, observed in La2/3Call3Mn03 and (Ndo.6ThO.4hj3SrII3Mn03, to magnetostrictive effects. Garcfa-Landa et al. (1998a, 1998b) studied the oxygen-isotope effect on the field-induced I-M transition in Pr2l3Ca1l3Mn03,and showed that the heavier isotope favours the insulating state. Hayashi et al. (200 1) observed the metamagnetic transition to the FMM state in pulsed fields up to 45 T in Ndo.45Sm0.55Mn03. Two different mechanism responsible for magnetostriction can be clarified: (i) in the PMI phase at T > Tc, the magnetostriction is isotropic 0"11 = A.d and gives rise to a volume distortion. This behaviour is related to the quenching of the charge localisation under the application of a magnetic field. (ii) In the FMM phase,
MAGNETOELASTICITY IN NANOSCALE HETEROGENEOUS MAGNETIC MATERIALS
177
20 0 -20
---
.s-
'f
<:
' -'
-40 -60 -80 -100 -120 -140 107 1()6
---eu c '-'
Q.
lOS 10" UP
(b)
IOZ
----T=80K --T=60K -T=10K
10 1 10° 0
4
2
6
8
12
10
J.1oH (T) 160
.!!---
140 120
10K (C)
s
E 100
60K
SO
SOX
~
60
100
40
200K
20 2
4
6
8
10
12
14
J.l.H (T) Fig. 7S. MagnetosJriction(a), magnetoresistance (b) and magnetisation (c) isotherms for G<1o.5 SrO.5 Mn03. After Garda-Landa et aI. (1998a. 1998b).
at T < Tc. the magnetostriction is anisotropic (AI = All - 1..1. '" 10-4) and typical in value and shape to that of a ferromagnetic 3d metal; its magnetovolume effect is negligible. The existence of Tv is also observed in Gdo.sSro.sMn03 (Garda-Landa et aI. 1998a. 1998b). see fig. 74. For this manganite, however. no FMM-PMI transition is observed. Instead. a gradual enhancement of the charge localisation (CL) with lattice distortion has been proposed as the mechanism responsible for the increase in the resistivity with decreasing temperature. Irreversibility's and sharp anomalies in the magnetostriction, magnetisation and magnetoresistance isotherms take place at low temperatures (T < 90 K) (see fig. 75(a---<:». which have been attributed to the crossover from the CL to an inhomogeneous charge-ordered (CO) state. For temperatures lower than 42 K. the CO state was found to coexist with a cluster glass (CG) state.
178
N.H. DUC and P.E. BROMMER
-
220
~~\1'1"-~-1Iliiii~~:::::::~=240
cg
K K 200 K
b .,. -100 )(
180 K
.... ·150
~
·200 ~--160K
.250~d-~b).~:;;:;;;;~iiiiiiiiiiiiiiiii
o
2 3 4 Magnetic field (T)
5
Fig. 76. Magnetostriction isotherms for (Nd 1_ y Srn , )O.5Sr0.5 Mn03 (Y = 0.938). After Kuwahara et aI. (1996) .
r-- - - - -
•18
--,
-18 -14 .:1)
s> a
-e-'
-20
«
---I
·10
~
Smcontent Fig. 77. Composition dependence of magnetostriction and magnetoresistance for (Lal-xSmx)zI3SrI/3Mn03' After Cao et al. (1999).
Magnetostriction measurements have also been interpreted as proof for the existence of magnetic polarons above T c in La213Srl/3Mn03 perovskites (De Teresa et al. 1997). See below. however. for an alternate interpretation. as discussed by Demin et al. (1997) and others. In a (Ndl-ySmy)o.sSro.sMn03 (y = 0.938) single crystal. magnetostriction shows a clear hysteresis and abrupt change in applied magnetic fields (fig. 76). These phenomena were described as a field-induced first-order insulator to metal phase transition. which accompanies a metamagnetic (from AFI to FMM) transition (Kuwahara et al. 1996). A large linear (Joule) magnetostriction with a value up to -180 X 10-6 was observed for bulk polycrystalline (Lal-xSmxhj3SrII3Mn03 (x = 0.33) at T = 77 K (Cao et al. 1999). Joule magnetostriction and magnetoresistance show a similar concentration dependence (see fig. 77). A somewhat different picture is presented by Demin et al. (1997. 1998) and Koroleva and Demin (1999). on the basis of their work on Lal-xSrxMn03 and also by Abramovichet al.
MAGNETOELASTICITY IN NANOSCALE HETEROGENEOUS MAGNETIC MATERIALS 30
Lao.oSr
.1MnO
179
'J'II1 .1[
/"
20
j V
III[
./
II.
o~
I
5
20
/ -, ~ lOO~
·10
·20
<: r-,
o
iIO I[
25
Fig. 78. Magnetostriction isotherms for Lao. 9SrO.1 Mn03' After Popov et aI. (1998).
(2000), on the basis oftheir work on Smo.ssSro.4sMn03' According to these authors these systems should be treated as 'magnetic two-phase states', i.e., in this case, ferromagnetic 'clusters' embedded in a antiferromagnetic semiconductor. The structural phase transition from the orthorhombic semiconducting phase to the metallic rhombohedral phase is then caused by (or accompanied by) a transition to a conducting mainly ferromagnetic twophase state (either AF clusters in a conducting FM matrix, or percolation and tunnelling between the increased FM clusters, still in the AF matrix). Maignan et aI. (2001) ascribe the possibility to form a similar two-phase structure in CaMn l-xRux03 perovskites to specific relationships between Ru and Mn ions. Respaud et aI. (200 I) determined B vs T magnetic phase diagrams of electron-doped Sml-xCaxMn03 in fields up to 50 T. Introducing Sm leads to increasing FM correlations. For x < 0.8 abrupt metamagnetic transitions were observed, whereas around 0.85 phase separation was found. Popov et aI. (1998) studied magnetostriction and field-induced structural phase transitions in a series of Lal-xSrxMn03 (x = 0,0.05,0.1,0.175) perovskite single crystals (twins), in pulsed magnetic fields up to 23 T. Anomalies in the All (8) curves were observed at 20 T for LaMn03. These were associated with a spin-reorientation AyFI: .... AI:Fy when the magnetic field B is applied along the b-axis (AyFI: indicates an antiferromagnetic structure with moments along the b-direction in combination with a small ferromagnetic canted moment in the c-direction; the proposed transition can - almost - be regarded as an ordinary spin-flop transition). For Lao.9Sro.IMn03 (Tc ~ 170 K), the longitudinal magnetostriction has no anomalies at low temperatures (T < 130 K), while near Tc: the magnetostriction increases rapidly up to one order of magnitude and even changes in sign (see fig. 78). This complicated behaviour was suggested to be associated with a structural phase transition related to a polaron ordering process. A strong hysteresis of the magnetostriction was observed for x = 0.175 (fig. 79). Because of these phenomena accompanying the structural transition, the initial state of the crystal is not re-established after the magnetic-field pulse.
180
N.H. Due and P.E. BROMMER
20
I'--
1~,B25S ~
O,175M% 0 3
-- t>
...1 41(
./
-
10
5
/
/
/
-> /
5
L
/ / V
1511
(
o o
111
10
I(
15
Fig. 79. Magnetostriction isotherms for Lao.825SrO.175 Mn03. After Popov et aI. (1998).
1.5
...
= S
"
(a) 1.0 0.5
5r=0.11 H=O
0.0
a
s
100 150 200 Temperature (K)
(b)
1.5
~
50
250
{
Sr = 0.11
1.0 0.5
300
0
I
f
~o-"
:
p'o-o-"-o-O~
0.0 ~ 0.0
,0.1
0.2
0.3
0.4
0.5
M 2 (Am 2/kg)2 Fig. 80. Plot of w(T) (a) and w(M2) (b) for Lao.89SrO.11 Mn03. After Dabrowski et aI. (2000).
Kadomtseva et al. (2000) measured thermal expansion and longitudinal and transverse magnetostriction in pulsed magnetic fields up to 25 Tin Lal-xSrxMn03 single crystals (x = 0.1, 0.125 and 0.15). The results were ascribed to a suppression of the O' phase and field-induced transitions to a new orbital-ordered ferromagnetic state.
MAGNETOELASTICITY IN NANOSCALE HETEROGENEOUS MAGNETIC MATERIALS
(b) La2-zxSr'+2xM~
181
x=
0.36
0.4
0.45
o
100 200 Temperature (K)
o
1 Temperature (K)
200
Fig. 81. Temperature dependence of the striction along (a) the ab-plane and (b) the c-axis in the absence of magnetic fields for La2_2xSf(+2xMn207 (0.3 ~ x ~ 0.45) crystals. Arrows indicate the magnetic transition temperature. After Kimura et al. (1998).
Mukhin et al. (2000) found that increasing Sr doping in Lal-xSrxMn03 does suppress the (quasi- )ferromagnetic resonance frequency, whereas the (quasi- )AF resonance frequency is only slightly decreased (20%). This behaviour corresponds to a canted magnetic structure and its evolution with increasing x. Dabrowski et at. (2000) measured the magnetostriction (and thermal expansion in fields), the magnetisation and the resistivity of Lal- xSrxMn03 perovskite samples (x = O.ll, 0.13 and 0.165), which were also used in neutron diffraction studies (Dabrowski et al. 1999). Large striction effects were observed at the ferromagnetic transition. This indicates coupling of the local spin moments and charge carriers to the crystal lattice. Magnetic fields suppress coherent Jahn-Teller (IT) orbital ordering near x = 0.13 and remove incoherent IT orbital ordering near x = 0.165. The observed strong spontaneous volume magnetostriction was associated with the square of the magnetisation w(T) '" M 2(T) (see fig. 80). The authors claim to have derived, in this way, a correct description of the intricate phase transitions and spin reorientation in the framework of the localised spin model. Eto et al. (200 I) studied the effect of hydrostatic pressure on the magnetostriction and the magnetisation of a polycrystalline Euo.58Sro.42Mn03 sample. At 6 K and ambient pressure, the estimated magnetostriction of about 400 ppm falls down in increasing fields
182
N.H. Due and P.E. BROMMER
s: <=
x-o.3
---
X-O.4
' -'
<=
...
'-'
.J ;;:...
:c
~
J
"-s <=
' -'
--J.
;;:...
:c
J
----
<= i
Q.
;;:... :I:
~
o
246 ~oH (T)
o
246
8
JIoH (T)
Fig. 82. Field dependence of the in-plane magnetostriction (6Lab/Lab(0)1 (upper panel), the inter-plane (or c-axis) magnetostriction (6LcI Lc:Mn207, (aHc): x = 0.3 and (dHf): x = 0.4. After Kimura et al. (1998).
from I T to 2.4 T, i.e. in the 'antiferromagnetic insulator' (AFI) region. The field of 2.4 T corresponds to the AFI-FMM (insulator-metal) transition as signalled by the observed CMR. With increasing pressure, the magnetostriction becomes smaller and the metalinsulator transition occurs at lower fields. In decreasing fields (from 5 T down to zero field), no transitions were observed: the (partial) FMM state apparently remains. In fact, at intermediate pressures, the magnetostriction measured in increasing fields becomes negative with respect to the values observed in decreasing fields. At pressures above 1.15 GPa, the magnetostriction almost disappears, indicating that then EUO.58 Sr0.42Mn03 behaves as a ferromagnetic metal (FMM state). The 3D perovskites can be regarded as the limit for n ~ 00 of the (doped) layered manganese oxides with formula (RI-yAv)n+IMnn03n+1 [R: rare earth, A: divalent cation]. Colossal magnetoresistance has been found in some highly anisotropic, almost two-dimensional, bilayered (n = 2) members, based on (La, Sr), (La, Ca), (Nd, Sr) or (Sm, Sr), see e.g. references in Szymczak (2000) or Garcia-Landa et al. (2001). These results triggered further research on magnetostrictive effects. Giant magnetostriction (GMS, up to A ....., 0.05%) has been reported for bilayered (n = 2) La2-zxSrl+zxMnz07 crystals, which exhibit huge magnetostrictive effects (Kimura et aI. 1998). This system shows a
MAGNETOELASTICITY IN NANOSCALE HETEROGENEOUS MAGNETIC MATERIALS
(a)
+
183
Mn06 octahedron
~
= =
x2-f-
f=l=3z2-,2~
XV, yz, zx
~3Z2_~ eg x2-f~
EF
EF _
e
-,band ,=
xy, yz , zx
~11
e"band
2g
(b)
doping level
•
..
.
•
•
• 'maonetic
x-0.4
So [AJ
eo [AI [AI [AI Mn-O(3) [AI
Mn-0(1)
Mn-O(2)
3.876(2) 20.140(2) 1.95
3.860(2) 20.380(2)
1.98 2.06 1.93
2.00 1.94
moments x-O.4S 3.878(1) 20.053(2) 1.94 1.97 1.94
Fig. 83. (a) Schematic electronic structure of a Mn3+ ion in a Mn06 octahedron with IT distortion. The in-plane eg band in the layered manganite shows a different band dispersion and bandwidth depending on the respective orbital states. (b) Doping-level dependence of lattice distortion at room temperature in La2-2x Srl+2x Mn207. Thick arrows on the right hand of respective crystal structures indicate the spin structures within a bilayer unit at low temperatures. After Kimura et aI. (1998).
large spontaneous distortion at T c (fig. 81) as well as a highly anisotropic field-induced striction with respect to the crystal axes (fig. 82). The magnetoelastic behaviour does vary systematically with the doping level (x) and may be attributed to the field-induced change in the orbital-state occupancy in the two-dimensional band. The most striking result is the difference in sign between the magnetostriction of the x = 0.3 sample and that of the x = 0.4 sample (see fig. 82). By applying magnetic fields in the ab-plane, the ab-plane expands but the c-axis shrinks for x 0.3. Just the opposite is observed for x = 0.4. To understand the origin of these magnetotransport and magnetoelastic properties, the orbital degrees of freedom of the eg-like conduction electrons of Mn 2+ were taken into account. The electronic structure of Mn3+ ions in Mn06 octahedron with IT distortion is sketched in fig. 83a. It is clearly seen from this figure that an expansion of the c-axis stabilises the 3z2 r 2 orbital state. The (doped) e g electrons, however, prefer to occupy the x 2 _y 2 orbital state when the c-pararneter is diminished. Doping-level dependence of lattice distortion at room
=
184
N.H. DUC and P.E. BROMMER
800x10"
-400
r----------------,
'--''--'-...L---'---'--L-~_'_..L_.L_L_l'__'___L~~
o
2
4
6
8
10
12
14
16
lloH (T) Fig. 84. Paral1el and perpendicular magnetostriction isotherms of Lao.5SrO.5Co03 at selected temperatures. After Ibarra et al. (\998).
temperature in La2-2xSrl+2xMn207 crystals is presented in fig. 83b. The lattice parameter of the a (b) axis slightly increases with increasing .r, whereas that of the c axis decreases more rapidly. Since the orbital character is strongly correlated with lattice deformations, the observed structural distortions, induced by changing temperature, magnetic field and doping level, reflect sensitively changes in the orbital state. In the case of the low-doped samples (x ~ 0.36), the cooling- or field-induced distortion appears to stabilise the x 2 _ y2 orbital state. By contrast, the lattice distortion toward the FM state (or by applying magnetic field) has been understood in terms of the stabilisation of the 3z 2_r2 orbital state. In a study of a series of perovskites R(Co,Mn)03 and R(Mn,Ni)03 (R = Eu, Gd, Tb, Dy, Y), Troyanchuk et al. (1997) found large negative magnetostrictive effects of the order of 10- 4 in Eu(Coo.sMnO.S)03 at 4.2 K. The magnetostriction was not saturated in the highest available field of 12 T. For Th(Coo.sMno.s)03, the magnetostrictive effects were somewhat smaller. Moreover, at 5 T a change of sign was observed, ascribed to the metamagnetic transition. The magnetostrictive properties of Lal-xSrxCo03 cobaltates were studied by Ibarra et al. (1998). It was found that the magnetostriction in the compounds with x = 0.0 and x = 0.08 is negligible. Large magnetostrictive effects were observed for x = 0.3 and x = 0.5. Their behaviour, however, is different from that of manganites. The parallel and perpendicular magnetostriction isotherms are presented in fig. 84 for Lao.sSrO.SCo03. Since All and AJ.. are of opposite sign and display large values, a huge anisotropic magnetostriction is obtained: At = All - Al., is as large as 1 x 10-3 (fig. 85). The maximum volume magnetostriction (w = All + Al.) is reached near Tc ::::: (250 K), with a value of about -140 x 10-6 at B = 14.2 T, which is one order of magnitude lower than found in the manganites. Such a huge anisotropic magnetostriction cannot be explained on the basis of the usual spin-orbit coupling mechanism. Moreover, this finding suggests a different nature of the magnetovolume effect in cobaltates compared to manganites. Indeed, it was proposed that the magnetostriction of Lal-xSrxCo03 has its origin in orbital instability of C0 3+ ions under the influence of a magnetic field, giving rise to a transition from a nondegenerate low-spin (t2g 6 , S = 0) state to an orbital degenerated intermediate-spin (lzg se g,
MAGNETOELASTICITY IN NANOSCALE HETEROGENEOUS MAGNETIC MATERIALS
185
2500
....
«Cl
lSK
La•.,Sr•. l CoO]
2000 1500 1000
SOO 0 1200
lSK
La•. 5 Sr•. 5 CoOl
lOOK
800
....
«- 600 Cl
400 200
0 0
10
S
1S
J10H (T) Fig. 85. Anisotropic magnetostriction (At) isotherms for Lao.7SrO.3Co03 (a) and Lao.5SrO.5Co03 (b) at selected temperatures. After Ibarra et aI. <1998).
S = 1) state. In this configuration. the two-fold degenerate eg level of intermediate Co3+ splits into two singlets (L = 0). and the triplet tZg into a singlet and a doublet (L = 1). Due to the degeneracy of the doublet level with nonzero angular momentum, a strong intraatomic spin-orbit coupling is created which couples to the lattice strain to give rise to a large anisotropic magnetostriction. 10. Potential applications of magnetostrictive materials Technical aspects and potential applications of magnetostrictive materials have been presented by Du Tremolet de Lacheisserie (1993). Different kinds of magnetostrictive devices based on Terfenol-D were reviewed by Houqing et al. (1997), Claeyssen et al. (1997) and Ludwig and Quandt (2000). Marin and Hernando (2000) present a number of applications using. on the one hand. highly magnetostrictive amorphous materials (e.g. FeSiBCuNb wires), and, on the other hand, zero-magnetostrictive amorphous, highly inductive materials, such as (Feo.06Coo.94hz.sSil2.sBls. According to Osaka (2000), zero magnetostriction is also a prerequisite for electrodeposited soft magnetic films to be used for magnetic recording heads 'in the next century'. It is also interesting to point to the so-called 'gyromagnetic' effect, observed in Fe-Si-B amorphous wires with a particular magnetic-domain structure (Chiriac et al. 2000b). A large growing interest is manifest today for physical micro-systems of reduced dimensions. typically between 10 and 103 JLm. Such systems may satisfy the need to
186
N.H. Due and P.E. BROMMER
perform functions which are not fulfilled by existing electronic circuits, i.e. sensing functions (micro-sensors) and functions of interacting with the environment (microactuators). In the cases where a simple motion is to be obtained, magnetostrictive amorphous R-T thin films, which combine several specific properties, are very promising. The working principle of the magnetostrictive thin-film devices is based on the bending transducer which consists at least of a film-substrate compound, where the substrate is non-magnetostrictive. Upon magnetisation the magnetostriction in the film causes the compound to bend, similar to the bending of a bimetallic strip. The advantages of magnetostrictive devices with respect to their piezo-electric competitors are the larger deformations, higher forces and energy densities, lower sound velocity and Young's modulus, and low operating voltage. Moreover, direct electric contacts can be avoided. The disadvantage is the coil, which is difficult to make small because of the field requirements. Developing films with giant magnetostriction at low fields is necessary to solve these problems. In addition, as magnetostrictive devices using thin films are very small, the price of material is not a problem. So, such MEMS could find large scale applications, for instance in electronics, optics, medicine, automobile industry, geophysical explorations, and ocean environmental protection as well. At present, some devices are already used for specific applications. We present here some typical examples, such as a micromechanicalswitch, a micro-motor and a micropump, demonstrating the above-mentioned advantages of magnetostriction, especially for the fact that moving parts are wireless. The simplest motion which can be thought of is realised by a bimorph bending (as schematised in fig. 4) as a mechanical switch. In this case, although Sm-T films exhibit less pronounced magnetostriction compared to Tb-T ones, the combination of a negative- with a positive-magnetostriction film allows the fabrication of magnetostrictive bimorphs which enhance the total deflection, and reduce the initial curvature of cantilevers (fig. 86a, see Honda et al. 1994). A 3-mm long cantilever actuator is found to exhibit a large deflection of above 100 JLm in a magnetic field as low as 0.03 T. With this cantilever, a deflection of more than 500 JLm at resonant frequency in an alternating field of 0.03 T has been reached. One of the main drawbacks of the magnetostrictive actuators is their thermal drift. For bulk Terfenol-D actuators, the thermal expansion (10- 5 K- 1) develops strains comparable to the magnetostrictive ones for t1T = 150 K. For a simple rectangular bimorph cantilever as illustrated in fig. 86a, the strains due to thermal expansion and to the magnetoelastic coupling are comparable for only t1T = 75 K (Du Tremolet de Lacheisserie et al. 1998). A torsion based, thermal-drift free microactuator was invented by Betz (1996, 1997). It is basically a unimorph structure composed of one magnetostrictive film deposited on a passive substrate. The special feature is a square shape maintained by hinges at three comers (figs 87a, b). The useful displacement due to magnetostriction is obtained at the fourth free comer, without thermal displacement. The different deformed shapes are due to the anisotropy of magnetostriction strains and the isotropy of thermal strains. Various types of the so-called magnetostrictive "inchworm" type of motor have been proposed and built. A two-leg travelling machine using a magnetostrictive bimorph actuator with 7.5 JLm-thick polyimide is shown in fig. 86b (Honda et al. 1994; Arai and Honda 1996). In an alternating magnetic field, it can travel in one direction. The maximum speed of approximately 5 mmls was obtained around the mechanical resonant frequency
MAGNETOELASTICITY IN NANOSCALE HETEROGENEOUS MAGNETIC MATERIALS
187
(a)
Tb-Fe(1 ,urn)
Polyirnide (7.5,urn) (b)
Sm-Fe (1 ,urn) Fig. 86. (a) A side view of the cantilever actuator fabricated by combining TbFe and SmFe films. After Honda et al, (1994). (b) Two-leg linear magnetostrictive micromotor. After Honda et al, (1994).
(a)
(b) Fig. 87. Drift free microactuator: (a) thermal deformation and (b) magnetostriction deformation. After Betz (1997).
of 200 Hz. Similarly, a many-leg linear-motor was also fabricated using a micromachined Si(llO) substrate (10 /Lm) and TbFe films, see fig. 88 (Halstrup et al. 1996; Claeyssen et al. 1997). The 4 /Lm-thick TbFe films were deposited on both sides of the substrate.
188
N.H. DUC and P.E. BROMMER
?"~f,s1 • Leg }J2
Silicon plate
{
Magnetostrictive thin film }J2
Fig. 88. Many-leg linear magnetostrictive micromotor. After Claeyssen et al. (1997).
Applying a magnetic excitation field of 10 mT at a frequency of approximately 775 Hz and a magnetic bias field of 10 m'T, this motor can be operated at a speed of 3 mm/s. A rotating magnetostrictive ultrasonic micromotor, however. consists of a free Ti rotor (20 mm diameter. thickness of 100 J-Lm. three 300 J-Lm-thick teeth) on which a magnetostrictive film of 4.6 J-Lm-thick in three sectors is deposited. An ac magnetic field of 20 mT and a bias magnetic field of 40 mT are applied transversally to the film. Operating at a frequency of 2.86 klfz, the propulsion mechanism of vibrating teeth on a friction layer leads to a rotational speed of 0.5 rls (Claeyssen et al. 1997). Gibbs et al. (1997) describe a MEMS pressure sensor based on the magnetoelastic properties of an amorphous Fe-Si-B-C coating (derived from METGLASS2605SC) on GaAs substrate. The world-wide first magnetostrictive thin film micropump prototype was made of four laser micro-machined Si(lOO) wafers in combination with a bimorphous TbDyFe(l5 J-Lm)/Si(l (0)(50 J-Lm)/SmFe(l5 J-Lm) membrane and cantilever-type passive valves (fig. 89) (Quandt and Seemann 1996; Quandt and Ludwig 1997; Quandt et al. 1997b). The radial magnetic field circuit is directly placed on the membrane to permit a good penetration by the magnetic field. The micropump is operated using an oscillating rectangle pulse for the membrane actuation. At the frequency of 2 Hz a maximum yield of approximately 290 J-LVmin of methanol or an outlet pressure of 4.9 mbar can be reached. Later. Quandt and Ludwig (2000) proposed a more simple construction based on Si membranes coated with giant magnetostrictive TbFeIFeCo multilayers. Optical microactuators like a micromirror for scanning applications have been proposed by Orsier et al. (1996). A two-dimensional bimorph (Si + magnetostrictive film) is driven remotely by two differently oriented magnetic fields working at different frequencies in order to obtain the bending and torsional vibrations due to the magnetostrictive strain. Berger et al. (2000) proposed to use magnetostrictive thin films in scanning probe microscopy. This idea allows overcoming misinterpretation of MFM images due to the tip magnetisation by using non-magnetic tips. (Co.Fe)-AI-O granular films were used in preparing the core (dimension of 2 mm x 2 J-Lm x 300 J-Lm) of a high-frequency spiral shaped inductor. The best properties were obtained with (Coo.92Feo.o8)-AI-OISi02 multilayers, which have magnetostriction almost
MAGNETOELASTICITY IN NANOSCALE HETEROGENEOUS MAGNETIC MATERIALS
189
TbOyFe film (20 11m) 51 (RI1 0 nvn x 50 11m) SmFe 111m (20 11m)
Si (100) (180. 240 11m).
by laser micropallerning
Fig. 89. Schematic cross-section of the magnetosttictive membrane type micropump. After Quandt (1997).
zero after annealing as the core material. A maximum quality factor Qrnax = 25 at a frequency of 300 MHz was observed (Ohnuma et aL 1999). A coil using a granular film with >.. = 10 x 10-6 had Qrnax = 8 at a frequency of 120 MHz. Combination of magnetostrictive and piezoelectric materials have also been suggested (Arai et at. 1995). Using a piezoelectric substrate (or thin film) on which a magnetostrictive film is deposited, one can operate in two different modes: either the magnetostrictive film can be used as an actuator leading to a sensor signal in the piezoelectric substrate, or the function of both layers could be exchanged using the inverse effects in both materials. A stress-operated memory device consisting of an ellipsoidal magnetic particle array and an electrostrictive grid is proposed by Novosad et al, (2000). In this device, the magnetic state of the particle can be controlled by the magnetostriction effect. The design is sketched in fig. 90a. In the writing process, the driving voltages are simultaneously applied to two pairs of the selected contacts (e.g. ±UI and ±U2 in the illustration) resulting in an electric field with a vector sum of two electric fields. Varying the intensity and the polarity of the applied voltage (fig. 90b) can effectively rotate the direction and the amplitude of the electric field. Consequently, the rotatable stress can be generated at the selected intersection in the piezoelectric grid, which initiates the magnetisation reversal of the magnetic particle (e.g. the magnetisation of particle B is switched, whereas the final magnetic states of the particles A and C are not affected). For the design of this kind of stress-operated memory device, ferroelectic materials such as lead zirconat titanate (PZT), barium strontium titanate (BST) and lead lanthanum zirconate titanate (PLZT) would be suitable. The magnetic particles should be magnetically soft with large magnetostriction. In a (microscale) prototype Ni particles were applied, but Pd-Co and the spring type multilayers (MSMM, discussed in section 5.2) were also mentioned as promising materials.
190
N.H. Dueand P.E. BROMMER
(a)
(b)
Fig. 90. (a) Schematic design of a stress-operated memory device. (b) The magnetic states of particles A, B and
e (see (a» as a function of a driving electric field. The magnetisation of the particle B is switched, whereas the final magnetic states of the particles A and e are not affected. After Novosad et al. (2000). 11. Summary and concluding remarks Recent results for nanoscale heterogeneous magnetic systems have been reviewed. For applications, both zero-magnetostriction (soft-magnetic) materials and materials exhibiting giant magnetostrictive effects (for actuators) are of interest. Reliable magnetostrictive devices (MEMS) have been designed on the basis of amorphous Terfenol and Terfenol-D (TbDyFe2) alloys, although the magnetostriction of these amorphous alloys has been found to be one order of magnitude lower than that of their traditional, well-known crystalline counterparts. Magnetic investigations have shown that the GMS-properties of amorphous R-Fe alloys suffer from the sperimagnetic character of the Fe and R subsystems. Fortunately, an alternative solution has been found by preparing nanocrystalline R-Fe alloys in which the magnetic anisotropy is reduced, while the exchange energy (ordering temperatures) and the GMS remain satisfactorily high. By optimising the annealing temperature and time, i.e. the nanocrystallisation, the magnetostriction value can be
MAGNETOELASTICITY IN NANOSCALE HETEROGENEOUS MAGNETIC MATERIALS
191
doubled. In particular, a giant parallel magnetostriction (An) of 800 x 10-6 has been achieved in a (Tbo.7DYO.3)O.3FeO.7 film with grain sizes around 10 nm. This size, however, is rather close to the exchange length in R-T alloys, so the coercive field is increased (less suitable for MEMS, where fields of a few mT are preferred). In addition, annealing promotes the segregation of other Fe-rich phases, which - on the one hand - have low magnetostriction, but - on the other hand - may improve the magnetostrictive softness. Good results are obtained for nanocrystaIIine multi layers in which the crystallite growth is delimited by the layer thickness. In amorphous thin films, however, it is strongly preferable to replace iron by cobalt. Near the RC02 composition, the amorphous alloys present higher ordering temperatures and higher magnetostriction than the equivalent ironbased alloys. In fact, the magnetostriction has been optimised in a series of thin films of the type a-(Tb,Dy)(Fe,Co)n. These materials showed a high, record, magnetoelasticity of p.2 = -63.5 MPa and AY. 2 = 1020 x 10-6 , which is almost fully developed at low fields. GMS obtained in this series of alloys has been explained in terms of an increase in the ferromagnetic coupling strength within the (Fe.Co) subsystem, and the effect of field annealing in inducing a well-defined uniaxial anisotropy. StilI better performances were obtained on spring type Rtf MSMM, where the saturation field of the magnetostrictive, amorphous Tb-FeCo is lowered by means of exchange coupling with the soft-magnetic Fe-Co layers. In addition, the increase of the coupling exchange field between the layers does close the cone angle in the sperimagnetic Tb-FeCo structure, thus increasing its magnetostriction. In this case, layers must be sufficiently thin, in order that a noticeable volume of the R-T layer may be submitted to the large molecular field. Deposition under an applied field and field annealing are rather effective in creating a well-defined uniaxial anisotropy and, then, in increasing the magnetostriction in the direction of interest. In view of applications, some interesting values of the magnetostriction and of the magnetostrictive susceptibility are summarised in table 2. Apart from technical considerations for applications, we stress that studies on magnetoelastic effects in thin films also are of fundamental interest. At the surface of any alloy, the symmetry is broken, for instance because neighbouring atoms are missing. Thus, surface (and interface) contributions to the magnetoelastic coupling must be taken into account. This contribution is usually negligible in bulk materials, but this is no longer true for thin films and multilayers where surface and interface effects on the magnetic and magnetostrictive properties have been experimentally evidenced. For a better understanding of the very complex properties of these systems, however, very complex further experimental as well as theoretical studies are needed. Significant improvements in the field of giant magnetostriction have stimulated the design and manufacturing of microactuators and motors (sometimes prototypes only), taking advantage of wireless magnetic excitation, in first instance at room temperature (or higher temperatures). For cryogenic applications, magnetostrictive actuators require low-temperature magnetostrictive materials. In practice, single crystals of TbO.6DY0.4Zn I (Terzinol) were used (Teter et aI. 2000). The major advantage of this material is that a 50 mT apllied field suffices to achieve a large magnetostriction of 5 x 10-3. In this context, perovskites and rare earth superlattices are also possible candidates.
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chapter 3
MAGNETIC AND SUPERCONDUCTING PROPERTIES OF RARE EARTH BOROCARBIDES OF THE TYPE RNi2B2C
K.-H. MOLLER, G. FUCHS, S.-L. DRECHSLER Leibniz-Institut fUr Festkorper- und Werkstofforschung Dresden POB270116, 0-01171 Dresden Germany
V.N. NAROZHNYI
Institute for High Pressure Physics, Russian Academy of SCiences Troitsk, Moscow Region, 142190 Russia
Handbook of Magnetic Materials. Vol. 14 Edited by K.H.J. Buschow @ 2002 Elsevier Science B. V. All rights reserved
199
CONTENTS I. Introduction . . . . . . . . . . . . .
1.3. On the interplay of superconductivity and magnetism ..
202 202 202 207
1.4. Specific features of the RNi2 B2C compounds
215
I. I. Discovery of the RNi2B2C superconductors 1.2. Boron and carbon based superconductors . . .
2. Crystal structure and chemical composition
. .
2.1. The LuNi2B2C-type structure
218 .
2.2. Lattice distortions due to magnetoelastic effects
. .
221
2.3. Single-, double- and triple-layer borocarbides (nitrides) 2.4. Related R-T -B-C(N) phases 3. Basic properties of YNi2B2C and LuNi2B2C
218
223 .
224
.
226
226
3. I. Normal state electronic properties and the superconducting stale 3.2. The upper critical field. . . . . . . . . . . . . . . . . .
.
230
3.3. Magnetotransport
.
234 240
3.4. Characteristics of superconducting YNi2B2C and LuNi2B2C 4. Magnetic and superconducling properties of RNi2B2C
241
.
243
4.1. Magnetic order and the crystalline electric field . 4.2. CeNi2B2C
246
4.3. PrNi2B2C
247
4.4. NdNi2B2C
252
4.5. SmNi2B2C . . .
253
4.6. GdNi2B2C ..
254
4.7. TbNi2B2C ..
256
4.8. DyNi2B2C
257
4.9. HoNi2B2C
259
4.10. ErNi2B2C
266
4.11. TmNi2B2C ..
268
270
4.12. YbNi2B2C ..
272
5. Vortex lattices in RNi2B2C superconductors .. 5.1. Vortex lattice in non-magnetic borocarbides
272
5.2. Vortex lattice and magnetic order in ErNi2B2C and TmNi2B2C .
276
5.3. Vortex pinning and magnetic order
.
277
6. Superconductivity in R(Ni,T}2B2C and (R, R')Ni2B2C .
277
6.1. R(Ni,T}2B2C compounds (T = Co, Cu, Pd, PI etc.)
277
200
MAGNETIC AND SUPERCONDUCfING PROPERTIES OF RNi2B2C 6.2. Effects of disorder . . . . . . . . . . . . . . . . . . . .
201 279
6.3. Magnetic impurities in a nonmagnetic superconductor
286
6.4. Nonmagnetic impurities in an antiferromagnetic superconductor
288
7. Conclusions . . . Acknowledgements References . . . . .
289 291 291
1. Introduction
J.J. Discovery ofthe RNi2B2C superconductors
Superconductivity in quaternary rare-earth transition-metal borocarbides (RTBC ) has been discovered when for seemingly single-phase polycrystaIline samples of the hexagonal compound YNi4B, at about 12 K, a drop in resistivity as well as in susceptibility has been observed (Mazumdar et al. 1993). However, the superconducting phase in all investigated YNi4B samples was at least a minor fraction of the material (~ 2%). It had been suggested that the superconductivity in the YNi4B samples may be due to a phase stabilized by the presence of an element other than Y, Ni and B. This was supported by the observation of bulk superconductivity in polycrystaIline material with the nominal composition YNi4BCo.2 (Nagarajan et al. 1994). At the same time Cava et al. (l994a, 1994b) reported results on superconductivity in mu1tiphase YPd5B3Co.35 with a transition temperature Teas high as 23 K and single-phase materials of the composition RNhB2C (R =Y, Lu, Tm, Er, Ho with r, ~ 15.5 K, 16.5 K, 11 K, 10.5 K, 8 K), respectively. Obviously, the superconducting behaviour of the YNi4B and YNi4BCo.2 samples mentioned above is caused by YNi2B2C. Consequently this was the discovery of the first superconducting quaternary intermetaIlic compound. In the case of the Y-Pd-B-C system the classification of the phase being responsible for T c ~ 23 K was much more complicated because, so far, only multiphase superconducting material can be prepared for this system. Not all of the phases in superconducting Y-Pd-B-C materials could be identified and evidence for at least two superconducting phases has been reported (Hossain et al. 1994a). Only quite recently it has finally been shown by a microanalysis technique that YPd2B2C is the 23 K superconducting phase (Dezaneti et al. 2(00). A typical de susceptibility-versus-temperature transition curve for polycrystaIline LuNhB2C and YNi2B2C with T c ~ 16.5 K and 15 K is shown in fig. 1. The growth of very high quality single crystals of nickel borocarbide superconductors (see e.g. Xu et al. 1994) almost immediately after their discovery has had a profound impact on the quality of the work performed. Thus many of the pitfalls of the early research on other complex materials, such as high T c superconductors, carried out on polycrystaIline samples of variable quality, have essentially been avoided (Cava 2(01). J.2. Boron and carbon based superconductors
According to the BCS theory of superconductivity the critical temperature (I)
202
MAGNETIC AND SUPERCONDUCI1NG PROPERTIES OF RNi2B2C
RNi2B2C
~&TI-1 ::i 0
o.5 i
Cl ::J
E 0 .0
~
;-2 ..
i:!
14
203
I
I
16
IS
T(KI
Gi '1'
o
FC
i" -0.5
R=V
~
Lu
ZFC
-1. 0
.J
5
15 10 TemperalUf. (K)
20
Fig. I. Temperature dependence of the de magnetic susceptibility of LuNi2B2C and YNi2B2C in a magnetic field of 20 De. ZFC and FC means zero field cooling and field cooling, respectively (after Nagarajan et al, 1994).
is determined by the Debye temperature OD representing the phonon spectrum, the normal state electron density of states N(EF) at the Fermi level and some measure V of the electron-phonon interaction (Bardeen 1992). Although formula (1) had been derived for simple systems with the superconductivity driven by electron-phonon interaction, under the condition N(EF)V « I, it has been successfully applied to describe qualitatively superconductivity in a very wide class of materials. The value of OD monotonically increases with the inverse mass of the atoms participating in the lattice vibrations of the considered material. Therefore low-mass elements and their compounds are considered as candidates for superconductors with high critical temperature. Thus, monatomic or diatomic forms of metallic hydrogen are expected to exhibit superconductivity at quite high temperatures (Ashcroft 1968; Richardson and Ashcroft 1997). However, hydrogen based superconductivity has not yet been found. The difficulty is to have, simultaneous with the large Debye temperature, conduction electrons with a large N(EF) and a sufficiently large V. Besides hydrogen, lithium and beryllium other light elements such a boron and carbon should be beneficial for increasing T c . For carbon this prediction has been excellently confirmed recently (see table 1). A critical temperature as high as 117 K could be achieved upon hole doping of the pristine solid version of the fullerene C60 intercalated by CHBr3 (Schon et al. 2001, see fig. 2). Because C60 is a strong electron acceptor and, consequently, chemical hole doping of this material is difficult it was done by electrostatic means using a field-effect transistor device geometry. An advantage of this method is that, contrary to chemical doping, the doping level can be varied without changes and imperfections in the crystal lattice. The intercalation with electronically inert spacer molecules such as CHCh or CHBr3 results in a lattice expansion and, consequently, the electronic bands narrow and the density of states increases. Thus the doping level and the value of N(EF) can be controlled independently. It should be noted that the frequency spectrum of C60 intramolecular vibrations extends to high energies and several of these modes couple significantly to the electronic states providing considerable intramolecular
~ TABLE 1 Some boron and carbon containing superconductors Boron and borides T, (K) B
Carbon and carbides T, (K)
Space gr. Structure
11.2 [I] HP
C60 ~/CHBr3
YBI2 ZrB12
4.7 (2) 5.8 [2)
Fm3m UB I2
Rb3C60
52 [l2] ET 117 [13] ET 28 (14) 12.8 [l5) HP
Fm3m BiF3 organic
YB6 LaB6
7.1 [2) 5.7 [2]
Pm3m CaB6
BEDT-TTFbased salt YC2
MgB2 ReB2
39 [3) 6.3 [4)
P61mmm A1B2
La2C3 (Y,Thh C3
11 [l7] 17 [l8)
I4Immm CaC2 143d PU2C3
NbB TaB
8.3 [5] 4.0[5)
Cmcm CrB
MOS6 C 44
NbCy
13 [l91 11.8 [20)
Fm3m NaCI
M02B
5.1 [61
M02C
12.2 [51
orthorh.
Re3B
4.7 [4)
LuRuB2 YRuB2
10.0 (7) 7.8 (7)
14/mcm CuA12 Cmcm Re3B Pnma LuRuB2
YOS3B2 LuOs3B2
6.0 (7) 4.7 [8)
P6Immm CeC°3B2
LaNiC2 (La,Th)NiC2 LaBrC YIC Y(Br,I)C
4.0 [16]
2.7 [21] 7.9 [22) 7.1 [23J 10.0 [24) 11.6 [241
Borocarbides T, (K)
Space gr. Structure
Amm2 CeNiC2 C2Im Gd2C212
LuB2C2 YB2C2
2.4 [26] 3.6 (26)
M02BC
7.5 (27)
LuNi2B2C ScNi2B2C ThNi2B2C YNi2B2C YPd2B2C YPt2B2C YRu2B2C
16[28) 15 [29) 8 [30) 15.5 [28] 23 [31,32,35) 10 [331 9.7 [341
Space gr. Structure P4/mbm LaB2C2 Cmcm MOzBC 14/mmm LuNi2B2C
~
;I: 3: c:
Ccm :oc ~
~
3:
~
TABLE 1 (Continued) Boron and borides
Te(K)
~B4
8
LuRh.i B4
8
YR!4 B4
10
9 [9,IOJ 12 [9,IOJ 11 [9,1OJ
('5
Carbon and carbides
M03Al2C
10 [l9J
Space gr. Structure P4132
MgNi3C
8.5 [25]
Pm3m
Space gr. Structure P42/nmc CeC04B4 [II]
Te(K)
Borocarbides T e (K) Space gr. Structure
tl-Mn SrTi03
HP- under high pressure, ET - electric field induced doping using field-effect transistor geometry, [I] Eremets et aI. (2001), [2] Matthias et aI. (1968), [3] Nagamatsu et aI. (2001), [4] Strukova et aI. (2001), [5] Savitskii et aI. (1973), [6] Havinga et aI. (1972), [7] Ku and Shelton (1980), [8] Lee et aI. (1987), [9J Fischer and Maple (1982), [10] Maple and Fischer (1982), [11] The alternative types LuRu4B4 (s.g. I41/acd) and LuR!4B4 (s.g. Ceca) have also been reported for theRR!4B4 compounds (RogI1984), [12] Schon et aI. (2000), [13] Schon et aI. (2001), [14] Rosseinsky et aI. (1991), [IS] WJ1liams et aI. (1991), [16] Gulden et aI. (1997), [l7J Giorgi et aI. (1969), [18] Krupka et aI. (1969), [19J Fink et aI. (1965), [20] Gusev et aI. (1996), [21J Lee et aI. (1996), [22] Lee and Zeng (1997), [23] Simon et aI. (1991), [24] Henn et aI. (2000), [25] He et aI. (2001), [26] Sakai et aI. (1982), [27] Lejay et aI. (1981), [28] Cava et aI. (l994b), [29] Ku et aI. (1994), [30] Lai et aI. (1995), [31] Tominez et aI. (1998), [32] Dezaneti et aI. (2000), [33] Cava et aI. (1994d), [34] Hsu et aI. (1998), [35] Cava et aI. (1994a).
~ o CIl
I ~
s~ .."
~ iii CIl
o"rl ~
Z
':;' t:tI
..,
o
~
206
K.-H. MULLER et aI.
A
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Gate
I
:::tl
o L.......L-.o.....L...L..L..L-L......u......L...................L............... ...J o 20.-0 80 80 100 120 1.-0 180 180 200 Temperature (K)
Fig. 2. Resistivity-vs.-temperature transition curves for some C60 based superconductors. (A) Variation of the hole doping from 1.3 to 3.2 holes per C60 molecule. Inset: the field-effect transistor geometry used in the experiment. (B) Comparison of optimum hole-doped C60. as grown and intercalated with CHCI3 and CHBr3) respectively (Schon et al. 2(01).
electron-phonon interaction. Therefore these phonon modes and their coupling to the electrons will not much be influenced by the doping and intercalation procedure. The maximum value of T c achieved in C60 by hole doping without lattice expansion is 52 K (see table I; Schon et al. 2000). Electron doping of C60, which can be done by chemical as well as electrostatic means, results in lower values of T c because of the higher density of states in the valence band than in the conduction band. As an example, the chemically electronically doped bulk material Rb3C60 has a T c of 28 K (Rosseinsky et al. 1991; see table I). Superconductors with remarkably high critical temperatures have also been found among organic compounds and inorganic carbides (see table I). At ambient pressure boron is an insulator consisting of 12-atom icosahedral units. As reported by Eremets et al. (2001), under high pressure B becomes not only metallic, as predicted by Mailhiot et al. (1990) but even superconducting and it has a positive pressure derivative of the critical temperature d T c / dP . Pressure induced superconductivity has also been found in organic compounds (e.g. BEDT-TTF in table I), spin-ladder cuprates (Uehara et al. 1996) and many other materials. Obviously pressure can cause, through various mechanisms, crystallographic and electronic structures that are favorable for superconductivity. On the other hand the electronic bands of a metal will broaden if the material is compacted which is consistent with the fact that negative dT c/dP has been observed for many superconductors (Wijngarden and Griessen 1992). Therefore pressure
MAGNETICAND SUPERCONDUCTING PROPERTIES OF RNi2B2C
8Co)
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20
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induced superconductivity, also in the case of boron, is expected to be characterized by a nonmonotonic pressure dependence of T c with a maximum value of T c at a certain pressure. Such a behaviour has been confirmed, e.g. for iron (Shimizu et a1. 200 1) and spinladder cuprates (Dagotto 1999). Superconductivity is also known for many borides (see table 1). The most surprising example is MgB2 a binary compound with a simple crystal structure, which is well known for many years (Russel et a1. 1953). But, unbelievably, its transport and magnetic properties had not been investigated until quite recently although there was an intensive search, on a large international scale, for higher values of T c in the family of binary compounds. The highest critical temperatures were achieved for A15type compounds with a maximum value of about 23 K which could not be improved since the early seventies until the discovery of the high- T c cuprate superconductors in 1986 (Bednorz and MUller 1986; Wu et a1. 1987). In 2001 Nagamatsu et al, (2001) found a critical temperature as high as 40 K for MgB2 (see fig. 3). Electronic structure calculations show that MgB2, being essentially metallic boron held together by covalent B-B and ionic B-Mg bonding, is electronically a typical sp metal (Kortus et al. 2(01). The crystal structure of MgB2 may be regarded as that of completely intercalated graphite with carbon replaced by boron. Thus the band structure of MgB2 is graphitelike, but with n bands falling deeper than in graphite, and two-dimensionality features are assumed to be important for the superconductivity in this compound as well as in the surface of the above discussed solid C60 doped by electrostatic means (Ann and Pickett 2001; Belashchenko et a1. 200 I). A strong influence of 2D effects on T c had been discussed by Ginzburg (1964, 2000) but these aspects are yet to be understood. On the other hand, the electronic structure of the quaternary borocarbides RNizB2C is clearly three-dimensional (see section 3.1). The lattice structure of LuB2C2 and YB2C2 (see table 1) contains wellseparated BC layers, suggesting 2D behaviour. However, the electronic properties of these low-Z', superconductors are not yet well investigated. J.3. On the interplay ofsuperconductivity and magnetism
The discovery of the RTBC superconductors generated great excitement for two reasons. First. T c ::::; 23 K in the Pd-system was, at that time. the highest known transition
208
K.-H. MULLER et aI.
temperature for bulk intermetallics. Such a high T c had been reported for thin Nb3Gefilms, two decades before (Gavaler et al. 1974). Apart from the relatively high values of their T c the RTBC have attracted a great deal of attention because they contain rareearth magnetic moments in high concentration, which are coupled by exchange interaction. The interplay between the two collective phenomena magnetism and superconductivity has been an active area of interest for many years (reviews: Fischer and Maple 1982; Maple and Fischer 1982; Bulaevskii et al. 1985; Fischer 1990). In this section we will briefly review this problem starting with compounds where superconductivity and magnetism completely (to our present knowledge) exclude each other, then continuing with systems for which some kind of coexistence of these two phenomena was observed and finishing with the recently discovered coexistence of superconductivity and weak itinerant ferromagnetism. 1.3.1. Superconductivity and magnetic ordering as antagonistic phenomena In the usual BCS theory of superconductivity electrons are paired with opposite spins and, obviously, they cannot give rise to magnetically ordered states. Hence magnetic order and superconductivity should be antagonistic. In high- T c cuprate materials, depending on the doping rate, the Cu 3d electrons (or holes) contribute to a localized antiferromagnetic (or spin glass) state or they participate in superconductivity, i.e. the two phenomena do not coexist (Aharoni et al. 1988; Luke et al. 1990). Intriguing forms of competition between superconductivity and ferromagnetism have recently been reported for the elements carbon and iron, where the two cooperative phenomena are related to different crystallographic structures. As discussed in section 1.1 pristine C60 consisting of dominantly van der Waals bounded C60 molecules becomes superconducting if doped by electrons or holes. On the other hand, under sufficiently high pressure and temperature, a layered rhombohedral structure of C60 forms where, within the layers, the C60 molecules are covalently bound. This phase is metastable at room temperature and ambient pressure. It shows a spontaneous magnetization, which is assumed to be based on unpaired electrons created by structure defects (Makarova et al. 2001; Xu and Scuseria 1995). It is well known that, at pressure above 10 GPa, Fe transforms from a ferromagnetic cubic phase into a non-ferromagnetic hexagonal phase. Wohlfarth (1979) argued that the hexagonal iron may be a low-temperature superconductor. This prediction has now been confirmed by Shimizu et at. (2001) who found superconductivity in Fe below 2 K at pressures P between 15 and 30 GPa. An interesting open question is whether high-pressure iron is an unconventional superconductor with Cooper paring mediated by magnetic fluctuations (as proposed by Fay and Appel in 1980) instead of phonons. At T = 0 the superconductivity disappears at a quantum critical point (P ~ 30 GPa in fig. 4). This may be due to reduced magnetic fluctuations or to a reduced density of states N (E F) caused by electron-band broadening at higher densities. 1.3.2. Superconductors with magnetic impurities The superconducting state can coexist with magnetic moments of localized electrons (e.g. of 4f type). It was experimentally found by Matthias et at. (l958a) that for rareearth impurities substituted into a superconductor T c rapidly decreases with increasing impurity concentration and that superconductivity is completely destroyed beyond a
MAGNETIC AND SUPERCONDUCfING PROPERTIES OF RNi2B2C
209
2000.----------.,.----,
hcp
o
20
40
60
Pressure (GPa) Fig. 4. Proposed temperature-pressure phase diagram of iron (after Saxena and Littlewood 2(01) with the ferromagnetic body-centered cubic (bee) phase. the paramagnetic face-centered cubic phase (fcc) and the hexagonal close-packed phase (hcp).
critical concentration of the order of one percent. This has been well understood by a theoretical approach of Abrikosov and Gor'kov (1961) who took into account that scattering by magnetic impurities leads to pair breaking. However, many systems with rare-earth magnetic moments show deviations from the behaviour predicted by Abrikosov and Gor'kov (AG). As has been proven theoretically (Keller and Fulde 1971; Fulde and Peschel 1972) and confirmed by many experiments, effects of crystalline electric fields on the magnetic moments result in a weaker decrease of T c with increasing impurity concentration compared to the AG prediction. On the other hand, it was demonstrated theoretically by Muller-Hartman and Zittartz (1971) and experimentally by Riblet and Winzer (1971) that effects of hybridization and strong correlation (Kondo effect) may cause a considerably stronger reduction of T c than predicted by AG. Furthermore the AG predictions will fail for higher concentrations of the rare-earth magnetic moments which are usually coupled by certain types of indirect exchange interaction and show cooperative magnetic phenomena. The first example where such deviation from the AG behaviour has been realized is CeRu2 where over 30% of non-magnetic Ce can be replaced by Gd (Matthias 1958b; Peter et al. 1971), Tb (Hillebrand and Wilhelm 1970; Ferdinandez-Baca and Lynn 1981) or Ho (Lynn et al. 1980; Willis et al. 1980) before superconductivity is suppressed. The measurements of susceptibility, specific heat and Mossbauer effect as well as neutron scattering clearly indicated that the ordering of the heavy-rare-earth magnetic moments in these materials is of spin-glass or, strictly speaking, cluster-glass type with short range ferromagnetic order (Roth 1978; Davidov et al. 1977). For the pseudobinary systems (Gd,La)Ru2 (Jones et al. 1978) and (Nd,Th)Ru2 (Huser et al. 1983) which are superconducting spin glasses or cluster glasses, similar as the (R,Ce)Ru2 systems mentioned above, even so called reentrant superconductivity occurs as shown in fig. 5 for the compound Nd(l.3sThO.6SRu2. The competition between superconductivity and ferromagnetic short-range order results in a complicated non-monotonic temperature dependence of the susceptibility. In the temperature range around 1 Kelvin the material is superconducting IxI < 0). Cooling below this temperature range would return the material into the normal state (X I > 0). A reentrance of superconductivity is observed below 0.2 K.
210
K.-H. MULLER et aI.
o
0.5
1.0
1.5
2.0
Temperature T (K) Fig. 5. Reentrant superconductivity in Nd(l.3SThO.6SRu2 (after HUser et aI. 1983). Upon cooling, first, the real part of the ac susceptibility, X', becomes negative, indicating superconductivity. Then the material reenters the normal state (X' > 0) and reentrance of superconductivity occurs at lower temperatures.
The reason why reentrant behaviour occurs in (Gd,La)Ru2 and (Nd,Th)Ru2 but not in the (R,Ce)Ru2 system may be that in the former compounds the magnetic correlation length of the spin-glass state is closer to the superconducting coherence length than in (R ,Ce)RU2 compounds. The reentrance of superconductivity at low temperatures (in fig. 5) is attributed to the well known fact that, in diluted magnetic materials, larger ferromagnetic clusters become unstable at low temperatures (HUser et al. 1983; Nieuwenhuys et al. 1979). J.3.3. Superconductivity and local-magnetic-moment cooperative phenomena To understand the interplay of superconductivity and magnetism in systems containing localized magnetic moments in high concentration Gor'kov and Rusinov (1964) extended the AG theory taking into account cooperative magnetic phenomena. They concluded that ferromagnetism would destroy superconductivity because the conduction electrons will be polarized by exchange interaction with the ordered magnetic moments. Ginzburg (1956) had pointed out, already before, that superconductivity and ferromagnetism in (type-I) superconductors can only coexist if the magnetic induction caused by the magnetization M s is smaller than the critical field of the superconductor, i.e, the spontaneous magnetization has to be sufficiently small. For type-Il superconductors this conclusion has to be modified as only states must be excluded which, at the same time, are homogeneously magnetized and homogeneously superconducting. This will be achieved if the induction caused by M s is smaller than the lower critical field He I. An alternative solution of the dilemma is the self-induced formation of vortex structures (see e.g. Fulde and Keller 1982). A further possibility is that the electromagnetic coupling of superconductivity and magnetism causes an oscillating magnetic (instead of homogeneous ferromagnetic) order which coexists with a homogeneous superconducting state. The wavelength of the oscillations is governed by the penetration depth A of the superconductor (Blount and Varma 1979; Matsumoto et al. 1979). An alternative mechanism for oscillatory magnetic order has been proposed by Anderson and Suhl (1959): the strength of the exchange interaction between the rare-earth magnetic moments mediated by the conduction electrons (RKKY interaction) is changed in the superconducting state because the electron-spin susceptibility is reduced in the long-wavelength range. Consequently
MAGNETIC AND SUPERCONDUCTING PROPERTIES OF RNi2B2C
211
the effective exchange interaction in the superconducting state will have a maximum at a finite wavelength, leading to an oscillatory magnetic state, even if the material would be ferromagnetic in the absence of superconductivity. The wavelength of this state is controlled by the coherence length ~ of the superconductor. It was predicted by Baltensperger and Strassler (1963) that antiferromagnetic order may coexist with superconductivity. The first examples of compounds where true long range magnetic order coexisting with superconductivity has been observed are ternary Chevrel phases RM06SS and RRh4B4 compounds (see Fischer and Maple 1982; Maple and Fischer 1982). In these materials there is a separate fully occupied rare-earth sublattice. It is assumed that the magnetic moments and the superconducting electrons in these compounds belong to different more or less "isolated" sublattices, which supports superconductivity to exist despite the high concentration of localized magnetic moments (Lynn 200 I). The magnetic ordering temperatures are low (~ I K) whereas T e is considerably larger. Therefore it cannot be excluded that magnetostatic interaction dominates the energies in the magnetic subsystem. It was found that in ErRh4B4 (Fertig et al. 1977) and HoM06Ss (Ishikawa and Fischer 1977) superconductivity is in competition with ferromagnetic longrange order, which results, in a reentrant behaviour and in coexistence of superconductivity with oscillatory magnetic states (Thomlinson et al. 1982; Lynn et al, 1984). For most of the superconducting RM06SS and RRh4B4 compounds the magnetic interactions favor antiferromagnetic order with a magnetic unit cell on a length scale small compared to ~ and A which results in a relatively weak influence on the superconducting state i.e. antiferromagnetic order and superconductivity do readily accommodate one another. The antiferromagnetic transition in these materials has been confirmed by neutron scattering (see Thomlinson et al. 1982). Initially this transition had been observed as an anomaly in the upper critical field (Ishikawa et al. 1982). In particular, a near-reentrant behaviour has been found for some of the antiferromagnetic ternary compounds i.e. reentrant behaviour occurs if a sufficiently high magnetic field is applied, as shown in fig. 6 for GdM06SS. To explain the near-reentrant behaviour it is usually argued (see Maple and Fischer 1982) that, in the vicinity of the antiferromagnetic ordering temperature TN, the applied field induces a remarkable degree of ferromagnetic order which has been confirmed for various compounds. In the case of GdM06Ss, additionally, large spin fluctuations below TN have been assumed to enhance the near-reentrant behaviour (Ishikawa et al. 1982). Machida et al. (1980b) extended the theory of antiferromagnetic superconductors (Baltensperger and Strassler 1963), taking into account effects of the antiferromagnetic molecular field caused by aligned local magnetic moments in addition to spin fluctuations. They found that the anomalies of Ha in RM06SS (R = Gd, Tb, Dy) can be explained by the formation of energy gaps of spin density waves on the Fermi surface. Morozov (1980) as well as Zwicknagl and Fulde (1981) integrated the concept of Baltensperger and Strassler (1963) into the Eliashberg theory and they found that the influence of the antiferromagnetic staggered magnetization on the phonon-mediated quasiparticle attraction also results in an anomaly, in particular a reduction below TN, of H eZ(T). The cuprates RBazCu307-,s with the orthorhombic (nearly tetragonal) Rl23-type structure exist for R = Y and all 4f elements with the exception of Ce and Tb, For 0<8 < 0.6 they are cuprate-mixed-valence high-Z', superconductors, with the exception
ZIZ
K.-H. MULLER et al. 1.0
GdMo~8
0.8
as
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IX 0.4 0.2 0 0.5
1.0
Temperature
1.5
(K)
Fig. 6. Resistance-vs-temperature curves of a GdMo6Sg sample for different values of the applied magnetic field. indicating near-reentrant superconductivity i.e. reentrant behaviour at finite field only (nominal composition Gd1.2Mo6Sg; after Ishikawa et aI. 198Z).
of R = Pro The value of T c is about 90 K and it practically does not depend on the choice of R. GdBazCu307 shows three-dimensional antiferromagnetic ordering with TN ~ 2.2 K and a staggered magnetic moment of 7.4JlB which is close to the Hund's rule Gd 3+ free ion value (Paul et al. 1988). Since TN does not much change if [, is increased from 0 to I and the material becomes a semiconductor with antiferromagnetic ordering of the Cu 2+ magnetic moments (Dunlap et al. 1988) the Gd magnetic order cannot be dominantly governed by indirect exchange via conduction electrons (RKKY interaction) and the two antiferromagnetic structures on the R and the Cu sublattices are only weakly coupled to each other. On the other hand the value of TN ~ 2.2 K is too high to be explained by dipolar interactions only. Thus the type of magnetic coupling of the R magnetic moments is not yet fully understood. For R = Nd, Srn, Dy, Er, Yb the single-R 3+-ion crystal field splitting results in magnetic (doublet) ground states and the RBa2Cu307 compounds with these R elements show antiferromagnetic ordering with TN ~ I K. For R = Dy and Er the R magnetism (as well as the Cu magnetism) is two-dimensional (Lynn 1992). For R = Ho the crystal field ground state in the R 123 structure is a singlet. Nevertheless, antiferromagnetic ordering (TN = 0.17 K) has been observed also for this compound and the Ho magnetic moments have assumed to be induced in the electronic singlet ground state by nuclear hyperfine interaction (Dunlap et al. 1987). In these R 123 superconductors the superconductivity persists below TN. Hence there is no measurable effect of the ordered magnetic moments on superconductivity. This supports that exchange interaction between the conduction electrons and the rare-earth magnetic moments is minor and pairbreaking due to exchange scattering is weak. On the other hand, the relatively high value of TN ~ 2.2 K (for Gd123) suggests that some small indirect exchange between the rareearth magnetic moments operates across the CU02 layers (Fischer 1990). The situation is totally different for Prl23 where antiferromagnetic order of the Pr magnetic moments develops at T N ~ 17 K and superconductivity does not occur. The superconductivity in Prl23 which has been recently reported by Zou et al. (1998) is not yet understood or even finally secured. It may be connected with a modified composition of the samples as well as a modified occupation of the lattice sites by Pr and Ba ions (see Narozhnyi and
MAGNETIC AND SUPERCONDUCTING PROPERTIES OF RNi2B2C
213
Drechsler 1999). The anomalous behaviour of Prl23 has been attributed to hybridization of Pr 4f states with 0 2p states, completely disrupting the quasiparticles which form the Cooper pairs in the CU02 planes and dramatically increasing the exchange interactions between the Pr magnetic moments (Fehrenbacher and Rice 1993; Lynn 1997; Skathakumar et al. 1997). A further consequence of the hybridization of the Pr 4f electrons, besides the enhanced value of TN and the absence of superconductivity, is a considerable interaction of the Cu magnetic subsystem with the Pr subsystem: contrary to the behaviour of the RI23 materials mentioned above Prl23 shows Cu antiferromagnetism in the whole range of 0 = 0 ... 1 with an ordering temperature TN[CU] of about 300 K (instead of TN[CU] ~ 410 K for YI23 at 0 ~ 0.9). Furthermore, below TN ~ 17 ... 20 K an incommensurate magnetic structure develops involving both the Pr and the Cu moments where the Cu moments are found to be non-collinear (see Boothroyd 2000). Coexistence of superconductivity and magnetic order has also been reported for ruthenocuprates with typical composition RuSr2RCu20g or RuSr2(R,CehCu201O, with R = Sm, Eu or Gd, where the magnetic-ordering temperature TN = 100 ... 180 K is much higher than T; = 15 .. .40 K (Bauernfeind et al. 1995; Braun 2001). Neutron diffraction experiments (Lynn et al. 2001) have shown that TN is related to basically antiferromagnetically ordered magnetic moments in the Ru sublattices and, in the case of RuSr2GdCu20g, the Gd moments order independently antiferromagnetically at 2.5 K. The small ferromagnetic component reported for these materials for temperatures below TN is attributed to spin canting resulting in weak ferromagnetism of Dzyaloshinsky-Moria type and to explain the coexistence of this type of magnetism with superconductivity it has been assumed that the magnetically ordered Ru sublattice is practically decoupled from the superconducting CU02 planes (Bernhard et al. 1999; FeIner 1998, FeIner et al. 1999). In the Heusler alloy ErPd2Sn superconductivity and antiferromagnetic order coexist although there is no clear separation between the superconducting and the magnetic sublattices and T c ~ 1.17 K is not much different from T N ~ I K (Shelton et al. 1986; Stanley et al. 1987). However, the focus on this interesting compound was short lived because of the discovery of the high T c cuprate superconductors (Lynn 200 I). An interesting theoretical prediction is that, similar as in the p-wave superconductors discussed in the next subsection, non-magnetic impurities in an antiferromagnetic superconductor cause pair breaking (Morozov 1980; Zwicknagl and Fulde 1981) whereas non-magnetic impurities in a non-magnetic superconductor are not expected to destroy superconductivity (Anderson 1959). 1.3.4. Superconductivity and itinerant-electron magnetism Fay and Appel (1980) predicted unconventional superconductivity (p-wave paring, i.e. spin triplet pairing) mediated by longitudinal spin fluctuations to coexist with itinerant ferromagnetism if the magnetization is small enough. These authors also declared ZrZn2 as a candidate for this phenomenon. For reasons of time-reversal symmetry, in p-wave superconductors all impurities are pair breakers (Foulkes and Gyorffy 1997) and, therefore, superconductivity will be observed only in very clean samples. This behaviour is different from that of BCS (s-wave) superconductors where nonmagnetic impurities do not destroy superconductivity (Anderson 1959). Matthias and Bozorth (1958) had found that ZrZn2 is ferromagnetic although both elements, Zr and Zn, are non-ferromagnetic. These authors
K.-H. MULLER et aI.
214
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also were the first who suggested that ZrZn2 could be a superconductor. Wohlfarth (1968) showed that ZrZn2 is a weak itinerant d-electron ferromagnet. Now the superconductivity in ZrZn2 has been confirmed for very pure samples (Pfleiderer et al. 200 1). At ambient pressure the Curie temperature T c and the critical temperature Teare 28.5 K and 0.29 K, respectively. Under hydrostatic pressure T c and T c disappear at the same pressure. Therefore the ferromagnetic state is assumed to be a prerequisite for superconductivity and the above mentioned p-wave pairing mechanism is assumed to be valid for this material. Superconductivity coexisting with weak itinerant ferromagnetism has also been reported for UGe2 (Saxena et al. 2000) and URhGe (Aoki et al. 2001) and it has been assumed to be based on the same magnetic p-wave pairing mechanism as in ZrZn2 (Huxley et al. 2001). In UGe2 the superconductivity is pressure induced and, as in the case of ZrZn2, it disappears at the same pressure as the ferromagnetism (see fig. 7). However, the magnetic moments are expected to be more localized in UGe2 than in ZrZn2 because they are due to f -electrons rather than d -electrons. Therefore Suhl (200 I) and Abrikosov (200 1) developed an alternative pairing model based on interaction of the conduction electrons with ferromagnetically ordered localized spins which can only lead to an s-wave order parameter. This concept is supported by experiments of Bauer et al. (2001) who showed that, different from the case of ZrZn2. high-purity specimens with long mean free paths are not necessary in UGe2 in order to observe superconductivity near the critical pressure where the magnetic ordering temperature vanishes. Furthermore, for the s-wave superconductivity not to be destroyed by magnetism the metal has to be a heavy-fermion type which also is supported by the experimental results of Bauer et al. (200 I). Superconductivity has also been found to coexist and compete with itinerant-electron antiferromagnetism (spin density waves) which has extensively reviewed by Gabovich et al. (2001). In summary, there are various forms of the interplay of magnetism and superconductivity, which can be divided into competition and coexistence phenomena. In the elements C
MAGNETIC AND SUPERCONDUCfING PROPERTIES OF RNi2B2C
215
and Fe different types of crystal structure and bonding between the atoms, both varied by preparation routes or thermodynamic parameters such as pressure, result in one of the antagonistic cooperative phenomena ferromagnetism or superconductivity. Strong competition is found in high- T c cuprates where, depending on the doping rate, Neel-type antiferromagnetism (or spin glass) or superconductivity occur, both based on copper d-electrons. Coexistence of localized magnetic moments (e.g. from 4 f -elements) with superconductivity is known for systems where the concentration of these moments is small enough or they are antiferromagnetically ordered and only weakly coupled to the conduction electrons. Even weak ferromagnetism of such localized moments can coexist with superconductivity.In RuSr2GdCu20g and (R,Ce)RuSr2Cu201O-8, probably, the Ru subsystem with weak ferromagnetism of Dzyaloshinsky-Moriya type is weakly coupled to and coexists with superconducting CU02 layers. Most surprising is the recently reported coexistence of weak itinerant ferromagnetism with superconductivity based on d or f electrons in ZrZn2, UGe2 and URhGe.
1.4. Specific features ofthe RNhB2C compounds A striking feature distinguishing the superconducting RTBC from other superconductors known until 1994 is that for certain combinations of elements Rand T superconductivity and antiferromagnetic order have been found to coexist in RT2B2C with the values of the magnetic ordering temperature TN being comparable with the T c values (see fig. 8) i.e. the magnetic energy is comparable with the superconducting condensation energy. Therefore the investigation of these compounds is expected to result in new insights into the interplay of superconductivity and magnetism. In addition to many specific studies in this field, published so far, there are various reports and review articles summarizing experimental and theoretical results on the superconducting and magnetic properties of these materials and comparing them with other superconductors, as e.g. Maple (1995), Canfield et a1. (1997b), Lynn (1997), Takagi et a1. (1997), Andreone et a1. (1998), Canfield et al. (1998), LuTmEr Ho Dy 20
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=
Fig. g. Critical temperatures for superconductivity, T c. and for antiferromagnetic ordering, TN, for RNi2B2C compounds with R = Lu, Trn, Er, Ho, Dy, Tb and Gd. DO is the de Gennes factor, g the Lan~ factor and J the total angular momentum of the R3+ Hood's rule ground state. The straight lines represent rough linear approximations.
216
K.-H. MULLER et al.
FeIner (1998), Gupta (1998), Nagarajan and Gupta (1998), Paranthaman and Chakoumakos (1998), Schmidt and Braun (1998), Hilscher and Michor (1999), Naugle et al. (1999), Drechsler et al. (1999), Schmiedeshoff et al. (2000), Tominez et al. (2000), Drechsler et al. (2oo1b), Muller and Narozhnyi (2001a). Also articles in this field are collected in the Proceedings of the NATO Workshop "Rare Earth Transition Metal Borocarbides", held in Dresden, Germany in June 2000 (Muller and Narozhnyi 2oo1b). The high values of TN demand that in quaternary borocarbides, different from the situation in high- T c cuprates and the classical magnetic superconductors, exchange coupling between the rareearth magnetic moments is the dominant magnetic interaction rather than magnetostatic interaction. Obviously the exchange is mediated by conduction electrons. Consequently also the interaction between the magnetic moments and the conduction electrons must be relatively strong. Figure 8 shows a linear scaling of TN and, roughly approximated, also of T c with the de Gennes factor (2)
of the R 3+ Hunds' rule ground state where g is the Lande factor and J the total angular momentum (de Gennes 1958). Such so called de Gennes scaling, at the same time for TN and T c- is known for various isostructural metallic R compounds, which is due to the fact that both effects, antiferromagnetism and the suppression of superconductivity are governed by exchange interaction of conduction electrons with R 4 f electrons. In some approximation both, TN and the difference I:i. T c of the critical temperature compared to that of a nonmagnetic (DG = 0) reference material can be written as (3)
where I is the strength of the exchange interaction between 4 f electrons and the conduction electrons and N(EF) is the density of states at the Fermi level (Fischer 1990). From fig. 8 it can be seen that both cases, TN < T« (R = Tm, Er, Ho) and TN > T c (R = Dy) occur in the series RNhB2C. A similar phase diagram as that in fig. 8 had been predicted by Machida et al. (1980a). As can be seen in fig. 9, de Gennes scaling does not work if a larger class of materials is considered within the series RNi2B2C. (As will be discussed in subsection 2.1, two lattice structures have been reported for ScNi2B2C. Therefore the position of Sc in fig. 9 is questionable and, in reality, the dashed line may be monotonous.) In particular there is a strong influence of the lattice parameters on T c which cannot be explained by only taking into account the variation of N(EF) in the expression (3). Obviously, T c also very much depends on nonmagnetic effects (see subsection 3.1). Useful means for the investigation of both superconducting and magnetic subsystems are measurements under high hydrostatic pressure P. The first results on the influence of P on T; of RNi2B2C (R = Y, Lu, Tm, Er and Ho) were reported by Schmidt and Braun (1994). Other groups report on results of high pressure studies also on other borocarbides (Gao et al. 1994; Murayama et al. 1994; Alleno et al. 1995b; Looney et al. 1995; Carter et al. 1995; Uwatoko et al. 1996; Bud'ko et al. 1996; Weht et al. 1996; Meenakshi et al. 1996, 1998; Jaenicke-Roessler et al. 1999, Cappannini et al. 1998; Oomi et al. 1999,2001; Murdoch et al. 1999; Matsuda et al. 2001; Dertinger 200 1; Falconi et al. 200 1). Highpressure studies on YNjzB2C at room temperature do not indicate any structural transition
MAGNETIC AND SUPERCONDUCfING PROPERTIES OF RNi282C
217
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QD
Q~ Q~ Q~ QTI Q ~ Lattice parameter a (nm)
Fig. 9. Transition temperature and lattice parameter a for RNi282C compounds with LuNi282C type structure (see subsection 2.1) for non-magnetic (Lai et aI. 1995) and magnetic R elements. The curves are guides to the eye. The (Lu, Y)-value is taken from Freudenberger et aI. (1998a).
up to P = 16 GPa (Meenakshi et al. 1996, 1998). The bulk modulus is measured to be 200 GPa and estimated to be 270 GPa from calculations based on the TB-LMTO method (Meenakshi et al. 1996). Values of the bulk modulus close to those mentioned above have been obtained for LuNi2B2C (210 GPa) within the local-density approximation (Weht et al. 1996). The results on the influence of P on T c in these materials are contradictionary. For example, Schmidt and Braun (1994) found that Tc(P) decreases linearly with pressure at rates of -0.058 KlGPa. This is in agreement with the results of Murayama et al. (1994), but is in contradiction with the data of Alleno et al. (1995b) who found a Tc(P) dependence with positive initial slope of +0.03 KlGPa and with a peak centered at P ~ 0.52 GPa. These observations indicate that even the sign of the pressure dependence of T c depends on the microstructure of the samples (Alleno et al. 1995b). Contrary to the behaviour of T cthe magnetic ordering temperature TN has found to increase with increasing pressure for all RNhB2C compounds investigated so far, i.e. for R = Gd (Bud'ko et al. 1996), Ho (Carter et al. 1995; Uwatoko et al. 1996; Dertinger 200 1) and Er (Matsuda et al. 200 1). The effect of pressure on the interplay between superconductivity and magnetism in borocarbides has been discussed for R = Tm (Oomi et al. 1999), Er (Matsuda et al. 2(01) and Ho (Uwatoko et al. 1996; Carter et al. 1995; Oomi et al. 2001; Dertinger 2(01). It was pointed out that the much stronger suppression of H c2 under high pressure observed for ErNhB2C and TrnNi2B2C, compared to RNhB2C compounds with non-magnetic R, may be connected with some instability of the superconducting state of these magnetic superconductors. Most extensively the influence of pressure has been investigated for HoNi2B2C (see also subsections 4.9.3 and 4.9.4). In this article we will report on the current status of research on the quaternary borocarbide superconductors starting from their discovery. We will concentrate on the magnetic and superconducting properties of RNhB2C compounds. Section 2 is devoted to the typical crystal structure of RNi2B2C and lattice distortions caused by magnetic ordering but also to other compounds and lattice structures which are related to RNi2B2C.
Z18
K.-H. MULLER et al.
Section 3 briefly summarizes electronic and superconducting properties of RNi2BZC compounds with nonmagnetic R elements. Special features are Fermi surface nesting characterized by the nesting wave-vector (0.55,0,0) and phonon softening at the same wave vector (subsection 3.1), and the positive curvature of the upper critical field as a function of temperature, He2(T), discussed in subsection 3.2. RNjzB2C compounds with 4 f elements R are considered in section 4. Among them, Ce and Yb are interesting because, in RNi2BzC, they show intermediate 4f-valence and heavy fermion behaviour, respectively. DyNjzB2C is outstanding because it is one of the exceptional antiferromagnetic superconductors with TN > T e . In HoNjzB2C three different types of magnetic order occur and the competition between superconductivity and magnetism is most complex. An exciting feature of ErNjzB2C is the coexistence of superconductivity with some kind of weak ferromagnetism. Results on flux line lattices in the borocarbides, including the transformation from hexagonal to square lattices, are presented in section 5. The investigation of pseudoquaternary compounds, reported in section 6, provides some more insight into the pair-breaking mechanisms in the borocarbides. A short summary and conclusions are presented in section 7. 2. Crystal structure and chemical composition 2.1. The LuN;zB2C-type structure
With the investigation of superconducting rare-earth transition-metal borocarbides the new LuNi2B2C-type structure, space group I4/mmm, has been discovered which can be considered as the ThCr2Si2-type, space group I4/mmm, interstitially modified by carbon (Siegrist et al. 1994a, 1994b). Figure 10 shows the nonmodified and the modified structures with Th -. Gd, Cr -. Co, Si -. Band Lu -. Gd, Ni -. Co, respectively. The family of ternary rare-earth transition-metal metalloid compounds with the ThCr2Si2-type structure is very large (Just and Paufler 1996) and a broad variety of magnetic and electronic properties have been observed in it. For example in SmMn2Ge2 both Sm and Mn carry a magnetic moment and two metamagnetic transitions occur connected with giant magnetoresistance effects (Brabers et al. 1993). Different collective phenomena as heavy-fermion behaviour, superconductivity and magnetic order have been found in the exotic compound CeCu2Si2 (Steglich et al. 1995). The LuNi2B2C-type structure has three open parameters, the two lattice constants a and c and the coordinate z of the boron atom. It has been pointed out by Godart et al. (1997) that the values of a and c of RNjzB2C compounds show a certain dispersion indicating a domain of existence which is in agreement with the variety of physical properties observed in many individual cases. The structure of the RNjzB2C compounds is highly anisotropic with a ratio cia of about 3. It has alternating sheets of Ni2B2 tetrahedra and RC layers. In a good approximation, the parameters c and z linearly decrease with increasing radius of R (where R is assumed to be in the trivalent oxidation state) whereas a linearly increases with the radius of R, with the exception of Ce (see subsection 4.2). Thus while going through the series of R elements from Lu to La, the structure shows a contraction along the tetragonal c-axis but an expansion perpendicular to it i.e. a decrease of the anisotropy characterized by cia and the boron shifts away from the RC-Iayers more in the vicinity of the Ni layers. However, the radius variation of the
219
MAGNETIC AND SUPERCONDUCTING PROPERTIES OF RNi2B2C
(8)
(b)
Fig. 10. (a) GdC02B2 has the ThCr2Si2-type structure, where Gd resides on the Th, Co on the Cr and B on the Si sites, respectively. (b) GdC02B2C has the LuNi2B2C-type structure i.e, the ThCr2Si2-type interstitally modified with C atoms. The lattice constants are a = 3.575 Aand c = 9.561 Afor GdC02B2 (Feiner et aI. 1984), a = 3.548 Aand c = 10.271 Afor GdC02B2C (Mulder et aI. 1995). respectively.
rare earth does not much affect the B-C distance and the B-Ni distance. Consequently, there is a remarkable reduction of the B-Ni-B tetrahedral angle from 108.8° for Lu to 102° for La which is expected to influence the variation of the electronic structure within the series of RNi2B2C compounds. The Ni-Ni distance in LuNhB2C (2.449 A) is smaller than that in metallic Ni (2.492 A) and underlines the metallic character of the RNizB2C compounds. Table 2 shows the known RT2B2C compounds (R: Sc, Y, La, Th, or 4f or 5f elements; T : 3d. 4d or 5d elements). Table 3 contains the superconducting compounds from table 2 as well as their superconducting transition temperatures T c and, if existing, magnetic ordering temperatures TN. Superconductivity in CeNizB2C has been reported (El Massalarni et al. 1998a) and is exceptional in that this is the only superconducting RNizB2C compound with a light rare-earth R and Ce is in a mixed-valence state (see subsection 4.2). Single crystals on which most of the physical investigation has been performed have been grown by the flux method (Xu et al. 1994) and it has also been proven to be possible to grow single crystals by floating zone (Takeya et al. 1996) and zone melting methods (Behr et al. 1999a). Various melting techniques have been used to prepare polycrystalline materials (see e.g. Torninez et al. 2000). c-axis aligned or even epitaxial RNizB2C thin films have been successfully prepared by pulsed laser deposition (Cimberle et al. 1997; Hase et al. 1997, 2(01) as well as magnetron sputtering technique (Arisawa et al. 1994; Andreone et al. 1996). Non-equilibrium methods as rapid quenching (Strom et al. 1996; Freudenberger 2(00) or mechanical alloying (GUmbel et al. 2(00) have been utilized to search for metastable phases. In some systems metastable phases form also in normal melting procedures. For example, ScNizB2C (Ku et al. 1994; Tomilo et al. 2001, 1999) and ThNhB2C (Sarrao et al. 1994; Hossain et al. 1994b; Zandbergen et al. 1994b) have been found to be metastable. In the case of ScNizB2C two different tetragonal lattice structures have been reported with the lattice parameters a 0.332 nm, c 1.004 nm
=
=
220
K.-H. MULLER et al.
