Thin Film Magnetoresistive Sensors

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Thin Film Magnetoresistive Sensors

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Series in Sensors Senior Series Editor: B E Jones Series Co-Editor: W B Spillman, Jr Solid State Gas Sensors Edited by P T Moseley and B C Tofield Techniques and Mechanisms in Gas Sensing Edited by P T Moseley, J O W Norris and D E Williams Half Effect Devices R S Popovi´c Thin Film Resistive Sensors Edited by P Ciureanu and S Middelhoek Biosensors: Microelectrochemical Devices M Lambrechts and W Sansen Sensors VI: Technology, Systems and Applications Edited by K T V Gratten and A T Augousti Automotive Sensors M H Westbrook and J D Turner Sensors and their Applications VII Edited by A T Augousti Advances in Actuators Edited by A P Dorey and J H Moore Intelligent Sensor Systems, Revised Edition J E Brignell and N M White Sensor Materials P T Moseley and J Crocker Ultrasonic Sensors R C Asher Sensors and their Applications VIII Edited by A T Augousti and N M White Eurosensors XII Edited by N M White Sensors and their Applications X Edited by N M White and A T Augousti

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Thin Film Magnetoresistive Sensors S Tumanski Warsaw University of Technology, Poland

Institute of Physics Publishing Bristol and Philadelphia

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© IOP Publishing Ltd 2001 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the publisher. Multiple copying is permitted in accordance with the terms of licences issued by the Copyright Licensing Agency under the terms of its agreement with the Committee of Vice-Chancellors and Principals. British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. ISBN 0 7503 0702 1 Library of Congress Cataloguing-in-Publication Data are available

Senior Series Editor: Professor B E Jones, Brunel University Series Co-Editor: Dr W B Spillman, Jr, Virginia Tech Production Editor: Simon Laurenson Production Control: Sarah Plenty Cover Design: Victoria Le Billon Marketing Executive: Colin Fenton Published by Institute of Physics Publishing, wholly owned by The Institute of Physics, London Institute of Physics Publishing, Dirac House, Temple Back, Bristol BS1 6BE, UK US Office: Institute of Physics Publishing, The Public Ledger Building, Suite 1035, 150 South Independence Mall West, Philadelphia, PA 19106, USA Typeset by Mackreth Media Services, Hemel Hempstead, Herts. Printed in the UK by MPG Books Ltd, Bodmin

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Contents

Preface 1

AMR SENSORS 1.1 Anisotropic magnetoresistive effect in thin ferromagnetic films 1.1.1 Essential information about magnetoresistive effects 1.1.2 The origin of anisotropic magnetoresistance in ferromagnetic metals 1.1.3 The theory of magnetoresistance in ferromagnetic metals 1.1.4 Thin ferromagnetic film as the magnetic field sensor 1.1.5 Applying the Stoner–Wohlfarth model for analysis of magnetoresistive effects 1.2 Biasing and stabilizing techniques 1.2.1 The biasing and stabilizing fields in ferromagnetic magnetoresistors 1.2.2 The real thin film – the multidomain structure and the dispersion of anisotropy 1.2.3 The sensors biased by the hard magnetic layer 1.2.4 The sensors biased by the current conducting layer 1.2.5 Biasing by exchange coupled antiferromagnetic layer 1.2.6 The soft adjacent layers (SAL) biasing technique 1.2.7 Dual element sensors 1.2.8 AC biasing techniques 1.2.9 The reverse mode of biasing 1.3 Design and performances of AMR sensors 1.3.1 The influence of the sample geometry on the MR effect 1.3.2 The influence of magnetization non-uniformity on the MR effect 1.3.3 Technological factors affecting the performances of AMR sensors 1.3.4 The design and construction of AMR sensors 1.3.5 The performances of AMR sensors References

ix

1 1 8 12 17 22 27 27 33 45 52 58 63 70 76 81 83 83 89 97 115 132 146

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3

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CONTENTS GMR SENSORS 2.1 Giant magnetoresistive effects 2.1.1 An historical review and the main terms 2.1.2 Oscillatory exchange coupling in the magnetic multilayers 2.1.3 Other coupling effects in multilayer structures 2.1.4 Theoretical models of giant magnetoresistance 2.1.5 Ferromagnetic multilayers as magnetic field sensors 2.2 Various types of GMR structures 2.2.1 Structures with antiferromagnetic coupling 2.2.2 Granular GMR structures 2.2.3 Spin-valve structures with asymmetric magnetic layers (uncoupled structures) 2.2.4 Spin valve structures with exchange-biased layer 2.2.5 Current perpendicular to plane (CPP) structures 2.2.6 Magnetic tunnel junction (MTJ) structures 2.2.7 Colossal magnetoresistance (CMR) thin film structures 2.2.8 Giant magnetoimpedance (GMI) structures 2.3 Preparation, design and properties of GMR sensors 2.3.1 The deposition of thin film GMR structures 2.3.2 Technological factors affecting the performances of GMR sensors 2.3.3 The shape effects in thin film GMR devices 2.3.4 Design and construction of GMR sensors References

266 276 286 299

APPLICATIONS OF MAGNETORESISTIVE SENSORS 3.1 Magnetic measurements 3.1.1 Magnetometers and compasses 3.1.2 Gradiometers, magnetic anomaly detection 3.2 Electrical measurements 3.2.1 Current transducers 3.2.2 Electrical transducers, switching and logic elements 3.3 Magnetoresistive elements in data storage applications 3.3.1 Magnetic Random Access Memory (MRAM) devices 3.3.2 Magnetic card readers 3.3.3 Magnetoresistive heads for tape and disk applications 3.3.4 Unshielded magnetoresistive reading heads 3.3.5 Shielded magnetoresistive heads 3.3.6 Yoke-type magnetoresistive heads 3.4 Transducers of mechanical values 3.4.1 Transducers of linear displacement 3.4.2 Transducers of angular position 3.4.3 Measurements of rotational speed

325 325 336 341 341 347 353 353 357 361 372 376 382 384 384 391 396

165 165 173 185 191 199 209 209 217 222 229 241 247 251 256 260 260

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CONTENTS

vii

3.5 Material testing and magnetic field imaging 3.5.1 Material testing by means of thin film magnetoresistors 3.5.2 Magnetic imaging systems References

400 400 406 417

List of Symbols List of Abbreviations Index

431 433 435

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Preface

Thin film magnetoresistive sensors (MR sensors) are widely used in various applications. The most important are their applications as read heads. MR sensors are also used as mechanical transducers and of course as magnetic field sensors, for example in compasses. There is a large variety of MR sensors on offer in the marketplace. However, market availability of MR sensors does not mean that the research in this field is less intensive. At scientific conferences devoted to magnetic sensors or to magnetism in general the subject of ‘magnetoresistance’ is covered in a large number of papers. Every year, each conference brings revolutionary news. The progress in thin film MR sensors is possible due to the large scientific and business interest. It has always been to the benefit of MR sensors that thin film technology and magnetoresistance were the objects of interest of other often better financial supported activities. For fundamental physics the investigations of phenomena in thin magnetic films were always valuable because it was easier to explain and to understand the magnetism in this specific form of magnetic material (in comparison with the bulk form). The most significant support for investigations of magnetoresistance in thin film arises from the computer industry because it is obvious that the next generation of high-density recording heads will be based on magnetoresistive effects. That is why the subject ‘thin film magnetoresistive sensors’ is broadly described in this book. Not only are classical measuring transducers described, but also other magnetoresistive devices, such as switching and logical elements, multipliers and insulators, memory devices and most importantly reading heads. Also the physics of thin magnetic films and thin film technology are presented comprehensively. The technology of GMR sensors is very sophisticated and refined and therefore it is described as an example of thin film technology. Thus this book describes not only one class of sensors, the magnetoresistive sensors, but also discusses many more universal subjects, such as magnetism of thin films, thin film technology and magnetic measurements. Therefore it should be useful for various kinds of readers. For high quality specialists it should be interesting as a comprehensive review of all available knowledge to date. The mathematical description is limited to only the most important definitions, therefore the level is also applicable to students and practising engineers. The book is especially addressed to engineers. The author is an engineer who has been active for more than thirty years in the field of industrial and magnetic measurements. That is why there is much practical information about the

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performances of sensors and the author’s experiences in design and construction of transducers. Usually MR sensors are divided into anisotropic MR sensors (AMR) and giant MR sensors (GMR). This classification results from the different mechanisms and features of these effects. The giant magnetoresistance is recently in vogue partially due to the very marketing name. Simultaneously the AMR sensors are treated as slightly old-fashioned. Meanwhile the AMR sensors still exhibit better sensitivity and are much simpler in technology. In the opinion of the author both types of MR sensors have their unique performances and both are more complimentary rather than competitive. That is why in this book AMR sensors and GMR sensors are presented equally. In fact knowledge about AMR sensors is more stabilized and therefore their properties can be discussed in detail. Research into GMR sensors is largely still in progress, and the most upto-date information is presented here. All three parts of the book: AMR Sensors, GMR Sensors and Applications are written as separate sections (with independent references and independent logical concept). So it is not necessary to read the book ‘from the beginning’. If, for example, readers are not interested in the physics of MR effects, and only want information about applications or performances of the sensors then it should be sufficient to read only the separate chapters. In both main parts the structure is the same – first the theory, then a description of the various types of sensors, and finally technology, design and performances. Thin film magnetoresistive sensors exhibit many unique features. They can be extremely small, with dimensions of parts of micrometres. They can detect a wide range of magnetic fields, from picotesla to several tesla. The measurement of DC and AC magnetic fields is possible. Because the sensors detect the field in the film plane they can be placed very near the investigated area, as tangential sensors. Some sensors available in the marketplace may cost only several dollars. MR sensors exist as well as sophisticated transducers, for example three-axis compasses. Therefore it is worth reading this book to gain a better understanding of the features of MR sensors and hopefully to use them more effectively. However, the author also recommends reading this book as a story of one of the most fascinating events of high technology. The sensors fabricated in nanometric atomic scale exhibit extraordinary, not fully understood phenomena. The expected future applications of these sensors, especially in data storage systems, open new perspectives for the whole of science. Slawomir Tumanski May 2000

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1 AMR Sensors

1.1 ANISOTROPIC MAGNETORESISTIVE (AMR) EFFECT IN THIN FERROMAGNETIC FILMS 1.1.1 Essential information about magnetoresistive effects The resistance of a material may depend on its state of magnetization. This phenomenon is called the magnetoresistive effect. We can change the magnetization of the material by applying an external magnetic field. Thus, the magnetoresistive effect may be used to construct magnetic field sensors. The magnetic field may influence the material resistivity in various ways (Heremans 1993, Lenz 1990, Caruso et al 1998, Popovi´c et al 1996). For example the magnetoresistive effect may be a consequence of the Lorentz force – similarly as in the Hall effect. The Lorentz force F is acting on particle with charge q moving with velocity v in a magnetic field B F q(v B).

(1.1)

As a result the Lorentz force deflects the path of the moving free charge carrier (figure 1.1(a)). It increases the path length causing a change in the material resistivity. Figures 1.1(b) and (c) present the current paths and

Figure 1.1 The origin of the magnetoresistive effect in semiconductors: (a) the influence of the Lorentz force on the current path length; (b) the current paths and equipotential lines in a conducting rectangular plate in the absence of the external field; (c) the same lines after application of the external magnetic field.

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equipotential lines in a rectangular plate of the conducting material. The resistance R(B) is proportional to the square of the magnetic field induction B perpendicular to the plate: B R(B) Ro –— (1 2CB2) o

(1.2)

where: R0 is the resistance of the material in the magnetic field B 0, B /0 is the magnetoresistivity coefficient, is the carrier mobility, and C is the coefficient depending on the geometry of the sample. The carrier mobility is especially large in semiconductors InSb and InAs and therefore these materials are most frequently used to prepare the magnetoresistors ( 7.7 104 cm2/Vs for InSb and 3 104 cm2/Vs for InAs). The coefficient C has been calculated by Lippmann and Kuhrt (1958). For l/w 0.35 (l – length of the plate, w – width of the plate) coefficient C is given by the expression l C 1 0.54 —. w

(1.3)

The l/w ratio should be as small as possible because in the long plate (large l/w ratio) the current path runs parallel to the edges and the Hall electrical field reduces the magnetoresistive effect. On the other hand, to obtain large resistances of the magnetoresistor it is required to elongate the magnetoresistor stripe. Various techniques are adopted to fabricate magnetoresistors with a long current stripe without sacrificing the magnetoresistivity (Popovi´c and Heidenreich 1989). For example shorting bars from a highly conductive metal are introduced into the stripe (figure 1.2(a)). The magnetoresistor consists then of many elementary magnetoresistors connected in series with a small l/w ratio.

Figure 1.2 Various design of semiconductor magnetoresistors: (a) magnetoresistor with shorting bars; (b) magnetoresistor with NiSb needles; (c) Corbino disk (Weiss 1966).

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A special kind of semiconductor magnetoresistors with NiSb needles has been developed by Weiss (1966). This magnetoresistor is called the “Feldplatte”. The NiSb needles are built into the polycrystalline InSb. Due to the much greater conductivity of NiSb the current path is larger and the resistance of the sensor is greater than for the simple InSb material (figure 1.2(b)). The magnetoresistive “Feldplatte” sensors are actually manufactured by Siemens AG. In a special geometrical form of magnetoresistor, known as the Corbino disk (Corbino 1911) (figure 1.2(c)), it is possible to obtain a pure magnetoresistive effect (without the Hall effect). The Corbino disk is equivalent to the plate with l/w 0 (the current lines are curved along logarithmic spirals). Unfortunately the Corbino disk structure does not ensure a large enough resistance of the sensor. Typical dependence of the relative change of resistance Rx /Ro on the external magnetic field for the InSb Corbino disk and the Feldplatte magnetoresistor are presented in figure 1.3.

Figure 1.3 Dependence of the relative change of resistance Rx /Ro versus the magnetic field B of the semiconductor magnetoresistors.

All metals exhibit the magnetoresistive effect (Jan 1957). In some semimetals, for example bismuth, this effect can be quite large. The bismuth spiral was the earliest material used for preparing magnetoresistors (Bublitz 1937). The maximal value of the relative change of resistivity x /o for pure bismuth is at room temperature equal to about 2 (for magnetic induction change from 0 to 2 T ). This change of resistivity is about 40 at liquid nitrogen temperature. The appearance of magnetoresistance in non-magnetic metals requires the application of a large external magnetic field. The change of resistivity is described by the Kohler rule (Kohler 1949) in the form of the expression:

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THIN FILM MAGNETORESISTIVE SENSORS B,T 273K ——— 1 f B ——— B0,T B0,T

(

)

(1.4)

where: B,T – resistivity in magnetic field B and temperature T. This rule is usually presented as the Kohler diagram. The Kohler diagram is the relation between /(0) and B/red. The reduced resistivity red is (T)/( ), where is the Debye temperature. An example of this plot is presented in figure 1.4.

Figure 1.4 The reduced Kohler diagram (B in Tesla).