TABLE 2 Known R-T -B-C compounds with the LuNi2B2C-type structure. Compounds printed in bold face are superconductors CeCo2B2C CeNi2B2C CePt2B2C CeRh2B2C DyNi2 B2C DyPt2 B2C DyRh2B2C ErNi2B2C ErRh2B2C GdC02B2 C
LuC02B2C LuNi2B2C NdNi2B2C NdPt2B2C NdRh2B2C PrNi282C PrPt2B2C PrRh2B2C ScNi2B2C SmNi2B2C
GdNi2B2C GdRh2B2C HoC02B2C HoNi2B2C HoRh2B2C LaIr2B2C LaNi2B2C LaPd2B2C LaPt2B2C LaRh2B2C
SmRh2B2C TbNi2B2C TbRh2B2C TbNi2B2C ThPd2B2C TbPt2B2C ThRh2B2C TmNi2B2C UNi2B2C URh2B2C
YCo2B2C YNi2B2C YPd2B2C YPt2B2C YRu2B2C YbNi282C
TABLE 3 8orocarbide superconductors with LuNi2B2C-type structure and their superconducting transition temperature T c and magnetic ordering temperature TN Compound
Tc
CeNi2B2C DyNi2B2C HoNi2B2C ErNi282C TmNi2B2C LuNi2B2C YNi2B2C ScNi2B2C ThNi2B2C
0.1 [IJ 6.2 [2J, 6.4 [3J 8 [4J, 7.5 [5J 10.5 [4,5J II [4,5J 16.5 [4,5J 15.5 (4] 15 [6J 8 [7J
TN(K)
II [2,18J 5 ... 8 [8,9,IOJ 6.8 [11,12J 1.5 [13,14J
Compound
Tc
YRu2B2C LaPd2B2C ThPd2B2C YPd2B2C LaPt2B2C PrPt2B2C YPt2B2C ThPt2B2C
9.7 [20J 1.8 [21) 14.5 [15J 23 [4,16,19J 10 ... 11 [l7,22J 6 {17,22J 10 .. _11 [l7,22J 6.5 [I5J
TN(K)
[I) EI Massalami et al. (1998a), [2J Cho et al. (1995a), [3J Tomy et al. (1995), [4J Cava et al. (1994b), [5J Eisaki et al. (1994), [6J Ku et al. (1994), [7J Lai et al. (1995), [8] Grigereit et al. (1994), [9J Goldman et al. (1994), [10] Canfield et al. (1994), [I I) Sinha et al. (1995), [12] Zarestki et al. (1995), [13] Cho et al. (1995b), [14] Lynn et al. (1997), [15] Sarrao et al. (1994), [16] Tominez et al. (1998), [17] Cava et al. (l994d), [18] Dervenagas et al. (1995a), {19] Dezaneti et al. (2000), {20] Hsu et al. (1998), {21J Jiang et al. (1995), {22] Buchgeister et al. (1995).
and a = 0.354 nm, C = 1.055 nm where only the latter phase has been found to be superconducting (Tomilo et al. 2(01). Therefore the dashed curve in fig. 9. in reality. may be monotonic because the lattice constant a of superconducting ScNi2B2C should be close to that of YNbB2C. Also it was found that some of the RNi2B2C compounds are rather stable. Thus YNi2B2C starts oxidizing and decomposing only above 850°C (Buchgeister and Pitschke 1996). Neutron diffraction data seem to provide evidence that all the crystallographic sites in RNbB2C are fully occupied and there is no site mixing (Tominez et al. 2000). However. the conventional diffraction techniques may be not enough sensitive to determine interchange or defects on the Band C sublattices in these compounds. Such effects may be one of the reasons why superconducting and magnetic properties of the borocarbide superconductors do very much depend on the metallurgical state of the samples (Lynn et al. 200l).
MAGNETIC AND SUPERCONDUCfING PROPERTIES OF RNi2B2C
221
TABLE 4 Structural and magnetic properties of RC02B2 and RC02B2C phases with the ThCr2Si2 and LuNi2B2C-type structure, respectively
z of the
RC02B2 RC02B2C
a (A)
YC02B2 YC02B2C
3.5598 [2]
9.342 [2]
0.3780 [5]
P [2] P (Pauli) [1,6]
LaC02B2 LaC02B2 C
3.6186 [2]
10.223 [2]
0.3750 [5]
P[2]
PrC02B2 PrC02B2 C
3.5985 [2]
9.951 [2]
NdC02B2 NdC02B2C
3.5920 [1,5]
9.8381 [1,5]
c(A)
B site (4e)
0.3750 [5J
Type of magnetic order
Tc (K)
F[2]
19.5 [2]
F(l,2J A[6J
32 [I] ""3 [6J
no (F imp [2]) A [6]
SmC02B2 SmC02B2 C
3.5806 [2J
9.673 [2J
GdC02B2 GdC02B2C
3.575 [l,5J 3.548 [3)
9.561 [1,5] 10.271 [3]
0.3750 [5]
TbC02B2 TbC02B2 C
3.5670 [5J
9.4889 [5]
0.3750 [5]
DyC°2 B2 Dy C02B2C
3.5548 [2]
9.331 [2]
HoC02B2 HoC°2B2C
3.5517 (2J 3.500 [6]
9.251 [2J 10.590 [6J
ErC02B2 ErC°2B2C
3.5450 [2J
9.161 [2]
F [l,2J A[3J A (helical) [4]
TN (K)
""6[6] 26 [1,2] 5.5 [3J ""7 [4]
? A [6]
""6 [6]
A [2] A [6]
9.3 [2J ""8 [6J
A [2J A [6], SR at 1.46 K A [2] A [6]
8.5 [2J 5.4 [6] 3.3 [2J ""4 [6]
F - ferromagnetic; A - antiferromagnetic; P - paramagnetic; imp - impurity phase; SR - spin reorientation; TC - Curie temperature; TN - Neel temperature; a and c - tetragonallanice parameters, z - coordinate of B with c as its unit. [IJ Feiner (1984), [2) Rupp et al. (1987), [3] Mulder et al. (1995), [4J Bud'ko et al. (1995a), [5] Just and Paufler (1996), [6] Rapp and El Massalami (1999).
It should be noted that for RNi2B2C the counterpart without carbon does not exist. Co is, so far, the only transition metal for which both the filled (with C) and the nonfilled structures could be prepared (see table 4). The examples of ferromagnetic GdC02B2 and antiferromagnetic GdC02B2C show that the introduction of interstitial carbon has a remarkable effect on the magnetic and, consequently, electronic properties of these compounds. 2.2. Lattice distortions due to magnetoelastic effects
Magnetic ordering in RNi2B2C compounds may result in a structural distortion caused by magnetoelastic effects. Using high-resolution neutron scattering on powder samples or high resolution x-ray diffraction on single crystals tetragonal-to-orthorhombic phase transitions have been observed for ErNizB2C (Detlefs et al, 1997a; Kreyssig et aI. 2(01), TbNizB2C (Song et al. 1999a; Kreyssig et al. 2001; Song et a1. 2001a, 2001b), DyNi2B2C
K.-H. MOLLER et aI.
222
TABLES at T = 1.5 K(after Kreyssig et aI. 2(01) for HoNi~ I B2C. DyNi~ I B2C. TbNi~ IB2C and ErNi~ IB2C (direction of the distortion from Del1efs et aI. 1999). The depicted direction for the distonion isthe direction, inwhich the (ab) basal plane is shortened, The distonion isquantified bythe ratio ofthe side length ofthe onhorhombic (ab) basal plane subtracted by I. All directions are described in the tetragonal reference system Magnetoelastic tetragonal-to-orthorhombic distortions
Compound
Propogation vector
Magnetic moment Value Direction
Distortion
Value
Direction
HoNi~IB2C
(00 l)
1O.2ttB
11 10j
0.0019
(I 10j
DyNi! IB2 C TbNi! IB2 C ErNi! IB2 C
(001)
8.0ttB
[I 10)
0.0034
[I I OJ
(0.55100)
8.2ttB
[100)
0.0062
[0 I OJ
(0.55400)
8.2ttB
[0 I OJ
0.0024
[0 10j
(332)
o
0
o o
o
10
g
-... l/)
E ::J o
borth :
o
154
156
U~----
26 (01 (a)
(b)
Fig. 1I. Onhorhombic distonion of tetragonal HoNi2B2C (a) upon cooling from 15 K to 1.5 K the neutron diffraction reflection (332) splits into two peaks. (b) Schematic presentation of the distortion: a, b - original tetragonal axes; dashed line: tetragonal basal plane; -+, t: shift ofthe Ho atoms leading tothe onhorhombic cell with the axes aorth' borth' Thick arrows: Ho magnetic moments inthe commensurate c-axis modulated structure (Kreyssig et aI. 1999a).
(Gasser et a1. 1998a; Kreyssig et al. 2001) and HoNi2B2C (Kreyssig et al. 1999a). The results of some of these investigations are summarized in table 5. Due to the different types of antiferromagnetic order occurring in these compounds (see section 4) different types (directions) of the orthorhombic distortion develop in the magnetically ordered state. Such magnetoelastic distortions are common in rare-earth compounds and result from a competition of elastic. magnetic and crystalline-electric-field energy (Morin and Schmitt 1990). It has been pointed out by Detlefs et al. (1999) that the lowering of lattice symmetry not only concerns the lattice structure but also has consequences for the magnetic structure and has to be taken into account for their determination as well as description. As an example. fig. 11 shows the splitting of a certain neutron-diffraction reflection. caused by the
MAGNETIC AND SUPERCONDUCTING PROPERTIES OF RNi2B2C
223
distortion, and a schematic representation of the distortion, for HoNhB2C, The distortion is a shortening of the tetragonal unit cell in [110] direction. 2.3. Single-, double- and triple-layer borocarbides (nitrides)
The RNi2BzC compounds can be considered as n = I variants of (RCIN)nNhBz structures where n RC or RN layers alternate with single NizBz layers (see fig. 12). For n = 2 the compounds YNiBC (Kitd et al. 1997), GdNiBC (EI Massalami et al. I995b), TbNiBC (EI Massalami et al. 1998b), DyNiBC (EI Massalami et al. 1998b), HoNiBC (EI Massalami et al. 1995a), ErNiBC (Chang et al. 1996a), YbNiBC (Hossain et al. 1998), LuNiBC (Siegrist et al. 1994a) and LaNiBN (Cava et al. 1994c) have been successfully prepared. Among them only LuNiBC was reported to be superconducting (Gao et al. 1994) which, however, is questioned (Cava 2001). Superconductivity was observed in R(Ni,Cu)BC by the substitution of Cu for Ni up to T c = 8.9 K for R = Y and up to T c = 6.4 K for R = Lu (Gangopadhyayand Schilling 1996). Superconductivity has been also reported for various RReBC samples which, however, consisted of unknown phases (R = Lu, Gd, Tb; Chinchure et al. 1999). ErNiBC is a ferromagnet (Chang et al. I996a). Comparative studies on RNiBC compounds have been presented by Fontes et al. (1999), Bourdarot et al. (2001) and Baggio-Saitovitch et al. (2001). For n = 3 the superconductor La3NizBzN3 has been successfully prepared (Cava et al. 1994c; Zandbergen et al. 1994a; Michor et al. 1996, 1998). Ce3NizB2N3 also exists but it is not superconducting above 4 K (Cava 200 I). For n = 4 the non-superconducting compounds LuzNiBCz (Zandbergen et al. 1994c) and Y2NiBC2 (Rukang et al. 1995) have been reported. However the relative positions of the layers do not appear to correlate overlong distances and the 2:1:1:2 phase is subject to severe microtwinning. So far no detailed analysis on the crystal structure and physical properties of the n = 4 compounds has been published. (c) lAJNi2B2NJ I41mmm (a) LuNi2B2C
l4Immm
=>
(b) LuNiBC P4Inmm
u c
Lu T,-16K
T,-3K?
T,-12K
Fig. 12. Tetragonal rare-earth nickel borocarbides (nitrides) with (a) single, (b) double and (c) triple RC(N)-Iayers and values of the superconducting transition temperature T c (Cava et al. 1994c; Gao et al. 1994; Zandbergen et al. 19943, respectively).
224
K.-H. MOLLER et al.
The investigation of the whole family of these multilayer compounds would help to understand the mechanisms for superconductivity and magnetism in the quaternary rareearth transition-metal borocarbides (Michor et al. 200 I; Baggio-Saitovitch et al. 200 I). However this report will be confined to magnetism and superconductivity in singlelayer RNi2B2C compounds i.e. compounds with (RCIN)nNi2B2 with n > I will not be considered further. 2.4. Related R-T -s-a N) phases
Besides the intermetallic compounds and lattice structures discussed in the previous subsections. there are various further quaternary. ternary and binary phases in the RT -B-C(N) systems which are related to the quaternary borocarbide superconductors. The presence of such phases in the samples. even in small amounts. may lead to wrong conclusions concerning the superconducting or magnetic behaviour of the main phase under investigation. Thus ferromagnetic impurity phases may pretend weak ferromagnetism or reentrant superconductivity. On the other hand superconducting impurity phases may simulate superconducting behaviour of the investigated main phase. Of particular interest are phases. which form in equilibrium with the I :2:2: I borocarbide superconductors. First. the series (RC)nNhB2 can be formally extended to (RC)n(Ni2B2)m with m i= I and/or n i= 1. Kito et al. (1997) prepared the n = 3, m = 2 quaternary borocarbide Y3Ni4B4C3 which is a tetragonal layered structure (proposed space group 14) built up of a half YNhB2C unit and a full YNiBC unit stacked along the c-axis, Measurements of resistance and susceptibility indicated a superconducting transition temperature of about 10 K (for a two-phase material containing the 3:4:4:3-phase together with the I: I: I :l-phase), In spite of the discovery of the LuNhB2C-type structure the crystal structures of quaternary superconducting R-T-B-C phases in the composition range near the stoichiometry I:2:2: I are far from being completely determined. This is particularly true for R-Pd-B-C compounds where the highest value of T e • 23 K for Y-Pd-B-C. had been reported (Cava et al. 1994a). Pd-based borocarbides have been prepared by arc melting (Cava et al. I994a; Sarrao et al. 1994) and also by non-equilibrium routes as rapid quenching (Strom et al. 1996; Freudenberger 2000) or mechanical alloying (Gumbel et aI. 2000). Although superconducting phases with LuNi2B2C-type structure have been identified for Th-Pd-B-C (Sarrao et al. 1994) and Y-Pd-B-C (Tominez et al. 1998) in all cases the samples have been found to be multiphase where (at least some of ) the phases of the mixtures are metastable and have a lattice structure with fcc symmetry (Strom et al. 1996; Freudenberger 2000). A detailed determination of that fcc structure from x-ray diffraction data is difficult and has not yet been achieved. An example of a nonidentified superconducting phase in the Th-Pd-B-C system appears in fig. 13. Figure 14 shows the x-ray pattern of a Ho-Pd-B-C sample with nominal I:2:2: I stoichiometry and the fcc lattice constants a of a series of R-Pd-B-C compounds prepared by rapid quenching (melt spinning). Among the numerous ternary rare-earth borocarbides the compounds RB2C2 with the LaB2C2-type structure (space group P4/mbm) consist of R layers and covalently bonded B-C networks alternatively stacked along the tetragonal c-axis (Bauer and Bars
225
MAGNETIC AND SUPERCONDUCTING PROPERTIES OF RNi2B2C 1.2r---"'---'-~-~---,
_ ~ It)
C\J
~
1.0 0.8 0.6
E 0.21- - - -
-- 0.4
a: 0.0 -0.2 5
.1
Th-Pd-B-C, non-identified 10
T [K]
15
20
t
25
t
Fig. 13. Transition curves (resistance R vs. temperature T) of arc melted Th-Pd-B-C with two superconducting phases: a not yet identified phase together with ThPd2B2C (Sarrao et al. 1994).
4.25
8
Ho-Pd-B-C
~7
'a:::l
.
.c
Sm· .·Eu Pr .·Nd
80
~4
~
~
.'::: 3
8N
Er. Gd
Dy
,-..
y.
~
'"
~ 2
Tm.·~Ho
Lu·
-
C 1 0
•
R-Pd-B-C
6 5
Ce
Tb
E 4.20 c
4.15
.....u ~
0
.''""
4.10 E 4.05
c, 0
.~
2.0
40 (a)
.sc 'iU 4.00 ..J 2.2 2.4 2.6 2.8 Atomic radius [nm] (b)
Fig. 14. (a) X-ray diffraction pattern of a rapid quenched sample with the nominal composition HoPd2B2C with typical fcc reflexes. (b) Lattice constant a of the non-identified fcc unit cell for different rapidly quenched samples of nominal composition RPd2B2C (Freudenberger 2(00).
1980). This series is interesting because it contains superconductors, YB2C2 and LuB2C2 (see table I), as well as magnetically ordered compounds with relatively complicated magnetic structures affected by quadrupolar interactions. DyB2C2 and HoB2C2 show a small spontaneous magnetization below Tc ~ 15 K (Yamauchi et at. 1999) and 5 ... 7 K (Sakai et at. 1981; Onodera et at. 1999), respectively. The ternary compounds RNi4B with the CeC04B-type structure (s.g. P6/mmm) are worth mentioning because YNi4B was the main phase on which trace superconductivity had been found leading to the discovery of the quaternary borocarbide superconductors (see subsection l.l). For R elements with partially filled 4f shells these 1:4: I compounds are magnetically ordered with ordering temperatures of 10.5 K, 39 K, 36 K, 18.5 K, 12 K, 6 K, 8 K and 3.5 K for R = Nd, Sm, Gd, Th, Dy, Ho, Er and Tm, respectively (Nagaraj an et at. 1995). HoNi4B has a spontaneous magnetization below Tc ~ 6 K (AlIeno et at. 2(01). Further ternary compounds possibly forming in equilibrium with RNhB2C are RNiC2 (space group Amm2, Behret aI. 1999b)
226
K.-H. MULLER et aI.
and RNi2C2 (Takeya et al. 1996) as well as R2Ni3B6 (orthorhombic, space group Cmmm) where H02NhB6 has a spontaneous magnetization below Tc ~ 12 K (Alieno et al. 2(01). There are also many binary compounds, which have to be considered as possible impurity phases in the quaternary borocarbides as e.g. Ni2B (s.g. I4/mcm), NbB and Ni3C (both s.g. Pnma) or RB2 (s.g. P6/mmm), RB4 (s.g. P4/mbm), RB6 (s.g. Pm3m), RB 14(s.g. Im3m) and R2C3 (s.g. I43d) where HoB2 is a ferromagnet with Tc = 15 K (Buschow 1980) and YB6, YB 12, Y2C3 are superconductors (Godart et al. 1995).
3. Basic properties of YNhB2C and LuNhB2C In this section we will briefly report on properties of RNi2B2C superconductors with elements R that have zero total angular momentum in their R 3+ Hund's rule ground state. Starting with the knowledge of these nonmagnetic borocarbide superconductors it will be easier to understand the behaviour of borocarbide superconductors with magnetic R 3+ ions, considered in sections 4 to 6. The superconducting transition temperature T c of the nonmagnetic RNhB2C superconductors, with R = Sc, Lu, Y, Th, are presented in fig. 9 and table 2. As already mentioned the position of Sc in fig. 9 might be questioned as the lattice constant a of superconducting ScNhB2C has recently been reported to be considerably larger (see subsection 2.1 and Tomilo et al. 2(01). Since superconducting ScNi2B2C is metastable and because Th is radioactive and thus more difficult to handle most published work on non-magnetic RNhB2C superconductors concerns YNi2B2C and LuNh B2C. 3.1. Normal state electronic properties and the superconducting state
Although the isomer shift of the Dy nucleus, determined by Mossbauer studies on DyNi2B2c' suggested that the Dy-C plane is insulating and the electrical conduction seems taking place mainly in the Ni-B sheets (Sanchez et al. 1996) it is now generally accepted that the RNhB2C compounds, despite their layered crystal structure, are three-dimensional in their electronic behaviour, and hence they are quite different from the layered cuprates (Lynn et al. 1997). Three-dimensional, nearly isotropic metallic behaviour was confirmed by measurements of the temperature dependence of resistivity, p(T), on single-crystalline YNi2B2C (see fig. 15) and LuNi2B2C over the entire temperature range T < 300 K (Fisher et al. 1997). A clearly three-dimensional, yet anisotropic electronic structure has also been experimentally determined using x-ray absorption spectroscopy (Lips et al. 1999). An isotropic character of the superconducting state of YNi2B2C was found by torque magnetometry (Johnston-Halperin et al. 1995). Different from the Cu in cuprate systems Ni does not carry a local magnetic moment in the quaternary borocarbides (Lynn 2001). For YNi2B2C this had been confirmed by Suh et al. (1996) analyzing susceptibility and NMR data as well as results of electronic structure calculations. These authors also could exclude antiferromagnetic spin correlations on the Ni sublattice. Electronic structure calculations clearly showed that the I:2:2: I borocarbides are three-dimensional metals with all atoms contributing to the metallic character and, although the main contribution to the density of states at the Fermi level, N(EF), arises from Ni 3d electrons, there is a considerable admixture of Y 4d as well as B 2p and C 2p electrons (Pickett and Singh 1994;
MAGNETIC AND SUPERCONOUCfING PROPERTIES OF RNi282C
227
40 35 30
e
25
u
a 20 ~
Q.
15 10
YNi 2B2C
5 0
0
50
100 150 200 250 300 Temperature (K)
Fig. 15. Isotropic metallic behaviour of the resistivity of YNi282C. measured along the tetragonal c-axis and a-axis of a single crystal (Fisher et al. 1997).
Mattheis 1994; Mattheis et al. 1994; Coehoorn 1994; Ravindran et al. 1998; see fig. 16). It has been concluded that the superconductivity in RNhB2C is related to the high density of states on its narrow peak at the Fermi level shown in fig. 16 for YNhB2C but also detected for LuNi2B2C and YPd2B2C (Coehoorn 1994). In the Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity the transition temperature T c strongly increases with N(EF): T c = 1.13BDexp(-ljN(EF)V),
(4)
where 00 is the Debye temperature characterizing the phonon spectrum of the material which limits the attractive range of the electron-phonon (el-ph) interaction. V is some measure of the electron-phonon interaction and N(EF)V« 1 is provided (Bardeen et al. 1957a. 1957b). For LaNi2B2C the value of N(EF) is about half of that for LuNhB2C or YNhB2C (Mattheiss et al. 1994; Divis et al. 2000) and it has been argued that, according to equation (4). this is the reason why LaNhB2C is not superconducting. However it has been pointed out by Drechsler et al. (1999) that the superconductor LaPt2B2C with T; ~ 11 K has a similar or even lower value of N(EF) compared to LaNizB2C (Singh 1994). Consequently, since OD is similar for all RNhB2C compounds. there must also be a considerable variation of the parameter V across the series of the quaternary borocarbides, which affects T c according to equation (4) or these materials are not simple BCS superconductors. A remarkable boron isotope effect has been observed for YNi2B2C as well as LuNi2B2C supporting the classification of these materials as phonon mediated superconductors (Lawrie and Franck 1995; Cheon et al. 1999. see fig. 17). The BCS theory predicts for the isotope effect T c '" M -a where M is the mass of the atoms which substantially participate in the lattice vibrations being relevant for the superconductivity, and a = 0.5 is the isotope exponent. For YNi2B2C and LuNi2B2C Cheon et al. (1999) found aD ~ 0.21 and 0.11, respectively, as the partial isotope exponents of boron. No
228
K.-H. MULLER et aI.
15
10
-
total
--- NI-3d
5
,
"8
-
.
Y-5p
I
--- Y-4d
II
"
I _\
I
"'~ - 1·"\.../
, -
-10
\, \~
C-2p
-8
-6
-4
-2
o
2
4
energy (eV) Fig. 16. Total and partial density of states calculated for YNi282C. using the local density approximation. The Fermi level EF is at zero energy (Rosner et aI. 2001).
carbon isotope effect could be observed in YNi2B2C i.e. no change of T c when 12C is substituted by l3C (Lawrie and Franck 1995). Although at first glance the observation of a clear B isotope effect seems to prove the el-ph mechanism and the special role of a high-frequency B Aig related phonon near 100 meV which strongly modulate the NiB4 tetrahedral bond as suggested by Mattheiss (1994), a more detailed analysis shows that this phenomenon is probably much more complex and electronic degrees of freedom are involved, too (Drechsler et al. 2oo1a, 2001b). In fact, any attempt to reproduce the isotope effect within the standard classical phonon scenario based on the Eliashberg theory (Shulga et al. 1998» requires a significant coupling to those high-frequency modes and limits in this way the total coupling strength to Aph < 0.7, at variance with the analysis of specific heat data pointing to a larger coupling strength Aph ~ 1. (We remind the reader that the Eliashberg and BCS coupling constants are approximately related as Aph ,....., (N(EF)V + 11-*)/0 - N(EF)V); compare eq. (4), 11- * ~ 0.1 is the Coulomb pseudopotential.) In addition, the nearly twice as large isotope exponent observed for YNjzB2C in comparison with that of the closely related compound LuNi2B2C can be understood in such a nonclassic scenario. Analyzing thermodynamic data and phonon densities of states Hilscher and Michor (999) concluded that for 1:2:2:1 borocarbides the BCS weak-coupling limit is not
MAGNETIC AND SUPERCONDUCfING PROPERTIES OF RNi282C
229
0.0
-0.2
Q'
-0.4
M
~__ -0.6 ~
-0.8
14.0
14.5
15.0
15.5
Temperature (K) Fig. 17. Field cooled magnetization measured for increasing temperature at /-LoB = 2.5 mT on single crystalline YNi2B2C with the two isotopes lOB (solid lines) and I I B (dotted lines), clearly indicating a boron isotope effect (after Cheon et al, 1999).
fulfilled and strong-coupling effects arise from the presence of particular low-frequency optical phonon modes. This is also supported by point-contact spectroscopy (Yanson et al. 1997). These effects can well be described by strong-coupling corrections of Carbotte (1990). Hilscher et al. (2001) have shown that a strong drop of T c from LuNhB2C or YNhB2C to LaNi2B2C can be predicted by using the formula of McMillan (1968) who calculated T c in the framework of the Gor'kov-Eliashberg theory which takes into account strong coupling effects as well as details of the phonon spectrum and of the electron-phonon coupling (Allen 1991). However in this approach, the electronic structure is described by an isotropic single band which may be the reason why some problems with the borocarbide superconductors remained unsolved despite the mentioned above corrections to the BCS theory, as e.g. the question why LaPt2B2C and YRu2B2C are superconducting but LaNi2B2C and YCo2B2C are not, or the anisotropy and the unusual temperature dependence of H c2 discussed in subsection 3.2 where an extension of the single-band theory to a two-band structure is introduced. The key to the mentioned problems is the complex Fermi surface (FS) of the quaternary borocarbides, which consists of several sheets and is highly anisotropic with strongly varying values of the Fermi velocity VF (Drechsler et al. 200 1a; Rosner et al. 200 1). Therefore T c will not be governed by the overall density of states N(EF) but by the partial density of states (DOS) of slow electrons that have been shown to stem from nested regions with nesting vectors r ~ (0.5 ... 0.6,0,0). For LuNhB2C a nesting feature had been predicted by Rhee et al. (1995) and has been confirmed by positron annihilation (Dugdale et al. 1999). The nesting vector r also reappears in phonon softening observed in LuNhB2C and YNhB2C
230
K.-H. MULLER et aI.
(Dervenagas et al. 1995b; Zarestky et al. 1999). Probably the normal-state resistivity p is isotropic (see fig. 15) because it is related to groups of electrons with relatively large VF being less anisotropic and not associated with FS nesting. In LaNi2B2C nested regions are missing and there is a smaller dispersion of VF (Rosner et al. 200 I). 3.2. The upper critical field
The upper critical field H c2(T) is a fundamental quantity of type-II superconductors. It provides deep insight (i) into the coupling strength, (ii) into the electronic structure, (iii) into the symmetry and anisotropy of the order parameter, (iv) into the presence of various disorder related scattering processes, and, in the case of magnetic rare earth ions present, into (v) the anisotropy of the crystal field and local exchange processes. All these factors affect the magnitude, the shape and the anisotropy of H c2 (T). Naturally, it is a very difficult task to take into account all of them on equal footing within a consequent microscopic theory. In this respect borocarbide superconductors are very complex systems quantitatively not yet well understood. However, due to the rich variety of possible isoelectronic chemical substitutions systematic investigations are possible and as a consequence much qualitative insights can be gained. The experimental data, reported in the literature, on the upper critical field H c2 of YNhB2C and LuNhB2C scatter considerably due to paramagnetic signals from impurities that are difficult to avoid in the nominally non-magnetic borocarbides (Mun et al. 1998). Nevertheless it has clearly been shown for both compounds that H c2 is anisotropic not only with respect to the tetragonal c-axis and the basal plane but also within that plane (Xu et al. 1994; Takagi et al. 1997; Rathnayaka et al. 1997; Metlushko et al. 1997; Du Mar et al. 1998). Figure 18 shows, as an example, the determination of H c2 and its anisotropy from the measured temperature dependence of magnetization of a LuNhB2C single crystal in an applied magnetic field. (It is interesting that a finite slope for H c2 (T) as T ..... 0 was found for LuNi2B2C, see Schmiedeshoff et al. 2001). The out-of-plane anisotropy can be described within the phenomenological one-band GL theory of superconductivity (Ginzburg and Landau 1950) or its microscopic derivation from the BCS theory (Gor'kov 1959) by an effective mass anisotropy. In the case of LuNhB2C (fig. 18) the degree of the out-of-plane anisotropy of H c2 is nearly temperature independent and the resulting mass anisotropy, mUm: ::::: 1.35, is in good agreement with the Fermi surface anisotropy resulting from band structure calculations (Mattheis 1994). The in-plane anisotropy cannot be explained within the (local) GL theory. In principle, nonlocal extension introduced by Hohenberg and Werthamer (1967) might be helpful to overcome this difficulty. In this approach, valid for weak anisotropies, in addition to the second rank mass tensor, a fourth rank tensor is introduced. The nonlocal effects were predicted to be observable in sufficiently clean materials where the transport mean free path I becomes larger than the coherence length ;. Strictly speaking, the correct description of strongly anisotropic cases as the nested (quadratic) parts of the Fermi surface would require the introduction of a large number of higher order ranked tensors or a discrete description (Maska and Mierzejewski 2001). Therefore the frequently used simple nonlocal approaches mentioned below should be taken with some caution despite its certain success in describing the physics of vortex lattices (see chapter 5). At least the
MAGNETIC AND SUPERCONDUCTING PROPERTIES OF RNi2B2C
231
(b)
0
s
-0.5
i" I.e
- 1
~
-1.5 H=3.0T
- 2
--<100> --<110> --<001>
-2.5 - 3 8.5
9
9.5
10
10.5
11
T(K) Fig. 18. Temperature dependence of the magnetization of a LuNi2B2C single crystal in a field of 3 T applied along the crystallographic directions c, a and (110), clearly showing an out-Qf-(tetragonal basal) plane anisotropy as well as an in-plane anisotropy of H c2 where H c2(T) is determined by the indicated linear extrapolation (after Metlushko et aI. 1997).
clear microscopic meaning of the effective quantities present in the weak anisotropic case is lost in the strongly anisotropic one. The nonlocal effects can result in an anisotropy in H c2 due to anisotropy of the pairing state (Shiraishi et al. 1999) or anisotropy in the shape of the Fermi surface. In the case of {LaSr)Cu04, for example, the anisotropy of H c2 has been explained by a d x2-y2 pairing state (Takanaka and Kuboya 1995). The results of Metlushko et al. (1997) on H c2 and the field dependence of specific heat suggested the superconductivity of the borocarbides to be of d-waves nature too (Nohara et al. 1997; Wang and Maki 1998). However, now it is widely believed that the borocarbides are conventional s-wave superconductors (Prozorov et al. 1994; Cywinski et al. 1994; Ekino et al. 1996; Yang et al. 2000; Won and Maki 200 I) which was concluded from magnetic properties, muon spin resonance, tunneling spectroscopy, specific heat, inelastic light scattering etc., but the quasiparticle energy gap is strongly anisotropic. This anisotropy and/or the anisotropic shape of the Fermi surface (see Drechsler et al. 1999) are assumed to cause the mentioned basal anisotropy of H c 2 because the borocarbide superconductors are usually clean-limit type II superconductors. In the clean limit for an anisotropic Fermi surface the non-local corrections to H c2 are given by H c2(T, ¢J) = D[l
+ (-3/2 + 0.34C)t + 0.34Atcos(4¢J)]t,
(5)
where t = 1 - T / T c- ¢J is the angle in the basal plane, measured with respect to the tetragonal a-axis, A and C contain averages of the Fermi velocity and can be estimated from electronic-structure calculations or taken, together with D, as fitting parameters (Metlushko et al. 1997). For LuNjzB2C these authors found C = 9.4, A = 0.43 and a very good agreement of the experimentally determined dependence of H c2 on T and ¢J with equation (5). Also the data of H c2 measured in c direction could very well be reproduced
232
K.-H. MULLER et al.
Iii o -.;:; '5 2 ~
a. ::::>
---- ...... single band'" ...... -I ...... limp = 17cm .....
0.3
0.6
Temperature
0.9
r/r,
Fig. 19. Hez(T) of a LuNi2B2C single crystal measured parallel to the tetragonal c-axis (0). The solid curve was calculated using a two-band model (see text). Dashed lines: isotropic single-band (l5B) models with two values of Y imp (see text; after Shulga et al. 1998).
by a corresponding formula. A special feature of equation (5) is, for appropriate values of A and C, a positive curvature of the temperature dependence of H c2 near T c- which does not occur in the BCS theory. Such an upward curvature has been observed along all crystal orientations, for LuNizBzC as well as YNi2BZC. An example is shown in fig. 19. The anomalous S-like shape of Hcz(T) as compared with the standard paraboliclike Werthamer-Helfand Hohenberg (WHH) is roughly characterized by three parameters, the two curvature exponents near T = 0 and T = T c and the inflection point in between. An empirically found simple expression which only contains a single exponent a, is
(6) Usually H* cZ does not exceed H cz(O) by more than about 10 to 15%. Since experimentally it is somewhat inconvenient to perform measurements at very low temperatures and relatively high fields high accuracy extrapolations of H c2 (0) are impossible. For qualitative discussions H c2(0) can often be replaced by H* c2, keeping in mind the small uncertainty mentioned above. It has been pointed out by Shulga et a1. (1998) that the non-local approach leading to results as equation (5) does not cover all of the experimental results as e.g. the fact that the reported anisotropy of H cZ of YNjzB2C is significantly smaller than that of LuNjzB2C but its positive curvature is even larger. Therefore these authors analyzed H cZ(T) within the microscopic Eliashberg theory of superconductivity (Eliashberg 1960). First they tried to explain the experimental data on H c2(T) taking into account only an isotropic single-band (ISB) effective electronic structure. The standard ISB approach (Carbotte 1990) describes quantitatively the renormalization of the physical properties of metallic systems due to electron-phonon (el-ph) interaction. The input parameters are the density of states N(EF),
MAGNETIC AND SUPERCONDUCTING PROPERTIES OF RNi2B2C
233
the Fermi velocity VF, the impurity scattering rate Yimp, the Coulomb pseudopotential JL* and the spectral function a(w)2F(w) of the el-ph interaction. These parameters can be determined from experimental data on the normal-state low-temperature electronic specific heat, the plasma frequency (from optical conductivity), H c2(0), T c and its isotope exponent a, and the low-T resistivity p(O) or the Dingle temperature TD (from de Haasvan Alphen experiments). The el-ph coupling constant Aph = 2 Jdwa(w)2F(w)/w has been estimated to be Aph ~ 0.7 which indicates an intermediate coupling regime where H c2(T) should be insensitive to details of a(w)2F(w). It was found that the ISB approach cannot reproduce the experimental data on H c2(T) of LuNi2B2C and YNhB2C. In the example of fig. 19 not only the positive curvature is absent in the ISB results but, even more importantly, also the value H c2 (0) can only be achieved for the unrealistically high scattering rate Yimp = 300 cm " ! whereas realistic values Yimp ~ 17 em"! result in a too low ISB value of H c2(0). It should be noted that for weakly or moderately anisotropic system in the clean limit as the nonmagnetic borocarbides under consideration, the evaluation of a quantity Q'" H c2(0)(V 2F)FS/(l + Aph)2.4Tc2 (with (V 2F)FS as the Fermi velocity averaged over the whole Fermi surface) is helpful to classify them as pronounced multi-band superconductors (for details see Shulga and Drechsler 2001; Fuchs et al. 2001). Superconductors with Q ~ 1 can be described by the isotropic single band model. A typical example is Nb for which Q ~ 1.4 was obtained (Shulga and Drechsler 200 1). If the value of Q departs significantly from I, a multi-band or unconventional description is required. This Q-criterion is more faithful than the often used oversimplified phenomenological models. For YNhB2C a value Q ~ 4 is obtained which is in accord with the above mentioned numerical result showing that the experimental H c2 (T) data obtained for YNi2B2C can not be described by the standard ISB approach. Thus Shulga et al. (1998) extended their calculation considering two bands in the Eliashberg analysis where one of the two Fermi velocities, VPI, is considerably smaller than the Fermi surface average of vp. These slow electrons have a strong el-ph coupling and are mainly responsible for the superconductivity. Noteworthy, slow electrons in LuNhB2C and YNhB2C stem from nested regions on the Fermi surface whereas in the nonsuperconducting compound LaNi2B2C there is no nesting and, consequently, a smaller dispersion of VF (Rosner et al. 2001). The dispersion of VF in YNhB2C has been confirmed by de Haas van Alphen experiments (Goll et al. 1996). The values of H c2 (0) and of Teare reduced by the presence of the faster electrons that have a moderate el-ph coupling only. On the other hand, the positive curvature of H c2(T) is caused by interband coupling between the slow and the fast electrons. In the example of fig. 19 the experimental H c2( T ) curve could be well reproduced by taking the velocity ratio VF2/VFI ~ 4.5 and adjusting the other input parameters of the two-band model to experimental data from the literature. Figure 20 shows that, within the two-band model, the value H c2(0) as well as the degree of positive curvature can be considerably varied by changing the scattering rate Yimp (Shulga and Drechsler 2001; Fuchs et al. 2001). As expected, in the clean limit H c2 decreases with increasing Yimp. This prediction has been experimentally confirmed for pseudoquatemary (Lu,Y)NhB2C compounds where an increase of substitutional disorder results in a decrease of H c2(T) (see subsection 6.2, Fuchs et aI. 2001). On the other hand. for larger values of Yimp (quasi-dirty limit) H c2 is predicted to increase with increasing
234
K.-H. MULLER et al.
"tImp = 0
10 10 E-o
65 COl
:t 5
10
TIKI
15
, ,,
0' 0
,
100
200
300
Fig. 20. (a) Temperature dependence of the upper critical field calculated within a two-band model for several impurity scattering rates Yimp (cm- I ). (b) calculated H c2(0)-VS.-Yimp curve illustrating the transition from the clean to the dirty limit. Dotted line: H c2(0)-Yimp dependence in the dirty limit. (Drechsler et al. 2000; Fuchs et al. 200 I).
Y imp. Consequently H c2 has a minimum at a certain value of Y imp if the other input parameters of the two-band model are kept constant. We conclude this subsection with several remarks on the interpretation of the anisotropy of H c2. The largest in-plane anisotropy reported by Metlushko et al. (1997) coincides with the direction of the nesting vector (0.55,0,0). Another manifestation of strong local anisotropy effects is provided by deviations from the () (angular) dependence due to anisotropic effective masses (Fermi velocities)
(7) where y 2 = mc/mab and () measures the angle between the magnetic field and the tetragonal c-axis (see e.g. Tinkham 1994). Due to the interaction with the nearly isotropic weakly coupled electrons the strong anisotropy of the nested parts of the Fermi surface is washed out. In fact, deviations from eq. (7), i.e. a stronger angular dependence near () = tt /2, have been observed for YNhB2C by Winzer et al. (2002). 3.3. Magnetotransport Investigations of the normal state magnetoresistance (MR) as well as the Hall effect and the thermal conductivity in the normal and superconducting mixed states give an important information about the electronic structure and the properties of vortex lattice of the investigated materials. 3.3.1. Normal state magnetoresistance The normal state magnetoresistance of the nonmagnetic compounds YNi2B2C and LuNi2B2C, on poly- as well as single crystals, has been studied by several groups (see, e.g., Takagi et al. 1994; Mazumdar et al. 1996; Rathnayaka et al. 1997; Fisher
MAGNETIC AND SUPERCONDUCTING PROPERTIES OF RNiz8ZC
235
et aI. 1997; Narozhnyi et al 1999a). It was found (Fisher et aI. 1997) that the in-plane magnetoresistance (i.e. the current flowing perpendicular to the e axis), with the magnetic field H parallel to the current, of a LuNhB2C single crystal for temperatures between 40 and 200 K is small, positive and is proportional to H 2 . For single crystalline YNhB2C the in-plane magnetoresistance, with applied field parallel to the e axis, was found to be quite large (6.5% for H = 45 kOe at T = 25 K) in comparison with normal metals (Rathnayaka et al. 1997). It was observed that the resistance varies nearly as H 2 for low fields, and seems to become linear with H at higher fields. At T = 15K the values of MR are ~ 7.5% and 8% for H parallel and perpendicular, respectively, to the e axis indicating a very small anisotropy in the magnetoresistance. The value (~7.3% for H = 45 kOe at T = 20 K) as well as the field dependence of MR for a LuNhB2C single crystal were found to be very similar to that observed for a YNhB2C single crystal (Rathnayaka et aI. 1997). A similar value of MR has been reported for a YNi2B2C polycrystalline sample (Mazumdar et aI. 1996). At the same time, for LuNhB2C polycrystalline samples considerably larger values of the magnetoresistance were reported by two groups: 40% for H = 80 kOe at T = 18 K (Takagi et aI. 1994) and 90% for H = 160 kOe at T = 20 K (Narozhnyi et al. 1999a). A comparative study of the magnetoresistance of high quality LuNi2B2C and YNi2B2C polycrystalline samples prepared under the same conditions and having high residual resistance ratios (Narozhnyi et aI. 1999a) has revealed a clear difference in the behaviour of their MR. For H = 160 kOe at T = 20 K MR is about 90% for LuNi2B2C and is nearly three times smaller for YNhB2C (~33%). A possible reason for the very large positive MR in LuNhB2C and for the significantly larger MR of the polycrystalline sample (Narozhnyi et aI. 1999a) compared to single crystal data (Rathnayaka et aI. 1997) is the formation of open orbits on the Fermi surface of that compound for H ..le. (When a magnetic field is applied, the resulting electron orbits may be closed or open depending upon the topology of the Fermi surface.) The possibility of the formation of open orbits for borocarbides was pointed out by Kim et aI. (1995), Lee et al. (1994) and Rosner et al. (2001). It is well known (Lifshitz et aI. 1973) that open orbits can lead to large values of MR ,...., H 2 , whereas closed orbits should give rise to saturation of MR for large H. In that case, for polycrystals, the averaging of MR should lead (Lifshitz et aI. 1973) to a practically linear dependence of the resistivity on H (so called Kapitza's law). In accordance with this, the observed dependencies for LuNi2B2C polycrystals are approximately linear (Narozhnyi et aI. 1999a). The MR(H) dependence for polycrystals, in the case of open orbits for some directions of H, should be stronger than that observed for single crystals for H lie where only closed orbits could be expected. Therefore, the significantly larger MR found for the LuNi2B2C polycrystals, in comparison with that observed for the single crystal for Hlle, can be considered as an indication for the open-orbits formation in LuNi2B2C for H ..le. For YNi2B2C a substantially smaller MR has been seen (Mazumdar et al. 1996; Rathnayaka et al. 1997). The differences in the properties of these very similar compounds should be connected with a difference between their electronic structure. As has been noted by Lee et al. (1994) the Fermi surface topology of the borocarbides is very sensitive to the position of the Fermi level, which may be slightly different for the two cases, Lu and Y, due to, e.g., different lattice constants. Recently the difference in the Fermi surface topology between LuNi2B2C and YNhB2C has been discussed in more detail by Rosner et al. (200 I). From the reported results the
236
K.-H. MULLER et al.
formation of open orbits seems to be easier in case of LuNhB2C in comparison with YNhB2C, but a more careful investigation is necessary for a better understanding of the observed phenomenon. It should be also noted that a change of sign of the normal state magnetoresistance from positive at low temperatures to negative at T ~ 80 K when H = 40 kOe was reported for YNi2B2C single crystals (Chu et al. 2000). As mentioned above, only positive MR was observed for LuNi2B2C single crystals for temperatures between 40 and 200 K (Fisher et al. 1997). The sign reversal was interpreted by Chu et al. (2000) as an indication of the presence of magnetically related scattering, which could result from suppression of spin fluctuations. 3.3.2. The Hall effect The Hall effect has been studied only for some borocarbides. The normal state Hall coefficients RH were found to be negative and only weakly temperature dependent for polycrystalline borocarbides based on R = Y (Fisher et al. 1995; Narozhnyi et al. 1996; MandaI and Winzer 1997), La (Fisher et al. 1995), Ho (Fisher et al. 1995; MandaI and Winzer 1997) and Gd (MandaI and Winzer 1997). A negative but strongly temperature dependent RH was found for the heavy-fermion compound YbNhB2C (Narozhnyi et al. 1999b). A comparative study of the Hall effect for nonmagnetic YNhB2C and LuNhB2C borocarbides has revealed a pronounced difference in the behaviour of these two closely related compounds in the normal state (Narozhnyi et al. 1999a; Freudenberger et al. 1999a). Weakly temperature dependent low field Hall coefficients were observed for both compounds. At the same time the RH (T) curve obtained for LuNi2B2C at H = 50 kOe exhibits a pronounced temperature dependence below 60 K (see fig. 21) connected with a nonlinearity found for the field dependence of the Hall resistivity Pxy(H) at low T. This nonlinearity is clearly seen for LuNhB2C in fig. 22(a, b) where the Pxy(H) dependencies for LuNi2B2C and YNjzB2C are shown in the normal and in the mixed states. Linear Pxy(H) dependencies extrapolated from the low H region are also shown in fig. 22(a, b) by dashed lines. The deviation from linear Pxy(H) dependence increases with lowering temperature. It should be underlined that no nonlinearity in the Pxy(H) dependence is
o
E
~
0.4 .... ~
0
~~----I ~ 0.2
ocr.0.0 L.-_ _
-
o
H=50 kOe ~'--
_ _-'--,,----_ _-::-'
200
100
300
T (K)
Fig. 21. Absolute value of the Hall coefficient IRHI (obtained at H = 50 kOe) as a function of temperature T for polycrystalline LuNi282C and YNi282C samples. Dotted line - linear extrapolation of high temperature data for LuNi282C. Solid lines are guides for the eye (Narozhnyi et al. 1999a).
237
MAGNETIC AND SUPERCONDUCTING PROPERTIES OF RNi2B2C
E
0.1
(J
~
f \
jj Ipxyl- (Plll 1/ ff __P=2·0 T=9K
(e) 0.01
LuNi B C 2
2
::
-0-
,: 0.1
eO'~20K
0
YNi B C 4O,IOK..,c'
~~0.2
E 0.1
2 4.5K
9,"0
~
'0
•
2~
H (kOe)
40K
0.0
a
I ~/12 ~'14
T
10
1
10
~ 20
25
30
H (1<00)
(b)
T T
"'1 •
p..
0
10
0.01
/\
i
II
()~
0.00.1<'
1
'l
Ai •
cf
0.=
K
1
u p E erEt"10K1-
0.1 ~
~
.J'"'j
50 100 1 5 0 "
3.
E
T=10K
--- r-n
Pxy - P",
P=2.1
(d) - . - T=8K - - T=10K
h=8K
; 30
H (kOe)
40
50
0.1
1
10
P", (jUl em)
Fig. 22. (a. b) Absolute value of the Hall resistivity IPxyl vs. magnetic field H for polycrystalline LuNi2B2C (a) and YNi2B2C (b). The dashed lines are low-field asymptotes to the normal state curves. The insets show the results for H up to 160 kOe. (c. d) Hall resistivity IPxyl vs. longitudinal resistivity Pxx for LuNi2B2C (c) and YNi2B2C (d). In the insets !Pxy! and Pxx vs. H are simultaneously shown for T = 10 K (after Narozhnyi et aI. I999a).
observed for YNi2B2C (see the inset of fig. 22b). No indications of nonlinear Pxy(H) dependencies have been observed also for Ho-, Gd-, La- and Yb-based borocarbides. (Fisher et al. 1995; Mandai and Winzer 1997; Narozhnyi et al. 1999b). The values of the Hall coefficient reported for LuNizB2C and YNizB2C (Narozhnyi et al. 1999a) are comparable with those obtained for YNi2B2C (Fisher et al. 1995; Mandai and Winzer 1997) but they are about five times (LuNi2B2C) or ten times (YNizB2C) smaller than the value resulting from band structure calculations (Pickett and Singh 1994) for LuNi2B2C (3 x 10-9 m 3 C- I = 3 x 10-IIQcmOe- 1) . The reason for these deviations is not clear so far. Possibly the constant relaxation time approximation used by Pickett and Singh (1994) is not valid for LuNhB2C having several bands crossing the Fermi level. It is also not excluded that correlation effects have to be taken into account. The estimation of the carrier density from the RH value at T = 300 K. by using a single band model which is a rough approximation. gives 1.5 and 2.4 carriers per unit cell for LuNizB2C and YNhB2C, respectively. The Hall effect in the superconducting mixed state has been investigated only for LuNi2B2C and YNizB2C (Narozhnyi et al. 1999a; Freudenberger et a1. 1999a). The Hall resistivity Pxy of both compounds is negative in the mixed as well as in the normal state
238
K.-H. MULLER et al.
and has no sign reversal below T c- contrary to the behaviour of high- T c superconductors (Galffy and Zirngiebl 1988). In the mixed state the behaviour of the both systems is quite similar, see fig. 22 (Narozhnyi et al. 1999a). Below T c in low fields it was shown that Pxy = 0, see the Pxy(H) curves obtained at, e.g., T = 10 K (fig. 22(a, bj), At higher fields (in the region close to the resistive superconducting transition) the Hall resistivity increases in its absolute value and gradually reaches the Pxy(H) curve obtained in the normal state at temperatures slightly above T c. The Hall resistivity curve Pxy(H) in the mixed state shifts with increasing temperature to lower magnetic fields similar to the behaviour usually observed for the longitudinal resistivity curve Pxx(H). In the mixed state two regions concerning the behaviour of Pxy and Pxx can be distinguished. At low magnetic fields both Pxx and Pxy vanish. For higher fields it is clearly seen that the scaling behaviour IPxy I = Apxxf3 holds for both compounds (see fig. 22(c, dj). The value of fJ is 2.0 ± 0.1 and 2.1 ± 0.1 for Lu- and V-based samples, respectively. It decreases to 1.7 ± 0.1 for unannealed LuNi2B2C sample having an approximately one order of magnitude higher resistivity at T = 17 K. This may be connected with an increase of the pinning strength due to the considerably larger concentration of defects leading to a larger resistivity in this sample. The decrease of the scaling exponent with increasing pinning strength was obtained in the WDT theory (Wang et al. 1994), taking into account the backftow current of vortices due to the effects of pinning. Another manifestation of the pinning effects, predicted by the WDT model. can be seen in the insets of fig. 22(c, d) where the Pxy(H) and Pxx(H) curves in the superconducting transition region are simultaneously shown. For decreasing fields, Pxx vanishes at definitely lower values of H than Ipxy I as it was pointed out by WDT. From these results it is clear, that pinning effects are considerably important for the mixed state HaIl effect in the investigated borocarbides. 3.3.3. Thermal conductivity Thermal conductivity was measured for YNhB2C and LuNhB2C (Sera et al. 1996; Boaknin et al. 2000, 2001) as well as for HoNi2B2C and DyNhB2C (Sera et al. 1996; Hennings et al. 200 I) single crystals. It was found that for all borocarbides investigated so far the thermal conductivity in the entire temperature range from T c to room temperature is dominated by electrons (Sera et aI. 1996; Boaknin et al. 2000; Hennings et al. 200 I). Below T c the phonon contribution increases considerably with decreasing temperature and below 5 K the thermal conductivity is mainly due to phonons whose mean free path is limited mainly by sample boundaries. An unusually high phonon peak centered at T ~ 5 K was observed for LuNi2B2C (Boaknin et al. 2000, see fig. 23). A similar behaviour of the thermal conductivity, but with an about three times smaller value of the peak, was reported for YNhB2C (Sera et al. 1996). For magnetic RNi2B2C (R = Ho and Dy) the thermal conductivity exhibits a marked loss of scattering at TN (Sera et al. 1996; Hennings et al. 200 I). Both systems do not show a phonon enhancement below T c- as reported for nonmagnetic borocarbides. Results on the thermal conductivity in the superconducting mixed state have been reported for LuNi2B2C for temperatures down to 70 mK (T c/2oo) and magnetic fields from H 0 to above H c2 70 kOe (Boaknin et al. 200 I, see fig. 24). It was found that as soon as vortices enter the sample, the thermal conductivity at T -+ 0 grows rapidly, showing unambiguously that delocalized quasiparticles are present even at the
=
=
MAGNETIC ANDSUPERCONDUCTING PROPERTIES OF RNi2B2C
r.
200
:
fi ~150
......
T~
239
...
\./'
~
Ii 100
it
50 ..........~""'-~ 10 15
OL-_........,~
o
5
.........._--' 25 20
T(K)
Fig. 23. Thermal conductivity of LuNi2B2C vs. temperature for a heat current in the basal plane (a-axis). Note the change of slope at T c (with an arrow showing the resistive transition) and the large phonon peak at 5 K (Boaknin et al. 2(00).
1.0
......................... _.. _
_
LUNi282~//
I-
--
0.4
~.
~
•
..../
0
../.~~
I-
0.6
~
./'/0
0.8
oJ
--
./
../
~
.ci
j
i
Nb
..D'
0.2
......rr···
0.0 ...~--L._lQQl"""--=---L..~........J'--"'--...L----'---' 0.0 0.2 0.4 0.6
0.8
1.0
1.2
H IHc2 Fig. 24. Magnetic field dependence of the electronic thermal conductivity at T --+ O. normalized to its value at H c2. Circles are for LuNi2 B2C. squares for UPt3 and diamonds for Nb. Note the qualitative difference between the activated thermal conductivity of the s-wave superconductor Nb and the roughly linear growth seen in UPt3. a superconductor with a line of nodes (Boaknin et al. 200 I).
lowest energies. The electronic transport grows with the magnetic field similar to the behaviour of the heavy fermion superconductor UPt3. for which lines of nodes in the gap were found. and very different from the exponential dependence of electronic thermal conductivity characteristic of s-wave superconductors. It was concluded by Boaknin et al. (2001) that the gap function of LuNi2B2C must have nodes or at least very deep minima. The estimation of the gap anisotropy has given a value of 10 (at least). unprecedented in phonon-induced superconductivity. An even larger gap anisotropy of about 100 has been
K.-H. MULLER et aI.
240
reported by Izawa et al. (2002) for YNi2B2C. The thermal conductivity will be discussed together with the specific heat of borocarbides in the mixed state in section 6. The behaviour of the thermopower of the borocarbides will not be considered in this paper. The discussion of this particular problem can be found in the review article of Naugle et al. (1999). 3.4. Characteristics of superconducting YNi282C and LuNi282C
Here we will summarize. from the previous subsections as well as from literature. some typical properties and representative parameters (see table 6) of the superconducting state of YNi2B2C and LuNhB2C where completeness is not attempted. These materials are usually clean-limit type II superconductors. However by substitutional disorder on the rare earth site in (Y.Lu)NhB2C or on the transition-metal site in Lu(Ni.CohB2C the residual resistance ratio RRR = p(3oo K)/ p(T c ) . where p(T) is the normal state resistivity. and the mean free path I of the electrons in the normal state can be considerably reduced TABLE 6 Property
LuNi2B2C
r; (K) IJ.OH c2 (T) lJ.oHcl (mT) IJ.OH c (T) ~(O)
(run)
A(O) (nm) K(O) /).C (rnl/mol K) r (mJlmol K2 )
sctvr;
N(EF) (l/eV) VF (105 m1s) Aph
IJ.* 90(K) /).(0) (meV) /).(O)/kBT c
1 (nm)
RRR To (K)
15.5 [I) II [2) 30 [3]. 8 [5] 0.23 [3) 8 [4).10 [5).5.5 [12) 120 [4). 350 [5J IS (4). 35 [5) 460(3) 18.5 [3) 1.77 [3) 4.31 [7) 0.85 ... 3.8 [2).4.2 [12) 0.9 [3]. 1.02 [IOJ "::0.1 (2).0.13110) 490 (3) 2.2 (8) 2.1 [3). 1.7 (8) 33 [II) 43 (2) 2.8 (2)
16.5 [I) 7.5 [2).9 (6) 30 [3]. 80 [6) 0.31 [3].0.54 [6) 6 [4.6] 130 [4]. 71 [6) 22 [4). 12 (6) 695 [3) 19.5 [3]. 35 (6) 2.21 [3) 4.05 (7) 0.96 ... 3.7 [2).4.2 [12] 0.75 [3). 1.22 [10] "::0.1 (2).0.13[10) 360[3] 2.2 (8) 2.2 [3). 1.7 [8) 70[6).29[11) 27 [21.44 [9) 4 (2)
T c - superconducting transition temperature. H c2 - upper critical field at T = O. H c I - lower critical field at T = O. H c - thermodynamical critical field at T = O. ~(O) - coherence length at T = O. A(O) - penetration depth at T O. K(O) Ginzburg-Landau parameter at T O. /).C - specific heat jump at T e • y - normal state Sommerfeld constant. N(EF) - density of state at the Fermi level in states per eV and unit cell. VF - Fermi velocity. Aph - electron-phonon coupling constant. IJ. * - Coulomb pseudopotential, 8D - Debye temp.• /).(0) - quasiparticle energy gap at T = 0.1- mean free path. RRR - residual resistance ratio p(300 K)/ p(T ":: T c ). To - Dingle temperature.
=
=
[I) Cava et aI. (l994b). [2) Shulga et aI. (1998). [3) Michor et aI. (1995). (4) Hilscher and Michor (1999). [5) Prozorov et aI. (1994). [6) Takagi et aI. (1994). (7) Divis et aI. (2000. [8) Ekino et aI. (1996). [9) G. Fuchs priv, comm.• [10) Manalo et aI. (2001). [II) Du Mar et aI. (1998). [12) Heinecke and Winzer (1995).
MAGNETICAND SUPERCONDUCfING PROPERTIES OF RNi2B2C
241
moving the systems towards dirty-limit superconductivity (Freudenberger et al. 1998a; Fuchs et al. 2001; Schmidt and Braun 1997; Cheon et al. 1998). They have a threedimensional globally isotropic electronic structure but due to the complicated shape of the Fermi surface there is a strong dispersion in the Fermi velocity. This results in a positive curvature of the function H c2(T) near T c which can be formally described by non-local corrections to the phenomenological theory of Ginzburg, Landau and Abrikosov or, in a detailed analysis within the Eliashberg theory, by taking into account at least a two-band electronic structure (Shulga et a1. 1998). According to the two-band model the degree of positive curvature of H c2 (T) decreases if the materials become generally more dirty i.e. the interband scattering rate increases. This prediction has been confirmed by experiments on the pseudoquaternary (Y,Lu)NhB2C compounds. The anisotropy of the Fermi surface also causes anisotropy in H c2 (T) and in ~ (0) (Metlushko et al. 1997; Takagi et al. 1997). The values of the BCS ratios llC/yT c and Il(O)/kBT c and of Aph indicate moderate electron-phonon coupling. However the Eliashberg analysis of Shulga et al. (1998) and Shulga and Drechsler (200 1) showed that this statement has to be modified as the different groups of electrons have different strengths of coupling: strong, intermediate and weak where the strongly coupled (nested) electrons are mainly responsible for superconductivity but the properties of the superconducting state are considerably affected by interaction of the strongly coupled with moderately coupled electrons. The quaternary borocarbides have been classified as conventional s-wave superconductors with a strongly anisotropic energy gap (see e.g. Boaknin et a1. 2001; Andreone et al. 2001). The superconductivity in YNhB2C and LuNi2B2C is far from being fully understood. In their future analysis the other non-magnetic borocarbide superconductors from table 2 should be included for comparison. 4. Magnetic and superconducting properties of RNi2B2C In this section RNhB2C compounds will be considered where R are 4f elements with an incompletely filled f-shell, which are sometimes entitled magnetic R-elements. EuNhB2C does not exist and PmNi2B2C is not investigated because Pm has no stable isotope. From fig. 9 it can be clearly seen that the 4f-electrons must have a considerable influence on the superconductivity in RNhB2C because, for spacings in the crystal structure which are comparable to those for non-magnetic R-elements, the transition temperature T c of RNi2B2C with magnetic R-elements is considerably smaller or the superconductivity is even completely suppressed. The calculated density of states N(EF) of RNhB2C superconductors has nearly the same values for magnetic R-elements (see table 7) as for non-magnetic R-elements (Divis et a1. 2000). In order to investigate the 4f-electron magnetism in these compounds various measurements have been performed such as elastic (Skanthakumar and Lynn 1999) and inelastic (Gasser et a1. 1997) neutron scattering, muonspin relaxation (Le et a1. 1997), Mossbauer effect (Felner 2001), x-ray resonant exchange scattering (Detlefs et a1. 1997b), magnetization and magnetic susceptibility (Cho 1998), resistivity and magnetoresistance (Fisher et al. 1997), specific heat (Hilscher and Michor 1999) etc where only one representative reference is given in each case. Results of such experiments are summarized in figs 8 and 9 and in table 7. The relatively large values of
242
K.-H. MULLER et al. TABLE 7 Type of the ground state of RNi2 B2C compounds
Compound
Ground state
TN (K)
CeNi2B2C PrNi2B2C NdNi2B2C SmNi2B2C GdNi2B2C TbNi2B2C Oy Ni2B2C HoNi2B2C ErNi2B2C TrnNi2B2C YbNi2B2C
Mixed valence [16,17) (SC [I)) AFM(7) AFM [7,24) AFM [24J SOW (26) SOW [7,14]IWFM [14,19J AFM [2,6,7J/SC [2,3] AFM [8,9]1SC [4,5) SOW [lI,12J (WFM [21,22)) SC [4,5J SOW [7,18,29J/SC [4,5J Heavy fermion [23,15)
4.0(7) 4.8 (25) 9.8 [31,33) 19.4 [16,25,26,30) 15.0 [7,14J 11.0 [2,6) 5 ... 8 [8,9,10) 6 [27J...6.8 [11,12) 1.5 [28.13.7J
To (K)
N(EF)
(0.1 [I])
2.4 (32) 2.00 [20J 2.10 [20J 2.97 [20J 3.57 [20J 4.11 [20J 4.16 [20J 4.04 (20) 4.32 (20) 4.02 (20)
6.2 [2), 6.4 (3) 8 (4), 7.5 [5J 10.5 [4,5,27) II [4,5)
SC - superconducting, AFM - commensurate antiferromagnet structure, SOW - incommensurate antiferromagnet order (spin density wave), WFM - weak ferromagnetism; TN - magnetic ordering temperature, T osuperconducting transition temperature and N (E F) - density of states at the Fermi level.
[I) El Massalami et aI. (1998a), (2) Cho et al, (1995a), (3) Tomy et al. (1995), (4) Cava et al. (1994b), (5) Eisaki et aI. (1994), (6) Dervenagas et aI. (1995a), (7) Lynn et al. (1997), (8] Grigereit et aI. (1994), (9) Goldman et al. (1994), (10) Canfield et aI. (1994), [Il) Sinha et al. (1995), (12) Zarestki et al. (1995), (13) Cho et al. (1995b), [14J Dervenagas et al. (1996), [l5J Yatskar et al. (1996), [16J Gupta et al. (1995), [17J Alleno et al. (1995a), (18) Chang et aI. (1996b), [I9J Cho et aI. (l996a), (20) Divis et aI. (2000), (21) Canfield et al. (1996), [22J Kawano et aI. (1999), {23J Ohar et al, (1996), {24J Detlefs et al, (1997b), {25] Nagarajan et al. (1995), (26J Detlefs et al. (1996), [27] Cho et aI. (1995c), [28J Movshovich et al. (1994), [29] Sternlieb et aI. (1997), (30) EI Massalami et al. (1995c), (31) Prassides et al. (1995), [32] Divis (2001), [33] Hossain et al. (1995).
the magnetic ordering temperature and its approximate scaling with the de Gennes factor point to a strong interaction between the R magnetic moments which is clearly dominated by RKKY-type exchange rather than by dipolar interaction. Usually these compounds are antiferromagnetically ordered where the magnetic structure, in particular the local direction of the R magnetic moments, is the result of a competition between the exchange interaction and crystalline electric fields (which will be discussed in subsection 4.1). In some cases (R = Tb and Er) weak ferromagnetism has been observed i.e. a small net magnetic moment as a result of some canting of the antiferromagnetically ordered R magnetic moments. In other cases (e.g. R = Ho, see subsection 4.9), besides the groundstate magnetic structure further magnetic structures occur at elevated temperatures. The exchange interaction between the 4f electrons and the conduction electrons in RNi2B2C seems not to induce Ni magnetic moments, i.e. as in the case of non-magnetic R -elements, no Ni magnetic moments have been detected in these compounds so far (Skanthakumar and Lynn 1999). As an interesting result, fig. 25 shows that the quadrupole splitting ~EQ observed by Mossbauer spectroscopy on the Ni site (diluted by 57Fe) is strongly correlated with the B-Ni-B bonding angle which is supposed to have a strong influence on the superconducting transition temperature To via the coupling to high-frequency phonons connected with boron (Mattheis et al. 1994). Although the electronic structure as well as superconductivity and magnetism in RNi2B2C are three-dimensional phenomena different types of large anisotropy have been reported. Thus the isomer shift in DyNi2B2C is
MAGNETIC AND SUPERCONDUCTING PROPERTIES OF RNi2B2C
243
0.6
0.5
~~ •
Gel 0
Nd
"iii'
0.4
.§.
0.3
Tb
E
~Ho E'Tb
-0
Dy
W <:I 0.2 0.1
0.0
Ho
0
•
1.35
RNIBC RNI1l2C
1.40
1.45
1.50
1.55
c'la observed in various RNiBC and RNi2B2C compounds Fig. 25. Room temperature quadrupole splitting I~EQI as a function of a structural parameter (e'la) which is a measure of the B-Ni-B bonding angle in these compounds (after Baggio-Saitovich et aI. 2001).
significantly smaller than in metallic Dy or DyM2Sh (Sanchez et al. 1996) which has been assigned to relatively strong covalent bonds between the Rand C atoms. A strong anisotropy concerning the dependence of the exchange interaction between the R magnetic moments on their position in the crystal structure has been reported by Cho et al. (1996b) who derived, from magnetization data, a ratio of the exchange constants between Ho magnetic moments in HoNi2B2C for the line connecting the two Ho atoms being parallel and perpendicular to the tetragonal c-axis, Jll/h, of nearly 10. These authors used the misleading terms exchange anisotropy and anisotropic exchange interaction. One has to be careful in using such notations: exchange anisotropy, also called exchange biasing, is a totally different phenomenon discovered by Meiklejohn and Bean (1957) and anisotropic exchange interaction is used for cases where the interaction depends on the direction of the two interacting moments with respect to the lattice (see e.g. in Yosida 1996). The exchange interaction considered by Cho et al. (l996b) is, however, isotropic. In subsection 4.1 we will consider the influence of crystalline electric fields on the magnetic properties and in the following subsections we will briefly report on the behaviour of the individual RNjzB2C compounds from R = Ce to Vb. 4.1. Magnetic order and the crystalline electric field
The ground state magnetic structures of some borocarbides, including all magnetic RNhB2C superconductors are shown in fig. 26. These structures are characterized by the value of the ordered R magnetic moment (JL) and its direction with respect to the crystallographic axes as well as to the neighboring R magnetic moments. A further characteristic property of these structures is their propagation wave vector q which may be commensurate or incommensurate with respect to the lattice structure. The value of (JL) is the result of the interplay between the single ion anisotropy due to crystalline electric fields (CEF) and the RKKY exchange interaction between the R 3+ ions.
244
K.-H. MOLLER et al.
~
~
,
.-- - ..
Jt!'"
.>
»:
»:
v
.-
~
V
t
,. ./'
(3)
~
Pr, Dy, Ho
, -'"
,./ ----.
./'
./
q
----.
(b) Er
(c) Tb
q
v
V'"""
-- -- .. q
(d)Tm
Fig. 26. Different types of magnetic structures in the ground state of RNi2B2C compounds. (a) For R = Pr, Dy or Ho commensurate antiferromagnetic structure. (b. c and d): for R = Er, Tb and Tm incommensurate antiferromagnetic structures (spin density waves) with a propagation vector q in the (a. b)-plane. (b) Moments in the (a. b) plane and 1- to q. (c) Moments in the (a. b) plane and II q. (d) Moments lie and 1- to q (after Lynn et aI. 1997).
If the CEF interaction is much stronger than the exchange interaction, the magnetic subsystem can be described, in zero approximation, by the single-ion CEF quantum states. The energy of the (21 + I) fold degenerated Hund's free-ion ground state characterized by the total angular momentum 1 wil1 split into CEF energy levels. According to a theorem of Kramers (1930), in a system containing an odd number of electrons, al1 energy levels wil1 have an even degeneracy. Since Ce3+, Nd 3+ , Sm3+, Gd3+ , Dy 3+ , Er 3+ and Yb3+ have an odd number of electrons (see table 8), the CEF ground state of these so cal1ed Kramers ions is, at least, two fold degenerated and consequently they will carry a magnetic moment i.e. this ground state will split in an external magnetic field. Hybridization and correlation effects can suppress those 4f magnetic moments as, in particular, observed for R = Ce or Yb i.e. for one electron or hole in the free R 3+4f shel1 (see tables 7 and 8). On the other hand the non-Kramers ions Pr, Tb, Ho and Tm contain an even number of electrons and consequently their CEF states can be singlet states which of course are nonmagnetic. For R = Pr in RNhB2C with point symmetry of D4h at the R-site, indeed, the CEF ground state level is a singlet whereas that for R = Tm it is a doublet (Rotter et al. 200 I). For R = Ho and Tb the situation is more complicated because singlets as well as doublets are close to the CEF ground state level. As can be seen in table 8, the RNhB2C compounds show a staggered magnetic moment (J..L) for al1 4f elements but Ce and Yb, Consequently, the moment (J..L) in PrNi2B2C, and probably in HoNhB2C, is induced due to mixing of the CEF ground state with higher states through RKKY interaction. The local directions of the R magnetic moments are governed by the CEF (with the exception of the case R = Gd, see subsection 4.6). There are two types of magnetic structures with the moments either parallel to the c axis (R = Tm, Sm; table 8) or perpendicular to c. This different behaviour can be explained, in most cases, by second order CEF effects. The CEF are usually characterized by the CEF coefficients A nm (Hutchings 1964) which are
245
MAGNETIC AND SUPERCONDUCTING PROPERTIES OF RNi2B2C TABLE 8 Properties of free R 3+ ions
R3+
Ce Pr Nd Sm Gd Tb Dy Ho Er Tm Vb Lu
n I 2 3 5 7 8 9 10 II 12 13 14
Hund's rules quantum numbers L J S
1/2 1 3/2 5/2 7/2 3 5/2 2 3/2 I 1/2 0
3 5 6 5 0 3 5 6 6 5 3 0
5/2 4 9/2 5/2 7/2 6 15/2 8 15/2 6 7/2 0
g
6/7 4/5 8/11 2/7 2 3/2 4/3 5/4 6/5 7/6 8/7
DG
0.18 0.80 1.8 4.56 15.8 10.5 7.1 4.5 2.6 1.2 0.32 0
aJ
(IL)
(10- 2)
ILp [ILBI
ILs [ILBI
[ILBI
-5.71 -2.10 -0.64 4.13 0 -1.01 -0.64 -0.22 0.25 1.01 3.17 0
2.5 3.6 3.6 0.85 7.9 9.7 10.7 10.6 9.6 7.6 4.5 0
2.1 3.2 3.3 0.7 7 9 10 10 9 7 4 0
0 0.81 2.10 ? 7 7.8 8.5 8.6 7.2 3.4 0 0
lie J.e J. J.
II J.. II J. J. J. J.
1/
n - number of 4f electrons. S - total spin, L - total orbital angular momentum, J - total angular momentum, g - Lande factor, DG - de Gennes factor, a J - second Stevens coefficient, ILp - paramagnetic moment, ILs - saturation moment; (IL) - staggered magnetic moment in RNi2B2C where the orientation of the moments with respect to the c-axis is given in the last column (Lynn et aI. 1997; Skanthakumar and Lynn 1999; Detlefs et aI. 1996, 1997b; EI-Hagary et aI. 2oooa; Allenspach and Gasser 2000).
approximately the same in all RNi2B2C compounds (Gasser et al. 1996). In lowest nonvanishing order the interaction of an R ion with the CEF is proportional to aJA20 with aJ as the second order Stevens factor which roughly speaking characterizes the shape of the 4f charge density for the R3+ ion. Table 8 shows that for all R 3+ ions with aJ < 0 the moments are within the (a,b)-plane, for aJ > 0 the moments are parallel to the c axis, with the exception of Er. This case is more complicated and was discussed in detail by Cho et al. (1995c): in that case higher order CEF coefficients can not be neglected. On the other hand, the susceptibility X at higher temperatures is known to be determined by A20 and aJ only. Measurements of X on ErNi2B2C single crystals at higher temperatures gave results which are compatible with table 8 i.e, X measured perpendicular to c is smaller than measured parallel to c (X.l < Xp). Only at temperatures below about 150 K Cho et al. (l995c) found X p < X.l which is interpreted as being due to the influence of higher order CEF terms and is in accordance with the structure of fig. 26b. The experimental values (J.t) of the ordered R magnetic moments in RNjzB2C as well as their preferred directions, summarized in table 8, could be well reproduced by a self-consistent mean-field approach taking into account some general assumptions on the RKKY interaction and experimental CEF-data (Gasser et al. 1996; Gasser and Allenspach 2001; Rotter et al. 2001). The direction of the ordered R magnetic moments with respect to their R neighbors in the RNjzB2C lattice is dominated by the RKKY interaction and, in consideration of the magnetically easy axes, they usually are parallel or anti parallel. However in some cases small deviations from the strongly parallel or antiparallel alignment of neighbors have been reported. Examples are the spiral structure and the a-axis-modulated structure observed in HoNjzB2C at elevated temperatures (see
246
K.-H. MULLER et a1.
...
10.8 r-.,....rT".".-rr--,-1r"'T",..........,~----.10.6
••
.:( 10.4
o 10.2 10.0
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c
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.~
3.7 3.6
3.5 0.82
Vb Er V Tb Ce4 ' Nd Ce" Pr Lu Tm HoDy Gd 8m
La
1.10
Lanthanide Radius [A] Fig. 27. Lattice constants a and c of RNi2B2C for various elements R versus the ionic radii of R 3+ ions. In the case of R = Ce (open symbols), both the radii of Ce 3+ and Ce 4 + do not fit the curve observed for the other rare earths (Siegrist et al. 1994b).
subsection 4.9.1) or the weak ferromagnetism in TbNhB2C (subsection 4.7) and in ErNhB2C (subsection 4.10). Whether the magnetic long-range order is commensurate or incommensurate is the result of the competition between CEF and RKKY interactions. Incommensurability is a typical effect of the RKKY interaction and. as expected. it occurs in the magnetic structures reported for GdNi2B2C (see subsection 4.6). However incommensurate magnetic structures have been observed also for other RNi2B2C compounds in their ground states or metamagnetic states (see fig. 26 and table 8 as well as the following subsections). Since the RKKY interaction is mediated by the conduction electrons the incommensurate magnetization structures depend on details of the electronic structure. This is the reason why the nesting vector T ~ (0.55. O.0) discussed in subsection 3.1 manifests itself as a modulation wave vector of different incommensurate structures as found in various RNi2B2C compounds (see the following subsections).
4.2. CeNi2B2C The lattice parameters of CeNi2B2C do not fit the linear relationship found for the other RNizB2C compounds (see fig. 27). Neither the trivalent nor the tetravalent radius for Ce falls on the corresponding straight lines. The approximate valence Ce 3.75+ obtained by interpolation reveals a (homogeneously) mixed or intermediate valence of cerium in this compound (Siegrist et a1. I994a. 1994b ). X-ray absorption spectroscopy at the CeLIII edge confirms that the Ce ions are in an intermediate-valence state (Alleno et a1. 1995a). Measurements of magnetic susceptibility and specific heat as well as neutron diffraction experiments showed that Ce is essentially nonmagnetic and there are no magnetic transitions in CeNi2B2C although. as discussed in subsection 4.1. Ce 3+ is a Kramers ion and. therefore. it has a magnetic CEF ground state (Alleno et a1. 1995a;
MAGNETIC AND SUPERCONDUCTING PROPERTIES OF RNi282C
247
20
•• -;r
..:
15
~
~
Ii
• CePt t .aAuo.6BzC •o~ ceRhaBzC A CeNlaBaC • CePdzBzC
10
"b :;:. H
5
0
0
100
200
300
T (I<) Fig. 28. The magnetic susceptibility X versus temperature for various CeT282C compounds, indicating zero magnetic moment for tbe smaller T atoms Ni and Pd but finite paramagnetic moment for the larger T atoms Co. Rh and (PI,Au) (after Caner et al. 1995).
Carter et al. 1995; Lynn et al. 1997). Interestingly, for CeT2B2C with T = Ni, Co, Rh, Pd, (Pt.Au) it was found that the behaviour of Ce changes from nonmagnetic to magnetic with increasing T d-ion size (Carter et al. 1995). As shown in fig. 28, in the large-size limit, CePtI.5Auo.sB2C has a paramagnetic moment of 2.6JLB, which is close to the Ce 3+ free-ion Hunds-rule value (see table 8). On the other hand Ce is essentially nonmagnetic for T = Ni and Pd. From the variation of T c as a function of the lattice constant a one would expect CeNhB2C to be superconducting (see fig. 9). The change of electronic structure caused by the variation of lattice parameters and/or the distortion of the B-Ni-B tetrahedral angle may be one reason for the absence of superconductivity for the light rare earth RNhB2C compounds, including the case R = Ce (Siegrist et al. 1994b; Mattheiss et al. 1994). Probably these phenomena cause the reduced density of states at the Fermi level N(EF) (designated in table 7) and absence of Fermi surface nesting. The value of N(EF) ofCeNhB2C in table 7 was calculated assuming Ce to be trivalent, i.e. neglecting hybridization of the 4f electrons and, consequently, intermediate valence. The influence of the latter effects on the suppression of superconductivity in CeNi2B2C has not yet been theoretically analyzed. Based on ac magnetic susceptibility and specific heat measurements, EI Massalami et al. (l998a) claimed that they observed superconductivity in CeNhB2C with T c of about 0.1 K. If this will be confirmed the mechanisms for superconductivity in the whole borocarbide series should be reconsidered. 4.3. PrNi2B2C
The lattice parameters of PrNi2B2C (Siegrist et al. 1994b, see fig. 29) fit well the linear relationship derived for the other rare earth based borocarbides (except CeNhB2C). Therefore the valence state of Pr in PrNi2B2C is close to 3+. The magnetic susceptibility
248
K.-H. MULLER et al.
0.2 ~~----;--;--r=====;] SCR (a) 12 H II [110] SCA ........ H II [110] _ ••••••••
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100 T (K) 200
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· · ~~R
15 T(K) 30
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}~
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. - ... __ ._-_.----------600 200 -.-2 2 400 I (K) _._~_
Fig. 29. (a) Magnetic susceptibility x(T) of a PrNizB2C single crystal (SCR) for field H parallel to the e axis (Hlle) or ab plane (HlllllOJ). Powder averaged (AVR) data and results (depicted by crosses) for polycrystal (PeR) are also shown. Inset: laX(T)/aTj vs. T for PrNi2BzC single- and polycrystal. (b) X-I(T) vs. T, obtained from the data in (a). The dotted line is a fit of the AVRdata to the Curie-Weiss law for 200 < T < 300 K. (c) Specific heat C p vs. temperature T of a PrNiZBZC polycrystalline sample. The results for YbNiz BzC (Yatskar et al. 1996) and YbNiBC (Hossain et al. 1998) are also shown. (d) Cp/T vs. T Z, obtained from the data in (c). Dotted lines are the results of fits for 20 < T < 30 K to linear dependence. Insets: (c) C p vs. T and (d) C piT vs. r 2 plotted on expanded scales (after Narozhnyi et al. 1999c, 200la).
of polycrystalline PrNhB2C samples shows a tendency to saturate below 5 K with no well-defined peak at these temperatures (Hossain et al. 1995). Neutron-diffraction measurements (Lynn et al. 1997) have shown that PrNi2B2C orders antiferromagnetically at TN ~ 4 K (see table 7). Neutron diffraction shows that PrNhB2C is a commensurate antiferromagnet that consists of ferromagnetic sheets of Pr moments in the a-b plane, with the sheets coupled antiferromagnetically along the c axis (fig. 26a). As discussed in subsection 4.1 Pr has a singlet CEF ground state in PrNi2B2C and, therefore, its ordered magnetic moment is of induced type. Its value of 0.81 Il-B is considerably smaller than the free-ion value (table 8). No superconducting transition has been seen for PrNhB2C (Lynn et al. 1997, see table 2). Clear deviations of the properties of PrNizB2C from those of "normal" magnetic borocarbides (R = Gd-Tm) were pointed out by Narozhnyi et al. (l999c, 2oooa, 2001a, 2001b), based on measurements of magnetic properties, specific heat, electrical resistivity and magnetoresistance. Magnetic properties of PrNi2B2C have been studied for single- and polycrystalline samples. The magnetic susceptibility X(T) of a PrNjzB2C single crystal (SCR) is plotted in fig. 29a for two directions of magnetic field (H lie and H II[110]). The powder averaged data [Xavr = (2Xllo + Xc)/3] for the single crystal and the results for a PrNhB2C
MAGNETIC AND SUPERCONDUCTING PROPERTIES OF RNi2B2C
249
polycrystal (PCR) are also shown. A high degree of magnetic anisotropy XIIO/Xc ~ 11 is observed at T ~ 2 K, but it rapidly decreases with increasing temperature. This is in agreement with the fact that below TN the direction of the Pr magnetic moments is within the ab-plane (Lynn et a1. 1997). Below TN, the magnetic susceptibility for H Ilab grows monotonically with decreasing T and the only indication on an AFM-transition is the maximum of laXab(T)/aTI curves seen in the inset of fig. 29a. The X-I(T) dependence for powder averaged (AVR) data is close to linear for high T, but at T < 100 K it deviates significantly from the Curie-Weiss law (CWL) X-I (T) = C/(T - (J), where C = N /-L zerr /3kB is the Curie constant, /-Leff the effective magnetic moment, (J the paramagnetic Curie temperature and N the number of J>r3+ ions. A fit of AVR data to the CWL for 200 < T < 300 K is shown in fig. 29b as a dotted line. For Hllc, HII[IIO], AVR, and PCR the values of /-Leff for Pr3+ are very close and equal 3.76, 3.77, 3.77, and 3.76 /-LB, respectively. These values are slightly higher than the value J.Lp = 3.58/-LB for the isolated Pr 3+ (see table 8). The values of (J are found to be (Jc = -110 K, (J\IO = -12 K, (Javr = -40 K, and (Jpcr = -44 K. It should be emphasized that for magnetic borocarbides with "normal" magnetic behaviour (with R = Gd-Tm) the values of (Javr determined at high T are close to the observed TN (Cho et a1. 1995a, 1995b, 1995c, 1996a, 1996b). Their Xab -I (T) and Xc-I (T) dependencies can have pronounced deviations from the CWL, which are caused by crystal field effects. At the same time the powder averaged Xavr - J (T) dependencies for all these borocarbides are close to linear down to TN effectively concealing the anisotropy (Cho et a1. 1995a, 1995b, 1995c, 1996a, 1996b). Therefore, both the observed for PrNizB2C deviations of Xavr -I (T) from the CWL at TN < T < 100 K and the value of l(Javrl = 40 K, which is one order of magnitude higher than TN ~ 4 K, show the difference in the magnetic behaviour from those of "normal" RNjzBzC. To some extent similar deviations were reported by Yatskar et a1. (1996) and Dhar et a1. (1996) for the heavy fermion system YbNizBzC for which (Javr = -130 K and a nonlinear X-I (T) dependence was found at T < lOOK. These anomalies can be considered as an indication of the increased, with respect to "normal" RNizB2C borocarbides, indirect exchange interaction between Pr ions in PrNjzBzC which may be connected with some hybridization between the Pr4f levels and the conduction electrons. Results of specific heat measurements for a PrNjzBzC polycrystalline sample are presented in fig. 29(c, d) (Narozhnyi et a1. 1999c, 2001a). For comparison the results for YbNi2B2C (Yatskar et a1. 1996) and YbNiBC (Hossain et a1. 1998) are also shown. The Cp(T) dependence for PrNjzBzC has a broad maximum at T ~ 4.3 K which is close to T N ~ 4 K determined by neutron diffraction (Lynn et a1. 1997) and to the position of the maximum on laXab(T)/aTI curves, see the inset of fig. 29c. The shape of the maximum of Cp(T) is quite different from the A-type anomaly which is a characteristic feature of AFM ordering in "normal" borocarbides. The dotted lines in fig. 29d are the results of fits of the data obtained for 20 < T < 30 K to the dependence C piT = y + {JT2. These give y ~ 250, 150, and 15 mJ K- z mol-I for PrNjzB2C, YbNjzB2C, and YbNiBC, respectively. Comparing the results for these three compounds, one can say that YbNi2BZC reveals a relatively large y even at high T and shows heavy-fermion features at low T where Cp(T) reaches 530 mJK- 2 mol"! (Yatskaret a1. 1996; Dharet a1. 1996); YbNiBC has a y comparable with that of the nonmagnetic YNjzB2C and LuNizB2C borocarbides
250
K.-H. MULLER et aI.
SZ 1'002~ . Pr
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cr
c
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T (K)
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Lu
(b)
II
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~
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a.
a.
10 T (K) 20
100 T (K) 200
Fig. 30. (a) Resistivity peT) of a PrNi2B2C polycrystal. Numbers denote the values of H in kOe. Results for TbNi2B2C (Muller et aI. 1998) are also shown. Inset: P vs. T for 0 < T < 300 K. (b) Normalized resistivity Pn(T) = p(T)/p(300 K) vs. temperature T for a PrNi2B2C polycrystal in comparison with the results for YNi2B2C. LuNi2B2C. and LaNi2B2C, Inset: Low temperature part of Pn vs. T. (e) The difference between Pn of RNi2B2C (R = Pr, Lu, Y) and LaNi2B2C (left axis) and between Pn of PrNi2B2C and YNi2B2C (right axis).
(Hilscher and Michor 1999) but exhibits AFM ordering at T ::::::: 4 K (Hossain et al. 1998) which manifests itself as a sharp A-type anomaly. For high temperatures (20 < T < 30 K) PrNi2B2C has values of the specific heat and y (obtained by the extrapolation to T = 0) higher than those of YbNi2B2c' but it shows AFM ordering at TN ::::::: 4.3 K which complicates the interpretation of specific heat data. The large linear term in Cp(T) may be connected with an increased electronic contribution due to, e.g., hybridization of the conduction electrons with Pr4f states. However, a possible Schottky contribution connected with low lying levels of the Pr3+ multiplet splitted by crystalline electric field can also give a considerable "effective" linear contribution to the specific heat. The question to what extent the large linear term in C p(T) ofPrNi2B2C is connected with an enhanced electronic contribution should be clarified by specific heat measurements in a magnetic field (which should suppress the AFM transition) preferably extended to temperatures below I K. Results of electrical resistivity measurements for polycrystalline PrNhB2C are shown in fig. 30a (Narozhnyi et al. 1999c, 2001a). For comparison, the data for TbNhB2C (Muller et al. 1998) are also shown. For PrNi2B2C a gradual but pronounced drop in resistivity was found below se 10 K. A magnetic field H = 50 kOe only slightly shifts the p(T) curve for PrNi2B2C, see fig. 30a. The p(T) dependence for PrNi2B2C at T < 10 K and the influence of H on p(T) has an anomalous character with respect to other magnetic borocarbides. (A sharp anomaly in p(T) at TN is typical for "normal" borocarbides as, e.g., for TbNhB2C (Muller et al. 1998). This anomaly disappears in magnetic fields of the order of 50 kOe due to the suppression of the AFM transition by the magnetic field.) At the
MAGNETIC AND SUPERCONDUCTING PROPERTIES OF RNi2B2C
251
same time the character of p(T) as well as the influence of H on it for PrNhB2C is rather similar to the behaviour earlier observed for the anomalous YbNhB2C (Yatskar et al. 1996, 1999; Dhar et at. 1996) for which no indication of magnetic transitions was observed down to 50 mK. The results described above suggest that the drop in p(T) reported for PrNhB2C is connected with some peculiarities in scattering of conduction electrons by Pr ions at low temperatures rather than with AFM ordering because the drop in p(T) develops at T » TN (Narozhnyi et al. 2oo1a). The contribution of Pr ions to the scattering of conduction electrons can be estimated by comparison of the resistivity for different borocarbides. For this purpose the normalized temperature dependencies of resistivity Pn(T) = p(T)j p(3oo K) are shown in fig. 30b for R = Pr, Y, Lu, and La (Narozhnyi et al. 2oooa, 2oola, 2oo1b). It was found that, for 200 < T < 300 K, Pn(T) of PrNhB2C is very similar to that of YNi2B2C and LuNhB2C and is significantly different from Pn(T) for nonsuperconducting LaNi2B2C. Therefore, to obtain the contribution in Pn(T) from the Pr ions it is more reasonable to use, as a nonmagnetic reference YNhB2C or LuNi2B2C rather than LaNhB2C. The difference [Pn(Pr) - Pn(Y)] is shown as solid curve in fig. 30c. Magnetic scattering increases with decreasing T and has a pronounced maximum at T ~ 25 K. Such a behaviour is typical for some heavy-fermion systems (see, e.g., Lee and Shelton 1987). It is also of interest to compare the temperature dependencies of resistivity of RNhB2C (R = Y, Lu, Pr) with that of nonsuperconducting nonmagnetic LaNjzB2C. The differences [Pn(R) - Pn(La)] are shown in fig. 30c. It is clearly seen that the superconductors YNi2B2C and LuNi2B2C have very similar additional contributions to resistivity in comparison with nonsuperconducting LaNhB2C. For PrNi2B2C the representation [Pn(Pr) - Pn(La)] = [Pn(Pr) - Pn(Y)] + [Pn(Y) - Pn(La)] shows that the additional contribution to Pn(T) of PrNi2B2C in comparison with LaNjzB2C ("Pr-La" curve in fig. 30c) can be considered as composed of the two terms discussed above. The first term ("Pr-Y" curve) has a maximum at low temperatures connected with the scattering by Pr ions. The second term ("Y-La" curve) has a broad maximum at T ~ 150 K. Therefore the absence of superconductivity in PrNi2B2C may be supported by the increased scattering of conduction electrons by Pr ions at low temperatures (Narozhnyi et al. 2oo1a, 2oo1b). The substantial deviations of the B-Ni-B tetrahedral angle from the ideal value (Siegrist et al. I994b) and the decreased value of the calculated electronic density of states for light rare earth based borocarbides (Mattheiss et al. 1994; Divis et al. 2000; see table 7) is usually considered as the main reason for the absence of superconductivity in PrNhB2C (see also subsections 2.1 and 3. I). It should be noted however that no hybridization effects between 4f and conduction electrons were taken into account in these band structure calculations. Analyzing the influence of the Ni-Ni distance in borocarbides on T c (Lai et al. 1995, fig. 9), one could expect T c ~ 6 K from the PrNhB2C lattice parameters, if the Pr3+ ion would be nonmagnetic. The additional suppression of T c due to magnetic pair breaking by Pr ions can be estimated in the framework of the Abrikosov-Gor'kov theory using the de Gennes scaling roughly valid for borocarbides with T c > TN (Eisaki et al. 1994, see subsection 1.4). This suppression is about 2 K. Therefore, in case of a "normal" behaviour ofPrNhB2C, it would expected to be superconducting with T c ~ 4 K. (A similar analysis for RNhB2C with R = Nd, Sm, Gd shows that magnetic scattering will fully suppress possible superconductivity in accord with the experiments, see subsections 4.44.6.) The measurement of p(T) has shown (Narozhnyi et al. 1999c, 2oola) that there is no
252
K.-H. MULLER et a1.
...
~
t
~
~
t
17
+-
Nd
-+
Sm
Fig. 31. Observed magnetic structures of NdNi2 B2C and SmNi2B2C (after Skanthakumar and Lynn 1999).
indication of superconductivity in PrNi2B2C at T down to 0.35 K. Measurements of T c for diluted Y t-xPrxNizB2C samples have shown that the superconductivity suppression rate laTe/axl for this system is about 35 K. which is about 20 times largerthan expected from de Gennes scaling for Y l-xGdxNizB2C (Narozhnyi et al. 1999c, 2001a. 2001b). Partially. this rapid suppression of T c is connected with the difference in the ionic radii of y3+ and Pr3+ ions. Nevertheless. after the influence of the difference of ionic radii of Pr3+ and y3+ was taken into account. the pure magnetic contribution to IaT cI ax I ~ 18 K is still about 9 times larger than expected from a comparison with de Gennes scaling (Narozhnyi et al. 2001a. 2001b). This correlates with the value of TN. which for PrNi2B2C is about 4 times higher than expected from the de Gennes scaling. Both TN and IaTe/ax I should be proportional to [2DG (see. e.g., Canfield et al. 1998 and subsection 1.4), where [ is a measure of the exchange interaction between 4f levels and conduction electrons. and DG is the de Gennes factor. The observed simultaneous deviations of TN and IaTe/ax I from the expected values may be considered as an indication of the anomalously high value of I, This seems to be an independent manifestation of 4f-conduction electron hybridization in PrNizB2C. Noteworthy is the analogy between the anomalous behaviour of Pr in borocarbides with the well known anomalous properties of Pr-containing cuprates (Lynn 1997. see subsection 1.3). For PrBa2CU307-y. e.g .• it is widely accepted that the absence of superconductivity and anomalously high TN are connected with the increased hybridization effects of 4f-levels with planar oxygen derived states being important for superconductivity of doped holes. Although the reason for the anomalous behaviour of PrNbB2C is not completely understood so far. it is possible to say that the anomalously increased Neel temperatures and the rapid suppression of superconductivity for Y l-xPrxNizB2C and Y l-xPrxBa2CU307-y type systems are characteristic features for both Pr-based borocarbides and cuprates.
This borocarbide is a non-superconducting antiferromagnet with the magnetic structure shown in fig. 31. According to the empirical curves of fig. 9 the absence of superconductivity in NdNizB2C is expected to be mainly caused by two reasons. Firstly. the change of the lattice spacings is expected to cause the changed electronic structure compared to
MAGNETIC AND SUPERCONDUCTING PROPERTIES OF RNi282C
253
the cases R = Sc, Lu and Y. in particular the reduced density of states at the Fermi level N(Ep) labeled in table 7 (Siegrist et al. 1994b; Mattheiss et al. 1994). However these effects of the lattice structure are not sufficient to explain the absence of superconductivity for R = Nd as ThNi2B2C is a superconductor in spite of its relatively large lattice constant a (see fig. 9). The second mechanism suppressing superconductivity in NdNizB2C is the rare-earth magnetism. As discussed in subsection 4.1. Nd3+ is a Kramers ion whose individual magnetic moment cannot be quenched by crystalline electric fields. Magnetic ordering in NdNi2B2C at TN = 4.8 K had been reported by Nagarajan et al. (1995) and Gupta et al. (1995) who measured the magnetic susceptibility on polycrystalline samples and found a paramagnetic moment of 3.61lB per Nd ion which agrees with the free-ion value IIp in table 8. The magnetic structure of NdNi2B2C (fig. 31). including the staggered Nd magnetic moment (2.1 IlB. see table 8) has been determined by Lynn et al. (1997) using elastic neutron diffraction. This structure has been confirmed by X-ray resonant exchange scattering (XRES; Detlefs et al. 1997b). 4.5. SmNi2B2C
The fact that SmNi2B2C is not a superconductor can be understood by similar reasons as in the case of NdNizB2C. Although the calculated density of states N(Ep) of SmNi2B2C is larger than that of NdNizB2C. it is considerably smaller than that of the superconducting RNizB2C compounds (see table 7). Furthermore Sm 3+ is a Kramers ion (see subsection 4.1) and therefore. Sm magnetic moments will be present which also are unfavorable for superconductivity. Magnetic ordering in SmNizB2C at about 9.8 K had been observed by Hossain et al. (1995) and Prassides et al. (1995) who measured magnetic susceptibility and muon spin relaxation. respectively. The paramagnetic moment has been determined by EI-Hagary et al. (2000a) who analyzed the temperature dependence of magnetic susceptibility and found a modified Curie-Weiss law. X = xo + C /(T - 0). with a paramagnetic Curie temperature (J = -23 K and. resulting from the Curie constant C. a paramagnetic Sm moment of IIp = O.6IlB which is relatively close to the Sm 3+ freeion value O.851lB (see table 8). The constant term Xo = 3.7 X 10-6 cm 3/g has been attributed to van Vleck paramagnetism due to J multiplet spacing and coupling of the J = 5/2 ground state to the J = 7/2 state. These authors also found an anomaly of the specific heat of SmNi2B2C at about I K below TN which they assumed to be associated with some spin reorientation transition. Since Sm is highly neutron absorbing no neutron diffraction studies on SmNizB2C have been performed. Fortunately the magnetic structure of this compound could be determined by the XRES technique mentioned in subsection 4.4 (Detlefs et al. 1997b). It should be noted that the two magnetic structures of NdNizB2C and SmNi2B2C in fig. 31 have the same modulation wave vector (1/2, O. 1/2). but the magnetic moments in the two compounds have different directions. In both cases. the magnetic unit cell is double the chemical unit cell along the a and c directions while it is the same along b. Typical XRES integrated-intensity curves from which the structures of fig. 31 could be derived are shown in fig. 32. Since the magnetic structure of NdNi2B2C has independently determined by neutron diffraction. the XRES results for this material can be considered as a proof of the ability of x-ray resonant exchange scattering to determine moment directions with no a priori information. Unfortunately the staggered magnetic moment (Il) in SmNi2B2C cannot be determined by XRES.
254
K.-H. MULLER et al.
40 ~30
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~ 20
=- 10 ~300
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~ 200
=- 100 O......*~::!: - '-: ==-.L.- - zf'- -'-: !'"''"~=-'""""*:- ' s;. ~ 0 0 0 _oN ...!... ...!... ...!...
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50
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s:. 0
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Fig. 32. The integrated intensity of magnetic reflections of x-ray resonant exchange scattering measured for NdNi2B2C and SmNi2B2C, Dashed line and full line: model calculations for a magnetic moment parallel to the tetragonal a-axis and c-axis, respectively (after Detlefs et al. 1997b).
The absence of superconductivity in GdNizB2C is understandable for various reasons. According to the tendency of the transition temperature T c of RNizB2C compounds with heavy R-elements to approximately follow a de Gennes scaling (see fig. 8) T c of GdNi2B2C should be zero. Furthermore, Gd 3 + has no orbital momentum Land, consequently, it has a spherical charge density resulting in a vanishing Stevens coefficient OIJ (see table 8). Therefore the magnitude as well as the direction of the Gd magnetic moment in GdNizB2C are nearly insensitive to crystalline electric fields (CEF) and Gd can be considered as the most effective magnetic pair breaker among the R elements (Cho et al. 1996c). Additionally, the lattice parameters of GdNi2B2C are different from those of superconducting RNi2B2C compounds and according to the T c-vs.-a curve in fig. 9 a hypothetically non-magnetic GdNi2B2C compound would have a reduced value of T cwhich also manifests itself in a reduced density of states at the Fermi level N(EF) (see table 7). Measurements of the magnetic susceptibility, at temperatures up to 300 K, on GdNi2B2C single crystals confirmed the magnetic isotropy of this compound and yielded an effective paramagnetic moment JLp = 8.1 JLB which is close to the Gd3+ free-ion value of 7.9JLB (see table 8) and agrees with the value measured by Gupta et al. (1995) on a powder sample whereas measurements of magnetization at low temperatures indicate a magnetic ordering temperature TN ~ 20 K and a spin reorientation transition temperature TR ~ 14 K (Canfield et al. 1995; see also fig. 33). Due to the weak influence of the CEF in this compound its magnetic structure is expected to be governed by the RKKY exchange interaction as well as the electronic structure
MAGNETIC AND SUPERCONDUCfING PROPERTIES OF RNi2B2C
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including the shape of the Fermi surface. Since natural Gd strongly absorbs neutrons and non-absorbing Gd isotopes are expensive neutron diffraction has not been used to determine the magnetic structure in GdNjzB2C. Combining resonant and non-resonant xray magnetic scattering Detlefs et al. (1996) confirmed the value of TN = 19.4 K and showed that below TN this compound forms incommensurate antiferromagnetic states with a wave vector q ~ (0.55,0,0) which is close to the nesting vector discussed in subsection 3.1. Between TN and 13.6 K the magnetic structure is equivalent to that of ErNi2B2C in its ground state i.e. the ordered magnetic moment is along the b axis (see fig. 26). Below TR = 13.6 K an additional ordered component of the magnetic moment develops along the c-axis. The two magnetic phase transitions have been observed also by 155Gd Mossbauer spectroscopy which reveals a bunched spiral-like low-temperature structure with the Gd magnetic moments rotating within the (b,c)-plane (Mulder et al. 1995; Tomala et al. 1998; see fig. 34). The value of the staggered Gd moment (JL) in
256
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GdNi2B2C has not yet been experimentally determined. However, since Gd 3+ is a spinonly ion with the spin S as large as 7/2 no remarkable deviations from the ideal value (J1.) = J1.s = 7J1.B (see table 8) are expected to be caused by crystalline electric fields or quantum fluctuations or effects of hybridization. 4.7. TbNi2B2C
According to figs 8 and 9 TbNi2B2C does not superconduct (Tomy et aI. 1996c) and, as in the case of GdNhB2c' the absence of superconductivity is suggested to be mainly caused by (ordered) 4f-magnetic moments. The magnetic structure is an incommensurate spin density wave along the a-axis with the magnetic moments parallel to the modulation vector of this SDW and to the a-axis (see fig. 26 and tables 7 and 8). The relation of this magnetic structure to the orthorhombic lattice distortion discussed in subsection 2.2 has been determined by resonant magnetic x-ray scattering (Song et aI. 200 Ia). The modulation vector q = (0.55,0,0) practically coincides with the nesting vector found in most of the quaternary borocarbide superconductors (see subsection 3.1). This fact together with the high density of states at the Fermi level (N(EF), see table 7) suggests that without the 4f-local-moment magnetism TbNi2B2C would be a superconductor. Below 8 K Cho et aI. (l996a) found a small ferromagnetic component within the (a.b )-plane of a TbNi2B2C single crystal and, in this temperature range, magnetization-vs.-field curves show (a small) ferromagnetic hysteresis. These phenomena have been attributed to weak ferromagnetism of Dzyaloshinsky-Moriya-type (Dzyaloshinsky 1957; Moriya 1960) where, similar as in NiF2, the combination of crystalline electric fields and spin-orbit coupling is the particular underlying microscopic mechanism. The onset of weak ferromagnetism has also been confirmed by x-ray magnetic circular dichroism measurements (Song et aI. 200lb). A magnetic phase diagram with a domain of a weak ferromagnetism, as proposed by Cho et aI. (l996a), is shown in fig. 35. At temperatures where the weak ferromagnetism occurs the intensity of elastic neutron diffraction shows a weak anomaly (Dervenagas et aI. 1996; Lynn et aI. 1997). The presence of weak ferromagnetism has also been supported by Mossbauer spectroscopy and muon spin relaxation (J1.SR; Sanchez et aI. 1998). The MH isotherms at low temperatures show that for H perpendicular to the c-axis TbNi2B2C undergoes a series of metamagnetic states before finally saturating into a ferromagnetic state (Tomy et al. 1996a; Canfield and Bud'ko 1997; see fig. 36). On the other hand, for H parallel to c, the M-H isotherms are linear as in simple antiferromagnets. This indicates that the direction of the ordered Tb magnetic moments is strongly confined to the (a. b)-plane in agreement with the negative sign of the Stevens coefficient <XJ of Tb 3+ (see table 8). The metamagnetic transitions are accompanied by large values of magnetoresistance which remains considerably large even above the ordering temperature T N ~ 15 K (Tomy et aI. 1996a; MUlier et al. 1998). This points to strong spin-disorder scattering and, may be. to reorientation of magnetic short-range order. So far no theoretical model has been published describing the magnetic structure in the ground state or the metamagnetic states of TbNi2B2C. Such model would have to take into account Fermi surface nesting of the conduction electrons which mediate the exchange coupling of the Tbmoments.
MAGNETIC AND SUPERCONDUCfING PROPERTIES OF RNi2B2C
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4.8. DyNi2B2C
In agreement with the overall behaviour of the RNhB2C compounds with heavy 4f elements R, shown in fig. 8, this compound is the unique member of the RNhB2C series in which the onset of superconductivity takes place in an antiferromagnetically ordered state i.e. TN = II K > T c = 6.3 K (also see table 7). It should be noted that in the ruthenocuprates discussed in subsection 1.3 also antiferromagnetic order (and even
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weak ferromagnetism) coexists with superconductivity and TN is considerably larger than T c. The ground-state magnetic structure of OyNhB2C shown in fig. 26a consists of ferromagnetic sheets, with the Dy magnetic moments parallel to the [110] direction, which are antiparallel in adjacent Dy planes. For a field H applied parallel to the a-axis, at temperatures below 2 K, resistivity p versus H curves show a strong hysteresis i.e. upon decreasing H the onset of superconductivity occurs at a much lower value of H than the upper critical field obtained for increasing H (Peng et al. 1998). No hysteresis effects have been observed for Hllc and the hysteresis in superconductivity is almost zero for HII[ 110]. Winzer et al. (1999) have related this hysteresis of the p-vs.-H transition curves to hysteresis in the metamagnetic transitions reported earlier (Lin et al. 1995; Tomy et al. 1996b; Canfield and Bud'ko 1997; Naugle et al. 1998). A strength-of-field angle-of-field phase diagram of the metamagnetic states, derived from resistivity and magnetization data for T < 2 K is shown in fig. 37a. In this diagram the arrows symbolize the direction of magnetization which is assumed to be identical with those [110] directions which are either near parallel (t) or near antiparallel (-!,) or near perpendicular (~) to H. The hysteresis of the metamagnetic transitions has also been considered to be the reason why, upon warming, field cooled OyNhB2C single crystals exhibit the near-reentrant superconductivity presented in fig. 37b. It should be noted that without the specific magnetic prehistory of the sample in fig. 37b i.e. for cooling the sample in the measuring field near-reentrant behaviour does not occur (Peng et al. 1998), In the non-superconducting antiferromagnetic state the resistivity measured on single crystals in the (a,h)-plane (Cho et al. 1995a) as well as on polycrystalline samples (Lin et al. 1995) strongly decreases with decreasing temperature, resulting in a normal-state resistance ratio p(TN)/ peT c) of typically 2.5. This is attributed to reduced spin-disorder scattering due to magnetic ordering but is not yet really understood. The metamagnetic transitions result in a positive low-temperature magnetoresistance as large as 30% (Peng et al. 1998) similar as
259
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in the case of TbNi2B2C (see Tomy et al. 1996a). It would be interesting to know whether at least one of the metamagnetic states of fig. 37 has a modulation vector q close to the nesting vector r = (0.55.0,0) as observed for HoNjzB2C (see subsection 4.9.2). 4.9. HoNi2B2C
HoNi2B2C is one of the most interesting compounds among the borocarbide superconductors. As can be seen in fig. 38a, resistivity-versus-temperature curves measured at zero magnetic field H show a sharp transition into the superconducting state at T c ~ 8 K. For relatively small fields (e.g. 0.13 Tesla in fig. 38a) near-reentrant superconductivity similar as in GdM06Ss (see fig. 6) is observed which was first reported by Eisaki et al. (1994). Figure 38a also shows that the temperature range near TN where the reentrant behaviour occurs does not much depend on the value of H. Therefore TN is considered to be some intrinsic temperature indicating a magnetic phase transition. This is supported also by measurements of the specific heat C p (see fig. 38b) which shows a peak near the temperature TN. No separate anomaly of C p is found at T c. This is due to the fact that the high-temperature tail of the specific-heat anomaly is still much higher than the expected jump in C p associated with the superconducting transition (Canfield et al. 1994). However, a jump in C p due to the onset of superconductivity has nevertheless been determined from the difference of C p data measured at zero field and at 200 mT where, in the vicinity of T c- the superconductivity is suppressed: ~Cp ~ 140 mJ/molK (EI-Hagary et al, 1998). Other distinct features of the temperature dependence of C p are the two shoulders above the main peak (marked by arrows in fig. 38b). These features indicate two further phenomena of magnetic ordering, which will be discussed in subsection 4.9.1. Special behaviour at temperatures near and above TN was also observed for various other physical properties. Thus the thermal conductivity shows a discontinuous increase at TN (Sera et al. 1996). The
260
K.-H. MULLER et aI.
(a)
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temperature dependence of the microwave impedance has a maximum at TN. which disagrees with BCS calculations (Jacobs et al. 1995). Point-contact studies of Rybaltchenko et al. (1999) revealed that the superconducting order parameter satisfied the BCS theory only below 5.5 ... 5.8 K whereas at higher temperatures an anomalous superconducting state is observed. Investigating HoNjzB2C one has to consider that between TN and T c the magnetic and superconducting properties are very sensitive to details of the preparation procedure and to small deviations from the ideal stoichiometry (Wagner et al. 1999; Dertinger et al. 2001; AlIeno et al. 2001; see also subsection 4.9.3). 4.9.1. Types of magnetic order in HoNi2B2C It has been shown by elastic neutron diffraction that at zero magnetic field in HoNi2B2C three different types of antiferromagnetic order occur which. in a certain temperature range, even may coexist (Grigereit et al. 1994; Goldman et al. 1994). Upon cooling the commensurate structure of figs 26a and 39a largely forms at TN ~ 5.2 K. This structure with its ferromagnetic sheets in the tetragonal basal plane is in accordance with results of Cho et al. (1996b) who analyzed the susceptibility of single crystals and found Ho-Ho nearest-neighbor exchange constants that are positive within the basal plane but negative and considerably weaker along the c-axis. As will be discussed in subsection 4.9.4 significant neutron scattering intensity of this structure is also observed above TN. Additionally. in the temperature range TN < T < T c there is an incommensurate spiral structure along the tetragonal c-axis with a modulation vector '['2 ~ (0. 0.0.916) where. as in the ground state. the magnetic moments are ferromagnetically aligned in the (a. b)plane. The ferromagnetic sheets in adjacent layers have a relative orientation of about 163.40 instead of 1800 for the ground state (see fig. 39(b and a». Utilizing high-resolution x-ray scattering Hill et al. (1996) showed that this c-axis spiral is characterized by two wave vectors. ql = (0,0,0.906) and q2 = (0,0,0.919). The c-axis spiral has been
MAGNETIC AND SUPERCONDUCTING PROPERTIES OF RNi282C
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successfully described in a quasi-linear mean field model taking into account crystalline electric fields and the RKKY interaction and supposing the presence of ferromagnetic sheets (Amici and Thalmeier 1998). Furthermore, in a small temperature range above TN an a -axis modulated incommensurate magnetization structure occurs with a modulation vector t) ~ (0.58,0,0) which is close to the nesting vector known from other borocarbide superconductors in particular LuNhB2C and YNi2B2C (see subsection 3.1). The exact form of this a" structure is still unknown. From results of neutron diffraction experiments on powder samples Loewenhaupt et a1. (1997) concluded that the a" -structure has an oscillating component of magnetic moments perpendicular to the (a,h)-plane as shown in fig. 39c. On the other hand a study by Detlefs et a1. (2000) of metamagnetic phases suggests that the a" -structure has only magnetic moments perpendicular to the c-axis (see subsection 4.9.2). Experimental as well as theoretical work must be done to clarify the form of the a" -structure and its underlying mechanism which is obviously connected with Fermi surface nesting. 4.9.2. Metamagnetic transitions and magnetoresistance For magnetic fields H applied perpendicular to the tetragonal c-axis ofHoNi2B2C single crystals, measurement of magnetization as well as elastic neutron diffraction show up to three metamagnetic transitions similar to those visible in fig. 36 for ThNi2B2C (Cho et a1. 1996b; Rathnayaka et at. 1996; Canfield et a1. 1997a; Campbell et a1. 2000a; Detlefs et a1. 2000). It was concluded that in a strength-of-field angle-of-field phase diagram, besides the paramagnetic phase at elevated temperatures and the simple antiferromagnetic phase (t ..J,) at low temperatures and low fields, three additional low-temperature phases occur for sufficiently high fields. These metamagnetic phases are denoted by the arrow combinations t t..J, and t t - in fig. 40. Here it is assumed that in all of the magnetically ordered phases the local magnetic moments are directed along [110] axes that are either near parallel (arrow t) or near antiparallel (..J,) or near perpendicular (- ) to the applied field. As a very important result Detlefs et at. (2000,2001) found by elastic neutron diffraction at 2 K that
262
K.-H.MULLER er al.
the second metamagnetic phase (tt-+) has a modulation vector r3:::::: (4/7,0,0). In this experiment the angle 0 of H with respect to the [110] direction was 15°. A similar result has been reported by Campbell et al. (2000a) who measured at 0 = 45° i.e. for H parallel to [100] and found that the second metamagnetic transition results in a magnetic phase that is characterized by an incommensurate wave vector of about (0.61,0,0). The presence of an a*-metamagnetic phase at 2 K is also supported by results of Kreyssig et al. (l999b) who performed elastic neutron-diffraction experiments on HoNhB2C powders and also detected three different metamagnetic phases. The extension of the low-temperature metamagnetic phases to incommensurate zero-field phases at elevated temperatures, as shown in fig. 40, has also been supported by specific heat measurements of Jae-Hyuk Choi et al. (2001a). Further experimental work should be done in order to determine the complete region in the H -T -O-space where the phase (t t -+ ) of fig. 40 exists. Also it has to be clarified whether this phase in its whole range of existence is really characterized by an incommensurate propagation vector r3 = (~, 0, 0) and how much ~ varies across the phase diagram. It is interesting to note that in HOI-xRxNi2B2C compounds with R = Y or Lu and x ~ 0.25 the value of ~ weakly increases with increasing x. The wave vector r3 is ubiquitous in the quaternary borocarbides (Canfield and Bud'ko 2(01) as (i) the borocarbide superconductors show Fermi-surface nesting characterized by a nesting vector equal to r3 (see subsection 3.1), (ii) in some of the RNhB2C compounds, in particular for R = Y and Lu, phonon softening is observed for a wave vector r3 (see section 3.1), (iii) zero-field incommensurate magnetization structures with r3 as the modulation vector occur in RNi2B2C for R = Gd, Tb, Ho and Er (see subsections 4.6, 4.7,4.9.1 and 4.10) and (iv) a metamagnetic phase with a modulation vector close to r3 has been reported also for TmNhB2C (see subsection 4.11). A further unsolved problem is whether or not the metamagnetic phase (t t -+ ) in fig. 40 has components of magnetization perpendicular to the (a, h)-plane, at least in a limited region of the phase diagram, as proposed by Loewenhaupt et al. (1997) for H = O. Two microscopic approaches have been presented in literature which, until recently, had been believed to reasonably describe the magnetic phase diagram of fig. 40b. Amici and Thalmeier (1998) used the quasi one-dimensional model mentioned in subsection 4.9.1 in which the presence of ferromagnetically ordered Ho layers with their magnetic moments oriented perpendicular to the tetragonal c-axis is supposed from the very beginning and the competition of RKKY interaction along the c-axis with the crystalline electric field is analyzed. The so-called clock model of Kalatsky and Pokrovsky (1998) is also a semiclassical approximation which starts with the assumption that the strong single-ion anisotropy confines the Ho magnetic moments to the four directions [110]. Both models predict the phase boundaries of fig. 40b as well as the temperature dependence of the c-axis commensurate-toincommensurate transition surprisingly well. However both models cannot explain the origin of the a" -phase observed at zero field (see subsection 4.9.1) or at finite field as reported by Detlefs et al. (2000). Possibly these problems can only be solved by a more detailed description of the RKKY interaction, taking into account the Fermi-surfacenesting features. Figure 41 shows that in the normal state HoNi2B2C has a considerably large magnetoresistance MR of negative sign. (The positive sign of MR* in fig. 41a is due to the alternative normalization of this quantity which has been introduced so that data
263
MAGNETIC AND SUPERCONDUCTING PROPERTIES OF RNi2B2C
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from normal and superconducting states can be included in the same figure.) The normal state MR of HoNi2B2C is isotropic concerning the direction of the applied field with respect to the measuring current and it has been pointed out by Fisher et al. (1997) that the temperature and field dependence of MR can be attributed to spin-disorder scattering. However the large values of MR observed above the magnetic ordering temperature (fig. 41b) are not yet explained. May be they are related to magnetic short-range order or low-dimensionality magnetic ordering (MUller et al. 2001a). Such ordering effects at small length scales or in low dimensionality may also be the reason for the high-temperature tails observed for the specific heat (fig. 38b) and the neutron scattering intensity (subsection 4.9.4). The large normal-state values of MR· (fig. 41a) may be connected with the reorientation of ordered magnetic moments i.e. metamagnetic transitions as discussed above. 4.9.3. Reentrant and near-reentrant behaviour Now it is generally accepted that single-phase stoichiometric HoNi2B2C has the nearreentrant behaviour presented in fig. 38a although some of the numerous investigated HoNbB2C samples show real reentrant behaviour at zero field. It can be summarized that depending on details of the preparation route HoNi2B2C samples are found to be magnetically ordered superconductors with near-reentrant behaviour or reentrant superconductors or even non-superconducting magnetically ordered materials (Schmidt et al. 1995). It has been pointed out by AlIeno et al. (2001) that this variation in the superconducting properties may be due to the fact that HoNbB2C forms in equilibrium with ferromagnetic phases in the Ho-Ni-B-C system as e.g. HoB2C2 (~7 K), H02NbB6 (~ 12 K), HoNi4B (~6 K) etc which have Curie temperatures (quoted in brackets) in the temperature range of interest (4-8 K) and may coexist with HoNhB2C microscopically. It is well known that ferromagnetism favors reentrant behaviour (see subsection 1.3). The formation of such secondary phases is supported by nonstoichiometry. Therefore the chemical characterization of the sample is of prime importance. However, due to the presence of the two light elements Band C the various classical characterization techniques as chemical analysis, intensity analysis of x-ray or neutron diffraction, transition electron
264
K.-H. MULLER et al.
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microscopy. high resolution electron microscopy etc are almost inefficient in determining compositions. Recently the carbon content of the phases in HoNi2B2C samples could be successfully determined using nuclear- and electron-probe microanalysis (Alieno et al. 200 I). Furthermore. it has been underlined by Wagner et al. (1999) and Schmidt and Braun (1998) that HoNi282C has a finite homogeneity range which may result in a corresponding range of magnetic and superconducting properties. These authors could continuously (reversibly as well as irreversibly) change the superconducting properties of HoNi2B2C samples, in particular the transition temperature T c and the reentrant behaviour. by appropriate heat treatment procedures. An example is shown in fig. 42a. As expected the reentrant behaviour is also sensitive to small concentrations of impurity elements in the samples. As an example, fig. 42b shows that the substitution of 0.5 percent of Ni by Co is sufficient to cause reentrant behaviour. Uwatoko et al. (1996) have shown that reentrant superconductivity in single-crystalline HoNi2B2C can also be induced by hydrostatic pressure of II kbar. For increasing pressure they found an increase of TN and a decrease of T c. These authors attribute their results to an enhanced coupling of the conduction electrons with the Ho magnetic moments, due to the increased pressure. A more detailed investigation of the influence of hydrostatic pressure P on the superconducting and magnetic properties of HoNi282C was done by Dertinger (2001). He found dT c/dP = -0.32 K/GPa and. depending on whether or not the samples are superconducting (due to the chemical or microstructural variations discussed above). dTN/dP = 0.2 K/GPa or 1.4 K/GPa. respectively, with TN as the temperature where the commensurate antiferromagnetic structure of figs 26a and 39a appears. Dertinger also found that the a-axis modulated structure a" of fig. 39 is much more sensitive to pressure, compared to the other two magnetic structures of fig. 39, and it even disappears at relatively low values of P. Interestingly he observed near-reentrant behaviour also at temperatures and pressures where the a *-structure had disappeared. Therefore Dertinger concluded that the near-reentrant behaviour in HoNi2B2C cannot mainly be caused by the presence of the a" incommensurate magnetic structure. This problem will be further discussed in the next subsection.
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As a general empirical rule for HoNi2B2C samples, the appearance of reentrant behaviour caused by stoichiometric effects or pressure or magnetic field is always connected with a reduced value of T c.
4.9.4. Interplay ofsuperconductivity and magnetism It is obvious that the commensurate antiferromagnetic structure of fig. 39a coexists with superconductivity in HoNi2B2C, similar as in DyNizB2C. On the other hand, as can be seen in fig. 43(a and c) the superconductivity is suppressed in the small temperature range where the two incommensurate magnetic structures of fig, 39(b and c) occur. Now the question is which of these two structures is more relevant for the near-reentrant behaviour. In YO.lsHoo.8sNi2B2C the situation is totally different (fig. 43(b and dj), Here the a*
266
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structure again is localized at the same temperatures as the reentrant behaviour but the c* spiral exists in a very broad range of temperature. Thus the a" structure is more closely related to the near-reentrant superconductivity in Yo.ISHOO.8SNi2B2C (as well as Luo.lsHoo.8SNhB2C, Freudenbergeret al. 1998b) than the c" spiral. The same conclusion follows from a comparison of the temperature dependence of the upper critical field shown in fig. 43(e and f) with the neutron diffraction data (fig. 43(c and dj), This seems to be in contradiction to the results of Dertinger (2001) (discussed in the previous subsection) who found a near-reentrant behaviour of a HoNi2B2C sample in which the a" structure had been suppressed by pressure. Thus further experiments have to be done to elucidate the connection between the (near-) reentrant behaviour and the various magnetic structures in HoNhB2C. In a theoretical analysis the onset of the c* spiral was found to depress superconductivity (Amici et al. 2(00). However this approach does not take into account the a" structure. As discussed in subsection 4.9.1 the a" structure is related to Fermi surface nesting. It was theoretically shown by Machida et al. (l980b) that if antiferromagnetic ordering is connected with Fermi surface nesting the superconducting state may be heavily disturbed. For HoNhB2C the strong correlation between the near-reentrant behaviour and the a" magnetic ordering has first been emphasized by Muller et al. (1997) and has now been underlined also by Canfield and Bud'ko (2001). The crucial role of the a" structure manifests itself also in s7Fe Mossbauer spectra that, between TN and T c- show a magnetic hyperfine field at the Ni-site in HoNi2B2C (Sanchez et al. 1996) and in enhanced vortex pinning found by local Hall probe magnetization measurements (Dewhurst et al. 1999). 4.10. ErNi2B2C
As can be seen from figs 8 and 26 as well as tables 3 and 7 superconducting ErNilB2C starts to magnetically order at 6.8 K in a SDW with the modulation vector q parallel to the a-axis and the Er magnetic moments parallel to b (or vice versa; Sinha et al. 1995; Zarestky et al. 1995). Thus, as already discussed in subsection 4.1, the case R = Er is the only exception from the simple rule relating the sign of the second Stevens coefficient aJ with the direction of the staggered magnetization {11-} with respect to the tetragonal c-axis in RNhB2C. The modulation vector q is close to modulation vectors found in GdNhB2C, TbNi2B2C and HoNhB2C and to the nesting vector in the RNi2B2C superconductors (see subsection 3.1). Measurements of the specific heat and extrapolation of magnetizationvs.-field curves to zero field indicate, near 2.3 K, a second phase transition to an ordered state that has a net magnetization of roughly 0.3311-B per Er atom and represents a similar type of weak ferromagnetism (WPM) as observed in TbNi2B2C (Canfield et al. 1996). Neutron scattering results confirm the microscopic coexistence of a net magnetization (with a periodicity of 20 lattice spacings a) with superconductivity in ErNhB2C (Kawano et al. 1999; Choi S.-M. et al. 2oo1b). Probably this type of coexistence represents domainlike structures with the period smaller than the London penetration depth rather than self-induced vortex structures (see subsection 1.3 and Ng and Varma 1997). KawanoFurukawa (200 I) analyzed the temperature dependence of a certain critical field Her which is derived from magnetization-vs-field curves of superconducting ErNi2B2C and is close to the lower critical field He I. As shown in fig. 44, H cr(T) is sensitive to the magnetic prehistory of the sample. It is assumed that this phenomenon is connected with
MAGNETIC AND SUPERCONDUCfING PROPERTIES OF RNi282C
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the formation of different types of ferromagnetic-domain structures. A commensurate lowtemperature phase with a net ferromagnetic component of about OAILB per Er atom has been obtained by Jensen (2002) using a mean-field approach. The WFM is assumed to cause the enhanced flux pinning observed in ErNi2B2C at low temperatures (Gammel et aI. 2000). Significant vortex pinning is also observed in the temperature range above 2.3 K and has been attributed to the onset of a-axis incommensurate magnetic ordering (Dewhurst et aI. 200 I a, 200 Ib). Saha et al. (2000) conclude that localized ferromagnetic spin components at twin boundaries between antiferromagnetic domains cause enhanced flux pinning. For sufficiently large fields ErNi2B2C shows a hexagonal-to-square vortex lattice transition (Eskildsen et al. 1997b) similar as observed in nonmagnetic RNi2B2C superconductors (see section 5). As can be seen in fig. 45, a series of up to three metamagnetic transitions occurs in ErNi2B2C if a magnetic field H is applied perpendicular to the tetragonal c-axis whereas the magnetization-vs.-field curve for H parallel to c is simply increasing, with a slight negative curvature, as known for usual antiferromagnets (Szymczak et al. 1996; Canfield and Bud'ko 1997). It was shown by elastic neutron diffraction that the first two metamagnetic transitions are due to incommensurate antiferromagnetic states with different values of the a -axis modulation, and the third transition is due to a state in which the Er moments are ferromagnetically aligned (Campbell et aI. 2ooob). These magnetic structures are not yet theoretically analyzed. Such an analysis would have to take into account features of the conduction-electron structure (e.g. Fermi surface nesting) which influence the 4f-moment magnetism via RKKY interaction as well as crystalline electric fields resulting in anisotropy of magnetic and superconducting properties. Thus in ErNjzB2C the upper critical field H c2 is strongly anisotropic and has some irregularity at TN (see fig. 46) but, contrary to HoNi2B2C, it does not show near-reentrant behaviour (Cho et al. 1995c; Canfield et aI. 1998; Bud'ko and Canfield
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4.11. TmNi2B2C
As can be seen in fig. 47 the temperature dependence of the specific heat C(T) of TmNi2B2C shows pronounced anomalies at the critical temperature T c as well as the magnetic ordering temperature TN, which is different from the behaviour of HoNizB2C where the magnetic contribution to C(T) dominates (fig. 38). Neutron diffraction revealed a transversely polarized spin density wave as the ground state magnetic order in TmNi2B2C with magnetic moments parallel to c (see fig. 26 and table 8) and a modulation vector of (0.093,0.093,0) (Skanthakumar and Lynn 1999). Thus TmNi2B2C is the only magnetic RNi2B2C superconductor with the magnetic moments parallel to the tetragonal c-axis, which. however. is a natural consequence of CtJ being positive for Tm3+ (see subsection 4.1. in particular table 8). It has been proposed by Nergaard et at. (2000) that the magnetic structure of TmNi2B2C is caused by the
269
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Anderson-Suhl mechanism discussed in subsection 1.2 i.e, the reduction of the longwavelength part of the RKKY interaction in the superconducting state. From crystal field excitations determined by inelastic neutron scattering the saturated magnetic moment of TmNi2B2C has been calculated to be 4.7/J.B per Tm site (Gasser et al. 1996) which is considerably larger than the mean staggered magnetic moment observed by elastic neutron diffraction (table 7). Gasser et al. (1998b) explained this discrepancy by the presence of two different magnetic moments, one close to the calculated value and one of about O.l/J.B as observed by Mulders et aI. (1998) using Mossbauer spectroscopy and /J.SR, which may be due to carbon-boron disorder. For applied in-plane magnetic fields above 0.9 T Nergaard et al. (2000) found a low-temperature metamagnetic phase with a wave vector (0.48,0,0) which is relatively close to the nesting vector r = (0.55,0,0) discussed in subsection 3.1. For fields applied along the e-axis several magnetic flux line lattice symmetry transitions as well as transitions of the magnetic structure which are hysteretic have been observed by small-angle neutron scattering (Eskildson et al. 1998, 1999; Paul et aI. 200 1). Results of neutron scattering experiments for both Hila and H lie have been summarized by Eskildsen et al. (2001a) in magnetic field-vs.-temperature phase diagrams for TmNi2B2C. Figure 46 also shows that, contrary to the case of ErNi2B2C, H c2 of TmNi2B2C is larger for H.le than for Hlle. This is in accordance with results ofCho et al. (1996b) who found a larger paramagnetic susceptibility in TmNi2B2C for H lie, resulting in a larger Tmsublattice magnetization. Consequently, a larger effective field acting on the conduction electrons via exchange interaction is expected for Hlle. Nagarajan et at. (1999) showed by muon spin relaxation (/J.SR)that in TmNi2B2C quasistatic magnetic correlations persist up to 50 K which possibly represent magnetic short range order along the magnetically easy e-axis for T > TN = 1.5 K.
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4.12. YbNi2B2C
According to the lattice constants of YbNi2B2C (Siegrist et al. 1994b) Yb should be close to trivalent in this compound (see fig. 27). From de Gennes scaling roughly valid for heavy R-elements in RNi2B2C (see subsection 1.4) one would expect YbNjzB2C to be a magnetic superconductor with T c of about 12 K and a magnetic ordering temperature of 0.4 K. However, no indications of a superconducting or a magnetic transition were observed down to ~ 0.05 K (Lacerda et al. 1996; Bonville et al. 1999). These anomalies are connected with a heavy fermion behaviour of the system. Specific heat measurements at low temperatures yield a Sommerfeld coefficient y of 530 mJ mol"! K- 2 (see fig. 48) which is much larger than y for the nonmagnetic LuNi2B2C (~ II ml mol"! K- 2) indicative of an enhanced electron effective mass due to hybridization between the 4f electrons of Yb and the conduction electrons (Yatskar et al. 1996; Dhar et al. 1996; Beyermann et al. 1999). This is consistent with broad excitation spectra obtained from inelastic neutron scattering (Sierks et al. 1999; Boothroyd et al. 200 I; Rotter et al. 200 1). It was found that the excitation spectrum of YbNjzB2C extends above 150 meY. Three inelastic peaks were observed by Boothroyd et al. (200 I). These peaks are centered at energies of 3 meV, 17 meV, 43 meV and resemble CEF transitions. The observed splitting is approximately twice that predicted by a CEF model for the R site based on an analysis of the data from the Er, Ho and Tm borocarbides (Gasser et al. 1996). Therefore the CEF model does not describe YbNi2B2C. High-resolution neutron studies of polycrystalline YbNi2B2C have shown a clear evidence of inelastic scattering below I meV (Sierks et al. 1999). The experiments on YbNi2B2C single crystals show that the magnetic scattering below I meV appears to be highly localized in some region of reciprocal space, and may be associated with the heavy fermion properties (Boothroyd et al. 2001). Another indication on 4f conduction-band hybridization in YbNi2B2C was obtained (Mazumdar et aI. 2001) from polarization-dependent x-ray-absorption near-edge structure (XANES) spectroscopy performed on RNizB2C single crystals (with R = Er to Lu). The combined influence of the 4f conduction-band hybridization and the crystal field in YbNi2B2C and YbNiBC has
MAGNETIC AND SUPERCONDUCfING PROPERTIES OF RNi2B2C
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been discussed by Rams et a1. (2000) on the basis of the thermal variation of the quadrupole hyperfine interaction using the 172Yb. The resistivity ofYbNi2B2C decreases monotonically with decreasing temperature (see fig. 49), but drops pronouncedly below ""50 K (Yatskar et a1. 1996; Dhar et al, 1996). A quadratic temperature dependence of the resistivity was found below 1.5 K which is a characteristic feature of strong-electron correlation (Yatskar et a1. 1996). A complicated behaviour of the magnetoresistance MR was found by Lacerda et a1. (1996), Yatskar et a1. (1999) and Christianson et a1. (2001). Above 5 K the MR is negative and approximately isotropic, whereas at low T it is strongly anisotropic and changes its sign below 1 K for H .le, see fig. 50. A strong temperature dependence of the Hall coefficient RH was reported by Narozhnyi et a1. (l999b) which is in contrast with the weak temperature dependent RH observed for several other borocarbides (see subsection 3.3). The magnetic susceptibility has a Curie-Weiss behaviour above 150 K (Yatskar et a1. 1996; Dhar et a1. 1996) with the paramagnetic moment close to that of free Yb3+ ions (see table 8). Below r - 100 K the temperature dependence of X strongly deviates from the Curie-Weiss law. These deviations and the rather large Weiss temperature (0 ~ -130 K) indicate a significant 4f conduction-electron hybridization. In accordance with this, data on NMR of II B show that YbNhB2C manifests local moment behaviour for T > 50 K and nonmagnetic, itinerant correlated behaviour for T < 5 K (Sala et a1. 1997). The rapid suppression of superconductivity reported for (Lu,Y)I-x YbxNhB2C systems (Bud'ko et a1. 1997; Hossain et a1. 1997; Rathnayaka et a1. 1999) has been attributed to changes from a superconducting regime to a single-impurity Kondo regime to a Kondo lattice (heavy Fermion regime) as x is increased from zero to one. Interestingly the Kondo temperature TK ~ 10 K is relatively invariant across the series (Bud'ko et a1. 1997) and is not much different from the value of T c of YbNi2B2C, estimated above by de Gennes scaling arguments.
272
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5. Vortex lattices in RNhB2C superconductors 5.1. Vortex lattice in non-magnetic borocarbides Type II superconductors had been discovered by Shubnikov et al. (1937). Abrikosov (1957) has theoretically proven for these materials that (i) they are characterized by K > 1/.j2 where K = )../~ is the Ginzburg-Landau parameter. )" the penetration depth and ~ is the coherence length. The coherence length of ideally pure material. ~o. is related to ~ by I I ~ = 1I ~o + 1I I Where I is the quasiparticle mean free path (Bardeen 1992). (ii) for HcI < H < Hcz where Hel and H e2 are the lower and the upper critical field. respectively. a mixed state is formed i.e. flux penetrates in quantized units in nonsuperconducting domains called vortices or flux lines in a superconducting matrix and (iii) in the isotropic case the flux lines form a two-dimensional hexagonal lattice. Such lattices have been observed in many materials by small angle neutron scattering (SANS). electron microscopy. magnetooptical or other techniques and. in recent years. also by scanning tunneling microscopy (STM. see Brandt 1995). For LuNi2B2C as well as YNi2BzC. at sufficiently high fields applied parallel to the tetragonal c axis. square vortex lattices as shown in the figs 51a and 52 have been observed (De Wilde et al. 1997; Yethiraj et al. 1997.1998; Paul et al. 1998; Ghosh and Shrivastiava
273
MAGNETIC AND SUPERCONDUCTING PROPERTIES OF RNi282C
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1998; Song et a1. 1999b; Eskildsen et a1. 2oo1c; Vinnikov et a1. 2oo1a, 2001b; Gammel et al. 2(01). The occurrence of square vortex lattices can be understood by non-local corrections to the Ginzburg-Landau-Abrikosov theory (De Wilde et al. 1997) or to the London model (London and London 1935; Kogan et al. 1996, 1997a, 1997b) which describes superconductors with large GL parameters K. In the standard Ginzburg-Landau or London model, there is no coupling between the vortex lattice and the underlying crystal structure. Therefore, the orientation of the vortex lattice is arbitrary and no structural transitions of the hexagonal vortex lattice are expected. Taking into account the coupling between the vortex lattice and the crystal structure, one obtains a nonlocal relation between the current density j and the vector potential A within a domain size of approximately ~ 0 around the vortex core instead of the local relations between j and A of the standard
274
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Ginzburg-Landau or London approaches. The nonlocality which is influenced by the Fermi surface adds a short-range potential V(r) to the intervortex interaction, with the symmetry of the crystal. In the case of tetragonal s-wave materials as the borocarbides, this potential has a square symmetry. It disturbs the isotropic field and current distributions around the vortex core and makes the vortex current paths of an isolated vortex "squarish" close to the core, whereas at large distances a circular symmetry is recovered similar to that found in an isotropic superconductor. Therefore, the influence of this potential on the structure of the vortex lattice is negligible for large intervortex spacing in the low field limit. In this limit the vortex lattice is hexagonal. With decreasing intervortex spacing or increasing applied field Hlle, this potential drives the hexagonal vortex lattice into a square one at a certain field HO(T). This transition is schematically shown in fig. 53. This transition proceeds via a rhombohedral distortion along the vortex lattice unit cell diagonals, thus preserving the orientation with respect to the crystalline lattice. The transition field Ho can be estimated from the London penetration depth A, which is 160 nm for YNi2B2C in the [I 00] direction. An intervortex distance of 160 nm corresponds to an applied field of 800 Oe (for a square lattice) or 920 Oe (for a hexagonal lattice) which approximately coincides with the fieldHo = I kOe at which the hexagonal-square transition was observed in YNjzB2C for Hlle (Paul et al. 1998; Eskildsen et al. 1997a). In addition to the hexagonal-square transition, a reorientation transition of the hexagonal vortex lattice from a state with the diagonal of the rhombic unit cell along [110] direction to [100] direction has been observed for YNi2B2C (Paul et al. 1998). Figure 51b shows that for H applied perpendicular to c the transition to a (nearly) square lattice occurs at a field of about I Tesla and at ~ 0.8 Tesla a reorientation transition of the diagonal of the rhombic cell takes place (Sakata et al. 2000). The elastic moduli of the vortex lattice around the transition field Ho of have been analyzed within the nonlocal London model by Miranovic and Kogan (2001). In particular. the square vortex lattice was found to be soft with respect to shear displacement along the square sides [110] or [I 10]. The temperature dependence of the hexagonal-square transition field Ho of LuNi2B2C was investigated by SANS (Eskildsen et al. 2001c). At temperatures below 10 K, HO was found to be only weakly temperature dependent. Above 10K, a sharp increase
275
MAGNETIC AND SUPERCONDUCTING PROPERTIES OF RNi282C 10
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0.8
Fig. 54. (a) Transition line HO(T) (circles) of LuNi2B2C. Inset: HO(T) (dashed line) predicted by the GL theory without fluctuations. The solid lines in (a) show H c2(T). (b) Transition lines HO(T) predicted by the nonlocal London theory including thermal fluctuations for various values of p which is a measure of nonlocality (after Gurevich and Kogan 2001).
of Ht: was observed. The Ho(T) line curves up to avoid H c2(T) and becomes twovalued. This means that in a small temperature range with increasing applied field firstly a transition from a hexagonal to a square vortice lattice and then, at fields H -+ H c2, a re-entrant transition to a hexagonal vortice lattice is observed. This unexpected behaviour has been explained by thermal fluctuations in the framework of the nonlocal London theory (Gurevich and Kogan 2001). Experimental data for the transition line HO(T) of LuNhB2C and results of numerical calculations HO (T) are shown in the figs 54(a and b), respectively. It should be noted that nonlocal effects are restricted to the clean limit of type II superconductivity. They are suppressed by scattering and vanish in the dirty limit. This suppression was investigated on Lu(Nil-xCoxhB2C compounds (Gammel et al. 1999; Eskildsen et al. 2000). It is well known that LuNhB2C which is in the clean limit can be changed into a dirty-limit superconductor by doping with 9% Co (Cheon et al. 1998). Co doping results in a decrease of the mean free path and an increase of the zero temperature coherence length shifting the transition field Ho to higher fields. In particular, Ho increases from r - I kOe (for x = 0) over 10.2 kOe (for x = 4.4%) to 14 kOe for (x = 6%). In the dirty limit (for x = 9%), no transition to a square vortice lattice was observed (Eskildsen et al. 2000). The transition field can be calculated numerically within the nonlocal London model. The symmetry changes of the vortex lattice in borocarbide superconductors affect their pinning properties as was shown for YNhB2C (Silhanek et al. 2001). For the field orientation Hlle, the reorientation transition of the vortex lattice mentioned above was found to be associated with a significant kink in the volume pinning force F p, whereas in the basal plane (for H .Lc) the signature of nonlocal effects is a fourfold periodicity of F pIn addition to the vortex lattice occupying the main part of the H - T -phase diagram of borocarbide superconductors, several other vortex phases have been identified in the nonmagnetic borocarbides. Mun et al. (1996) found, by transport measurements on YNhB2C,
Z76
K.-H. MULLER et al.
a vortex liquid between the vortex lattice phase and the normal state and a vortex glass phase at low temperatures and high magnetic fields. A vortex glass transition is also suggested by results of Eskildsen et al. (1997a) who found, for YNizBzC as well as LuNizBzC, a static disorder of the square vortex lattice for H > 0.2H cZ where collective pinning of the flux lines breaks down. The change from vortex lattice through vortex glass and then to vortex liquid has also been seen by NMR measurements (Lee et al. 1999,2(00). Peculiarities of the vortex pinning near H cZ and, in particular, the peak effect in the critical current density ic observed in borocarbides (Eskildsen et al. 1997a; Song et al. 1999b) can be explained by softening of the shear moduli of the vortex lattice near H cZ (Larkin and Ovchinnikov 1979). Additionally, a pronounced dip anomaly in the ac screening response in the mixed state of YNizBzC and LuNhBzC single crystals was observed which was found to be connected with the peak effect in ic (Narozhnyi et al, 2000b).
5.2. Vortex lattice and magnetic order in ErNizBzC and TmNi2BzC An interesting question is whether the subtle effects of non-locality and, in particular, the hexagonal-square transition of the vortex lattice would be preserved in the superconducting state of magnetic superconductors such as RNi2BzC with R = Er and Tm. In ErNi2B2C single crystals, this transition was observed by SANS investigations and magnetic decoration at temperatures above as well as below the Neel temperature TN. At T = 3.5 K, i.e. in the antferromagnetic state, the hexagonal-square transition occurs for the field orientation Hllc at above Ht: '" 500 Oe (Eskildsen et al. 1997b). Whereas the square lattice was found to be aligned with the [110] direction of the host crystal, the hexagonal lattice has domains aligned along [100] or [010]. Of special interest is the question whether the vortex lattice is influenced by the magnetic order. For both symmetries of the vortex lattice, a significant coupling between the magnetic ordering and the flux lines was evidenced in the weakly ferromagnetic state below 2.5 K by a rotation of the flux lines away from the direction of the applied field Hllc, whereas at higher temperatures the vortex lattice was found to be well aligned with the applied field (Yaron et al. 1996). The angle between the vortex lattice and the applied field increases with decreasing temperature up to about 10 at 1.5 K. Contradictory results were reported for TmNi2B2C for the field orientation Hllc. In the paramagnetic state, no square lattice, but rather a distorted rhombic lattice was found by Paul et al. (200 I) by SANS studies. On the other hand, only the square vortex lattice was reported by Eskildsen et al, (2001a) in the range of low magnetic fields, as well in the paramagnetic and the anti ferromagnetic state. Detailed SANS studies of the magnetic structures and the vortex lattice were performed on a TmNhB2C single crystal below TN '" 1.5 K (Eskildsen et al. 1998, 2001a). In the low-field region (H < 2 kOe) the same incommensurate modulated state was observed as in zero magnetic field (Lynn et al. 1997). The Tm spins order into a squared spin density wave with a modulation vector q = 0.94(a* + b*) and the moment parallel to the c-axis. In this field range, H < 2 kOe, a square vortice lattice was found for all temperatures below TN. Above 2 kOe a magnetic transition into a more complex structure is observed with additional peaks of the SANS signal appearing around the [100] and [010] directions. Coincident with the magnetic transition at 2 kOe, the vortice lattice undergoes a rhombic distortion and becomes hexagonal for fields above 4 kOe. There is a second magnetic transition
MAGNETIC AND SUPERCONDUCTING PROPERTIES OF RNi282C
277
probably into a saturated paramagnetic state at H = 10 kOe and T = 100 mK. These studies revealed an intimate coupling between the vortex lattice and the magnetic structure. However, the origin of the vortex lattice transitions in relation to the magnetic transitions is not understood so far.
5.3. Vortexpinning and magnetie order Studies on vortex pinning in ErNi2B2C (Dewhurst et al. 2001a, 2001b) and HoNhBzC (Dewhurst et al. 1999) revealed significant bulk pinning for H lIe only in the temperature range in which the a" incommensurate magnetic structure exists (T < 6 K for ErNizBzC, 5 K < T < 6 K for HoNhBzC). In HoNhBzC, the superconductivity is weakened in the narrow temperature range 5 K < T < 6 K in which the incommensurate a" and e* magnetic structures occur (see figs 43(a, c, e)). It was suggested that the enhanced pinning in the same temperature range is caused by a direct interaction between the vortice lattice and a" magnetic states or domains thereof (Dewhurst et at. 1999). Two scenarios were discussed: (1) the suppression of H c2 by magnetic pair-breaking might be accompanied by a corresponding periodic modulation of the coherence length ~ 0 oc H cZ -0.5 which could result in core pinning of vortices; (2) the domains connected with the modulation of the a" magnetic structure along the a-axis may cause pinning for vortices by the interaction with the domain walls. Magneto-optical investigations on ErNizBzC single crystals for the field direction H lie provided evidence for the formation of antiferromagnetic domain walls at T < TN and their interaction with the vortex lattice resulting in enhanced pinning (Saha et at. 2(00). This interaction was found to be mediated by a weak ferromagnetic spin component localized in the domain walls. The weak loeal ferromagnetism setting in immediately below TN is expected to suppress the superconductivity at the domain walls by pair-breaking (Saba et al. 2(00). On the other hand, no significant increase in pinning was found at T < TN for the field direction H .Lc (James et al. 2(01) in which the vortices are aligned perpendicular to the e-axis. Because the planar domain boundaries are directed along [110] and [110] with the ferromagnetic moment parallel to the domain plane direction (e-axis), these planar pinning centers are expected to become ineffective when the vortices are tilted away from the e-axis. Therefore, the observed pinning anisotropy below TN strongly supports the idea that magnetic domain boundaries are responsible for the significant bulk pinning found in ErNizB2C in the antiferromagnetic state below TN for HI/e. Additionally, a strong increase in bulk pinning was observed in ErNhBzC in the state of weak ferromagnetism below T = 2.5 K for both orientations Hlle and H .Lc (Gammel et al. 2000; James et al. 200 I). The origin of this pinning effect is not understood so far. As possible explanation of the enhanced pinning below T = 2.5 K, a point disorder pinning mechanism was proposed (James et al. 200 1).
6. Superconductivity in R(Ni,ThBzC and (R, R')NizBzC 6./. R(Ni,ThBzCeompounds(T
= Co, Cu. Pd. Ptete.)
As can be seen in table 2, the LuNizBzC type structure is formed with many transitionmetal T elements and it is natural to investigate series of mixed compounds R(Ni,ThBzC
278
K.-H. MULLER et al.
500.0
Q' c
480.0
~
CD
460.0
x Co ~
-~
55.0 45.0
• Cu - - Co (rigid band filling Cu (rigid band filling)
!!
!
35.0
ZJ
25.0
Z
0.2
0.4
0.6
0.8
doping level x Fig. 55. Debye temperature. liD. and density of states at the Fermi level. N(EF). for Y(Nil-xCox12B2C and Y(Nil_xCUx 12B2C as a function of the CoICu substitution level x. Symbols: results derived from a relativistic band calculations in the atomic sphere approximation. Curves (in lower panel): rigid band model. After Ravindran et al. (1998).
in order to search for improved properties but also to get more insight into the microscopic mechanisms underlying the superconductivity and magnetism in these materials. Most work has been done in replacing Ni in RNi2B2C by its neighbors in the periodic table i.e. Co, Cu, Pd, Pt, but also by other transition metals, see e.g. Hilscher and Michor (1999). The transition temperature T c is reduced by Ni -+ Cu (R = Y, Choi et al. 1998) as well as Ni -+ Co (R = Y: Schmidt et al. 1994; Hoellwarth et al. 1996; R = Dy, Ho, Er, Tm, Lu: Schmidt and Braun 1997; R = Ce: El Massalami et al. 1997; R = Gd: Bud'ko et al. 1995b, 1995c; R = Ho: Lynn et al. 1996; R = Er: Felner et al. 1997a and Bud'ko and Canfield 2000b; R = Lu: Cheon et al. 1998). This can be qualitatively understood within the framework of a simple rigid-band picture assuming a more or less rigid band structure across the substitutional series and a varying degree of band filling due to the different number of conduction electrons in Co, Ni, Cu. Thus the Fermi level EF is shifted away from the local maximum of N(EF) or from the state with optimum conditions for occurrence of superconductivity which is found at T = Ni. More detailed electronic-structure calculations of Ravindran et al. (1998) have shown that the rigid-band model reproduces N(EF) rather well (see fig. 55). However for larger x the value of N(EF) of Y(Nil-xCoxhB2C compounds again increases with increasing x and the two parent compounds for x = 0 and x = 1 do not much differ in their N(EF). Nevertheless YC02B2C is neither a superconductor nor a magnetic system. Ravindran et al. (1998) have concluded that this difference is due to stiffening of the lattice with increasing x. These authors emphasize that, although both Co and Cu have an ionic radius of 0.72 A, which
MAGNETIC AND SUPERCONDUCTING PROPERTIES OF RNi2B2C
279
is larger than that of Ni (0.69 A), the substitution of Co for Ni in YNhB2C results in a contraction of the lattice, whereas Ni ~ Cu leads to lattice expansion. Also the ratio cIa of the lattice parameters depends on the doping level. Such local-structure aspects may affect the superconducting properties in addition to the simple effects of band filling. Suppression of superconductivity has also been investigated for Ni replaced in YNhB2C by other 3d-elements such as Fe and Ru (Bud'ko et a1. 1995c) and Mn (da Rocha et a1. 200 1). Substitution of Co or Cu for Ni has also been done in quaternary superconducting compounds with alternative lattice structures such as YNil-xCuxBC, LuNil_xCuxBC (Gangopadhyay and Schilling 1996) and La(NiJ-xCuxhB2N3, La(Nil-xCoxhB2N3 (Michor et a1. 1998). An interesting problem is how the properties of RNhB2C change upon Ni replacement by the isoelectronic metals Pd or Pt. Modest decrease of T c with increasing doping level has also been reported for substitutions Ni ~ Pt or Pd in ErNhB2C and TmNi2B2C (Bonville et a1. 1996; Feiner et a1. 1997b). Interestingly, the magnetic ordering temperature TN decreases for these substitutions in the case of TmNi2B2C but it increases (even up to TN > T c ) for ErNhB2C. This difference in the behaviour of the Tm- and Er-based compounds is not yet understood (Feiner et a1. 1997b). In summary the change of T« with varying x in R(Nil-x TxhB2C superconductors can rather well be understood taking into account the variation in the lattice structure and the band-filling levels. However there are properties as e.g. the anisotropy of the superconducting gap (Yokoya et a1. 2000) or the field dependence of the electronic specific heat (Lipp et a1. 200 1) or the vortex core radius (Nohara et a1. 1999) in Y(Ni l-xPtx hB2C which cannot be explained considering the mixed compounds as more or less homogeneous systems. It will be discussed in the next subsection that disorder on the lattice sites has a remarkable influence on the properties of such mixed-compound superconductors. 6.2. Effects ofdisorder
Since R = Sc, Y, La and most of the 4f elements form RNhB2C compounds with the LuNhB2C-type structure it is relatively easy to prepare and investigate pseudoquaternary compounds (R, R')Ni2B2C in order to realize intermediate states. (It should be noted, however, that for large difference of ionic radii of Rand R' miscibility gaps were found for x near 0.5, see Freudenberger et a1. 2oo1b.) This may help to better understand the intrinsic mechanisms for superconductivity and magnetism and their interplay in these compounds. In particular, Freudenberger et a1. (1998a) and Fuchs et a1. (2001) have investigated (R, R')NhB2C compounds with both elements Rand R' being non-magnetic as e.g. Y and Lu. For a fictive 'gray' system with a fictive R ion of averaged size resulting in averaged lattice constants the value of T c would be on the upper curve in fig. 9 with a value even higher than T c of both parent compounds. However, the real pseudoquaternary system Yx Lu l-xNhB2C has a considerably lower value of T c than the 'gray' system. As shown in fig. 56 the concentration dependence of T c is non-monotonic with a minimum near x = 0.5. A similar behaviour was found also for other quantities characterizing the electronic state of the system as the upper critical field H c2* and the parameter ex (from H c2(T) = H c2*(1 - T fTc) I+a) which is a measure for the positive curvature of H c2(T), the residual resistance ratio RRR = Pn(300 K) f Pn(T d where Pn(T) is the normal-state
280
K.-H. MOLLER et aI.