Apart from the ordinary magnetoresistive effect in metals previously discussed, an anomalous magnetoresistance effect appears in ferromagnetic materials (Mott 1936, Smit 1951, Dorleijn 1976). This anomalous effect in transition metals is explained as the spin-orbit interaction. In this effect the resistivity depends on the orientation of magnetization with respect to the direction of the electric current. Therefore this effect is often called the anisotropic magnetoresistance (AMR) (McGuire and Potter 1975, Mapps 1994, Kwiatkowski and Tumanski 1986, Ciureanu 1992, Dibbern 1989). In comparison with the magnetoresistive effect in semiconductors and nonmagnetic metals anisotropic magnetoresistance occurs for much smaller magnetic fields. The anisotropic magnetoresistance was discovered in 1857 by William Thomson (Lord Kelvin) (Thomson 1857). In a paper entitled “Effects of magnetization on the electric conductivity of nickel and of iron” he described the results of an experiment on a small rectangular piece of ferromagnetic material “subjected to magnetic force”. He also mentioned the anisotropic nature of this effect stating that “iron acquires an increase of resistance to the conduction of electricity along, and a diminution of resistance to the conduction of electricity across, the lines of magnetization”.

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5

Figure 1.5 presents the change of the resistivity of NiCo alloy versus the magnetic field induction. The longitudinal resistivity l of the material magnetized parallel to the current direction is larger than the transverse resistivity t of the material magnetized perpendicularly to the current direction. The magnetoresistivity coefficient / is defined as follows l t —– —– ————– av 1 2 – l – t 3 3

(1.5)

where: av – the average resistivity (resistivity of the demagnetized specimen).

Figure 1.5 The change of resistivity of NiCo alloy versus the external magnetic induction (McGuire and Potter 1975).

As a material for preparing AMR sensors the thin film of the NiFe alloy (permalloy) is most frequently used. Figure 1.6 presents as an example the R/R f(B) dependence for a thin film permalloy magnetoresistor. The thin film permalloy exhibits a magnetoresistivity coefficient equal to about 2.5%. The thin film in comparison to the bulk material offers several advantages. The magnetization process of thin film is relatively simple and fast – approximate to a single domain model. For full magnetization, a relatively small (about 1 mT), external magnetic field is needed. Thin film in the form of the path enables to obtain large resistance of the magnetoresistor. It is convenient that these films are fabricated using standard semiconductor technology. In 1988 Baibich and co-workers discovered another magnetoresistive effect utilising thin ferromagnetic films (Baibich et al 1988). Because the obtained magnetoresistive coefficient was much larger than the AMR effect ( R/R larger than 150% at T 4 K has been reported), this effect was called the giant

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Figure 1.6 The typical transfer characteristic of an AMR permalloy thin film magnetoresistor.

magnetoresistive (GMR) effect (Fert and Bruno 1996, Parkin 1996, Levy 1994, Daughton 1999, Smith and Schneider 1998, Grünberg 1999, Coehoorn 1999). The GMR magnetoresistor consists of magnetic layers separated by a very thin non-magnetic layer. The GMR effect may be explained as the scattering effect of electrons through the non-magnetic interface – spin-dependent scattering. Figure 1.7(a) presents an example of the transfer characteristic determined for the Fe/Cr multilayer structure by Baibich and co-workers. The GMR magnetoresistance in multilayers at room temperature is about 30–40% and needs a much larger magnetic field than AMR. The most promising and recently most frequently used is another GMR thin film structure developed by Dieny and co-workers (Dieny 1994). It is called the spin valve (SV) (Dieny 1994, Daughton 1996, Kools 1996). Currently spin valve magnetoresistive sensors with magnetoresistive coefficient R/R 5–15% and saturation field

Figure 1.7 Examples of transfer characteristics of GMR sensors: (a) Fe/Cr multilayer T 4 K); (b) spin valve sensor at room temperature.

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B 2.5 mT are available. Figure 1.7(b) presents transfer characteristics determined for the spin valve structure. Lately promising results have been reported in another multilayer structure – in magnetic layers separated by a very thin insulator layer (Moodera et al 1995, Gallagher et al 1997). It is expected that this magnetic tunnel junction (MTJ) structure could be the most sensitive GMR sensor. The magnetoresistive effect has been recently reported in magnetic oxides (for example in doped manganate perovskites La–Ca–Mn–O thin films) (Jin et al 1994, Sun 1998). This has been called the colossal magnetoresistance (CMR) effect because the change of resistance is very large. Magnetoresistivity as large as 1010 (for T 60 K and B 7 T) has been achieved (Chen et al 1996). Magnetoresistance is not only reported in thin film structures. Permalloy sensing elements have been obtained in micro-fiber shape by rapid solidification (Ciureanu et al 1993, Ciureanu et al 1994). Magnetoresistive nanowires have also been prepared by the electroplating method (Piraux et al 1994, Blondel et al 1994). The giant magnetoimpedance effect (GMI) as some kind of magnetoresistance may also be considered. The GMI effect occurs in wires and thin film structures supplied by high frequency voltages and obtains very sensitive magnetic field sensors (Panina 1995, Mohri et al 1997). Figure 1.8 presents a comparison of a range of magnetic fields detected by various measuring methods. Using magnetoresistive sensors it is possible to detect magnetic fields ranging from picotesla to several tesla. Figure 1.9 presents a comparison of the sensitivity of various magnetoresistive sensors. For large magnetic fields (one tesla or more) semiconductor magnetoresistors or GMR multilayers are recommended (in this range of magnetic field Hall sensors are used most widely). For detecting small magnetic fields the permalloy magnetoresistive sensors are the most suitable. Detectable Field Range

Figure 1.8 The typical field range of various magnetic field sensors (Caruso 1998).

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Figure 1.9 The typical field range of various magnetoresistive sensors – AMR: anisotropic magnetoresistance; SV: spin valve sensors; InSb: semiconductor magnetoresistors; GMR: multilayer GMR sensors; CMR: colossal magnetoresistance (Heremans 1993).

Spin-valve sensors obtain larger output signals than AMR sensors (but for larger magnetic fields). Therefore they are useful for reading information from magnetic tapes or disks (in magnetoresistive heads) where small dimensions of the sensor are the most important parameter. Due to large magnetoresistivity GMR heads allow reading of information with the highest density reported to date. The most frequently used are AMR and GMR/SV sensors – they are also available as commercial products (Philips, Siemens, Honeywell, Nonvolatile Electronics). The semiconductor magnetoresistors are of smaller technical importance due to rather strong temperature dependence and high non-linearity (Popovi´c et al 1996). The thin film magnetoresistive effects and sensors presented above (with the exception of semiconductors described elsewhere (Popovi´c and Heidenreich 1989, Metschl 1987, Wieder 1971)) will be described in more detail in the next chapters.

1.1.2 The origin of anisotropic magnetoresistance in ferromagnetic metals The microscopic origin of electrical transport in ferromagnetic metals was described in detail in many papers in the 1960s and the 1970s. As a basis for these papers Smit’s results of investigations of magnetoresistance in ferromagnetics (Smit 1951) have been used. Smit had explained the phenomenon of anisotropic magnetoresistivity using Mott’s two-current model of conduction in transition metals (Mott 1936). Jan (1957) and McGuire and Potter (1975) summarized the knowledge about anisotropic magnetoresistance.

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It is convenient to explain the anisotropy of magnetoresistance by taking into account the existence of spin-orbit coupling and the anisotropic scattering mechanism of s and d electrons (Kondo 1962, Berger 1965, Vu Dinh Ky 1967). Figure 1.10(a) shows density of states curves for ferromagnetic nickel determined by Langlinais and Callaway (1972) and figure 1.10(b) shows the same curves in a simplified schematic form. This band structure is split into two different sub-bands representing the different orientations of the electron spins (with magnetic moments parallel or antiparallel to the total magnetization). When the 3d band is not fully filled, scattering of 4s electrons to the 3d band is probable. The current of 4s electrons with small effective mass m* s (comparable with free electron mass) is predominant. The 3d electrons with large effective mass m*d are low mobile (for iron m*d 30 m* s ). Due to magnetic ordering the 3d sub-bands are not equally filled. Therefore there is another probability of scattering from the 4s state to the 3d state than from the 4s state to the 3d state. For ferromagnetic nickel only scattering from the 4s state to the 3d state is probable, because the 3d sub-band is below the Fermi level.

Figure 1.10 Density of states curve of ferromagnetic nickel: determined by Langlinais and Callaway (1972a) and in simplified form (Miedema and Dorleijn 1975b).

In Smit’s model it is assumed that the influence of the magnetic field and spin-orbit interaction cause mixing of d and d states. It can be demonstrated that this mixing is anisotropic and the probability of sd scattering is larger for electrons travelling parallel to the magnetization. Thus resistivity l is larger than t, as shown in figure 1.5. Figure 1.11 shows the main idea of Mott’s two-current model of conductivity in ferromagnetic metals. The current can be divided into two parts, one current of s- electrons with parallel spin direction, and the other with the opposite spin. Then the resistivity can be described with the following formula 1 1 1 — ————— —————. ss sd ss sd

(1.6)

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Figure 1.11 Two-current model of the conduction in ferromagnetic metals.

Further developing this two-current model, Marsocci (1965) and Thomas and co-workers (1969) determined the spin-orbit interaction in nickel–iron thin films with respect to the crystalline axes. Let us consider a ferromagnetic fcc crystal with x,y,z axes corresponding to the main crystal axes. The current is in [100] direction (along the x axis) and the magnetic field is rotated in the (100) plane (y–z plane) with the angle to current direction. The atomic wave functions for the d electrons in XYZ space are 1 yzf (r) 2 zxf (r) 3 xyf (r) 1 4 (x2 – y2) f (r) 2 1 5 ——– — (r2 3z2) f (r). 2√ 3

(1.7)

The spin-orbit interaction operator is of the form

[

]

1 1 K (L · S) K Lz Sz – (Lx iLy)(Sx iSy ) – (Lx iLy )(Sx iSy ) 2 2

(1.8)

where: L is the orbital angular momentum operator, Sx Sy Sz are the Pauli matrices and K is the spin-orbit interaction coefficient. The spin operators for assumed directions can be determined by

( )

1 0 1 Sx – , 2 1 0 1 sin i cos Sy – , 2 i cos sin

( (

1 cos Sz – 2 i sin

i sin cos

) )

.

(1.9)

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11

Taking into account equations 1.7–1.9 and using first-order perturbation theory, the perturbed wave functions can be described as (Thomas et al 1969) K — — — 1 1 —— 2 i sin 3 i cos 4 √ 3 5 , 2

(

)

K — — — 2 2 —— 1 i sin 3 4 i cos √ 3 5 i cos , 2

(

)

K — — 3 3 —— 1 i cos 2 2 4 i sin , 2

(

)

(1.10)

K — — 4 4 —— 1 2 i cos 2 3 i sin , 2

(

)

— K — — — 5 5 —— √ 3 1 √ 3 2 i cos , 2

(

)

where is the exchange energy and / exponents of wave functions indicating the directions of spin. The spin-orbit interaction causes non-symmetrical mixing of wave functions and the resultant perturbed wave function is a complex dependence on the angle . Knowing wave functions it is possible to determine respectively: the scattering potentials V, the transition probabilities Psd, relaxation times sd and conductivities l and t. All these parameters are the complex function of the angle (Thomas et al 1969). Potter (1974) demonstrated calculations of the magnetoresistance conductivity of ferromagnetic NiCu alloys. After sophisticated calculations the following results have been reported:

{

[( ) (

Ns K 2 N 2.6 ——ln 0.06 — ——s Nd Nd

)]

N K 2 K l o 10.007 —–d —– 0.4 ——— Ns 2 2

2

[ ()

]}

(1.11) 2 Nd K 2 K Ns K 2 N t o 10.007 —– 1.2 —– 1.76 ——— 2.6 ——ln 0.03 — ——s Ns 2 2 Nd Nd

{

[ ( ) ( )]

[ ()

]}

where: is splitting between the uppermost two d bands, 2 is exchange splitting, K is the spin-orbit coupling parameter, Ns, Nd – density of s, d states respectively, (Ns /Nd) is a term due to isotropic ss scattering and ns e2ss 0 ———–. ms

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The coefficient of magnetoresistivity according to equation (1.5) can be calculated as l t 3(t l ) —– ———–—— ————–. av 1 2 t 2l – l – t 3 3

(1.12)

For NiCu 70/30 the parameters in equation (1.11) have been estimated as: Nd /Ns 14, K 0.1 eV, K/ 0.33, K/2 0.125, K/(2) 0.09 and /av 0.44%. Figure 1.12 shows the conductivities for majority and minority spins versus the Nd /Ns parameter (Nd /Ns 14 for pure Ni and Nd /Ns 21 for Ni71Cu29). The anisotropic magnetoresistance is mainly influenced by the conductivity of minority spins, as only minority spin s electrons can scatter into d states (see figure 1.10).

Figure 1.12 The conductivity of minority and majority spin electrons determined by Potter (1974) for NiCu alloy.

1.1.3 The theory of anisotropic magnetoresistance in ferromagnetic metals Under isothermal conditions the Ohm law for a chemically homogeneous metal is described by the following expression 3

Ei ∑ij Jj ij Jj

(1.13)

j1

where: J (J1 J2 J3) is the current density, E (E1 E2 E3) is the electric field and ij is the tensor of resistivity. If this metal is in the external magnetic field H the resistivity tensor depends on the magnetic field strength or on the magnetization M

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AMR SENSORS Ei ij (H)Jj ij (M)Jj .

13 (1.14)

If the metal is a saturated single crystal the magnetization may be described by the direction cosines of magnetization with respect to the crystallographic axes M (M cos 1, M cos 2, M cos 3,)

(1.15)

and the resistivity tensor in equation (1.13) depends only on Ei ij (a)Jj .

(1.16)

Taking into account the crystal symmetry (Birss 1964, Bhagavantam 1966) the resistivity tensor can be simplified. After expansion using MacLaurin’s series this tensor is described by the expression ij 1 2 ij ij () ij (0) k —— – k l ——— ... k 2 k l aij akij cos k klij cos k cos l ... .

(1.17)

The resistivity tensor can be divided into a symmetric part ijs and an asymmetric part ija ij ji ijs ———— ; 2

ij ji aij ———— . 2

(1.18)

Taking into consideration Onsager’s theory of irreversible thermodynamics in the form ij () ij ()

(1.19)

it is assumed that ijs () ijs () jis () aij () aij () aji ().

(1.20)

An asymmetric part of the expression (1.17) aij akij cos ak mlkij cos m cos k cos l ...

(1.21)

represents the Hall effect and does not take part in Joule heating of the material. The magnetoresistivity is represented by a symmetric part ijs aij aklij cos k cos l ... .

(1.22)

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According to Neumann’s principle, any type of symmetry, which is exhibited by the point group of the crystal, is possessed by every physical property of the crystal. For the m3m group, representing the ferromagnetic crystals with cubic symmetry, Birrs (1964) determined the following condition aij 0

except

a11 a22 a33

aklij 0

except

a1111 a2222 a3333

aklij 0

except

a1122 a1133 a2233 a3322 a3311 a2211.