16 K 15 K 0.3
16 K 15 K
0.2 12 T
0.2 0.1 lOT
8T 40 0
~
10 T 0.7
~
\0 Lu 0.2
RRR
c
0.5 0.3 20
x 0.6 0.8 (a)
18
~ V
Lu
0.2
x
0.6
0.8
V
(b)
Fig.56. Concentration dependence of various electronic properties of polycrystalline Yx Lu 1_ x Ni2B2C obtained from measurements of (a) the resistivity and (b) the specific heat. The meaning of the parameters is explained in the text.
resistivity, as well as the two parameters y Nand f3 describing the field dependence of the electronic specific heat in the mixed state. C '" y (H) T, namely (8)
where YN is the normal-state Sommerfeld constant (Fuchs et al. 2001; Lipp et al. 2(01). These quantities have their highest values for the pure compounds and show a minimum near x = 0.5. This behaviour has been attributed to disorder-induced local lattice distortions due to the different size of the ionic radii of Y and the Lu. A quantitative analysis shows that the sensitivity to the site disorder is most pronounced for the magnitude of H c2(0), somewhat less for a and weakest for T c . Therefore, the parameter H c2(0) can be considered as the most sensitive measure of the perfection of the clean limit superconductor. The field dependence of the linear-in-T electronic specifice heat contribution y(H)T of the polycrystalline YxLul-xNi2B2C samples of fig. 56 is shown in fig. 57. YNjzB2C and LuNjzB2C exhibit significant deviations from the usual linear y(H) law which are described in eq. (8) by the parameter f3. These deviations are even larger than those reported for a YNjzB2C single crystal and for a polycrystalline LuNjzB2C sample (Nohara et al. 1997) in which y(H) was found to follow a square-root law y(H) ex JH corresponding to f3 = 0.5. In particular, a very strong sublinearity of y(H) (with f3 = 0.67) was observed for the polycrystalline LuNjzB2C sample in fig. 57. The origin for the observed y(H) ex H l-fJ dependence will be discussed in more detail at the end of this section. As shown in fig. 57, the deviation from the linear y(H) law is significantly reduced with increasing disorder
MAGNETIC AND SUPERCONDUCTING PROPERTIES OF RNi282C
~
i' ~
281
0.6 X
0.4 0.2
=0.25 0.5 0.75
0.0 0.0
0.2
0.4
0.6
0.8
1.0
HI HC2(O) Fig. 57. Specific heat contribution y(H) of the vortex core electrons in the mixed stale (normalized by the Sommerfeld parameter y N) of the Y x Lu I-x Ni2 82C samples from fig. 56 as function of the applied magnetic field (normalized by H <2(0)). The straight line y(H) ex H corresponds to the usual s-wave behaviour in the dirty limit.
reaching values of fJ '" 0.4 in the range of Y concentrations between 0.25 and 0.75 (see also fig. 56). Growing degree of substitutional disorder results in a reduction of the other abovementioned quantities. However, the microscopic mechanism, which mediates disorder to T c and to the other physical quantities, is not yet clarified. Typical scenarios for disorder effects could be: the peak of the density of states at the Fermi level, N(EF), may be broadened or the phonon spectrum may be modified by disorder (Manalo et al. 200 1) or the scattering rate of the conduction electrons may increase. As already discussed in subsection 3.2, the latter mechanism has been successfully treated in a two-band model for H c2(T) taking into account the dispersion of the Fermi velocity in these clean-limit type II superconductors (Shulga and Drechsler 200 I; see also subsection 3.2, in particular fig. 20). In this model two bands of electrons with different Fermi velocities are considered. The electrons with the low Fermi velocity have a strong electron-phonon coupling and are responsible for the superconductivity, whereas by the electrons with the large Fermi velocity, which have a moderate el-ph coupling only, the values of H c2(0) and T c are reduced. The typical positive curvature of H c2(T) near T c is caused by interband coupling between the slow and fast electrons. This model predicts a transition from the clean to the quasi-dirty limit for increasing scattering rate of the conduction electrons on impurities. Within the clean limit, H c2 (0) and the parameter ex for the positive curvature of H c2(T) near T c decrease with increasing scattering rate (see fig. 20). In this way, the observed minimum of H ez" and ex for x ~ 0.5 (see fig. 20) can be explained by the increased scattering rate in the samples with substitutional disorder at the rare-earth site. The comparison of the two-band model (fig. 20) with the experimental data for YxLul-xNjzB2C (fig. 56) indicates that also the most disordered sample is not yet in the dirty limit because their curvature remains positive. From the experimental data for the Sommerfeld constant YN in fig. 56, conclusions on the influence of substitutional disorder on the rare-earth site of YxLul-xNi2B2C
282
K.-H. MOLLER et a1. ~
OJ
0 <, 4.2
---Y.Lu, .•NhBzC ------
Ul
Cl
]
~
0' 'Z
4.0
CPA-prediction
21
N""' lo<
0
20
experimental data
E
...,
<,
"
19
S z
»-
"
18 1.10
s:
----------------
?- 1.05
OJ
-<
1.00 phenomenological
0.95
0
0.5 X
Fig. 58. Composition dependence of the density of states N(EF) at the Fermi level (0) of YxLul_xNi2B2C calculated by CPA, experimental data for the Sommerfeld parameter YN and the phenomenologically extracted values of the electron-phonon coupling constant Aei-ph (in this article usually written as Aph), using eq. (9).
compounds on their electronic structure can be drawn. According to the well known expression
(9) the Sommerfeld constant YN is closely related to the density of states at the Fenni level N(EF) and the electron-phonon coupling constant Aph. Calculations of N(EF) within the coherent potential approximation (CPA) revealed that N(EF), as function of the Y concentration, passes through a minimum which only slightly deviates from the linear interpolation between the values for the pure samples (Rosner et al. 2000, see upper panel of fig. 58). The maximum deviation from this dashed line in fig. 58 is only about 1% and can not explain the observed variation of the Sommerfeld constant by about 10%. Therefore, taking into account eq. (9), it was concluded that the local lattice distortions due to the different size of the Y and Lu ions in the YxLul-xNhB2C compounds mainly reduce the electron-phonon interaction (Rosner et al. 2000). The dependence of Aph on the Y concentration resulting from eq. (9) and N(EF) is shown in the lower panel of fig. 58. With values for Aph between 1.0 and 1.1, medium coupling strengths are estimated for the Yx Lu I-x Ni2B2C compounds. An alternative (to the non-monotonic variation of electron-phonon interaction with increasing of x as discussed above) interpretation of the minimum of YN(X) observed in YxLUI-xNi2B2C was proposed by Manalo et al. (2001). Analyzing the thermodynamic properties of YxLul-xNi2B2C in the framework of the Eliashberg theory including anisotropy effects, they explained the minimum of YN(X) by a
MAGNETIC AND SUPERCONDUCTING PROPERTIES OF RNi2B2C
283
10
E £ :I:
~
9
lu on Vslles
• 8 7 Q
6
;......- quasl-dlrty limit
0.0
0.1
0.2
0.3
0.4
0.5
Impurity concentration Fig. 59. Suppression of the upper critical field H c2(O) in YxLul_xNi2B2C (filled circles) and Y(Nil_xPtx hB2C (open circles). After Lipp et al. (2001).
corresponding reduction of the density of states N(EF) at medium x values, whereas Aph was found to change monotonously between the Aph values of YNhB2C and LuNhB2C. As noted above, the dirty limit is not reached in YxLUI-xNhB2C, even in the case of maximum disorder. On the other hand, the transition from clean to dirty limit superconductivity has been reported for Y(Ni,PthB2C by Nohara et al. (1999) by substituting 20% Pt on Ni sites. It is not unexpected that the superconducting properties are much more affected by disorder in the Ni-B network than in the rare-earth subsystem which plays the role of a charge reservoir only, whereas the Ni-B network is assumed to be much more involved in the superconductivity of the quaternary borocarbides. Systematic investigation of the influence of substitutional disorder on the properties of Y(Nil-xPtxhB2C compounds were performed in a wide concentration range x ~ 0.75 by Lipp et al. (2001). It should be noted that the phase formation of compounds with larger Pt concentrations is much more complicated than of those with small Pt content because these RPt2B2C phases become metastable for decreasing size of the rare-earth element R (Cava et al. 1994<1). Therefore, no single-phase YPt2B2C could be synthesized. Improvement of the phase purity of YPt2B2C has been obtained in samples in which platinum had been partially replaced by gold (Cava et al. 1994e; Buchgeister et al. 1995). In fig. 59, the effect of PI (on Ni sites) and Lu impurities (on Y sites) on HdO) of Y(NiJ-xPtxhB2C and YxLul-xNi2B2C, respectively is compared in the range of x ~ 0.5. It is clearly seen that H c2 (0) is much stronger suppressed by Pt impurities on Ni sites than by Lu impurities on Y sites. The quasi-dirty limit in the Y(Nil-xPtxhB2C compounds is observed at a Pt concentration of x = 0.1, where H c2(O) has its lowest value. The positive curvature of H c2(T) which is typical for the clean limit practically disappears in the quasi dirty limit. This is shown in fig. 60, where the influence of increasing disorder on the superconducting parameters of Y(Nil-xPtx hB2C (Lipp et al. 2002) is summarized. An unexpected concentration dependence is found for the parameter fJ which describes, according to eq. (8), the deviation of the field dependence of the electronic specific heat in the mixed state from the linear law expected (Nohara et al. 1997) for isotropic s-wave superconductors in the dirty limit. The large deviations from this linear y (H) law observed
284
K.-H. MULLER et aI. 16 K 14 K
12 K
II-+-+-+-+--+-+-+--+--I-+-+-tl
0.2
15 0.2
0.4
0.6
Pt concentration x Fig. 60. Concentration dependence of various properties of polycrystalline Y(Nil-xPtxhB2C obtained by specific heat measurements: transition temperature T c; exponent IX and parameter H c2* from eq. (6); upper critical field H c2(0) at T = 0, where the dotted line schematically describes the dirty limit corresponding to the isotropic single band case (in reality there is a finite intersection with the field-axis for the dotted asymptotic line, see Shulga and Drechsler 2002); exponent f3 of eq. (8) for the curvature of the electronic specific heat in the mixed slate and Sommerfeld constant YN (after Lipp et aI. 2001).
for YNi2B2C become smaller in the quasi-dirty limit, however, they do not disappear. It was pointed out by Lipp et al. (200 1) that for intermediate deviations from linearity of y(H) ({3 = 0.15-0.35) the specific heat data of borocarbides at low magnetic fields can be discussed in the context of the conventional s-wave picture as well as within the framework of a d-wave model in the dirty limit. At low fields, the HlnH dependence of y(H) predicted for d-wave pairing in the dirty limit (Barash et al. 1997; Kiibert and Hirschfeld 1998) is not very distinct from the H l-fJ behaviour which favours s-wave superconductivity. This is illustrated in fig. 61. Thus, considering results on y(H) only, a possible unconventional pairing in borocarbies cannot be ruled out. But not only the peculiarities of the physics of the vortex state in the quasi-dirty limit are not understood so far. Also the basic understanding of the vortex physics in the clean limit is still far from a satisfactory level. Experimental y(H) data for YNhB2C and LuNhB2C reported by Nohara et al. (1997) can be described approximately by y(H) ex.jH or, with eq. (8), by {3 = 0.5, while even higher values of {3 were found for the YNhB2C and LuNhB2C samples presented in fig. 56b and fig. 57 (Lipp et al. 200 1; Fuchs et al. 200 1). A nonlinear H dependence close to y(H) ex.jH has been reported for some unconventional superconductors with gap nodes in the quasiparticle spectrum of the vortex state such as YBa2Cu307 (Wright et al. 1999) and the heavy fermion superconductor UPt3 (Ramirez et al. 1995), but also in some clean s-wave superconductors such as CeRu2 (Hedo et al. 1998) and NbSez (Nohara et al. 1999; Sonier et al. 1999). Attempts to explain the unusual y(H) dependence of borocarbides include a shrinking of the vortex core with increasing
MAGNETIC AND SUPERCONDUCfING PROPERTIES OF RNi2B2C
285
Y(Nlo.75Pfo.~2B2C
.r- 16 ~
e
12
r(lf) - H"/I P=O.17
~
.§, 8
.....•..
.'. \
~
..«
r(lf) - HlnH
~
4
1
2
IIo H (T)
3
4
Fig. 61. Magnetic field dependence of the specific heat contribution y(H) of the vortex core electrons in the mixed state for Y(Nio.75Pto.25h B2C, The dashed line is a fit according to eq. (8) with fl = 0.17. the solid line corresponds to the y(H) Q( H In H dependence predicted by ad-wave model in the dirty limit (Barash et aI. 1997; Kubert and Hirschfeld 1998).
applied field (Nohara et al. 1999; Sonier et al. 1999), field-induced gap nodes (Hedo et al. 1998) and d-wave symmetry (Wang and Maki 1998). The y(H) law in conventional s-wave superconductors is linear because all quasiparticles are confined within the vortex core of radius ~ (coherence length). Therefore, the quasiparticle density of states as a function of the field H, N(H), is proportional to the number of vortices which scales with the magnetic field resulting in N(H) ex NF~2H, where N F is the DOS at the Fermi level in the core (Izawa et al. 200 I). Experimental data for the microwave surface impedance in the vortex state of YNhB2C (lzawa et aI. 2(01) are consistent only with a linear N(H) dependence. This means that the number of quasiparticles within the core is field-independent since the flux flow dissipation causing the microwave surface impedance mainly comes from the quasiparticles localized in the cores. This result excludes the scenario of the core shrinking with magnetic field as an origin of nonlinear y(H) and indicates that delocalized quasiparticle states around the vortex cores, similar as in d-wave superconductors, are responsible for the nonlinear y(H) dependence ofYNi2B2C (lzawa et a1. 2(01). The presence of such delocalized quasiparticles has been verified in LuNi2B2C and YNi2B2C by investigation of the thermal conductivity (Boaknin et a1. 2001; Izawa et a1. 2002, see subsection 3.3.3). Recently the strong sublinear field dependence of the electronic specific heat has been addressed theoretically for an s-wave two-band superconductor by Nakai et a1. (2002) in the context of MgB2. Within the framework of Bogoliubov-de Gennes theory (i.e. the BCS theory extended to inhomogeneous systems) under some additional assumptions: (i) equal densities of states N(EF) and Fermi velocities of holes and electrons in each band, and (ii) no attractive interaction of quasi particles within the second band, i.e. only an induced attraction due to Cooper pair tunneling from the first band, Nakai et a1. (2002) found that the curvature exponent fJ (in our notation) depends sensitively on the gap ratio of the two gaps on the strongly and weakly coupled bands. The larger that ratio, the more pronounced is the sublinear behaviour. Slightly above the lower critical field where the vortices start to
K.-H. MULLER et 31.
286
interact, the smaller gap is somewhat suppressed and the number of quasiparticles outside the core is enhanced which mimics an unconventional behaviour of the specific heat in the mixed state. In our opinion that appealing picture can be qualitatively transfered to the nonmagnetic borocarbides under consideration. Then in other words, at least in the clean limit the two (multi)-band character of the borocarbides manifests itself by two unusual curvature exponents a and f3, the former of the upper critical field near T c and the latter of the sublinear field dependent specific heat. There is also a recent alternative attempt to explain the nonlinear field dependence of specific heat by a special single band anisotropic (s + g-wave)-gap model which results in f3 = 0.5 (Maki et al. 2002). More detailed theoretical and experimental investigations are desirable to quantify the influence of realistic density of states, disorder, anisotropy and other effects on the magnitude of f3 in the general multiband approach as well as in this single band (s + g-wave)-gap model. 6.3. Magnetic impurities in a nonmagnetic superconductor
For the investigation of the interplay of local moment magnetism with superconductivity in (R,R')Ni2B2C compounds at least one of the two elements Rand R' should be chosen to be magnetic. Figure 62 shows the influence of dilution of R = Lu and Y by R' = Ho, Dy, or Gd on the superconducting transition temperature T c. For Gd, Y l-xNhB2C the dependence of T; on x, or the effective de Gennes factor DG = xDG[R] + (I - x)DG[R'] where DG[R] is the de Gennes factor of the free (Hunds rule) R3+ ion, can be well described by the expression (10) of the classical theory of Abrikosov and Gor'kov (1961) for magnetic impurities in a nonmagnetic superconductor (solid line in fig. 62a; see also subsection 1.3). In eq. (10), Te o is the superconducting transition temperature without magnetic impurities, N(EF) is the conduction electron density of states at the Fermi level, I is a measure of the exchange
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MAGNETIC AND SUPERCONDUCTING PROPERTIES OF RNi282C
287
coupling between conduction electrons and magnetic R3+ ions, and 1/1 is the digamma funtion. The solid line in fig. 62a was found to describe also the T c-versus-DG-dependence for rs, Y l-xNhB2C (Freudenberger et al. 2000). For Dy or Ho impurities in LuNi2B2C and YNhB2c' the Tc-versus-DG-curves in fig. 62 become more flat i.e. the pair breaking effect of Dy and Ho is less pronounced than that of Gd. This is caused by the influence of crystalline electric fields acting on Dy 3+ and H0 3+ thus reducing the magnetic degrees of freedom of these ions (Cho et al. 1996c; Freudenberger et al. 1998b), as described by Fulde and Keller (1982) in a modified Abrikosov-Gor'kov-theory, As can be seen in fig. 62, the decrease of T e with increasing DG is stronger for (Lu,R')NhB2C than for (Y,R')NbB2C (R' = Ho, Dy, Gd). Obviously this observation is related to the considerably smaller ionic radius of Lu 3+ compared to that of y 3+ , Ho3+. Dy 3+ and Gd 3+ . Thus in (Lu, R')NbB2C larger distortions in the rare-earth sublattice will occur than in (Y,R')Ni2B2C, which might result in enhanced pair breaking. The detailed mechanism for this effect is still unknown. Besides changes in the electronic properties caused by the change of average lattice constants and the effects of disorder on the electronic density of states and on the scattering rate. as discussed in the previous subsection. also the parameter I describing the exchange interaction between the 4f and the conduction electrons may be more strongly modified by the stronger lattice distortions (Michor et al. 2000). Interestingly, EI-Hagary et al. (2ooob) found a correlation between the specific heat jump associated with the superconducting transition. f::!..C. and the transition temperature T e. f::!..C ,..", T e2• being valid for all superconducting (YI-xR'x)Ni2B2C compounds (R' = Gd, Dy, Ho, Er) including the parent compounds DyNi2B2C (with TN > T e) and HoNhB2C, ErNhB2C (TN < T d. This observation was attributed to the Sommerfeld constant y as well as the density of states N (E F) to be almost constant within this series of heavy rare earth solid solutions and their boundary compounds. Another interesting interplay of disorder and local-moment magnetism has been observed in Tb, Y'-xNi2B2C single crystals with 0 < x < 0.4 (Bitterlich et al. 2001; see also Cho et al. 200 1) with respect to the magnitude. anisotropy. and the shape of the H e2(T) curves (see fig. 63). First with increasing Tb concentration one observes the expected decrease of the general magnitude of H cz- But this decrease develops rather differently for fields applied parallel or perpendicular to the basal plane « 100) direction; the in-plane anisotropy is very small): there is a much steeper decrease for fields in in-plane direction. Hence the anisotropy of H e2 changes its sign already at a small Tb content of x ~ 0.1. The maximal anisotropy occurs near x ~ 0.2 where macroscopic antiferromagnetism in the Tb subsystem does not develop. However. locally antiferromagnetically ordered cluster might occur. The shape of H e2(T) changes. too. Deviations from eq. (6) do appear although a positive curvature remains near Tc in spite of the disorder present. Compared with the nonmagnetic borocarbides discussed above an even more pronounced S-like shape develops. Quite interestingly. the heavy fermion- weak-SDW superconductor URU2Sh (Brison et al. 1995) exhibits nearly the same shape of H e2(T) caused there by ordering of weak U-derived moments. The mechanism of these phenomena is not yet investigated. Strong magnetic pair-breaking effects have been reported for (Y,R)Pd2B2C. Also in these compounds the drop in T e follows de Gennes scaling. with the exception of R = Ce, Eu and Yb (Ghosh et al. 2001).
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6.4. Nonmagnetic impurities in an antiferromagnetic superconductor
As can be seen in fig. 62, for medium and high concentrations of Dy in (Y,Dy)Ni2B2C or (Lu,Dy)NjzB2C the Tc-versus-DG-curves are strongly non-monotonic and even go to T c = O. The steep branches of these curves for high Dy concentrations can be interpreted as being based on electron scattering on non-magnetic (Y or Lu) impurities in the antiferromagnetic superconductor DyNjzB2C. This strong depression of superconductivity has been interpreted as pair breaking due to creation of magnetic holes (Nagarajan 2001). However it had been shown in the theoretical analyses presented by Morozov (1980), Zwicknagl and Fulde (\ 981) and Nass et al. (\ 982) that other types of nonmagnetic impurities should also be efficient in suppression of superconductivity (see also Morosov 2001). As a consequence of this phenomenon the value of T c of DyNjzB2C is very sensitive to the presence of non-magnetic impurities or, more generally, to the metallurgical state of the samples. May be that this is the reason why the identification of superconductivity in DyNi2B2C was delayed compared to the other borocarbide superconductors and the published experimental data on the properties of DyNjzB2C as well as of Dy-rich pseudoquatemary compounds (Y,Dy)Ni2B2C scatter much (Hossain et al. 1999; Michor et al. 1999; Freudenberger et al. 2001a). As has been pointed out by Levin et al. (1984) and Gupta (1998) the depression of superconductivity in antiferromagnetic superconductors by non-magnetic impurities may be the reason why not many antiferromagnetic superconductors with T c < TN are known. In principle there is no reason as to why many more such materials should not exist. However, in most such cases T c may already have been suppressed beyond observation by non-magnetic impurities that are always present to some degree. A very strong decrease of T c is observed if the Ho in HoNjzB2C is diluted by La (see fig. 64). This observation is not yet well understood and various mechanisms are in discussion. On the one hand, La has a much larger ionic radius than Ho. Hence large distortions will occur around the La impurities. Furthermore, below 6 K HoNi2B2C is an
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antiferromagnetic superconductor. Therefore in a certain concentration range the La ions may act as non-magnetic impurities in an antiferromagnetic superconductor (see the kink in the Ho-La curve in fig. 64). The third reason which has to be taken into account for the decrease of T c in (Ho,La)Ni2B2C is the tendency of RNhB2C compounds to have small or zero values of T c if the ionic radius or the lattice constant a is relatively large (Lai et al. 1995), as shown in fig. 9. Superconductivity is absent in LaNi2B2C because the electronic structure of that compound remarkably deviates from that in YNi2B2C and LuNhB2C (see subsection 3.1).
7. Conclusions The development in the research on borocarbide superconductors is remarkable for just a several years past from their discovery till the end of 200 I. In the following we will select some ideas and conclusions from Lynn et al. (200 I). The rapid progress in the study of borocarbides is closely connected with the availability of high quality polycrystalline samples over a wide range of compositions as well as single crystals early in the development of the field. The main trends of the superconducting properties and ordering of the rare-earth's magnetic moments have been elucidated. One of the most interesting aspects of borocarbides is the possibility to observe coexistence and competition between superconductivity and magnetic order. Most of the zero-field magnetic structures have been obtained, but a number of key questions remains to be clarified. A variety of both commensurate and incommensurate magnetic structures was observed. To explain these structures theoretically a detailed understanding of the role of superexchange versus indirect exchange, combined with single-ion crystal field and hybridization effects, is needed. Inelastic neutron scattering experiments giving the form of magnetic excitation spectra can provide a detailed picture of these interactions. Another significant aspect to be investigated is the coupling of the rare earth ions to the conduction electrons. It would be interesting to know what is the extent of the Ni d-electron polarization in these materials. Additional experimental and theoretical efforts
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K.-H. MULLER et al.
are necessary to understand magnetic phase diagrams of these compounds. The recently found coupling of the magnetic and crystallographic structures through magnetoelastic interaction constitutes an additional complication for this study. Superconducting and electronic properties of borocarbides exhibit rich and interesting behaviour. The band structures have been investigated in some detail for most of the materials, and the Fermi surface features have been investigated for a few systems. More work will be needed to fully elucidate the electronic behaviour. The superconductivity is thought to be phonon mediated. A direct manifestation of the electron-phonon coupling is observed in the remarkable boron isotope effect and in softening of the phonon spectrum at the nesting wave vector along the a axis, which is no doubt related to some of the observed magnetic structures. The relation of the corresponding a-axis modulated incommensurate magnetic structure to the superconductivity in HoNjzB2C still needs to be resolved. This a-axis magnetic structure itself remains to be experimentally determined in HoNizBzC. Although most of the results on superconducting properties of borocarbides can be interpreted in the framework of the s-wave model, a d-wave approach was also proposed to explain some features. A direct determination of the symmetry of the superconducting order parameter, in terms of the k dependence of the superconducting gap, using electronic phase-sensitive techniques needs to be carried out. Also the influence of disorder on superconducting parameters should be studied in more detail. Particularly interesting are the dynamics and the structure of the vortex lattice, and the structure of the vortices themselves, particularly when rare earth magnetic moments are present and even are ordered. The absence of superconductivity for light rare earths based borocarbides has been explored to some extent but the reasons for this are not completely clear so far. Although YbNizB2C is neither superconducting nor magnetically ordered, it reveals interesting properties at low temperatures where the formation of a heavy fermion state was observed. Some indications of an anomalous behaviour of PrNi2B2C were found, similar in some respects to that observed for YbNi2BzC. More work is necessary to understand these anomalies. The investigation of pseudoquaternary compounds with different rare earths on the R site in RNjzBzC revealed much insight into the pair breaking mechanisms in these materials, such as pairbreaking by magnetic impurities in nonmagnetic superconductors or by nonmagnetic impurities in antiferromagnetic superconductors, the modification of both effects by crystal fields, as well as the influence of chemical pressure or disorder caused by the inhomogeneous occupation of the R site. The crystal chemistry of these systems is quite complicated and not fully understood, and more work in this area would be profitable, particularly in searching for new materials in this class. A fundamental problem, which needs more exploration, is the interaction and possible coexistence of superconductivity and weak ferromagnetism discussed for ErNi2BzC. One of the important questions related to this problem is the possibility of the formation of a spontaneous vortex phase. The problem of coexistence of superconductivity and weak ferromagnetism in borocarbides is closely related with the same issue for ruthenocuprates with typical compositions RuSrzGdCuzOs or RuSrz(Gd,CehCuzOIO, for which magnetic ordering temperatures were reported being much higher than T e . These and various other very interesting superconductors have been discovered after the superconducting quaternary borocarbides, as e.g. MgBz with Teas high as 40 K, chemically or by electrostatic means hole doped C60 with T e up to 117 K, the itinerant weak ferromagnet ZrZnz, the ferromagnet UGez and
MAGNETIC AND SUPERCONDUCTING PROPERTIES OF RNi2B2C
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hexagonal (nonferromagnetic) Fe (both under high pressure). Quaternary borocarbides as well as the other unconventional superconductors mentioned above are fascinating materials for which an intriguing interplay between superconductivity and magnetism is observed. There is no doubt that further investigation of such systems will give new insight in the fundamental physics of these two macroscopic quantum cooperative phenomena. Acknowledgements
In writing this article the authors had close cooperation with J. Freudenberger, A. Kreyssig, M. Loewenhaupt, H. Rosner, L. Schultz and S. Shulga. The authors also would like to acknowledge many stimulating discussions with G. Behr, H. Bitterlich, H.E Braun, T. Cichorek, K. Dorr, Z. Drzazga, D. Eckert, J. Eckert, H. Eschrig, J. Fink, P. Gegenwart, A. Gladun, A. GUmbel, K. Hase, A. Handstein, B. Holzapfel, D. Lipp, W. LOser, A.I. Morosov, K. Nenkov, I. Opahle, C. Ritter, C. Sierks, K. Winzer, S. Wimbush and M. Wolf. This report encloses many results and insights from discussions with the participants of the workshop on borocarbides, supported by NATO, held in June 2000 in Dresden. This work has been supported by DFG (SFB463 and MUlOI5/4-2) and RFBR (01-02-04002). References Abrikosov, A.A .. 1957. Zh. Eksp. Teor. Fiz. 32, 1442 (eng!. transl .• 1957. Sov. Phys. JETP 5, 1174). Abrikosov, A.A .. 2001. J. Phys.: Condens. Matter 13. L943. Abrikosov, A.A .• and L.P. Gor'kov, 1961. Sov. Phys. JETP 12. 1243. Aharony, A.• R.I. Birgeneau, A. Coniglio, M.A. Kastner and H.E. Stanley. 1988. Phys. Rev. Lett. 60, 1330. Allen. P.B.• 1991. in: Encyclopedia of Physics. eds R.G. Lerner and G.L. Trigg (VCH Publishers, New York) p. 1198. Alieno. E.• Z. Hossain. C. Godart. R. Nagarajan and L.C. Gupta. 1995a. Phys. Rev. B 52. 7428. Alieno. E.. U. Neumeier. 1.0. Thompson. P.C. Canfield and B.K. Cho. 1995b. Physica C 242. 169. Allene, E.• P. Berger. E. Leroy and C. Godart. 2001. in: Rare Earth Transition Metal Borocarbides (Nitrides): Superconducting. Magnetic and Nonnal State Properties. eds K.-H. Muller and V.N. Narozhnyi (Kluwer Acad. Publ., Dordrecht) p. 265. Allenspach, P.• and U. Gasser. 2000. 1. Alloys and Compo 311. I. Amici. A.• and P. Thalmeier, 1998. Phys. Rev. B 57.
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chapter 4
SPONTANEOUS MAGNETOELASTIC EFFECTS IN GADOLINIUM COMPOUNDS
A. L1NDBAUM Institut fiir Festkorperphysik, Technische Universitlit Wien Wiedner Hauptstrasse 8-10/138, A-1040 Wien Austria e-mail: [email protected]
M. ROTTER Institut fUr Angewandte Physik, Technische Universitiit Dresden 0-01062 Dresden Germany e-mail: [email protected]
Handbook of Magnetic Materials, Vol. 14 Edited by K.HJ. Buschow @ 2002 Elsevier Science B. V. All rights reserved
307
CONTENTS Abstract
309 309
.
I. Introduction . . 2. Experimental methods
...
311
3. Microscopic Theory of Magnetoelastic Effects in Gd compounds .
311
4. Magnetovolume effects in cubic systems
315 316 317 317 318 319 320 320 322 323 324 327 329 329 331 334 336 336 339 341 342 342
.
4.1. GdAlz
4.2. GdNiz 4.3. GdIn3 4.4. GdCuZIn and GdPdZIn .
5. Spontaneous distortions of the crystal symmetry .. 6. Hexagonal systems . . . . . . . . . . 6.1. Gadolinium . .
6.2. GdNi5 6.3. Gdj ln
.
.
6.4. GdCuAI and GdNiAI .
6.5. GdCuSn
.
7. Tetragonal systems
.
7.1. GdAgZ and GdAuz . .
7.2. GdzCuzIn and GdzNiz_xIn .. 7.3. GdNizBzC . 8. Orthorhombic systems
.
8.1. Magnetostructural transitions in Gd5(SixGel_x)4 compounds . . .
8.2. GdNi . . . . 8.3. GdNil_xCUx 8.4. GdCu
8.5. GdPt . 8.6. GdCuZ'
344
8.7. GdZnz.
350 351 352 353 354 355 359 359
8.8. Gd(CUI_xNix}z . . .
8.9. Gd3Ni and Gd3Rh .. 8.10.
GdBaZCu307-~
..
9. Monoclinic systems . . . . 10. Summary and conclusions Acknowledgements References . . . . .
308
Abstract The spontaneous magnetoelastic effects in Gd compounds are reviewed showing that the strain dependence of the magnetic exchange interactions leads to significant effects. These effects are equal in magnitude to well established single ion contributions in other rare earth compounds with non vanishing orbital momentum (coming from the strain dependence of the crystal field). In some cases the exchange contribution can produce giant magnetostriction (GMS) or induce structural phase transitions. In order to extract the influence of the Gd-Gd exchange interactions. we consider only Gd compounds with partner elements showing no or only weak induced magnetic moments. The current status of the theory is presented and compared to measurements performed by temperature dependent x-ray diffraction and results of dilatometric measurements.
Key words: Pacs Magnetostriction 75.80 1. Introduction
In the past decade research on Gd compounds has been of interest for several reasons. They are ideal model systems for the study of exchange interactions which are not disturbed by the crystal field (Fontcuberta et a1. 1997; Hernando et a1. 1996). Recently Kobler et a1. (1998. 1999b) showed that it is necessary to consider higher order exchange interactions to account for the behaviour of several ferromagnetic and antiferromagnetic systems with vanishing orbital momentum. New experiments indicate that the temperature dependence of the spontaneous magnetization may not be described by the well known Bloch law (Kobler et a1. 1999a). Another interesting and often surprising point is that the spontaneous magnetoelastic effects in Gd compounds have been found to be of the same magnitude as in other rare earth compounds (Gratz and Lindbaum 1994). This shows that the contribution of the exchange interaction to the magnetoelastic Hamiltonian is of equal importance as the crystal field contribution and varies over several orders of magnitude: as an example. in Gdj ln the spontaneous magnetoelastic effects are smaller than 10-4• whereas GdNi exhibits spontaneous magnetostriction effects of more than one percent (Gratz and Lindbaum 1998) and can therefore be classified as a GMS (giant magnetostriction) system. A further important family ofGMS systems are the Gds(SixGel-x)4 compounds. In some of these compounds so-called magnetostructural transitions have been observed. i.e, the giant spontaneous as well as forced magnetoelastic effects can be connected with structural transitions (Morellon et a!. 1998a; Morellon et a1. 2000). 309
310
A. LINDBAUM and M. ROTfER
It should be pointed out that also in compounds based on other rare earths it was necessary to consider not only the crystal field interactions, but also the contribution of the exchange interactions, in order to understand the observed magnetostrictive effects (e.g. in the case of NdCU2 - see Rotter et aI. 2002). However, in Gd compounds this exchange contribution can be studied without any ambiguity arising from the crystal field interaction, because L = 0 for Gd 3+. Due to the large absorption of thermal neutrons by the natural Gd isotope, neutron diffraction experiments are difficult. Therefore the magnetic structures are often unknown and in many cases no model for the spontaneous magnetostriction could be developed. A number of attempts have been made to extract information about the magnetic structure from specific heat experiments (Rotter et aI. 2oolb; Mallik and Sampathkurnaran 1998; Bouvier et aI. 1991; Blanco et aI. 1991) and recently magnetic x-ray scattering using synchrotron radiation has opened new possibilities (Detlefs et aI. 1996; Rotter et aI. 2000b). The main subject of the present chapter is to review available experimental studies of spontaneous magnetoelastic effects in intermetallic Gd compounds. The aim is to show that the magnetic exchange interactions can lead to a wide variety of spontaneous magnetoelastic effects, including pronounced negative and positive magnetovolume effects as well as large anisotropic effects. Note: with positive (negative) effects we always mean that in the magnetically ordered state the corresponding lattice parameter or the volume is larger (smaller) than the values obtained by extrapolation from the paramagnetic temperature range. This means: with positive or negative we mean the sign of the magnetostrictive strains, which are defined relative to the paramagnetic range (and not the sign of the magnetic contribution to the thermal expansion coefficient). The concept of exchange-striction was already introduced by Callen and Callen (1965), however, up to now only few studies on this subject are available. In order to extract the influence of the magnetic exchange interactions, we consider only Gd compounds with partner elements, which show no or only very small induced magnetic moments. This means that we exclude for instance compounds with Co, Fe or Mn, whereas compounds with Ni showing only weak induced magnetic moments are included in our study. For a review of thermal expansion anomalies and spontaneous magnetostriction in rare-earth intermetallics with Co and Fe the reader is referred to the chapter of Andreev (1995). Invar effects in transition metals and alloys have been reviewed by Wasserman (1990). The reader is also referred to the review by Morin and Schmitt (1990), dealing generally with magnetoelastic effects in rare earth intermetallics, including two ion as well as single ion magnetic interactions, with a special emphasis on quadrupolar interactions. The present chapter is complementary to these reviews and concentrates on spontaneous magnetoelastic effects caused by the Gd-Gd magnetic exchange interaction in non-cubic systems. It should contribute to a more complete picture of magnetoelastic effects. The chapter is organized as follows: section 2 gives a short account of the most important experimental methods used for the measurement of magnetically induced effects on the crystal structure. The current state concerning the microscopic theory of magnetoelastic effects in Gd systems is reviewed in section 3. Then some selected results for cubic systems are presented, showing that not only symmetry conserving effects (section 4: magnetovolume effects) are possible, but also very small distortions of the symmetry (section 5). Then follows in section 6 to 9 the main part of the chapter, namely a review of
SPONTANEOUSMAGNETOELASTIC EFFECTS IN GADOLINIUMCOMPOUNDS
3II
spontaneous magnetoelastic effects in non-cubic systems from hexagonal to monoclinic, showing a wide variety of anisotropic (but symmetry conserving) effects, as well as magnetovolume effects. Finally, all the presented results are summarized and discussed in section 10. 2. Experimental methods X-ray diffraction at variable temperatures, on the one hand, and thermal expansion measurements using dilatometric methods, on the other hand, are the two most important experimental methods for measuring spontaneous magnetoelastic effects. The main advantage of the x-ray diffraction method lies in the direct measurement of the lattice parameters, allowing the determination of anisotropic effects also in polycrystalline samples. Especially distortions of the crystal symmetry can easily be detected by this method. However, the resolution of x-ray diffraction is much smaller than that of dilatometry using the capacitance or interferometric method. When good and well oriented single crystals are available, the dilatometric method is very reliable and much more sensitive than x-ray diffraction in measuring isotropic effects (volume effects) as well as anisotropic effects. However, the detection of spontaneous distortions of the crystal symmetry is difficult when using dilatometric methods. A review of the most common types of capacitance dilatometers was given by Rotter et al, (1998). Depending on the temperature a resolution of /:}.[/ [ from 10- 10 to 10-9 is possible. The resolution of the x-ray diffraction method is only about 10-5 to 10-4 , i.e. when no effects are visible in the x-ray results, this means only that the effects are smaller than the latter values. The high sensitivity makes the capacitance method one of the best tools for detecting phase transitions. But due to thermal hysteresis effects in the dilatometer materials absolute measurements of length differences for large temperature intervals are less reliable than with the x-ray method. In addition, in many cases the intrinsic strains differ from the length changes measured on a macroscopic sample, due to grain boundaries, microstresses and lattice defects. For a very detailed review of all experimental methods used for thermal expansion measurements in solids the reader is referred to Taylor et al. (1998). 3. Microscopic Theory of Magnetoelastic Effects in Gd compounds In order to analyze spontaneous magnetoelastic effects quantitatively it is first necessary to separate the magnetic contributions to the thermal expansion (i.e. the magnetostrictive strains) from the lattice contribution. This is usually done by comparison with a nonmagnetic isostructural reference compound or by extrapolating the temperature variation of the lattice parameters from the paramagnetic range by assuming a simple Debye model for the lattice contribution (see e.g. Barron et al, (1980». Because in most of the cases presented in this chapter the latter method has been applied, we give a short account. According to Gruneisen rules, and assuming a quasiharmonic approximation together with a simple Debye model for the phonons and a classical y T electronic specific
312
A. LINDBAUM and M. ROITER
heat contribution, the following formula for the nonmagnetic contribution to the thermal expansion can be derived (see e.g. Lindbaum (1994)): (I)
with
(2) Here K I, K2 and the Debye temperature eD are parameters which can be obtained by fitting (I) and (2) to the thermal expansion in the paramagnetic temperature range. The electronic contribution in (I), Eel = K I T 2 • is usually much smaller than the lattice contribution Ephon. i.e. in most cases it makes no difference when only Ephon is taken into account for determining the nonmagnetic contribution to the thermal expansion. We now turn to the main issue of this paragraph. Usually the magnetostriction of solids is analyzed within the framework of a phenomenological model which takes account of the crystal symmetry (Clark 1980). Whereas this serves for practical purposes it is not possible to derive expressions for the temperature and magnetic field dependence of the strains. For such an analysis it is necessary to develop a microscopic theory of magnetoelastic effects. Whereas a lot of results have been derived for the single ion magnetoelastic effects (for an overview see Morin and Schmitt 1990), much less attention has been paid to the effect of exchange interactions. However, already in the 60's the influence of the exchange interactions on the microscopic magnetoelastic properties have been discussed for ferromagnets and cubic crystals (Callen 1968; Clark et al. 1965; Callen and Callen 1963). Single ion and isotropic exchange contributions to the magnetostriction have been analyzed theoretically by Callen and Callen (1965) and it was shown how to obtain explicit expressions for the magnetostriction in different symmetries. In the following short review of the microscopic theory of magnetoelastic effects caused by the exchange interactions we follow Morin and Schmitt (1990) and generalize it to the case of arbitrary magnetic structures and give general expressions valid for any crystal symmetry. We will neglect the influence of the crystal field. The analysis is restricted to first order effects assuming that the magnetoelastic energy is small compared to the magnetic exchange energy. Furthermore any dynamical coupling between the lattice and the magnetic exchange (magnon-phonon interaction) will be neglected and we consider only the long wavelength static limit. The analysis is based on the bilinear two ion exchange interaction J. ..J(ij)J) between the total angular momenta J of rare earth atoms on the sites i and j. This exchange interaction shows an anisotropy. which in the case of Gd compounds is expected to be small and mainly due to the classical dipole interaction (Jensen and Mackintosh 1991). The exchange parameters ..J(ij) of the exchange Hamiltonian depend on the position of the atoms in the crystal-leading to magnetoelastic interactions (Morin and Schmitt 1990). It is possible to calculate the magnetostrictive strains E U , if we assume, that the Hamiltonian
SPONTANEOUSMAGNETOELASTICEFFECTS IN GADOLINIUM COMPOUNDS
313
may be written as a sum of exchange, Zeeman and elastic contributions. H = Hex Hex
+ Hze + Eel,
L
= -~
(3)
(4)
Ji 3(ij, E)Jj,
i.j(i¥J)
(5) a fJ = -I,", L.JCafJE E .
Eel
(6)
2 afJ Note that for the components E a of the strain tensor E and for the elastic constants cafJ Voigt's abbreviated notation is adopted (i.e, ex = 1,2,3,4,5,6 denote 11,22,33, 12, 13,23 respectively) - see e.g. Barron et aI. (1980). Starting point is the Taylor expansion of the magnetic exchange parameters with respect to the components of the strain tensor E, leading to the so-called magnetoelastic Hamiltonian.
-~
LJi 3(ij, E)Jj ~
LJi 3(ij, E= O)Jj
-~
ij
ij
I
a
=
- 2" LEaJi J(aj(ij)Jj + ...
(7)
ij
with
~
J(a)
(..)_ [a JUj,a E)] I)
-
aE
.
(8)
£=0
Usually the analysis is limited to the first order in the strain (harmonic approximation) and second order terms (anharmonic coupling) are neglected. This second order magnetoelasticity has not been analyzed for the compounds under consideration. By definition the Gibbs free energy is given by F
= -kBTlnZ
(9)
with the partition sum (10)
Here kB denotes the Boltzmann constant. In our first order approach the trace in (10) is calculated using the states of the unperturbed system, i.e. without taking into account the magnetoelastic interactions, by putting E= 0 in (3)-(6). In practice, these eigenstates of the
314
A. LlNDBAUM and M.
norrsn
unperturbed system may be calculated by a mean field approach (Jensen and Mackintosh 1991; Rotter et al. 2001b). We now insert the Hamiltonian 11. into (9) and (10) and minimize the free energy F with respect to the strains E a by putting zero the derivative (11) Using the elastic compliances saf3 which are related to the elastic constants by (see e.g. Barron 1998) 6
L Cf3 ysya = Oaf3,
(12)
y=1
equation (11) yields the final result a _ I " , af3(J . .J= (. ')J .) ~s , (f3) IJ J T.W f3.ij
-"2
E
(13)
Equation (13) shows that the complete temperature and field dependence of the strains (y, y' = 1, 2, 3 label the can be calculated from static correlation functions (Jt J cartesian components of the angular momentum J) where () r.n denote thermal expectation values (Callen and Callen 1965). As already mentioned above, a mean field theory may be used to evaluate (13) and calculate the magnetostriction. In some cases it is more convenient to Fourier transform this expression (13):
r)T."
E
a
'" ="21 ~s
a f3 (
(14)
= } L q J(P)(q)Jq T."
f3.q
with the definitions Ji
= LJqexp(-iqRj ) ,
(15)
q
3(f3) (ij) =
L 3(f3) (q)exp[-iq(Ri -
Rj)]'
(16)
q
In the case, that the magnetoelastic interaction is dominated by the isotropic contribution (i.e. ] (f3) reduces to a scalar .1<(3)' coming from the strain dependence of the Heisenberg interaction (compare the analysis of GdCU2 in section 8.6), equations (13) and (14) reduce to (17)
SPONTANEOUS MAGNETOELASTICEFFECTS IN GADOLINIUM COMPOUNDS
€a = ~ :E(~::>a/l
J(/lj(q») (J-qJq)T,H'
315
(18)
/l
q
In principle the correlation functions OT,H in expressions (14) and (18) can be evaluated, if the Fourier transform of the magnetic moments is known (for instance from neutron diffraction experiments). Re-inserting (14) or (18) into the magnetoelastic interaction (7) results in higher order terms of magnetic interactions, which we have neglected in our discussion. Although not analyzed in detail by theory, experimental data gives some clear indication of the importance of higher order terms in the Hamiltonian of Gd compounds in and the momenta Ji. A compound near a structural instability such as both, the strains the Gd5(SixGel-x)4 system can only be described by considering higher order terms in the elastic energy. Kobler et a1. (1998, 1999a) have pointed out the importance of fourth order exchange interactions in compounds with pure spin magnetism (i.e, biquadratic, three spin and four spin interactions) such as GdMg and GdAg. Additional comment deserve magnetostriction measurements near the ordering temperature Tc reflecting critical phenomena. Few data for critical expansion is available, such as have been reported by Dolejsi and Swenson (1981) for the case of Gd metal. The thermal expansion coefficient in the critical region should assume the form I(T - Tc)/ Tci- a . The critical exponent ex should be the same as for the specific heat and depend only on the universality class (dimensionality, No. of degrees of freedom) of the system. For Gd metal this universality class has been determined by Frey et a1. (1997). A last point which has to be discussed are the magnetovolume effects caused by magnetic moments in the conduction band or of the d-electrons of partner elements like Ni. A simple model, based on the Stoner model for itinerant magnetism, shows that the kinetic energy increase associated with magnetic ordering in a band leads to a magnetic pressure PM, which can be expressed by the following formula (Janak and Williams 1976):
€a
(19) where D, V and M denote the electronic density of states at the Fermi energy, the volume and the magnetic moment, respectively. Since the density of states increases with increasing volume (i.e. ~:~ ~ > 0), the magnetic pressure PM is positive, leading to a magnetically induced increase of the volume. With this outlook on topics of current research we conclude the theoretical part of this chapter and turn to the discussion of available experimental data.
4. Magnetovolume effects in cubic systems In this section some examples for spontaneous magnetovolume effects in cubic Gd based compounds will be presented. As will be discussed in section 5, in cubic systems also distortions of the crystal symmetry have been observed. In all cases of our knowledge these distortions are, however, very small compared to strains which conserve the crystal symmetry and which will be the main topic of the rest of this chapter. The symmetry breaking effects are so small that they probably can only be observed in the highly symmetric cubic systems, where the detection of such distortions is easier.
A. LINDBAUM and M. norrsn
316
4.1. GdAlz
GdAh crystallizes in the pure CIS structure (cubic Laves phase, MgCuz type, space group F d3m) without vacancies on the Gd sites, which lead to a superstructure of C 15 in case of GdNiz (see section 4.2). The magnetic properties of the RAh compounds have been extensively investigated in the past. Within this series, GdAlz has the highest Curie temperature (Tc ~ 168 K) and is considered as a good example of a Heisenberg ferromagnet (du Tremolet de Lacheisserie 1988; Taylor and Coles 1975). Neutron diffraction experiments at 4.2 K gave a rather small magnetic moment on the Gd sites (6.6 /LB) with a 0.6 /LB moment in the conduction band (Abell et al. 1983). The magnetic anisotropy is very small (as expected for an S-state ion) and both NMR data (Kaplan et al. 1973) and torque measurements (Burd and Lee 1977) indicate [Ill] as the easy magnetization direction. Measurements of the thermal expansion using a strain gauge method (Pourarian 1980) showed a negative magnetovolume effect, in agreement with measurements of du Tremolet de Lacheisserie (1988) using a tube type dilatometer. However there are discrepancies concerning the size of the effect: du Tremolet de Lacheisserie (1988) obtained a 0 K value of (~ V / V)mag ~ -1.16 x 10- 3 , which is twice as large as the value ofPourarian (1980). Our own x-ray powder diffraction measurements (see fig. I) show also a negative magnetovolume effect, with a 0 K value of (~ V / V)mag ~ -1.4 x 10- 3 , in good agreement with du Trernolet de Lacheisserie (1988). This large negative magnetovolume effect is very interesting and has to be attributed solely to the volume dependence of the (indirect) Gd-Gd exchange interaction, since the induced itinerant magnetic moment in the conduction band should lead to a positive magnetovolume effect. The x-ray diffraction experiments revealed no detectable line splitting or broadening, showing that there is no change of the cubic symmetry within the detection limit of about 1 x 10-4 . From 7.905
GdAI 2 7.900
-<
7.895
(ij'
7.890
7.885
••• •••
7.880 0
50
••
••
100
•• • •
•
150
200
250
300
T[K] Fig. I. Temperature variation of the cubic lattice parameter of GdAlz measured by x-ray powder diffraction (this work). The small points connected by a line indicate the corresponding values of the isostructural YAlz (nonmagnetic reference), scaled to coincide with GdAIZ at Z50K. in order to allow a direct comparison.
SPONTANEOUS MAGNETOELASTIC EFFECTS IN GADOLINIUM COMPOUNDS
317
forced magnetostriction experiments on a single crystal, also reported by du Tremolet de Lacheisserie (1988), a very small spontaneous trigonal distortion of about (AL/ L)II J ~ 2 x 10-5 could be deduced. 4.2. GdNiz
During the past decades (and frequently up to now) the RNiz compounds (R: rare earth element) have been reported to crystallize in the cubic Laves phase structure (CI5). However, experimental as well as theoretical investigations showed that this is not true. Instead of showing the pure C 15 structure, most of them (including GdNiz) crystallize in a cubic superstructure of C15 with doubled lattice parameter due to ordered vacancies on the R sites. A single phase compound can only be obtained with the stoichiometry (1 - 8):2 and can be described within space group F43m with the 4a sites only partially occupied by the R atoms. The occupancy of the R 4a sites increases with decreasing radius of the R atom and reaches 1 for LuNiz (Latroche et al. 1990; Latroche et al. 1993). This instability of the pure C15 structure in the RNiz compounds (i.e, the tendency towards the formation of vacancies) can be understood by space filling arguments. Theoretical investigations, based on ab-initio total energy calculations, showed that the vacancies at the R sites reduce the total energy, thus increasing the stability relative to the neighboring compounds in the R-Ni phase diagram (Lindbaum et al. 1999). The existence of ordered R-vacancies in the RNiz compounds is not only important for the understanding of the mechanisms stabilizing the crystal structure. They must also be taken into account when investigating other physical properties, like e.g. the magnetic structure. The ordered vacancies change the local environment of the R sites, leading to a symmetry change of the crystal field as well as the magnetic exchange interactions. As an example, investigations on TbNiz showed that the ordered vacancies on the Tb sites are responsible for a temperature induced change of the magnetic structure at 14 K (Gratz et al. 1999a). An interesting property of the RNiz superstructures is a reversible temperature induced transition from ordered to disordered vacancies at high temperatures, first detected by anomalies in the transport properties and later directly observed by x-ray diffraction experiments (Gratz et al. 1996). Furthermore, high-pressure x-ray diffraction studies showed that there is also a pressureinduced order-disorder transition (Lindbaum et al. 2002). The magnetic properties of GdNiz have been largely investigated in the past (see e.g. Buschow 1977; Jesser and Clad 1986). It orders ferromagnetic ally below Tc ~ 74 K and shows a weak Ni 3d polarization opposite to the 4f Gd moments. This weak itinerant Ni moment is a possible reason for the observed positive magnetovolume effect, which has been measured by low temperature x-ray powder diffraction (see fig. 2), reaching a value of (A V / V)mag ~ 0.6 x 10-3 at 0 K (estimated by comparison with the nonmagnetic reference compound YNiz). No line splitting or broadening of the x-ray lines could be observed below the magnetic ordering temperature. This means that a possible distortion of the cubic symmetry is smaller than 1 x 10- 4 . 4.3.
ca«,
The RIn3 systems crystallize in the cubic AuCu3 type of structure and are known for salient features as valence fluctuations and the presence of various magnetic structures (see e.g.
318
Fig. 2. Temperature variation of the cubic lattice parameter of the CI5 superstructure of GdNi2 measured by x-ray powder diffraction (this work). The small points connected by a line indicate the corresponding values of the isostructural YNi2 (nonmagnetic reference), scaled to coincide with GdNi2 at 150 K, in order to allow a direct comparison.
Lin et a1. 1996 and references therein). GdIn3 is antiferromagnetic with a Neel temperature TN of about 43 K. Magnetization measurements on a single crystal by Staliriski et a1. (1979) showed, that the Neel temperature varies with the crystallographic axis along which the magnetic field is applied reaching the highest value along [100]. This observed variation of TN suggests that the magnetic structure is a spiral antiferromagnetic one (Nagamiya 1967). Grechnev et a1. (1995) investigated the effect of pressure on the magnetic susceptibility of RIn3 compounds and performed also ab-initio calculations of the volume derivatives of the band structure and the exchange parameters. Their study supports the view that the RKKY-type R-R interaction is mainly mediated by the s- and p-electrons. Figure 3 shows the variation of the cubic lattice parameter, measured by x-ray powder diffraction. As can be seen, there is no volume effect or only a small negative one with an absolute value at 0 K smaller than 0.3 x 10- 3.
4.4. GdCu2In and GdPdzln Further examples of cubic systems with very weak negative magnetovolume effects are GdCu2In and GdPd2In, both crystallizing in the cubic Heusler structure L21 (Webster 1969). Both compounds order antiferromagnetically below about 10 K with some complicated and up to now unknown magnetic structure (see e.g. Parsons et a1. 1998; Taylor et a1. 2000 and references therein). Specific heat measurements on both compounds show very similar results for the magnetic contributions (Parsons et a1. 1998), but the corresponding effect on the crystal volume is 5 times larger in GdCuzIn (measured by Taylor et a1. 2000 on polycrystalline samples using a capacitance dilatometer). However, the estimated value of the magnetovolume effect at 0 K is very small in both. It is (~V / V)mag ~ -10 x 10-5 for GdCu2In and (~V / V)mag ~ -2 x 10-5 for GdPd2In.
SPONTANEOUS MAGNETOELASTIC EFFECTS IN GADOLINIUM COMPOUNDS
319
4.610
Gdln 3
4.605 4.600
~ C':l
4.595 4.590 4.585 0
50
100
150
200
250
300
T [K] Fig. 3. Temperature variation of the cubic lattice parameter of GdIn3 measured by x-ray powder diffraction (this work). The full line corresponds to a fit of a Debye model to the whole temparature range, the dashed line shows an extrapolation from the paramagnetic range obtained from fitting the Debye function only to the data points above TN.
5. Spontaneous distortions of the crystal symmetry Unfortunately, symmetry distortions have not been widely investigated in Gd compounds, because they are usually very small and therefore experiments are difficult. Some old data is available for cubic compounds. Isotropic exchange interactions which stay isotropic also under a strain such as Heisenberg and RKKY type do not lead to spontaneous symmetry distortions in ferromagnetic cubic systems (Morin and Schmitt 1990). However, such distortions have been (indirectly) found in ferromagnetic systems from forced magnetostriction measurements on single crystals (e.g. a spontaneous tetragonal distortion (6.//1)00 I :::::: -3.7 X 10- 4 in GdZn by Rouchy et al. (1981), and a small spontaneous trigonal distortion (6..1/1)/11:::::: 2 x 10-5 in GdAlz by du Tremoletde Lacheisserie (1988». These distortions have to be attributed to the presence of anisotropic exchange interactions in these ferromagnetic compounds, but the origin of the exchange anisotropy has not yet been clarified. In contrast to the cubic ferromagnets, in cubic antiferromagnets also isotropic exchange may lead to symmetry distortions, as for instance the small trigonal distortions in the antiferromagnetic compounds GdAs, GdSb and GdBi, ranging from 10-5 to 10- 4 , which were directly measured by x-ray diffraction experiments by Hulliger and Stucki (1978). Diffraction in external fields would be necessary to show unambiguously if in these antiferromagnets the distortion is due to isotropic or anisotropic exchange interactions. The source of exchange anisotropy in Gd compounds is still topic of current investigations and in special cases, such as symmetry distortions of the cubic ferromagnets, measurements of magnetoelastic properties can make important contributions to this problem.
320
A. LINDBAUM and M. R01TER
6. Hexagonal systems 6.1. Gadolinium Pure gadolinium crystallizes in the well known hexagonal close-packed (hcp) structure (see fig. 4), which is described within the space group P63/mmc with Gd on the 2c-sites (point symmetry 6m2). Gadolinium has the highest magnetic ordering temperature among all rare earth elements. The magnetic properties of Gd metal have been extensively studied (see e.g. McEwen (1978) and Dan'kov et al. (1998) and references therein). It shows ferromagnetic ordering below Te = 294 K and remains ferromagnetic down to liquid helium temperature. The saturation moment is 7.55 JLB per atom (Nigh et al. 1963), i.e. there is an additional moment of 0.55 JLB compared to the 7 JLB corresponding to a local 4f moment with S = 7/2. This additional moment is usually attributed to a conduction-electron polarization (see e.g. Cable and Wollan (1968». The paramagnetic to ferromagnetic transition at Te is of second order type and the universality class has been determined by Frey et al. (1997). Neutron diffraction experiments performed by Cable and Wollan (1968) showed that from Te down to the spin reorientation temperature TSR ~ 232 K the moments are aligned along the hexagonal axis (i.e. c-direction). Below TSR the moment direction departs from this direction and the angle between the hexagonal axis and the moment direction changes with temperature. Here it is worthwhile to mention that the magnetic properties of gadolinium are up to now a puzzle. In a Nature paper, Coey et al. (1999) reported that gadolinium is probably not really a ferromagnet between TSR and Te, but that the magnetic structure is some long-period modulated structure, similar to the incommensurate order found in erbium. This conclusion has been drawn from susceptibility measurements around Te and TSR, but experiments for observing the long-period modulation are still missing. More recent susceptibility and low field magnetization measurements performed by Kaul and Srinath (2000) confirm again the widely accepted view that gadolinium is a collinear ferromagnet between Te and TSR. The thermal expansion of gadolinium has been studied several times (for a collection of data see e.g. Touloukian et al. (1976». Since there is some disagreement mainly concerning the temperature variation of the lattice parameter a, we remeasured the anisotropic thermal
Gd (2c) Fig. 4. hcp structure of gadolinium.
SPONTANEOUS MAGNETOELASTIC EFFECTS IN GADOLINIUM COMPOUNDS
321
expansion of a polycrystalline Gd sample by means of x-ray diffraction between 10 K and 400 K. The result is shown in fig. 5. As can be seen from the temperature variation of a and c there is a pronounced anisotropic magnetic contribution below Tc: The estimated values at 0 K of the magnetic contribution are (6.a/a)mag ::;:;: 1.0 x 10- 3 and (6.c/c)mag::;:;: 3.0 x 10-3 • This leads to a clearly visible magnetically induced change of the cia ratio of (6.(c/a)/(c/a))mag::;:;: 2.0 x 10- 3 • However, what is much more peculiar is the big magnetovolume effect with a 0 K value of (6. V / V) mag ::;:;: 5.0 x 10- 3 . The size of this magnetovolume effect is comparable to R-Fe or R-Co compounds, like for
Gadolinium :lI:
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100 150 200 250 300 350 400
T [K] Fig. 5. Temperature variation of the hexagonal lattice parameters and of the volume of pure gadolinium measured by x-ray powder diffraction (this work). The values have been normalized to 300 K in order to show the relative changes. (The values at 300 K are a = 3.632 ± 0.002 A. c = 5.782 ± 0.002 A.) The lines represent the extrapolation of the lattice contribution from temperatures above TC assuming a Debye temperature of 184 K (Bodriakov et aI. 1998). The lowest part of the figure shows the magnetovolume effect, obtained by subtracting the lattice contribution from the volume expansion.
322
A. LINDBAUM and M. RUITER
Ni (3g)
Fig. 6. CaCuS -type hexagonal crystal structure of GdNis.
instance RFe2 and RC02, where the large magnetovolume effects of about 2 to 9 X 10- 3 are attributed to the itinerant character of the magnetic moments of Co or Fe (see e.g. the review by Andreev (1995), p. 68). The volume effects caused by localized magnetic moments are usually one order of magnitude smaller. A possible reason for the unexpected large positive magnetovolume effect in gadolinium is the large induced itinerant magnetic moment of about 0.55 /LB in the conduction band (see above). 6.2. GdNi'j
Intermetallic compounds of the general composition AB'j have been extensively investigated as possible hydrogen storage media. Because of the ability of LaNi'j to absorb large amounts of hydrogen (up to 6.7 atoms per formula unit - see van Vucht et al. (1970» also GdNi'j-based systems have been investigated with respect to their hydrogen sorption properties (see e.g. Blazina et al. (1999) and Bobet et al. (1998». GdNis crystallizes in the well known hexagonal CaCus type (space group P6/mmm). As shown in fig. 6, the structure is built up of two types of basal plane layers alternating along the c-axis, one at z = 0 composed of Gd (la-sites with high point symmetry 6/mmm) and Ni (2c-sites), the other one at z = 1/2 only composed ofNi atoms (3g-sites). The magnetic properties of GdNis have been intensively studied in the past and are now well understood (Franse and Radwariski 1993; Mulders et al. 2000). The magnetic interaction is strong compared to the other RNis compounds (de Gennes scaling) with an ordering temperature of Te ~ 31 K. GdNis is a ferrimagnet with ferromagnetically ordered Gd moments of 7 /LB aligned parallel to the hexagonal axis. These Gd moments induce an antiparallel moment of 0.16 /LB on the Ni atoms. There is a weak magnetic anisotropy caused by the dipolar interaction between the Gd moments (Yaouanc et al. 1996). In the past GdNi'j has also been used as a testing ground for validating muon spin relaxation theories in magnetic materials (de Reotier and Yaouanc 1997). No spontaneous magnetostriction could be detected within the sensitivity of the x-ray diffraction experiments. As can be seen in fig. 7 there is no significant difference in the temperature dependence of the lattice parameters between GdNis and the nonmagnetic isostructural YNis. The reason for the vanishing or very small (i.e. < 10- 4 ) effects in this compound could be that only one atom among six is a Gd atom, leading to weak magnetic and magnetoelastic interactions. A further example for a compound with a low concentration of Gd atoms, also showing weak or vanishing effects, is the tetragonal GdNi2B2C (see section 7.3).
SPONTANEOUSMAGNETOELASTICEfFECTS IN GADOLINIUM COMPOUNDS
{c
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TrKj Fig. 7. Anisotropic thermal expansion of GdNiS measured by x-ray powder diffraction (this work). The lines indicate the corresponding values of the isostructural YNis (nonmagnetic reference), scaled to coincide with GdNis at 150 K for allowing a direct comparison (the da ratio has not been scaled).
6.3. Gdz/n Gd-In crystallizes in the hexagonal Ni-In-type structure (space gr. P63/mmc), which has two crystallographically different sites for Gd (Palenzona 1968). The unit cell of the structure is shown in fig. 8. As can be seen from this figure the structure is composed of hexagonal layers with the stacking sequence ABACA. The A layers at z == 0 and z = 1/2 contain only Gd atoms on the cell comers (2a-sites with quasi-cubic point symmetry 3m). The Band C layers at z = 1/4 and z = 3/4 contain each one Gd atom (2d-sites with hexagonal point symmetry 6m2) and one In atom (2c-sites, also 6m2). Interestingly, the Gd sublattice forms a double hexagonal close packed structure (dhcp), which differs only by the stacking sequence of the hexagonal planes from a hcp structure formed by elemental gadolinium (see section 6.1). However, the distances of the Gd atoms are very different. The Gd-Gd distance within the hexagonal planes is much larger in Gd-In (0 ~ 3.63 Afor gadolinium and 0 ~ 5.41 Afor GdjIn), whereas the distances in direction of the hexagonal axis are much smaller (gadolinium: c ~ 5.78 A, Gdjln: c/2 ~ 3.38 A). The magnetic properties of Gd-In show interesting features: it becomes ferromagnetic below 190 K, but there is a second magnetic transition at about 100 K to an antiferromagnetic structure. Under a magnetic field this metamagnetic transition is shifted to lower temperatures and fields of about 1 Tesla can completely restore the ferromagnetic state (McAlister 1984; Gamari-Seale et al. 1979; lee et al. 1996). lee et al. (1996) reported that
324
A. LINDBAUM and M. RUITER
c Gd (2d)
/
In (2c)
Gd (2a)
Fig. 8. Nij In-type hexagonal crystal structure of Gd2In.
the temperature- and magnetic field dependence of the magnetization shows that the system is not a simple ferromagnet between 100 and 190 K, but a helical ferromagnet. McAlister (1984) reported that magnetization, resistivity and magnetoresistivity measurements support the suggestion that the low temperature structure below 100 K could be a spiral antiferromagnetic structure. Measurements of the magnetization and magnetoresistance in the vicinity of the metamagnetic transition support that the low temperature structure is different from simple antiferromagnetic (Stampe et al. 1997). Ravot et al. (1993) reported a propagation vector (0, 0, ~ obtained by neutron powder diffraction experiments at 20K. As can be seen in fig. 9 there is no spontaneous magnetostriction effect within the sensitivity of the x-ray diffraction experiments (~ 1 x 10-4 ) at both magnetic transition temperatures of 190 K and 100 K, respectively. This is interesting and unexpected, since this compound is characterized by a strong Gd-Gd magnetic interaction, leading to the relatively high magnetic ordering temperature of 190 K. Despite this strong magnetic exchange interaction the cia ratio as well as the volume are absolutely unaffected by the ordering of the Gd moments. Note that GdzIn has the second highest magnetic ordering temperature of all systems reviewed in the present chapter after pure Gd metal (see section 6.1), which shows pronounced anisotropic spontaneous magnetoelastic effects as well as a large positive magnetovolume effect. Further studies including field-induced magnetostriction experiments on single crystals are necessary in order to clarify why there is no pronounced spontaneous magnetostriction detectable in Gd-In.
i),
6.4. GdCuAl and GdNiAl
The RCuAI (R = rare earth except for La and Eu) compounds belong to a large group of ternary intermetallics showing the ZrNiAl-type hexagonal structure with space group P62m (Szytula 1991). All the R atoms occupy equivalent positions (3g sites) with point symmetry mm only. The structure is built up of two types of basal plane layers (with and without R atoms) alternating along the c-axis (see fig. 10). While the magnetic properties of the compounds with light R atoms are rather complex, ferromagnetic ordering has been deduced from magnetization measurements on polycrystalline samples for Gd and the other heavy R atoms. In the case of GdCuAI the
SPONTANEOUS MAGNETOELASTIC EFFECTS IN GADOLINIUM COMPOUNDS
325
Gd 2In 5.42
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5.40 5.39
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1.248 1.247 1.246
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171
>
170
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50
100
150
200
250
300
T [K] Fig. 9. Anisotropic thermal expansion of Gdj ln measured by x-ray powder diffraction (Gratz and Lindbaum 1998). The lines are the result of filling Debye functions. The arrows indicate the two magnetic transitions at 190 K and 100 K (see text).
magnetic ordering temperature is Tc ~ 82 K. Javorsky et aI. (1998) reported a second magnetic transition at TR ~ 37 K observed in specific heat and susceptibility data. Powder x-ray diffraction experiments with an external magnetic field performed by Andreev et al. (1999) (for a description of the method see e.g. Gratz et aI. (1999b» showed that in GdCuAI the magnetic moments are aligned along the c-axis below Tc as well as below the second magnetic transition at TR. Measurements of the temperature dependence of the hexagonal lattice parameters using low-temperature x-ray powder diffraction (Andreev et aI. 1999) show clear anomalies below the magnetic ordering temperature (82 K) in both the aCT) and c(T) curves (see fig. II). An estimation of the spontaneous magnetostriction by extrapolating from the paramagnetic range to low temperatures shows a monotonous increase of the magnetostriction which reaches quite large values at 0 K «~ala)mag = -1.7 x 10-3 3 and (~clc)mag = 3.0 x 10- ) . This leads to a pronounced change in the cia ratio of (~(cla)/(cla»mag ~ 4.7 x 10- 3 , but only to a small volume effect «~ VIV)mag ~
326
A. LINDBAUM and M. R01TER
Cu (lb)
Fig. 10. ZrNiAl-type hexagonal crystal structure of RCuAI.
+ (!:i.C/C)mag = -0.4
10- 3 ) , which is near the size of the experimental error. There was no measurable effect at the second magnetic transition at 37 K which has been observed by Javorsky et al. (1998). GdNiAI crystallizes like GdCuAI in the hexagonal ZrNiAI-type structure, but a pronounced anomaly in the hexagonal lattice parameters at about 200 K has been observed and attributed to a transition between two slightly different forms of the ZrNiAI-type structure (Merlo et al. 1998). The atomic position parameters XGd ~ 0.583 and XAI ~ 0.232, which are not fixed by space group symmetry, do not change significantly at this structural transition (Jarosz et al. 2000). As reported by Merlo et al. (1998) and Javorsky et al. (1995), GdNiAI orders ferromagnetically below about 60 K, and two other magnetic transitions occur at 30 and 14 K. which are probably due to the occurrence of antiferromagnetic order, but no further information concerning the easy axis in the ferromagnetic state and the magnetic structures below the two additional transitions could be found in literature. However, as reported by Merlo et al. (1998), a further magnetic transition has been observed in this compound in the paramagnetic range at about 180 K. Above this temperature the paramagnetic moment of Gd (obtained from a Curie-Weiss fit of susceptibility data) agrees with the calculated free ion value, but below a 9% higher value has been found. Merlo et al. (1998) suggest that this transition could be connected with the structural transformation at about 200 K, and that below this transition the slightly different interatomic distances could be responsible for a larger polarization of the conduction electrons. The temperature variation of the lattice parameters, as measured by x-ray diffraction by Merlo et al. (1998) and Jarosz et al. (2000), shows no significant anisotropic spontaneous 2(!:i.a/a)mag
X
SPONTANEOUS MAGNETOELASTIC EFFECTS IN GADOLINIUM COMPOUNDS
327
GdCuAI
~
7.08
4.09
7.06
4.08
7.04
4.07
:< ~
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~
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7.02
4.05
0.580 00 0
cia
0.578
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0 0
,
176 ~
175 ~
>
0.576 174 0.574 0
100
200
300
T [K] Fig. II. Anisotropic thermal expansion of GdCuAI measured by x-ray powder diffraction (Andreev et a1. 1999). The lines are extrapolations from the paramagnetic range. TC and TR indicate the magnetic ordering temperature and the second magnetic transition observed by Javorsky et a1. (1998), respectively.
magnetostriction, neither due to the ferromagnetic ordering between about 60 K and 30 K nor due to the two additional magnetic transitions at 30 and 14 K. This is in contrast to the behaviour of GdCuAI (see fig. II), where a pronounced change of the cia ratio due to the magnetic ordering has been observed. But note that there is a clear positive volume anomaly with an estimated 0 K value of about (~ V I V)mag ~ 0.8 x 10- 3 in GdNiAI (Jarosz et al. 2(00). This positive volume effect, which does not exist in GdCuAI, may be due to an induced itinerant magnetic moment at the Ni sites. In general the above comparison of the isostructural GdNiAI and GdCuAI shows that the magnetoelastic effects can be strongly influenced by the partner elements of Gd, i.e. exchanging Cu by Ni can change the behaviour completely. 6.5. GdCuSn
GdCuSn crystallizes in the hexagonal NdPtSb-type structure (Pacheco et al. 1998), which is an ordered form of the CaIn2 type, which had been reported as the structure of GdCuSn before (Komarovskaja et al. 1983). The correct structure of GdCuSn is described within the space group P63mc with Gd on the 2a-sites (point symmetry 3m), Cu on the 2b-sites (also point symmetry 3m) with ZCu ~ 0.81 and Sn also on the 2b-sites with ZSn ~ 0.23. The hexagonal unit cell of the structure is shown in fig. 12.
328
A. LINDBAUM and M. norrsa
Sn (2b)
ell (2b) Gd (2a) Fig. 12. NdPtSb-type hexagonal crystal structure of GdCuSn.
Fig. 13. Possible magnetic structure of GdCuSn (Bialic et al. 1997).
Already in 1977 bulk magnetic measurements showed that GdCuSn orders antiferromagnetically below about 24 K (Oesterreicher 1977). Only a few years ago conclusions about the magnetic structure were drawn from Mossbauer experiments by analyzing the Gd and Sn resonance spectra (Bialic et al. 1997). The authors of this work suggest a mag0) with antiferromagnetic order netic structure described by the propagation vector (0, within the hexagonal Gd planes and ferromagnetic stacking along the c axis. Figure 13 shows this magnetic structure schematically. Figure 14 shows the temperature dependence of the lattice parameters as well as of the volume of GdCuSn measured by low temperature x-ray diffraction. As can be seen there is a significant spontaneous anisotropic magnetostriction effect due to the magnetic ordering. An estimation of the magnetic contribution to the thermal expansion of GdCuSn at 0 K by extrapolating from the paramagnetic range down to lowest temperatures gives the values (lia/a)mag ~ 0.3 x 10-3 and (lic/c)mag ~ -l.l x 10- 3 . This leads to a clearly visible magnetically induced change of the cia ratio of (li(c/a)/(c/a»mag ~ -1.4 x 10- 3 , and a negative volume magnetostriction «li V / V)mag ~ -0.5 x 10-3 ) . Therefore GdCuSn is, like GdAh (section 4.1) and GdCuAI (section 6.4), an example for a compound where the Gd-Gd exchange interaction leads to a negative magnetovolume effect.
!'
SPONTANEOUS MAGNETOELASTICEFFECTS IN GADOLINIUM COMPOUNDS
GdCuSn
4.532
~
329
4.528
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7.36 7.35
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u
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7.32 1.625
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u
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131.0
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o
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50
100
150
200
250
300
T [K] Fig. 14. Anisotropic thermal expansion of GdCuSn measured by x-ray powder diffraction (Gratz and Lindbaum 1998). The lines represent the extrapolation of the lattice contribution from the paramagnetic range by fitting Debye functions.
7. Tetragonal systems 7.1. GdAgZ and GdAuz
GdAgz and GdAuz crystallize in the tetragonal MoSiz-type structure (Dwight et a1. 1967). The space group is 14/mmm with Gd on the 2a-sites (point symmetry 4/mmm) and Ag(Au) on the 4e sites. The Z atomic position parameter of the 4e sites (point symmetry 4mm) is about 1/3. For GdAgz a value of ZAg = 0.327 ± 0.004 has been determined from neutron diffraction experiments (Gignoux et a1. 1991). This structure can roughly be viewed as being composed of three tetragonally distorted body centered cubes along c-direction, as shown in fig. 15. GdAg2 has first been reported to order magnetically at about 27 K from resistivity measurements (Ohashi et a1. 1975). Further studies by Gignoux et al. (1991) including specific heat. resistivity and magnetization measurements. as well as neutron powder
A. LINDBAUM and M. aorraa
330
c Ag.Au (4e)
/
Gd (2a)
a
Fig. 15. Tetragonal MoSiz-type structure of GdAgZ and GdAuz.
diffraction experiments, showed that this compound orders antiferromagnetically below TN ~ 22.7 K with two further first-order magnetic transitions at TRI ~ 21.2 K and TR2 ~ 10.8 K. The neutron diffraction experiments showed that the magnetic order is incommensurate with a propagation vector of about (0.362, 0, 1) and that the moment direction seems to change from [110] below TR2 to [001] above TR2 (due to the small temperature range between TN and TRI it was not possible to investigate the magnetic structure with neutron diffraction for this range). The observed first-order magnetic transitions in the ordered range have been attributed to anisotropic terms in the two-ion GdGd exchange interaction. A further peculiarity, also mentioned by Gignoux et al. (1991) is that the magnetic ordering temperature of GdAg2 is lower than in TbAg2 (TN ~ 34.8 K), violating the De Gennes law. This has been referred to a change in the conduction band due to the boundary situation of GdAg2 concerning the crystal structure, i.e. only the RAg2 with heavy R, starting from Gd, show the MoSh type of structure. Figure 16 shows the temperature dependence of the lattice parameters as well as of the volume of GdAg2 measured by low temperature x-ray diffraction. As can be seen there is a pronounced spontaneous anisotropic magnetostriction effect due to the magnetic ordering with no significant change at TR2. An estimation of the magnetic contribution to the thermal expansion by extrapolating from the paramagnetic range down to 0 K gives the values (l::.a/a)mag ~ 0.3 x 10- 3 and (l::.c/c)mag ~ -0.6 x 10- 3 . This leads to a clearly visible magnetically induced change of the cia ratio of (l::.(c/a)/(c/a»mag ~ -0.9 x 10- 3 , but to no measurable volume magnetostriction within the sensitivity of the x-ray experiment (!(l::.V/V)magl <0.1 x 10- 3 ) . GdAu2 orders like GdAg2 antiferromagnetically, but at a much higher ordering temperature of TN ~ 50 K (Tung et al. 1996). Neutron diffraction studies for determining the magnetic structure are in progress. Figure 17 shows the temperature dependence of the lattice parameters as well as of the volume of GdAu2, also measured by low temperature x-ray diffraction. In contrast to GdAg2 there is no measurable spontaneous magnetoelastic effect at all. The magnetically induced change of c/ a as well as the volume magnetostriction of GdAu2 is smaller than the experimental resolution (i.e, < 10-4 ) . This
SPONTANEOUS MAGNETOELASTTC EFFECTS IN GADOLINIUM COMPOUNDS
GdAg 2
3.730 3.725
~ ell
3.720
331
T R2
~f
N •T RI
3.715 9.29
,...., 9.28
~ u
9.27 9.26 129.5
,...., (")
129.0
o~
;>
128.5 128.0 2.494
ell 2.493 ...... u
2.492 2.491 0
50
100
150
200
250
300
T [K] Fig. 16. Anisotropic thermal expansion of GdAg2 measured by x-ray powder diffraction (this work). The lines represent the extrapolation of the lattice contribution from the paramagnetic range by fitting Debye functions. The arrows indicate the different magnetic transition temperatures (see text).
different behaviour concerning the spontaneous magnetostriction may - like the different TN (see above) - also be connected with conduction band properties, leading to a different RKKY exchange coupling of the Gd moments.
7.2. Gd2Cu21n and Gd2Ni2-x1n As reported by Kalychak et al. (1990) the R2CU2In compounds (with exception of R = Eu and Yb) crystallize in the tetragonal M02FeB2 type of structure (space group P4/mbm). In case of the R2Nhln compounds this structural type occurs only for R = La, Ce, Pr and Nd. The other R2Ni2In compounds including R = Gd show the orthorhombic Mn2AIB2 type of structure (space group Cmmm). But with an off-stoichiometric content of Ni (R2Nh-xIn with x = 0.22) the tetragonal M02FeB2 type of structure is also formed for R = Sm to Lu. This means that Gd2Cu2In and Gd2NiI.78In have the same crystal structure, allowing again a direct comparison of the spontaneous magnetoelastic effects in two compounds, which differ only by one of the partner elements of Gd. Figure 18 shows the arrangement of the
332
A. LINDBAUM and M. ROTfER
GdAu 2
3.730 3.725
-<......
3.720
~
3.715 9.02
....., 9.01
......
ooc:t: u
9.00 8.99
.....,
125.0
~
......
ooc:t:
>
124.5 124.0 2.421
~
....... 2.420 u
2.419 2.418 0
50
100
150
200
250
300
T [K] Fig. 17. Anisotropic thermal expansion of GdAu2 measured by x-ray powder diffraction (this work). The lines represent the result of fitting Debye functions to the whole temperature range.
c
I~~~~--J-Gd _~_
In (2a)
•
.._
_fl__ .