(1.23)

The magnetoresistivity tensor s through fourth order can be described as co c1 cos2 1 c2 cos 1 cos 2 c2 cos 1 cos 3 s c2 cos 1 cos 2 co c1 cos2 1 c2 cos 2 cos 3 c2 cos 1 cos 2 c2 cos 2 cos 3 co c1 cos 1

[

]

(1.24)

where: co a11 a1122; c1 a1111 a1122, c2 a2323. The magnetoresistivity tensor for a rectangular prism declined on the angle with respect to crystallographic axes is described as J·E (,) ——— ijs () cos i cos j . J2

(1.25)

Taking into account equations (1.22–1.24) the expression (1.25) can be rewritten as

(∑

(,) co c1

3

)

2

∑cos

cos 1 cos 1 c2

i1

i

cos j cos i cos j . (1.26)

ij

Equation (1.26) is similar to the Döring formula (Döring 1938) describing the even effects in cubic crystals

(

)

1 (,) 1 cos2 1 cos2 1 cos2 2 cos2 2 cos2 3 cos2 3 – 3

22 (cos 1 cos 2 cos 1 cos 2 cos 2 cos 3 cos 2 cos 3 cos 3 cos 1 cos 3 cos 1)

(1.27)

3 3 where: 1 — a11[100] , 2 — a11[111]; 2 2 and a11[100], a11[111] are the resistivities measured along an edge and a diagonal of the cubic prism. Taking into account the symmetry conditions, the asymmetric component in equation (1.16) can be described as axial vector a123 J , and the symmetric

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component as (a11a1122)J 2a2323(J·). Equation (1.16) can be written in vector form E t J · ( · J) H ( J)

(1.28)

where H is the Hall coefficient and l – t. According to equation (1.26) the resistivity tensor is

[

t cos2 1

cos 1 cos 2 H cos 3

cos 1 cos 2 H cos 3

t cos2 2

cos 1 cos 3 H cos 2

cos 2 cos 3 H cos 1

cos 1 cos 3 H cos 2

]

cos 2 cos 3 H cos 1 . t cos2 3

(1.29) For a simplified case when the magnetic field is in the film plane (cos 3 0, cos 2 sin 1) matrix (1.29) is

[

t sin2 l cos2

1 – sin 2 2

H sin

1 – sin 2 2 H sin

t cos2 l sin2

H cos

H cos

t

]

. (1.30)

Thus the dependence of resistivity on the orientation of the magnetization vector can be described as () t sin2 l cos2 .

(1.31)

The dependence (1.31) is more often presented as the so-called Voigt–Thomson formula, where it is assumed that the current is in one axis and resistivity is a dependence of the angle () t sin2 l cos2 t cos2

(1.32)

where the angle is an angle describing the orientation of the magnetization with respect to the current direction. Usually in the initial state the magnetoresistor is magnetized along the current direction ( 0) and R(H 0) Rl.

(1.33)

Therefore it is convenient to present expression (1.32) with respect to the l value as: () l · sin2 .

(1.34)

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THIN FILM MAGNETORESISTIVE SENSORS The relative change of resistance can be described in the form Rx —— —— sin2 Rx

(1.35)1

where magnetoresistivity coefficient is l t —— ———— . l In case of polycrystalline sample it is necessary to determine the average resistivity of a large number of randomly oriented crystallites. When the orientation of the current density vector J is described by the polar coordinates

and and the orientation of the vector of magnetization M by the angle (for the fixed value of the angle ), then the resistivity of polycrystalline film is possible to calculate by integrating (,) 1 2 2 —— ∫d ∫ d ∫ d (,). 82 0 0 0

(1.36)

This integration has been calculated by Birss (1960). The following results have been reported: t (l t ) cos2

(1.37)

where: 1 1 1 3 1 t ko – k1 — k2 – k3 — k4 — k5 5 10 5 35 70 3 2 1 3 1 l ko – k1 — k2 – k3 — k4 — k5 5 10 5 7 35 and ko a11 a1122 a111122 k1 a1111 a1122 a112211 a112233 k3 a112233 2a111122 k4 a111111 a111122 a112211 a112233 k5 2a112323 2a111212. 1 The ‘minus’ sign in equation 1.35 indicates that the resistance of the sensor is largest when the angle between the current and magnetization is zero (Rl ). After applying the external field resistance decreases.

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The resistivity of the demagnetized polycrystalline sample is (Birss 1960) 1 1 1 2 dem ko – k1 – k4 – l – t . 3 3 3 3

(1.38)

The formula (1.37) is similar to the Voigt–Thomson formula (1.32). From the above analysis it appears that the change of resistivity can be determined from the materials coefficients (for example a11[100] and a11[111] from equation (1.25)) as a dependence on the angles and . In the special case of thin ferromagnetic film it is possible to describe this change of resistivity as a dependence only on the angle (knowing the magnetoresistivity coefficient /). As it will be proved in the next chapter, in the case of thin ferromagnetic film, there exists a relatively simple dependence between the angle and external magnetic field strength H x.

1.1.4 Thin ferromagnetic film as the magnetic field sensor For users of magnetoresistive sensors the most important aspect is the dependence R/R f(H). Thin film is usually anisotropic with uniaxial anisotropy in the film plane. When the thin film structure is anisotropic then in the absence of external magnetic field H the resultant vector of magnetization M is directed along the anisotropy axis (the so-called easy axis of magnetization L – see figure 1.13). To magnetize the thin film (to rotate the vector of magnetization) the magnetic field should be directed perpendicular to the anisotropy axis (and in the film plane). Therefore it is usually assumed that the measured field component Hx is perpendicular to the resultant easy axis of magnetization (for convenience it will be assumed that the y axis is the anisotropy axis as in figure 1.13). To determine the desired dependence Rx/Rx f(Hx) it will be assumed under simplified conditions that the thin film is magnetized uniformly and by coherent rotation of magnetization. This assumption is valid for the single domain state of the thin film. As will be shown in the next chapters in real thin film structures it is possible to ensure conditions very near to this assumption. The direction of the magnetization vector M can be calculated by minimizing the expression of the free energy of the system. This energy W is described as W H · M Ku sin2

(1.39)

where is the angle of magnetization direction with respect to the anisotropy

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THIN FILM MAGNETORESISTIVE SENSORS

Figure 1.13 The thin film ferromagnetic path – the simplest ferromagnetic magnetoresistive sensor (L – anisotropy axis).

axis (figure 1.13) and Ku is the anisotropy coefficient. The first term in equation (1.37) represents the magnetostatic energy and the second one is the anisotropy energy. Equation (1.37) can be rewritten as 1 W o Ms Hx sin o Ms Hy cos – o Ms Hk sin2 . 2

(1.40)

The external magnetic field H is represented by two components Hx and Hy and the magnetization M is represented by the angle and the saturation magnetization Ms. The anisotropy is described by the anisotropy field Hk: 2K Hk ——u . Ms

(1.41)

The minimization of the energy with respect to the magnetization angle leads to W —— o Ms Hx cos o Ms Hy sin o Ms Hk sin cos 0. (1.42) For a small value of the angle we can assume that cos 0 and sin ≈ tg and then from (1.42) the requested dependence f(H) is expressed as Hx sin ———— . Hk Hy

(1.43)

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When the magnetoresistor path is situated along the anisotropy axis ( 0) the angle between the magnetization direction and current direction is equal to the angle

(1.44)

and it is possible to determine the angle as a function of measured field Hx: Hx sin ———— . Hk Hy

(1.45)

Taking into account equations (1.32) and (1.33) the resistance of the sensor with its path along the anisotropy axis can be expressed as 1 R(H) Rl R —–——— H x2 (Hy Hk )2

(1.46)

and the change of resistance is described by the following expression R 1 ——–x —– ——–—— H x2. Rx (Hy Hk )2

(1.47)

Figure 1.14 presents the calculated and experimentally determined transfer characteristics of a magnetoresistive magnetic field sensor with its path along the anisotropy axis. This kind of sensor is non-linear with the parabolic characteristic Rx /Rx f(Hx). In the general case of the path situated in an arbitrary direction with respect to the anisotropy axis the angle is expressed as .

(1.48)

In this case the change of resistance is described by the following expression

[

Rx H x2 ——– —– cos2 cos 2 ——–—— Rx (Hy Hk )2 ——————— 2 Hx 1 ———— . (Hy Hk )

√ (

Hx sin 2 ———— Hx Hk

)]

(1.49)

The change of resistance Rx /Rx f(Hx) is the sum of the square and quasilinear components. Figure 1.15 presents an example of the calculated transfer characteristics for various locations of the path with respect to the anisotropy axis.

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Figure 1.14 The change of the resistance of a magnetoresistor with the path along the anisotropy axis: (a) Hy 0; (b) Hy 0.5 Hk ; (c) Hy Hk (grey lines – experimental results).

Figure 1.15 The change of the resistance of a magnetoresistor with the path inclined of the angle with respect to the anisotropy axis (Hy 0).

The pairs of the magnetoresistors with the angles 1 0 and 2 0 90° (for example 1 0° and 2 90° or 1 45° and 2 45°) are complementary (differential) and can be connected in the neighbouring arm of the bridge circuit. It is an important behaviour of these magnetoresistors because in this way it is possible to compensate the temperature error. Especially interesting is the case of the magnetoresistor with a path located on the angle 45° with respect to the anisotropy axis. Its change of the resistance is described by following expression;

[

——————— 2 Hx 1 ———— (Hy Hk )

√ (

R 1 Hx ——–x —– – ———— Rx 2 Hx Hk

)]

(1.50)

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and for a small value of the measured magnetic field (Hx0.5 Hk) R 1 Hx ——–x —– – ———— . 2 Hk Hy Rx

(

)

(1.51)

When four differential magnetoresistors are connected into the bridge circuit supplied by the voltage Uo the constant component is eliminated and the output signal Uout is described by the expression: 1 Uout —– Uo ———— Hx . Hk Hy

(1.52)

If the orthogonal component Hy is very small (Hy << Hk) this sensor is a linear transducer of the measured magnetic field: U Uout —– —–o Hx . (1.53) Hk Figure 1.16 presents the experimentally determined transfer characteristics of such a quasi-linear magnetoresistive magnetic field sensor.

Figure 1.16 The change of the resistance of the quasi-linear magnetoresistor ( 45°) (black lines: calculated data; grey lines: experimental results).

To obtain the linear characteristics of a magnetoresistive sensor the following condition should be fulfilled (Hx 0) 45.

(1.54)

Figure 1.17 presents three typical methods used to obtain the linear transfer characteristics of thin film magnetic field sensors. The first one is the inclination of magnetoresistor path with respect to the anisotropy axis (Hebbert and Schwee 1966, Hebbert 1968, Oberg 1968). In the second

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Figure 1.17 Linear transfer characteristics of thin film magnetic field sensors: (a) the inclination of the current path by the angle 45°; (b) the inclination of the electrodes by the angle 45° (Barber-pole structure); (c) the inclination of the magnetization vector by the angle 45° (biasing of the sensor).

method the path is along the anisotropy axis and the current flows inclined by an angle of 45° due to the appropriate shape of the electrodes. It is called the Barber-pole structure (Kuijk et al 1975, Kuijk 1977, Gorter 1977). In the third method instead of current direction the magnetization direction is initially inclined by 45° with respect to the anisotropy axis (Bajorek et al 1974, O’Day et al 1974, Bajorek and Thompson 1975). It is obtained by biasing the sensor with the magnetic field in the x direction. Some authors (Hebbert and Schwee 1966, Gordon 1977, Paul et al 1970, Hoffman and Birtwistle 1982, Vieth et al 1994) have proposed the reversed method of applying the external magnetic field. If the additional bias field Hxo perpendicular to the anisotropy axis is equal to the anisotropy field Hk, then it can be assumed that sin 1. From the equation (1.42) the angle is then described by the expression Hy cos ———— . Hxo Hk

(1.55)

For the case 45° the dependence R/R f(H) is described as R 1 —— —– ———— Hy . R Hxo Hk

(1.56)

When the biasing field Hxo has a value near to Hk then the magnetoresistive sensor is theoretically infinitely sensitive to the measured magnetic field Hy directed along the anisotropy axis. The sensitivity of the real magnetoresistor is far from this expectation. This problem will be described in more detail in the next chapters.

1.1.5 Applying the Stoner–Wohlfart model for analysis of magnetoresistive effects The equations, presented in the previous subsection, describing the thin film magnetoresistive effect, are valid only when the applied external magnetic field

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is relatively small. In general it is convenient to use the Stoner–Wohlfarth physical model (Stoner and Wohlfarth 1991) for analysis of the magnetic behaviour of a single domain. The model of Stoner and Wohlfart is a very simplified one. It ignores the interaction between domains in a multidomain system and neglects other magnetizing processes, for example the movement of domain walls. Surprisingly despite such limitations, the SW model correctly explains many processes occurring in thin film magnetoresistors. For example using this model it is possible to analyse MR responses for magnetic fields of arbitrary value and arbitrary direction (still under the assumption that it is a single model state). It is possible to determine the direction of magnetization from the conditions of minimum energy: W —– 0

and

2W —— 0. 2

(1.57)

The border between stable and unstable directions of magnetization (a critical value of H) is determined solving the following equations W —– 0

and

2W —— 0. 2

(1.58)

The solution of equations (1.58) is a hypocycloid described by the expression: 3 – 2

( ) ( ) H —–x Hk

H —–y Hk

3 – 2

1.

(1.59)

This curve is usually presented in the form of a normalized Stoner–Wohlfarth asteroid (figure 1.18). 3 –

3 –

h x2 h y2 1

(1.60)

where hx Hx /Hk and hy Hy /Hk. Figure 1.18 illustrates how to determine the position of the magnetization vector for a given value of the magnetic field vector h hx hy. The direction of the magnetization vector M can be found by drawing a line tangent to the asteroid from the tip of the applied magnetic field vector h. When the field vector h1 is inside the asteroid it is possible to draw two tangent lines declined by the angles 1! or 1" with respect to the anisotropy axis. The stable position of the magnetization vector (M1! or M1") is chosen by taking into account the “magnetic history” of the film. When the vector h2 is outside the asteroid only one position of the magnetization vector M2 is possible.

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Figure 1.18 Determination of stable magnetization direction from the Stoner–Wohlfart asteroid.

Figure 1.19 illustrates the graphical method of the determination of the transfer characteristic Rx f(Hx). The tangent lines have been drawn for a varying Hx component and a fixed Hy component. Next the angles and can be determined. Knowing the value of the angle it is possible to calculate the Rx /Rx directly from the Voigt–Thomson formula (equations 1.32 or 1.35).

Figure 1.19 Graphical method of determination of the transfer characteristic Rx f(hx) for hy 0.6.