(4h)
CU,Ni (4g)
a
atoms within the tetragonal unit cell. The Gd atoms occupy one type of crystallographic site, namely the 4h-sites with only orthorhombic point symmetry mm (atomic position parameter XGd ~ 0.18). The Cu atoms occupy the 4g-sites (mm, atomic position parameter
SPONTANEOUS MAGNETOELASTIC EFFECTS IN GADOLINIUM COMPOUNDS
333
.:::[t ...t~
~~
7.50
3.820 3.815
[::.~.~ •
3.810 •••
0.510 0.509 () 0.508
••
<':l
0.507 217
;;;" ~
;>
•
e.
t===~~~~~~!!'~~~
216 215
o
50
100
150
200
250
300
T [K] Fig. 19. Anisotropic thermal expansion of Gd2CU2In measured by x-ray powder diffraction (this work). The lines represent the extrapolation of the lanice contribution from the paramagnetic range by fining Debye functions.
XCu ~
0.38) and the In atoms occupy the high-symmetry sites 2a with point symmetry
41m. Fisher et al. (1999) reported first about the magnetic properties of R2CU21n compounds. Magnetization as well as electrical resistivity measurements showed that all the investigated magnetic compounds (R = Gd to Tm) order ferromagnetically with relatively high ordering temperatures, varying between 27 K for H02Cu21n and 86 K for Gd2Cu2ln. The easy axis varies among the investigated compounds. For Gd2Cu21n it is parallel to the tetragonal c axis. For the isostructural Gd2Ni 1.781n no report concerning the magnetic properties could be found in literature. The only available information comes from unpublished susceptibility measurements (Hilscher 2(01), indicating that Gd2Ni 1.781n orders antiferromagnetically below TN ~ 20 K. Figures 19 and 20 show the anisotropic thermal expansion obtained by x-ray powder diffraction for Gd2Cu21n and Gd2Nil.781n, respectively. Within the sensitivity of the experiments no magnetovolume effect can be observed in both compounds (I(~ V I V)magl < 0.1 x 10-3 ). But the comparison of the anisotropic effects shows pronounced differences. For Gd2Cu21n the estimation for the magnetic contribution to the thermal expansion by ~ extrapolating from the paramagnetic range down to 0 K gives the values (~ala)mag -1.9 x 10-3 and (~clc)mag ~ +3.8 x 10-3 . This leads to a large magnetically induced ~ 5.7 x 10- 3 . In the case of Gd2Ni 1.78In the change of the cia ratio of (~(cla)/(cla))mag
334
A. LINDBAUM and M. ROTfER
Gd 2Ni l .7SIn
7.43
:< ........
7.42
C<:l
7.41
......
o
.T N
7.40 3.705 3.700
u
3.695 0.500 0.499
~ u
0.498
......
~
o
204
;> 203 202 0
50
100
150
200
250
300
T[K] Fig. 20. Anisotropic thennal expansion of Gd2Nil.78ln measured by x-ray powder diffraction (this work). The lines represent the extrapolation of the lattice contribution from the paramagnetic range by fitting Debye
functions.
observed anisotropic effects are much smaller «da/a)mag ~ -0.2 x 10-3, (dc/c)mag ~ 0.4 x 10- 3 , (d(c/a)/(c/a»mag ~ 0.6 x 10- 3) . This means that, like in the case of GdCuAI and GdNiAI (see section 6.4), the exchange of the Cu atoms by Ni atoms leads to a strong decrease of the anisotropic magnetoelastic effects. However, it has to be noted, that in the present case the change of the partner element of Gd leads also to a strong decrease of the magnetic Gd-Gd interaction itself, reflected in the pronounced decrease of the magnetic ordering temperature. This may also be a reason for the weaker spontaneous magnetostriction in the Ni compound. 7.3. GdNi2B2C Since the discovery of the RT2B2C borocarbides (T = transition metal) much attention has been paid to the physical and structural properties of the whole series of isotypic compounds, because of the high superconducting transition temperatures and because of the interesting interplay between magnetic ordering and superconductivity. These compounds crystallize in the tetragonal LuNi2B2C type of structure, which might be
SPONTANEOUSMAGNETOELASTICEFFECTS IN GADOLINIUM COMPOUNDS
c
335
Gd (2b)
Fig. 21. The tetragonal unit cell of GdNi2B2C.
regarded as a variant of the ThCr2Sh type with two additional carbon atoms in the tetragonal unit cell (Siegrist et al. 1994). The tetragonal unit cell of the structure is shown in fig. 21. The space group is 14/mmm with R on the 2b sites (high point symmetry 4/mmm), Ni on the 4d sites, B on the 4e sites and C on the 2a sites. The only fractional coordinate not fixed by symmetry is ZB which takes a value of ~ 0.14 in case of GdNhB2C (Belger et al. 1998; Lynn et al. 1997). Detlefs et al. (1996) have investigated the magnetic structure of GdNhB2C with resonant and nonresonant magnetic x-ray-scattering techniques. These studies showed that between TN ~ 19-20 K and TR ~ 14 K the magnetic structure is of the transverse sine-modulation type with an incommensurate propagation vector of (~0.55, 0, 0). The magnetic moments of Gd lie within the basal plane perpendicular to the propagation vector. Below TR a component of the Gd moment develops along the c axis with the same propagation vector as the component in the basal plane. Further information on the magnetic structure below TN has been gained by 155Gd Mossbauer spectroscopy (Tomala et al. 1998), suggesting a bunched spiral-like magnetic structure with the moments rotating within the b-c plane. Despite the considerable efforts devoted to resolve the magnetic structures of GdNhB2C, the absence of superconductivity in this compound remains an open question. Concerning the spontaneous magnetostriction, GdNhB2C is a further example of only very weak effects. As can be seen in fig. 22 there is no effect visible within the sensitivity of the x-ray diffraction experiments, neither in the volume nor in the c/ a ratio. Measurements on a single crystal using capacitance dilatometry showed effects of about 5 x 10-5 (Massalami 2002). These small effects are in accordance with the analysis of ErNhB2C (Doerr et al. 2002), where the magnetoelastic phenomena have been attributed to crystal field effects only (compare the different situation in the RCU2 compounds which show a significant exchange contribution - see section 8.6). Like for GdNis (see section 6.2), the reason for the small (i.e. < 10-4 ) effects in this compound could also be that only one atom among six is a Gd atom, leading to weak magnetoelastic effects.
336
A. LINDBAUM and M. R01TER
GdNi282C
-<...... ~
3.580 3.578 3.576 3.574
~TN
10.380 0< ...... 10.374 o 10.368 10.362 ........
133.0 ........
(")
0< ......
>
132.8 132.6 132.4 2.900
~ u
2.898 2.896 0
50
100
150
200
250
300
T [K] Fig. 22. Anisotropic thermal expansion of GdNiZB2C measured by x-ray powder diffraction (this work). The lines indicate extrapolations from the paramagnetic range obtained by fitting Debye functions to the temperature range above TN.
8. Orthorhombic systems 8.1. Magnetostructural transitions in Gd5(SixGel-x)4 compounds
A giant magnetocaloric effect (MCE) has been discovered in the Gd5(SixGel-x)4 pseudobinary system with x"'; 0.5 (Pecharsky and Gschneidner Jr. 1997a, 1997b, 1997c, 1999). In the composition range 0.24 ~ x ",; 0.5 the MCE is connected with a first-order transition from a high-temperature paramagnetic to a low-temperature ferromagnetic state, at temperatures ranging from 130 K to 276 K (Pecharsky and Gschneidner Jr. 1997b). A study by Morellon et al. (l998a) on Gd5(Sio.45Ge0.55)4 (i.e. x = 0.45) has revealed that on cooling this transition is accompanied by a structural transition from a monoclinic structure in the paramagnetic state to an orthorhombic structure in the ferromagnetic state. Furthermore this magnetostructural transition can be induced reversibly by an external magnetic field, leading to strong magnetoelastic effects (Morellon et al. 1998a) as well as to a giant negative magnetoresistance (Morellon et al. 1998b; Levin et al. 1999, 2000). In
SPONTANEOUS MAGNETOELASTIC EFFECTS IN GADOLINIUM COMPOUNDS
400
I
I I I I I I
350
g ~
1-0
....C':S
300
200
~
0.
a
150
~
Eo-<
M
PM
I I 0(1) I PM I I L-I
--
0(11) : :
250 PM
~
1-0
I I I I I I
337
100
II I I I I I I I I I
0(1)
FM
_----l 0(11)
A
Gd s(Si xGe l _x)4
50 0 0.0
0.2
0.4
0.6
0.8
1.0
X Fig. 23. Magnetic and crystallographic temperature-composition phase diagram of the GdS(SixGel_x)4 compounds (after Morellon et aI. (2000». FM, PM, AF label different magnetic phases (FM: ferromagnetic, PM: paramagnetic, AF: antiferromagnetic). 0(1), M and 0(11) label different crystallographic structures (0(1): orthorhombic GdsSi4 structure, M: monoclinic structure, 0(0): orthorhombic GdSGe4 structure). The solid line marks the first-order magnetostructuraI phase boundary.
contrast to the compounds with 0.24 :::::; x :::::; 0.5, the Ge-rich compounds with x :::::; 0.2 order antiferromagnetically (or ferrimagnetically) at about 125 K (second-order transition) and then experience a further first-order transition to a low-temperature ferromagnetic state, connected with a giant MCE (Morellon et al. I998a). One example for the interesting magnetoelastic properties of the Gds(SixGe l-x)4 pseudobinary system is the compound Gds(Sio.1 GeO.9)4 (i.e. x = 0.1). In contrast to the compounds with 0.24 :::::; x :::::; 0.5, which show a monoclinic structure, this compound crystallizes in an orthorhombic structure (GdsGe4 type), which is similar to the GdsSi4 type of the Si-rich compounds (Pecharsky and Gschneidner Jr. 1997d). Both, the GdsGe4and the GdsSi4 type are described within space group Pnma, the Gd atoms occupy three different crystallographic sites (Gdl: 4c, Gd2: 8d, Gd3: 8d), and the Ge and Si atoms are statistically distributed over three sites (MI: 4c, M2: 4c. M3: 8d). The only difference between the two types lies in different fractional coordinates, which are not fixed by symmetry (for a comprehensive structural study of the Gds(SixGel-x)4 pseudobinary system see Pecharsky and Gschneidner Jr. (l997d) and Morellon et al. (2000». For illustrating the magnetic and crystallographic properties of the Gds(SixGel-x)4 system, the magnetic and crystallographic temperature-composition phase diagram is shown in fig. 23. Ac-susceptibility measurements by Morellon et al. (2000) showed, that (on heating) Gds(Sio.IGeo.9)4 undergoes a first-order transition from a ferromagnetic to an antiferromagnetic state at Tc = 81 K, followed by a second-order transition to the paramagnetic state at TN = 127 K. Measurements of the thermal dependence of the lattice parameters
338
A. LINDBAUM and M. ROITER
7.9
7.8
rEr --c-o- -
7.7
a -e - - - - -..()
0(1) I 0(11) 7.6
I
.........,
888
r...-.·--.. . --
l"1
~
>
880
--.- .....
872
o
50
_ _ _d
-...,
100
150
200
250
300
T [K] Fig. 24. Thermal dependence of the lattice parameters and the volume of Gd~(Sio.1 Geo.9 )4, measured by x-ray powder diffraction. The shown data have been extracted from Morellon et al. (2000). The dashed lines serve as a guide for the eyes.
using x-ray powder diffraction, reported by the same authors and shown in fig. 24, revealed a very pronounced spontaneous magnetostriction at the first-order ferromagnetic to antiferromagnetic transition at Tc = 81 K, whereas no significant effects could be observed at TN. On cooling through Tc the following abrupt changes of the lattice parameters are visible: (I:::.ala)mag ~ -16 x 10-3 , (!:!.blb)mag ~ 3 x 10-3 , (I:::.clc)mag ~ 7 x 10-3 and
~ -6 x 10- 3 . The change of the c]a ratio is (~~/~~)
)mag ~ 23 x 10- 3 . This means that the anisotropic effects are larger than 2%, i.e. Gds(SlO.1 GeO.9)4 can be classified as a giant magnetostriction (GMS) compound (Engdahl 1999). Furthermore, Rietveld analysis of the x-ray powder patterns showed, that the spontaneous magnetostriction at Tc is connected with a significant change of some of the fractional coordinates (Morellon et al. 2000), leading mainly to a shifting of atoms in the a-direction, where the magnetostriction is largest. The obtained atomic positions are very similar to the values determined for Gds Sia (Pecharsky and Gschneidner Jr. 1997d). This means that the antiferromagnetic to ferromagnetic transition is not only accompanied by a giant magnetostriction of the lattice parameters, but also by a structural change. In order to (I:::. V I V)mag
SPONTANEOUS MAGNETOELASTIC EFFECTS IN GADOLINIUM COMPOUNDS
339
Fig. 25. Orthorhombic structures of GdS(Sio.1GeO.9)4 below and above the magnetostructural transition. The dolled boxes and the arrows indicate roughly the shifting of the atoms in the GdSGe4 type (0(11» compared to the GdsSi4 type (0(1)).
illustrate this magnetostructural transition from the high-temperature Gd5Ge4 type to the low temperature GdsSi4 type, fig. 25 shows the orthorhombic unit cells, with atomic positions obtained from Rietveld fits below (30 K) and above (100 K) the transition. The main difference between the two orthorhombic structures is a common shifting (in a-direction) of the atoms in the upper half of the unit cell relative to the atoms in the lower half. Forced magnetostriction measurements using a strain gauge technique, also performed by Morellon et al. (2000), indicate that the magnetostructural transition can be induced reversibly by an external magnetic field. This means that there is a remarkable resemblance of the observed magnetostructural transition in Gds(Sio.IGeo.9)4 with the transition in Gd5(Sio.4sGeo.ss)4 (Morellon et al. 1998a), where the transition is also dominated by a drastic reduction of the lattice parameter a. However, it has to be pointed out, that in Gds(Sio.IGeo.9)4 no change of the symmetry is involved in the magnetostructural transition. 8.2. GdNi
GdNi crystallizes in the orthorhombic CrB type of structure (space group Cmcm). The Gd atoms are located on the 4c sites with point symmetry mm (0, YGd ~ 0.14, The Ni atoms also occupy the 4c sites with YNi ~ 0.43 (see e.g. Buschow (1980». It is interesting to note that among the RNi compounds there exists a second type of orthorhombic structure. Only the compounds with R from La to Gd crystallize in the CrB type. The compounds with R from Dy to Tm and Y show the less symmetric FeB type with space group Pnma (see e.g. Burzo et al. (1990». As reported by Blanco et at. (1992) TbNi crystallizes in a monoclinic intermediate structure. Figure 26 shows the orthorhombic unit cell and the atomic arrangement of the CrB type of structure. (The shown orthorhombic cell is not the
i).
340
A. LINDBAUM and M. ROTTER
__---+t.Gd (4c)
b
Fig. 26. Orthorhombic CrB-type structure of GdNi.
primitive unit cell. since the lattice is base centered orthorhombic. i.e. there is an additional lattice point in the centre of the a-b planes.) As shown by neutron diffraction experiments and magnetization measurements, GdNi is a simple collinear ferromagnet with the magnetic moments parallel to the b-axis below Tc ~ 69 K (Blanco et al. 1992). The magnetic moment at 4.2 K is 7.3 ± 0.1 /-LB. NMR spectra of this compound are also consistent with a direction of magnetization along the b-axis for this compound (de Jesus et al. 2(00). The spontaneous magnetostriction, obtained by x-ray powder diffraction, shows, like for Gd5(Sio.IGeo.9)4 (see section 8.1), very large anisotropic effects (see fig. 27). The estimated values at 0 K in the different crystallographic directions are (6a j a ) mag ~ 4.0 X 10- 3 • (6bjb)mag ~ 5.4 x 10- 3 • (6cjc)mag ~ -8.2 x 10- 3 and (6 V j V)mag ~ 1.2 x 10-3 . Especially the spontaneous magnetically induced contraction in the c-direction of almost I % is outstanding. The magnetically induced change of the c jb ratio reaches (~~/1~»mag ~
-1.36 x 10-2 and therefore GdNi has to be considered as a GMS compound (Engdahl 1999). Whether the observed giant magnetostriction of the lattice parameters is connected with a change of the atomic positions. has not been determined. i.e. further studies are necessary in order to answer the question whether GdNi shows, like Gd5(Sio.IGeo.9)4. a magnetostructural transition and whether this transition can be induced by a magnetic field. The relatively large positive volume effect could be due to an induced itinerant Ni moment (Paulose et al. 1996), which is confirmed by a comparison with GdPt (see section 8.5). A further hint for the existence of an induced Ni moment could be the temperature dependence of the magnetization. which deviates remarkably from the typical bahaviour of rare earth systems (see e.g. Walline and Wallace (1964». The volume effect has also been measured by a strain gauge technique with a reported value of about 1.8 x 10-3 at 10 K (Espeso et al. 1994). In addition to the large positive volume effect below Tc • this strain gauge experiments showed a very small negative effect of about 10-5 around Tc , too small for being detectable with x-ray powder diffraction. The reason for this small additional effect is unclear.
SPONTANEOUS MAGNETOELASTIC EFFECTS IN GADOLINIUM COMPOUNDS
341
GdNi 3.78
~ CIl
••• ~Tc
3.77
••
3.76
•• •
10.32 10.30
o~ .0
•
10.28
•
10.26 4.24
o~ u
4.22
•• •
•
•
4.20 165.2
;;:; 164.8 o
>
164.4 164.0 163.6 0
50
100
150
200
250
300
T [K] Fig. 27. Anisotropic thermal expansion of GdNi measured by x-ray powder diffraction (Gratz and Lindbaum 1998). The lines represent extrapolations of the lattice contribution from the paramagnetic range. obtained by fitting Debye functions.
8.3. GdNil_xCUx
The assumption that an induced itinerant Ni moment plays an important role for the pronounced positive magnetovolume effect in GdNi, is supported by the fact that by substituting Cu for Ni the volume effect becomes smaller. For Cu concentrations x higher than 20% the FeB type of structure is formed instead of the CrB type of structure. Magnetization measurements and neutron powder diffraction experiments showed that with 30% Cu the system is, like GdNi, a simple collinear ferromagnet with a very similar ordering temperature of Tc ~ 68 K and with the magnetic moment direction parallel to the b-axis of the FeB structure (Blanco et al. 1992). However, the volume effect of (~V / V)mag ~ 0.6 x 10- 3 at 10 K (Espeso et al. 1994) is about two to three times smaller than in GdNi. Furthermore, for Cu concentrations higher than 35% the magnetic structure changes from ferromagnetic to antiferromagnetic (Gignoux and Gomez-Sal 1976). The neutron diffraction studies by Blanco et al. (1992) showed that the compound with a Cu concentration of 60% orders in a helimagnetic structure with a propagation vector
342
A. LINDBAUM and M. RaITER
(0,0,0.25) with the moments lying in the a-b plane (TN ~ 63 K). The magnetovolume effect for this compound reaches a value of (~V / V)mag ~ 0.8 x 10- 3 at 10 K (Espeso et al. 1994).
8.4. GdCu The RCu series is characterized by a structural instability. The light rare-earth based compounds crystallize in the orthorhombic FeB-type structure, while the heavy ones do so in the cubic CsCI-type structure. GdCu is the first in the series to adopt this cubic structure at room temperature, but is unstable, showing a tendency to transform into the FeB type at low temperatures. But this martensitic structural transition occurs only in a bulk (polycrystalline) sample, whereas powdered samples keep the CsCI structure down to lowest temperatures (Blanco et al. 1999). Studying the spontaneous magnetoelastic effects in the orthorhombic FeB-type phase of GdCu is very interesting with respect to a comparison with the isostructural GdPt (see section 8.5). As reported by Blanco et al. (1999), neutron diffraction patterns of powder and bulk polycrystalline samples of GdCu were obtained for both structures: in the cubic CsCI type of structure, which orders antiferromagnetically at TN ~ 150 K, a propagation vector of 0) has been found with the moments probably parallel to the c-axis (note that other noncollinear magnetic structures might give rise to the same neutron-diffraction pattern). In the orthorhombic low temperature phase (TN ~ 45 K) the available diffraction patterns suggest a magnetic propagation of (0 and a helimagnetic arrangement of the moments normal to the [0 II] direction. Furthermore it has been concluded that a simple RKKY model of an isotropic exchange interaction can be used to understand the stability of the magnetic structure in the cubic high temperature phase, whereas anisotropy in the magnetic interactions has to be taken into account for the orthorhombic low temperature phase. Concerning the spontaneous magnetoelastic effects in GdCu the only available data are the lattice parameters, as obtained by Blanco et al. (1999) from the above mentioned neutron diffraction patterns at variable temperatures. Due to the relatively low resolution of these neutron diffraction experiments concerning the determination of the lattice parameters it is only possible to give qualitative results. Figure 28 shows data for the orthorhombic FeB type, indicating a large anisotropic spontaneous magnetostriction with a negative sign in the b direction (roughly -I x 10- 2), accompanied by somewhat smaller positive effects in the a (roughly 5 x 10-3 ) and c (roughly 3 x 10- 3 ) directions. This behaviour of GdCu in the FeB type is similar to that of the isostructural GdPt (see section 8.5) and suggests, that the kind of magnetic ordering (GdPt: ferromagnetic, GdCu: antiferromagnetic) has no influence on the qualitative behaviour of the spontaneous magnetostriction.
(& !
! !)
8.5. GdPt Like the RNi compounds, the RPt compounds crystallize in two different orthorhombic structures. The heavy RPt (R = Gd to Tm) show the FeB type of structure (space group Pnma), whereas the light RPt (R = La to Nd) show the more symmetric CrB type of structure with space group Cmcm (Dwight et al. 1965; Roy et al. 1978). The Gd atoms occupy the 4c-sites (x, y = z. point symmetry m) of the space group Pnma with
!'
SPONTANEOUS MAGNETOELASTIC EFFECTS IN GADOLINIUM COMPOUNDS
343
1.00
~
0.99
0
....
00 '-' Q.,
0.98
<::::
Eo 0.91 ,...:: ~ 0
....
00
0.96
'-'
~
>
GdCu (FeB phase)
0.95 0.94
o w
~
W
~
lOOIWl~IMIW
T [K] Fig. 28. Anisotropic thermal expansion of the orthorhombic FeB phase of GdCu obtained from neutron diffraction experiments on a bulk polycrystaIline sample (Blanco et aI. 1999). The lattice parameters (lp) at 180 K are: a 7.15 ± 0.01 A. b 4.527 ± 0.008 A. c 5.471 ± 0.008 A.
=
=
Pt (4c)
__-:c: :-": ~': .~-- 'c
=
Gd (4c)
-.;:.~
G
o
I
GI a Fig. 29. Orthorhombic FeB-type structure.
0.180 and ZGd ~ 0.133. The Pt atoms also occupy the 4c-sites with XPt ~ 0.036 and ZPt ~ 0.623. Figure 29 shows the orthorhombic unit cell and the atomic arrangement of this structure type. The RPt compounds are ferromagnets with relatively low ordering temperatures (Castets et at. 1980, 1982). GdPt has the highest ordering temperature among all RPt compounds XGd ~
(Tc ~68
K).
Figure 30 shows the temperature dependence of the lattice parameters of GdPt, obtained by x-ray powder diffraction. The estimated values of the spontaneous magnetoelastic
A. LINDBAUM and M. ROTrER
344
GdPt 7.095
:< ........
7.090
~
7.085 7.080
•
•
•
f-'-'-'-'-...J....L:r:....LL.Ll-L.L...J....L.LLL.Ll-L.L...L.L.LL~
I
~ .0
~
4.500 4.495 ~ 4.490
••
4.485 5.595
r-I
...~ ..........,.............
•
........ 5.590
~
••
5.585
•
5.580 \----'----------'------'----'--------'------', ........
178.5
M
~
:>
178.0 177.5
o
50
100
150
200
250
300
T [K] Fig. 30. Anisotropic thermal expansion of the orthorhombic GdPt measured by x-ray powder diffraction (this work). The lines represent extrapolations of the lattice contribution from the paramagnetic range, obtained by fitting Debye functions. effects at 0 K are (/),.a/a)mag ~ 1.4 x 10- 3 , (/),.b/b)mag ~ -2.3 x 10- 3 , (/),.C/c)mag ~ 0.9 x 10-3 and !(/),. V /V)mag! < 0.1 x 10- 3 . This means that the pronounced linear effects, which are dominated by a negative magnetostriction in the b-direction, compensate each other, leading to a volume effect smaller than the experimental resolution. This is a further hint that the observed volume effect in GdNi (see section 8.2) is due to an induced itinerant Ni moment, since GdNi has a related crystal structure, almost the same magnetic ordering temperature and is also ferromagnetic. 8.6. GdCU2
Among the presented systems in this chapter, GdCU2 is one for which a variety of studies dealing with the magnetic properties and spontaneous as well as field-induced magnetostriction have been done in the past and also more recently (Rotter et al. 2oola).
SPONTANEOUS MAGNETOELASTIC EFFECTS IN GADOLINIUM COMPOUNDS
345
AIBz• type
R
AlB z- type
CeCuz· type
Fig. 31. The, upper part shows the highly symmetric hexagonal AIBZ type of structure. In the lower part the hexagonal cell of the AlBZ structure is doubled along the hexagonal axis (left), which allows a direct comparison with the ceCuZ type (right).
Since we think that this compound can be viewed as a model system for the investigation of magnetoelastic effects, it follows a relatively detailed description of magnetoelastic effects of GdCuz.
8.6.1. Crystal structure All 1:2 compounds of lanthanides with Cu exhibit the orthorhombic CeCu2-type structure (see e.g. Debray (1973), space group l mma, Ce on 4e sites with point symmetry mm, Cu on 8h), with the exception of LaCu2. LaCu2 displays the related hexagonal AIB2 structure with space group P6/ mmm (Storm and Benson 1963). The orthorhombic CeCu2 structure can be viewed as a distorted AIB2-type structure (see fig. 31). In some RCU2 compounds a martensitic transition in high magnetic fields has been observed and associated with a conversion of the CeCu2 to the AIB2 type of structure (Svoboda et al. 1999). Furthermore for LaCu2 a pressure induced transition from the AIB2 type to the CeCu2 type has been predicted by ab-initio total energy calculations and experimentally observed by high-pressure x-ray diffraction with a diamond anvil cell (Lindbaum et al. 2000, 1998). The atomic position parameters of GdCU2,which are not fixed by space group
346
A. LINDBAUM and M. ROlTER
-
4.0
bO
.lll: <,
3.0
N
S ~
2.0
:::&l
1.0
a
0.0 '---_--"-_ _"'---_---'-_ _- ' - - _ - - - l o 10 30 40 20 50 T (K) Fig. 32. Temperature dependenceof the magnetization of GdCU2 (Roller et aI. 2000b).
symmetry, have been determined from neutron diffraction experiments and are discussed below (see section 8.6.3). 8.6.2. Magnetic properties Investigations of GdCu2 in the magnetically ordered state (TN:::::: 42 K) revealed that in this compound no change of the magnetic structure exists in zero external magnetic field (Koyanagi et al. 1998; Luong and Franse 1981; Luong et al. 1985). The magnetic entropy as calculated from the specific heat reaches its theoretical value of R In 8 at 47 K, just above TN (Koyanagi et al. 1998). In high magnetic fields the anisotropy in the magnetization does not exceed a few percent (Borombaev et al. 1987). Measurements of the anisotropy in the magnetization of a single crystal (see fig. 32) revealed an anomaly at T:::::: 10 K (Rotter et al. 2000b), the origin of which is still the topic of current research. Neutron scattering experiments on polycrystalline and single crystal samples (Rotter et at. 2000a), as well as magnetic scattering experiments using synchrotron radiation (Rotter et at. 2000b), showed that the modulation vector of the magnetic structure is Qo = (~ I 0) and that the type of ordering can be viewed as an antiferromagnetic modulation of the moments in the b direction and a cye/oidal propagation in the a direction with a pitch angle of 120 degrees. The proposed magnetic structure of GdCU2 is shown in fig. 33. The magnetic unit cell consists of three structural unit cells aligned in the a direction. From the projection into the ac-plane the cycloidal propagation in the a direction can be seen. The filled and open symbols denote two different neighboring ac planes showing the antiferromagnetic propagation in b direction. A Rietveld refinement of the powder data at 2 K gives a magnetic Gd moment of 6.9 ILB (Rotter et at. 2000a). 8.6.3. Spontaneous magnetostriction The thermal expansion of GdCu2 has been measured already in 1985 on polycrystals by dilatometric experiments (Luong et at. 1985) and later by x-ray diffraction on powder (Gratz and Lindbaum 1994) and single crystals (Borombaev et at. 1987). The most recent measurements have been performed on a single crystal produced by the Bridgeman
SPONTANEOUS MAGNETOELASTICEFFECTS IN GADOLINIUM COMPOUNDS
347
c
•
Gdy=O.75
o
Gdy=O.25
Fig. 33. Magnetic structure of GdCU2. the different symbols denote atoms belonging to the same ac plane. for simplicity the copper atoms are not shown. The magnetic structure can be viewed as a superposition of three simple antiferromagnetic lattices asindicated bythe numbers (Rotter et aI. 2000a). method and using a capacitance dilatometer down to 500 mK in a magnetic field of 015 T. Figure 34 shows the thermal expansion measured along the a-, b- and c-axis in zero field in comparison with results of powder x-ray diffraction (Rotter et al. 2001a; Gratz and Lindbaum 1994). Below the ordering temperature TN the thermal expansion shows a pronounced negative spontaneous magnetoelastic effect in the a-direction, and a positive one in the b- and c-direction. These anisotropic contributions cancel each other leading only to a small magnetovolume effect. The estimated 0 K values of the spontaneous magnetostriction, obtained by the powder x-ray diffraction experiments are (~a/a)mag ~ -2.1 x 10- 3 , (~b/b)mag ~ 1.2 x 10-3, (~c/c)mag ~ 1.5 x 10- 3 and 3 (L\ V / V)mag ~ 0.6 x 10- . In case of GdCU2 not only the magnetoelastic effects on the lattice parameters have been investigated, but also the magnetically induced influence on the atomic positions. The atomic position parameters ZGd, ycu and ZCu, which are not fixed by space group symmetry, have been determined from the neutron diffraction patterns at 2 and 60 K (shown in Rotter et al. (2000a» by Rietveld analysis: at 2 K the obtained values are ZGd = 0.5403(8), ycu = 0.0523(8) and ZCu = 0.1653(10). At 60 K (i.e. above TN ~ 42 K) the values are: ZGd = 0.5429(6), ycu = 0.0527(5) and ZCu = 0.1653(6). As can be seen there is only for Gd a significant difference in the atomic position between the paramagnetic and magnetically ordered state, whereas for Cu the differences are very small (as expected for a pure lattice contribution). This suggests that the observed shifting of the Gd atoms is due to the magnetic ordering.
8.6.4. Field induced magnetostriction Figure 35 shows the field induced magnetostriction for external fields along the a-, b- and c-axis (Rotter et al. 2001a). All measurements were done with increasing
348
A. LINDBAUM and M. RO'ITER
o
-0.001 o
o
-0.002
o
~
~ -0.003
o
c
o
-0.004
o o
o
o
o
o
o
b
00
00
-0.005 0.000
v
>
~
>
VV
-0.001
v
v
VV
v
-0.002
VV
VV
-0.003
v
v
VV
VVV
v l,:aI~~
o
50
100 150 200 250 300
T(K) Fig. 34. Nonnalized thermal expansion of GdCU2 along the orthorhombic a-, b- and c-direction (upper figure) facilitates the comparison and the volume expansion calculated from these data (bottom figure, the factor with the upper figure). The symbols denote the results of powder x-ray diffraction (Gratz and Lindbaum 1994), the lines correspond to expansion measurements on a single crystal using the capacitance method (Rotter et al. 200la). The values €H=O denote the relative length changes in the ordered state with respect to the nonmagnetic state.
!
and decreasing field and they show only a small hysteresis. Below /-LoB = 5 T the magnetostrictive effects are rather small. Above this value two remarkable kinks occur at 5.5 T and 8.0 T, approximately, which are connected to the two magnetic phase transitions which were also found in magnetization measurements (Borombaev et al. 1987). Above 8.0 T the system is in the induced ferromagnetic state and no further transitions could be seen when continuing some of the scans up to 15 T (Rotter et al. 2oo1a). From all the data it is evident that the field induced magnetostriction is strongly different for the different crystallographic axes (leading again to a very small volume effect) but is nearly independent of the magnetic field direction. The only difference between the different field directions was found examining the low field behavior more closely (see the inset in fig. 35,
SPONTANEOUS MAGNETOELASTIC EFFECTS IN GADOLINIUM COMPOUNDS
b.a/a /-
.........
-
I
I
E-o
0.5
....J
<, ....J
<3
349
1.0
Hila g Hllb Hllc ---------------f--------c.u Ha b.b/b H b + Hc Hlla---Hllb===__ Hllc--__ :I:
t
1
1 . 10 -
3
t o
6
8
Fig. 35. Magnetostriction Sa]«, l:1b/b and l:1c/c of GdCU2 for magnetic fields parallel to the orthorhombic a-. b- and c-axis at 4.2 K (Rotter et aI. 200 la). The arrows indicate the position of phase transitions. For each curve the hysteresis is shown. The inset shows the low field data of the derivative of l:1c/ c with respect to the magnetic field.
there the derivatives of the Sc]« curves are shown as an example). showing some small differences between the curves. A transition at 0.6 T and 1.2 T is observed for fields parallel to a and c. respectively. No phase transition is observed for Bllb. This is in accordance with the findings from the magnetization experiments on a single crystal (Borombaev et al. 1987) and can be attributed to the fact, that in zero field the moments are confined to the ac-plane.
8.6.5. Discussion A model for describing the magnetoelastic properties of GdCU2 has been proposed by Rotter et al. (200la). following the ideas outlined in section 3. Using eqs (13) and (14) the magnetostriction has been calculated. By a comparison of the model with the experimentally determined spontaneous (fig. 34) and field-induced magnetostriction
350
A. LINDBAUM and M. ROITER
(fig. 35), it could be shown that the magnetoelastic interaction is dominated by the next neighbor exchange interaction in the b-direction (for a detailed explanation see Rotter et a1. (200la». In the b-direction the Gd atoms have the shortest distances and are arranged in zig-zag like chains. Another point which has to be discussed is the possible origin of the magnetoelastic interaction. Note the experimental result that the strains do not depend on the direction of the magnetic field (see fig. 35), i.e. EHlla ::;::: EHllb ::;::: EHlle == Esat. It follows, that the derivatives of the diagonal components of the exchange interaction tensor with respect to any strain E are equal (Rotter et a1. 2oola). Such a behaviour may be attributed to the fact that the magnetoelastic interaction in GdCU2 is dominated by the isotropic exchange and thus can be described by eqs (17) and (18). The anisotropic exchange interaction which leads to the observed magnetic structure with moments restricted to the ac-plane is small and does not contribute to the magnetoelastic interaction. When aligning the moments ferromagnetically with a magnetic field of about 9 Tesla (see fig. 35), the signs of the magnetoelastic strains tsa]«, li.bjb and Sc]«: are reversed (compared to the spontaneous magnetostriction), in agreement with the supposed model. However, this does not change the fact that the sign of the magnetostriction in the a-direction remains opposite to the other two directions. Finally, it has to be mentioned that, in addition to the magnetically induced effects on the lattice parameters, there is also a shifting of the Gd atoms within the unit cell. As discussed above, the relative atomic position parameter ZGd changes by about -0.003 due to the magnetic ordering. 8.7. GdZm
GdZn2 crystallizes in the orthorhombic CeCu2 type of structure (see section 8.6), but shows in contrast to the isostructural GdCU2 ferromagnetic order with Tc ::;::: 68 K (Debray et a1. 1970). As discussed in section 8.6, GdCu2 shows a cycloidal antiferromagnetic structure, whereas GdZn2 is a simple ferromagnet (Debray et a1. 1970). Due to this difference concerning the magnetic structure it seems very interesting to compare the two compounds with respect to the spontaneous magnetoelastic effects. Figure 36 shows the spontaneous magnetostriction of GdZn2, measured by x-ray powder diffraction (Ohta et a1. 1995). The measurements indicate, like in GdCU2, a negative spontaneous magnetostriction in the a-direction and a positive in the b- and c-directions, but the effect in the a direction is very small and at the limit of the resolution of the experiment. The estimated values at 0 K are: (li.aja)mag::;::: -0.2 x 10- 3 , (li.bjb)mag::;::: 1.4 x 10- 3 , (li.cjc)mag::;::: 1.9 x 10- 3 and (li.VjV)mag::;::: 3.1 x 10- 3 . This means that, interestingly, the spontaneous magnetoelastic effects in GdZn2 are qualitatively very similar to GdCU2, although the magnetic structures are very different. However, the quantitative comparison of the spontaneous magnetoelastic effects shows pronounced differences. The contraction in the a-direction is almost zero or at least much smaller than in GdCU2, whereas the expansion in the other directions is similar, leading to a much larger volume effect.
SPONTANEOUS MAGNETOELASTIC EFFECTS IN GADOLINIUM COMPOUNDS
351
GdZn 2 4.510
.......,
~
4.505 4.500
~
4.495
~ .0
7.23 7.22 7.21 7.20 7.19
•
7.59 ......., 7.58
~ u
7.57 7.56 7.55
247 ......., 246 <> 245 (")
244 0
50
100
150
200
250
300
T [K] Fig. 36. Anisotropic thermal expansion of the orthorhombic GdZn2. measured by x-ray powder diffraction (the data points have been extracted from Ohta et aI. (1995». The lines represent extrapolations of the lattice contribution from the paramagnetic range.
8.8. Gd(CUI-xNixh
A further possibility to study the influence of the magnetic structure on the spontaneous magnetoelastic effects is the comparison of GdCU2 with the solid solution Gd(Cu I-x Nixh. This is possible since up to a Ni content of about 40% the CeCu2 type of structure remains stable. On the other hand there is a pronounced change of the magnetic properties due to the Ni substitution. The magnetic ordering temperature increases from 42 K (x = 0) up to about Ito K for x = 0.3 and, interestingly, the magnetic structure changes from antiferromagnetic to ferromagnetic above a Ni concentration of about x = 0.15 (Poldy and Kirchmayr 1974; Gratz and Poldy 1977). Measurements of the spontaneous magnetostriction of the ferromagnetic compound Gd(Cuo.gNio.2h (Tc ~ 95 K) by x-ray diffraction (Borombaev and Markosyan 1987) show, like for GdZn2, qualitatively the same results as for the antiferromagnetic GdCU2, i.e. a contraction in the a-direction and an expansion in the other directions. This means that again the spontaneous magnetoelastic effects remain qualitatively the same, when changing
352
A. LINDBAUM and M. ROITER
c Fig. 37. Orthorhombic Fe3C-type structure of Gd3Ni and Gd3Rh.
from the complicated antiferromagnetic structure of GdCU2 to a simple ferromagnetic one. But again a quantitative comparison shows pronounced differences. The estimated values at 0 K for Gd(Cuo.gNio.2h are (Ila/a)mag ~ -3.5 x 10-3• (Ilb/b)mag ~ 4.9 x 10- 3 • (IlC/c)mag ~ 0.8 x 10-3 and (Il V / V)mag ~ 2.2 x 10- 3. In contrast to the pure GdCU2 (see section 8.6) the spontaneous magnetostriction is dominated by a very large effect in b-direction. The (positive) volume effect is. like in the ferromagnetic GdZn2. much larger than in GdCU2. Possibly. the ferromagnetic order in Gd(Cuo.gNio.2h and GdZn2 is responsible for a larger volume effect. But note that in the case of Gd(Cuo.gNio.2h it could also be an induced itinerant Ni moment which is responsible for the larger volume effect. 8.9. Gd3Ni and Gd3Rh Gd3Ni and Gd3Rh crystallize in the Fe3C type of structure. which is described in the space group Pnma. The Gd atoms occupy two different crystallographic sites. namely the 4c sites (point symmetry m) and the 8d sites (point symmetry I). whereas the Ni (Rh) atoms are only located on the 4c sites. Figure 37 shows the unit cell and the atomic arrangement of this structure type. As an example the atomic position parameters of Gd3Ni at room temperature as reported by Kusz et at. (2000) are given: Gd(l): 4c sites (~0.033. ~ 0.859); Gd(2): 8d sites (~ 0.678. ~ 0.435. ~ 0.175); Ni: 4c sites (~0.388. ~ 0.059). As reported by Talik and Neumann (1994) and Talik and Slebarski (1995) the two compounds Gd3Ni and Gd3Rh show some complicated antiferromagnetic structure with ordering temperatures of TN ~ 100 K and TN ~ 112 K. respectively. The spontaneous magnetostriction has been measured by single crystal x-ray diffraction between 10 and 300 K (Kusz et at. 2000). As can be seen from figs 38 and 39. both compounds show pronounced linear as well as volume effects. Gd3Ni is characterized by a large positive spontaneous magnetostriction in a-direction (the estimated value at OK is (Ila/a)mag ~ 2.9 x 10- 3). whereas the effects in b- and c-direction are about two
!.
!.
SPONTANEOUS MAGNETOELASTIC EFFECTS IN GADOLINIUM COMPOUNDS
353
Gd3Ni
• •• • • ~TN •
......... 6.94 o~ CIS
6.93 6.92
••• • •
......... 9.68
o
.D
9.67
......... o
u
• ••• •
6.33 426 .........
• ••••
r"l
o
>
424 0
50
100
150
200
250
300
T [K] Fig. 38. Anisotropic thermal expansion of the orthorhombic Gd3Ni, measured by single crystal x-ray diffraction (the data points have been extracted from Kusz et al. (ZOOO». The lines represent extrapolations of the lattice contribution from the paramagnetic range.
times smaller «~b/b)mag ~ 1.3 x 10- 3, (~C/C)mag ~ - 1.3 x 10- 3). The resulting volume 3 effect of (~V / V)mag ~ 2.9 x 10- is abouttwice as large as in the earlier discussed GdNi. Gd3Rh, on the other hand, is characterized by a negative spontaneous magnetostriction in ~ -2.5 x 10- 3) and by an almost uniform a-direction (estimated value at 0 K (~a/a)mag ~ 2.0 x 10-3, (~c/c)mag ~ 2.6 x 10- 3) . The expansion of the b-e plane «~b/b)mag 3 resulting volume effect of (~ V / V)mag ~ 2.1 x 10- is smaller than in Gd3Ni. A possible reason for this difference could be that in the case of Gd3Ni an induced itinerant Ni moment enhances the positive volume magnetostriction.
8.10. GdBazCu307-1J The magnetostriction in high Tc-superconductors has been investigated on polycrystalline samples of GdBazCu307-1J using the capacitance method (Zieglowski 1988). This compound orders antiferromagnetically below TN = 2.2 K. The spontaneous magnetostriction
354
A. LINDBAUM and M. RaITER
Gd3Rh
7.19 ,......., 7.18 0< ....... 7.17 ~ 7.16 7.15 9.60
••• •••
,.......,
0< ....... 9.59
• • •
.0
•
9.58
-<....... u
r;:;'
0< .......
>
••• • •
6.35 6.34
•
••
• •
437
•••
436 435 0
50
100
150
200
250
300
T [K] Fig. 39. Anisotropic thermal expansion of the orthorhombic GdJRh. measured by single crystal x-ray diffraction (the data points have been extracted from Kusz et al, (2000». The lines represent extrapolations of the lattice contribution from the paramagnetic range.
is not sensitive to the occurrence of superconductivity showing that magnetic order and superconductivity are decoupled in this compound. Varying the superconducting properties by a temperature treatment of the sample showed, that in contrast to the spontaneous magnetostriction the field induced magnetostriction is strongly dependent on the superconducting properties.
9. Monoclinic systems Only two examples with monoclinic structures could be found. One is the already discussed Gds(SixGel-x)4 system in the concentration range 0.24 ~ x ~ 0.5 (see section 8.1). A second is the compound GdS1r2, investigated by Kusz et al. (2000), which has a monoclinic structure related to the orthorhombic structures of Gd3Ni and Gd3Rh (see section 8.9). The authors reported the temperature dependence of the orthorhombic
SPONTANEOUSMAGNETOELASTICEFFECTS IN GADOLINIUM COMPOUNDS
355
lattice parameters, showing only for the b-direction a significant magnetostriction. The temperature dependence of the monoclinic angle has not been reported.
10. Summary and conclusions As shown in the preceding sections, there is a wide variety of spontaneous magnetoelastic effects in Gd-based systems, from very small (below 10- 4) up to effects larger than 10-2 (GMS). Not only the anisotropic spontaneous magnetostriction can reach very large values (such as the GMS of (~~%~) )mag = -1.36 x 10-2 in GdNi or of (~~C a~) )mag = 2.3 x 10- 2 in Gds(Sio.1 Geo.9)4), but also the magnetovolume effects can be unexpectedly large (e.g.: (t.:)mag = +0.5 x 10- 2 in pure Gd metal). The occurrence of GMS in Gd compounds shows that not only the crystal field (as pointed out by Engdahl (1999)), but also the exchange interaction has to be considered as a source of GMS. In the tables 1 and 2 the spontaneous magnetoelastic effects of the systems presented in this chapter are summarized. As can be seen from these tables, for any kind of the magnetic ordering (i.e. ferromagnetic or antiferromagnetic) examples exist with large and small effects. However, there is a tendency to larger effects in ferromagnetic systems. Second, the observed effects depend strongly on the partner elements of Gd, which can be seen from a comparison of isostructural systems, like for instance GdCuAI and GdNiAl, Gd2Cu2In and Gd2Ni2-xIn, or GdAg2 and GdAu2. Such comparisons show, that changing one of the partner elements can have a strong influence on the spontaneous magnetostriction. How far the qualitative behaviour of the spontaneous magnetostriction is determined by the type of crystal structure, remains unclear: A comparison of the CeCu2-type compounds GdCU2, Gd(Cuo.sNio.2h and GdZn2, having different magnetic structures, shows that the qualitative behaviour of the magnetostriction is always the same, i.e, the sign of the magnetostriction in the a-direction is opposite to those of the b- and c-directions. This holds also true when changing the magnetic structure of GdCu2 from antiferromagnetic to ferromagnetic by applying a magnetic field. Furthermore also the comparison of the FeB-type compounds GdCu (antiferromagnetic) and GdPt (ferromagnetic) supports the conclusion. that the qualitative behaviour of the spontaneous magnetostriction is connected with the crystal structure. But on the other hand the compounds Gd3Ni and Gd3Rh, which are both antiferromagnetic and have the same crystal structure, show different qualitative behaviour of the spontaneous magnetostriction. In case of Gd3Ni it is the magnetostriction in the c-direction, which has opposite sign compared to the other directions, wheras in Gd3Rh it is the a-direction. Third, it is obvious that in systems with a small number of Gd atoms (e.g. GdNis and GdNhB2C) the effects are very small, since the magnetic as well as magnetoelastic interactions are weaker in systems with low Gd concentration. This is supported by the studies on GdCU2, showing that at least in case of this compound the magnetostriction is dominated by the next neighbor exchange interaction (i.e. in case of a compound with low Gd concentration smaller effects have to be expected due to the smaller number of next neighbors). But note that systems with high Gd concentration do not necessarily have large effects. In Gd2In, for instance, two out of three atoms are Gd, leading to strong magnetic
.... .... 0TABLE I Summary of the spontaneous magnetostriction in non-eubic systems showingpronouncedanisotropic effects, ordered with respect to the size of the effects. The presented values are the estimated values at 0 K Method Gds(Si(l.I Geo.9)4 (0) GdNi (0) GdCu (FeB) (0) Gd(ClI().8Nio.2h (0) Gd2Cu21n (t) Gd3Rh(0) GdCuAI (h) Gd3Ni (0) GdPt (0) GdCU2 (0) GdZn2 (0) Gd(h) GdCuSn (h) GdAg2 (t)
x raj x [bJ n lcl x [dJ x [eJ x[f] x [gJ x[f] x lel x [h] x [iJ x lel x [bJ x [eJ
Gd2Ni2_xln (t)
X
[eJ
Sa]« [l0-3J -16 +4.0 5±3 -3.5 -1.9 -2.5 -1.7 +2.9 +1.4 -2.1 -0.2 +1.0 +0.3 +0.3 -0.2
tlb/b [l0-3J +3 +5.4 -1O±3 +4.9 +2.0 +1.3 -2.3 +1.2 +1.4
Sc]« [l0-3J
svrv
Te(N)
+7 -8.2 3±3 +0.8 +3.8 +2.6 +3.0 -1.3 +0.9 +1.5 +1.9 +3.0 -l.l -0.6
[1O- 3J -6 +1.2 -2±5 +2.2 < 0.1 +2.1 -0.4 +2.9 <0.1 +0.6 +3.1 +5.0 -0.5 < 0.1
Te-81 K Te=69K TN =45 K Te =95 K Te=86K TN = 112 K [6J Te =82 K TN = lOOK [8J Te =68 K TN =42K Te =68 K Te=294K TN=24K TN =23 K
+0.4
< 0.1
TN=20K[l5J
Propagation (000) [lJ (000) (O! !) (000) [4J (000)
Moment direction [OIOJ [2J [x, y, z = -yJ [3J [001][5J
~
r-
(000)
[OOIJ [7J
Z
0
t:l:l
(000) [9J (j 10) (000) [IIJ (000) (O! 0) (0.3620 l)
i; [xOzJ [IOJ
>232 K: [00 IJ [12J [OOIJ [l3J > 10.8 K: [00 IJ < 10.8 K: [I 10][14J
x, n indicate the experimental method ~-ray, neutron). Note: < means that the absolute value is smaller than this value, which is about the resolution of the experimental technique. (h), (t), (0) indicate the crystal system (hexagonal, ~etragonal, Qrthorhombic). In addition Te(N), the propagation vector and the direction of the magnetic moment are tabulated. References for magnetostriction measurements: raj Morellon et aI. (2000), [bJ Gratz and Lindbaum (1998), [cJ Blanco et aI. (1999), [dJ Borombaev and Markosyan (1987), [eJ this work, [f] Kusz et aI. (2000), [gJ Andreev et al, (1999), [h) Gratz and Lindbaum (1994), [iJ Ohta et aI. (1995). References for magnetic properties: [I] Morellon et aI. (2000), [2J Blanco et aI. (1992), [3] Blanco et aI. (1999), [4] Poldy and Kirchmayr (1974), [5] Fisher et aI. (1999), [6J Talik and Neumann (1994), [7] Andreev et aI. (1999), [8] Talik and Siebarski (1995), [9] Castets et aI. (1980, 1982), [10] Rotter et al, (2ooob, 2oooa), [II] Debray et aI. (1970), [12J Cable and Wollan (1968), [13J Bialic et aI. (1997), [l4J Gignoux et aI. (1991), [15J Hilscher (2001).
:::
8~
§ tr1 ::I:l
TABLE 2 Summary of the spontaneous magnetostriction (estimated values at 0 K) of the systems with very small or not determined (n.d.) anisotropic effects. The table is ordered with respect to the size of the observed volume effects Method
fI1aja
[10- 3]
GdNiAI (h) GdNio.4ClI().6 (0) GdNio.7ClI().3 (0) GdNi2 (c) GdCu21n (c) GdPd2In (c) GdIn3 (c) GdNis (h) Gd2In (h)
x [a] d[b] x [c] d[d] d[d] x [a] d [e] d [e] x [a] x [a] x[f]
GdAu2 (t) GdNi282C (t)
x [a] x [a]
GdAI2 (c)
Sb [b [10- 3]
Sc]« [10- 3]
fI1VjV
<0.1 <0.1
<0.1 < 0.1
[10- 3] -1.4 -1.16 +0.8 +0.8 +0.6 +0.6 -0.10 -0.02 ""-0.3 <0.1 <0.1
<0.1 <0.1
<0.1 < 0.1
<0.1 <0.1
""+0.3 n.d. n.d.
n.d. n.d.
""+0.3 n.d. n.d.
TC(N) TC= 168 K
Propagation (000)
Moment direction [II I] [I]
V>
C3 z
~
s C
V>
3': TC=60K TN =63 K TC =68 K Tc=74K
TN=IOK[5] TN = IOK[5] TN =43 K [6] TC =31 K Tc = lOOK TN = 50 K (10) TN =20K
>30 K: (000) [2] (000.25) (000) (000)[4]
~ [xyO] [3] [0 I 0] [3]
z
~
V>
~ (000) >100 K: he1.FM [8] <100 K: (00 [9]
[00 I] [7]
(0.5500)
>14 K: [01 0) <14K: [Oyz) (11)
t)
~
z
x, d indicate the ~-ray or J!ilatometric method. Note: < means that the absolute value is smaller than this value. which is about the resolution of the experimental technique. (c). (h), (I), (0) indicate the crystal system (£ubic. hexagonal, !etragonal, Qrthorhombic). In addition Te(N), the propagation vector and the direction of the magnetic moment are tabulated. References for magnetostriction measurements: [a) this work. [b] du Tremolet de Lacheisserie (1988), [c)larosz et aI. (2000), [d) Espeso et al, (1994). [e] Taylor et al. (2000), [f] Gratz and Lindbaum (1998). References for magnetic properties: [I) Kaplan et al, (1973); Burd and Lee (1977), [2] Merlo et aI. (1998); Javorsky et al. (1995), (3) Blanco et al, (1992), [4] Buschow (1977); lesser and Clad (1986), (5) Parsons et aI. (1998); Taylor et al, (2000), [6] Stalniski et al. (1979), [7] Franse and Radwanski (1993); Mulders et al. (2000). [8] lee et aI. (1996), [9] Ravot et aI. (1993), [10] Tung et al. (1996). (11) Detlefs et al, (1996); Tomala et al, (1998).
o
§z ~
~
I ..., U. -.I
358
A. LINDBAUM and M. ROTIER
interactions, reflected in the high ferromagnetic ordering temperature of 190 K, but the associated magnetoelastic effects are smaller than 10- 4. Gd5(Sio.IGeO.9)4 is one representative of the Gd5(SixGel-x)4 compounds, where a magnetic transition is not only connected with a giant magnetostriction of the lattice parameters, but also with an instability of other structural parameters. Furthermore this magnetostructural transition can be induced reversibly by a magnetic field and is connected with a giant magnetocaloric effect (Morellon et al. 2000; Morellon et al. 1998a). This example shows that the measurement of the spontaneous magnetostriction could be very useful for finding systems showing magnetostructural transitions and giant magnetocaloric effects. What is not shown in the tables, are spontaneous distortions of the crystal symmetry, which are usually very small (i.e. < 10- 4) and have only been observed in cubic systems, where the detection of symmetry distortions is easier. To our knowledge the largest symmetry breaking effect has been observed for cubic GdZn by Rouchy et al. (1981), namely a tetragonal distortion of (tll/ 1)001 ::::: -3.7 x 10-4 (see section 5). One of the maybe most interesting and unexpected observations concerning spontaneous magnetoelastic effects in Gd compounds are the large magnetovolume effects, ranging from (~: )mag = +5.0 x 10- 3 in pure Gd metal to (~: )mag = -6 x 10-3 in Gd5(Sio.1 Geo.9k The size of the magnetovolume effect in pure Gd is comparable to typical systems with Fe or Co, where the observed positive magnetovolume effects are associated with the itinerant character of the Fe or Co moments. In all Gd systems, presented in this chapter and showing pronounced magnetovolume effects (i.e. absolute value larger than 0.5 x 10- 3), these effects are always positive (only with the exception of GdAh and Gd5(Sio.1 GeO.9)4). This suggests that the polarization of the conduction electrons or the delectrons of partner atoms like Ni, induced by the molecular field of the Gd moments, plays an important role for the magnetovolume effects in Gd systems. This is also supported by the fact that the largest positive magnetovolume effects are observed in ferromagnetic systems, where the Gd molecular field inducing a polarization of the s, p or d electrons, is largest. As an example, the contribution of the induced itinerant moment can be demonstrated by substituting Cu for Ni in GdNi: by replacing 30% of the Ni atoms by Cu, neither the type of the magnetic ordering (ferromagnetic), nor the Curie temperature is changed, but the magnetovolume effect is reduced from + 1.2 x 10- 3 in GdNi to +0.6 x 10- 3 in GdNio.7CUO.3, because, in contrast to the Cu d-electrons, the Ni d-electrons can be polarized by the Gd molecular field. A second example, which demonstrates not only the role of an induced Ni moment but also of the type of magnetic ordering, is the comparison of the antiferromagnetic GdCuz with the isostructural, but ferromagnetic Gd(Cuo.gNio.zh. In the latter the magnetovolume effect is almost four times larger. However, one should not forget about the large negative magnetovolume effects in Gd5(Sio.1 GeO.9)4 and GdA}z. In the case of GdA}z the large negative magnetovolume effect has to be attributed to the volume dependence of the (indirect) Gd-Gd exchange interaction since an induced itinerant magnetic moment should lead to a positive magnetovolume effect. This means that not only an itinerant magnetic moment, but also the volume dependence of the (indirect) Gd-Gd exchange interaction can lead to pronounced magnetovolume effects> 10- 3. In the case of Gds(Sio.1 Geo.9)4 the magnetostriction is connected with a magnetostructural transition and the large negative magnetovolume effect is probably due to the rearrangement of the atoms in the unit cell.
SPONTANEOUS MAGNETOELASTIC EFFECTS IN GADOLINIUM COMPOUNDS
359
Finally, we would like to point out the importance of investigations of the fieldinduced magnetostriction in Gd compounds. Such investigations are very important for a quantitative analysis of the spontaneous magnetostriction, which has for instance been shown by the studies on GdCu2. The lack of systematic studies of the field-induced magnetostriction in Gd compounds may be one reason why only in a few cases a quantitative description of the spontaneous magnetoelastic effects in Gd compounds has been performed. Acknowledgements This work has been supported by the Austrian Academy of Sciences (APART 10739), by the Austrian Science Fund FWF (Project P14932), and by the Deutsche Forschungsgemeinschaft DFG (SFB 463). Further we would like to thank E. Gratz (TU Vienna) for fruitful discussions. References Abell, J.S., JX Boucherle, R.Osborn, B.D. Rainford and J. Schweizer. 1983. J. Magn. Magn. Mat. 3134,247. Andreev, A.• P. Javorsky and A. Lindbaum, 1999. Journal of Alloys and Compounds 290, 10. Andreev, A.V., 1995. in: Handbook of Magnetic Materials. vol. 8. ed. K.H.J. Buschow (Elsevier Sci. Pub.) p.59. Barron, T.H.K., 1998, in: Thermal Expansion of Solids. vol. 1-4. ed. e.Y. Ho. CINDAS Data Series on Material Properties (ASM International) ch, I, p. I. Barron, T.H.K.• I.G. Collins and G.K. White. 1980. Adv. Phys. 29. 609. Belger. A.• U. Jaenicke-Rossler. D. Lipp, B. Wehner. P. Paufter and G. Behr, 1998. Physica C 306.277. Bialic, D., R. Kruk, R. KmieC and K. Tomala, 1997, Journal of Alloys and Compounds 257, 49. Blanco. J.A .• 1.1. Espeso, I. Garcfa-Soldevilla, J.C. Gomez-Sal, M.R. Ibarra. C. Marquina and H.E. Fischer. 1999. Phys. Rev. B 59. 512. Blanco. J.A .• D. Gignoux and D. Schmitt. 1991, Phys. Rev. B 43.13145. Blanco, J.A .. J.e. Gomez-Sal, I. Rodrfguez-Fernandez, D. Gignoux, D. Schmitt and J. Rodriguez-Carvajal. 1992, J. Phys.: Condens. Matter 4, 8233. Blazina, Z.• B. Sorgic and A. Drasner, 1999, J. Phys.: Condens. Matter 11. 3105. Bober, I.-L.. S. Pecbev, B. Chevalier and B. Darriet, 1998. Journal of Alloys and Compounds '1.67, 136.
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Author Index
Akinaga, H., see Yamada, M. 13 Alam, M.A., see Dugdale, S.B. 230, 240 Alameda, 1.M., see Dieny, B. 163 Albertini, E, see Morellon, L. 309, 336, 337, 339, 358 Alejandro, G. 175 Algarabel, P.A., see de Teresa, J.M. 176, 178 Aigarabel, P.A., see Garda-Landa, B. 182 Aigarabel, P.A., see Ibarra, M.R. 175, 176 Aigarabel, P.A., see Morellon, L. 309, 336-339, 356,358 Ali, M. 109 Aliaga-Guerra, D., see Bud'ko, S.L. 278, 279 Aliyev, M.l. 5, 14 Allen, P.B. 229 Alieno, E. 216, 217, 225, 226, 242, 246, 260, 263, 264 Alieno, E., see Bonville, P. 213, 270 Alieno, E., see Feiner, 1. 213, 216, 279 Alieno, E., see Godart, C. 220, 242, 260 Alieno, E., see Nagarajan, R. 288 Alieno, E., see Rams, M. 221 Alieno, E., see Tominez, E. 216, 219, 220, 242 Allenspach, P. 245 Allenspach, P.,see Gasser, U. 208, 222, 241, 245, 269 Allenspach, R., see Back, C.H. 174 Allenspach, R., see Weber, W. 114 Almesh, N. 19 Alp, E.E., see Dunlap, B.D. 256 Al'tshuler, B.L. 53, 60 Alves, E 172 Amann, A., see Rathnayaka, K.D.D. 227, 278 Amaral Jr., M.R., see EI Massalami, M. 219, 220, 242, 247 Amato, A., see Le, L.P. 235 Amato, A., see Mulders, A.M. 322, 357 Amaya, K., see Shimizu, K. 231 Ambrose, T.M., see Park, Y.D. 74 Amici, A. 261, 262, 266 Anagnostopoulos, T., see Gamari-Seale, H. 323 Andersen, N.H., see Chang, L.J. 242
Abe, E. 14, 15,71 Abe, E., see Ohno, H. 74 Abe, E., see Zhao, 1.H. 10 H. 273 Abe, H., see Abe, H., see Shen, A. 9, 15, 16 Abe, T., see Munekata, H. 36 Abell, J.S. 316 Abernathy, C.R., see Overberg, M.E. 13 Abernathy, C.R., see Theodoropolpu, N. 14 Abernathy, D.L., see Detlefs, C. 261, 262 Abolfath, M. 25,49,52,54,55,57,58 Abrahamsen, A.B., see Eskildsen, M.R. 265, 269, 273,274 Abrahamsen, A.B., see Gammel, P.L. 223, 279 Abrarnovich, A.I. 178, 179 Abrikosov, A.A. 209,214,272, 286 Acet, M., set' Gratz, E. 317 Achard, J.C., see Latroche, M. 317 Adachi, G., see Sakai, T. 205, 273, 274 Adhikari, T. 14 Adroja, D.T., see Tomy, c.v. 256, 258 Aegerter, C.M., see Paul, D. McK. 258, 269, 276 Afalfiz, L., see Tomy, C.Y. 256, 259 Afalfiz, L.A., see Tomy, C.Y. 258 Aharony, A. 208 Ahilan, K., see Saxena, 5.5. 209 Ahmet, P., see Kuwahara, S. 13, 14 Ahmet, P., see Matsumoto, Y. 78 Akai, H.43 Akai, H., see Kamatani, T. 76, 78 Akiba, N. 65, 68, 69 Akiba, N., see Chiba, D. 65, 66 Akiba, N., see Ohno, H. 68, 69 Akiba, N., see Shen, A. 7-9, 25, 54, 57, 58, 61, 62 Akiba, N., see Sugawara, Y. 32 Akimitsu, J., see Ekino, T. 259 Akimitsu, J., see Nagamatsu, J. 202, 203 Akimitsu, J., see Uehara, M. 216, 217, 264 Akimoto, R., see Saito, H. 13 Akinaga, H. 13, 14, 78 Akinaga, H., see Ofuchi, H. 14 Akinaga, H., see Okabayashi, J. 79
xue.