Figure 1.20 presents the reverse situation – varying of the Hy component. When the magnetic field hy decreases from hy1 to hy2 there is a moment when hy reaches the critical value hyc. At this moment the direction of the magnetization suddenly changes. When the magnetic field again increases the change of resistance has another character – the full cycle of magnetization makes the hysteresis loop. Let us return to the case presented in figure 1.19 and assume that the large magnetic field in the y direction has changed the initial magnetization to the antiparallel state (figure 1.21). In this way “the magnetic history” of the thin film has been changed. Now the angle increases as the magnetic field Hx increases, but only to the critical value hxc. When hx reaches this value the direction of

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25

Figure 1.20 Graphical method of determination of the magnetization direction for hx 0 and hx 0.3.

Figure 1.21 Graphical method of determination of the transfer characteristic Rx f (hx) for hy 0.6 (thin film initially magnetized by hyHk).

magnetization jumps to the previous state. Thus hysteresis appears even for the magnetic field in the x direction. Figure 1.22 presents graphically the determined transfer characteristics for the case when the magnetic field is applied by the angle 45° with respect to the x axis. Every time the magnetic field vector reaches its critical value the vector of magnetization jumps to the opposite direction.

Figure 1.22 Graphical method of determination the transfer characteristic Rx f(hx) for the external field inclined by the angle 45° to the anisotropy axis.

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The experiments confirm the results of graphical determination of the resistance by means of the Stoner and Wohlfarth model. Figure 1.23 presents a comparison of theoretical and experimental investigations for varying component hy and fixed component hx.

Figure 1.23 Comparison of the theoretical (a) and experimental (b) results of determination of Rx = f(hx) dependence (varying Hy field for the constant Hx field).

Of course it is not necessary to determine graphically the direction of magnetization vector by means of the Stoner and Wohlfarth model. It is possible to use the numerical model of the Stoner–Wohlfarth asteroid. Kwiatkowski and co-workers (1983) presented a numerical model enabling the computation of resistance directly from the Stoner–Wohlfarth asteroid. When the tangent line starts at a point with coordinates xoyo and the tangent point is described by coordinates xiyi the following nonlinear equation can be solved

[

yo 1 (x )

3 – 2

]

1 – 2 3 i

[

(xo xi ) 1 (x )

1 – 2

]

1 – 2 3 i

1 –

(xi2) 6 0.

(1.61)

A tangency condition requires that a derivative of the asteroid equation at the tangent point should be equal to the slope of a line drawn through the xoyo point yo yi dy ———– —– x xi . xo xi dx

(1.62)

It is easy to state that there are four solutions of equation (1.61) if the starting point is inside the asteroid and two solutions if it is outside the asteroid. The correct choice should consider “the magnetic history” of the thin film. Figure 1.24 presents an example of a flow diagram used for the selection of the tangent point for the starting point inside the asteroid (Kwiatkowski et al 1983).

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Figure 1.24 Flow diagram used to select the tangent point in the numerical model of the Stoner–Wohlfart asteroid.

1.2 BIASING AND STABILIZING TECHNIQUES 1.2.1 The biasing and stabilizing fields in ferromagnetic magnetoresistors Usually it is necessary to bias the sensor with an additional magnetic field. Correct application of biasing is crucial for the proper operation of the sensor. The main goals of biasing of the sensor are as follows: • a magnetic field perpendicular to anisotropy axis is used in the sensor with the path along the anisotropy axis to improve the linearity; • a magnetic field applied along the anisotropy axis1 to improve the stability of the sensor. A biasing field may be used for other goals, for example to prepare a differential pair of magnetoresistors, to eliminate temperature zero drift, to improve signal-to-noise ratio as it will be demonstrated below. In many papers these two fields are called transverse and longitudinal bias fields. To differentiate between these fields, the transverse field will be called the biasing field and the longitudinal field will be called the stabilizing field. 1

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Figure 1.25 The hysteresis of the transfer characteristics of the quasi-linear sensor: (a) hysteresis for various ranges of the measured field; (b) hysteresis for various values of the stabilizing field.

Figure 1.25 presents experimentally determined transfer characteristics of the quasi-linear 2 sensor. When the applied measured magnetic field is sufficiently small the characteristic is without hysteresis. For a larger magnetic field hysteresis may appear. Applying a very large field can demagnetize the sensor and the magnetoresistive effect can vanish after removal of this magnetic overload. The explanation of this effect was proposed by West (West 1960, West 1961) taking into account the multi-domain structure of the film. This model is presented in figure 1.26. In thin film, surface fluctuations of anisotropy may appear called the anisotropy dispersion (Crowther 1963). Let us start with the initial state (figure 1.26a) when all domains are magnetized parallel to the anisotropy axis (with angular small dispersion of anisotropy). After applying a transverse field the magnetization rotates toward the field direction (figure 1.26(b)). When the magnetic field reaches the critical value some directions of magnetizations jump to opposite directions as described in the previous section – in conformity with the Stoner–Wohlfarth model. When the magnetic field is removed then the localized directions of magnetization may be aligned antiparallel as shown in figure 1.26(c). Thus this magnetic film may be partially demagnetized after removing the magnetic overload. To recover the 2 In a later part of the book the sensor with a path inclined by the angle to the anisotropy axis will be called quasi-linear, the sensor with the Barber-pole structure will be called the Barber-pole sensor. The sensor with a path along the anisotropy axis will be called simply the sensor or single path sensor.

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Figure 1.26 The model of transverse magnetization process (after West 1961).

previous state of magnetization it is necessary to apply a sufficiently large stabilizing magnetic field along the anisotropy axis. It should be remembered that even in the case of the single-domain state, hysteresis may appear – as was described in the previous section (figure 1.21 or 1.22). The difference is that in the case of the single-domain state this hysteresis is reversible and the film cannot be demagnetized. A similar effect was described by Kools (Kools et al 1998). The domain structure in yoke magnetoresistive elements was observed using the Bitter technique. The permalloy element in the mono-domain state was magnetized with a strong transverse field. After application of this field, fishbone pattern closure domains have been observed (figure 1.27(a)). The domains were separated by 180° Neel walls. The same thin film element with stabilizing longitudinal field was insusceptible to domain creation after application of a large transverse field (figure 1.27(b)). The creation of domain was explained by the initial differences of magnetization in various parts of the element caused by the demagnetizing fields.

Figure 1.27 The domain patterns observed using the Bitter technique in the yoke type AMR sensor after application of a strong transverse field: (a) without and (b) with the stabilizing field (Kools et al 1998).

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Figure 1.28 presents two experimentally determined characteristics of the magnetoresistive sensor reported by Das (1991). In the first characteristic significant Barkhausen noise (small jumps) is visible. After application of the stabilizing field the noise vanished. Also in this analysis the domain structure has been observed (figure 1.28). The noise is connected with the multi-domain state which may be refashioned into the mono-domain state after applying the stabilizing field. In the mono-domain state the magnetization process is obtained by rotation of magnetization while in the multi-domain state magnetization is also caused by domain wall movement. The movement of domain walls is responsible for Barkhausen noise (Tsang and Decker 1981, Tsang 1984).

Figure 1.28 The transfer characteristics and domain structure in the yoke type MR sensor: (a) without and (b) with the stabilizing field (Das 1991).

From the previous examples it is obvious that the longitudinal biasing field is imperative to avoid domain activity and that noise and hysteresis are connected with this activity. The value of the stabilizing field depends on the geometry of the sensor and expected value of the transverse field. Figure 1.29 illustrates the easy axis field required to suppress the Barkhausen noise determined experimentally by Decker and Tsang (1980). The stabilizing field should not be too large because sensitivity depends on the value of stabilizing field Hs:

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AMR SENSORS R H2x ——–x —– ————– Rx (Hk Hs ) 2

or

31 ———————– 2 Hx 1 ———— . (Hk Hs )

√ (

R Hx ——–x —– ———— R Hk Hs

)

(1.63)3

Figure 1.29 Experimentally determined easy axis field required to suppress the Barkhausen noise as a dependence on the geometry of the sensor – aspect ratio w/L (Decker and Tsang 1980).

As previously mentioned the characteristic of the sensor with its path along the anisotropy axis is non-linear (figure 1.30). To improve the linearity of this kind of sensor (most frequently used as magnetoresistive reading heads) the displacement of the operating point to the linear part of the characteristic is necessary. The point of inflection is usually chosen as the best operating point – as shown in figure 1.30.

Figure 1.30 The choice of bias field to transfer the operating point into the most linear region of the transfer characteristic (A: point of inflection).

It is recommended that the sensor is applied as the pair of two differential magnetoresistors. Using differential sensors it is possible to suppress some errors, for example temperature errors and distortion of the output wave. It is 3

In the equations “minus” and “1/2” will be neglected for convenience (see equations 1.46, 1.50)

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very easy to prepare the Barber-pole or quasi-linear sensors as the differential pair – by applying the angle of 45° and 45°. It is more difficult to obtain the differential pair of the sensor with the path along the anisotropy axis. One of the methods is to bias two sensors with magnetic fields of opposite directions (figure 1.31). When such magnetoresistors are connected into the bridge circuit (in adjacent arms) then the resistor change is described by the expression: Rx (Hx Hxo )2 —— —– ————— Rx Hk2

(1.64)

and the resultant output signal may be expressed as: R Rx2 2 Hxo Uout K —–—x1 —–— K —— —— Hx . Rx Rx Hk2

(

)

(1.65)

Figure 1.31 Two differentially biased magnetoresistive sensors (a) and their resultant transfer characteristic (b).

Using two opposite-biased magnetoresistors it is possible to obtain an almost linear sensor. The linearization principle of two differential magnetoresistive sensors is illustrated in figure 1.31(b). Temperature zero drift caused for

Figure 1.32 Elimination of the zero drift by applying a square-wave AC biasing field ( Uo: zero drift; Ux: the signal proportional to the measured field).

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example by different temperatures of magnetoresistors connected into the bridge circuit can be difficult to eliminate. Tumanski has shown the advantage of using a square wave bias to reduce temperature drift (Tumanski 1984). By biasing the sensor with an AC bias field the output signal of the sensor (proportional to the measured value of the Hx field) is alternating. This output signal may be easily separated from DC temperature zero drift. Various methods of biasing and stabilizing of magnetoresistive sensor have been proposed. The most widely used methods are presented in figure 1.33. The MR sensor film may be magnetized by the external magnet or coil, by the hard magnetic layer or by the current conductor (shunt layer). One of the most frequently used methods is the flux closure system with soft adjacent layer – the SAL method. The use of shields or two paired sensors may improve sensor linearity and stability. Linear and self-bias construction involves the Barber-pole design. All these methods will be described in the following sections.

Figure 1.33 Various methods of biasing : (a) the permanent magnet system; (b) hard magnetic layer system; (c) coil system (d) exchange bias using antiferromagnetic material; (e) and (f) current conducting layer system; (g) soft adjacent layer system; (h) double sensors.

1.2.2 The real thin film – the multidomain structure and the dispersion of anisotropy The assumption that the thin film of a magnetoresistor is in mono-domain state and is magnetized by coherent rotation of magnetization is a large simplification because in real magnetic thin film, dispersion of anisotropy occurs and during magnetization complex domain changes appear. The deviation from singledomain state may result in Barkhausen noise and in the large differences between the Stoner–Wohlfarth model and the effects in the real thin film.

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Domain effects are especially significant in small thin film elements, where demagnetizing fields play an important role. Many groups have investigated the domain structure of thin film magnetoresistors4 (Druvesteyn et al 1979, Herd and Ahn 1979, Jones 1979, Kryder 1980, Collins and Husni 1981, Decker et al 1981, Tsang and Decker 1982, Ozimek and Paul 1984, Berchier 1984, van den Berg 1987, Corb 1988, Smith 1988, Tsang et al 1988, Cross et al 1995, Ye et al 1996, Akhter et al 1998). Especially interesting are simultaneously analyses of domain structure and magnetoresistive behaviour. Figure 1.34 presents the change of domain structure in a small permalloy element (12 24 m) during application of the transverse magnetic field (i.e. perpendicular to the anisotropy axis) and determined by Tsang and Decker (Decker and Tsang 1980, Tsang and Decker 1981, Tsang and Decker 1982).

Figure 1.34 The change of domain structure during magnetizing by a hard-axis field (the sensor was initially saturated along the hard axis by a magnetic field) (Tsang and Decker 1981).

Consider the thin film element initially saturated by applying a large transverse magnetic field. After reducing this field the ripple structure along the easy axis appears as indicated in figure 1.34(a). This change of magnetic field is free of jumps and noise. Further reduction of the magnetic field (to H 0) causes creation of the well-established buckling domain patterns (as in figure 1.33(b). The creation of this form of domain is motivated by the minimum of the energy in such a system. Also this change of magnetic field does not cause jumps at the transfer characteristic. When the magnetic field is further reduced (it increases in the opposite direction) a large number of sudden jumps in MR output can occur (see curve in figure 1.34). This Barkhausen noise is connected with wall state transitions, when reversed polarity Neel wall segments nucleate and expand (figure 1.34(c)). These N to N wall state transitions are the major source of Barkhausen noise. Further changes of magnetic field lead to the closure pattern presented in figure 1.34(d). Looking at this process of domain To find detailed information about domain and domain structure analysis (with a lot of examples) the excellent book of Hubert and Schäfer (1998) is recommended. 4

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pattern nucleation, intensification and annihilation it is clear that the stabilizing field directed along the anisotropy axis diminishes Barkhausen noise by inhibiting the formation of the buckling domain pattern. Figure 1.35 shows the domain activity of a small sample (20 40 m) initially magnetized by a large longitudinal field (determined by Tsang and Decker 1982). Initially the sample is in an almost single-domain state (only several additional domains exist near the edge of the sample due to the demagnetizing field) (figure 1.35(a)). After applying the transverse field the magnetization in the centre rotates while near the end the buckling domains structure appears (figure 1.35(b,c)). Further increasing of the magnetic field creates buckling domains with opposite magnetizations (figure 1.35(d)). Figures 1.35(e,f) present the high density buckling pattern after applying a large transverse field (this situation resembles the process shown in figure 1.26).

Figure 1.35 The change of domain structure during magnetizing by a hard-axis field (the sensor was initially saturated along the anisotropy axis by a magnetic field) (Tsang and Decker 1982).

Figure 1.36 illustrates the easy-axis magnetizing cycle determined by Kryder (Kryder et al 1980). Initially saturated by a longitudinal field the narrow stripe (6.4 m wide) was magnetized by a longitudinal field of opposite direction. For small magnetic fields a slight magnetization ripple occurs (figure 1.36(a)). Next these ripples transform into buckling domains (figure 1.36(b)). The buckled magnetization configuration furthur occurs with meandering flux patterns (figure 1.36(c)). When the magnetic field is further increased the triangular domains at the edges vanish (figure 1.36(d)). Application of a field of about 5 kA/m was necessary to restore quasi-single-domain state again. It should be stated that the coercivity of the film before forming the stripe was less than 240 A/m. For a given geometry of the sample the above described domain activities can be theoretically explained by micromagnetic calculations, taking into account the energy of the system (excluding the situations when domains nucleate on the defects) (Smith 1988, Yan and Yurisch 1989, Koehler 1993). The total energy is the sum of the following components: Wex – exchange energy, Wk –

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b)

c)

d)

Figure 1.36 The change of domain structure during magnetizing by a magnetic field directed along the anisotropy axis (Kryder et al 1980).

magnetocrystalline energy, Wd – demagnetizing energy and Wa – external applied field energy. Wtot Wex Wk Wd Wa .

(1.66)

When the sample is discretized into a squared element of edge size h this energy may be expressed as (Yan and Yurisch 1989): A 1 Wtot — ∑m1 · ∑mn Ku∑(m1 · e)2 –∑Mi · Dij · Mj ∑Mi · Ba (1.67) h2 1 2 ij n 1 i where: A – exchange constant, Ku – anisotropy constant, D – demagnetizing tensor. To calculate domain nucleation and domain motion the complex set of equations with a large number of unknowns should be computed. Additionally the magnetic history should be taken into account (Corb 1988). Yan and Jurisch (1989) computed the closure domain patterns for some simplified conditions – starting from an assumed initial domain configuration. Figure 1.37(a) shows the results of calculations of the domain pattern.

Figure 1.37 The magnetization distribution in small permalloy sensors: calculated by Yan and Jurisch 1989(a) and by Köhler et al 1993(b,c).

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A micromagnetic simulation program to compute the magnetization patterns in small thin film elements has been proposed by Köhler (Köhler et al 1993). Figure 1.37(b,c) shows the results of computation of magnetization patterns for two cases: when the element (dimensions 4 1 m) is biased by a stabilizing field (figure 1.37(b)) and without a stabilizing field (figure 1.37(c)). Using the micromagnetic model Smith (1988) computed conditions of domain wall nucleation during the magnetization cycle reported by Tsang and Decker (1982). This magnetization cycle is shown in figure 1.38. Initially the element is in the single-domain state (figure 1.38(a)). After applying the magnetic field the magnetization rotates “quasi-coherently” because in the central region this rotation is larger than near the edge due to the influence of the demagnetizing field (figure 1.38(b)). When the magnetic field exceeds the certain critical value H1 in the central region magnetization changes direction – at this moment two Neel walls nucleate (figure 1.38(c)). For further increase of the magnetic field the central domain increases (figure 1.38(d)). During the reverse cycle the certain critical value of magnetic field H2 exists when the domain walls collapse together and fold (figure 1.38(e)).

Figure 1.38 The mechanism of domain walls nucleation during the magnetization cycle (Smith 1988).

Figure 1.39 presents results of computations of the magnetization distribution in the stripe for given values of magnetic field inclined by 4° from the anisotropy axis. When the magnetic field reaches certain critical values (corresponding with the angles 25° and 44.5°) the non-equilibrium conditions force domain-wall nucleation. The main reasons for domain creation is the influence of the geometry of the element (the demagnetizing fields) connected with dispersion of anisotropy. The influence of demagnetizing fields is illustrated in figure 1.40(a). Due to the shape anisotropy after applying the transverse field the magnetization near the edges remains longitudinal while the magnetization in the central parts rotates. Therefore to suppress domain activities a large aspect ratio l/w is recommended

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Figure 1.39 The calculated magnetization distribution near the critical value of magnetizing field (near the condition of the wall nucleation) (Smith 1988).

Figure 1.40 The geometrical conditions of domain creation: influence of non-uniformity of the demagnetizing field (a) and the domain in the lead part of the magnetoresistor (b) (Tsang and Decker 1982).

(see figure 1.29). In the long element the longitudinal demagnetizing field responsible for buckling domain formation is reduced. The sharp and jutting out regions of thin film may also be a source of domain nucleation. As reported for example by Ye and co-workers (1966), by simple modification of the geometry (by covering the multi-domain part of leads with gold), significant suppression of noise has been obtained. The multi-domain state of thin film magnetoresistive sensor contributes to the existence of Barkhausen noise, distortion of the transfer characteristic and perturbation of the Stoner–Wohlfarth threshold in the switching elements (Comstock et al 1988). Davidson and co-workers (1984) have proved theoretically and experimentally that stripe domains cause the distortion of the displacement curve when the sensor is used as a reading head. Figure 1.41 compares the displacement curve in two cases – when thin film is the single domain (figure 1.41(left)) and the three-domain structure (figure 1.41(right)). The presence of multi-domain in the reading head practically makes the head unusable to track detection.

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Figure 1.41 The reading of magnetic track signal by a one-domain element (left) and a threedomain element (right) (Davidson et al 1984).

As was mentioned before the dispersion of anisotropy may be the reason for the creation of the multi-domain structure. The angular dispersions of anisotropy 90 or 50 are defined as those angles for which respectively 90% or 50% of the local easy axes lie with of the average easy axis direction (Crowther 1963). Similarly the dispersion of magnitude anisotropy may be defined as the anisotropy range covering certain parts of whole local anisotropies. Dispersion of anisotropy depends on the technological conditions, such as composition of the film (Lampert et al 1968, Smith 1961), substrate temperature (Battarel and Galinier 1969, Carpuat 1969, Mayer 1966, Flur 1967, Chapman et al 1981), deposition field strength, geometry, film thickness, grain size (West and Simmons 1966), anisotropy field, vacuum during deposition (Chapman et al 1981), compositional non-uniformity (Ahn and Beam 1966). Thus it may be stated that the dispersion of anisotropy is one of the parameters determining thin film quality. Figure 1.42 shows the dependence of the dispersion of anisotropy on some technological factors. The composition of the film of the smallest dispersion is practically the same as composition of minimal magnetostriction (Wilts and Humphrey 1968). It confirms the hypothesis of close connection between

Figure 1.42 The dependence of anisotropy dispersion on: (a) material composition; (b) substrate temperature during deposition (1: ordinary vacuum; 2: ultrahigh vacuum; 3: sputtering); (c) grain diameter.

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dispersion of anisotropy and surface fluctuations of stress (Crowther 1963). The dispersion of anisotropy depends also on the substrate temperature and the annealing condition. For ultrahigh vacuum the dispersion of anisotropy is significantly lower than for ordinary vacuum (Chapman et al 1981). Dispersion of anisotropy depends also on the grain diameter as shown in figure 1.42(c) (West and Simmons 1966). The dispersion of anisotropy is a direct consequence of the polycrystalline nature of the film. In the polycrystalline film a characteristic fluctuation of the magnetization called ripple structure appears (Hoffman 1968, Harte 1968). The ripple structure is a reaction of the film to a statistical perturbation of the crystal anisotropy of individual grains. According to Hoffman’s theory (Hoffman 1968) the dispersion of anisotropy is directly proportional to 2D2 —–— tHk

(1.68)

where: is an average of the randomly oriented torque due to the effective anisotropy energy within the grain, D is the mean grain size, t is the thickness of the film, Hk is the anisotropy field of the film. The existence of anisotropy dispersion means easier creation of the domains and noise. It also means that behaviours of thin film magnetoresistors may be far from the Stoner–Wohlfarth model. For example pure single-domain thin film magnetoresistors should be insensitive to the orthogonal field component. Figure 1.43(a) presents theoretical transfer characteristics for this case. Only during the reverse of direction of magnetization can the spikes of Rx Rxm occur. Figure 1.43(b,c) presents such characteristics determined experimentally for the canted biased sensors of the same shape but of different anisotropy dispersion. In the case of relatively small dispersion of anisotropy (figure

Figure 1.43 The change of the resistance during easy-axis magnetization cycle: (a) ideal Stoner–Wohlfarth model; (b) magnetoresistive sensor of low anisotropy dispersion; (c) magnetoresistive sensor of large anisotropy dispersion.

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1.43(b)) the switching threshold is perturbed. But in the case of large dispersion of anisotropy (figure 1.43(c)) practically for all longitudinal fields (below certain Hsmax value) local switching occurs. The sensor is then sensitive to the orthogonal component, which is undesirable. To eliminate the effects of a partial change of magnetization the stabilizing field should be large enough to remove the operating point from the area imminent to switch. The magnetic field along the anisotropy axis ensuring that the whole film area is switched (Hsmax in figure 1.43(b,c)) may be recommended as the stabilizing field value necessary to save the sensor work. The smaller dispersion of anisotropy the smaller stabilizing field is required. According to the Stoner–Wohlfarth model the larger the dispersion of anisotropy the smaller transversal field hxcr causes change of magnetization (figure 1.44(a)). The critical value of the transversal field hxcr can be extended by applying the additional stabilizing field hso (hxcr hso /tg ) – as demonstrated in figure 1.44(a). Figure 1.44(b) presents the simplified model of the film with dispersion of anisotropy. The thin film may be substituted by two magnetoresistors with anisotropy axis split by the angle (assuming that the film is composed from non-interacting small regions with various anisotropy).

Figure 1.44 The simplified model of thin film with anisotropy dispersion: (a) the critical curve of the magnetized film with anisotropy dispersion; (b) substitution of element with anisotropy dispersion by two elements of declined anisotropy axis.

Figure 1.45 presents the direction of the magnetization vector in both component magnetoresistors. The angle for both magnetoresistors can be described as: ! — 4

and

" — . 4

(1.69)

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Thus the change of resistance of both magnetoresistors may be described by the expressions R!x Rm (sin 2 cos 2 cos 2 sin 2)

(1.70)

R"x Rm (sin 2 cos 2 cos 2 sin 2).

(1.71)

The resultant change of resistance is then R!x R"x Rx —————– Rm sin 2 cos 2 Rx cos 2 . 2

(1.72)

Figure 1.45 The magnetization of two elements of declined anisotropy axes.

Due to the dispersion of anisotropy the change of resistance is reduced by cos 2. Similar results were reported by Stobiecki et al (1972). Roux-Buisson and Bruyere (1969) determined the influence of dispersion anisotropy as the coefficient (122) equal to cos 2 for small values of . Applying the stabilizing field Hs reduces the dispersion of anisotropy to (Stobiecki et al 1972): o (h) ——— 1 + hs

(1.73)

where: hs Hs /Hk. The influence of the dispersion of anisotropy on the magnetoresistive effect may be described by the coefficient k: 2 Rx k Rx cos ———· Rx . 1 + hs

(1.74)

Figure 1.46(a) presents the results of calculations of the transfer characteristic determined for various values of anisotropy dispersion (assuming the model presented in figure 1.44(b)). Fortunately typical dispersion of anisotropy usually

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Figure 1.46 The transfer characteristics of the magnetoresistive sensor calculated using the twoelement model (a) and determined experimentally (b).

does not exceed several degrees. Nevertheless the experimentally determined transfer characteristics of the sensor may significantly differ from the theoretical calculated values using Stoner–Wohlfarth model (figure 1.46(b)). Several models of thin film and dispersion of anisotropy have been proposed. De Ridder and Fluitman (1990) recommended the extended model of orthogonal susceptibility (Coren 1964, Green and Yarbrough 1970) to describe the hysteresis of thin film with dispersion of anisotropy. Recently numerical micromagnetic calculations include the domain structure in the mathematical model of thin film magnetoresistors. Shiiki and co-workers (1996) proposed a numerical model of the magnetoresistive sensor with dispersion of anisotropy. The calculated area was divided into sub-regions of randomly distributed anisotropy. The magnetization distribution at different stages of the magnetization process was calculated by numerical integration of the Landau–Lifshitz–Gilbert equation. After sophisticated calculations the distribution of magnetization and anisotropy field distribution were determined (figure 1.47). Knowing these distributions it is possible to find the conditions under which buckling domains occur. It was proved that when dispersion increased the buckling was more pronounced, leading to larger Barkhausen noise. Furthermore buckling did not completely disappear when the applied field was weakened to a smaller value.

Figure 1.47 The anisotropy field distribution in the element with dispersion of anisotropy – calculated by Shiiki and co-workers (1996).

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Generally the magnetization process is too complex and has too large a number of unknowns to calculate the magnetoresistive response in the real magnetic thin film. It is practically impossible to separate effects of the fluctuations of anisotropy caused by anisotropy dispersion, inhomogeneities, stresses, non-uniformity of demagnetizing fields and domain structure. All these components influence the magnetization in different ways and the physics of these influences is different. Therefore successful modelling of the film with dispersion anisotropy is possible only for simplified conditions. To calculate the magnetoresistive response of the real sensor with nonuniformity of anisotropy a simplified technical model has been proposed (Kwiatkowski et al 1983). The thin film magnetoresistor was replaced by an equivalent sum of magnetoresistors with different anisotropy. It was assumed that the distribution of anisotropy was close to the Gaussian distribution (such distribution was confirmed experimentally by Ehvesman and Olson 1966). The resulting resistance of the magnetoresistor was computed as the sum of 2k 1 components, as the 3 distribution interval was divided into 2k subintervals. The constant of Gaussian distribution was assumed as 50 /0.675. The change of resistance was calculated using the following expression: Rx

k

∑

{[

nk1

( )} [

3 1 p —– n – 2k 2

( )]}

3 3 p —– n – 2k 2

[

3 Rm # —– (n 1) 2k

]

(1.75)

where: p( ) – the probability of the anisotropy direction falling into the interval differing from the mean direction, Rm ( # n ) the function Rx f(H) for the anisotropy axis making an angle (# n ) with the mean direction. Figure 1.48 compares theoretical and experimental transfer characteristics of the magnetoresistor. After experimental determination of the angle from the dependence Rx f(Hx), the Rx f(Hy) characteristic was then computed. Calculated characteristics correlate quite well with experimental ones. Thus the

Figure 1.48 The comparison of experimentally determined transfer characteristics of a magnetoresistive sensor with calculated ones ((a): SW single-domain theory; (b): calculated using multi-element model; (c): experiment.

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multi-element model, although very simple, better represents the real magnetoresistive element than the single domain or two-element model presented in figures 1.44(b) and 1.46(a).

1.2.3 Sensors biased by the hard magnetic layer To produce the magnetic field that is necessary to bias or stabilize the magnetoresistive sensor the external source of magnetic field may be used. The simplest way is to place the external magnet near the thin film. Two examples of such a design are presented in figure 1.49. In the construction presented in figure 1.49(a) the magnet is mounted on the back of the conventional sensor package providing an auxiliary field of 3.6 kA/m. In the construction presented in figure 1.49(b) the sensitivity of the sensor may be fluently changed by the displacement of the magnet (Kuijk et al 1979).

Figure 1.49 Two examples of MR sensors using an external permanent magnet biasing system: (a) Philips KM110B sensor (Philips technical information) and (b) a magnet moved by screw (Kuijk et al 1979).

The use of the external magnet is possible only when the dimensions of the transducer are not limited. In most applications, especially in the case of reading heads, the dimensions of the sensor should be small. Moreover a large magnet is not recommended because it can destroy the measured magnetic field. Therefore the magnet is more often substituted by a thin hard magnetic film. Bajorek and co-workers (1974) proposed to use the permanent magnet layer made of hard magnetic material integrated with magnetoresistive film. This layer can be deposited adjacent to the permalloy film – most often placed above the film, but sometimes underneath (Liao et al 1994) or in the neighbourhood (Smith 1990). The application of two permanent magnet films has also been proposed (Nouchi et al 1982). Usually the thin insulating film (for example SiO2 film) is deposited to separate the hard magnetic layer from the magnetoresistive film. The magnetoresistive stripe then works as a flux concentrator, as shown in figure 1.50. To improve the quality of the permanent magnet layer the deposition of a Cr underlayer is recommended (Liao et al 1994, Smith et al 1990).