363
364
AUTHOR INDEX
Andersen, N.H., see Eskildsen, M.R. 265, 267. 269,273-276 Andersen, N.H., see Gammel, P.L. 223, 267, 277, 279 Andersen, N.H., see Nergaard, K. 225 Anderson, P.W. 210, 213 Ando, K.4O Ando, K., see Hayashi, T. 62. 63 Ando, K.• see Saito. H. 13 Ando, K., see Shimizu, H. 4 I Ando, K., see Shioda, R. 18 Ando, K., see Szczytko, J. 19 Ando, M. 38 Andre, G., see Ravot, O. 324, 357 Andrearczyk, T., see Ferrand, O. 5, 49, 54, 60 Andreev, A. 325, 327. 356 Andreev, A.V. 95,310,322 Andreone, A. 215, 219, 241 Andres. K., see Matthias, B.T. 202 Anh, O.T.N.,see Due, N.H. 140. 142, 157, 158 Ann. J.M. 207 Annett, J.F., see Gabovich, A.M. 238 Ansaldo, E.A.• see Bernhard, C. 213 Antropov, V.P.• see Belaschenko, K.O. 207 Antropov, V.P., see Kortus, J. 244 Aoki, O. 214 Appel, J., see Fay, O. 213 Appl, S., see Lee. WH. 251 Aragwal, P., see Saxena, S.S. 209 Arai, K.1. 186, 189 Arai, K.I.. see Hayashi, Y. 117. 119-121. 133 Arai, K.I., see Honda, T. 119, 133. 186, 187 Arai, K.I.. see Kikuchi, S. 132. 133 Arai, K.I., see Tanaka. T. 132 Aranson, I., see de Wilde, Y. 266. 277 Aranson, I., see Metlushko, V. 240 Arata, l. 47, 63 Arata, I., see Ohno, Y. 63, 64, 73 Areas, J. 172 Areiszewska, M., see Osinniy, V. 33 Arimoto, H., see Matsuda, Y.H. 37,38 Arimura, H.• see Tanaka, T. 132 Arisawa, S. 219 Armstrong, WO. 173 Arnaudas, J.I. 159.160 Arnaudas, J.I., see Ciria, M. 106. 159 Arnaudas, J.I.• see de la Fuente, C. 162 Arnaudas, J.I.• see del Moral, A. 159-162 Arnold, Z., see de Teresa, J.M. 178 Arnold, Z., see Morellon, L. 309, 336, 337, 339. 358 Arnoult, A., see Haury, A. 5,49, 54 ArnouIt, A., see Kossacki, P. 49, 74 Aronov, A.G., see Al'tshuler, B.L. 53, 60
Arons. R.. see Rotter, M. 346, 347. 356 Arrott, A. 23 Anita, C .• see Andreone, A. 215 Asahi, H.• see Hashimoto. M. 10. 14 Asahi, H., see Kanamura, M. 73 Asami, K., see Kanamura, M. 73 Asamitsu, A., see Kimura, T. 181-183 Asamitsu, A., see Kuwahara, H. 178 Ashburn. J.R., see Wu, M.K. 208 Ashcroft, N. W. 203 Ashcroft, N.W, see Richardson, C.F. 279 Askenazy, S., see Respaud, M. 179 Asklund, H.• see Sadowski, 1. 9, 16.77 Atkinson, WA., see Jungwirth. T. 49, 53, 55,60, 66, 74 Ausloos, M., see Gabovich, A.M. 238 Awano, H. 151 Awschalom, D.O., see Beschoten, B. 41, 47 Awschalom, D.O., see Harris. J.G.E. 26 Awschalom, D.O., see Johnston-Halperin, E. 71 Awschalom, D.O., see Kawakami, R.K. 5, 10,63, 75 Awschalorn, D.O., see Kikkawa, J.M. 75, 79 Awschalom, D.O., see Malajovich, I. 79 Awschalom, D.O .• see Ohno, Y. 70. 71 Awschalom, D.O., see Salis, G. 79 Awschalom, D.O., see Wolf, S. 4 Azaf, U .• see Feiner, I. 241. 255 Azbel', M. Ya., see Lifshits, I.M. 258 Baberschke, K., see Davidov, O. 216 Back, C.H. 174 Back. C.H.• see Weber. W. 114 Baeumer, M., see Schneider, J. 19 Bagchi, S.N., see Hossain, Z. 242, 248, 253 Baggio-Saitovitch, E .• see Bourdarot, F.218 Baggio-Saitovitch, E., see EI Massalami, M. 223 Baggio-Saitovitch, E., see Sanchez, O.R. 226, 256, 266 Baggio-Saitovitch, E.M. 223, 224, 243 Baggio-Saitovitch, E.M., see Bud'ko, S.L. 216, 217,271, 278, 279 Baggio-Saitovitch, E.M., see EI Massalami, M. 242,278 Baggio-Saitovitch, E.M., see Fontes, M.B. 213 Baines, C., see Mulders, A.M. 275 Bak-Misiuk, J., see Sadowski, J. 5, 9,15,16,26, 77 Bakker, K., see Brabers, J.H.V.J. 272 Balakrishnan, G., see Garcia-Landa, B. 182 Balakrishnan, G., see Tomy, C.V. 256, 259 Balandin, A., see Vrijen, R. 79 Balbashov, A.M., see Demin, R.V. 178
AUTHOR INDEX Balbashov, A.M., see Kadomtseva, A.M. 180 Balbashov, A.M., see Mukhin, A.A. 181 Balbashov, A.M., see Popov, Yu. F. 179, 180 Ball, P.4 Ballentine, C.A., see O'Handley, RC. 109 Baltensperger, W. 211 Bancroft, N.J., see Paul, D. McK. 258 Barabara, B.. see Ferrand, D. 27 Baran, M., see Szymczak, R 234, 235, 240 Baran, M., see Zuberek, R 154 Barandiaran, J.M., see Gutierrez, 1. 170 Barandiaran, J.M., see Hernando, A. 94 Barandiaran, J.M., see Slawska-Waniewska, A. 169 Baranyak, V.M., see Kalychak, Y.M. 331 Barash, Y.S. 284, 285 Barbara, B., see Feiner, I. 213, 216 Barbara, B., see Ferrand, D. 5,49, 54, 60 Barbashov, M.N., see Masterov, V.F. 19 Barber, B.P., see Eskildsen, M.R. 267, 269, 276 Barber, B.P., see Gammel, P.L. 273 Bardeen,J.203,227,272 Bardyszewski, W., see Kossacki, P. 49, 74 Bardyszewski, W., see Szczytko, 1. 41, 47 Baril, L. 110 Barkov, T.L .. see Vinnikov, L.Ya. 260, 264, 273 Barner, C., see Gratz, E. 317 Baron, T. 5 Baron, V.V., see Savitskii, E.M. 214 Barratt, J.P., see Boothroyd, A.T. 223 Barron, T.H.K. 311, 313, 314 Barron, T.H.K., see Taylor, R.E. 311 Bars, 0 .. see Bauer, J. 225 Barthelemy, A. 93 Barthem, V., see EI Massalami, M. 205, 206 Basu, S., see Adhikari, T. 14 Basu, S., see Akinaga, H. 13 Batlogg, B., see Carter, SA 202, 205, 224 Batlogg, B., see Cava, R.I. 202, 205, 220, 223, 240.242,283 Batlogg, B., see Eisaki, H. 231, 240 Batlogg, B., see Schon, J.H. 203, 205, 206, 238, 259 Batlogg, B., see Takagi, H. 215, 230, 241 Ball, A.1. 120 Bauer, E., see El-Hagary, M. 245, 253 Bauer, E., see Michor, H. 223. 224, 279, 287 Bauer, E.D. 214 Bauer. J. 225 Bauernfeind. L. 213 Baxter, D.V. 32 Beach. R.S. 159 Beach, RS., see O'Donovan, K.V. 159
365
Bean, cr, see Meiklejohn, W.H. 230. 231, 234, 241 Beatrice, C; see Pasquale, M. 119 Becker, R. 95 Becla, P., see Szczytko, J. 41 Bedair, S.M., see Reed, M.L. 14, 77 Bednorz, J.G. 207 Begaerts, R., see van Esch, A. 5, 26, 30, 34, 55 Behr, G. 219, 225 Behr, G., see Belger, A. 335 Behr, G., see Billerlich, H. 210, 287, 288 Behr, G., see Drechsler, S.-L. 229, 234 Behr, G., see Lindbaum, A. 345 Behr, G., see von Lips, H. 260-262 Belaschenko, K.D. 207 Belashenko, K.D., see Kortus, 1. 244 Belger, A. 335 Belger, A., see Behr, G. 225 Belger, A., see Jaenike-Roessler, U. 277 Belitz, D. 48 Belov, K.P. 126 Belson, H., see Clark, A.E. 94 Beltran, M., see Koksharov, Yu.A. 168 Ben Youssef, 1., see Due, N.H. 168 Ben Youssef, J., see Le Gall, H. 111, 143, 147, 148 Bender, H., see Akinaga, H. 14 Bender, H., see de Boeck, J. 5, 9 Bender, H., see van Esch, A. 10 Bennett, B.R., see Jonker, J.T. 70 Beno, M., see Dunlap, B.D. 212 Benoit Ii la Guillaume, C. 42, 60 Benoit Ii la Guillaume, C., see Bhattacharjee, A.K. 20,46,47 Benson, K.E., see Storm, A.R 345 Berciu, M., see Bhatt, R.N. 48, 60 Berciu, M., see Kenett, M.P. 60 Berger, P., see Alieno, E. 225. 226, 260, 263, 264 Berger, P., see Tominez, E. 216, 219, 220, 242 Berger, R 188 Bernhard, C. 213 Bernhard, C., see Henn, R.W. 238 Bernhoeft, N.R., see Pfleiderer. C. 226, 237 Berry, J.1••see Malajovich, I. 79 Berry, 1.1.,see Potashnik, SJ. 5, 9, 34, 50, 56, 77 Beschoten, B. 41, 47 Beschoten, B., see Ohno, Y. 70, 71 Betz, 1. 94. 103. 106, 119-122. 128, 133, 141, 142, 163, 186, 187 Betz, J., see du Tremolet de Lacheisserie, E. 186 Betz, J., see Due, N.H. 94. 103. 119, 123-127, 129, 130, 133 Betz, 1., see Givord, D. 120, 133, 141, 163, 165 Betz, 1., see Halstrup, B. 187 Betz, J., see Orsier,E. 188
366
AUTHOR INDEX
Betz, 1.• see Quandt, E. 94.141, 157. 158. 188 Bewley. R.I.. see Boothroyd. A.T. 223 Bewley. R.I.• see Cywinski. R. 207 Beyermann, W.P.270 Beyermann, W.P.• see Bud'ko, S.L. 267 Beyermann, W.P.• see Canfield, P.C. 215. 252. 267.270 Beyermann, W.P., see Cho. B.K. 242. 249. 256, 257 Beyennann, WP.• see Christianson, A.D. 236 Beyermann, WP.• see Lacerda, A. 205, 217. 220. 251.289 Beyermann, WP.• see Rathnayaka, K.D.D. 227. 278 Beyermann, W.P., see Schmiedeshoff, G.M. 205. 206.230 Beyermann, WP.• see Yatskar. A. 251. 271. 272 Bhatnagar, A.K., see Naugle. D.G. 266 Bhatnagar, A.K., see Rathnayaka, K.D.D. 271 Bhatt. R.N. 48, 60 Bhatt, R.N.• see Kenett, M.P.60 Bhatt. R.N.• see Paalanen, M.A. 49 Bhatt. R.N.• see Wolff. P.A.48 Bhattacharjee, A.K. 20. 46. 47 Bhattaeharjee. 1.K.• see Lynn. 1.W.220. 226. 242, 244.245.247-249.253.256.276 Bialic, D. 328. 356 Bin. L.• see Rukang, L. 221 Birgeneau, R.I.• see Aharony, A. 208 Bischof. A.• see Back, C.H. 174 Bischof. A.• see Weber. W. 114 Bishop. 0.1 .• see Canfield. P.C. 262. 266. 268 Bishop. 0.1 .• see Eskildsen. M.R. 267. 269, 273-276 Bishop. 0.1 .• see Gammel. P.L. 223. 267. 273. 277, 279 Bishop. 0.1 .• see Kogan. V.G.207 Bishop. 0.1 .• see Yaron, U. 242. 248, 249. 251. 270.271 Bither. T.A. 14 Bitoh, T.• see Makino. A. 169 Bitterlich, H. 210. 287. 288 Bitterlich, H., see Behr, G. 219 Bitterlich, H.• see Drechsler. S.-L. 229 Bitterlich, H.• see laenike-Roessler, U. 277 Blaha, P.. see Divis. M. 242 Blanco. 1.A. 310. 339-343. 356.357 Blanco. 1.A.• see Espeso, 1.1. 340--342,357 Blanco. 1.M., see Zuberek. R. 173 Blasco. 1.• see de Teresa, 1.M. 176. 178 Blasco. 1.• see Ibarra, M.R. 175. 176. 184. 185 Blasco. 1.. see Morellon. L. 309. 336-339. 356. 358 Blasius. Th.• see Bernhard. C. 213
Blasius, Th.• see Henn, R.W. 238 Blazina, Z. 322 Blinowski, 1. 47, 51, 76 Blount, E.I. 238, 239 Blundell, S.1.•see Nagarajan. R. 288 Boaknin, E. 238. 239. 241. 279. 285 Boatner, L.A.• see Paul, D. McK. 272. 274 Bober, 1.-L. 322 Bochi, G. 113 Bodriakov, V.Y.321 Boebinger, G.S.• see Christianson. A.D. 236 Bogaerts, R.• see van Esch, A. 10 Bohm, H., see Jarosz, 1. 326. 327, 357 Bohm, H.• see Kusz, 1.352-354. 356 Bohn, M.• see Tominez, E. 216, 219. 220, 242 Bolle. C.• see Eskildsen. M.R. 269. 276 Bolle. C.A.• see Eskildsen. M.R. 267, 276 Bonville. P. 213. 270 Bonville. P., see Godart, C. 220. 242. 260 Bonville. P., see Rams. M. 221 Boothroyd, A.T. 223. 270 Borchers.LA. 159 Borchers. 1.A.• see Beach. R.S. 159 Borchers, 1.A.• see Erwin. R.W. 159 Borghs, G.• see Akinaga, H. 14 Borghs, G., see de Boeck. 1. 4. 5. 9 Borghs, G.• see Ofuchi, H. 14 Borghs, G.• see van Esch, A. 5. 10.26.30.34.55 Borornbaev, M.K. 346. 348. 349. 351. 356 Borsa, E. see Sala, R. 243 Borsa, E. see Suh, B.l. 214 Boselli, M.A.• see Louriero da Silva 62 Bosselli, M.A. 61 Boucherle, 1.X.• see Abell. 1.S. 316 Bouchilloux, P.• see Claeyssen, E 185. 187. 188 Bourdarot, F. 218 Bourdarot, E. see Detlefs, C. 261. 272. 273 Bourdarot, E. see Svoboda, P. 345 Bouree, E. see Michor, H. 288 Bourgognon, C, see Ferrand, D. 27 Bourlen, P.• see Detlefs. C. 261, 272. 273 Bourre-Vigneron, E, see Ravot, D. 324. 357 Bouvier. M. 310 Boyer, L.L.. see Kortus, 1. 244 Bozorth, R.• see Clark. A.E. 312 Bozorth, R.M. 156. 173 Bozorth, R.M.• see Matthias. B.T. 205 Bourgognon, C.• see Ferrand. D. 5. 49. 54. 60 Brabers, 1.H.V.l. 272 Brabers, 1.H.V.1.• see Mulder. EM. 269 Braithwaite. D.• see Aoki, D. 214 Braithwaite, D.• see Huxley. A. 211 Braithwaite. D.• see Saxena, S.S. 209
AUTHOR INDEX Brandao, D.E .. see da Rocha, F.S. 205 Brandt, E.H. 213 Braun. H.F. 287 Braun, H.F., see Bauernfeind, L. 213 Braun. H.F., see Dertinger, A. 216, 217, 264, 266 Braun. H.F., see Schmidt, H. 216, 263, 264, 278 Braun, H.F., see Wagner, T.A. 231, 285 Brewer, E.G., see Pinkerton. F.E. 168, 173 Brewer, J.H., see Luke, G.M. 212 Brill, J see Sonier, J.E. 213 Brison, J.-P., see Aoki, D. 214 Brison, J.P. 220, 283 Bromberg. L. see Teter. J.P. 191 Brommer, P.E.• see Due, N.H. 96, 114, 115 Broto, J.M., see Respaud, M. 179 Briicher, E., see Bernhard, C. 213 Briickel, T., see Kobler. U. 309 Brum, J., see Abolfath, M. 25. 49, 52, 54, 55. 57, 58 Bruning, H.C.A.M., see van Vucht, J.H.N. 322 Bruno, P., see Crepieux, A. 27 Bruskov, V., see Kalychak, Y.M. 331 Bruynseraede, C., see de Boeck, J. 5. 9 Bucher. E., see Ramirez. A.P. 271 Buchgeister, M. 220, 221 Buchgeister, M., see Gasser, U. 241 Buchgeister, M., see Prassides, K. 231, 240 Buckley, R.A., see Batt, AJ. 120 Bud'ko,S.L.208,216,217,267,271,278,279 Bud'ko, S.L., see Canfield, P.C. 215, 216, 252. 256-258.261,267,270 Bud'ko, S.L .• see Choi, S.-M. 271 Bud'ko, S.L., see Christianson, A.D. 236 Bud'ko, S.L., see Detlefs, C. 261, 272. 273 Bud'ko, S.L.. see EI Massalami, M. 278 Bud'ko, S.L.. see Fontes, M.B. 213 Bud'ko. S.L.. see Gammel, P.L. 273 Bud'ko, S.L., see Rathnayaka, K.D.D. 227, 278 Bud'ko, S.L., see Sanchez, D.R. 226, 256, 266 Bud'ko, S.L., see Song, C. 284, 285 Bud'ko, S.L., see Vinnikov, L.Ya. 260, 264, 273 Bud'ko, S.L., see Yatskar, A. 251, 271, 272 Budraa, N.K., see Yatskar, A. 251, 271, 272 Buhrman. R.A., see Wolf, S. 4 Bukowski. Z., see Dabrowski, B. 181 Bulaevskii, L.N. 226 Bullock, M., see Dervenagas, P. 242, 256 Bullock, M., see Kogan, V.G. 207 Burd, J. 316, 357 Burlet, P., see Svoboda, P. 345 Burzo, E. 339 Busbridge, S.c., see Wang, B.W 94 Buschow, K.HJ. 261, 262, 317, 339, 357 Buschow, K.HJ.• see Brabers, J.H.VJ. 272
.w.,
367
Buschow, K.H.J., see Grechnev, G.E. 318 Buschow, K.HJ., see Kaplan, N. 316, 357 Buschow, K.H.I., see Liu, 1.P. 123 Buschow, K.HJ., see Mulder, F.M. 269 Buschow, K.HJ., see Mulders, A.M. 275, 322, 357 Buschow, K.HJ., see Tung, L.D. 330, 357 Bushnell, S.E. III Butera, A., see Alejandro, G. 175 Butler, WH., see Schultbess, T.C. 44 Buzdin, A., see Brison, J.P. 220, 283 Buzdin, A.I., see Bulaevskii, L.N. 226 Bychkova, M.I., see Savitskii, E.M. 214 Cable, J. W. 320, 356 Calemczuk, R., see Huxley, A. 211 Callen, E. 310, 312, 314 Callen, E.R. 97, 161 Callen, H.B., see Callen, E. 310, 312, 314 Callen, H.B., see Callen, E.R. 97, 161 Campbell, AJ. 220, 242, 259. 267 Campbell, A.M .• see lames, S.S. 267 Campbell, LA. 1I4 Caneiro, A., see Alejandro, G. 175 Canepa, F., see Cimberle, M.R. 227 Canepa, F., see Merlo, F. 326, 357 Canfield, P.C. 215, 216, 242, 252, 254, 256-258, 261,262,266-268,270 Canfield, P.c., see Alieno, E. 216, 217 Canfield, P.C., see Beyermann, W.P. 270 Canfield, P.C., see Boaknin, E. 238, 239, 241, 279. 285 Canfield, P.c., see Boothroyd, A.T. 223 Canfield. P.C., see Bud'ko, S.L. 208, 267, 278 Canfield, P.C., see Cheon, K.O. 223,227,229 Canfield, P.e., see Cho, B.K. 220, 241-243, 245, 249,254,256,257,260,261,267,269,287 Canfield, P.C.• see Choi, S.-M. 271 Canfield, P.C., see Christianson, A.D. 236 Canfield, P.C., see de Wilde, Y. 266, 277 Canfield, P.c., see Dervenagas, P. 230, 242, 245. 255,256 Canfield, P.C., see Detlefs, C. 221, 222, 241, 242, 245,253,254.261.262,272,273,310,335,357 Canfield, P'C., see Du Mar, A.C. 212 Canfield, P.C., see Dugdale, S.B. 230. 240 Canfield, P.c., see Eskildsen, M.R. 265, 267, 269, 273-276 Canfield, P.C., see Fisher, I.R. 223, 333, 356 Canfield, P.C., see Gammel, P.L. 223, 267, 273, 277, 279 Canfield, P.c., see Goldman, A.1. 233 Canfield, P.C., see Hennings, B.D. 260 Canfield, P.C., see Hill, J.P. 209
368
AUTHOR INDEX
Canfield. P.C.• see Jacobs. T. 216 Canfield. P.C.• see Johnston-Halperin, E. 209 Canfield. P.e., see Lacerda, A. 205. 217, 220, 251. 289 Canfield. P.C.• see Le, L.P. 235 Canfield. P.C.• see Lynn. J.W. 216 Canfield. P.C., see Matsuda. N. 210 Canfield. P.C.• see Mazumdar, Ch. 229 Canfield. P.C.• see Metlushko, V. 240 Canfield. P.C.• see Movshovich, R. 265. 266 Canfield, P.C., see Mun, M.O. 216, 217. 230 Canfield. P.C.• see Narozhnyi, V.N. 248-252 Canfield. P.C.• see Naugle. D.G. 216. 240 Canfield. P.C.• see N0rgaard. K. 225 Canfield. P.C., see Oomi, G. 216, 217 Canfield. P.C.• see Rathnayaka, K.D.D. 227, 230, 234.235.271.278 Canfield. P.e.. see Rybaltchenko, L.F. 267, 277 Canfield. P.C., see Sala. R 243 Canfield. P.C., see Schmiedeshoff, G.M. 205, 206, 230 Canfield. P.C.• see Song. C. 221, 256. 273. 276, 284,285 Canfield. P.C., see Sternlieb, B. 219, 224 Canfield. ac., see Suh. B.I. 214 Canfield. P.C.• see Tomala, K. 219. 335. 357 Canfield. P.C.• see Uwatoko, Y. 273 Canfield. P.C., see Vinnikov, L.Ya. 260, 264. 273 Canfield. P.C.• see Xu. M. 225 Canfield. P.C.• see Yang.I.-S. 229 Canfield. P.C.• see Yanson, LK. 276 Canfield. P.C.• see Yaron, U. 242. 248. 249, 251. 270.271 Canfield. P.C.• see Yatskar, A. 251. 271. 272 Canfield. P.C., see Zarestky. J. 212. 230 Cao, G., see Skanthakumar, S. 241, 242. 245. 252. 268 Cao, L.• see Eversmann, K. 216 Cao. Q.Q. 178 Cao. Y.• see Gao. L. 245. 269. 270 Capehart. T.W.• see Herbst. J.e.M. 168. 173 Capehart. T.W., see Pinkerton. EE. 168. 173 Capellmann, H.• see Taylor. J.W. 318. 357 Cappannini, O.M. 229. 232 Cappannini, O.M., see Weht. R 206 Carbone, J.P. 216, 217. 247 Cardona, M.• see Sapega, V.F. 20. 47 Carlson. K.D., see Williams. J.M. 209 Carman. G.P.• see Duenas, T.A. 168. 173 Carter, SA 202. 205, 224 Carter. SA, see Cava, R.I. 202. 205, 220. 223. 240.242.283 Casey Jr.• H.C. 38 Cassinese, A.• see Andreone, A. 241
Castano, F.I., see Stobiecki, T. 109 Castets, A. 343, 356 Castillo. LA.• see EI Massalarni, M. 219, 220, 242, 247 Causa. M.T.• see Alejandro, G. 175 Cava, R.I. 202. 205. 220. 223. 240. 242. 283 Cava. R.I., see Carter, S.A. 202, 205. 224 Cava, R.I., see Eisaki. H. 231, 240 Cava, R.J., see Fisher, LR. 226. 227. 235. 236. 241, 263 Cava. RJ .• see Grigereit, T.E. 205 Cava, RJ., see He. T. 284, 285 Cava, R.I., see Lynn. J.W 213. 215, 249. 252 Cava, R.J., see Mattheiss, L.F. 208 Cava, RJ.• see Murayama, e. 216 Cava, RJ.• see Nohara, M. 279. 283-285 Cava, R.I.• see Sarrao, J.L. 205 Cava, R.I., see Siegrist. T. 218. 246,247,251, 253.270,335 Cava. R.I.• see Takagi. H. 215. 230, 231, 241 Cava, R.I.• see Zandbergen, HW. 219. 220, 223, 242,266 Cezairliyan, A .• see Taylor. R.E. 311 Chaika, A.N.• see Strukova, G.K. 226 Chaikin. P.M., see Jones. T.E. 218, 221 Chakoumakos, B.C.• see Paranthaman, M. 212 Chandra, G.• see Mazumdar, Ch. 270 Chang. L.J. 241, 242, 275, 278 Chang. L.L., see Krol, A. 17 Chang, L.L., see Munekata, H. 5. 6, 10. 11. 17.36 Chang, L.L.• see Ohno, H. 5. 10, 11, 32, 34. 35 Chang, L.L.. see von Molnar. S. 34 Chantis, A.N., see Petukhov, A.G. 70 Chao, C.Y.-P. 69 Chaoshui, X.• see Rukang, L. 221 Chapman, R.A. 19,37 Chappert, J. 116 Chatterji, T., see Kobler, U. 309. 315 Chatlopadhya~A.60
Chazalviel, J.-N. 36 Chelkowski, A .• see Burzo, E. 339 Chen. H.Y.• see Wang, J.H. 176 Chen, J.W, see Lin, M.S. 205 Chen, L.F.. see Kawakami. RK. 5. 10. 63 Chen, LJ.• see WU, R.Q. 105 Chen. Q., see Chu. RK. 219 Chen, T.Y., see Wang. J.H. 176 Chen, X. 10 Chen. Y.Y.• see Lee, WH. 205 Chen. Y.Y.• see Lin. M.S. 205 Cheon, K.O. 223. 227. 229 Cheon, K.O., see Gammel, P.L. 267, 277 Cheong. H.D., see Jonker. J.T. 70
AUTHOR INDEX Chevalier. B.• see Bober, 1.-L. 322 Chevalier. B.• see Lejay,P. 279. 280. 283. 284 Chiang. H.C.. see Hsu, Y.Y. 209. 210 Chiba, Chiba, Chiba, Chiba,
D. 65. 66 D.• see Akiba, N. 65 D.• see Ohno, H. 74 D.• see Zhao. J.H. 10 Chien. c.i, 27. 168 Chikazumi, S. 130 Chikyow, T.• see Kuwahara. S. 13. 14 Chikyow, T.• see Matsumoto. Y. 78 Chinchure, A.D. 220. 242. 249. 258 Chinchure, A.D.• see Ghosh. G. 230 Chiriaco H. 168.169. 185 Chiriaco H.. see Hristoforou, E. 106 Chisten, D.K.• see Kogan.V.G. 273 Chrnaissem, 0 .• see Dabrowski. B. 181 Cho. B.K. 220.241-243. 245.249.254. 256.257. 260.261.267.269.278.287 Cho, B.K.• see Alieno. E. 216. 217 Cho, B.K.. see Canfield. P.C. 215. 242. 252. 254, 256-258.266-268.270 Cho. B.K.. see Dervenagas, P. 230. 242. 245. 255. 256 Cho. B.K.• see Detlefs. C. 221, 310, 335. 357 Cho, B.K.• see Goldman. A.I. 233 Cho, B.K.• see Hill. J.P. 209 Cho, B.K.• see Jacobs. T. 216 Cho, B.K.. see Johnston-Halperin, E. 209 Cho, B.K.. see Le. L.P. 235 Cbo, B.K.• see Lee. K.H. 276, 288 Cho, B.K.• see Matsuda. N. 210 Cho, B.K., see Movshovich, R. 265. 266 Cho. B.K.. see Mun, M.O. 216. 217. 230 Cho, B.K .• see Oomi, G. 216, 217 Cho, B.K.• see Rathnayaka, K.D.D. 230. 234. 235, 271 Cho. B.K.. see Suh, BJ. 214 Cho, B.K.• see Uwatoko, Y. 273 Cho. B.K.. see Xu. M. 225 Cho. B.K.. see Yang. I.-S. 229 Cho, B.K.• see Yanson, I.K. 276 Cho, B.K .• see Zarestky, J. 230 Cho, J.H.• see Kogan. V.G. 273 Choi, C.K. 262 Choi, E.-M.• see Choi, 1.-H. 266 Choi, E.S., see Choi. C.K. 262 Choi. J.-H. 266 Choi, S.-M. 271 Choi, Y.S.• see Lim. S.H. 142 Chok, E.P.• see Jones. TE. 218. 221
Chopra. H.D. 144 Christen. D.K., see Song. K.I. 221, 256 Christensen.N.E.• see Cappannini, O.M. 229. 232
369
Christensen, N.E.• see Weht.R. 206 Christianson. A.D. 236 Chtchelkanova, A.Y.• see Wolf. S. 4 Chu. C.W.• see Dezaneti,L.M. 242. 249. 251, 270, 271
Chu. C.W. see Gao. L. 245. 269. 270 Chu. C.W.• see we, M.K. 208 Chu. R.K. 219 Chu, S.N.G.. see Theodoropolpu, N. 14 Chu, WK.• see Chu, R.K. 219 Chuang. S.L.. see Chao. c.Y.-P. 69 Chubukov, A.V.• see Movshovich, R. 265. 266 Chun, S.H.• see Potashnik, SJ. 5. 9. 34. 50. 56. 77 Chung. L.L.• see Soo, Y.L. 17 Cibert, 1.. see Dietl. T. 29.49--54.57.58.73.75 Cibert, 1.. see Ferrand.D. 5. 27. 49. 54. 60 Cibert, J.•see Haury. A. 5.49.54 Cibert, 1.. see Kossacki, P. 49. 74 Cichorek, T, see Drechsler. S.-L. 228. 229 Cichorek, T. see Lipp, D. 226. 283 Cimberle, M.R. 227
Cirafici,S.• see Merlo. F. 326. 357 Ciria, M. 106. 159 Ciria, M.. see Arnaudas, J.I. 159. 160 Ciria, M.. see del Moral. A. 159--162 Civale, L.. see Silhanek, A.V. 205 Clad. R.• see Jesser.R. 317. 357 Claeyssen, F. 185. 187.188 Clark. A.E. 94. 133.312 Clarke. R.. see Lee. C.H. 113 Clausen. C.• see Hansen, P. 115. 117 Clausen. K.N., see Jehan, D.A. 159 Clausen. K.N.• see Swaddling.P.P. 159 Cloud. WH .• see Bither.T.A. 14 Cochrane,R.W 122 Coehoom, R. 115.231 Coehoorn, R.. see Liu, J.P. 123 Coehoorn, R.• see Mulder.F.M. 269 Coey,1.M.D. 4.116, 126. 175.320 Coey, 1.M.D.,see Chappert, J. 116 Cogliati, E.• see Andreone, A. 219 Cohen. A.M.• see RodriguesBitterncourt, A.C. 69 Coldren. I.. see Johnston-Halperin, E. 71 Coles. B.R.• see Taylor. R.H. 316 Collins. J.G.• see Barron,T.H.K. 311. 313 Colton. RJ., see Wandass. 1.H. 106 Comenescu, G.• see Chen. X. 10 Conder. K.• see Garda-Landa. B. 176. 177 Coniglio.A.• see Aharony, A. 208 Conner.R.A.• see Dwight. A.E. 329. 342 Continentino, M.A.• see Fontes. M.B. 213 Cooke. D.W, see Nagarajan, R. 288 Cooper,J.R.. see Fisher. I.R. 223. 226.227.235. 236.241.263
370
AUTHOR INDEX
Cooper. L.N .• see Bardeen, J. 227 Cooper. S.L.. see Yang. I.-S. 229 Corenzwit, E.• see Matthias. B.T. 202. 209. 213 Correia. J.G .• see Wahl. U. 14 Costa. E. see Alves. F. 172 Cottrell, S.P., see Nagarajan, R 288 Cowen. J.A., see Stampe, P.A. 324 Cowley. R.• see de la Fuente. e. 162 Cowley. R.A .• see Jehan, D.A. 159 Cox. S.EJ.• see Nagarajan, R 288 Crabtree. G.W. see de Wilde, Y. 266. 277 Crabtree, G.W.• see Dunlap. B.D. 212 Crabtree, G.W. see Metlushko, Y. 240 Crangle, J.• see Parsons. MJ. 318. 357 Crepieux, A. 27 Crow. lE., see Skanthakumar, S. 241,242,245, 252.268 Crowell, P.A., see Beschoten, B. 41, 47 Cubitt. R., see Cywinski. R. 207 Cubitt. R., see Paul, D. McK. 258, 269, 276 Cunningham, lE., see Erwin, RW 159 Cywinski, R 207 Czapkiewicz, M.• see Stobiecki, T. 109 Czopnik, A. see Grechnev, G.E. 318 Czopnik, A., see Narozhnyi, V.N. 213, 248. 251, 252 Czopnik, A., see Staliriski, B. 318. 357 da Costa, M.S .• see EI Massalami, M. 205. 206 da Cunha Lima, I.C., see Bosselli, M.A. 61 da Cunha Lima. I.C., see Gummich, U. 48 da CUnha Lima, I.C., see Louriero da Silva 62 da Rocha, ES. 205 Dabrowski. B. 180, 181 Dadashev, 1.5., see Aliyev, M.1. 5, 14 Dagotto, E. 209 Dai, D.S., see Wang, J.H. 176 Damsma, H., see Havinga, E.E. 205 Dancaster, J.L., see Gibbs, M.RJ. 94 Danh, T.M. 94, 116-118, 122, 126 Danh, T.M., see Due, N.H. 94,117-119.126, 131-133. 140, 142, 143, 148. 150, 157, 158, 167 Dan'kov, S.Y. 320 Darriet, B., see Bobet, l-L. 322 Das Sarma, S. 79 Das Sarma, S., see Chattopadhyay, A. 60 Das Sarma, S., see Zutic, I. 71 Date, V.G., see Hossain. Z. 242, 248, 253 Daughton, J.M., see Wolf, S. 4 Davidov, D. 216 Davies, H.A., see Batt. AJ. 120 Davis. M.R., see Luke, G.M. 212
Davydov, A.A., see Makarova, T.L. 286 de Andrade, M.e., see Rathnayaka, K.D.D. 227. 278 de Andrade. M.C., see Sarrao, lL. 205 de Andrade, M.C., see Zandbergen, H.W 223 de Boeck, 1. 4, 5, 9 de Boeck, 1.. see Akinaga, H. 14 de Boeck, 1., see Ofuchi, H. 14 de Boeck, J.. see van Esch, A. 5, 10,26, 30, 34. 55 de Boer, C; see Schmiedeshoff, G.M. 230 de Boer, F.R., see Brabers, 1.H.V.I. 272 de Boer. ER, see Liu, 1.P. 123 de Boer. F.R.. see Mulder. EM. 269 de Chatel, P.E, see Liu, J.P. 123 de Gennes, P.-G. 175, 260 de Groot, P.AJ., see Arnaudas, J.I. 159, 160 de Groot, PAJ., see Ciria, M. 106, 159 de Jesus, Y.L.B. 340 de Jonge, WJ.M., see Draaisma, HJ.G. 172 de Jonge, WJ.M., see Eggenkamp, P.TJ. 60 de la Fuente, C. 162 de la Fuente. C.• see Arnaudas, 1.1. 159. 160 de la Fuente, C., see Ciria, M. 106, 159 de la Fuente. C., see del Moral, A. 159-162 de Melo, M.A.C., see Sanchez. D.R. 226. 266 de Reotier, P.D. 322 de Reotier, P.D., see Mulders, AM. 322, 357 de Reotier, P.D., see Yaouanc, A. 322 de Teresa, J.M. 176, 178 de Teresa, L.M., see Garcia-Landa, B. 176, 177 de Teresa, J.M .• see Ibarra, M.R. 175 de Wilde. Y. 266, 277 Debray, D. 345 Debray, D.K. 350, 356 Decamps, B., see Tominez, E. 216, 219, 220 Degtyareva, V.F., see Strukova, G.K. 226 del Moral, A. 159-162 del Moral, A., see Amaudas, J.I. 159. 160 del Moral, A.. see Ciria, M. 106, 159 del Moral, A., see de la Fuente, C. 162 del Moral, A., see de Teresa, J.M. 176, 178 del Moral, A., see Garda-Landa, B. 182 Delerue, C; see Grandidier, B. 18 DeLong, L.E., see Fertig. WA. 205 Demchenko, D.O., see Petukhov, A.G. 70 Demin, R.V. 178 Demin, RV.• see Koroleva, L.I. 178 Demishev, S.L., see Bud'ko, S.L. 271 den Boef, 1.H., see Henning. le.M. III Denisson, C.J.M., see Dime, EWA. 15 I Dennis, K.W, see Canfield, P.e. 242, 266, 268 Dertinger, A. 216, 217, 220, 242, 264, 266 Dertinger, A., see Schmidt, H. 216, 264 Dertinger, A., see Wagner, T.A 231, 285
AUTHOR INDEX
Dervenagas, P. 230. 242, 245. 255. 256 Dervenagas, 1'.• see Detlefs, C. 261 Dervenagas, 1'., see Goldman. A.I. 233 Dervenagas, P., see Zarestky, J. 230 Desai. P.O., see Touloukian. Y.S. 320 DeSavage, B.F.. see Clark. A.E. 312 DeSimone, D. 6 Desmoulins, J.B .• see Alves, F. 172 Detlefs, C. 221. 222,241.242,245.253,254.261, 262.272,273.310,335,357 Detlefs, C., see Hill. J.P. 209 Detlefs, C.• see Song. C. 273, 276, 284. 285 Detwiler, J.D., see Schmiedeshoff, G.M. 205. 206 Dewhurst, C.D. 202. 205. 220, 267. 277 Dewhurst. C.D., see James. S.S. 267 Dewhurst. C.D .• see Paul. D. McK. 258 Dewhurst. C.D .• see Saha, N. 225 DeWilde, Y.• see Andreone, A. 215 Dezaneti, L.M. 242. 249. 251, 270. 271 Dhar, S.K. 227. 240-242. 251 Dhar. S.K.. see Bonville. P. 213 Dhar, S.K .• see Godart, C. 218 Dhar, S.K .• see Gupta. L.C. 216,288 Dhar, S.K .• see Hossain. Z. 205, 219. 220. 223. 242.248-250.253,271,288 Dhar, S.K .• see Mazumdar, Ch. 234. 235 Dhar, S.K .. see Nagarajan. R. 216. 225. 242. 253 Dhar, S.K., see Rams. M. 221 Dickey. R.P.• see Bauer, E.D. 214 Dickey. R.P.• see Rathnayaka, K.D.D. 227, 278 Dieny. B. 110. 163 Dietl. T. 5. 23. 25. 27. 29. 30, 40, 41. 47-59,73-77 Dietl. T.• see Akiba, N. 68. 69 Dietl. T.• see Benoit a la Guillaume, C. 42. 60 Dietl. T., see Ferrand. D. 5.27,49.54.60 Dietl. T., see GI6d. P. 49 Dietl, T., see Haury. A. 5,49, 54 Dietl. T.. see Kossacki, P. 49, 74 Dietl, T., see Nagai, Y. 37.49 Dietl, T., see Ohno, H. 74 Dietl. T.• see Omiya, T. 30-33. 47. 55 Dietl. T.• see Wojtowicz, T. 32 Dietzel. A., see Berger. R. 188 Digle, R.• see I1egems, M. 19 Dinnebier, R.E.. see Dertinger, A. 216. 217. 264.
266 Dime. F.W.A. 151 Divincenzo, D.• see Vrijen, R. 79 DiVincenzo. D.P.• see Loss, D. 79 Divis, M. 216, 227, 231, 242 Divis. M.• see Javorsky. P. 326. 357 Dmytrakh, 0., see Kalychak, Y.M. 331 Dobrosavljevic-Grujic, Lj., see Kogan, V.G. 207. 273
371
Dobrowolski. W.• see Kossut, J. 5 Dobrowolski. W.• see Osinniy. V. 33 Doerr. M. 335 Doerr. M.• see Rotter. M. 310. 311. 314. 344, 346-350.356 Doerr, M.• see Svoboda, P. 345 Doh, H., see Choi. J.-H. 266 Dolejsi, D.A. 315 Domagala, J.Z., see Sadowski. J. 5. 9.15. 16,26. 77 Dong, J., see Wang. Z.D. 216. 217 Donwey, J.w., see Dwight, A.E. 342 Donze. 1'.. see Peter. M. 214 Dorandziriski, R.• see ZajIlC. M. 13 Doring, W.O.• see Becker. R. 95 Dorlijn, J.w.F. 36 Dormann, E.• see Kaplan. N. 316. 357 Downey. J.W.• see Dwight. A.E. 329 Doyle. R.A.• see Dewhurst, C.D. 267. 277 Draaisma, H.J.G. 172 Drasner, A.• see Blazina, Z. 322 Drechsler, S.-L. 216. 228. 229. 234 Drechsler. S.-L.. see Bitterlich, H. 210, 287. 288 Drechsler. S.-L., see Freudenberger, J. 219. 224. 225.266.279.287.288 Drechsler. S.-L.. see Fuchs. G. 209 Drechsler, S.-L.. see Lipp, D. 226. 283 Drechsler, S.-L., see Narozhnyi, V.N. 248. 251 Drechsler, S.-L.. see Rosner. H. 205. 206. 228-230.233,235 Drechsler. S.-L., see Shulga, S.V. 218, 223, 233. 241, 246, 281, 284 Drechsler. S.-L.. see von Lips. H. 260-262 Drew, H.D.• see Liu, S. 37 Driscol, D., see Salis. G. 79 Drost, R.. see Garda-Landa, B. 176. 177 Drzazga, Z., see Tomala, K. 219 Du, R.• see Erwin. R.W. 159 Du. R.R., see Borchers. J.A. 159 Du, Y.W.• see Cao, Q.Q. 178 Du Mar. A.C. 212 du Tremolet de Lacheissene, E. 94. 96, 97. 101. 104-108. III. 149. 185. 186.316,317.319. 357 du Tremolet de Lacheisserie, E.• see Givord, D. 120. 165 du Tremolet de Lacheisserie, E.• see Rouchy, J. 319,358 Duc. N.H. 94-96. 103, 114-119. 123-127, 129-133. 140, 142. 143. 148-153, 157. 158. 167. 168 Due, N.H.• see Danh, T.M. 94.116-118.122.126 Due, N.H., see Givord, 0.120.165
372
AUTHDRINDEX
Duenas, T.A. 168. 173 Dufeu, D., see Ferrand. D. 5, 27.49,54.60 Dugaev, V.K.• see Litvinov, v.1. 48 Dugdale. S.B. 230. 240 Duhaj, P.• see Skorvanek. I. 168 Dunlap, B.D. 212, 256 Dunmore, F., see Liu. S. 37 Duran, A.• see Falcony, R. 213 Durst. A.e., see Wolff. P.A. 48 Dusek, C.• see Michor, H. 223. 279 Dwight. A. 126 Dwight, A.E. 329, 342 Dybzinski, R.• see Dabrowski, B. 181 Dynowska, E., see Szuszkiewicz, W. 66 Dzyaloshinsky, I.E. 220, 242. 251, 259 Early. E.A .• see Luke. G.M. 212 Eckert, D., see Hase, K. 205 Eckert, D., see Milller. K.-H. 209, 216 Eckert. D.• see Narozhnyi, V.N. 213, 248-252 Eckert, J., see Gilmbel, A. 242, 253. 254 Edwards, P.P.48, 49 Efimov, Y.V., see Savitskii, E.M. 214 Eger, R.• see Simon. A. 227 Eggenkamp, P.TJ. 60 Eguchi, R.. see Katsumoto, S. 20, 37,50 Eisaki, H. 231, 240 Eisaki, H.• see Cava. R.J. 202, 205. 220. 223, 240, 242.283 Eisaki, H., see Murayama, C. 216 Eisaki, H.• see Takagi, H. 215, 230, 241 Ekino, T. 259 El Ghannami, M., see Hernando, A. 122, 168 EI Massalami, M. 205. 206. 219, 220, 223, 242, 247.278 EI Massalami, M.• see Bud'ko, S.L. 216. 217 El Massalami. M.• see Doerr, M. 335 El Massalami, M.• see Rapp, R.E. 261 EI-Hagary, M. 232, 245. 253, 287 EI-Hagary, M., see Manalo, S. 236, 237 El-Hagary, M.• see Michor, H. 224, 287 El-Masry, N.A., see Reed, M.L. 14,77 El-Metoui, M., see Kreisel, J. 18 Eliashberg, G.M. 223 Elyutin, D.P., see Belov, K.P. 126 Emerson. J.P., see Wright. D.A. 207 Enders. A., see Sander. D. 106, 107, 113 Endo, A., see Hayashi. T. 26 Endo, A., see Ohno, H. 5. 15-17,22, 25. 26, 54. 55,57.58 Endo. A., see Oiwa, A. 20-23, 31, 36, 49. 50, 55 Endo, A., see Shea, A. 7-9. 11,25.36,54,57,58 Endo,T. 10
Eng~,G.95,338, 340. 355 Enser, J., see ROller, M. 344.347-350 Ensslin, K., see Salis, G. 79 Eremets, M.I. 274. 276 Erickson. DJ., see Willis, J.D. 258 Eriksson, D., see Ravindran, P. 229 Ernst, G., see Eskildsen. M.R. 269,275 Emstberger, B., see Schmidt, H. 216. 264 Erwin, n.w 159 Erwin, R.w., see Borchers, J.A. 159 Erwin, RW., see Lynn. J.W. 220, 226. 242. 244. 245,247-249.253.256,276 Erwin, R.W.• see Rhyne. J.J. 93 Erwin, S.C., see Park. Y.D. 74 Erwing, R.W., see Beach, R.S. 159 Esaki, L., see Munekata, H. 5. 6, 10, 17 Eschrig, H.• see Drechsler. S.-L. 216, 228, 229. 234 Eschrig, H.• see Rosner, H. 205, 206. 228-230. 233.235 Escudero, R.• see Falcony, R. 213 Eskildsen. M.R. 265. 267, 269. 273-276 Eskildsen. M.R .• see Gammel, P.L. 223. 267, 277. 279 Eskildsen, M.R., see Nergaard, K. 225 Eskildsen, M.R., see Varon, U. 242, 248. 249. 251, 270.271 Espeso, J.1. 340-342, 357 Espeso, J.I., see Blanco. J.A. 342, 343. 356 Esquinazi, P.• see Makarova, T.L. 286 Eto, T.181 Etourneau, J.• see Lejay, P. 279, 280, 283, 284 Ellig, W., see Wagner, T.A. 231, 285 Evans Jr., e.A.. see DeSimone, D. 6 Everitt, B.• see Beach, R.S. 159 Eversmann, K. 216 Evetts, J.E., see Huang, J. 96, 109, 117
Fabian, J., see Das Sarma, S. 79 Fabian, J., see Zutic, I. 71 Fahnle, M. 105 Falcony, R. 213 Fan, X.-J., see Matsumoto. Y. 78 Farber, P. 133, 139, 140. 145, 147, 148, 158 Farrell, D.• see Canfield, P.e. 215 Farrell, D.E.• see Johnston-Halperin, E. 209 Faschinger, W., see Schott, G.M. 5. 7.16 Fauth, F., see Gasser. U. 241 Fay, D. 213 Fedorych, D.M. 19,58 Fehrenbacher. R. 219. 221 Feiner, L.F. 175 Felder, R.I., see Cava, R.I. 202, 205, 220, 223. 240.242,283
AUTHOR INDEX Feiner, I. 209. 213, 216. 241, 255. 278. 279 Feiner, I., see Godart. C. 220. 242. 260 Feiner. I., see Hodges, J.A. 278 Feiner. I., see Prozorov, R. 284 Felser, C., see Gulden, Th. 219, 224 Ferdeghini, C., see Cimberle, M.R. 227 Ferell. R.A., see Lynn, J.W. 220, 226, 242, 244, 245,247-249,253,256,276 Fernandez-Baca, J.A. 211 Fernandez-Diaz, M.T., see Rotter, M. 346, 347, 356 Fernandez-Diaz, T., see Gratz, E. 317 Femandez-Rossier, J. 49, 53, 54 Ferrand, D. 5, 27, 49, 54, 60 Ferrand, D., see Dietl, T. 29,49-54,57,58,73,75 Ferrand, D., see Kossacki, P. 49, 74 Fert, A., see Barthelemy, A. 93 Fertig, W.A. 205 Feyerherm, R, see Le, L.P. 235 Fiederling, R. 70 Fiedler, J., see Johnston-Halperin, E. 209 Field, S.B., see James, S.S. 267 Filatova, I.V.• see Komarovskaja, L.P. 327 Finazzi, M., see Ohldag, H. 20,44, 45, 50 Fink, HJ. 205, 208, 211 Fink. J., see Behr; G. 219 Fink, J., see Drechsler. S.-L. 234 Fink, J., see von Lips, H. 260---262 Fink, J., see Mazumdar, Ch. 229 Finnemore, D.K., see Canfield, P.C. 254 Finnemore, D.K., see Johnston-Halperin, E. 209 Finnemore, O.K., see Xu, M. 225 Finskaya, V., see Tomilo, Zh. 219, 220, 226 Finskaya, Y.M., see Tornilo, Zh.M. 205, 220, 224 Fischer, H.E., see Blanco, J.A. 342, 343, 356 Fischer, H.E., see Rotter, M. 346, 347, 356 Fischer, K., see Kobler, U. 309, 315 Fischer, 0. 208, 212, 216, 236, 237 Fischer, 0., see Ishikawa, M. 211, 212, 285 Fischer, 0., see Maple, M.B. 215 Fischer, 0., see Peter, M. 214 Fischer, S.E 139, 140 Fisher, I.R. 223,226,227.235,236,241,263, 333,356 Fisher, I.R, see Cheon, K.O. 223, 227, 229 Fisher, I.R., see Dugdale, S.B. 230, 240 Fisher, I.R., see Eskildsen, M.R. 269, 276 Fisher, I.R., see Gammel, P.L. 267, 277 Fisher. M.E. 61 Fisher, R.A., see Wright. D.A. 207 Fishman, G., see Ferrand, D. 5, 27, 49. 54, 60 Fishman, G., see Gaj, J.A. 36, 51 Fisk, Z., see Sarrao, J.L. 205 Fisk, Z., see Zandbergen, H.W. 223
373
Fisun, V.V., see Yanson, I.K. 276 Fleming, R.M .• see Cava, RJ. 202, 223 F1ik, G., see Schatz, F. 118. 130, 131. 133, 135 Flouquet, J., see Aoki, D. 214 Flouquet, J., see Brison, J.P. 220, 283 Flouquet, J., see Huxley, A. 211 Flouquet, J., see Saxena, S.S. 209 Flynn, C.P., see Borchers, J.A. 159 Flynn, C.P., see Erwin. R.W. 159 Flynn, C.P., see O'Donovan, K.V. 159 Fnidiki, A., see Due, N.H. 168 Fomicheva, L.N., see Narozhnyi, Y.N. 235-238, 248-252 Fompeyrine, J., see Berger, R. 188 Fontana, E, see Andreone, A. 215 Fontcuberta, J. 309 Fontenille, J., see Baron, T. 5 Fontes, M.B. 213 Fontes, M.B., see Bud'ko, S.L. 216. 217, 271, 278, 279 Fontes, M.B., see Sanchez, D.R. 226, 256, 266 Forester, D.W. 117 Forgan, E.M., see Cywinski, R. 207 Forgan, E.M., see Paul, D. McK. 258, 269, 276 Forgan, E.M .• see Yethiraj, M. 272 Foulkes, I.E 217. 241. 279 Fraga, G.L.E, see da Rocha, ES. 205 Franck, J.P., see Lawrie, 0.0.241 Francois, I., see van Esch, A. 10 Frankel, RB., see Story, T. 5 Franse, J.J.M. 122,322,357 Franse, J.J.M., see Luong. N.H. 346 Franse, J.J.M., see Tung, L.D. 330, 357 Franse, J.J.M., see Yaouanc, A. 322 Freeman, A.J. 105,109 Freeman, AJ., see Shick, A.B. 105 Freeman, AJ., see Wu, R. 105 Freeman, AJ., see WU, R.Q. 105 Freeman, AJ., see Zhao, Y.-J. 42, 44, 78 Frere, P.E.M., see Gibbs, M.RJ. 94 Freudenberger, J. 219, 224, 225, 233, 234, 236, 237,241,266,279,280,284,287-289 Freudenberger, J., see Behr, G. 219 Freudenberger, J., see Drechsler, S.-L. 228, 229, 234 Freudenberger, J., see Kreyssig, A. 205, 221, 222, 262 Freudenberger, J., see Lipp, D. 226, 283 Freudenberger, J., see Loewenhaupt. M. 273 Freudenberger, J., see Mllller, K.-H. 216 Freudenberger, J., see Narozhnyi, V.N. 213, 236, 237,248.251,252,271,276,288 Freudenberger, J., see Rotter, M. 223
374
AUTHOR INDEX
Freudenberger, 1.• see Sierks, C. 275 Frey, E. 315. 320 Frolich, H. 48 Prone, K.• see Zuberek, R. III. 156 Fuchs. D.T., see Salis. G. 79 Fuchs, G. 209 Fuchs. G .• see Bitterlich, H. 210. 287. 288 Fuchs. G .• see Buchgeister, M. 220 Fuchs, G .• see Drechsler. S.-L. 228. 229. 234 Fuchs. G., see Eversmann, K. 216 Fuchs. G.• see Freudenberger, 1. 219. 224. 225. 233.234.236.237,241.266,279.280,284. 287-289 Fuchs. G.• see Kreyssig, A. 205. 221. 222 Fuchs. G .• see Lipp, D. 226. 283 Fuchs. G .• see Milller, K.-H. 209, 216. 250. 256 Fuchs. G .• see Narozhnyi, V.N. 213. 236, 237. 248-252,271.276,288 Fuchs. G .• see Shulga, S.V. 233, 241. 281 Fujii. H.• see Arisawa, S. 219 Fujii. H.• see Ekino. T. 259 Fujimori, A.. see Mizokawa, T. 44. 46 Fujimori, A.• see Okabayashi, 1.13,21.31.44-46, 50.55,79 Fujimori, H. 120 Fujimori. H.• see Lim. S.H. 142 Fujimori. H.• see Ohnuma, S. 173. 174. 189 Fujimori, H .• see Shima. T. 120. 156 Fujino. Y.• see Miyazaki. T. 117, 118. 122-124. 133. 136. 137 Fukamichi, K.. see Novosad. V. 189. 190 Fukumura, T. 26 Fukumura, T.. see Matsumoto, Y. 78 Fukumura, T.• see Shono, T. 26. 58. 59 Fukunaga. H., see Narita. K. 108 Fulde. P. 210. 214. 287 Fulde, P.• see Amici. A. 266 Fulde. P., see Keller. 1. 235 Furnagalli, P. 36. 40 Fumagalli, P.• see Munekata, H. 11.36.57.58 Furdyna.l.5 Furdyna,1.• see Szczytko,1. 19 Furdyna, 1.K.• see Baxter. D.V. 32 Furdyna, 1.K.. see Chen, X. 10 Furdyna, 1.K.. see Liu, X. 5. 26 Furomoto, S.• see Shimizu. K. 231 Furrer. A.• see Gasser. U. 222. 241. 245, 269 Gaal, P.S.• see Taylor. R.E. 311 Gabovich, A.M. 238 Gaj. 1.A. 36. 51 Galazka, R.R. 5 Galazka, R.R .• see Story. T. 5
Galff"y. M. 275 Gallagher. K.• see Coey, 1.M.D. 320 Galli. M.• see El-Hagary, M. 245. 253 Gamari-Seale, H. 323 Gambino. R.I .• see Munekata, H. 10. 11.36.57, 58 Gammel. PL 223.267.273,277.279 Gammel, P.L.. see Canfield. P.e. 262. 266. 268 Gammel, PL. see Cheon, K.O. 227. 229 Gammel. P.L.. see Choi, S.-M. 271 Gammel. P.L.. see Eskildsen, M.R. 265, 267, 269. 273-276 Gammel. P.L.. see Kogan. V.G. 207 Gammel. P.L.. see Yaron, U. 242. 248, 249. 251, 270.271 Gangopadhyay, A.K. 216, 223 Gangopadhyay, A.K., see Looney. C. 208 Gao.L. 245. 269.270 Gao. L.. see Wu. M.K. 208 Garcia. D.• see Stobiecki, T. 109 Garda. 1.• see de Teresa. 1.M. 176. 178 Garcia. 1.• see Ibarra. M.R. 175. 176 Garda Escorial, A., see Hernando, A. 122. 168 Garcia-Arribas, A., see Gutierrez. 1. 170 Garcfa-Beneytez, J.M., see Areas. J. 172 Garcfa-Beneytez, J.M .• see Tejedor, M. 168 Garda-Landa. B. 176. 177, 182 Garcia-Landa, B.• see Ibarra, M.R. 184. 185 Garda-Landa. B.• see Morellon, L. 309. 336, 337, 339.358 Garcfa-Soldevilla, J., see Blanco. 1.A. 342. 343. 356 Garcia-Tello, P.• see Zuberek, R. 173 Gamier, A., see Orsier, E. 188 Gasser. U. 208. 222. 241, 245. 269 Gasser. U.. see Allenspach, P. 245 Gasser. U.. see Mulders. A.M. 275 Gavaix, A.• see Kreisel. J. 18 Gavaler, 1.R. 273 Gavigan. J.P. 123 Gavrilenko, V.I.. see Freeman, A.J. 105. 109 Gayrnann, A. 37 Geballe, T.H.• see Matthias. B.T. 202 Gebauer. J.• see Luysberg, M. 7.33 Gebicki, W. 13 Gebicki, w.. see Zajllc. M. 13 Gegenwart, P.• see Drechsler, S.-L. 228. 229 Gegenwart, P.• see Lipp, D. 226. 283 Gegenwart, Ph., see Steglich, F. 242 Geibel. Chr.• see Steghch, F. 242 Geiser. U., see Williams. 1.M. 209 Geng, W.T.• see Zhao. Y.-l. 42, 44, 78 Gerlach, B., see Quandt, E. 117. 122 Gesench, H.P., see Gayrnann, A. 37
AUTHOR INDEX Ghazali, A., see Bosselli, MA 61 Ghazali, A., see Leroux-Hugon, P. 36 Ghazali, A., see Louriero da Silva 62 Ghivelder, L., see EI Massalami, M. 219, 220. 242,247 Ghosh. G. 230 Ghosh, P.K. 287 Gianni. L., see Andreone, A. 241 Gibbs, D.• see Detlefs, C. 221, 222, 310, 335. 357 Gibbs. D., see Hill, J.P. 209 Gibbs. M.RJ. 94. 188 Gibbs. M.RJ., see Lafford, A. 156 Gibbs, M.RJ.• see Zuberek, R. Ill, 156. 157. 170 Giebultwicz, T.M., see Kepa, H. 66 Gignoux, D. 329. 330. 341, 356 Gignoux, D.. see Blanco, J.A. 310, 339-341, 356. 357 Gignoux, D.. see Castets, A. 343, 356 Ginzburg, V.L. 205. 207, 210 Giordanengo, B.• see Bud'ko, S.L. 216, 217, 278 Giordanengo, B.• see EI Massalami, M. 242, 278 Giordanengo, B., see Fontes. M.B. 213 Giorgi, A.L. 226 Giorgi. A.L., see Krupka, M.e. 205 Givord, D. 120. 133, 141, 163, 165 Givord, D.. see Betz, J. 94. 120. 121, 133 Givord, D.• see Coey, J.M.D. 126 Givord, D., see Dieny, B. 163 Givord, D.. see Due. N.H. 94. 103, 115. 116. 119. 123-127. 129, 130. 133 Givord, D.. see Gavigan, lP. 123 Givord, D.. see Orsier, E. 188 Givord, D.• see Quandt. E. 94. 141, 157, 158. 188 Gladczuc, L., see Dabrowski. B. 180. 181 Gladczuk, L., see Szymczak. R. 234, 235. 240 Gladun, A.• see Drechsler, S.-L. 228. 229. 234 Gladun, A., see Lipp, D. 226. 283 Glarum, S.H., see Rosseinsky, MJ. 209 Gl6d.P.49 Go. G.S .• see Lee. K.H. 288 Go. J., see de la Fuente, C. 162 Godart. C. 218, 220. 242, 260 Godart. C.• see Alieno, E. 225, 226, 242. 246. 260. 263,264 Godart, c., see Bonville, P. 213. 270 Godart, C., see Dhar, S.K. 227. 240--242. 251 Godart. C., s.~e FeIner, I. 213. 216. 279 Godart. C.• see Ghosh, G. 230 Godart. C.• see Gupta, L.C. 216, 288 Godart. C., see Hossain, Z. 219, 223, 242, 248-250.253.271 Godart. C., see Lynn, J.W. 213, 220. 289. 335 Godart, C., see Mazumdar, Ch. 234. 235, 270
375
Godart, C.• see Nagarajan. R. 216, 225. 242. 253. 288 Godart. C; see Rams, M. 221 Godart, C.• see Sanchez. J.P. 219. 220. 224. 225 Godart. C.• see Sinha. S.K. 213 Godart, C.• see Tominez, E. 216, 219. 220, 242 Godwal, B.K.. see Meenakshi, S. 216. 217. 243 Goedkoop, J.B.• see Ohldag. H. 20. 44. 45, 50 Golden. M.S., see Drechsler. S.-L. 234 Golden. M.S.• see von Lips. H. 260-262 Golden. M.S.• see Mazumdar, Ch. 229 Goldman. A.• see Zarestky, J. 212 Goldman, A.I. 233 Goldman, A.I., see Dervenagas, P. 230, 242. 245. 255.256 Goldman. A.I.. see Detlefs. C. 221. 222. 241. 242. 245,253,254 Goldman. A.I., see Hill. J.P. 209 Goldman. A.I.• see Song. C. 221, 256. 273. 276, 284.285 Goldman. A.I., see Sternlieb, B. 219. 224 Goldman. A.I., see Yaron, U. 242. 248, 249. 251, 270.271 Goldman. A.I.• see Zarestky. J. 230 Goldmann. A.I., see Detlefs, e. 310, 335. 357 Goldstein. B., see Almesh, N. 19 Goll.G.230 Golnik, A.• see Bernhard. C. 213 Gomes, A.A.• see da Rocha, F.S. 205 G6mez-Polo, c, see Hernando. A. 122. 168 Gomez-Sal, J.C .• see Blanco. J.A. 339-343. 356. 357 Gomez-Sal, J.C.• see Casters. A. 343. 356 Gomez-Sal, rc, see Espeso, J.I. 340--342. 357 G6mez-Sal, J.C., see Fontcuberta, J. 309 Gomez-Sal, J.C., see Gignoux, D. 341 Gomez-Sal, J.C.• see Hernando. A. 309 Gong, Sh., see Jiang. X. 119 Gonzalez, L, see Szumiata, T. 105. 172 Gonzalez, J.• see Szymczak. H. 174 Gonzalez, J.• see Zuberek, R. 173 Good. W.• see Song, C. 284. 285 Goodenough. lB. 75 Gopalakrishnan. K.V.• see Nagarajan. R. 225. 242. 253 Gopolakrishnan, L, see Luke, G.M. 212 Gorbenko, O.Y.• see Abramovieh, A.I. 178. 179 Gordon. J.E.• see Wright. D.A. 207 Goremychkin, E.• see Gratz, E. 317 Gor'kov, L.P. 210, 220, 242, 260 Gor'kov, L.P.• see Abrikosov, A.A. 209. 286 Gorochov, 0 .• see Ravot, D. 324. 357 Gorria, P.• see Gutierrez. J. 170 Gorria, P.• see Slawska-Waniewska, A. 169
376
AUTHOR INDEX
Gortenmulder, TJ., see Zandbergen, H.W. 223 Gosk, 1., see Zajac, M. 13 Gossard, A.C., see Harris, J.G.E. 26 Gossard, A.C., see Johnston-Halperin, E. 71 Gossard, A.C., see Kawakami, R.K. 5, 10, 63, 75 Gossard, A.C., see Salis, G. 79 Gotaas, J.A., see Lynn, J.W. 220, 226, 242, 244, 245,247-249,253,256,276 Gotard, C., see Mauger, A. 4 Goto, T., see Due, N.H. %, 114 Goto, T., see Oomi, G. 216 Grabias, A., see Stobiecki, T. 109 Grabtree, C.W., see Andreone, A. 215 Gradmann, U. 93,151 Grandidier, B. 18 Grant, J.B., see Mailhiot, C. 208 Gratz, E. 309, 317, 325, 329, 341, 346-348, 351, 356,357 Gratz, E., see Lindbaum, A. 317, 345 Gratz, E., see Pacheco, J.V. 327 Gratz, E., see Rotter, M. 310, 311, 344, 346-350, 356 Graw, G., see Behr, G. 219,225 Grazioli, C., see von Lips, H. 260-262 Grechnev, G.E. 318 Greenough, R.D., see Jerems, E 117 Greneche, 1.M., see Slawska-Waniewska, A. 170 Grest, G.S., see Levin, K. 235 Grest, G.S., see Nass, MJ. 258 Griessen, R., see Wijngaarden, RJ. 205 Grietens, B., see van Esch, A. 5, 26, 30, 34, 55 Grigereit, T.E. 205 Grigereit, T.E., see Sinha, S.K. 213 Grishin, A.M., see Strom, V. 205 Grosche, EM., see Saxena, S.S. 209 Grossinger, R., see Holzer, D. 168 Grossinger, R., see Skorvanek, I. 168 GrUbel. G., see Detlefs, C. 261, 262 Grundy, PJ. 117 Grundy, PJ., see Williams, P.I. 119, 122, 133 Grzanka, E., see Zajllc, M. 13 Gschneidner Jr., K.A., see Dan'kov, S.Y. 320 Gschneidner Jr., K.A., see Levin, E.M. 336 Gschneidner Jr., K.A., see Pecharsky, V.K. 336-338 Gu. K.M., see Cao, Q.Q. 178 Gu, T., see Detlefs, C. 241, 242, 245, 253, 254 Guan, W.Y., see Ku, H.C. 284, 285 Guasconi, P., see Cimberle, M.R. 227 Gubbens, P.C.M., see Mulders, A.M. 275, 322, 357 Gubbens, P.C.M., see Yaouanc, A. 322 Gubin, S.P. 168 Gubin, S.P., see Koksharov, Yu.A. 168
Guebels, N., see Kawakami, R.K. 5, 10,63 Guerevich, A., see Kogan, VG. 273 Guha, S. 10 Guimaraes, A.P., see de Jesus, VL.B. 340 Gulden, Th. 219, 224 Gulden, Th., see Henn, R.W. 238 Gumbel, A. 242, 253, 254 Gumrnich, U. 48 Guo, L., see Chen, X. 10 Guo, S.P. 7,10 Guo, S.P., see Ofuchi, H. 17 Guo, S.P., see Shen, A. 7, 9, 15, 16,54,58 Guo, Y., see Mathieu, R. 175 Gupta, L.C. 216, 275, 288 Gupta. see AlIeno, E. 242. 246 Gupta. L.C., see Bonville, P. 213, 270 Gupta, t.c., see Chinchure, A.D. 220, 242, 249, 258 Gupta, L.C., see Dhar, S.K. 227, 240-242, 251 Gupta, L.C., see Ghosh, G. 230 Gupta, L.C., see Godart, C. 218, 220, 242, 260 Gupta. L.C., see Hossain, Z. 205, 219, 220, 223. 242.248-250,253,271,288 Gupta. L.C., see Jacobs, T. 216 Gupta, L.C .• see Lynn, 1.w. 213, 220, 289, 335 Gupta. L'C; see Mazumdar, Ch. 234, 235, 270 Gupta, L.c., see Meenakshi, S. 216, 217. 243 Gupta, L.C., see Nagarajan, R. 216, 225, 242, 253, 269.288 Gupta, L.C., see Rams. M. 221 Gupta. L.C.• see Sanchez, J.P. 219. 220, 224, 225 Gupta, L.C., see Sinha, S.K. 213 Gurevich, A. 205 Gurney, B.• see Baril, L. 110 Gurney, B.A .• see Dieny, B. 110, 163 Gusev, A.I. 219 Gutierrez. J. 170 Gutjahr-Loser, Th. 104, 114 Gutowska, M., see Dabrowski. B. 180. 181 Gyax, EN.• see Mulders, A.M. 322, 357 Gygax, EN., see Le, L.P. 235 Gyorffy, B.L.. see Foulkes. I.E 217, 241. 279 Gyorgy, E.M .• see Cava, RJ. 205.220,283
i.c..
Haas. M.K., see He, T. 284, 285 Habbicki, A.T., see Park, Y.D. 74 Haddon, R.C., see Rosseinsky, MJ. 209 Hafner, 1.. see Lindbaum, A. 317. 345 Hagenmuller, P., see Lejay, P. 279, 280, 283, 284 Hagmann, N., see Jehan, D.A. 159 Hahn, T., see Taylor, R.E. 311 Halstrup. B. 187 Han. K.S .• see Lee, K.H. 276. 288
AUTHOR INDEX Han. S.H., see Lim, S.H. 142 Han. S.H.• see Sarrao, J.L. 205 Han, S.H., see Zandbergen, H.W. 223 Han, Z.P., see Cywinski. R. 207 Handstein, A., see Eversmann. K. 216 Handstein, A., see Freudenberger, J. 236. 237. 289 Handstein, A., see Fuchs, G. 209 Handstein, A.• see GUmbel. A. 242. 253. 254 Handstein, A.• see Kreyssig, A. 222 Handstein, A.• see MUlier. K.-H. 209. 216, 250. 256 Handstein, A.• see Narozhnyi, V.N. 236. 237. 271 Haneda,S.5, 12, 16 Haneda, S.• see Kuwabara, S. 13. 14 Haneda, S., see see, Y.L. 12 Hankiewicz, E.M.• see Fedorych, O.M. 19.58 Hansen, P. 115. 117. 126 Hansen. P., see Mergel, D. 96 Hanson. M.• see Kawakami, R.K. 5. 10. 63. 75 Hao. J.. see ue, X.C. 19 Hara, K.. see Haneda, S. 12. 16 Harada, K.• see Eskildsen, M.R. 269, 275 Harada, Y.• see Katsumoto, S. 20. 37. 50 Harigae, S.• see Haneda, S. 12, 16 Harima, H., see Kanamura, M. 73 Harmon, B., see Dervenagas, P. 242. 256 Harmon. B., see Kogan. V.G.207 Harmon. B.N.• see Cho, B.K. 254, 287 Harmon. B.N., see Rhee, J.Y. 209 Harmon. B.N., see Song, C. 221.256 Harmon, B.N.• see Suh, BJ. 214 Harris, J.G.E. 26 Harris. R.• see Cochrane. R W. 122 Harrison, J.C., see Zandbergen, H.W. 223 Hartmann. 0 .. see Frey, E. 315, 320 Hartmann. Th. 10 Hartmann. Th.• see Heimbrodt, W. 10 Harwit, A.. see Munekata, H. 10 Hase, K. 205,219 Hasegawa,T., see Fukumura, T. 26 Hasegawa, T.. see Matsumoto. Y.78 Hasegawa,T., see Shono, T. 26. 58. 59 Hasegawa, Y., see Medvedkin. G.A. 77 Haselwimmer, R.K.W., see Saxena, S.S. 209 Hashimoto. M. 10, 14 Hashimoto. Y.• see Hayashi. T. 9. 26. 34 Hashimoto, Y., see Katsumoto, S. 20. 37. 50 Hass. K.C. 46 Hatano, T.• see Arisawa, S. 219 Haury, A. 5, 49. 54 Haury, A., see Dietl. T. 47-49. 53. 54. 74 Hauser, R.• see El-Hagary, M. 245. 253 Hauser. R., see Michor, H. 223, 279, 287
377
Hausermann-Berg, L.S.• see Shelton. R.N. 207. 208 Havela, L.. see Javorsky, P. 325-327, 357 Havinga, E.E. 205 Hayashi, T. 5.9.26,34.62,63.65. 176 Hayashi. T., see Ando, K. 40 Hayashi. T.• see Katsumoto, S. 20, 37, 50 Hayashi. T.• see Okabayashi, J. 13.21,31,44-46. 50.55 Hayashi, T.• see Shimizu. H. 7.16,34,41.55 Hayashi. T., see Shioda, R. 18 Hayashi. T.• see Szczytko, J. 19 Hayashi. Y. 117. 119-121. 133 Hayashi. Y.• see Honda. T. 119 Hayata, K., see Medvedkin, G.A. 77 Hayden. S.M.• see Pfleiderer.C. 226. 237 Hayward, M.A., see He. T. 284. 285 Hazama, Y. 79 He. H., see Lee. C.H. 113 He. T. 284, 285 Heathman. S., see Lindbaum, A. 317. 345 Hebard, A.F.. see Rosseinsky,MJ. 209 Hebard. A.F.• see Theodoropolpu, N. 14 Hebard. F.. see Overberg, M.E. 13 Hedegard, P.• see NlIIrgaard, K. 225 Hedo,M.24O Heffner. R.H.• see Le, L.P. 235 Heiman. D., see ue, X.C. 19 Heimbrodt, W. 10 Heimbrodt, w., see Hartmann, Th. 10 Heinecke, M. 205 Heinecke. M.• see Goll, G. 230 Heinecke. M.• see Shulga, S.V. 233, 241. 281 Heitzmann, H.• see Mergel, D. 96 Hellberg. C.S., see Park. Y.D. 74 Hellmann. P., see Steglich, F. 242 Hemley, RJ.• see Eremets, M.I. 274. 276 Henggeler,W., see Gasser. U. 241 Henn, RW. 238 Henn, RW.• see Gulden, Th. 219. 224 Henneberger. S.• see Frey. E. 315. 320 Hennel, A.M.• see Mac. W. 19 Henning. J.C.M. I I I Hennings, B.D. 260 Hennion, B.• see Szuszkiewicz, W. 66 Henriques. A.B. 15 Herbst, J.C.M. 168. 173 Herbst. J.F.. see Pinkerton. F.E. 168, 173 Herisson, D.• see Alves. F. 172 Herlach. F., see van Bsch, A. 5. 10, 26. 30. 34. 55 Hermann. J., see Zandbergen, H.W. 223 Hernando. A. 94, 108. 117, 122. 168.309 Hernando. A., see Areas, J. 172 Hernando. A., see Fontcuberta, J. 309
378
AUTHOR INDEX
Hernando, A., see Huang, J. 96,109,117 Hernando, A., see Marin, P. 185 Hernando, B., see Tejedor, M. 168 Hernando, see Slawska-Waniewska. A. 169 Herrer, G., see Twarowski, K. 170 Herrmann, J., see Sarrao, J.L. 205 Hervieu, M., see Maignan, A. 179 Her.re~G.93, 136, 145, 168, 169, 174 Herzer, G., see Tejedor, M. 168 Hewat, A.W., see Paul, D. McK. 272, 274 Hidaka, Y., see Luke, G.M. 212 Hien, T.D., see Luong, N.H. 346 Hiess, A., see Rotter, M. 310, 346, 356 Higo, Y. 65, 67 Higo, Y., see Grandidier, B. 18 Higo, Y.,see Ohya, E. 10 Higo,Y., see Tanaka, M. 67 Hilbers, M., see Garda-Landa, B. 182 Hill, J.P. 209 Hill, J.P., see Detiefs, C. 221, 222, 241, 242, 245, 253,254,310,335,357 Hill, N.A .• see Sanvito, S. 42~, 46 Hill, RW., see Boaknin, E. 238. 239, 241, 279, 285 Hillberg, M., see Sanchez, D.R. 226, 266 Hillebrecht, F.U., see Ohldag, H. 20.44,45.50 Hillenbrand, B. 216,228,240,241,250,278 Hillenbrand. B., see Peter, M. 214 Hilscher. G. 229, 333, 356 Hilscher, G .• see Divis, M. 242 Hilscher, G .. see EI-Hagary, M. 232, 245, 253, 287 Hilscher, G., see Gratz, E. 317 Hilscher, G .• see Javorsky, P. 326, 357 Hilscher, G .• see Lynn, J.W. 216 Hilscher, G .. see Manalo, S. 236. 237 Hilscher. G.• see Michor, H. 223. 224. 274. 279. 287,288 Hilscher. G., see Rotter, M. 310, 346, 347, 356 Hinks, D.G .. see Dunlap, B.D. 212,256 Hirakawa. K. 37 Hirakawa. K., see Katsumoto, S. 20. 37, 50 Hiramoto, T.• see Orsier, E. 188 Hirano. T., see Takeya, H. 211 Hirasawa, M.• see Koshihara, S. 72 Hirasawa, M.• see Munekata, H. 36 Hirasawa, M.• see Oiwa, A. 20-23,31.49.50,55 Hirata. K., see Arisawa, S. 219 Hirata, K.• see Izawa, K. 240. 285 Hirata, K.. see Sakata. H. 271 Hiroi, M.• see Sera, M. 213 Hirsch, J.E. 27 Hirscher, M., see Riedi, K. 118, 133, 135, 136 Hirscher, M.• see Schatz. F. 118. 130. 131, 133. 135
Hirscher, M., see Winzek, B. 137-139 Hirschfeld, PJ., see Kubert, C. 270, 271 Hirst. R.• see Russel. V. 260 Hison, C.• see Chiriac, H. 169 Ho. J.e., see Jiang. PJ. 226 Ho. J.C., see Lin. M.S. 205 Hodges, J.A. 278 Hodges, J.A., see Bonville, P. 213. 270 Hodges. J.A., see Godart. C. 220. 242. 260 Hodges. J.A., see Rams, M. 221 Hodges. J.A .• see Ravot, D. 324. 357 230 Hoellwarth, Hofmann, B. 136 Hofmann. M., see Kreyssig, A. 221, 222 Hohenberg, P.C. 202 Hohne, R.• see Makarova, T.L. 286 Hohnston-Halperin, E., see Kawakami. RK. 5, 10, 63 Holtzberg, F., see Methfessel, SJ. 72 Holubar, T, see Michor, H. 223 Holzapfel, B., see mise, K. 205, 219 Holzapfel, W.B.• see Gratz. E. 317 Holzer, D. 168 Homrna, M., see Kikuchi, S. 132, 133 Homma, M .• see Tanaka. T. 132 Honda, F., see Oomi, G. 216,217 Honda, K., see Oomi, G. 216. 217 Honda, T 119, 133, 186, 187 Honda, T. see Arai, K.I. 186. 189 Honda, T, see Hayashi, Y. 117, 119-121, 133 Hong, Z.. see Rukang, L. 221 Hongping, Z., see Houqing, Z. 185 Hori, H., see Sonoda, S. 14,77 Horiba, H., see Okabayashi, J. 21 Horikoshi, Y., see Shen, A. 7. 54, 58 Homer, G.e., see Teter, J.P. 191 Horr, P.H., see Wu, M.K. 208 Hoser, A., see Kobler, U. 309, 315 Hoser, A., see Kreyssig, A. 221,222 Hossain. Z. 205. 219, 220, 223. 242. 248-250, 253.271,288 Hossain, Z.• see Allene, E. 242, 246 Hossain, Z., see Bonville, P. 213, 270 Hossain, Z., see Dhar, S.K. 227, 240-242, 251 Hossain, Z., see Godart, e. 218, 220, 242, 260 Hossain, Z.• see Gupta. L.C. 216. 288 Hossain, Z.• see Jacobs, T. 216 Hossain, Z., see Lynn, J.w. 213, 220, 289, 335 Hossain, Z.• see Mazumdar, Ch. 270 Hossain, Z., see Meenakshi, S. 216,217,243 Hossain, Z., see Nagarajan, R 216, 225, 242, 253, 288 Hossain, Z., see Rams, M. 221
c.c.
AUTHOR INDEX Hossain. Z.• see Sanchez.1.P. 219. 220. 224. 225 Hossain.Z., see Sinha. S.K. 213 Houqing,Z. 185 Hovinen,A.• see Kuivalainen, P. 70 Hrabovski, D.• see Sadowski.J. 10 Hristoforou, E. 106 Hsieh. K.C.. see ue. X.c. 19 Hsu, Y.Y. 209. 210 Hsu, Y.Y.• see Lin. M.S. 205 Hu, X.• see Das Sanna, S. 79 Hu, Z.• see von Lips. H. 26(}...262 Hu, Z.• see Mazumdar, Ch. 229 Huang.C.Y.. see Taylor. R.E. 311 Huang. J. 96. 109. 117 Huang, Q.• see Bourdarot, F. 218 Huang. Q.•see Grigereit, T.E. 205 Huang. Q.• see He. T. 284. 285 Huang. Q.•see Lynn.J.W 213. 215. 220. 249. 252.289.335
Huang. S.• see Krol, A. 17 Huang. S.• see Soo, Y.L. 12. 13 Huang. S.W. see Soo, Y.L. 17 Huang. Z.I.• see Wu, M.K. 208 Hughes. R.I.• see Dugdale.S.B. 230. 240 Hull. G.W.• see Matthias. B.T. 202 Hulliger, F. 319 Hulliger, E. see Rupp, B. 207 Hults. WL.. see Nagarajan, R. 288 Hundley. M.P.. see Canfield.P.C. 254 Hundley. M.F.• see Movshovich, R. 265. 266 Hundley. M.F.• see Sonier.J.E. 213 Huong Giang, D.T.• see Due. N.H. 94. 133 Hupfeld, D., see Kobler. U. 309 Huse, D.A.• see Eskildsen.M.R. 269. 276 Huse, D.A.• see Varon. U. 242. 248. 249. 251.270. 271
Huser.D. 244 Hutchings.M.T. 214 Hutchinson. W.G.• see Chapman. R.A. 19.37 Huxley. A. 211 Huxley. A.• see Aoki, D. 214 Huxley. A.• see Saxena. S.S. 209 Hwang. C.-D .• see Kim. H. 223. 224 Iannotti. V. 106 Iavarone. M.• see Andreone. A. 215. 219. 241 Iavarone. M.• see de Wilde. Y. 266. 277 Ibarra. M.R. 175. 176. 184. 185 Ibarra.M.R.• see Blanco.J.A. 342. 343, 356 Ibarra.M.R.. see de Teresa.J.M. 176. 178 Ibarra. M.R.• see Garcia-Landa, B. 176. 177. 182 Ibarra. M.R.• see Morellon, L. 309. 336-339. 356. 358
379
Ichioka, M.• see Nakai. N. 236 Ibm. 1.. see Kim. H. 223. 224 Ikaida, T.• see Matsuda.Y.H. 38 Ikeda, S .• see Kit6. H. 273 Ilegems, M. 19 Iliew, N.• see Staliriski, B. 318. 357 Ilver, L.. see Sadowski. J. 5. 9. 10. 15. 16.26.62. 77 lmada, M.. see Nakano. H. 175 Imada, S.• see Ueda, S. 44 Inaba, K.• see Fukumura,T. 26 Infortuna, A.• see Pasquale.M. 119 Inoue. A.• see Makino. A. 169 Inoue. A.• see Suzuki. K. 168 Inoue. F.. see Awano. H. 151 Inoue. J. 48. 70 Inoue. J.. see Nonoyama, S. 70 Inoue. N.• see Satoh, Y. 9. 24 Inumara,K.. see He. T. 284. 285 Ionov, A.M.• see Strukova, G.K. 226 Ishibashi.T.• see Medvedkin, G.A. 77 Ishii. K.• see Kuwahara, S. 13. 14 Ishikawa, M. 211. 212. 285 Ishio, S.• see Ooike, T. 132. 133 Ishiwata, Y.. see Katsumoto, S. 20. 37. 50 Ishiyama, K.. see Hayashi.Y. 117. 119-121. 133 Ishiyarna, K.• see Honda,T. 119 Islam. A.H.M.Z.. see Dellefs. C. 222. 241. 242. 245.253.254 Islam. Z.• see Fisher.I.R. 333. 356 Islam. Z.• see Song. C. 273. 276 ISOLDECollaboration. see Wahl. U. 14 Isshiki, M.• see Nohara,M. 268. 269. 279. 283-285 Itoh, A.. see Awano. H. 151 Itoh, H.• see Inoue. J. 48. 70 Ivanov. V.Yu., see Kadomtseva, A.M. 180 Ivanov. v.Yu.• see Mukhin. A.A. 181 Ivanov. V.Yu.• see Popov. Yu. F. 179. 180 lye. Y.• see Akiba, N. 65. 68 lye. Y.• see Hayashi. T. 9. 26. 34 lye. Y. see Katsumoto, S. 20. 31. 37.49.50
lye. Y. see Koshihara, S. 72 lye. Y.• see Munekata, H. 36 lye. Y. see Ohno, H. 5. 15-17. 22. 25. 26. 54. 55. 57.58
lye. Y.• see Oiwa, A. 2~23. 31, 36. 49. 50. 55 lye. Y.• see Shen. A. 7-9. 11.25.36.54.57.58 Izawa, K. 240. 260. 285 Jablonski. R.. see Szczytko,J. 19 Jacobs. T. 216 Jacobs-Cook. A.I.• see Gibbs. M.R.I. 94 Jaenicke-Rossler. U.• see Belger,A. 335
380
AUTHOR INDEX
Jaenike-Roessler, U. 277 Jahnes, C.V., see Klokholm, E. 106 Jambrich, C., see EI-Hagary,M. 245, 253 James, S.S. 267 James, S.S., see Dewhurst. C.D. 202, 205, 220, 267,277 Janak, I.F.315 Janocko, M.A., see Gavaler, J.R. 273 Jansen, A.G.M., see GoD, G. 230
Jansen, A.G.M., see Rybaltchenko, L.F. 267, 277 Jansen, A.G.M., see Yanson,I.K. 276 Jansen, J., see Zandbergen, H.W. 219 Janzen, E., see Linnarson, M. 19 Jarlborg, T., see Dugdale, S.B. 230, 240 Iarosz,J. 326,327, 357 Jaroszyriski,J., see Ferrand. D. 5, 27,49, 54, 60 Jaroszyriski, J., see Wojtowicz,T. 32 Javorsky, P. 325-327, 357 Javorsky. P.• see Andreev, A. 325. 327, 356 Jedrzejczak, A.• see Osinniy, V. 33 Jee. C.S. 323. 357 Jehan, D.A. 159 Jensen, I. 220. 312. 314 Jensen, I., see Nergaard, K. 225 Jepsen, 0., see Gulden. Th. 219. 224 Jerems, F. 117 lesser, R. 317, 357 Iestadt, Th., see Nagarajan, R. 288 liang, Ch.• see liang. X. 119 Jiang. H.W.• see Vrijen, R. 79 Jiang. P.I. 226 Jiang. X. 119 Iianguo, L.. see Houqing, Z. 185 Jin, S. 175 Iohansson, B., see Ravindran, P. 229 Johnson, M.I.•see Shelton. R.N. 207. 208 Johnston. D.C.• see Canfield, P.C. 254 Johnston. D.C., see Cho. B.K. 220. 241-243, 245, 249,254,256.257.260.261,267,269.287
Johnston. D.C., see Fertig, W.A. 205 Johnston. D.C., see Goldman, A.I. 233 Johnston. D.C., see Johnston-Halperin, E. 209 Johnston. D.C., see Kogan, V.G. 273 Johnston. D.C.• see Mun, M.O. 230 Johnston, D.C.• see Sub, B.I. 214 Johnston, D.C.• see Xu. M. 225 Johnston, D.C.• see Zarestky, J. 230 Johnston-Halperin, E. 71, 209 Johnston-Halperin, E., see Canfield, zc. 215 Johnston-Halperin, E.• see Kawakami. R.K. 75 Jones, C.K.• see Gavaler, J.R. 273 Jones, R.V., see Smith, A.B. III Jones. T.E. 218, 221 Jonker, B.T.• see Park. Y.D. 74
Jonker, I.T. 70 Iorgensen, J.D., see Dabrowski, B. 181 Jorgenson, J.D., see Dunlap, B.D. 212 Joss, w.. see GoD, G. 230 Jouanne, M.• see Szuszkiewicz, W. 66 Julian, S.R.• see Brison, J.P. 220, 283 Julian, S.R.• see Saxena. 5.5. 209 Jungwirth, T. 27,49,53,55,60.66.74 Jungwirth, T., see Abolfath, M. 25. 49. 52, 54, 55, 57,58
Jungwirth, T., see Lee. B. 49, 54. 60. 74 Iunod, A.• see Peter. M. 214 Jurek. K.• see Javorsky, P. 325-327 Just. G. 262
Kacman,P. 46. 52 Kacman, P.• see Blinowski, J. 47. 51, 76 Kadomtseva, A.M. 180 Kadomtseva, A.M., see Popov. Yu. F. 179. 180 Kadono, R.• see Luke. G.M. 212 Kadowaki, K., see Arisawa, S. 219 Kadowaki, K.• see Kawano, H. 266. 267 Kadowaki, K.• see Sera, M. 213 Kadowaki, K.• see Takeya, H. 211 Kaganov,M.I., see Lifshits, I.M. 258 Kagayama,T.• see Matsuda. N. 210 Kagayama,T.• see Oomi, G. 216, 217 Kaindl, G., see von Lips, H. 260--262 Kaindl, G.• see Mazumdar, Ch. 229 Kaiser, C.T., see Mulders. A.M. 322. 357 Kalatsky, VA 242, 266 Kalatsky, VA, see Canfield, P.C. 215 Kalmer, G., see Gebicki, W. 13 Kalogirou, 0., see Speliotis, A. 119 Kalvius, G.M.• see Frey, E. 315, 320 Kalychak, Y.M. 331 Kamata, K., see Izawa, K. 260 Kamatani, T. 76, 78 Kamilov, K.I., see Kadomtseva, A.M. 180 Kamiriska, M., see Zajac, M. 13 Kanamura, M. 73 Kanamura, M.• see Hashimoto, M. 10, 14 Kanda, EA .• see Russel, V. 260 Kane, B.E. 79 Kaneko, H., see Wada, M. 118, 122, 133, 135 Kaneko, T., see Ohashi, M. 329 Kaneko, T., see Ohta, S. 350, 351, 356 Kanemitsu, Y.• see Ando, M. 38 Kaneyoshi 130 Kang, I.K., see Lim, S.H. 132, 133 Kanis, J.M., see Havinga, E.E. 205 Kanski, J., see Sadowski, J. 5, 9, 10, 15, 16,26, 62, 77
AUTHORINDEX Kao, Y.H., see Krol, A. 17 Kao, Y.H.,seeSoo. Y.L. 12.13. 17 Kaplan. N. 316. 357 Karl, W., see Gibbs. M.R.1. 94, 188 Karlsteen, M.• see Sadowski, J. 9, 16.62.77 Karlsteen, M.• see Szuszkiewicz, W. 66 Karrai, K.• see Liu, S. 37 Kasai, M.• see Kuwahara. H. 178 Kashevarova.. L.N.• see Makarova.. T.L. 286 Kastner, M.A., see Aharony, A. 208 Kasuya, T. 4 Kataev, G.I., see Belov, K.P. 126 Kataoka, N., see Fujimori, H. 120 Kataoka. N.• see Suzuki. K. 168 Katayama. T.. see Awano. H. 151 Katayama-Yoshida.. H. 76 Katayama-Yoshida, H., see Kato, R 43. 77 Katayama-Yoshida, H., see Sato, K. 43, 75, 76 Katayama-Yoshida. H., see Yamamoto. T. 29. 33 Kato, R. 43, 77 Kato, R., see Katayama-Yoshida. H. 76 Kato, Y.• see lzawa, K. 240. 285 Kato. Y., see Kawakami. RK. 75 Kato. Y., see Salis. G. 79 Katsui, A.• see Shibata. N. 5 Katsumoto, S. 9. 20,31,37.49.50 Katsumoto, S., see Akiba, N. 65. 68
Katsumoto, S., see Hayashi. T. 9. 26. 34 Katsumoto, S., see Koshihara, S. 72 Katsumoto, S., see Munekata, H. 36 Katsumoto, S.• see Ohno, H. 5, 15-17,22.25.26.
54,55,57.58 Katsumoto, S .• see Oiwa, A. 20-23. 31. 36, 49. 50.