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Figure 1.50 The methods of biasing the film using a hard magnetic layer.

The first realizations of the hard biasing film concept were not fully satisfying. One of the first methods of producing high coercivity Fe2O3 magnetic layer was the oxidation of permalloy film (Bajorek et al 1971). Also the hard magnetic film of magnetite Fe3O4 has been deposited (Bajorek and Thompson 1975). These hard magnetic materials were inhomogeneous and their surface was not smooth enough. Therefore the short-wavelength roughness caused the increase of anisotropy dispersion of the permalloy film. The application of cobalt-based alloys obtained hard magnetic layers with the desired parameters. Various hard magnetic materials have been tested, for example CoCr (Bajorek and Hempstead 1979), SmCo (Dibbern 1989), CoIr (Kitada et al 1984), CoNiCr (Liao et al 1994) or CoZrMo (Ishiwata et al 1984). The cobalt platinum thin film is often recommended as an excellent material for the bias of magnetoresistive sensors (Kitada and Shimizu 1983, Kitada et al 1985, Hill et al 1985, Hill et al 1986, Brucker and Spada 1990). Figures 1.51 and 1.52 show the behaviours of CoPt bias films tested by Kitada and co-workers (1985). The optimal material composition is about 25% of Pt – for such an alloy the coercivity reaches a maximum (figure 1.51). The bias field strength may be increased by changing the CoPt film thickness. The thickness of the insulator layer does not significantly influence the bias result (figure 1.52), because the whole stray field from the magnet layer is

Figure 1.51 The behaviours of the CoPt biasing layer system: the coercivity versus the layer composition; the bias field versus the thickness of the layer (Kitada et al 1985).

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Figure 1.52 The dependence of the bias field and coercivity on the insulator layer thickness (Kitada et al 1985, Hill et al 1986).

concentrated in the permalloy film. In the case of a shielded head the bias field may decrease with the increase of the spacer thickness due to absorption of part of the flux by the shield. The decrease of the spacer thickness strongly influences the coercivity of the magnetoresistive layer (figure 1.52). Therefore it is not recommended to decrease the insulator layer thickness below 2 m (Hill et al 1986). Experimentally determined behaviours of permanent magnet biasing sensors are presented in figure 1.53. The transfer characteristic of magnetoresistor changes only slightly with the spacer thickness. But by appropriate design of the thickness of the bias layer it is possible to obtain the transfer characteristic with a satisfying linearity.

Figure 1.53 The transfer characteristics of the MR sensor biased using a hard magnetic layer: various spacer thickness (bias layer thickness 30 nm) and various bias layer thickness (spacer thickness 200 nm) (Hill et al 1986).

It is important to find the optimal bias field value. As mentioned in previous sections it is assumed that the optimal is a bias field corresponding with the inflection point of the transfer characteristic. The symmetry of the output signal can act as an indicator of the correct choice of bias field. Figure 1.54 presents the dependence of positive and negative pulse asymmetry A/B versus bias field as determined by Jeffers and Karsh (1984) by directly investigating the output signal of the reading head.

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Figure 1.54 Experimentally determined a symmetry and sensitivity of MR sensor versus the bias field value (Jeffers and Karsh 1984).

It is interesting that the optimal bias field value of 10.6 kA/m was slightly different from the inflection point value (about 8.7 kA/m). Also interesting to note was that the optimal value of bias field ensuring the maximal value of the output signal (obtained after applying the 1.2 MHz tape signal) was 12 kA/m. Figure 1.55 presents the output signal waveform of the correctly biased, underbiased and over-biased sensor (Kitada et al 1985).

Figure 1.55 Experimentally determined waveform of the output signal of the sensor: (a) correctly biased; (b) over-biased; (c) under-biased (Kitada et al 1985).

To obtain a sufficiently large biasing field a magnetic layer of thickness larger than 5 m may be necessary. The preparation of such a thick layer by sputtering can be difficult due to stresses and poor adhesion to the substrate. Therefore Hill and Birtwistle (1987) proposed to pattern the hard magnetic layer to the thinner stripe placed only above the active part of MR sensor. Figure 1.56 presents the magnetic field profile determined for an array of magnets with various spacing between sensor and hard magnetic layers. For a certain value of this distance (80 m in the analysed case) it is possible to obtain a uniform magnetic field above the sensor. The results presented in figure 1.56 (right) show another important advantage of the design proposed by Hill and Birtwistle (1987). It is possible to obtain the pair of magnetoresistors biased at opposite directions by arrangement of the sensor. Thus it is possible to manufacture a differential pair of magnetoresistors. The differential magnetoresistors are much more accurate than single ones. For

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Figure 1.56 The bias field in the sensor biased using patterned hard magnetic layers: (left) the dependence of the field uniformity versus the distance between layers (A: 50 m; B: 80 m; C: 100 m); (right) the differentially biased magnetoresistors (Hill et al 1986).

example the temperature error in the differentially biased sensors is effectively suppressed. Also the influence of the orthogonal field component may be significantly minimized by applying the differentially biased pair of sensors (Paul et al 1970, Hill and Birtwistle 1987, Hill et al 1989). The detailed design of the sensor biased with permanent magnet material is possible only by numerical micromagnetic calculation (Smith et al 1990, Ishikawa et al 1993). Figure 1.57 shows the results of analysis of the hard magnet biased magnetoresistive sensor presented by Smith and co-workers (1990). The “L-bar” shape magnet layer placed above the MR film is the proposed optimal. Figure 1.57 presents the calculated distribution of the Hy bias field component.

Figure 1.57 The sensor with an “L-shaped” hard magnetic layer and calculated bias field components of the system (Smith et al 1990).

The designed permanent magnetic film also produces the easy axis field component Hx which is recommended for the stabilization or the MR layer. The stabilizing field is larger above the end parts of the MR stripe – this is desirable taking into account the larger demagnetizing field near the edge.

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The longitudinal stabilizing field should be larger near the end of the MR stripe because these parts of the magnetoresistor may be the source of noise. As was explained in the previous section the buckling domains are created firstly near the edges due to non-homogeneity of the demagnetizing field. Therefore it is not necessary to stabilize the whole MR stripe. Too large a stabilizing field additionally causes undesired influences to the media when the MR sensor is used as a reading head. Therefore it has been proposed to stabilize only the wing region of the sensor at the end part of the stripe (Kira et al 1987, Tsang 1987, Tsang 1989, Krounbi and Voegli 1987, Krounbi et al 1991). Figure 1.58 presents the idea of a partially stabilized magnetoresistive head (Tsang 1987, Tsang 1989). The track width Lw is established by the conductor leads in the middle part of the stripe while only the end parts are stabilized by exchange coupling with antiferromagnetic layers or by hard magnetic layers. Removal of the stabilizing field from the central part of the stripe increases the sensitivity of the sensor because the longitudinal magnetic field stiffens the magnetization. This end part method of stabilizing is often used as a supplement to other methods of biasing (Kikuchi et al 1994, Guo et al 1994, Suzuki et al 1996, Shen et al 1996, Zhu and O”Connor 1996).

Figure 1.58 The system with partially biased magnetoresistors: (a) the design of the system; (b) magnetics of the system – without and with transverse signal field (Tsang 1987).

Various shapes of permanent magnet parts have been considered (Krounbi et al 1991, Krounbi et al 1992, Shen et al 1996). It was found (Shen et al 1996) that an abutted structure (figure 1.59(a)) rather than overlay design (figure 1.59(b)) better suppresses the domain activity and assures the stabilizing effect. The overlap region between the abutted hard magnetic layer and the magnetoresistive film can greatly affect the stability of the sensor. The gradually bevelled edge is required to assure magnetic continuity and good electrical conduction. Champion and Bertram (Champion and Bertram 1995, Champion and Bertram 1996) have proved that the interface angle should be larger than 30°.

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Figure 1.59 The construction of the sensor with: abutted (a) and overlay (b) hard magnetic layer (Shen et al 1996).

The micromagnetic simulation may be useful to optimize the shape and dimensions of the permanent magnet part. Figure 1.60 shows two examples of such calculations reported by Kikuchi and co-workers (1994). The calculated contours in figure 1.60 represent the same rotation of magnetization. When the distance between hard magnetic layers is too large compared with spacing of the leads (figure 1.60(b)) the magnetization rotates outside the leads which may cause crosstalk in the data-reading application of the sensor.

Figure 1.60 The results of micromagnetic calculations of the system with wing hard magnetic layers: the rotation of magnetization contours for various distance between hard magnetic layer and film: (a) 8 m; (b) 10 m (Kikuchi et al 1994).

Hard magnetic film may be used as an additional method of biasing – for example in the shunt-bias or the Barber-pole sensors (Kamo et al 1985, Nagata et al 1995, Takada et al 1997). Figure 1.61 shows such a design proposed by Nagata and co-workers (1995). Normally it is assumed that Barber-pole structure is self-biased. It means that the magnetic field generated by the sense current acts as a stabilizing field. But to produce a sufficiently large stabilizing field a high value of the sense current is required. Moreover this structure is not stabilized when the sense current is absent. Therefore between shorting bars and the permalloy layer an additional hard magnetic film has been deposited. The Barber-pole structure supported by the hard magnetic layer exhibited better performances (noise, stability against large external field) than conventional design.

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Figure 1.61 The Barber-pole structure supported by hard magnetic film (Nagata et al 1995).

1.2.4 The sensors biased by the current conducting layer The sensors biased by the permanent magnet layer are difficult to manufacture and the magnetic bias field cannot be changed after deposition. The magnetic field can be generated by an electromagnetic system – as a field from the current conducting line. The current may flow by the solenoidal coil or by the planar coil (figure 1.62(a,b)). The magnetic field may also be generated by the current flowing in an additional layer from non-magnetic materials deposited on the MR film and separated by the insulator layer – insulated shunt-biased sensors (figure 1.62(c)). The current conducting layer can also be deposited directly on the MR layer in so-called shunt-biased sensors (figure 1.62(d)). Figure 1.62 shows the methods of biasing by the current conducting layer.

Figure 1.62 The various methods of biasing by the current conducting layer: (a) the planar coil; (b) the wounded coil; (c) current conducting layer – insulated shunt-biased sensor; (d) shunt-biased sensor.

Shunt biasing is the simplest because it requires minimum technology. The shunt layer should be prepared from a material with large resistivity to minimize the shunting effect that decreases the sensitivity. Various materials have been considered and titanium is preferred for shunt-biasing systems (Bajorek et al 1977, Brock and Shelledy 1974, Shelledy and Brock 1975, Nepela and Potter 1975). The resistivity of titanium is about 2 0.75 m while the resistivity of permalloy is about 1 0.25 m. For typical thicknesses of the layers –

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permalloy of t1 30 nm and titanium of t2 100 nm – almost 50% of the current is flowing through the biasing layer. Besides the enlarged power consumption it means that the magnetoresistivity coefficient R is reduced to 1t2 2t1 R (1 R) ———————–— 1. 1t2 2t1 1t2 R

(1.76)

A magnetoresistivity coefficient typically of 2% is reduced to the value of 0.9%. Another drawback of the shunt-biasing system is that the preparation is not as simple as expected. The permalloy reacts with the biasing layer creating an intermediate area of lower magnetoresistivity and larger coercivity (Kitada et al 1984, Kitada 1985). Therefore insulating film is often introduced between biasing layer and the magnetoresistive layer. Using a separated biasing layer it is possible to control the biasing current independently of the sensor current. The bias current may even be alternating. The additional current conducting layer may be used as a feedback system (van Niet and Vrecken 1979, Griffith 1982). a)

b)

Figure 1.63 The transfer characteristics of the insulated shunt-biased sensors determined for various sensor width: (a) w 25 m; (b) width w 40 m (Ciureanu 1988).

Detailed analysis of the insulated shunt-biased sensors has been presented by Ciureanu and Korony (Ciureanu 1992, Ciureanu and Korony 1988) and by Mapps and co-workers (1985). Figure 1.63 shows the transfer characteristics of two sensors of various widths biased by the current conducting layer. Correctly biased sensors should exhibit the operating point at the centre of the linear part of the characteristic. It may be roughly assumed that the optimal bias field Hb should be the half of the anisotropy field (the sum of anisotropy field Hk and demagnetizing field Hd):

(

)

1 1 t Hb — (Hk Hd ) — Hk — Ms . 2 2 w

(1.77)

Thus a narrower sensor requires a larger bias field. This field in the middle of a sensor may be expressed as:

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(1.78)

To calculate the average bias field more precisely Ciureanu and Korony (1988) have proposed following expression: 1 Hb — w

w/2

[

Ib 1 d d2 w2 Hb dy —– ———– ——– 1n ———— w w 4w d2 w / 2 tan — d

∫

(

]

)

(1.79)

where: d – distance between layers. Figure 1.64 presents results of calculations of the bias field for various dimensions of the sensor (Ciureanu and Korony 1988). The bias field is significantly lower near the end of the strip which may result in under-biasing of this part of the sensor (figure 1.64(a)). The uniformity of biasing may be improved by decreasing the distance between layers. To ensure the sufficient value of a bias field the biasing layer should be thick enough to cause an increase in the thickness of the sensor.

Figure 1.64 The influence of the geometry of the sensor on the bias effect: (a) the special distribution of the bias field; (b) bias field as a dependence on distance between sensor and conductor layer (Ciureanu 1988).

Beside non-uniformity of biasing another drawback of the shunt-biased sensor is additional heating caused by the current in the bias layer. Ciureanu (1992) experimentally determined the current density of the sensor with a copper bias layer. The self-heating effect of 10°C above room temperature has been caused by a current density of 0.4–0.6 106 A/cm2. Shelledy and Brock (1975) and O’Day (1974) proposed the design of differentially biased sensors. Figure 1.65 presents the idea and the construction of such an ‘E-shaped’ sensor. The currents in both magnetoresistors are at opposite directions and therefore fulfill the condition: Rx1(H) Rx2(H). It

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Figure 1.65 The differentially shunt-biased magnetoresistive transducer (O’Day 1974).

has been proved experimentally that, after connecting such sensors into a bridge circuit, the higher order harmonics components in the output signal were significantly suppressed (Shelledy and Brock 1975). The shunt-biasing method may be used as a supplementary method to other biasing systems. Figure 1.66 presents the magnetization distribution in shuntbiased and permanent layer biased sensors. In the first method the magnetization is largest in the middle of the sensor width, while in permanent magnet bias, magnetization is smallest in this part. Therefore a new biasing method has been proposed that combines both methods of biasing and utilizes their advantages (Kamo et al 1985). As shown in figure 1.66(c) such a combination results in an almost uniform distribution of the flux density.

Figure 1.66 The flux density distribution in the magnetoresistive path: (a) biased by hard magnetic layer; (b) biased by shunt layer; (c) biased by hard magnetic and shunt layers (Kamo et al 1985).

The magnetic field produced by current conducting layers can be used to stabilize the film in the case of Barber-pole sensors. In the Barber-pole sensor the shorting bars are deposited at 45° with respect to the anisotropy axis (figure 1.67). Thus the current has to flow initially at 45° to the direction of magnetization. The condition of linearity is fulfilled and the sensor does not need the biasing field. But the stabilizing field is needed in order to compress noise and hysteresis. This stabilizing field is produced by the current in the

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Figure 1.67 The design of the Barber-pole sensor (a) and the current lines in this structure (b).

Figure 1.68 The magnetic field produced by the elementary part of the shorting bar (a) and the resultant magnetic field generated above the Barber–pole structure (b) (calculated by Haudek and Metzdorf 1980).

shorting bars (figure 1.68(a)) (Feng et al 1977, Haudek and Metzdorf 1980, Metzdorf et al 1982, Tumanski and Stabrowski 1985, Tsang and Fontana 1982). The value of the stabilizing field depends on sensor geometry, and can be expressed by the formula (Tumanski and Stabrowski 1985): I a Hs —– ——— 4w a b

(1.80)

where: a,b – dimensions as in figure 1.67(a). Haudek and Metzdorf (1980) presented calculations of the stabilizing field component produced by the current in gold shorting bars deposited on permalloy (figure 1.68). The shorting bar was divided into elementary parts dI. The magnetic field was determined as a sum of the elementary fields dHi. Figure 1.68(b) presents the results of the calculations. For dimensions a 9 m, b 6 m, w 15 m, tAu 1 m a current of I 20 mA generates a magnetic field larger than 100 A/m. In most cases such a field is sufficient to ensure the stability of the sensor, without any hystersis. Figure 1.69(a) presents experimentally determined transfer characteristics of Barber-pole sensor. If the magnetic field does not overcome the recommended range of the sensor (1 kA/m) the characteristic is without hysteresis. If there is magnetic overload then the sensor exhibits hysteresis. Usually the intrinsic stabilizing field recovers after removing the overload. It is recommended that before measurements the sensor is placed in the external magnetic field along the anisotropy axis to be sure that all effects of the overload are removed. The stabilizing effect may also be achieved by resetting the sensor with a large-

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Figure 1.69 The experimentally determined transfer characteristics of the Barber-pole sensor and the design of Barber-pole sensor with an additional planar stabilizing coil: (a) the characteristic of the sensor with internal stabilizing field only; (b) the characteristic of the same sensor with an additional external stabilizing magnetic field.

amplitude, short pulse current – to magnetize the film without heating effects. Applying an additional external field along the anisotropy axis allows the operating range to be extended without the detrimental effect of overload (figure 1.69(a)). The Philips Company developed its Barber-pole sensor by introducing an additional planar coil in its KMZ51 model (figure 1.69). This coil was intentionally designed to produce the alternating, flipping field but it may also be used for extra stabilization or reset of the sensor. By using the planar bias coil it is possible to obtain differentially biased magnetoresistors. An example of the differential shunt-biased sensor developed by Mapps (Mapps et al 1987, Mapps 1997) is presented in figure 1.70. The bias conductor in the form of a double serpentine biases the adjacent magnetoresistors in opposite directions. The current conducting layers are the about 10% wider than the magnetoresistive layers. Due to bifilar arrangement of the serpentine the resultant magnetic field over the sensor is zero and does not disturb the measured magnetic field.

Figure 1.70 The differential MR sensors biased by the bifilar conductors designed by Mapps and co-workers (1987) (A,B: input of sensing currents; C: common output pad for sensing current; DE: input and output of bias current).

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The bias field can be produced by the solenoid wound on the sensor. The solenoidal coil may be integrated with the sensor. An example of such an arrangement, proposed by de Ridder (1988), is presented in figure 1.71. The coil was built from two patterned aluminium layers deposited at both sides of the magnetoresistive film. Two halves of the solenoid separated by the permalloy layer and two insulator layers were then connected via holes. Figure 1.71(b) presents the coil design which in used to increase the generated magnetic field locally near the edges. Such inhomogeneity of the magnetic field is desirable to compensate for the influence of the demagnetizing field at the edges.

Figure 1.71 The design of integrated coils generating the bias field (de Ridder 1988).

1.2.5 Biasing by exchange coupled antiferromagnetic layer A special kind of interaction may exist between ferromagnetic and antiferromagnetic layers called the exchange coupling or exchange anisotropy (Majklejohn and Bean 1956, Yelon 1971). The exchange coupling results in the torque that tends to maintain the spins of the ferromagnetic layer in their original position. Thus this coupling acts similar to biasing by a permanent magnet and may be used to bias or stabilize the magnetoresistive layer. As a result of the exchange coupling the hysteresis loop is shifted by the exchange field Hex (figure 1.72(left)). This field, analogous to the external magnetic field, can suppress domain activity. The first results of using the antiferromagnetic layer to stabilize the permalloy film have been presented by Hempstead et al (1978). FeMn was used as the antiferromagnetic material. Figure 1.72(left) presents the hysteresis loops determined for this coupled film. The exchange bias field is about 2 kA/m which is usually sufficient to stabilize the permalloy film. Figure 1.72(right) shows the dependence of the exchange field on the FeMn composition. The antiferromagnetic film may cause an increase of the coercivity of the resultant coupled layers. The coercivity, exchange field, and temperature behaviours of the exchange coupling film strongly depend on technological factors. These factors have been investigated by Tsang and co-workers (Tsang et al 1981, Tsang and Lee 1982). One of the most important parameters is the

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Figure 1.72 The characteristics of exchange coupling NiFe/FeMn layers: (left) the hysteresis loop; (right) dependence of coercivity and the exchange bias field on the FeMn composition (Hempstead et al 1978).

Figure 1.73 The dependence of the exchange field on temperature determined for NiFe/FeMn films (Tsang and Lee 1982).

temperature dependence of the exchange coupling effect. Figure 1.73 presents the typical dependence of the exchange field on the temperature. The Hex field decreases almost linearly with temperature, going towards zero at the blocking temperature Tc. This temperature is for NiFe/FeMn film at about 150 °C (Tsang and Lee 1982). Figure 1.74 presents the dependence of the exchange field and coercivity on the thickness of permalloy and FeMn layers determined by Mauri and co-workers (1987). The main drawback of using FeMn material as the biasing film is its poor resistance to corrosion. Other materials have been tested, for example Fe2O3 (Hempstead et al 1978, Cain et al 1987), TbCo (Cain et al 1987, Cain et al 1988, Cain and Kryder 1989), NiO (Soeya et al 1992, Lin et al 1995, Kim et al 1999), NiMn (Devasahayam 1996, Devasahayam et al 1997, Lin et al 1994). Also three-layered NiFe/NiFeNb/NiO films have been proposed (Soeya et al 1992). Recently, exchange coupling materials are of great interest due to their

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Figure 1.74 The dependence of the exchange field and coercivity on MnFe film and on the permalloy thickness (Mauri et al 1987).

application in GMR–spin valve magnetoresistive sensors. A comparison of various antiferromagnetic materials was carried out by Lin and co-workers (Lin et al 1995, Lin et al 1996). The results of their comparisons are presented in table 1.1. Table 1.1 The comparison of typical antiferromagnetic materials (after Lin et al 1995). Property

FeMn

NiO

NiMn

Exchange field [kA/m]

5

3.5

16

Coercive field [kA/m]

0.5

3

9

Resistivity [ cm]

130

108

175

Blocking temperature [°C]

150

200

450

Typical thickness [nm] Corrosion resistance

10

35

25

Low

Very high

High

FeMn is characterized by small coercivity and sufficient exchange field, but with low corrosion resistance. NiO exhibits large coercivity, but very high corrosion resistance and high resistivity. NiMn exhibits a large blocking temperature, but large exchange and coercive fields. High resistivity may be advantageous if the whole permalloy film is coupled, because the shunting effect is negligible. But in the patterned longitudinal bias (at the ends of magnetoresistive strip) high resistivity is not recommended. Thus the choice of exchange-couple films depends on the design and expected application of the sensor. To date FeMn is most widely used as the antiferromagnetic, exchangecoupling material. The phenomenon of exchange coupling between ferromagnetic and antiferromagnetic layers is not yet fully explained. It is assumed that this coupling results in the spin interaction between both materials. The spins in the antiferromagnetic film are rigidly held to its sublattice. As a result the external

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field should exceed a certain critical value of the field strength to overcome the pinning effect and reverse the spins in the permalloy film. In the macro scale the direction of the magnetization vector can be calculated by minimizing the expression of the free energy of the system. This energy W expressed by equation (1.38) can be rewritten in the form W o Ms tHx sin o Ku t sin2 o Kaf taf sin2 af o Jk cos ( af ) (1.81) where: t, taf – the thickness of the ferromagnetic and antiferromagnetic layer respectively, Kaf – anisotropy constant of the antiferromagnetic layer, Jk is the exchange coupling energy. Assuming that magnetization of the antiferromagnetic layer is pinned by the angle af 0 the minimization energy with respect to the magnetization angle leads to W —— Hx cos Hk sin cos Hex sin 0

(1.82)

where the exchange field is expressed by JK Hex —– . Mt

(1.83)

Introducing the simplifications condition that sin tg the direction of magnetization can be expressed in the form Hx ~ ———— sin . Hk Hex

(1.84)

Comparing with expression (1.41) it is clear that exchange coupling is equivalent to applying the additional field Hex along the anisotropy axis. Such a stabilizing field suppresses domain activity and decreases the anisotropy dispersion (equation (1.72)). The exchange field depends on the exchange coupling energy JK and is inversely proportional to the thickness t (see figure 1.74). Figure 1.75 presents the experimentally determined transfer characteristics of non-biased and exchange-biased MR sensors (Tsang 1989). After biasing the transfer characteristics are without hysteresis and noise. But the application of bias field causes a decrease of sensitivity. Therefore the exchange bias is often used only at the end of the sensor stripe (Tsang 1987, Tsang 1989, Mowry 1990, Yuan 1994) (figure 1.58). The stabilizing effect is then obtained without sacrifice of sensitivity, as presented in figure 1.75(c).

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Figure 1.75 The transfer characteristics of single path (a) and Barber-pole (b) sensor – 1: without the stabilizing field; 2: with the uniform exchange stabilizing field; 3: with the pattern exchange stabilizing field (Tsang 1989).

Several micromagnetic models of exchange-coupled films have been developed (Rave et al 1987, Smith and Cain 1991, Cain and Kryder 1990). Smith and Coin (1991) analysed exchange-coupled NiFe-TbCo bilayers represented by the following balance of energies:

[

0

W

∫

t1

[

t2

∫ 0

]

2

( ) ( )

d K1 sin2 1 A ——1 dz

M1Ha cos(1 H ) dz

d2 K2 sin2 2 A2 —— dz

2

]

M2Ha cos(2 H ) dz

Ki [1 cos(2i 1i )] Kb [1 cos2 2b ]

(1.85)

where: t, M, K, A – thickness, saturation magnetization, uniaxial anisotropy constant and exchange anisotropy constant, – angle of the in-plane magnetizations, Ha, H – parameters of applied field. Usually it is stated that exchange coupling originates in the formation of Bloch-type domain walls at a sublayer adjacent to the NiFe interface. The pictorial representation of the magnetization states of the NiFe–TbCo bilayer is presented in figure 1.76. The direction and strength of exchange coupling depends on the temperature treatment of the layers (Tsang and Lee 1982, Cain et al 1987, Howard et al

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Figure 1.76 The schematic representation of spin directions of NiFe–TbCo films: (a) as deposited; (b) after applying a small field; (c) after applying of large field (Cain and Kryder 1990).

1989). The direction of the anisotropy can be altered after the film is deposited by heating the film above the Neel temperature and cooling in a magnetic field along the new direction of the applied field. Using an exchange-biased permalloy magnetoresistor Cain et al (1989) realized the idea of dual bias. If the exchange field is directed by an appropriate angle to the sensor current direction it is possible to utilize both components of this field – one to stabilize the sensor and the second to bias the sensor. Figure 1.77 presents the transfer characteristic of the dual-exchange biased sensor.

Figure 1.77 The magnetoresistive transducer biased by the exchange field Hex inclined by the angle e with respect to the current direction and the transfer characteristic of the transducer (Cain and Kryder 1989, Cain et al 1989).

Lin and co-workers (1996) presented a comparison of hard-magnetic and antiferromagnetic stabilization schemes. Both methods exhibited good performances, such as quiet MR responses and high read sensitivity.

1.2.6 The soft adjacent layers (SAL) biasing technique Instead of using permanent magnet, shunt bias or exchange bias layers, ferromagnetic film may be used. As described in previous sections domain activity

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caused by demagnetization fields is a source of noise and hysteresis. The longitudinal demagnetization field can be reduced using flux closure schemes. By placing another soft magnetic film next to the MR layer it is possible to close the flux because this layer acts as the keeper (figure 1.78(a)). Thus the nucleation of the buckling domain at the edges is suppressed and the soft adjacent layer creates its own magnetic field biasing the MR film.

Figure 1.78 The soft adjacent layer bias technique: (a) the idea of the SAL method; (b,c) design and electrical connecting of SAL system proposed by Beaulieu and Nepala (1975).

The main idea of the SAL bias technique introduced by Beaulieu and Nepala (1975) is presented in figure 1.78(b,c). A magnetoresistive transducer consists of one MR element and a soft magnetic bias film that is electrically insulated from the MR element. The current flowing in the MR layer produces a vertical magnetic field in the soft adjacent layer. In the magnetized biasing layer the magnetic poles are created and these poles generate back the vertical bias field in the MR layer. This biasing field Hb depends on the thicknesses t1 and t2 of both layers (Beaulieu and Nepala 1975) 1 Hb — (M2t2 M1t1) w

(1.86)

where: M1, M2 – the vertical components of magnetization. It is recommended that the biasing layer used is thinner than the magnetoresistive layer. When the thickness ratio t2 /t1 is about 0.7 the magnetization in the MR film is rotated by 45° with respect to the anisotropy axis. Because in such conditions the soft adjacent layer is saturated its field is independent of the sensor current amplitude. Ooyen et al (1982) proved that the coupled films can be roughly analysed by minimizing the energy of the system with respect to the direction of magnetization in each film and by assuming that each film is magnetized homogeneously. The theoretical calculations of the soft adjacent layer magnetoresistive head has been presented by Jeffers and co-workers (1985). The total energy of the system is a sum of MR layer energy WMR , SAL layer energy WSAL and coupling energy WCPL. These energies can be expressed as (Jeffers et al 1985):

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[ (

65

]

t1 1 1 WMR ——— — Ms Hk sin2 (1 ) — Ms Hd1 sin2 1 MsHx sin 1 t1 t2 2 2

t2 1 1 WSAL ——— — Ms Hk sin2 (2 ) — Ms Hd 2 sin2 2 t1 t2 2 2 Is Ms Hx sin 2 Ms —— sin 2 2w 1 WCPL ———— Ms (t 1 H d2 t2Hd1) sin 1 sin 2 2(t1 t2)

)

(1.87)

where: t – thickness, Hd – demagnetizing field, – angle between the direction of magnetization and the anisotropy axis, – angle of misalignment between anisotropy axis of MR and SAL films, Hx – applied magnetic field, Hi Is /2w – magnetic field generated by the sensing current Is (w – width of the strip). The performances of manufactured sensors may be different than the results of theoretical calculations. Figure 1.79 presents a comparison of theoretical and experimentally determined transfer characteristics of SAL–MR sensor (Jeffers et al 1985). The experiment indicates that the stabilizing effect is not sufficient and the output is noisy and displays hysteresis. Application of a small additional stabilizing field (0.1–0.3 kA/m) decreases hysteresis and noise (Toussaint et al 1986). Therefore the SAL biasing technique is very often used with other stabilizing methods – for example with a permanent magnet or antiferromagnetic layers deposited at the ends of the strip. Two examples of the design of a SAL-biased MR sensor with additional stabilizing parts are presented in figure 1.80.