55 Katsumoto, 5., see Shen, A. 7-9. 11.25, 36,54. 57.58 Kaufmann. U.. see Schneider. J. 19 Kaul. A.R. see Abramovich, A.I. 178. 179 Kaul. S.N. 320 Kawae, T., see Choi. J.-H. 266 Kawai,T., see Saeki, H. 9. 24. 78 Kawai.T., see Ueda, K. 20. 46. 78 Kawakami.M., see Kobler. U. 309. 315 Kawakami.R.K. 5. 10, 63, 75 Kawakami,R.K., see Johnston-Halperin, E. 71 Kawamura.. M.• see Hayashi, T. 26 Kawanishi, K., see Awano, H. 151 Kawano, H. 266. 267 Kawano-Furukawa, H. 209 Kawasaki, M., see Matsumoto, Y. 78 Kayzel, EE., see Mulders, A.M. 322, 357 Kayzel, F.E., see Yaouanc, A. 322 Kealey.P.G.• see Paul, D. McK. 258 Keller, H.• see Garda-Landa, B. 176. 177
381
Keller. 1. 235 Keller, N.• see Brison. J.P. 220. 283 Keirn, M., see Fiederling, R 70 Kelsch, M., see Fischer. S.F. 139, 140 Kenett, M.P. 60 Kepa, H. 66 Kemavanois, N.• see Huxley, A. 211 Kes, P.H.• see Saba. N. 225 Khmelevskyi,S.•see Divis. M. 242 Khodorkovsky, Y.• see Koksharov, Yu.A. 168 Khotkevich, V.I., see Shubnikov,L.V. 228, 232, 233.240.241
Kieft. RE. see Luke. G.M. 212 Kihara.. T., see Okabayashi, J. 21 Kiiko, Y.M.• see Strukova.. G.K. 226 Kikkawa, J.M. 75. 79 Kikkawa, J.M.• see Malajovich, I. 79 Kikkawa, J.M., see Salis. G. 79 Kikuchi, S. 132, 133 Kikuchi, S., see Tanaka.T. 132 Kilcoyne, S.H., see Cywinski. R. 207 Kim. D., see Belov,K.P. 126 Kim. D.H.• see Lee, K.H. 276. 288 Kim. H. 223. 224 Kim, H.-J., see Choi, J.-H. 266 Kim. H.B., see Cho. B.K. 278 Kim. H.1.• see Lim. S.H. 142 Kim. I.G.• see Lee. J.I. 205 Kim. 1.. see Song, C. 284. 285 Kim, J.Y. 120. 133 Kim. J.Y., see Fujimori, H. 120 Kim. K.S., see Strom, V. 205 Kim. M.• see Freeman. A.1. 105, 109 Kim. M.S.• see Mun, M.O. 216, 217 Kim. S.• see Soo, Y.L. 12. 13 Kim, S.G., see Novosad. V. 189, 190 Kim. S.R., see Lim. S.H. 132. 133 Kim. Y.B.• see Yeo J. 27 Kimball. C., see Dwight, A. 126 Kimball. C.W., see Dabrowski. B. 180. 181 Kimura. A.. see Okabayashi, J. 13. 21. 31. 44-46. 50,55
Kimura, T. 181-183 Kimura. T., see Shimizu. K. 231 Kimura, Y.• see Koyanagi, A. 346 King. A.1.• see Russel. V. 260 Kini. A.M., see Williams. J.M. 209 Kinoshita, K., see Uehara. M. 216, 217. 264 Kioseoglou, G., see Soo, Y.L. 12, 13 Kioseoglow, G., see Jonker, J.T. 70 Kirby.RK.• see Taylor. R.E. 311 Kirby. R.K.• see Touloukian, Y.S. 320 Kirchmayr, H.• see Burzo, E. 339
382
AUTHOR INDEX
Kirchmayr, H.• see Poldy, C.A. 351. 356 Kirkpatrick. T.R.• see Belitz. D. 48 Kirschner. J.• see Gutjahr-Loser,Th. 104. 114 Kirschner. 1.. see Sander. D. 106, 107, 113 Kislov, V.v., see Gubin, S.P. 168 Kiss. T.• see Yokoya, T. 243 Kitagawa, I.. see Ogawa, T. 17.42.43 Kitagawa, I.• see Shirai. M. 17.41 Kitaguchi, H.• see Arisawa, S. 219 Kitai. T.• see Ohla, S. 350. 351, 356 Kitakami, 0 .. see Novosad. V. 189. 190 Kitamoto, Y., see Yanagi, S. 66 Kitazawa, H.• see Kito. H. 273 Kito, H. 273 Kiwata, H.• see Okabayashi, J. 21 Klamut, P.W.• see Dabrowski. B. 181 Klar, PJ.• see Hartmann. Th. 10 Klar, PJ.. see Heimbrodt, W. 10 Klausen. S.N., see Nfllrgaard. K. 225 KlauB. H.-H.• see Sanchez, D.R. 226. 266 Klavins, P.• see Hoellwarth, c.c. 230 Klavins, P.• see Lynn.1.w. 220. 226. 242. 244, 245,247-249,253.256,276
Klavins, P., see Shelton. R.N. 207. 208 Klavins, P.• see Stanley, H.B. 218 Klehe, A.-K.• see Looney,C. 208 Klein, M.V.• see Yang.I.-S. 229 Kleverman, M.• see Linnarson, M. 19 Kloc. Ch.• see Schon, 1.H. 203. 205. 206, 238. 259 Klokholm. E. 106 Klosowski. J••see Buchgeister, M. 220 KmieC. R.• see Bialic, D. 328. 356 Knupfer, M.• see von Lips. H. 260-262 Kobayashi. N.• see Ohnuma, S. 173. 174. 189 Kobayashi. N.• see Sera, M. 213 Kobayashi. S., see Sera, M. 213 Kobler. U. 309. 315 Koch, R., see Weber. M. 106 Kocbetkov, V.N.• see Freudenberger, J. 289 Kochetkov, V.N.• see Narozhnyi, V.N. 235-238. 248-252.271
Kodhihara, S.• see Haneda, S. 5, 12 Koepernik, K.. see Drechsler.S.-L. 228. 229. 234 Koepernik, K.• see Rosner, H. 205. 206. 228-230. 233,235
Kogan. V.G. 207. 273 Kogan. V.G., see Cheon, K.O. 227, 229 Kogan. V.G., see Eskildsen. M.R. 265 Kogan. V.G., see Gammel, P.L. 267, 277 Kogan. V.G.• see Gurevich. A. 205 Kogan. V.G.• see Miranovic, P. 222 Kogan. V.G.• see Vinnikov, L.Ya. 260. 264, 273 Kohl. F., see Schneider. J. 19 Kohmoto, M.• see Shiraishi. J. 272
Koida, T., see Matsumoto, Y. 78 Koike.1., see Novosad. V. 189, 190 Koinuma, H.• see Fukumura, T. 26 Koinuma, H.• see Matsumoto. Y. 78 Kojima, A., see Makino. A. 169 Koksharov, Yu.A. 168 Kolesnik, S.• see Dabrowski. B. 180, 181 Kolesnik, S.• see Ferrand, D. 5. 27, 49, 54. 60 Kolesov,V.V.• see Gubin, S.P. 168 Koleswicki,S., see Sadowski. J. 15.26 Komarovskaja, L.P. 327 Komelj. M.• see Fahnle, M. 105 Konczykowski. M.• see Izawa, K. 240, 285 Kondo, T.• see Kuwabara, S. 13, 14 Kondo, T.• see Moriya, R. 12 Kondo. T., see Soo, Y.L. 13 Konig. 1. 54. 55. 61. 71 Konig, J.• see Dietl. T. 49, 59 Konig, J•• see Schliemann, J. 61 Konishi. S. 108 Kono, J•• see Matsuda. YH. 38 Kontani, K., see Shimizu. K. 231 Kopcewicz, M.• see Stobiecki, T. 109 Kopelevich, Y.• see Makarova, T.L. 286 Koroleva, L.1. 178 Koroleva,L.I.. see Abramovich, A.1. 178. 179 Koroleva,L.I.. see Demin, R.V. 178 Kortan, A.R., see Rosseinsky, MJ. 209 Kortus, 1. 244 Kosaka, M.• see Eto, T. 181 Kosaka, M., see Yamauchi. H. 231 Koshelev, A.• see Metlushko, V. 240 Koshelev, A.E.• see de Wilde. Y. 266. 277 Koshihara, S. 72 Koshihara, S., see Haneda, S. 12
Koshihara, S.• see Matsumoto. Y 78 Koshihara, S.• see Munekata, H. 36 Kosobudsky, I.D.• see Koksharov, Yu.A. 168 Kossacki, P. 49, 74 Kossut, J. 5 Kossut, 1., see Furdyna, J. 5 Kosugi, M., see Ekino, T. 259 Kotani, T. 44 KOllar. A.• see Gratz. E. 317 Koyanagi, A. 346 Krajewski, lJ.. see Carter. SA 202, 205. 224 Krajewski, lJ.. see Cava, RJ. 202, 205. 220. 223. 240,242,283
Krajewski. lJ.. see Eisaki, H. 231, 240 Krajewski, Ll., see Grigereit, T.E. 205 Krajewski, r.r, see Lynn, J.w. 213. 215. 249. 252 Krajewski, r.r., see Siegrist, T. 218. 246. 247, 251. 253.270,335
AUTHOR INDEX Krajewski, 1.1., see Takagi, H. 215, 230, 241 Krajewski, 1.1., see Zandbergen, H.W. 219, 220, 242,266 Kramer, U., see Behr, G. 225 Kramers, H.A. 265 Kratzer, A., see Frey, E. 315, 320 Kraus, L. 109, III Krause, A., see Wagner, T.A. 231, 285 Krause, E, see Berger, R. 188 Krause-Rehberg, R., see Luysberg, M. 7, 33 Krebs, 1.1. 18 Kreisel, 1. 18 Kreitzman, S.R., see Luke, G.M. 212 Kremer, R.K., see Bernhard, e. 213 Kremer, R.K., see Gulden, Th. 219, 224 Kremer, R.K., see Henn, R.W. 238 Kremer, R.K., see Simon, A. 227 Krendelsberger, R., see Michor, H. 223, 279, 288 Kresse, G., sa Lindbaum, A. 345 Kreyssig, A. 205, 221, 222, 262 Kreyssig, A., see Dertinger, A. 216, 217, 264, 266 Kreyssig, A., see Drechsler, S.-L. 228, 229, 234 Kreyssig, A., see Freudenberger, 1. 219, 224, 225, 236,237,266,279,287 Kreyssig, A., see Loewenhaupt, M. 273 Kreyssig, A., see Muller, K.-H. 250, 256 Krikorian, N.H., see Giorgi, A.L. 226 Krikorian, N.H., see Krupka, M.C. 205 Krishnan, R., see Szymczak, H. 151 Krishnan, R., see Zuberek, R. III, 151 Krol, A. 17 Krolas, K., see Rams, M. 221 Kronmllller, H., see Farber, P. 133, 139, 140, 145, 147, 148, 158 Kronmilller, H., see Fischer, S.E 139, 140 Kronmilller, 1-1., see Hofmann, B. 136 Kronrnuller, H., see Riedi, K. 118, 133,135, 136 Kronmilller, H., see Schatz, E 118, 130, 131, 133, 135 Kronmuller, H., see Winzek, B. 137-139 Krug, K., see Drechsler, S.-L. 234 Krug, K., see Peng, Z.Q. 209 Krug, K., see Shulga, S.V. 233, 241, 281 Krug, K., see Winzer, K. 234 Krug von Nidda, H.-A., see Heimbrodt, W. 10 Kruk, R., see Bialic, D. 328, 356 Krupka, M.e. 205 Krupka, M.e., see Giorgi, A.L. 226 Ku, H.C. 205. 219, 220,284,285 Ku, H.C., see Hsu, Y.Y. 209,210 Ku, H.C., see liang, P.1. 226 Ku, H.C., see Lai, c.c. 276 Ku, H.C., see Lin, M.S. 205 Ku, K.C., see Potashnik, S.1. 5, 9, 34, 50, 56, 77
383
Kubert, C. 270, 271 Kubo, T., see Ofuchi, H. 17 Kuboya, K., see Takanaka, K. 219, 226 Kuijpers, EA., see van Vucht,l.H.N. 322 Kuivalainen, P. 32, 70 Kulatov, E. 43 xeue, M.L., see Bulaevskii, L.N. 226 Kumai, R., see Kuwahara, H. 178 Kumakura, H., see Arisawa, S. 219 Kumiski, M., see Twarowski, K. 170 Kunimoto, T., see Nagai, Y. 37,49 Kunkel, H.P., see Stampe, P.A. 324 Kurochkin, L., see Tomilo, Zh. 219, 220, 226 Kuroiwa, T. 38, 39 Kuroiwa, T., see Shen, A. 7-9, 11,25,36,54,57, 58,61,62 Kuroiwa, T., see Sugawara, Y. 32 Kusz, 1. 352-354, 356 Kusz, 1., see larosz,l 326, 327, 357 Kutner-Pielaszek, 1., see Kepa, H. 66 Kuwabara, S. 13, 14 Kuwabara, S., see Soo, Y.L. 13 Kuwahara, H. 178 Kuwahara, H., see Hayashi, T. 176 Kwak, r.r, see Jones, T.E. 218, 221 Kwok, W.K., see Dunlap, B.D. 212 Kwok, wx., see Williams,l.M. 209 Kwon, S.K., see Park, 1.H. 44, 45 Laabs, ED., see Vinnikov, L.Ya. 260, 264 Lacerda, A. 205, 217, 220, 251, 289 Lacerda, A., see Canfield, P.C. 215 Lacerda, A.H., see Beyermann, W.P. 270 Lacerda, A.H., see Christianson, A.D. 236 Lacerda, A.H., see Schmiedeshoff, G.M. 205, 206, 230 Lacerda, A.H., see Yatskar, A. 272 Lachovicz, H.K. 109 Lachowicz, H.K., see Slawska-Waniewska, A. 169 Lachowicz, H.K., see Twarowski, K. 170 Lafford, A. 156 Lai, C.C. 276 Lai, C.C., see Ku, H.e. 284, 285 Lamelas, F.1., see Lee, CH, 113 Lampalzer, M., see Hartmann, Th. 10 Lampalzer, M., see Heimbrodt, W. 10 Landau, L.D., see Ginzburg, V.L. 210 Lang, lL., see Song, C. 284, 285 Lang, M., see Steglich, F. 242 Langousche, G., see Wahl, U. 14 Lanoue, L., see Iannotti, V. 106 Lappas, A., see Prassides, K. 231, 240 Larkin, A.I. 227, 228
384
AUTHOR INDEX
Latroche, M. 317 Latroche, M., see Gratz, E. 317 Latroche, M., see Mazumdar, Ch. 234, 235 Lawrie, D.D. 241 Le, L.P. 235 Le, L.P., see Luke, G.M. 212 Le Gall, H. lll, 143, 147, 148 Le Gall, H., see Due, N.H. 168 Le Letty, R., see Claeyssen, F. 185, 187, 188 Lebedev, S.P., see Mukhin, A.A. 181 Lebenbaum, D., see Kaplan. N. 316, 357 LeBihan, T., see Lindbaum, A. 345 Lee, B.49, 54,60, 74 Lee, B.H., see Jungwirth, T. 49, 53, 55, 60, 66, 74 Lee, C.H. 113 Lee, E., see Sala, R. 243 Lee, E.W., see Burd, J. 316, 357 Lee.I.H., see Choi, C.K. 262 Lee, 1.1. 205 Lee, 1.0., see Cava, R.I. 202, 205, 220, 223, 240, 242 Lee, 1.0., see Eisaki, H. 231, 240 Lee, 1.0., see Takagi, H. 215, 230, 241 Lee, K.H. 276, 288 Lee, M., see Lee, K.H. 276, 288 Lee, S.-I., see Cho, BK 278 Lee, S.-I., see Choi, 1.-H. 266 Lee, S.-I., see Yang, I.-S. 229 Lee, S.I., see Lee, K.H. 276, 288 Lee, S.I., see Mun, M.a. 216, 217, 230 Lee, S.L., see Cywinski, R. 207 Lee, S.L., see Paul, D. MeK. 258, 269, 276 Lee, S.R., see Lim, S.H. 132, 133 Lee. W.C.,see Mun, M.a. 216, 217. 230 Lee, W.H. 205, 251, 276 Lees, M.R., see Garda-Landa, B. 176, 177, 182 Lees, M.R., see Tomy, C.V. 256, 258, 259 M. 13 Lefeld-Sosnowska, M., see Zaj~, Legvold, S., see Nigh, H.E. 320 Leja~~279,280,283,284
Lejay, P., see Brison, 1.P. 220, 283 Lenezowski, SKJ., see Brabers, 1.H.V.J. 272 Leroux-Hugon, P. 36,51 Leroy, E., see Alieno, E. 225, 226, 260, 263, 264 Lethuillier, P., see Bouvier, M. 310 Letoublon, A., see Song, C. 284, 285 Levin, E.M. 336 Levin, K. 235 Levin, K., see Nass, M.J. 258 Levitin. R.Z .• see Borombaev, M.K. 346, 348. 349 Levy-Clement, c., see Godart, C. 218 Levy-Clement, C., see Gupta, t,c. 216, 288 Levy-Clement, C., see Hossain, Z. 219 Levy-Clement, C., see Mazumdar, Ch. 234, 235
Lhermet, N., see Claeyssen, F. 185, 187, 188 Lhermet, N., see Halstrup, B. 187 Lhotel, E., see Aoki, D. 214 Li, H.S., see Gavigan, 1.P. 123 Li. S., see Rathnayaka, K.D.D. 227, 278 Li, Y., see Rukang, L. 221 Li, Y.X., see Wang, B.W. 94 Lieber. C.M., see Eskildsen, M.R. 267, 269. 276 Lienard, A., see Chappert, J. 116 Lienard, A., see Coey, 1.M.D. 126 Lienard,A.• seeDue,N.H.94,1l7-119,126. 131-133 Lifshits, I.M. 258 Liliental-Weber, Z., see Luysberg, M. 7, 33 Lim, S.H. 132, 133, 142 Lim, S.H., see Pasquale, M. 119 Lin, C.L. 318 Lin, C.L., see Jee, C.S. 323, 357 Lin, H.-H., see Konig, 1. 54, 55, 61, 71 Lin, H.-H., see Sehliemann, 1. 61 Lin, M.S. 205 Lin, M.S., see Jiang, P.J. 226 Lin, M.S., see Lai, c.c. 276 Lin, S.H., see Lin, M.S. 205 Lindbaurn, A. 312, 317, 345 Lindbaurn, A., see Andreev, A. 325, 327, 356 Lindbaum, A., see Gratz, E. 309. 317, 325. 329, 341,346-348,356,357 Lindbaum, A., see Rotter, M. 310, 314, 344, 346-350,356 Linnarson, M. 19 Lipatnikov, V.N., see Gusev, A.I. 219 Lipp, D. 226, 283 Lipp, D., see Belger, A. 335 Lipp, D., see Drechsler. S.-L. 228, 229, 234 Lips, von H. 260-262 Lister, S.J.S., see Boothroyd, A.T.223 Litfin, K., see Lindbaum, A. 345 Litterst, F.J., see Sanchez, D.R. 226, 266 Littlewood, P., see Saxena, S.S. 216, 217 Litvinov, V.1. 48 Litvinov, V.I., see Eggenkamp, P.T.J. 60 Liu, H.C., see Shen, A. 9, 15, 16 Liu, J.P. 123 Liu, S. 37 Liu, X. 5, 26 Liu, X., see Baxter, D.V. 32 Liu, X., see Chen, X. 10 Liu, X.c. 19 Liu, Z.X., see Wang, J.H. 176 Lloyd, S.H., see Paul, D. MeK. 258, 269, 276 Locquet, J.P., see Berger. R. 188 Loewenhaupt, M. 273
AUTHOR INDEX Loewenhaupt, M.• see Derringer, A. 216. 217. 264. 266 Loewenhaupt. M.• see Doerr. M. 335 Loewenhaupt, M.• see Drechsler. S.-L. 234 Loewenhaupt, M.• see Freudenberger, 1. 219. 224, 225.236.237,279 Loewenhaupt, M.. see Kreyssig, A. 205,221,222. 262 Loewenhaupt, M.• see Muller, K.-H. 250. 256 Loewenhaupt, M.• see Rotter, M. 223, 310. 311, 314,344.346-350.356 Loewenhaupt, M.• see Sierks, C. 275 Loewenhaupt. M.• see Svoboda, P. 345 Lofgreen, D.• see Johnston-Halperin, E. 71 Lohneysen, H. von. see Gaymann, A. 37 Lohneysen, H. von. see Pfleiderer.C. 226. 237 Loidl, A.• see Heimbrodt, W. 10 Loidl, A.• see Mukhin, A.A. 181 London. F. 216 London. H.• see London. F. 216 Lonzarich, G.G.• see Brison. J.P. 220. 283 Lonzarich, G.G.• see Pfleiderer, C. 226. 237 Lonzarich, G.G., see Saxena, S.S. 209 Look. D.C. 7 Looney. C. 208 Loong. C.-K.• see Sierks, C. 275 Lopez. D.• see Choi, S.-M. 271 Lopez. D., see Eskildsen, M.R. 273, 274 Lopez, D., see Gammel, P.L. 223 Lopez. D., see Gammel. P.L. 273 LOpez, D., see Gammel, P.L. 279 Lorberth, L., see Hartmann. Th. 10 Lord, D.G., see Grundy, PJ. 117 Lord, D.G.• see Williams. P.I. 119. 122. 133 LOser. W.. see Behr, G. 219, 225 LOser. w., see Bitterlich, H. 210. 287, 288 Loser, W., see Drechsler, S.-L. 229 Loss, 0.79 Lottermoser, L., see Song, C. 273. 276 Louriero da Silva 62 Lozovan, M.. see Chiriaco H. 169 Lubitz, P.• see Forester. D.W. 117 Ludescher, B., see Riedi. K. 118, 133. 135, 136 Ludwig, A. 129. 143. 145-147. 149, 154. 185 Ludwig. A., see Quandt. E. 94, 103, 119. 133. 141, 142. 144. 149. 150, 157, 158, 166. 188 Luke. G.M. 212 Luong. N.H. 346 Lupien. C.• see Boaknin, E. 238. 239. 241. 279. 285 Luysberg, M. 7, 33 Lynn, J.W. 209, 211, 213, 215. 216, 220, 226, 242, 244.245,247-249.252,253.256,276,278, 289.335
385
Lynn. J.W.• see Bourdarot, F.218 Lynn. J.W.• see Choi, S.-M. 271 Lynn, J.W.• see Femandez-Baca, J.A. 21 I Lynn, is«. see Godart. C. 220, 242. 260 Lynn, J.w.. see Grigereit, T.E. 205 Lynn. J.w.. see Sinha, S.K. 213 Lynn, J.w., see Skanthakumar, S. 221, 241. 242. 245,252,268 Lynn, 1.w., see Stanley. H.B. 218 Lynn, J.W., see Thomlinson, W. 234 Lyu,P.67 Ma, S.-K. 50 Ma. S.-K., see Fisher, M.E. 61 Mac, W.19 Mac, W.• see Szczytko, 1. 38.40,41,47,50 MacCarthy, K.T., see Overberg, M.E. 13 MacDolnald, A.H., see Jungwirth, T. 49, 53, 55, 60,66,74 MacDonald, A.H., see Abolfath, M. 25, 49, 52, 54, 55,57.58 MacDonald. A.H., see Dietl, T. 49, 59 MacDonald, A.H., see Jungwinh, T. 27 MacDonald, A.H., see Konig. J. 54. 55,61,71 MacDonald, A.H., see Lee. B. 49. 54, 60, 74 MacDonald, A.H., see Schliemann, J. 61 Machida, K. 206. 211. 266 Machida, K.• see Nakai, N. 236 Mackay. K., see Bell, J. 94, 120, 121, 133 Mackay, K., see du Tremolet de Lacheisserie, E. 186 Mackay, K., see Due, N.H. 94, 103. 119, 123-127, 129, 130, 133 Mackay, K., see Givord, D. 120. 133, 141, 163, 165 Mackay, K.• see Halstrup, B. 187 Mackay, K., see Orsier, E. 188 Mackay, K., see Quandt, E. 94, 141, 157. 158, 188 Mackintosh. A.R., see Jensen, J. 312, 314 MacLaughlin, D.E., see Le. L.P. 235 MacMorrow,D.F., see Swaddling. P.P. 159 Magnea, N.• see Baron. T. 5 Mahadevan, P. 78 Mahendiran, R., see Ibarra, M.R. 184. 185 Maignan, A. 179 Maignan, A., see Respaud, M. 179 Mailhiot, C. 208 Malta, J.P., see Matthias. B.T. 202 Majewski, J.A.• see B1inowski, J. 47, 51. 76 Majkrzak, C.F., see Kepa, H. 66 Majumdar. P., see Ye,J. 27 Mfu. F., see Makk, 1. 29, 33 Makarova, T.L. 286
386
AUTHOR INDEX
Makhija, A.V., see Rosseinsky, M.J. 209 Maki, K. 240, 281, 282
Maki, K., see Izawa, K. 260 Maki, K., see Shiraishi, 1. 272 Maki, K., see Wang. G.-E 238 Maki, K., see Won, H. 284 Makino, A. 169 Makino, A., see Suzuki, K. 168 Malajovich, I. 79 Malajovich, I.• see Beschoten, B. 41, 47 Malajovich, I., see Kawakami, R.K. 75 Malik, S.K., see Dunlap, B.D. 212,256 Mallik, R. 310 Malli)(, Roo see Paulose, P.L. 340 Manago, T., see Akinaga, H. 13, 78 Manalo, S. 236, 237 Manalo, S., see Michor, H. 274 Mandai. P. 205, 208, 211 Manfrinetti, P., see Cimberle, M.R. 227 Manini, P., see Andreone, A. 219 Mano, T.• see Okabayashi, 1. 21 Mano, T., see Yamada, M. 13 Mantler, M., see Gratz, E. 317 Mao, H.-K., see Eremets, M.I. 274, 276 Maple, M.B. 215, 230 Maple, M.B., see Bauer, E.D. 214 Maple. M.B., see Fertig, W.A. 205 Maple, M.B., see Fischer, 0. 208, 212, 216 Maple, M.B., see Luke, G.M. 212 Maple, M.B., see Rathnayaka, K.D.D. 227, 278 Maple, M.B., see Sarrao, 1.L. 205 Maple, M.B., see Zandbergen, H.W. 223 Maranowski, K.D., see Harris, 1.G.E. 26 Marchevsky, M.• see Saha, N. 225 Mariette. H., see Kulatov, E. 43 Marin. P. 185 Marinescu, C.S.• see Chiriaco H. 169. 185 Markert.l.T., see Luke. G.M. 212 Markosyan. AS., see Borombaev, M.K. 346, 348,
349,351,356 Marques, G.E., see Rodrigues Bitterncourt, A.C.
69 Marquina, C; see Blanco, 1.A 342, 343, 356 Marquina, C.• see de Teresa, J.M. 176, 178 Marquina, C.• see Garda-Landa, B. 182 Marquina, C., see Ibarra, M.R. 175, 176, 184, 185 Marre. D., see Cimberle, M.R. 227 Martin. C., see Maignan, A. 179 Martin. C .• see Respaud, M. 179 Martin, 1.M., see Tomy, C. V. 206, 258 Martino, L., see Pasquale, M. 119 Martynovich, A., see Kogan. V.G. 273 Maruyama, K., see Novosad. V. 189. 190
Masek, 1.29,33
Maska, M.M. 216, 217 Massalami, M. 335 Masterov, V.E 19 Mastukura, E, see Beschoten, B. 41, 47 Masumoto, T., see Makino, A. 169 Masumoto, T., see Ohnuma, S. 173, 174, 189 Masumoto, T., see Suzuki, K. 168 Matheny. A., see Beach, R.S. 159 Mathieu, P., see Sadowski, 1. 9. 16,77 Mathieu, R. 175 Mathieu, R., see Sadowski. 1. 62 Matsuba, K., see Sakata. H. 271 Matsubara, T., see Machida, K. 206, 211, 266 Matsuda, N. 210 Matsuda, N., see Oomi, G. 216, 217 Matsuda, Y., see Izawa, K. 240, 260. 285 Matsuda, Y.H. 37, 38
Matsukura, E 7, 9,21,29,30,48-50,55.56,63 Matsukura, E, see Abe, E. 14, 15,71 Matsukura, E, see Akiba, N. 65,68.69 Matsukura, F., see Ando, M. 38 Matsukura, E, see Arata, I. 47, 63 Matsukura, E, see Chiba, D. 65, 66 Matsukura, E, see Dietl, T. 23, 25.29,40,41.47, 49-58,73-75,77 Matsukura, E, see Fukurnura, T. 26 Matsukura, E, see Guo. S.P. 7,10 Matsukura,E, see Harris, J.G.E. 26 Matsukura, E, see Katsumoto, S. 31, 49 Matsukura, E, see Kuroiwa, T. 38, 39 Matsukura, F., see Matsuda. Y.". 37, 38 Matsukura, E, see Nagai, Y. 37,49 Matsukura, E, see Nojiri, H. 19 Matsukura, E, see Ofuchi, H. 17 Matsukura, F.. see Ohldag, H. 20, 44, 45, 50 Matsukura, E, see Ohno, H. 5,15-17,22,24-26, 28,54,55,57,58,68,69,74 Matsukura, E, see Ohno, Y. 63, 64, 70, 71, 73 Matsukura, Foo see Oiwa, A. 20-23, 31.49, 50. 55 Matsukura, E, see Omiya,T. 10,30-33,47,55 Matsukura, E, see Shen, A. 7-9, II, 15, 16,25. 36,54,57,58,61,62 Matsukura, E, see Shono, T. 26, 58, 59 Matsukura, E. see Sugawara, Y. 32 Matsukura, F.. see Szczytko, 1. 38,40,41.47.50 Matsukura, E, see Takamura, K. 7 Matsukura, E, see Tsuruoka, T. 18 Matsukura, E. see Ueda, S. 44 Matsukura, E, see Yang, 1. 9 Matsukura, E. see Zhao, 1.H. 10 Matsumoto, H. 227, 228. 230 Matsumoto, Y. 78 Matsumura, Y., see Wada, M. 122
AUTHOR INDEX Mattausch, H.• see Simon. A. 227 Manenberger, K.• see Kobler, U. 309 Mattheiss, L.F. 208, 227. 242. 247, 251. 253 Matthias, B.T. 202. 205, 209, 213 Matthias. B.T., see Fertig, W.A. 205 Mattis, D.C., see Methfessel, S. 4 Mattson, J.E., see Park, Y.D.74 Maude, D.• see Sadowski, 1. 9 Mauger, A.4 Mauri. D., see Dieny, B. 110. 163 Mazin, 1.1., see Kortus, J. 244 Mazumdar, c.. see Godart, C. 218 Mazumdar, c., see Tominez, E. 220. 242 Mazurndar, Ch. 229. 234, 235. 270 Mazumdar, Ch., see Gupta. t.c, 216, 288 Mazumdar, Ch.• see Hossain. Z. 219 Mazumdar, Ch .• see Jacobs. T. 216 Mazumdar. Ch .• see Nagarajan, R. 216, 225.242, 253,288 McAlister. S.P. 323, 324 McCallum. R.W.• see Fertig, W.A. 205 McCombe, B.D., see Chen. X. 10 McConnack. M., see Jin, S. 175 McEwen. K.A. 320 McGrath, O.F.K.• see du Tremolet de Lacheisserie, E. 105 McIntyre, GJ.. see Campbell. A.J. 220. 242. 259. 267 McK Paul, D,. see Garcia-Landa, B. 182 McKinstry. H.A., see Taylor. R.E. 311 McKinstry. ST.• see Taylor, R.E. 311 McMahan, A.K.• see Mailhiot, C. 208 McMillan, W.L. 216. 217 McMorrow, D.F., see Jehan, D.A. 159 Mean. B.J.• see Lee, K.H. 276, 288 Medvedkin, G.A. 77 Meenakshi, S. 216. 217, 243 Megges, K.• see Hartmann, Th. 10 Meiklejohn, W.H. 230. 231, 234, 241 Mencik, J.• see Quandt, E. 94, 141, 157 Meng, R.L., see Gao. L. 245, 269, 270 Meng, R.L., see we, M.K. 208 Menovsky, A.• see Mulders, A.M. 322, 357 Mergel. D. 96 Merle d'Aubigne, Y., see Dietl, T. 47-49. 53, 54, 74 Merle d' Aubigne, Y..see Haury. A. 5, 49, 54 Merle d' Aubigne, Y.. see Kossacki, P. 49, 74 Merlo, F. 326, 357 Mesot, J.• see Gasser, U. 222, 241 Methfessel, S. 4, 72 Methfessel, S.J. 72 Metlushko, V. 240 Metlushko, v., see de Wilde, Y. 266, 277
387
Meyer. J.R., see Vurgaftman. I. 62 Michor, H. 223, 224, 274. 279, 287. 288 Michor, H.• see El-Hagary, M. 232. 245. 253. 287 Michor, H., see Gratz, E. 317 Michor, H., see Hilscher. G. 229 Michor, H.• see Javorsky, P. 325-327 Michor, H., see Rotter. M. 310, 314 Michor, M.• see Divis, M. 242 Michor, M., see Manalo. S. 236. 237 Michurin, AV.. see Abramovich, AI. 178. 179 Micklitz, H., see Baggio-Saitovitch, E.M. 223, 224,243 Micklitz, H., see Sanchez. D.R. 256 Mielke, C.H.• see Yatskar, A 272 Mierzejewski, M., see Maska, M.M. 216. 217 Mihalisin, T.• see Jee, C.S. 323. 357 Mihalisin, T., see Lin, c.L. 318 Miiller. A.P.. see Taylor. R.E. 311 Milke. C.H., see Baxter, D.V. 32 MiJlerJr.•1.H.• see Chu, R.K. 219 Miller, L.L., see Cho. B.K. 242, 245. 249, 256, 257,267 Millis. AJ.• see Chattopadhyay, A. 60 Millis, A.J., see Ye,J. 27 Min. B.I.• see Lee. J.1. 205 Min, B.I.. see Park. 1.H. 44. 45 Mineev, Y.P., see Barash. Y.S. 284. 285 Ming, Z.H.• see Krol, A. 17 Ming, Z.H .• see Soo, Y.L. 17 Miotkowski, I.. see G16
388
AUTHOR INDEX
Mochiku, T.. see Arisawa, S. 219 Medler, R.• see Steglich, F. 242 Molchan. P.. see Tomilo. Zh. 219. 220. 226 Molchan. P.V.• see Tomilo, Zh.M. 205. 220. 224 Molenkamp. L.W.• see Fiederling, R. 70 Molenkamp, L.W.. see Schott, G.M. 5. 7.16 Molins, E.• see Slawska-Waniewska. A. 170 Moncton. D.E.• see Lynn. 1.W.211 Moncton. D.E.• see Thomlinson. W. 234 Mondragon. 1.. see Bud·ko. S.L. 216. 217 Mondragon. 1.. see EI Massalami, M. 242 Mcnemar, B.• see Linnarson, M. 19 Monthoux, P.• see Saxena. S.S. 209 Mook. H.A.• see Paul. D. McK. 272. 274 Moon. K.• see Lyu, P. 67 Mooney. K.P.• see Chen. X. 10 Mor, T.• see Vrijen, R. 79 Moreau. J.M.• see Roy. J.L. 342 Morellon, L. 309. 336-339. 356. 358 Morhange, 1.-F.. see Szuszkiewicz, W. 66 Mori. N.• see Murayama, C. 216 Mori. N.• see Uehara. M. 216. 217. 264 Morin.~94.256.310.312.319
Morin. P.• see Gignoux, D. 329. 330. 356 Morin. P.• see Rouchy, J. 319, 358 Morita, H.• see Fujimori, H. 120 Moriya, R. 12 Moriya, R.. see Oiwa, A. 73 Moriya, T. 211. 213.288 Morosov, A.I. 242. 269 Morotomo, Y. see Kuwahara. H. 178 Morozov, A.I. 288 Mortensen. K., see Eskildsen. M.R. 265. 267. 269. 273-276 Mortensen. K.• see Gammel, P.L. 223. 267. 277. 279 Mortensen, K.• see Yaron. U. 242. 248. 249. 251. 270.271 Mostoller. M., see Paul, D. McK. 272, 274 Motokawa, M.• see Akiba, N. 65. 68 Motokawa, M.• see Nagai. Y 37. 49 Motokawa, M.• see Nojiri, H. 19 Motokawa, M.• see Omiya, T. 30-33. 47. 55 Motome, Y.• see Nakano. H. 175 Movshovich, R. 265. 266 Mryasov, O.N.• see van Schlifgaarde, M. 29. 44 Much. G., see Hansen, P. 115.117 Mueller. R.M.• see KObler. U. 309, 315 Mukhin, A.A. 181 Mukhin. A.A.• see Kadomtseva, A.M. 180 Mukin. A.A.• see Popov. Yu. E 179. 180 Mulder. EM. 269 Mulders. A.M. 275. 322. 357 Mulders, A.M., see Gasser, U. 245
Mulders. A.M., see Yaouanc, A. 322 Muller, H.• see Gratz. E. 317 Muller, H.. see Rotter, M. 311. 344. 346-350, 356 Muller. J., see Ishikawa, M. 285 Muller. K.-H. 209. 216. 250. 256. 263 Muller. K.-H., see Bitterlich, H. 210. 287. 288 Muller. K.-H.• see Drechsler. S.-L. 228. 229. 234 Muller. K.-H.• see Eversmann, K. 216 Muller. K.-H.• see Freudenberger, J. 219. 224. 225,233.234.236,237.241,266,279,280. 284,287-289 Muller, K.-H.. see Fuchs. G. 209 Muller. K.-H.• see Kreyssig, A. 205. 221. 222. 262 Muller. K.-H.• see Lipp, D. 226. 283 Muller, K.-H.. see Loewenhaupt, M. 273 Muller. K.-H.• see Lynn, J.w. 216 Muller. K.-H.• see Narozhnyi, Y.N. 213. 236, 237, 248-252.271,276.288 Muller, K.-H.• see Shulga, S.V. 233. 241, 281 Muller. K.-H.• see Sierks, C. 275 MUller. K.A.• see Bednorz, J.G. 207 Muller, M.• see Schmidt, H. 263 Muller-Hartman. E. 219, 221. 255 Mun, M.O. 216. 217. 230 Munekara, H.• see Soo, YL. 12. 13 Munekata, H. 5. 6.10-12,17.36.57.58 Munekata, H.• see Endo, T. 10 Munekata, H.• see Fumagalli, P. 36. 40 Munekata, H.• see Guha, S. 10 Munekata, H.• see Haneda, S. 5. 12. 16 Munekata, H.• see Hirakawa. K. 37 Munekata, H.• see Koshihara, S. 72 Munekata, H.• see Krol, A. 17 Munekata, H.• see Kuwahara, S. 13. 14 Munekata, H.• see Matsuda, Y.H.38 Munekata, H.. see Moriya, R. 12 Munekata, H.. see Ohno, H. 5. 10. 11.32.34,35 Munekata, H., see Oiwa, A. 22, 36. 73 Munekata, H.. see Slupinski, T. 10. 36 Munekata, H., see Soo, Y.L. 17 Munekata, H.• see Szczytko, 1. 19 Munekata, H.• see von Molnar, S. 34 Munekata, H.• see Yanagi, S. 66 Murakami. M.• see Matsumoto. Y.78 Murakami. T.. see Luke, G.M. 212 Muranaka, T.• see Nagamatsu, J. 202. 203 Murayama, C. 216 Murday, 1.S.. see Wandass, J.H. 106 Murdoch.J.205.207 Murillo. N.• see Zuberek, R. 173 Murphy. C.B.• see Pinkerton, EE. 168. 173 Murphy. D.W., see Rosseinsky, MJ. 209 Muto, T.• see Ueda, S. 44
AUTHORINDEX Mydlarz, T.• see Jarosz. J. 326. 327. 357 MydIarz. T.• see Stalinski, B. 318. 357 Mydosh. J.A.. see Davidov,D. 216 Mydosh. lA.. see HUser. D. 244 Mydosh, J.A.• see Nieuwenhuys, GJ. 231. 280. 283.284 Myzenkova, L.P.. see Savitskii, E.M. 214 Nabarro, F.R.N.• see Frolich, H. 48 Naber. L.• see Michor, H. 223. 224. 279 Nabialek, A.• see Troyanchuk, 1.0. 184 Nabialek, A.. see Zuberek, R. III. 156 Nagai. Y. 37.49 Nagamatsu, J. 202. 203 Nagarniya,T. 318 Nagarajan, R. 216. 225, 242. 253, 269. 285. 288 Nagarajan. R., see Alieno. E. 242, 246 Nagarajan. R.. see Bonville. P. 213. 270 Nagarajan, R.• see Chinchure, A.D. 220. 242, 249. 258 Nagarajan, R.• see Dhar, S.K. 227, 240-242, 251 Nagarajan, R.• see Ghosh. G. 230 Nagarajan, R.• see Godart. C. 218. 220, 242. 260 Nagarajan, R., see Gupta, L.C. 216, 288 Nagarajan, R., see Hossain. Z. 205, 219. 220. 223. 242.248-250.253.271,288 Nagarajan, R.• see Jacobs. T. 216 Nagarajan, R.• see Lynn. J.w. 213. 220. 289. 335 Nagarajan, R.• see Mazumdar, Ch. 234. 235. 270 Nagarajan, R.• see Meenakshi, S. 216. 217, 243 Nagarajan, R.• see Rams. M. 221 Nagarajan, R.• see Sanchez, lP. 219, 220, 224. 225 Nagarajan, R.• see Sinha. S.K. 213 Nagarajan. v.; see Paulose, P.L. 340 Nagasaka, K.• see Nagai. Y. 37.49 Nagashima, A.• see Hazama, Y. 79 Nagashima, A.• see Okazawa, 0.13 Nagashima, A.• see Tazima, M. 7. 9 Nagata, T.• see Uehara. M. 216, 217. 264 Nagi, Y. 151 Nakagawa. N.. see Nagamatsu, J. 202. 203 Nakai. N. 236 Nakajima. M., see Kanamura, M. 73 Nakajima, Y.•.fee Izawa, K. 260 Nakamura. K.• see Arisawa, S. 219 Nakamura, K.• see Okabayashi, J, 21 Nakano. H. 175 Nakano. Y.,see Shimizu. H. 41 Nakata. K., see Akiba, N. 65 Nakayama. H.• see Kulatov, E. 43 Nakazoe, S.• see Okabayashi, J. 21 Nakotte. H.• see Brabers, J.H.VJ. 272 Nan. C.-W. 173
389
Narita, K. 108 Narozhnyi, V.N. 213. 235-238. 248-252. 271. 276.288 Narozhnyi, V.N., see Drechsler. S.-L. 234 Narozhnyi, V.N.• see Freudenberger, l 289 Narozhnyi, V.N.• see Fuchs. G. 209 Narozhnyi, V.N.• see Lynn. J.W. 216 Narozhnyi, V.N., see MUlier. K.-H. 209. 216. 263 Nass, MJ. 258 Nass, MJ.• see Levin. K. 235 Naugle, D.G. 216. 240. 266 Naugle, D.G., see Du Mar. A.C. 212 Naugle. D.G.• see Eskildsen, M.R. 269 Naugle. D.G.• see Hennings, B.D. 260 Naugle. D.G.• see Rathnayaka, K.D.D. 227, 230. 234.235.271.278 Navaro, 0., see Le Gall, H. III Ndjaka, J.M.• see Dieny, B. 163 Neagu, M.• see Chiriaco H. 168. 169 Neagu, M.• see Hristoforou, E. 106 Neel, L. 105 Nemeth. S.. see Akinaga, H. 14 Nemeth. S.• see Ofuchi, H. 14 Nenkov, K.• see Behr,G. 225 Nenkov, K.• see Bitterlich, H. 210. 287. 288 Nenkov, K.• see Drechsler. S.-L. 228. 229 Nenkov, K.. see Freudenberger.J. 219. 224. 225. 236.237.266.279.287.288 Nenkov, K.. see Fuchs. G. 209 Nenkov, K.• see Lipp, D. 226. 283 Nenkov, K.• see MUlier. K.-H. 209. 216 Nenkov, K.• see Narozhnyi, V.N. 248-252. 276. 288 Nenkov, K.A.. see Freudenberger; J. 289 Nenkov, K.A.• see Narozhnyi, V.N.213. 236. 237. 248.251.252.271 Neumann. K.U.• see Parsons. MJ. 318, 357 Neumann. K.U.• see Taylor.J.W. 318. 357 Neumann, M., see Talik. E. 352. 356 Neumeier. U .. see AlIeno, E. 216. 217 Ng, T.K. 210 Nguyen. L., see oeu G. 230 Niarchos, D.• see Speliotis, A. 119 Nickel. B.G.• see Fisher. M.E. 61 Niedermayer, Ch., see Bernhard. C. 213 Niedermayer, Ch.• see Henn, R.W. 238 Nieuwenhuys. GJ. 231. 280. 283, 284 Nieuwenhuys. GJ.• see Davidov, D. 216 Nieuwenhuys, G.J.• see EI Massalami. M. 219. 220,223.242.247 Nieuwenhuys, GJ.• see HUser. D. 244 Nieuwenhuys, GJ.• see Le, L.P. 235 Nieuwenhuys, GJ.• see Saba, N. 225 Nigam. A.K.• see Mazumdar, Ch. 270
390
AVTHORINDEX
Nigh, H.E. 320 Nikitin, SA, see Belov, K.P. 126 Nikitin, S.A., see Bodriakov, V.Y. 321 Nishi, T., see Medvedkin, G.A. 77 Nishida, N., see Sakata, H. 271 Nishihara, Y., see Zou, Z. 211, 213, 288 Nishikawa, N., see Satoh, Y. 9, 24 Nishikawa, Y.5 Nishinaga, T., see Hayashi, T. 5, 62, 63 Nishinaga, T., see Shimizu, H. 7,16,34,55 Nishizawa, K., see Sakai, O. 37, 61 Niu, Q., see Jungwirth, T. 27 Noakes, D.R., see Bernhard, C. 213 Noda, K., see Hayashi, T. 176 Noel, H., see Godart, C. 218 Noh, T.H., see Lim, S.H. 132, 133
Nohara, M. 268, 269, 279, 283-285 Nohara, M., see Izawa, K. 260 Nohara, Mo, see Takagi, H. 231 Nohara, M, see Yokoya, T. 243 Nojiri, H. 19 Nojiri, H., see Nagai, Y. 37,49 Nokura, K., see Machida, K. 206, 211, 266 Nold, E., see Quandt, E. 94,141, 157 Nonoyama, S. 70 Nonoyama, S., see Inoue, J. 48, 70 Nordblad, P., see Mathieu, R. 175 Nergaard, K. 225 Novak, M.A., see El Massalami, M. 205, 206 Novikov, D.L., see Shick, A.B. 105 Novo, J.M., see Hernando, A. 309 Novosad, V. 189, 190 Nowak, W.B., see Bushnell, S.E. III Nowicki, P.,see Slawska-Waniewska, A. 169-171 Nys, J.P., see Grandidier, B. 18 O'Bryan, H.M., see Jin, S. 175 Obukhov, S.A. 15 Obukhov, S.A., see Henriques, A.B. 15 O'Donovan, K.V. 159 Oesterholt, R., see de Boeck, J. 5, 9 Oesterreicher, H. 328
Ofuchi, H. 14, 17 Ofuchi, H., see Akinaga, H. 14 Ogawa, T. 17,42,43 Ogawa, To, see Shirai, M. 17,41 Oguchi, T., see Yokoya, T. 243 Oguchi, T., see Zhao, Y.-J. 78 O'Handley, R.C. 105, 109 O'Handley, R.C., see Bochi, G. 113 O'Handley, R.C., see Sun, S.w. 112, 152 Ohashi, M. 329 Ohashi, M., see Yamauchi, H. 231
Ohki, A., see Shibata, N. 5 Ohldag, H. 20,44, 45, 50 Ohno, H. 5, 9-11,15-17,22.24-26,28,32,34,
35,54,55,57,58,68,69,74,78 Ohno, H., see Abe, E. 14, 15,71 Ohno, H., see Akiba, N. 65, 68, 69 0000, H., see Ando, M. 38 Ohno, H., see Arata, I. 47, 63 Ohno, H., see Beschoten, B. 41, 47 Ohno, H., see Chiba, D. 65, 66 Ohno, H., see Dietl, T. 23,25,29,40,41,47,
49-58,73-75,77 Ohno, H., see Fukumura, T. 26 Ohno, H., see Guo, S.P. 7, 10 Ohno, H., see Harris, J.G.E. 26
0000. H., see Katsumoto, S. 31,49 Ohno, H., see Kuroiwa, T. 38, 39 0000, H., see Matsuda, Y.H. 37, 38 Ohno, H., see Matsukura, F. 7, 21, 29, 30,48-50, 55,56,63 Ohno, H., see Munekata, H. 5, 6, 10, 17 Ohno, H., see Nagai, Y. 37.49 0000, H., see Nojiri, H. 19 Ohno, H., see Ofuchi, H. 17 Ohno, H., see Ohldag, H. 20, 44, 45, 50 0000, H., see Ohno, Y.63, 64, 70, 71, 73 0000, H., see Oiwa, A. 20-23, 31, 36, 49, 50, 55 Ohno, H., see Omiya, T. 10,30-33,47,55 Ohno, H., see Salis, G. 79 Ohno, H., see Shen, A. 7-9, II, 15, 16,25,36,54, 57,58,61,62 Ohno, H., see Shono, T. 26, 58, 59 Ohno, H., see Sugawara, Y. 32 Ohno, H_, see Szczytko, J. 38, 40, 41, 47, 50 Ohno, H., see Takamura, K. 7 Ohno, H., see Tsuruoka, T. 18 0000, H., see Veda, S. 44 Ohno, H., see von Molnar, S. 34 Ohno, H., see Yang, J. 9 Ohno, H., see Yasuda, H. 7 Ohno, H., see Zhao, J.H. 10 Ohno, Y. 63, 64, 70, 71, 73 Ohno, Y., see Abe, E. 14, 15,71 Ohno, Y., see Akiba, N. 65, 68, 69 Ohno, Y., see Arata, I. 47, 63 Ohno, Y., see Chiba, D. 65, 66 Ohno, Y., see Guo, S.P. 7.10 Ohno, Y., see Kuroiwa, T. 38, 39 0000, Y., see Matsukura, F. 7. 63 Ohno, Y., see Ohno, H. 68, 69, 74 Ohno, Y., see Omiya, T. 10,30-33,47,55 Ohno, Y., see Salis, G. 79 0000. Y.• see Shen, A. 54, 58, 61, 62 Ohno, Y., see Takamura, K. 7
AUTHOR INDEX Ohno, Y., see Yang. J. 9 Ohno, Y.• see Zhao. J.H. 10 Ohnuma, S. 173. 174. 189 Ohoyama, K., see Yamauchi, H. 231 Ohsawa, A., see Novosad. V. 189, 190 Ohta, H.• see Kulatov, E. 43 Ohta. S. 350, 351, 356 Ohtani, K., see Akiba, N. 65. 68, 69 Ohtani, K.• see Ohno, H. 68. 69. 74 Ohtani, K.• see Ohno, Y. 63, 73 Ohtsuka, Y..see Hayashi, T. 5 Ohya, E. 10 Oiwa, A. 20-23. 31. 36,49,50.55,73 Oiwa, A.• see Akiba, N. 65. 68 Oiwa, A.. see Endo, T. 10 Oiwa, A., see Hirakawa. K. 37 Oiwa, A.• see Katsumoto, S. 31, 49 Oiwa, A.• see Koshihara, S. 72 Oiwa, A.• see Moriya, R. 12 Oiwa, A.• see Munekata, H. 36 Oiwa, A.• see Ohno, H. 5,15-17,22.25.26.54. 55,57,58 Oiwa, A.• see Shen, A. 7-9. 11.25.36.54.57.58 Oiwa, A.• see Slupinski, T. 10. 36 Oiwa, A., see Yanagi, S. 66 Oka, K., see Zou, Z. 211. 213,288 Okabayashi, J. 13,21. 3 1 . ~ . 50, 55. 79 Okabayashi. J.• see Yamada, M. 13 Okada. M.• see Kikuchi. S. 132, 133 Okada. M.• see Tanaka, T. 132 Okazawa, D. 13
Okazawa, D., see Tazima,M. 7. 9 Okumura. S.• see Kanamura, M. 73 Oles. A.M., see Feiner. L.F. 175 Oliveira, I.S., see de Jesus. V.L.B. 340 Oliveira, N.F.Yr.• see Henriques, A.B. 15 Oliver. S.A., see Bushnell. S.E. III Olsen. C.E., see Willis. J.O. 258 Omiya, T. 10,30-33,47,55 Omiya, T., see Matsukura, F. 7. 63 Omiya, T.• see Ohno, H. 74 Ong, N.P., see He, T. 284. 285 Onimaru, T., see Yamauchi. H. 231 Ono, K.• see Okabayashi, J. 21. 79 000. K.• see Yamada, M. 13 Onodera, H. 216. 217 Onodera, H.• see Yamauchi, H. 231 Onuki, Y.• see Koyanagi, A. 346 Onuki, Y., see Shimizu, K. 231 Ooike, T. 132. 133 Oomi, G. 216. 217 Oomi, G., see Eto. T. 181 Oomi, G., see Matsuda, N. 210 Oomi, G.• see Uwatoko, Y. 273
391
Oosawa, M.• see Sakata, H. 271 Opahle, I., see Drechsler. S.-L. 216, 228. 229 Opahle, I.. see Rosner. H. 205. 206. 228-230. 233. 235 Ordejon, P.• see Sanvito, S. 42, 43. 46 Orsier, E. 188 Ortelli, J.• see Peter, M. 214 Osaka. T. 185 Osborn. R.• see Abell, J.S. 316 Oscarsson, H.• see Sadowski. 1. 5 Oshima. M., see Akinaga, H. 14 Oshima. M., see Ofuchi, H. 14 Oshima. M., see Okabayashi.T, 21, 79 Oshima, M., see Yamada. M. 13 Osinniy, V. 33 Ossau•.W.• see Fiederling, R. 70 Ostenson, lE., see Vinnikov, L. Ya. 260. 264 Ostenson, J.E., see Xu. M. 225 Otani. Y., see Novosad, V. 189. 190 Ott. F., see Szuszkiewicz, W. 66 Ovari, T.-A., see Chiriaco H. 169. 185 Ovchinnikov, Yu.N.• see Larkin. A.I. 227. 228 Overberg, M.E. 13 Overberg, M.E., see Theodoropolpu, N. 14 Owa, S.• see Soo, Y.L. 13 Oxx, S., see Eskildsen. M.R. 269. 276 Paalanen, M.A. 49 Paccard, D.• see Roy. lL. 342 Pacheco. r.v 327 Pacheco, V.• see Gratz. E. 317 Padalia, B.D., see Godart. C. 218 Padalia, B.D .. see Gupta, L.C. 216. 288 Padalia, B.D., see Hossain. Z. 219 Padalia, B.D., see Mazumdar, Ch. 234. 235. 270 Padalia, B.D .• see Nagarajan. R. 216. 225. 242. 253 Pagola, S.• see Dertinger, A. 216. 217. 264. 266 Palczewska, M., see Szczytko, J. 19 M. 13 Palczewska, M .• see Zaj~. Palenzona, A. 323 Palenzona, A., see Cimberle, M.R. 227 Palomba, F.• see Andreone, A. 241 Palstra, T.T.M .• see Rosseinsky, MJ. 209 Pattiel, Y., see Dewhurst, C.D. 202, 205. 220. 267. 277 Paltiel, Y.. see James, S.S. 267 Panfilov, A.S., see Grechnev, G.E. 318 Panjukov, S. V.• see Bulaevskii, L.N. 226 Paranthaman, M. 212 Parasiris, A., see Rathnayaka, K.D.D. 271 Park. J.H. 44. 45 Park. K.T., see Zhao, Y.-J. 42, 44
392
AUTHOR INDEX
Park. Y.D.74 Park. Y.D.• see Jonker. J.T. 70 Park. Y.W., see Choi, C.K. 262 Parker, C.A.• see Reed. M.L. 14.77 Parker. E., see Fink. HJ. 205. 208. 211 Parkin. S.S.P.• see Dieny, B. 110, 163 Parmenter. R.H. 44 Parsons, MJ. 318. 357 Parthe, E.• see Roy. J.L. 342 Paschen. S.• see Hase, K. 205 Pashitskii, E.A. 48 Pasquale. M. 119 Passel. L.. see Lynn. J.W. 211 Paszkowicz, W.• see Zuberek, R. III. 156. 157. 170 Patil, S.• see Paulose, P.L. 340 Pattalwar, S.M.• see Hossain. Z. 223, 248-250 Paufler, P., see Belger, A. 335 Paufler, P.• see Jaenike-Roessler, U. 277 Pautler; P.• see Just. G. 262 Paul. D. MeK. 258, 269. 272. 274, 276 Paul. D.MeK.• see Campbell, A.1. 220. 242, 259. 267 Paul, D.MeK.• see Chang. L.J. 241. 242, 275. 278 Paul, D.MeK.• see Dewhurst, C.D. 202, 205. 220. 267.277 Paul, D.MeK., see James. S.S. 267 Paul. D.MeK., see Rybaltchenko, L.F. 267. 277 Paul, D.MeK.• see Saha, N. 225 Paul. D.MeK.• see Silhanek, A.V. 205 Paul. D.MeK.• see Song. K.I. 221. 256 Paul, D.MeK.• see Tomy.C.V. 206. 256. 258, 259 Paul. D.MeK.. see Yanson,I.K. 276 Paul. D.MeK., see Yethiraj. M. 272. 279 Paul-Boncour, V., see Gratz, E. 317 Paul-Boncour, V.• see Latroche, M. 317 Paulose, P.L. 340 Paulsen. C.• see Aoki, D. 214 Pearton, S.1., see Overberg, M.E. 13 Pearton, S.1., see Theodoropolpu, N. 14 Pecharsky. V.K.336--338 Pecharsky, V.K.. see Dan'kov, S.Y. 320 Pecharsky, V.K., see Levin, E.M. 336 Pechev, S.• see Bobet, J.-L. 322 Peck Jr.• W.F., see Carter. SA 202, 205. 224 Peck Jr.• W.F., see Cava, R.I. 202. 205. 220. 223. 240.242.283 Peck Jr., W.F.. see Eisaki, H. 231, 240 Peck Jr., W.F., see Grigereit, T.E. 205 Peck Jr., WF., see Lynn. J.W 213, 215. 249. 252 Peck Jr.• W.F.. see Siegrist. T. 218. 246. 247. 251. 253,270.335 Peck Jr.• W.F.. see Takagi. H. 215, 230. 241
Peck Jr., W.F., see Zandbergen, H.W 219, 220, 242.266 Pengo Z., see Winzer, K. 234 Pengo Z.Q. 209 Penny. T., see Munekata, H. II. 36 Penny. T.• see Ohno, H. 5, II. 32. 34. 35 Pepic, N.I.. see Obukhov, SA 15 Peralta, L.• see Wahl, U. 14 Pereheron-Guegan, A.• see Latroche, M. 317 Perez de Albeniz, I.. see Holzer. D. 168 Pernod, see Le Gall. H. 143. 147, 148 Peschel, I.. see Fulde, P. 210, 287 Pescia, D., see Back. C.H. 174 Peter. M. 214 Peterson. E.1., see Nagarajan, R. 288 Petroff, F., see Barthelemy. A. 93 Petrou, A., see Jonker. J.T. 70 Penit. K., see Beach. R.S. 159 Petukhov, A.G. 70 Peuzin, J.C., see du Tremolet de Lacheisserie, E. 106. 108, 186 Peuzin, J.C.• see Halstrup, B. 187 Peuzin, J.C.• see Orsier, E. 188 Pfleiderer,C. 226. 237 Phillips, N.E.• see Wright. DA 207 Picket, W.E.• see Kogan. V.G.273 Picken. W.E. 242. 253 Pickett. W.E.• see Ann. J.M. 207 Piercy. A.R.. see Wang, B.W 94 Pirnenov, A., see Mukhin, A.A. 181 Pinkerton, F.E. 168, 173 Pinkerton, F.E.. see Herbst, J.C.M. 168. 173 Pinkpank, M.• see Mulders. A.M. 322, 357 Pitschke, W.• see Buchgeister, M. 221 Planel, R.• see Gaj, J.A. 36. 51 Plesiewicz, W.. see Wojtowicz, T. 32 Plynn, C.P., see Beach. R.S. 159 Podsiadlo, S.• see Gebicki, W. 13 Podsiadlo, S.• see Zajac, M. 13 Pokrovsky, Y.L., see Canfield, P.C. 215 Pokrovsky, V.L.. see Kalatsky, VA 242. 266 Poldy. C.A. 351. 356 Poldy, C.A.• see Gratz. E. 351 Polk.D.E.120 Popov. Yu. F. 179. 180 Popov. Yu.F., see Kadomtseva, A.M. 180 Potashnik, S.1. 5. 9, 34. 50. 56. 77 Potel, M.• see Godart. C. 218 Poteshnik, S.1., see Chen. X. 10 Pototschnig. P., see Gratz, E. 325 Pourarian, F. 316 Pevzner, A.A.• see Bodriakov, V.Y. 321 Power, A.L.. see Gibbs. M.R.J. 94. 188 Prado, F.• see Alejandro. G. 175
AUTHOR INDEX Prados, c., see Hernando. A. 108. 117 Prados, C.• see Huang. J. 96. 109. 117 Prados, C; see Stobiecki, T. 109 Prasad. A.• see Luysberg, M. 7. 33 Prassides, K. 231. 240 Pratt. EL.. see Nagarajan. R. 288 Prejean. J.J.• see WUchner. S. 141. 163 Preobrazhensky, V.• see Le Gall. H. 143. 147. 148 Price. G.L. 15 Prida, V.M.• see Tejedor, M. 168 Prieto. C.• see Hernando. A. 108. 117 Prinz, G.A. 4 Proust. c.. see Boaknin, E. 279 Prozorov, R. 284 Prytkova, N.A.• see Tomilo, Zh.M. 205. 219. 220, 224.226 Pshechenkova, G.V.• see Belov, K.P. 126 Pugh. E.• see Saxena, S.S. 209 Purushotham, D.S.C.• see Hossain. Z. 242. 248, 253 Putti, M.• see Cimberle, M.R. 227 Qiu, X.D.• see Gao. L. 245. 269, 270 Quandt. E. 94.103.117-119.122.133.141.142. 144. 149. ISO. 157. 158. 166. 188. 189 Quandt. E.• see Ludwig. A. 129. 143, 145-147. 149. 154. 185 Quirion. G.• see Murdoch. J. 205. 207 Rader. 0 .. see Okabayashi, J. 21,31.44-46.50.55 Radha, S.• see Mazumdar, Ch. 270 Radwanski, R.I., see Franse, U.M. 122.322.357 Rainford, B.D.• see Abell, J.S. 316 Raj. P.• see Hossain. Z. 242, 248. 253 Rakhmanina, A.V.• see Makarova, T.L. 286 Rakoto, H.• see Respaud, M. 179 Ramirez. A.P. 175.271 Ramirez. A.P.• see Eskildsen. M.R. 267. 269. 275. 276 Ramirez. A.P.• see Gammel, P.L. 273 Ramirez, A.P.• see He. T. 284, 285 Ramirez. A.P.• see Rosseinsky, MJ. 209 Ramirez. A.P., see Varon. U. 242. 248. 249. 251. 270,271 Rams. M. 221 Ramsperger, U.• see Weber, W. 114 Rao. C.N.R., see Edwards. P.P. 48 Rao, K.V., see Strom, V.205 Rao, R.S.• see Meenakshi, S. 216, 217. 243 Rapp, R.E. 261 Rapp, R.E., see EI Massalami, M. 223 Radunayak~K.D.D.227,230,234,235,271.278
Rathnayaka, K.D.D.• see Du Mar. A.C. 212
393
Rathnayaka, K.D.D., see Eskildsen. M.R. 269 Rathnayaka, K.D.D.• see Hennings. B.D. 260
Rathnayaka, K.D.D., see Naugle, D.G. 216, 240, 266 Raveau, B., see Maignan, A. 179 Raveau, B.• see Respaud, M. 179 Ravindran, P. 229 Ravindran, P.. see Meenakshi, S. 243 Ravot, D. 324, 357 Razavi, ES .• see Murdoch. J. 205. 207 Rebizant, J••see Kobler, U. 309, 315 Rebouillat, J.P., see Chappert, J. 116 Rebouillat, J.P., see Coey, J.M.D. 126 Reed. MJ.• see Reed. M.L. 14,77 Reed, M.L. 14.77 Regan. K.A.• see He. T. 284, 285 Reich, S.• see Feiner. I. 241, 255 Reif, T.• see Svoboda. P. 345 Reimer. V.A.. see Borombaev, M.K. 346. 348. 349 Rempel. A.A.• see Gusev, A.I. 219 Reninger, T.. see Hofmann. B. 136 Respaud, M. 179 Ressouche, E.• see Aoki, D. 214 Ressouche, E.• see Huxley. A. 211 Reuscher, G.• see Fiederling, R. 70 Reuter. D., see Sander, D. 106 Rewiersma, M.J.F.M.• see HUser. D. 244 Rhades, W.w.. see Jin, S. 175 Rhee. J.Y. 209 Rhee, J.Y.• see Song. C. 221. 256 Rhee, J.Y.• see Suh, BJ. 214 Rhyne, J.J. 93 Rhyne. J.J.• see Beach. R.S. 159 Rhyne. J.J., see Borchers, J.A. 159 Rhyne. J.J.• see Erwin. R.W. 159 Riabinin, Yu.N., see Shubnikov, L.V. 228. 232, 233.240.241 Rialland, J.F., see Alves. F. 172 Riblet. G. 203 Rice. T.M.• see Fehrenbacher. R. 219. 221 Rice. T.M.• see Zhang. F.C. 42. 60 Richardson. C.F. 279 Richornme, E, see Due. N.H. 94, 133 Richter. M.• see MUller. K.-H. 216 Rieder. K.H.• see Weber. M. 106 Riedi, K. 118. 133, 135. 136 Riedi. P.C.93 Riedi, P.c.. see de Jesus. V.L.B. 340 Riseman, T.M.• see Luke. G.M. 212 Ritter. C.• see Chang, L.J. 241, 275. 278 Ritter. C.• see de Teresa. J.M. 178 Ritter, C.• see Freudenberger, J. 219. 224. 225 Ritter, C; see Garcfa-Landa, B. 176, 177 Ritter. c., see Kreyssig, A. 205. 221, 222. 262
394
AUTHOR INDEX
Ritter, C., see Loewenhaupt, M. 273 Ritter, C., see MUlier, K-H. 250, 256 Ritums, M.K., see Reed, M.L. 14,77 Ro, C., see Levin, K. 235 Roberts, J.C., see Reed, M.L. 14,77 Rodrigues Bitterncourt, A.C. 69 Rodriguez, C.O., see Cappannini, O.M. 229, 232 Rodriguez, C.O., see Weh!, R. 206 Rodriguez-Carvajal, J., see Blanco, J.A. 339-341, 356,357 Rodrfguez-Femandez, J., see Blanco, J.A. 339-341,356,357 Rodnguez-Pemandez, J., see Espeso, J.1. 340-342,357 Rogado, N., see He, T. 284, 285 Rogl, P.282 Rogl, P., see Michor, H. 223, 279, 288 Rogl, P., see Rupp, B. 207 Roig, A., see Slawska-Waniewska, A. 170 Roisnel, T., see Ravot, D. 324, 357 Rojo, J.M., see Fontcuberta, J. 309 Rojo, J.M., see Hernando, A. 309 Rosenkranz, M., see Hansen, P. 115, 117 Rosenkranz, S., see Gasser, U. 241 Rosne~H.205,206,228-230,233,235
Rosner, H., see Drechsler, S.-L. 216, 228, 229, 234 Rosner, H., see Fuchs, G. 209 Rosner, H., see von Lips, H. 260-262 Rosov, N., see Skanthakumar, S. 241, 242, 245, 252,268 Ross, K, see Dezaneti, L.M. 242, 249, 251, 270, 271 Rosseinsky, M.J. 209 Roth,S.244,245,270 Rothrock, B.D., see Taylor, R.E. 311 Rotter, M. 223, 310, 311, 314, 344, 346-350, 356 Rotter, M., see Doerr, M. 335 Rotter, M., see Gratz, E. 317 Rotter, M., see Lindbaum, A. 345 Rotter, M., see Svoboda, P. 345 Rouchy, J. 319, 358 Roudaut, E., see Castets, A. 343, 356 Roukes, M.L., see Wolf, S. 4 Roy, J.L. 342 Roychowdhury, V., see Vrijen, R 79 Ruf, R.R, see Munekata, H. 10 Ruf, T., see Heimbrodt, W. 10 Ruf, T., see Sapega, V.F. 20, 47 Ruffino, G., see Taylor, R.E. 311 Rukang, L. 221
Rupp, B. 207 Rupp Jr., L.W., see Cava, R.I. 202, 223 Rupp Jr., L.W., see Ilegems, M. 19 Rusinov, A.I., see Gor'kov, L.P. 220, 242, 260
Russel, V. 260 Russo, M.L., see Andreone, A. 215 Ruzmetov, D., see Baxter, D.V. 32 Ryabchenko, S.M., see Pashitskii, E.A. 48 Ryba, E., see Debray, OK 350, 356 Rybaltchenko, L.F. 267, 277 Sadowski, J. 5,9, 10, 15, 16,26,40,62,77 Sadowski, J., see Fedorych, O.M. 19,58 Sadowski, J., see Kepa, H. 66 Sadowski, J., see Osinniy, V. 33 Sadowski, J., see Szuszkiewicz, W. 66 Saeki, H. 9, 24, 78 Safaraliyev, G.I., see Aliyev, M.1. 5, 14 Saba, N. 225 Saba, N., see Dewhurst, C.D. 202, 205, 220 Saito, H. 13 Saito, T., see Miyazaki, T. 117, 118, 122-124, 133, 136, 137 Saitoh, Y., see Ueda, S. 44 Sakai, F., see Nohara, M. 268, 269 Sakai, O. 37,61 Sakai, T. 205, 273, 274 Sakata, H. 271 Sakon, T.. see Akiba, N. 65, 68 Sakon, T., see Omiya, T. 30-33,47,55 Sakurai, Y., see Konishi, S. 108 Sala, R. 243 Salamati, H., see Murdoch, J. 205, 207 Salamon, M.B., see Beach, R.S. 159 Salamon, M.B., see Borchers, 1.A. 159 Salamon, M.B., see Erwin, RW. 159 Salamon, M.B., see O'Donovan, KV. 159 Sales, B.C., see Paul, D. McK. 272, 274 Salis, G. 79 Salis, G., see Kawakami, R.K. 75 Samarth, N., see Malajovich, I. 79 Samarth, N., see Potashnik, S.l. 5, 9, 34, 50, 56,77 Saminadayer, K., see Baron, T. 5 Sampathkumaran, E., see MaIlik, R. 310 Sampathkumaran, E., see Paulose, P.L. 340 Sampathkumaran, E.V., see Eto, T. 181 Samsonenko, N.V., see Troyanchuk, 1.0. 184 Sanchez, D.R. 226, 256, 266 Sanchez, D.R., see Baggio-Saitovitch, E.M. 223, 224,243 Sanchez, D.R., see Bourdarot, F. 218 Sanchez, D.R., see Fontes, M.B. 213 Sanchez, 1.P. 219, 220, 224, 225 Sanchez, J.P., see Godart, C. 220, 242, 260 Sanchez, J.P., see Hodges, J.A. 278 Sanchez, J.P., see Tomala, K. 219, 335,357 Sanchez, M.L., see Tejedor, M. 168
AUTHOR INDEX Sanchez, R., see Alejandro, G. 175 Sande~D.95, 105-107, 113 Sander, D., see Gutjahr-Loser, Th. 104, 114 Sanina, V.A.• see Henriques. A.B. 15 Santi, G.. see Dugdale. S.B. 230, 240 Santoro. A.. see Grigereit, T.E. 205 Santoro, A.• see Lynn. J.w. 213. 215. 249, 252 Santos. A.D.. see Givord, D. 141, 163 Sanvito, S. 42-44. 46 Sapega, V.F. 20, 47 Sapega, V.F.. see Heimbrodt, W. 10 Sarkoz], Z.. see Due. N.H. 124-126 Sarrac, J.L.. see Zandbergen, H.W. 223 Sarrao, J.L. 205 Sarthour, R.. see de la Fuente. C. 162 Sasaki. T., see Sonoda, S. 14.77 Sasaki. Y., see Baxter, D.V. 32 Sasaki. Y.,see Chen, X. 10 Sasaki. Y.• see Liu, X. 5. 26 Sassik, H.• see Holzer. D. 168 Sassik, H., see Rotter. M. 310, 346, 347, 356 Sasso. c., see Pasquale. M. 119 Sato, K. 43, 75. 76 Sato, K.• see Abe. E. 14, 15 Sato, K.• see Medvedkin, G.A. 77 Satoh, Y. 9,24 Satoh, Y.. see Nishikawa, Y. 5 Savitskii, E.M. 214 Sawicki, M.• see GI6d, P. 49 Sawicki, M., see Kossacki, P.49, 74 Sawicki. M., see Wojtowicz,T. 32 Saxena, S.S. 209,216. 217 Scalbert, D.. see Benoit a la Guillaume, C. 42, 60 Schachinger, E., see Manalo, S. 236, 237 Schairer, W. 20 Schaper, A.• see Heirnbrodt, W. 10 Scharff, P., see Makarova, T.L. 286 Schatz. F. 118. 130, 131, 133, 135 Schatz. F., see Riedi, K. 118. 133. 135, 136 Schelleng, J.. see Forester. D.W. 117 Schenck. A.• see Le, L.P. 235 Schenck. A.• see Mulders. A.M. 322, 357 Scherschligt, J•• see Baxter. D.V. 32 Schiffer, P., see Chen. X. 10 Schiffer. P.• see Potashnik, SJ. 5, 9, 34, 50. 56. 77 Schiffmacher, G., see Godart, C. 218 Schiffmacher, G.• see Tominez, E. 216, 219, 220 Schilling. J.S.• see Gangopadhyay. A.K. 216. 223 Schilling, I.S., see Looney, C. 208 Schirber, I.E., see Williams, I.M. 209 Schliemann, J. 61 Schmidt, G., see Fiederling, R. 70 Schmidt, H. 216. 241, 263. 264. 278 Schmidt. H.. see Wagner,T.A. 231, 285
395
Schmidt. L.. see Brison. J.P. 220. 283 Schmidt, M., see Schairer. W. 20 Schmidthals, C., see Sander, D. 106 Schmiedeshoff, G.M. 205, 206, 230 Schmiedeshoff, G.M.• see Christianson, A.D. 236 Schmiedeshoff, G.M., see Lacerda, A. 205, 217, 220. 251, 289 Schmitt, D.. see Blanco, I.A. 310. 339-341, 356, 357 Schmitt, D.• see Bouvier, M. 310 Schmitt, D.• see Feiner. I. 213. 216 Schmitt, D., see Gignoux, D. 329. 330. 356 Schmitt. D.• see Morin, P. 94, 256, 310. 312, 319 Schneider, J. 19 Schneider. M.• see Lipp, D. 226. 283 Schneidewind, A.• see Kreyssig, A. 205 Schneidewind. A.• see Lindbaum, A. 345 Schneidewind. A., see Rotter, M. 310. 346, 356 Schneidner, I .• see Kraus, L. III Schnell. M., see Riedi, K. 118. 133, 135, 136 Schnell, M.• see Schatz, F. 118. 130. 131, 133, 135 Schnelle. w.. see Gulden, Th. 219, 224 Schnelle. W., see KObler. U. 309. 315 Schober. H.. see Loewenhaupt, M. 273 Schober. H.• see Rotter, M. 223 Schober, H., see Sierks, C. 275 Schon, J.H. 203. 205, 206, 238, 259 Schott, G.M. 5. 7.16 Schrieffer, J.R.• see Bardeen, J. 227 SChroeder, H., see Tam, A.C. 106 Schuller. K.I.• see Dunlap, B.D. 212 Schulthess, T.C. 44 Schultz. L., see Behr, G. 219 Schultz, L., see Bitterlich, H. 210. 287, 288 Schultz. L., see Drechsler, S.-L. 234 Schultz. L.. see Freudenberger, J. 219, 224, 225, 233,234.236,237,241,266,279,280,284. 287-289 Schultz, L., see GUmbel, A. 242. 253. 254 Schultz, L., see Hase, K. 205, 219 Schwabl, F., see Frey, E. 315, 320 Schwan, K., see Divis, M. 242 Schweizer, I., see Abell. J.S. 316 Scuseria, G.E., see Xu. C.H. 202. 219, 230 Seaman, C.L., see Luke. G.M. 212 Sechovsky, V., see Javorsky, P. 325-327.357 Seemann. K., see Quandt, E. 117, 122, 188 Seffar, A.• see Fontcuberta, J. 309 Segawa, Y., see Kuroiwa, T. 38. 39 Segmuller, A.• see Munekata, H. 5, 6, 10, 17 Segre, C; see Dunlap, B.D. 212, 256 Seidl, E., see Rotter, M. 346, 347, 356 Sell, D.O.. see Casey Ir., H.C. 38
396
AUTHOR INDEX
Sella. C.• see Szymczak. H. 151 Sella, C .• see Zuberek, R. III, 151 Semenov, Y.G. 48 Senda, M .• see Nagi, Y. 151 seo, J.W.• see Berger. R. 188 Seo, S.W.• see Lee. K.H. 276, 288 Sera, M. 213 Seto, K.. see Hayashi. T. 62. 63 Setoguchi, H., see Matsuda, N. 210
Settai, R.• see Koyanagi, A. 346 Sham. LJ.• see Fernandez-Rossier, J. 49, 53, 54 Shapiro. S.• see Sternlieb, B. 219. 224 Shapiro. S.• see Zarestky. J. 212 Shewn. I.. see Huxley, A. 211 Sheikin, I., see Saxena, S.S. 209 Shelton. R.N. 207. 208 Shelton. R.N .• see Hoellwarth, C.c. 230 Shelton. R.N .• see Ku, H.C. 205. 219. 220 Shelton. R.N., see Lee. W.H. 205. 251 Shelton. R.N., see Lynn. J.W. 220. 226, 242, 244. 245.247-249.253,256,276 Shelton, R.N .• see Stanley. H.B. 218 Shen, A. 7-9. II. 15. 16.25, 36. 54. 57, 58, 61, 62 Shen, A .• see Akiba, N. 65. 68 Shen, A .• see Beschoten, B. 41, 47 Shen, A., see Guo. S.P. 7,10 Shen, A.• see Katsumoto, S. 31,49 Shen, A.• see Kuroiwa, T. 38. 39 Shen, A., see Matsuda, Y.H. 37, 38 Shen, A., see Matsukura, F. 7. 21, 29. 30. 48-50, 55.56.63 Shen, A .• see Ofuchi, H. 17 Shen, A.• see Ohno, H. 5. 15-17,22.25.26.54. 55.57,58.68,69 Shen, A.• see Oiwa, A. 20-23. 31. 49. 50. 55 Shen, A., see Omiya, T. 10 Sben, A., see Sugawara, Y. 32 Shepelev, Yu.D.• see Shubnikov, L.V. 228. 232, 233.240.241 Sherwood. C .• see Gibbs. M.RJ. 94 Shestak, A.S., see Tomilo, Zh.M. 205. 220. 224 Shibata. A.• see Izawa, K. 240. 285 Shibata. N. 5 Shick, A.• see WU. R.Q. 105 Shick, A.B. 105 Shieh. J.H .• see Jiang. PJ. 226 Shieh. J.H., see Ku, H.C. 284, 285 Shieh. J.H .• see Lin, M.S. 205 Shima, T. 120. 156 Shima, T.• see Lim. S.H. 142 Shimada. H., see Hayashi. T. 5. 62. 65 Shimada. Y.. see Novosad. V. 189, 190 Shimizu. H. 7.16.34.41,55 Shimizu, H.• see Hayashi. T. 65
Shimizu, H.• see Higo, Y. 65, 67 Shimizu, H.• see Ohya, E. 10 Shimizu, K. 231 Shimizu, S., see Sonoda. S. 14,77 Shin. S., see Katsumoto, S. 20. 37, 50 Shin. S., see Yokoya, T. 243 Shioda, R. 18 Shiokawa, J., see Sakai, T. 205, 273. 274 Shrrai.M. 17,41,43.79 Shirai, M., see Akinaga, H. 13,78 Shirai, M .• see Ogawa, T. 17.42.43 Shiraishi, J. 272 Shirane, G., see Thomlinson. W. 234 Shirane, G., see Zarestky, J. 212 Shono, T. 26,58. 59 Shono, T.• see Fukumura, T. 26 Shono, T., see Matsumoto, Y. 78 Short. S.• see Dabrowski. B. 181 Shovkun, D.V.• see Strukova, G.K. 226 Shraiman, B.I., see Ye, J. 27 Shrivastava, K.N .• see Ghosh, P.K. 287 Shtelmakh, K.F.. see Masterov, V.F. 19 Shtrikman, H., see Dewhurst, C.D. 267. 277 Shtrikman, H., see James. S.S. 267 Shubnikov, L.V. 228. 232. 233,240,241 Shulga, S., see Drechsler, S.-L. 216.228 Shulga, S.Y. 218, 223, 233. 241. 246. 281. 284 Shulga, S.Y., see Drechsler. S.-L. 228, 229. 234 Shulga, S.V., see Freudenberger, J. 266. 287 Shulga, S.V.• see Fuchs. G. 209 Shulga, S.V.• see Rosner, H. 228-230. 233. 235 Shultz. AJ.• see Williams, J.M. 209 Siatek, K., see Sadowski, J. 15.26 Siegrist. T. 218. 246, 247, 251. 253. 270. 335 Siegrist. T.• see Cava. R.J. 202. 205. 220. 223. 240,242.283 Siegrist. T.• see Mattheiss, L.F. 208 Sienko. MJ.• see Edwards. P.P. 49 Sierks, C. 275 Sierks, c.. see Loewenhaupt, M. 273 Sierks, C .• see Rotter. M. 223 Siewenie, J.E .• see Dabrowski. B. 181 Sigle, W.• see Riedi. K. 118. 133. 135. 136 Sikka, S.K .. see Meenakshi, S. 216. 217. 243 Silhanek, A.V. 205 Simon. A. 227 Simon. A., see Gulden, Th. 219, 224 Simon. A., see Henn, R.W. 238 Simpson, J.A., see Swaddling. P.P. 159 Singh. DJ. 220. 242, 266 Singh. D.J .• see Pickett. W.E. 242. 253 Sinha, S.• see Erwin, R.W. 159 Sinha. S.K. 213
AUTHOR INDEX Sinha. S.K., see Lynn, 1.w. 213, 220, 289, 335 Sinitsyn, A. V., see Borombaev, M.K. 346. 348. 349 Sinning, S., see Doerr, M. 335 Siri, A.S., see Cimberle, M.R. 227 Skanthakumar, S. 221, 241, 242, 245, 252, 268 Skanthakumar, S., see Bourdarot, E 218 Skanthakumar, S., see Lynn, 1.w. 213, 220, 289, 335 Skolozdra, R.V., see Komarovskaja, L.P. 327 Skomski, R., see Sander, D. 106 Skorvanek, I. 168 Skumryev, V., see Coey, J.M.D. 320 Slaski, M., see Dunlap, B.D. 212, 256 Slawska-Waniewska, A. 169-171 Slawska-waniewska, A., see Szumiata, T. 105, 172 Slawska-Waniewska. A., see Twarowski, K. 170 Siebarski, A., see Talik, E. 352, 356 Sleight, A.W., see Luke, G.M. 212 Siupinski, T. 10, 36 Siupinski, T.. see Endo, T. 10 Siupinski, T., see Oiwa, A. 73 Siupinski, T., see Yanagi, S. 66 Slusky, 1.L., see He, T. 284, 285 Smetana. Z., see Borombaev, M.K. 346, 348, 349 Smith, A.B. III Smith, 1.L., see Nagarajan, R. 288 Smith, J.L., see Schmiedeshoff, G.M. 205, 206, 230 Snel, C.E., see EI Massalami, M. 219, 220, 242, 247 Socha, E, see Le Gall, H. 143, 147, 148 Soderholm. L., see Dunlap, B.D. 212 SOdervall, U., see Sadowski, J. 9,16,77 Sohn, H., see Luysberg, M. 7, 33 Sokulski, J., see Zuberek. R. III, 156 Soldatov, E.S., see Gubin, S.P. 168 Solinus, V., see Ohldag, H. 20,44, 45, 50 Solntseva, L.I., see Belov, K.P. 126 Song,C.221,256,273,276,284,285 Song, K.I. 221, 256 Song, O.-S., see Bochi, G. 113 Song, O.-S., see O'Handley, R.C. 109 Song, Y.S., see Choi, C.K. 262 Sonier, 1.E. 213 Sonoda, S. 14,77 Sontag, H. 106 Soo, Y.L. 12, 13, 17 Soo, Y.L., see Krol, A. 17 Sorgic, 8., see Blazina, Z. 322 Souche, Y., see Givord, D. 141, 163 Spanos, G., see Park, Y.D. 74 Specht, P., see Luysberg, M. 7, 33
397
Speck, 1.S., see Kawakami, R.K. 5, 10, 63 Spedding, EH.• see Nigh, H.E. 320 Speliotis, A. 119 Speriosu, V., see Baril, L. 110 Speriosu, V.S., see Dieny, B. 110, 163 Sqiatek, K., see Sadowski, 1. 5 Sridhar, S., see Eskildsen, M.R. 269, 276 Sridhar, S., see Jacobs. T. 216 Srinath, S., see Kaul, S.N. 320 Stachow, A., see Szczytko, J. 41 Stadelmaier, RH.• see Reed, M.L. 14,77 Staliriski, B. 318. 357 Stampe, P.A. 324 Stankiewicz, 1., see Morellon, L. 336 Stanley, H.B. 218 Stanley. H.E., see Aharony. A. 208 Stassis, C., see Dervenagas, P. 230. 242, 245, 255, 256 Stassis, C., see Detlefs, C. 221, 222, 241. 242, 245,253,254,310,335,357 Stassis, C., see Goldman, A.I. 233 Stassis, C .. see Hill. J.P. 209 Stassis, C., see Sternlieb, B. 219,224 Stassis, c., see Yaron, U. 242, 248, 249, 251,270, 271 Stassis, C; see Zarestky, 1. 212, 230 Stauss, G.H., see Krebs. U. 18 Steep, E., see GolI, G. 230 Steglich, E 242 Steiner, M.J., see Saxena. S.S. 209 Stephanovich, V.A., see Semenov, Y.G. 48 Stephens. J.M., see Kawakami, R.K. 75 Stephens, P.W., see Dertinger, A. 216, 217, 264, 266 Stemlieb, B. 219, 224 Stemlieb, B., see Goldman, A.I. 233 Stemlieb, BJ., see Hill, J.P. 209 Stemlieb, BJ., see Luke, G.M. 212 Stievenard, D., see Grandidier, B. 18 Stobiecki, T. 109 Stobiecki, T., see Zuberek, R. III, 156 Stolz, W.• see Hartmann, Th. 10 Stolz, w.. see Heimbrodt, W. 10 Storm. A.R. 345 Story, T. 5 Story, T., see Eggenkamp, P.TJ. 60 Story, T., see Kepa, H. 66 Story, T., see Osinniy, V. 33 Strassler, S., see Baltensperger, W. 211 Strom, J., see Sadowski, J. 15,26 Strom, V. 205 Stronach, C.E., see Bernhard, C. 213 Stronach, C.E.• see Luke. a.M. 212
398
AUTHOR INDEX
Strukova, G.K. 226 Struzhkin, V.V., see Eremets, M.I. 274, 276 Strzeszewski, J., see Gebicki, W. 13 Stucheli, N., see Ramirez, A.P. 271 Stucki, F., see Hulliger, F. 319 Stunault, A., see Rotter, M. 310, 346, 356 Subramanian, M.A., see Luke, G.M. 212 Suga, S., see Veda, S. 44 Sugatani, S., see Konishi, S. 108 Sugawara, W., see Arai, K.I. 189 Sugawara, Y. 32 Sugawara, Y., see Katsumoto, S. 31,49 Sugawara, Y., see Matsukura, F. 7, 21, 29, 30, 48-50,55,56,63 Sugawara, Y., see Ohno, H. 15,25,26,54,55,57, 58 Sugawara, Y., see Oiwa, A. 20-23, 31,49. SO. 55 Sugawara, Y., see Shen, A. 7-9, II, 15, 16,25,36, 54,57,58,61,62 Sugimoto, S., see Kikuchi, S. 132, 133 Sugimoto, S., see Tanaka, T. 132 Sugiyama, K., see Koyanagi, A. 346 Suh, BJ. 214 SuhI, H. 267 Suhl, H., see Anderson, P.W. 210 Suhl, H., see Matthias, B.T. 209, 213 Sullivan, J.M., see Park, Y.D. 74 Sulpice, A., see Bud'ko, S.L. 278 Sulpice, A., see EI Massalami, M. 223, 242 Sun, J., see Ohya, E. 10 Sun, S.W. 112, 152 Sun, S.W., see O'Handley, R.C. 105 Sun, Y.Y., see Dezaneti, L.M. 242, 249, 251, 270, 271 Sun, Y.Y., see Gao, L. 245, 269, 270 Sundaresan, A., see Eto, T. 181 Sundqvist, B., see Makarova, T.L. 286 Sungaila, Z., see Dunlap, B.D. 212, 256 Surdeanu, R., see Dewhurst, C.D. 202, 205, 220 Surdeanu, R., see Saha, N. 225 Surovaya, G.N., see Belov, K.P. 126 Suryanarayana, P., see Hossain, Z. 242, 248, 253 Suzuki, K. 168 Suzuki, N.• see Ogawa, T. 17, 42, 43 Suzuki, N., see Shirai, M. 17,41 Suzuki, S., see Fujimori, H. 120 Suzuki, S., see Sakai, O. 37, 61 Svechkarev, I. V., see Grechnev, G.E. 318 Svedlindh, P., see Mathieu, R. 175 Svedlindh, P., see Sadowski, J. 9, 16,62,77 Svidzinskii, A.A., see Barash, Y.S. 284, 285 Svoboda, P. 345 Svoboda, P., see Javorsky, P. 326, 357 Svoboda, P., see Lindbaum, A. 345
Svoboda, P., see Rotter, M. 310 Swaddling, P.P. 159 Swagten, HJ.M., see Eggenkamp, P.TJ. 60 Swenson, C.A., see Dolejsi, D.A. 315 Swenson, C.A .. see Taylor, R.E. 311 Swil\tek, K., see Kossacki, P. 49, 74 Swil\tek. K., see Sadowski, J. 9, 16,62.77 Swiatek, K., see Szczytko, J. 19 Swuste, C.H.W., see Eggenkamp, P.TJ. 60 Sysa, L., see Kalychak, Y.M. 331 Szczytko, J. 19,38,40,41,47,50 Szczytko, J., see Zajl\C, M. 13 Szewczyk, A., see Dabrowski, B. 180, 181 Szklarz, E.G., see Giorgi, A.L. 226 Szklarz, E.G., see Krupka, M.C. 205 Szumiata, T. 105,156, 172, 173 Szuszkiewicz, W. 66 Szymczak,H.95, 105, 106, 151, 152, 154-157, 170, 172, 174, 175, 182 Szymczak, H., see Dabrowski, B. 180, 181 Szymczak, H., see Lachovicz, H.K. 109 Szymczak, H., see Szumiata, T. 105, 156, 172, 173 Szymczak, H., see Szymczak, R. 234, 235, 240 Szymczak, H., see Troyanchuk, 1.0. 184 Szymczak. H.. see Zuberek, R. 105. III. 151, 154, 156,157, 170 Szymczak, R. 234, 235, 240 Szyszko, T., see G~bicki, W. 13 Szyszko, T., see Zajl\C,M. 13 Szytula, A. 324 Tabata, H., see Saeki, H. 9, 24, 78 Tabata, H., see Ueda, K. 20,46, 78 Tabuchi, M., see Ofuchi, H. 14, 17 Tachikawa, N., see Tsuruoka, T. 18 Tachiki, M., see Matsumoto, H. 227, 228, 230 Tailefer, L., see Boaknin, E. 238, 239, 241, 279, 285 Takagi, H. 215. 230, 231, 241 Takagi, H., see Cava, R.I. 202, 205, 220, 223, 240, 242,283 Takagi, H., see Eisaki, H. 231, 240 Takagi. H.• see Izawa, K. 260 Takagi, H., see Koshihara, S. 72 Takagi, H., see Luke, G.M. 212 Takagi, H., see Munekata, H. 36 Takagi, H., see Murayama, C. 216 Takagi, H., see Nohara, M. 268, 269, 279, 283-285 Takagi, H., see Yokoya, T. 243 Takahashi, H., see Uehara, M. 216, 217, 264 Takahashi, R., see Matsumoto, Y. 78 Takamura, K. 7
AUTHOR INDEX Takamura, K.• see Ando, M. 38 Takamura, K., see Zhao. J.H. 10 Takanaka, K. 219, 226 Takatani, Y., see Haneda, S. 12. 16 Takatani, Y.• see Soo, Y.L. 12 Takeda. K.• see Choi, J.-H. 266 Takeda, K.. see Shimizu, K. 231 Takeda. Y.• see Ofuchi, H. 14. 17 Takekawa, S.• see Kito, H. 273 Takenaka, M., see Shimizu. H. 41 Takeuchi, A., see EI Massalami, M. 242 Takeuchi, T., see Katsumoto, S. 20. 37, 50 Takeya, H. 211 Takeya, H.. see Doerr, M. 335 Takeya, H.• see Izawa, K. 240, 285 Takeya, H., see Kawano. H. 266. 267 Takeya, H., see Sakata, H. 271 Takeya, H.• see Sera. M. 213 Takeyama, S.• see Nojiri, H. 19 Takezawa, M., see Arai, K.I. 189 Talik, E. 352. 356 Talik, E.• see Jarosz, J. 326, 327, 357 Talik, E., see Kusz, J. 352-354. 356 Tallon, J.L., see Bernhard, C. 213 Tam. A.C. 106 Tam. A.C.• see Sontag, H. 106 Tanaka. M. 26. 67 Tanaka. M.• see Ando, K. 40 Tanaka. M.• see Grandidier, B. 18 Tanaka. M., see Hayashi, T. 5, 62, 63, 65 Tanaka. M.• .Iee Higo, Y.65, 67 Tanaka, M., see Ohya, E. 10 Tanaka. M., see Okabayashi, J. 13,21,31,44-46, 50,55 Tanaka. M.• see Saito. H. 13 Tanaka. M., see Shimizu, H. 7,16,34,41,55 Tanaka. M.. see Shioda, R 18 Tanaka, M., see Szczytko, J. 19 Tanaka. T. 132 Tanaka, T.. see Kikuchi. S. 132. 133 Tani, M.• see Shen, A. 9, 15, 16 Taniguchi, 0 .. see Awano, H. 151 Tanimoto. R, see Tsuruoka, T. 18 Taratynov, v.P.• see Belov, K.P. 126 Tatarenko, S., see Baron, T. 5 Tatarenko, S.• see Ferrand. D. 5. 27.49,54.60 Tatarenko, S.• see Haury. A. 5. 49. 54 Tatarenko, S.• see Kossacki, P.49. 74 Taylor. J.W. 318, 357 Taylor. RD.• see Willis, J.O. 258 Taylor. R.E. 311 Taylor. RE.• see Touloukian, Y.S.320 Taylor, RH. 316
Tazima, M. 7. 9
399
Teillet, J., see Danh, T.M. 94. 117. 118. 126 Teillet, J.• see Due. N.H. 94, 117-119. 126, 131-133. 142. 143, 148. 150. 167. 168 Tejedor, M. 168
Teresiak, A., see Narozhnyi, V.N. 248-252 Tesanovic, Z., see Ye, J. 27 Tessier. M.• see Szymczak. H. 151 Tessier, M., see Zuberek, R. Ill, 151 Teter, J.P. 191 Thalmeier, P.• see Amici. A. 261. 262, 266 Thalmeier, P., see Izawa, K. 260 Thalmeier, P., see Maki. K. 240, 281. 282 Thanh, H.N., see Danh, T.M. 94,117.118,126 Thanh. H.N., see Due, N.H. 94, 117-119. 126. 131-133 Theodoropoulou, N. 14 Theodoropoulou, N., see Overberg, M.E. 13 Thiel. R.C.• see Mulder, F.M. 269 Thilderkvist, M.• see Linnarson, M. 19 Thomas, G.A., see Liu, S. 37 Thomlinson. W. 234 Thomlinson. W., see Lynn. J.W. 211 Thompson, J.D.• see Alieno, E. 216, 217 Thompson. J.D., see Le. L.P. 235 Thompson. J.D., see Movshovich, R. 265, 266 Thompson. J.D., see Sonier. J.E. 213 Thompson. J.R.• see Kogan, V.G. 273 Thompson, J.R.• see Paul, D. McK. 272, 274 Thompson, J.R.• see Silhanek, A.V. 205 Thompson, J.R. see Song. K.I. 221. 256 Thompson. J.R., see Yethiraj, M. 279 Thomson. T.. see Riedi, P.C. 93 Thornton. M.J.• see Ziese, M. 4 Thorsen, A.C., see Fink, H.J. 205. 208. 211 Thuy. N.P., see Danh. T.M. 116. 122. 126 Thuy. N.P., see Due. N.H. 140. 142. 157, 158 Thuy, N.P., see Tung. L.D. 330. 357 Tiefel. T.H.• see Jin, S. 175 Tiercelin, N.• see Le Gall. H. 143, 147. 148 Tils, P., see Sierks, C. 275 Ting, C.S., see Wang, Z.D. 216. 217 Tinkham, M. 255 Tishin, A.M., see Dan'kov, S.Y. 320 Tishin. A.M., see Koksharov, Yu.A. 168 Tjutrina, L.V.• see Rybaltchenko, L.F. 267. 277 Togano, K.. see Arisawa, S. 219
Tokura, Y. 4 Tokura, Y.• see Kimura. T. 181-183 Tokura, Y.• see Kuwahara, H. 178 Tokura, Y., see Luke, G.M. 212 Tomala, K. 219. 335. 357 Tomala, K.• see Bialic, D. 328, 356 Tomilo, Zh. 219, 220, 226
400
AUTHOR INDEX
Tomilo, Zh.M. 205, 220, 224 Tominez, E. 216, 219, 220, 242 Tominez,E., see Dhar, S.K. 227, 24(}..242, 251 Tominez, E., see Godart, C. 220, 242, 260 Tomioka, Y., see Kimura, T. 181-183 Tomioka, Y., see Kuwahara, H. 178 Tomioka, Y., see Tokura, Y. 4 Tomka, G.J., see Arnaudas, J.1. 159, 160 Tomka, G.J., see Ciria, M. 106, 159 Tomka, G.J., see Riedi, P.C. 93 Tomlinson, P., see Levin, E.M. 336 Tompkins, M.V., see Schmiedeshoff, G.M. 230 Tomuta, M., see Chiriac, H. 168 Tomy, 206,256,258,259 Tomy, C.V., see Chang, L.J. 241, 242, 275, 278 Tomy, C.V., see Paul, D. McK. 258, 269, 276 Tomy, C.V., see Rybaltchenko, L.F. 267, 277 Tomy,e.V.• see Silhanek, A.V. 205 Tomy, C.V., see Song, K.1. 221, 256 Tomy, C.V., see Yanson, I.K. 276 Tomy, C.V., see Yethiraj, M. 272, 279 Torgeson, D.R., see Suh, B.J. 214 Torng, C.J., see Wu, M.K. 208 Toshima, T., see Nagi, Y. lSI Toth, L., see Fink, H.J. 205, 208, 211 Touloukian, Y.S. 320 Toussaint, 1.C., see Givord, D. 133, 141, 163 Toussaint, J.C., see Wiichner, S. 141, 163 Tovar. M .• see Alejandro, G. 175 Travkin, V.D., see Mullin, A.A. 181 Treger, D.M.. see Wolf, S. 4 Treutmann, see Heimbrodt, W. 10 Treyvaud. A., see Peter, M. 214 Trifonov, A.S., see Gubin, S.P. 168 Trippel, G. 106 Trochez, 1.e., see Fontes, M.B. 213 Troyanchuk, 1.0.184 Tsabba, Y., see Feiner, I. 241, 255 Tsuchiya, H., see Hayashi, T. 5 Tsuruoka,T. 18 Tsvyashchenko, A.v., see Narozhnyi, V.N. 235-238,248-252 Tuan, L.Q., see Due, N.H. 168 Tuan, N., see Javorsky, P. 326, 357 Tuan, N.A., see Due, N.H. 94, 133, 140, 142, 143, 148, ISO, 157, 158, 167 Tung, L.D. 330, 357 Twardowski, A., see Ando, K. 40 Twardowski, A., see Kepa, H. 66 Twardowski, A., see Mac, W. 19 Twardowski, A., see Matsuda, Y.H. 37, 38 Twardowski, A., see Szczytko, J. 19,38,40,41, 47,50 Twardowski, A., see Zajac, M. 13
c:v.
w.,
Twarowski, K. 170 Tworzydlo, 1., see Szczytko, 1. 41 Uchida, H., see Wada, M. 103, 118, 122, 133-135 Uchida, H.H., see Wada, M. 103, 118, 122, 133-135 Uchida, S., see Cava, R.I. 202, 205, 220, 223, 240, 242,283 Uchida, S., see Eisaki, H. 231, 240 Uchida, S., see Luke, G.M. 212 Uchida, S., see Murayama, e. 216 Uchida, S., see Takagi, H. 215,230,241 Ueda, K. 20, 46, 78 Ueda, S.44 Uehara, M. 216, 217, 264 Uemura, Y.J., see Luke, G.M. 212 Uher, C., see Lee, c.a 113 Uhlarz, M., see Pfleiderer, C. 226, 237 see Kreisel, 1. 18 Ulrici, Umezawa, H., see Matsumoto, H. 227, 228, 230 Urano, C., see Koshihara, S. 72 Urano, C., see Munekata, H. 36 Ushioda, S., see Tsuruoka, T. 18 Uspenskii, Yu.A., see Kulatov, E. 43 Ustinovich, S., see Tomilo, Zh. 219, 220. 226 Uwatoko, Y. 273 Uwatoko, Y., see Eto, T. 181
w.,
Vaast, C; see Bonville, P. 270 Vaglio, R., see Andreone, A. 215, 219, 241 van Bockstal, L., see van Esch, A. 5, 10, 26, 30, 34,55 van de Riet, E. 106 van der Beek, C.J., see Izawa, K. 240, 285 van Dover, R.B., see Cava, R.J. 202, 205, 220, 223,240,242,283 van Esch, A. 5, 10, 26, 30, 34, 55 van Esch, A., see de Boeck, 1. 5, 9 van Hoof, C., see de Boeck, J. 5, 9 van Roy, W., see van Esch, A. 10 van Schilfgaarde, M. 29, 44 van Schilfgaarde, M., see Belashchenko, K.D. 207 van Smaalen, S., see Dettinger, A. 216, 217, 264, 266 van Stapele, R.P. 75 van Sternbergen, A.S., see van Esch, A. 5, 26, 30, 34,55 van Vucht, J.H.N. 322 Vanacken, 1., see Respaud, M. 179 Vanelle, E., see Sadowski, J. 10 Vanoni, see Bud'ko, S.L. 216, 217 Vantomme, A., see Wahl, U. 14 Varma, C.M., see Blount, E.I. 238, 239
w.,
AUTHOR INDEX Vanna, C.M., see Ng, TK 210 Vasson, A., see Kreisel, J. 18 Vasson, A.-M., see Kreisel, J. 18 Vaterlaus, A., see Weber, W. 114 Vavra, W., see Lee, C.H. 113 Vazquez, M., see Areas, J. 172 Vazquez, M., see Hernando, A. 94 Vazquez, M., see Stobiecki, T. 109 Vazquez, M., see Tejedor, M. 168 Verbanck, G., see van Esch, A. 5, 26, 30. 34. 55 Verbeek, B.H .. see Nieuwenhuys, GJ. 231, 280, 283,284 Verdier, T., see Due, N.H. 94, 133 Verges, P., see Prassides, K. 231, 240 Vemiere, A.• see Brison, J.P. 220, 283 Vijayakumar, V., see Meenakshi, S. 216,217,243 Vijayaraghavan, R., see Dhar, S.K. 227, 240-242, 251 Vijayaraghavan, R., see Godart. C. 218 Vijayaraghavan, R., see Gupta. L.C. 216. 288 Vijayaraghavan, R., see Hossain, Z. 219, 242. 248. 253,271 Vijayaraghavan, R., see Mazumdar, Ch. 234, 235, 270 Vijayaraghavan, R., see Meenakshi, S. 216. 217, 243 Vijayaraghavan, R., see Nagarajan, R. 216. 225. 242,253 Vinnikov, L. Ya. 260. 264, 273 Viret, M .• see Coey, J.M.D. 4,175 Vittoria, C .. see Bushnell. S.E. III Vittoria, C., see Forester, D.W 117 Vogt, T., see Detlefs, C. 241, 242, 245, 253, 254 Voiron, I., see EI Massalami, M. 242 Voiron, J., see Gavigan. J.P. 123 Voiron, I., see Givord, D. 133, 141, 163 Voiron, I., see Wiichner, S. 141, 163 Voitenko, A. I., see Gabovich, A.M. 238 Vollmer, R, see Pfleiderer, C. 226, 237 Volz, K.. see Heimbrodt, W 10 von Lips, H. 260--262 von Lips, H., see Drechsler, S.-L. 234 von Lips, H., see Mazumdar, Ch. 229 von Molnar, S. 34 von Molnar, S., see Coey, I.M.D. 4, 175 von Molnar. S., see Munekata, H. 5, 6, 10, 17 von Molnar, S., see Ohno, H. 5, 10, ll, 32. 34, 35 von Molnar, S., see Wolf, S. 4 Vonrob'ev, G.P., see Popov, Yu. F. 179, 180 Vorderwisch, P., see Gasser, U. 241 Vorobev, G.P., see Kadomtseva, A.M. 180 Vouroutzis, N.• see Speliotis, A. 119 Vrijen, R. 79 Vukadinovic, N. III
401
Vukadinovic, N., see Le Gall, H. III Vulliet, P., see Sanchez, J.P. 219. 220. 224, 225 Vulliet, P., see Tomala, K. 219, 335, 357 Vurgaftman, I. 62 Waag, A., see Fiederling, R. 70 Wada,M. 103, 118, 122, 133-135 Wagener, W., see Sanchez, D.R. 226, 266 Wagner. T.A. 231, 285 Wahl, U.14 Walf. G.H., see Sanchez, D.R. 226, 266 Walker, E., see Peter, M. 214 Walker, I.R., see Saxena, S.S. 209 Wallace, WE., see Debray, DK 350, 356 Wallace. WE., see Walline, R.E. 340 Walline, R.E. 340 Walukiewicz, W 33 Wan, X., see Bhatt, R.N. 48 Wandass, J.H. 106 Wang. B.W. 94 Wang, G.-F. 238 Wang, H.H., see Williams. J.M. 209 Wang,I.H.176 Wang, K., see Vrijen, R. 79 Wang, S., see Ohno, Y. 63. 73 Wang, S., see Yang, J. 9 Wang, X., see Rhee, I.Y. 209 Wang, X.F., see Louriero da Silva 62 Wang, X.Q., see Jee, C.S. 323, 357 Wang. Y., see He, T. 284. 285 Wang, Y.Q., see Wu. M.K. 208 Wang, Z.D. 216, 217 Wang, Z.R., see Xu. M. 225 Wappling, R, see Frey, E. 315. 320 Wiippling, R, see Mathieu. R. 175 Ward, R.C.C., see Arnaudas, 1.1. 159, 160 Ward, RC.C., see Ciria, M. 106, 159 Ward. R.C.C., see de la Fuente. C. 162 Ward, R.C.C., see del Moral. A. 159-162 Ward. RC.C., see Jehan, D.A. 159 Ward. R.C.C.• see Swaddling. P.P. 159 Warden, M., see Cywinski. R. 207 Wasiela, A., see Ferrand. D. 5, 27.49,54,60 Wasiela, A., see Haury, A. 5.49, 54 Wasiela, A., see Kossacki, P. 49. 74 Wasserman, E.F. 310 Watanabe, M., see Katsumoto, S. 20, 37, 50 Watanabe. T., see Izawa, K. 260 Watanabe, T., see Yokoya, T. 243 Watts, R.• see Ali, M. 109 Watts. R.• see Gibbs. M.RJ. 94. 188 Wawro, A., see Zuberek, R. Ill, 154. 156, 157, 170
402
AUTHOR INDEX
Weber. E.R.• see Luysberg, M. 7. 33 Weber. M. 106 Weber. M.• see Schmidt. H. 264 Weber. W. 114 Weber. w.. see Back. e.H. 174 Webster. PJ. 318 Wecht. KW.• see Casey Jr.• H.e. 38 Wehner. B.• see Behr, G. 225 Wehner. 8.. see Belger. A. 335 Wehner. B.• see Jaenike-Roessler, U. 277 Weht.R.206 Wei. S.-H. 44 Wellman. PJ.• see van Esch. A. 5. 26. 30. 34. 55 Wells. M.R .• see Arnaudas, 1.1. 159. 160 Wells. M.R.. see Ciria, M. 106. 159 Wells. M.R .• see de la Fuente. C. 162 Wells. M.R .• see del Moral. A. 159-162 Wells. M.R.. see Jehan, D.A. 159 Wells. M.R .• see Swaddling. P.P. 159 Welp. U.• see de Wilde. Y. 266. 277 Welp. U.• see Metlushko, V.24O Weng. GJ.• see Nan. C.-W. 173 Wermeille. D.• see Song. C. 221. 256. 284. 285 Werner. D.• see Michor, H. 223. 279 Werthamer. N.R .• see Hohenberg, P.e. 202 Westgate. e.w.. see Chien. C.L. 27 Whangbo. M.H .• see Williams. J.M. 209 White. G.K .• see Barron. T.H.K. 311. 313 White. G.K .• see Taylor. R.E. 311 Widder. w.. see Bauernfeind. L. 213 Wiesner. U.• see Buchgeister, M. 220 Wijngaarden. R.I. 205 Wijngaarden. R.I .• see Saba, N. 225 Wilamowski. Z.. see Fedorych. O.M. 19. 58 Wildes. A.R .• see Boothroyd. A.T. 223 Wiley. J.D. 73 Wilhelm. M.• see Hillenbrand. 8. 216. 228. 240. 241. 250. 278 Wilhelm. M.• see Peter. M. 214 Wilhoit. D.. see Baril. L. 110 Wilhoit. DR. see Dieny, B. 110. 163 Wilkening. W.• see Schneider. J. 19 Wilkinson. I.. see Dugdale. S.B. 230. 240 Willemsen. B.A .• see Jacobs. T. 216 Williams. A.R .• see Janak. J.F. 315 Williams. G.• see Stampe, P.A. 324 Williams. J.M. 209 Williams. P.I. 119. 122. 133 Williams. P.I.• see Grundy. PJ. 117 Willis. J.O. 258 Willson. A.• see Park. Y.D. 74 Wilson. P.• see Chopra. H.D. 144 Wilson. R.• see Liu, S. 37 Wilson. R.G .• see Theodoropolpu, N. 14
Wimbush. S.C .• see Hase, K. 205 Winiarska, A.. see Tornala, K. 219 Winiarski. A.• see Jarosz. J. 326. 327. 357 Winzek.B, 137-139 Winzer. K. 214. 234 Winzer. K.• see Drechsler. S.-L. 234 Winzer. K.. see Goll, G. 230 Winzer. K.. see Heinecke. M. 205 Winzer. K.. see Mandal, P. 205. 208. 211 Winzer. K.. see PengoZ.Q. 209 Winzer. K.. see Riblet. G. 203 Winzer. K.• see Shulga, S.V. 233. 241. 281 Wisniewski. A.• see Dabrowski. 8. 180. 181 Wisniewski. A.• see Zuberek, R. Ill. 156. 157. 170 Witer, K.• see Hansen. P. 115. 117 Wohlfarth. E.P. 208. 231 Wojtowicz. T. 32 Wolf. M.• see Freudenberger, J. 236. 237 Wolf. M.• see MUller. K.-H. 216 Wolf. P.A.• see Story. T. 5 Wolf. S.4 Wolf. SA 4 Wolff. P.A. 48 Wollan. E.O .. see Cable. J.w. 320. 356 Won. H. 284 Won. H.. see Maki, K. 240.281.282 Wood. C.E.C .• see DeSimone. D. 6 Woodfield. B.F.. see Wright. D.A. 207 Wright. D.A. 207 Wr6bel. J.• see Kossacki, P. 49.74 Wrona. J.. see Stobiecki, T. 109 wu, G.H.. see Wang. s.w 94 Wu. J.• see Cao. Q.Q. 178 Wu. J.H .. see Wang. J.H. 176 wu, M.K. 208 we, R. 105 Wu, R.. see Freeman. AJ. 105. 109 Wu. R.Q. 105 WUchner. S. 141. 163 WUchner. S.• see Givord, D. 133. 141. 163 Wursch, Ch.• see Back. e.H. 174 WUrsch. Ch.. see Weber. W. 114 Wyder, P.• see Goll, G. 230 Wyder. P.• see Rybaltchenko, L.F. 267. 277 Wyder. P.• see Yanson, I.K. 276 Wylie. M.T.• see Cywinski. R. 207 Xiong. X.• see Dabrowski. B. 181 Xiurong, W.. see Houqing, Z. 185 Xu. C.H. 202. 219. 230 Xu. H.. see Jiang. X. 119 Xu. M. 225
AUTHOR INDEX Xu. M.• see Cho. B.K. 242. 245, 249, 267 Xu. M., see Johnston-Halperin, E. 209 Xu, M.• see Kogan. V.G.273 Xue, Y.Y.• see Dezaneti, L.M. 242, 249. 251. 270, 271 Xue, Y.Y.. see Gao, L. 245. 269. 270 Yablonovitch, E., see Vrijen, R. 79 Yakinthos, J.K., see Gamari-Seale, H. 323 Yakoby, E.R., see Prozorov, R. 284 Yamada, M. 13 Yamada, M.. see Okabayashi, J. 79 Yamaguchi. M., see Hayashi. Y. 117. 119-121. 133 Yamaguchi. M.• see Honda, T. 119, 133. 186. 187 Yamaguchi, Y.. see Onodera, H. 216, 217 Yamaguchi, Y.. see Yamauchi. H. 231 Yamamoto, K.• see Hazama, Y.79 Yamamoto, K., see Okazawa, D. 13 Yamamoto. K., see Tazima, M. 7. 9 Yamamoto,T. 29. 33 Yamamoto,T.• see Choi, 1.-H. 266 Yamamoto,T.• see Katayama-Yoshida. H. 76 Yamamoto. Y., see Sonoda, S. 14,77 Yamamura, M., see Haneda, S. 12, 16 Yamasaki,J., see Narita, K. 108 Yamauchi, H. 231 Yamauchi. H.. see Onodera, H. 216, 217 Yanagi, S. 66 Yanagi, S.• see Endo, T. 10 Yanagi, S.• see Slupinski, T. 36 Yanase, A., see Kasuya, T. 4 Yang, OX. see Chopra, H.D. 144 Yang, H.D., see Shelton. R.N. 207. 208 Yang, I.-s. 229 Yang, I.S., see Mun, M.O. 216. 217 Yang,1. 9 Yanhong, X.• see Houqing, Z. 185 Yanson, I.K. 276 Yao, Y.D.. see Lee. WH. 205 Yao, Y.D., see Lin, M.S. 205 Yaouanc,A. 322 Yaouanc, A., see de Reotier, P.O. 322 Yaouanc, A.• see Mulders. A.M. 322. 357 Yaron, tJ. 242, 248, 249. 251,270. 271 Yaron, tJ., see Eskildsen, M.R. 269, 276 Yasuda, H. 7 Yasuda,H.• see Abe, E. 14. 15.71 Yasuda, H., see Guo, S.P. 7 Yasuda. H., see Yang. J. 9 Yasuda,T.• see Kuroiwa, T. 38, 39 Yates. R.B., see Gibbs, M.R.1.94. 188 Yatskar, A. 251. 271, 272
403
Yatskar, A.• see Bud'ko, S.L. 267 Yatskar, A.• see Canfield, P.C. 215. 252, 267. 270 Yatskar, A., see Cho, B.K. 242, 249, 256, 257 Yatskar, A., see Lacerda, A. 205, 217, 220, 251, 289 Ye,J.27 Ye, J.• see zou, Z. 211. 213, 288 Yee, D.S.. see Sadowski. 1. 10 Yeshurun, Y.• see Prozorov, R. 284 Yethiraj. M. 272, 279 Yethiraj. M., see Chang. L.J. 242 Yethiraj, M., see Paul, D. McK. 258, 269, 276 Yethiraj, M.• see Song, K.I. 221, 256 Yokoya,T. 243 Yokoyama, H.• see Shima, T. 120, 156 Yoshida, Y., see Koyanagi, A. 346 Yoshino,1.. see Hazama, Y.79 Yoshino.J.• see Nishikawa, Y.5 Yoshino.1., see Okazawa, D. 13 Yoshino. J., see Satoh, Y.9. 24 Yoshino, J., see Tazima, M. 7,9 Yoshizawa, H.• see Kawano. H. 266. 267 Yosida, K. 223 You. Y.B.• see Jiang, P.1. 226 You. Y.B.• see Ku, H.C. 284,285 You. Y.B., see Lai, C.C. 276 You, Y.B., see Lin, M.S. 205 Youn, K.B., see Szymczak. H. 151 Youn, K.B.• see Zuberek, R. III. 151 Youn, S.1., see Lee, J.1. 205 Young, O.K., see Johnston-Halperin, E. 71 Young, D.K., see Ohno, Y. 70, 71 Yuen, T.• see Lin, C.L. 318 Yvon, K.. see Gratz, E. 317 Yvon, K.• see Pacheco. J.V. 327 Zackay, V.F.. see Fink, H.1. 205, 208, 211 Zaets, W., see Saito, H. 13 Zahn, G., see Jaemke-Roessler, tJ. 277 Zahn. P., see Drechsler. S.-L. 234 Zahurak, S.M.• see Rosseinsky, M.1. 209 Zajl\C, M. 13 Zalalutdinov, M., see Hayashi, T. 26 Zandbergen, H.W 219, 220, 223. 242, 266 Zandbergen, H.W, see Cava, R.I. 202, 205, 220, 223,240,242,283 Zandbergen, H.W., see He. T. 284, 285 Zandbergen, H.W., see Michor, H. 223, 279 Zandbergen, H.W, see Siegrist, T. 218. 246, 247. 251,253,270,335 Zapf. V.Z., see Bauer, E.D. 214 Zaremba, V.I., see Kalychak, Y.M. 331 Zarestky, J. 212, 230
404
AUTHOR INDEX
Zarestky, 1., see Dervenagas, P. 230, 242, 245, 255,256 Zarestky, J., see Goldman, A.1. 233 Zaslavsky, A., see Munekata, H. 1 I, 36, 57, 58 Zavada, J.M .. see Theodoropolpu, N. 14 Zavalii, P.Y., see Kalychak, Y.M. 331 Zawadski, J., see Buchgeister, M. 220 Zeldov, E., see Dewhurst, C.D. 202, 205, 220, 267, 277 Zeldov, E., see James, S.S. 267 Zene~C.43,48,50,51, 175 Zeng, H.K., see Lee, W.H. 205, 276 Zenitani, Y.,see Ekino, T. 259 Zenitani, Y., see Nagamatsu, 1. 202, 203 Zhang, F.C. 42, 60 Zhang, K.• see Dunlap, B.D. 212, 256 Zhang, S. 27 Zhang, S.Y., see Cao, Q.Q. 178 Zhang, Z.H., see Chu, R.K. 219 Zhao, G., see Garda-Landa. B. 176, 177 Zhao,I.H. 10 Zhao, T.S .• see Lee, J.1. 205 Zhao, Y.-I. 42, 44, 78 Zhou. X.Z., see Stampe, P.A. 324 Zhou, Y.-K., see Hashimoto, M. 10, 14
Zhou, Y.K., see Kanamura, M. 73 Ziebeck, K.R.A., see Parsons, M.J. 318, 357 Ziebeck, K.R.A., see Taylor, J.w. 318, 357 Zieglowski, 1. 353 Ziese, M. 4 Zimgiebl, E., see Galffy, M. 275 Zittartz, J., see Miiller-Hartman, E. 219, 221, 255 Zou,Z.211,213,288 Zuberek, R. 105, III, 151. 154, 156, 157, 170, 173 Zuberek, R., see Lafford, A. 156 Zuberek, R., see Slawska-Waniewska, A. 170, 171 Zuberek, R., see Stobiecki, T. 109 Zuberek, R., see Szumiata, T. 105, 156, 172, 173 Zuberek, R., see Szymczak, H. 151, 174 Zuckermann, M.J., see Cochrane, R.W. 122 Zudov, M.A., see Matsuda. Y.H. 38 Zunger, A. 45 Zunger, A., see Mahadevan, P. 78 Zunger, A., see Wei, S.-H. 44 Zutic, I. 71 Zutic, I.. see Das Sarma, S. 79 Zverev, Y.N., see Strukova, G.K. 226 Zvezdin, A.K., see Popov, Yu. F. 179, 180 Zymierska, D., see Zuberek. R. 105, 170
Subject Index
anisotropic thermal expansion, 356 anisotropy of H c2' 231 anomalous Hall effect - in diluted magnetic semiconductors, 10, II, 14, 15, 27,29.34,36,50 antiferromagnetic ordering - in RT2B2C compounds, 215 Arrott plots - of diluted magnetic semiconductors, 24, 28 atomic force microscopy (AFM) - of diluted magnetic semiconductors. 9,14 atomic-layer epitaxy (ALE) - of diluted magnetic semiconductors, 10 Bardeen-Cooper-Schrieffer (BCS) theory, 227 bending device, 109, 110, 113 bilinear two ion exchange interaction, 312 Bloembergen-Rowland indirect exchange - in diluted magnetic semiconductors, 48 Bloembergen-Rowland mechanism - in diluted magnetic semiconductors, 52 boron isotope effect, 227 - in YNi2B2C, 229 bound magnetic polarons (BMP) - in diluted magnetic semiconductors, 31, 60, 48 Brillouin behavior - of diluted magnetic semiconductors, 28 Brillouin function - in diluted magnetic semiconductors, 23, 51 Burstein-Moss shift - in diluted magnetic semiconductors, 40 Coo based superconductors, 206 cantilever, 113 - effect of clamping, 106 - experimental methods, 110, 159, 173 - general, definition, 94, 106 - in applications (devices, MEMS), 119, 186 CEF - derivation, expressions, 162 - general, definition, 111 - in ErILu superlattices, 162
charge localisation - in manganites (perovskite), 177 clean-limit type 11 superconductors, 281 coefficient of magnetostriction, 99, 102, 108 coherence length at T = 0 - of YNi2B2C and LuNi2B2C, 240 colossal magnetoresistance - in cobaltates (perovskite), 174 - in layered manganese oxides, 182 - in manganites (perovskite), 174, 175 Coulomb pseudopotential - of YNi2 B2C and LuNi2 B2C, 240 critical expansion, 315 critical scattering - in diluted magnetic semiconductors, 30 critical temperatures for superconductivity - of RT 2B2C compounds, 215 crystalline electric field - derivation, expressions, % - of RT2B2C compounds, 243 Curie-Weiss behaviour, 35 Curie-Weiss fit - of diluted magnetic semiconductors, 24 Curie-Weiss plot - of diluted magnetic semiconductors, 13 cyclotron resonance - in diluted magnetic semiconductors, 37 de Gennes scaling, 216 Debye model, 311 Debye temperature - of YNi2B2C and LuNi2B2C, 240 density of states (005), 74 - in diluted magnetic semiconductors, 21,44,45,47, 53,56,74 density of states at the Fenni level - for Y(Nil_xCoxhB2C and Y(Nil_xCuxhB2C, 278 - of RNi2B2C superconductors, 241 -ofYxLul_xNi2B2C,282 - of YNi2B2C and LuNi2B2C, 240 depression of superconductivity - in (Y,Dy)Ni2B2C and (Lu,Dy)Ni2B2C, 288
405
406
SUBJECf INDEX
diluted magnetic semiconductors (OMS). 4 Dingle temperature - of YNi2B2C and LuNi2B2C, 240 dirty limit - in YxLul_xNi2B2C. 281 OMS, 27, 51 double exchange - in diluted magnetic semiconductors. 51.60 double exchange mechanism - in diluted magnetic semiconductors. 19,43 Drude conductivity - in diluted magnetic semiconductors. 37 elastic modulus: l:!.E effect - general, definition, 93, 94, 150 electron spin resonance (ESR). 19.20 - of diluted magnetic semiconductors, 18 electron--phonon coupling constant - ofYNi2B2C and LuNi2B2C, 240 - in YxLul_xNi2B2C. 282 Eliashberg theory, 228 enhanced pair breaking - in (Y,R')Ni2B2C, 287 epitaxial misfit (mismatch), 113 epitaxial strains - in ErlLu superlattices, 162 - R/(YlLu] superlattices, 159 - second order (parameters), 105 expansion - derivation, expressions, 98 extended domain wall (EDW) - general, definition. 163 - (Nd,Co)/(Th,Co)/(Nd,Co) sandwich system, 163 - (Th.Co)/(Nd,Co)/(Th,Co) sandwich system. 163 - in (Th,Fe)/(Fe,Co,B,Si) muhilayers, 167 extended x-ray absorption fine structure (EXAFS) - of diluted magnetic semiconductors, 12. 17 Faraday rotation - in diluted magnetic semiconductors, 39, 78 Fermi velocity - of YNi2B2C and LuNi2B2C, 240 ferromagnetic imprinting - in diluted magnetic semiconductors, 75 ferromagnetic resonance (FMR) - in diluted magnetic semiconductors, 19 ferromagnetic semiconductors, 1,75 field induced magnetostriction - in GdCU2, 347 field-effect transistor (FET) - of diluted magnetic semiconductors, 73 first principles calculation - of diluted magnetic semiconductors, 78 first-principles studies
- of diluted magnetic semiconductors, 41 form effect, 93. 95 full potential augmented plane wave (FLAPW) method - in diluted magnetic semiconductors, 42 GdCu, 343 giant magnetoresistance (GMR) - in (Tb,Fe)/(FelCo) multilayers, 151 - in granular solids, 168 - in trilayer structures of diluted magnetic semiconductors, 64 Ginzburg-Landau parameter at T = 0 -ofYNi2B2C and LuNi2B2C, 240 GMS, \16, 132, 191 - in (Tb,Fe.Co)/Fe multilayers, 157 - in a-Tb(Fe,Co). 127 - in layered manganese oxides, 182 - in low fields, 157, 186 - of RT alloys, 116, 140 - optimalisation, optimal values. 117. 191 Gor'kov-Eliashberg theory, 229 Hall coefficient - for LuNi2B2C and YNi2B2C, 236, 237 Hall effect - for YNi2B2C and LuNi2B2C. 236 Hall resistivity heterostructures - for LuNi2B2C and YNi2B2C, 237 - of diluted magnetic semiconductors, 61 hexagonal vortex lattice - in YNi2B2C and LuNi2B2C, 274 hybridisation - between 3d and 5d states, 114, 115 (In,Mn)As quantum dots (QDs), 17 induced anisotropy, 103 - experimental methods. 108,109 - FeffbFeCoIFe sandwich, 144 - in a-(Tb,Fe) thin films, 119 - in nanocrystalline alloys, 172 - thickness dependence. 113 infrared (lR) and far infrared (FIR) transmission spectra - of diluted magnetic semiconductors, 37 infrared spectroscopy - of diluted magnetic semiconductors, 19 initial-susceptibility method, 109 insulator-to-metal transition - in diluted magnetic semiconductors, 15, 19.21,49 interdiffusion, 139, 152, 155. 158 - in terfecohanIFe rnultilayers, 157 interlayer coupling - in trilayer structures of diluted magnetic semiconductors, 64, 66
SUBJECT INDEX intermediate valence of cerium - in CeNi2B2C. 246 interplay of superconductivity and magnetism. 207 - in RT2B2C compounds. 265 intra-center correlation energy - in diluted magnetic semiconductors. 41 Jahn-Teller distortion - in diluted magnetic semiconductors. 18 Jahn- Teller effect - in layered manganese oxides. 183 - in manganites (perovskite), 175 Joule magnetostnction, 93 - derivation. expressions. 96 - in manganites (perovskite), 178 Kerr effect - in diluted magnetic semiconductors. k . P Hamiltonian - in diluted magnetic semiconductors. k . P interactions - in diluted magnetic semiconductors. k . P Luttinger matrix - in diluted magnetic semiconductors.
78 46
57 52
lattice constants - of diluted magnetic semiconductors. 7. 9. 12. 15. 17 lattice constants a and c - of RNi2B2C. 246 lattice distortions - in RT2B2C compounds. 221 lattice properties - of diluted magnetic semiconductors. 15 layered manganese oxides. 182 linear combination of atomic orbitals (LCAO) - in diluted magnetic semiconductors. 42 local lattice configuration - of diluted magnetic semiconductors. 17 local-spin density approximation (LSDA) - in diluted magnetic semiconductors. 42. 43 London penetration depth for YNi2B2C. 274 low-temperature annealing - of diluted magnetic semiconductors. 9. 10 lower critical field at T = 0 - ofYNi2B2C and LuNi2B2C. 240 LuNi2B2C-type structure. 218 Luttinger-Kohn 6 x 6 Hamiltonian - in diluted magnetic semiconductors. 69
Mossbauer spectra - in nanocrystalline alloys. 170 - in terfecohan, 126 - in terfecohan/(Y.Fe) multilayers, 150 magnetic anisotropy
407
- derivation. expressions. III - in diluted magnetic semiconductors. 23. 24, 54. 57 - in thin films. 122 - of diluted magnetic semiconductors. 36 - optimalisation, optimal value. 190 - perpendicular/in-plane. 116 - thickness dependence. 141 magnetic circular dichroism (MCD) - in diluted magnetic semiconductors. 40 magnetic domains - in diluted magnetic semiconductors. 26. 58 magnetic impurities in a nonmagnetic superconductor. 286 magnetic order - in ErNi2B2C and TmNi2B2C. 276 - in RT2B2C compounds. 243 magnetic ordering temperature - of RT2B2C compounds. 220 magnetic ordering temperatures TN - of RI'2B2C compounds. 219 magnetic pair-breaking effects - for (Y.R)pd2B2C. 287 magnetic phase diagrams - of HoNi2B2C. 261 magnetic polarons - in manganites (perovskite), 178 magnetic pressure. 99 magnetic properties - of diluted magnetic semiconductors. 21 magnetic stiffness - in diluted magnetic semiconductors, 54 magnetic structure of GdCU2. 346 magnetic structures - in the ground state of RNi282C compounds. 244 - of HoNi2B2C, 260 - of NdNi282C and SmNi2B2C. 252 magnetic susceptibility for various CeT2B2C compounds. 247 magnetic-anisotropy oscillations in ultrathin films. 114 magneto-optic Kerr effect - in thin anisotropic films. 109 magnetoelastic coefficient. 113 - in (Tb.Fe)/(Fe.Co) multilayers, 142 - in (Tb,Fe)/Fe multilayers, 143 - in a-Tbtfe.Co), 122, 127 - R/[ YlLu I superlattices, 159 magnetoelastic coupling - derivation. expressions. 96, 97, 99, 107. 108 - second order (parameters). 105 - strain (stress) dependence. 113 magnetoelastic effects - in Gd compounds. 311 - in RT2B2C compounds. 221
408
SUBJECf INDEX
magnetoelastic interactions, 312 magnetoresislance - in trilayer structures of diluted magnetic semiconductors, 65 - of diluted magnetic semiconductors, 13, 15, 27, 32, 38 - of RT2B2C compounds, 261 magnetoresislance (MR) sensors, 4 magnetoresislance - of YNi2B2C and LuNi2B2C, 234 magnetoresistivity -ofHoNi2B2C,263 magnetostriction, 120,314 - (Th,Co)/(Nd,Co)/(Th,Co) sandwich system, 163 - crystalline-fraction dependence, 169 - in (Co,Fe)-AI-O granular systems, 173 - in (Co,Pd)/Ag multilayers, 155 - in (Fe,Co)/Au multilayers, 156 - in (Sm,Fe,B) thin films, 143 - in (Sm,Fe,B)/(Th,Fe,B) multilayers, 156 - in (Tb.Fe) thin films, 142 - in (Th,Fe)/(Fe,Co) multilayers, 147 - in (Th,Fe)/Fe multilayers, 142, 143 - in a-(Sm,Fe), 120 - in a-(Sm,Th)Fe-B, 120 - in a-(Th,Co), 120 - in a-(Th,Dy)(Fe,Co), 128 - in a-(Th,Dy)Fe, 122, 130 - in a-(Th,Fe) thin films, 117 - in a-Th(Fe,Co), 127 - in applications (devices, MEMS), 186 - in cobaltates (perovskite), 184 - in low fields, 118 - in nanocrystalline «Th,Dy),Fe), 135 - in nanocrystalline «Th.Dy).Mo)Fe2. 138 - in nanocrystalline «Th,Dy),Zr )Fe2' 138 - in nanocrystalline (Th,Dy)(Fe,Nb), 119 - in nanocrystalline alloys, 168 - in nanocrystalline terfenol-D, 134 - in ThDyFe + ZrlNb multilayers, 139 - in terfecohan, 130 - magnetisation or field dependence, 128 - of a (Th,Co)/(Nd,Co)/(Th,Co) sandwich system, 163 - optimalisation, optimal value, 130 - principal modes, 100 magnetostriction in high TC-superconductors. 353 magnetostrictive spring magnet type multi layers, 140 magnetostrictive susceptibility, 121, 128, 132, 191 - of (Th,Fe)(Fe,Co) multilayers, 94 - of (Th,Fe)/(Fe,Co) multilayers, 148 - of (Th,Fe)/(Fe,Co,B.Si) multilayers, 149, 167 - of (Th,Fe,Co)IFe multilayers, 158 - of a (Nd.Co)/(Th,Co)/(Nd,Co) sandwich system, 163 - of a (Th,Co)/(Nd,Co)/(Th,Co) sandwich system, 163
- of a FelThFeCoIFe sandwich. 167 - of a-fIb.Co), 121 - of Sm(Fe,Co), 122 - of terfecohan/(Fe,Co) multilayers, 149 - of terfecohan/(Y,Fe) multilayers, 149 - optimalisation, optimal value, 149 magnetostructural transition, 336, 339 magnetotransport properties - of diluted magnetic semiconductors. 27 magnetovolume effect - in cubic systems, 315 - in gadolinium, 322 - in hexagonal systems, 320 - in monoclinic systems, 354 - in orthorhombic systems, 336 - in tetragonal systems, 329 MBE, 6, 13, 19 - of diluted magnetic semiconductors, 13, 14 MBE-grown (Ga,Mn)N films, 14 MCD,41 mean field approximation (MFA) - in diluted magnetic semiconductors, 61 mean free path - of YNi2B2C and LuNi2B2C, 240 mean-field theory - of diluted magnetic semiconductors, 73 mean-field Zener model, 50, 60 - in diluted magnetic semiconductors, 50, 55, 59, 60, 75, 77 MEMS - in applications (devices. MEMS), 94, 186, 188, 190 - optimalisation, optimal value, 149 metal-insulator transition (MIT), 4, 41, 49. 56, 60 - in diluted magnetic semiconductors, 15,22,29,49 metal-organic vapor-phase epitaxy (MOVPE) - of diluted magnetic semiconductors, 10 metamagnetic transitions - in RT2B2C compounds, 261 microscopic theory of magnetoelastic effects, 312 migration-enhanced epitaxy (MEE) - of diluted magnetic semiconductors, 9 modified Brillouin function - in diluted magnetic semiconductors, 35 MOKE - experimental methods, 109 - in FeB/CulFeB sandwiches. 109 molecular beam epitaxy (MBE) - of diluted magnetic semiconductors, 5, 6 molecular-field approximations - in diluted magnetic semiconductors, 42, 51 Monte-Carlo studies - of diluted magnetic semiconductors, 61 MR, 12,32,65
SUBJECT INDEX MSMM, 140 - in (Tb,Fe)/(Fe.Co) rnultilayers, 144 - in applications (devices. MEMS). 150. 189. 191 - in terfenol-DlFiniment multi layers. 145 multi-band superconductors. 233 multilayer structures - in diluted magnetic semiconductors. 61 nanocrystallisation, 168 Nb spacer layers. 139 nesting vectors. 229 non-local corrections to H c2. 231 nonmagnetic contribution to the thermal expansion, 312 normal state Sommerfeld constant - ofYNi2B2C and LuNi2B2C. 240 optical conductivity - of diluted magnetic semiconductors. 37 optical spectroscopy - of diluted magnetic semiconductors. 19 orthorhombic distortion - of tetragonal HoNi2B2C. 222 p-d exchange. 55 - in diluted magnetic semiconductors. 20. 21, 52. 69 p-d hybridization - in diluted magnetic semiconductors. 42. 44. 47. 75 p-d interaction - in diluted magnetic semiconductors, 46 pair breaking - in (Y.Dy)Ni2B2C and (Lu.Dy)Ni2B2C. 288 penetration depth at T = 0 - of YNi2B2C and LuNi2B2C, 240 perovskites, 174 photo-induced ferromagnetism - in (In.Mn)AslGaSb. 72 photoemission - in diluted magnetic semiconductors. 21. 31.44.46 photoemission spectroscopy - of diluted magnetic semiconductors. 13 photoluminescence (PL). 20 - of diluted magnetic semiconductors. 10. 19. 38, 78 positive curvature of H c2 (T), 233 quadrupole splitting - in various RNiBC and RNi2B2C compounds. 243 quantum dots (QDs). 10, 17 - of diluted magnetic semiconductors, 17 quantum well states in ultrathin films, 114 quasiparticle energy gap at T = 0 -ofYNi282C and LuNi282C, 240 Raman scattering - of diluted magnetic semiconductors. 20
409
reentrant and near-reentrant behaviour - of HoNi2B2C. 263 reentrant behaviour - in HoNi282C. 264 reentrant superconductivity - in Ndo.35'Tho.65Ru2. 210 reflection high energy electron diffraction (RHEED), 7 - of diluted magnetic semiconductors. 7, 8 reorientation transition of the hexagonal vortex lattice. 274 residual resistance ratio p(300 K)/ peT ~ Te) - of YNi282C and LuNi282C. 240 resistivity - ofYNi282C. 227 resonant tunneling diode - of diluted magnetic semiconductors. 69 resonant tunneling diode structures - of diluted magnetic semiconductors. 68 resonant tunneling diodes (lITDs) - of diluted magnetic semiconductors. 67 RHEED patterns - of diluted magnetic semiconductors. II rhombohedral distortion - in YNi2B2C and LuNi2B2C. 274 RKKY function - in diluted magnetic semiconductors. 61 RKKY interaction - in diluted magnetic semiconductors. 57 RKKYmodel - in diluted magnetic semiconductors. 52. 60 RNi2B2C superconductors, 202 RTD.68 Ruderman-Kittel-Kasuya--Yosida (RKKY) mechanism - in diluted magnetic semiconductors. 48 Ruderman-Kittel-Kasuya--Yosida oscillations - in diluted magnetic semiconductors. 44 SAMR - experimental methods. 108 sandwich system. 163 - (Nd.Co)/(Tb.Co)/(Nd,Co) sandwich system. 163 - (Tb.Co)/(Nd.Co)/(Tb,Co) sandwich system. 163 - FelTbFeCoIFe sandwich, 167 scanning Hall microscope - of diluted magnetic semiconductors. 26 scanning tunneling microscopy (STM) - of diluted magnetic semiconductors. 7, 18 secondary electron spin-polarisation spectroscopy (SESPS).112 - experimental methods. 112 small-angle magnetisation rotation. 108
410
SUBJECT INDEX
SMFMR,III - in ColAg multilayers, 154 - in nanocrystalline alloys, 171 - in Ni/[TilAg/Pb] multilayers, 154 Sommerfeld constant - in YxLUI_xNi2B2C, 282 specific heat jump at T c - of YNi2B2C and LuNi2B2C, 240 sperimagnetism, 116 - in a (Th,Co)/(Nd,Co)/(Tb,Co) sandwich system, 163 - in a-(Th,Co), 120, 122 - in a-(Th,Dy)(Fe,Co), 123 - in amorphous (R,T) alloys, 123 speromagnetism of (Y,Fe), 116 spin coherence - in diluted magnetic semiconductors, 75 spin valve, 110 spin-orbit coupling, 96 - in amorphous (R,T) alloys, 116 - in diluted magnetic semiconductors, 27,49,52, 57, 75 - in manganites (perovskite), 175,184 spin-orbit interaction - in diluted magnetic semiconductors, 46, 53, 56 spin-density waves - in diluted magnetic semiconductors, 49 spin-dependent scattering - in lrilayer structures of diluted magnetic semiconductors, 64 spin-disorder scattering - in diluted magnetic semiconductors, 27,47,60 spin-injection - in diluted magnetic semiconductors, 71 spin-injection in ferromagnetic semiconductor heterostructures, 70 spintronics, 4 - in diluted magnetic semiconductors, 6 spontaneous distortions of the crystal symmetry, 319 spontaneous magnetoslriction in non-cubic systems, 356 spring magnets, 140 spring-magnet type multilayer, 141 square vortex lattices - in YNi2B2C and LuNi2B2C, 272 SQUID, 23 Stevens factor, 114 - in a-(Sm,Fe), 119 strain dependence of the Heisenberg interaction, 314 strain modulated ferromagnetic resonance, III structural and magnetic properties - of RC02B2 and RC02B2C phases, 221 of RNi2B2C compounds, 218 superconducting properties of RNi2B2C, 241 superconducting transition temperature
- in Hoj RI_xNi2B2C, 289 - ofRT2B2C compounds, 219, 220 - of YNi2B2C and LuNi2B2C, 240 superconductivity and itinerant-electron magnetism, 213 superconductivity - in R(Ni,ThB2C and (R, R')Ni2B2C, 277 superconductors with magnetic impurities, 208 superexchange - in diluted magnetic semiconductors, 24, 47 suppression of the upper critical field H c2(0) - in YxLul_xNi2B2C and Y(Nil_xPtxhB2C, 283 surface anisotropy, 93, lOS, 113, 152 surface magnetisation, 112, 152 - of C076Cr4B20, 113 -of Fen Cr6 B 17, 113 surface magnetoelastic coefficient, 113 surface magnetoslriction, 105, lSI, 159 - derivation, expressions, 152 - in a-(Tb,Fe) thin films, 155 - in HoILu superlattices, 159 - in nanocrystalline alloys, 172 - in NilAg multilayers, 154 - in ultrathin films, 173 -thickness dependence, 152 surface morphology - of diluted magnetic semiconductors, 9, 14 symmetry transformations, 98 TEM in diluted magnetic semiconductors, 10 temperature-pressure phase diagram of UGe2, 214 TerCoNeel, 94 terfecohan, 94, 142,148,149 terfeconeel, 94 terfenol, 94 terfenol-D,94, 123 - in applications (devices, MEMS), 185 - in composites, 173 thermal conductivity - of LuNi2B2C, 239 - of RT2B2C compounds, 238 thermal expansion - of gadolinium, 320 - of GdCu, 343 - of Gd2Cu21n, 333 - of Gd2In, 325 - of Gd2 Ni I.7SIn, 334 - of Gd3Ni, 353 - of Gd3Rh, 354 -ofGdAg2,331 -ofGdAu2,332 -ofGdCu2,346 - of GdCuAI, 327
SUBJECT INDEX - of GdCuSn. 328, 329 - of GdNi, 341 - of GdNizBzC, 336 - of GdNi5, 323 - of GdPt, 344 -ofGdZnz,351 thennodynamical critical field at T = 0 - of YNiZBZC and LuNizBzC, 240 total and partial density of states - for YNiZBzC, 228 transmission electron microscopy (TEM) - of diluted magnetic semiconductors, 9 transverse susceptibility, 109 tunnel magnetoresistance - in trilayer structures of diluted magnetic semiconductors, 64 tunneling magnetoresistance (TMR) - in diluted magnetic semiconductors, 66 - in trilayer structures of diluted magnetic semiconductors, 64 two fluids model - in diluted magnetic semiconductors, 49, 51 type of the ground state of RNizBzC compounds, 242 type-II superconductors, 230 upper critical field H cZ - for TmNizBzC and ErNizBzC, 268 upper critical field Hcz(T), 230 upper critical field at T = 0 - ofYNizBzC and LuNiZBzC, 240 upper critical field. H cz(T) of YNizBzC and ThO.I YO.9NizBzC Tbo.z Yo.gNiz BzC, 288 Van-Vleck type paramagnetism - in diluted magnetic semiconductors, 12 Vegard's law, 16 Verdet constant - of diluted magnetic semiconductors, 39 Villari effect. 103 - experimental methods, 108, 109, III
and
411
virtual crystal approximation - in diluted magnetic semiconductors, 47, 60 virtual-crystal model - in diluted magnetic semiconductors, 51 volume dilatation, 98 volume magnetostriction, 93 - derivation, expressions, 96 - in cobaltates (perovskite), 184 - in manganites (perovskite), 175 - in ultrathin films, 173 vortex glass phase, 276 vortex lattice - in ErNizBzC and TmNizBzC, 276 vortex lattice phase, 276 vortex lattices - in RNizBZC superconductors. 272 vortex liquid. 276 vortex pinning - in ErNizBzC and HoNiZBZC, 277 x-ray absorption spectroscopy (XAS) - of diluted magnetic semiconductors, 20 x-ray diffraction. 7. 62 x-ray diffraction curves - of diluted magnetic semiconductors. 16 x-ray diffraction rocking curve - of (Ga.Mn)AslGaAs superlattices, 62 x-ray magnetic circular dichroism (XMCD) - in diluted magnetic semiconductors. 20.41,44 x-ray photoemission spectra (XPS) - of diluted magnetic semiconductors, 46 XMCD results - of diluted magnetic semiconductors. 46 Zener approach - in diluted magnetic semiconductors. 48 Zener model - in diluted magnetic semiconductors, 50. 56. 57, 60 Zhang-Rice states - in diluted magnetic semiconductors. 42. 60
Materials Index
c-ThCoz,1I5 c-Th(Fel_xCoxh.126
a-DYI_x Fex,1I9 amorphous Fe<JI_xZr7BxCuz. 171 amorphous Fe93-xZr7Bx. 171 a-(SmFeZ)99.Z6BO.74. 120 a-(Th.DY)O.4ZFeO.5S. 122 a-Tht_xCox.120 a-(Th I-x Dy r )( Fe 0.45COO.55 h.t. 128 a-TbCoz, 115 a-Tb-Fe, 120 a-Th-(Fe,Co), 141 a-Th(Feo.45C00.55)Z.I, 127 a-Tb(Feo.55 C00.45) 1.5, 126 a-ThFez. 115. 126
DyBZC z,225 Dy/Lu,159 DyMZSiz,243 DyNi2B2C. 218. 220. 222, 226, 242, 257. 258, 265. 287,288 DyNiBC,223 DyPtzBzC,220 DyRhz BzC, 220 DylY.159 (Er32/Lu 10140 superlattice, 162 ErNizBzC, 217. 218. 220, 222. 242, 245, 246, 266269,276.277,287,290 ErNiBC.223 ErPdzSn.213 ErRhzB zC.220 ErRh4B4, 205. 211 ErN, 159 EuO.4 EuSe,4
B,204 BEDT-TTF, 206 BEDT-TIF-based sail. 204 C6Q,203, 204,206. 290 C6Q/CHBr3. 204 CaMnl_xRux03 perovskites, 179 (Cd.Mn)Te. 5,40. 76 (Cdt_xMnx)GePz,77, 78 Cdt_xMnxS.6O CdCrZS4,4 CdCrzSe4,4 CdGePz, 77, 78 Ce3Ni2B2N],223 CeCozBzC.220 CeNizBzC, 220, 242. 246. 247 CePt 1.5AuO.5 BzC. 247 CePt2BzC,220 CeRhzBzC.220 CeRu2. 209. 284 CeTZBzC with T = Ni. Co. Rh, Pd, (Pt,Au). 247 (COI_x Fex)-AI-O, 173 C03ZPd6S/Ag multilayers, 156 CoIAg multilayers, 155 Co doped ZnO. 78 CrAs. 43. 78 CrSb.78 c-Tht_xCox.122
Fe. 148,208.291 (Fe,Cu.Nb.Si,B) ribbons. 168 (Fe.Nb.B) ribbons. 169 (Fe,Zr,B) ribbons, 168 (Fe.Zr,Nb,B) ribbons. 169 Fe(25 nm)/ThFeCo(5000 nm)IFe(25 nm) sandwich, 167 Fe73.5CUINb3Si13.5B9, 171 Fe73.5SiI5.5B7Nb3CUt,l72 Fe74.3Nb2.7CUISit5.5B6.5.172 Fe77Cr6B17. 113 Fe84Nb3.5Zr3.5BsCu" 172 FeS5Zr7B6CuZ, 170. 171 Fe9QHf7B3. 169 FeB/CufFeB trilayers, 109 FeCoIAu multilayers, 156 (Ga.Cr,Mn)As, 13 (Ga.Cr)As, 13 413
414
MATERIALS INDEX
(Ga,Cr)N. 14 (Ga,Cr)Sb. 14. 15 (Ga,Fe.Mn)As, 12 (Ga,Fe)As.12 (Ga.Fe)N. 14 (Ga,Mn)As. 5-10. 12. 13. 15-26. 30-34. 36-41. 4550.52.61-71.73,75.77 (Ga.Mn)As:Sn. 24 (Ga,Mn)N. 13. 14.43.77 (Ga,Mn)P:C.14 (Ga,Mn)Sb, 14. 15.71 Gao.75Feo.25 N,43 Gao.7SMno.2S N• 43 Gao.75Mno.2SNO.7S00.2S.43 Gao.93S Mno.063 As. 45 Gao.947Mno.OS3As. 23, 27. 55 Gao.9S7 Mno.043 As. 59 Gao.9SMno.osAs. 56. 58 (Gao.9SMno.os)As. 65. 66 (Gao.962MnO.03S)As.26 Gao.96S Mno.03S As. 58 (Gao.96SMnO.03S)As. 22, 68 (Gao.97Mno.03)As. 65. 66 Gao.9Mno.1As. 77 Gal_xMnxAs.7. 17.21-24.29-33.38-40.42--44.46. 50.55-58,65.67 Gal_xMnxN.43 oa, 320. 356 (Gd.La)Ru2. 209 Gdo.sSro.sMn03.177 Gd1.2Mo6SS.212 (GdI23).212 Gd2Cu2ln. 331. 356 Gd2ln. 323. 357 Gd2Ni2_xln. 331, 356 Gd3Ni. 352. 356 Gd3Rh. 352. 356 Gds(Sio.1 GeO.9)4.356 GdS(SixGel_x )4. 336 GdAg2. 329. 356 GdAI2.316.319.357 GdAs.319 GdAu2. 329. 357 GdBa2Cu307,212 GdBa2Cu307_8.353 GdBi.319 GdC02B2.219 GdCo2B2C. 219. 220 GdCu,342 Gd( Cuo.sNio.2h.356 Gd(CU1_xNixh.351 GdCU2. 344.356 GdCu2ln, 318, 357 GdCuAI, 324. 356
GdCu (FeB). 356 GdCuSn. 327, 356 Gd/Fe multilayers, 155 Gdln3. 317. 357 GdMo6SS. 211, 212 GdNi. 339. 356 GdNi0.4CUO.6.357 GdNio.7CuO.3.357 GdNil_xCux.341 GdNi2. 317, 357 GdNi2B2C. 220.242,246.254-256 GdNi2B2C, 334, 357 GdNis. 322. 357 GdNiAI. 324. 357 GdNiBC, 223 GdPd2ln. 318. 357 GdPt. 342, 356 GdRh2B2C.220 GdSb,319 oa,y l-xNi2B2c' 286 GdZn.319 GdZn2, 350, 356 (Hg.Fe)Se, 5 (Ho,La)Ni2B2C.289 HOI_xRxNi2B2C compounds with R = Y or Lu, 262 H02Ni3B6. 226. 263 {H031ILu19150 superlattices, 159 {Ho61Y6ItOO.159 HoB2C2, 225. 263 HoC02B2C, 220 HoILu, 159 HoMo6SS' 211 HoNi2B2C. 217. 220. 222. 223. 242-245. 259-261. 263-267.277.287.288.290 HoNi4B.225 {HolIlLu IS}SO superlattices, 162 HoPd2B2C,225 HoRh2B2C, 220 HolY, 159 (In.Ga.Mn)As. 10 (In,Mn)As. 5, 6, 10-12, 15, 17, 19.21, 31, 34. 3(r38. 40,66,72-74 (lno.9sMnO.os)(Aso.2Sbo.g), 73 (lno.9sMno.os)(Aso.gSbO.2).73 Inl_xMnxAs, 17,35.43.56.57 InSb:Mn,15 (La,Sr)Mn03,4 (La,Th) NiC2,204 Lao.60Y0.07Cao.33Mn03' 175 Lao.62Tbo.OSCao.3S Mn03. 176
MATERIALS INDEX (Lal_xSmxhI3SrI/3MnOJ (x =0.33),178 Lal_xSrxCoOJ, 184 LaI_xSrxMnOJ, 178, 179 La2_2xSrl+2xMn207, 182, 184 La2C3,204 LaJ Ni2B2N3,223 LaB6,204 LaBrC,204 LaIr2B2C,220 LaNi2B2C,220,227,229,250,251,289 LaNiBN,223 LaNiC2,204 LaPd2B2C,220 LaPt2B2C,220 LaRh2B2C.220 (LaSr)Cu04,231 La2/JCal/JMnOJ, 176 La2/JSqI3MnOJ,178 (Lu,Dy)Ni2B2C,288 (Lu,Y) I-x YbxNi2B2C, 271 LuO.I 5HOO.S5Ni2B2C, 266 LU2NiBC2,223 LuB2C2, 204, 207, 225 LUC02B2C, 220 Lu(Nil_xCoxhB2C, 275 LuNi2B2C, 202-204, 217, 219, 220, 226, 227, 229241,250,261,270,273-276,280,283,284,286, 289 LuNiBC,223 LuOSJB2,204 LuRh4B4' 205 LuRuB2,204 MgB2,204, 207,285, 290 MgNi3C,205 MnAs, 7, 9, 10, 17, 18,22,29,42,43,62,63,75,77, 79 Mn doped InSb, 15 M02B,204 M02BC,204 M02C,204 MOJA12C, 205 M056C44, 204 Nb,239 NbB,204 NbCy,204 (Nd,Th)Ru2,209 Ndo.J5Tho.65 Ru2,209 Ndo.45 Srno.55 MnOJ,176 (Ndo.6Tho.4h/JSrI/3MnOJ, 176 (Ndl_ySmylo.5Sr0.5MnOJ,178 Nd~~onNd~o, 163 NdNi2B2C, 220, 242, 252-254
415
NdPt2B2C,220 NdRh2B2C, 220 Ni2B,226 NiJB,226 NiJC,226 Ni/Ag multilayers, 154 NiIPb,154 NilTi, 154 (Pb,Sn,Mn)Te, 5 (Pr 123), 212, 213 PrBa2CuJ07-y,252 PrNi2B2C, 220, 242, 247-251, 290 PrPt2B2C, 220 PrRh2B2C,220 Pr2/JCal/3MnOJ, 176 (RI23),211
R2CJ,226 R2NiJ B6,226 RB12,226 RB2,226
RbJC6Q, 204, 206 RB4,226 RB6,226 RBa2CuJ07-~, 211 (RC)n Ni2B2,224 R(Co,Mn)OJ,I84 ReJB,204 ReB2,204 RMo6SS,211 R(Ni,Cu)BC, 223 R(Ni,ThB2C compounds (T = Co, Cu, Pd, 1'1), 277 RNi2B2C, 202 RNi2C2,226 RNiBC, 223 RNiC2,225 RReBC,223 RRh4B4,211 RuSr2(Gd,CehCu20 IQ, 290 RuSr2GdCu20S,290 RuSr2(R,Ceh CU20IQ,213 RuSr2RCu20g,213 ScNi2B2C, 204, 216, 219, 220, 226 (Sm,Fe,B), 142 (Sm,Th)Fer B,120 Srno.J7COO.6J, 121 Sm0.55SrO.45Mn03,179 Sml_xCaxMnOJ, 179 Sml_xNdxFe2/Fe composites, 173 Sm-Co,122 Sm-Fe,119
416
MATERIALS INDEX
(SmFe2)100-x B x • 120 SmFe2/Fe. 173 SmFeBffbFeB multilayers, 156 SmNi2B2C. 220. 242. 252-254 SmRh2B2C.220 Sm(TblsFeS2)/(Fe75Co25). 143 TaB. 204 (Th.DY)I_xFe2Zrx.137 Tho. IYO.9Ni2B2C. 288 (Tho.27DYO.73)0.42Feo5S. 130 (Th0.27DYo.73)(Fel-xCoxh.124
terfecohan/(Y0.2Feo.s) multilayers, 149 terfeconeel, 94 terfenol-D, 122. 132. 135. 173 ThNi2B2C. 204. 219. 220 ThPd2B2C.220.225 Th-Pd-B-C. 225 ThPt2B2C, 220 ThRh2B2C.220 TmNi2B2c' 220 TmNi2B2C. 217.242.262.268.269.276 UGe2. 214. 290 UNi2B2C.220 UPt3. 239. 284 URh2B2C.220 URhGe. 214. 215 VAs. 43 (Y.Dy)Ni2B2C.288 (Y.ThhC3. 204 YO.15Hoo.S5Ni2B2C. 265. 266 YI_xFex.116 Y l-xPrxNi2B2C. 252 Y2 C3. 226 Y2NiBC2.223 Y3Ni4B4C3.224 YB 12.204.226 YB2C2. 204. 207. 225 YB6. 204. 226 YBa2Cu307.284 YbNi2B2c' 220. 242. 249. 251. 270, 271. 290 YbNiBC. 223. 249 Y(Br,IlC.204 YC2.204 YCo2B2C.220 YIC.204 Y(Ni.PthB2C.283 Y( NiO.75 Pto.25h B2C. 285 Y(Nil_xCoxhB2C.278 Y(Ni I-x Ptx hB2C. 283. 284 YNi2B2C.220 YNi2B2C. 202-204. 216. 226. 227. 229. 230. 232238.240.241,261.273-276.280.283-289 YNi2B2C.250 YNi4B.202 YNi4BCo.2.202 YNiBC.223 YOS3B2,204 YPd2B2c' 202. 204. 220 YPd5B3CO.35.202 YPt2B2C.204 YRh4B4.205
MATERIALS INDEX YRU2B2C.220 YRu2B2C.204 YRuB2.204 YxLUI_xNi2B2C, 280-282
(Zn.Co)S.5 (Zn.Mn)Se. 26 ZrBI2,204 ZrZn2.213, 214,290
417