Figure 1.79 The theoretical and experimentally determined transfer characteristic of the SALbiased sensor (Jeffers et al 1985).

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Figure 1.80 SAL-biased sensors supplemented by permanent magnet (a) or antiferromagnetic (b) stabilizing layers. (A – SAL layer, B – MR layer, C – leads, D – permanent magnet, E – insulator, F – MnFe layer, G – titanium layer.)

Toussaint and co-workers (1986) analysed various factors affecting the performance of the SAL-biased sensor comparing the calculated and experimental results. Two problems that seriously degrade sensor behaviours have been diagnosed: MR–SAL electrical shorting and misalignment of easy axis MR and SAL films. Figure 1.81(b) presents the effect caused by electrical shorting between MR and SAL elements. The secondary peak appears in the R/R f(H) characteristic. The easy axes misalignment results mainly in hysteresis which is demonstrated in figure 1.81(c). Easy axis misalignment can be overcome by the application of a small additional stabilizing field. The shorting effect can be distinguished by observing the primary peak when the current is increased.

Figure 1.81 The transfer characteristics of the SAL-biased sensor: (a) ideal; (b) of partial shorting between layers; (c) of misalignment between MR layer and SAL layer anisotropy axes (Toussaint et al 1986).

More exact modelling of the SAL–biased sensor is possible by micromagnetic calculations. Several micromagnetic models have been proposed (Guo et al 1994, Smith 1987, Fujimoto 1997, Ishi et al 1996, Shiiki and Mitsui 1994). The most comprehensive and complex analysis of coupled SAL–biased MR sensors are presented by Smith (1987). The equilibrium conditions have been formulated as follows:

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[

67

]

2A mˆ (r) Ha (r) Hd (r) Hk mz (r) zˆ —— 2m(r) 0 Ms 2A mˆ (r) —–— (nˆ · )mˆ (r) surface 0 Ms

[

nˆ

]

(1.88)

outward surface normal

M Ms mˆ , mˆ (mx, my, mz), [m ˆ ] 1. The transfer characteristics of the sensor and the influence of geometrical factors on the sensor performances have been determined. Figure 1.82 presents a comparison of calculated and experimentally determined transfer characteristics of the sensor. The main difference is caused by domain activity not being fully incorporated in the mathematical model. After applying an additional stabilizing field (0.24 kA/m) both characteristics are very similar (figure 1.82(b)).

Figure 1.82 Theoretical and experimentally determined transfer characteristics of the SAL-biased sensor: (a) sensor without additional stabilizing field; (b) the same sensor after applying a small (240 A/m) stabilizing field (Smith 1987).

Figure 1.83 shows the dependence of magnetization distribution in the MR layer on the SAL/MR thickness ratio calculated by Smith (1987). For a given geometry (width 7.5 m, distance between layers 100 nm and thickness of MR film 40 nm) and a given sense current (I 30 mA corresponding to J 107 A/cm2) a certain value of SAL thickness (t2 0.8 t1) is required to ensure that the MR film is properly biased (sin 0.707). The SAL is magnetized at the edge parts of the width, while the MR layer is not fully magnetized in this part of the strip. The uniformity of magnetization depends on sensor width and on the current generating the magnetic field as demonstrated in figure 1.84. For a given geometry of the sensor (t1 40 nm, t2 34 nm, distance 100 nm) when the width of the strip is too small (below 7.5 m) the bias magnetization distribution may be very non-uniform (figure 1.84(a)). Similarly when the current is too small (below current density of 107 A/cm2) the SAL layer is not

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fully saturated and bias magnetization distribution in MR layer is also nonuniform. Once SAL saturation is achieved further increase of the current does not influence bias magnetization distribution.

Figure 1.83 The magnetization distribution in SAL and magnetoresistive layers computed for various t2 /t1 ratio (Smith 1987).

Figure 1.84 The magnetization distribution computed for various sensor width (a) and various current densities (Smith 1987).

In the soft adjacent layer biasing method it is possible to obtain a differential pair of sensors. The idea of such a design proposed by Kitada and Shimizu (Kitada et al 1989, Kitada and Shimizu 1992) is presented in figure 1.85. Currents of opposite direction bias the sensor differentially. Both magnetoresistors are biased with the field of opposite direction. After connecting such magnetoresistors in adjacent arms of the bridge circuit the linear sensor is realized as illustrated in figure 1.85(right). It is relatively easy to prepare both layers from the same material. But there are other design criteria for the soft adjacent layer and for the MR layer. The resistivity of SAL should be as high as possible to minimize current shunting. The high magnetoresistivity coefficient is undesirable. The magnetostriction, coercivity and anisotropy should also be small. The magnetization of the biased film can be described by the expression (Tsang 1984):

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Figure 1.85 The three-terminal differentially SAL-biased sensor and its transfer characteristics (Kitada and Shimizu 1992).

M —–y 2J Ms

— y√ 2 cosh ——– — √ gt 1 —————– — h√ 2 cosh ——– — √ gt

[

]

(1.89)

where: g – distance between layers, J – the sensor current density. It is clear that large permeability is recommended to ensure adequate biasing with moderate sensor current. Various materials for the bias layer have been proposed: CoZrMo, NiFeCr or AlFeSi. Chen and co-workers (1988) analysed various ternary NiFeX materials as soft biasing films – NiFeNb and NiFeZr have been recommended. Maruyama et al (1988) proposed another design of the soft adjacent layer technique. The insulator layer was substituted by a conducting layer. In this way the problem of shorting between SAL and MR layers was solved. It was proved that a SAL-biased sensor with a biasing layer of amorphous CoZrMo and a conducting separator of titanium was the attractive alternative for a classical (with insulator layer) design. The soft adjacent layer bias technique is advantageous among the various biasing schemes, because its structure is relatively simple and results are satisfactory. IBM has used the SAL technique in both tape and disk magnetoresistive heads constructions (Mallinson 1996). A similar effect to that of the SAL bias method may be realized in shielded magnetoresistive heads. As illustrated in figure 1.86 the shields alter the field

Figure 1.86 The shielded self-bias method (Mallinson 1996).

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produced by the sensor current and mirror images appear in the shield. When the spacing between both shields is different, the field H1–H2 appears which can bias the layer. This off-centre displacement sensor method is attractive, because no extra bias structure is required. Unfortunately the magnetic field generated by this method is insufficient to fully bias the sensor.

1.2.7 Dual element sensors Dual element sensors are the evolution of SAL bias sensors and form the transition to the next generation of magnetoresistive sensors – GMR sensors. In SAL bias sensors the second ferromagnetic layer is non-productive and therefore it seems logical to substitute this layer by an active magnetoresistive layer. O’Day (1973) proposed a dual element magnetoresistive head processing two magnetoresistive elements with a central current conductor generating a bias magnetic field for both magnetoresistors (figure 1.87(a)).

Figure 1.87 The dual element magnetoresistive transducers with current conducting layer (a) and with insulator separator (b) (Voegeli 1975, 1986).

Following this idea Voegeli (1975,1986) proposed removing the shunting current conducting layer and constructing the sensor assembly comprising two magnetostatically coupled magnetoresistors separated by an insulator layer (figure 1.87). The sensor current of one element serves to magnetically bias the other element in a differential sensing mode (figure 1.88). Such a structure has several advantages by comparison with other bias methods: there is no need of an additional bias layer, the demagnetizing field effect due to coupling between layers is diminished, sensitivity is doubled, differential pair of the magnetoresistors is simply obtained. It is no wonder that this type of the sensor leads the field when used as high density recording read heads (Moore and Cote 1976, Kelley et al 1981, Smith et al 1992, Yuan and Bertram 1993, Anthony et al 1994, Hsu et al 1995, Shi et al 1997, Tsang et al 1996, Tsang et al 1997, Hu et al 1999). Two magnetoresistors placed very near each other results in magnetoresistive sensors working in the gradiometer mode (Indeck et al 1988, Gill et al 1989).

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Figure 1.88 The idea of differentially biasing the dual element sensor.

Instead of detecting magnetic field strength these sensors detect the change of magnetic field (the gradient of magnetic field). In the common mode rejection condition this sensor is insensitive not only to the spatially uniform magnetic field, but also to thermal as well as stress influences. The measurement of only the gradient of magnetic field is convenient for reading digital information from tape or disk.

Figure 1.89 Differentially biased dual element sensor (a) and its connection to the amplifier circuit (b,c).

The differentially biased pair of magnetoresistors is obtained when the current in neighbouring sensors is in the same direction – as illustrated in figure 1.89(a). The sensor may be connected to the adjacent arms of the bridge circuit (figure 1.89(b)) or directly to the differential input of the amplifier (figure 1.89(c)). The resistance of both magnetoresistors can be described as Rx1 Ro Rx Rx2 Ro Rx .

(1.90)

Thus, the output signal in the bridge circuit (figure 1.89(b)) is as follows: Rx1Ro Rx 2Ro 1 Uout IKu ——————— — IKu Rx Rx1 Rx2 2Ro 2 while in the circuit presented in figure 1.89(c) the output signal is

(1.91)

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THIN FILM MAGNETORESISTIVE SENSORS I Uout — Ku [(Ro Rx ) (Ro Rx )] IKu Rx . 2

(1.92)

To obtain the gradiometer mode both sensors should be biased at opposite directions (figure 1.90(a)). Therefore the currents in adjacent layers should also be in opposite directions. The resistance of both magnetoresistors can then be described as: Rx 1 Ro Rx1 Rx 2 Ro Rx2 .

(1.93)

Figure 1.90 Gradiometer sensor (a) and its connection to the amplifier circuit (b).

Thus, the output signal in the bridge circuit (figure 1.89(b)) is as follows Rx1R4 Rx2R3 I Uout IKu ——————— — Ku ( Rx1 Rx2). Rx1 Rx2 2Ro 2

(1.94)

It is possible to connect the sensors directly to the amplifier by applying two separate supply sources as demonstrated by Gill and co-workers (1989). The numerical and experimental analysis of the magnetoresistive gradiometer has been presented by Indeck and co-workers (1988). The total energy of the system was described by the expression: I tMs sin 1 2Ms wt Hk1 W sin 1 Hx1 —– ———–— cos2 1 ———– —— 2w 2w L2 2

(

)

(

)

I tMs sin 2 2Ms wt Hk2 sin 2 Hx2 —– ———–— cos2 2 ———– —— 2 2w 2w L 2

(

)

Ms t 4Ms tW —— sin 1 sin 2 ——— cos 1 cos 2 w L2

(

) (1.95)

where: w, L, t – width, thickness and length of each strip, I – current in each stripe, t/w and 4wt/L2 – demagnetization factors.

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Figure 1.91(a) presents the responses of the single layer and the gradiometer sensors detecting the field gradient. Figure 1.91(b) presents the comparison of the temperature effect on the operating null point. The gradiometer sensor was practically immune to temperature zero drift.

Figure 1.91 The comparison of gradiometer sensor MRG and conventional single element sensor MRE: (a) the response to longitudinally recorded transition; (b) temperature offset drift (Indeck et al 1988).

The modified design of the dual magnetoresistive sensor was proposed by Smith and co-workers (Smith et al 1992, Smith and Yuan 1994) (figure 1.92). The insulator layer between two magnetoresistors has been substituted by a conductive layer, for example, titanium. Such a sensor is much easier to make because four (or at least three) terminals can be replaced by two leads. The proposed sensor is immune to electrical shorting between the MR elements.The currents in both magnetoresistors flow in the same direction and because both elements are connected in parallel the sensor is practically insensitive to a uniform magnetic field. Therefore the sensor can be treated as a gradiometer. The resultant resistance of the sensor is described as (R Rx1)(R Rx 2) ~ 1

Rx1 Rx 2 Rx ————————— — R ( Rx1 Rx 2) ————– 2R ( Rx1 Rx 2) 2 R

[

1 ~— [R ( Rx1 Rx 2)]. 2

] (1.96)

The detailed micromagnetic analysis of the dual element magnetoresistive sensor has been presented by Smith and co-workers (1992, 1994). Two kinds of biasing are possible. The antisymmetric biasing is when easy axes are initially established as b2 b1 (for example b1 45° and b2 135°) (figure 1.92(left)). It is also possible to bias the layers symmetrically, when b2 b1 (for example b1 45° and b2 45°) (figure 1.92(centre and right)). The symmetric or antisymmetric state can be created by the appropriate initial magnetizing procedure (Trindade and Kryder 1994).

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Figure 1.92 The modified dual element magnetoresistive transducer with conductive gap (g) spacer (left) in symmetric (S-DMR) or antisymmetric (A-DMR) initially biasing of the elements (centre and right) (Smith and Yuan 1994).

For the symmetric and antisymmetric states the change of resistance depends on the common mode field as follows (Trindade and Kryder 1994):

R

s t —— —— ———–— (sin 2b1 1 sin 2b 2 2) R s 2s t g

( ) ( )

R

s t —— —— ———–— (sin 2b1 1 sin 2b 2 2) R as 2s t g (1.97)

where: t, g – thickness of MR layer and the spacer, , s – resistivity of permalloy and spacer material, – change of the direction of magnetization caused by the external field component. From (1.97) it can be stated that both symmetric and antisymmetric modes are insensitive to a common mode transverse magnetic field, but only the antisymmetric mode is insensitive to a common mode longitudinal field. Detailed analysis (Trindade and Kryder 1994, Trindade and Kryder 1996) proved that the antisymmetrically biased dual element sensor demonstrated the advantages relative to the symmetrical mode of biasing. Figure 1.93 presents results of the comparative analysis of various kinds of reading heads reported by Smith and co-workers (1992). The double element sensor DMR is advantageous compared to the shielded and unshielded single layer sensors (SMR and UMR respectively) when high density recording (above 1/ 6 m 1) is used. The gradiometer mode GDR proved that this type of sensor is the most viable option for high track densities. Trindade and Kryder (1996) analysed various materials for the spacer in the dual magnetoresistive head. TaN was recommended due to good thermal stability and smoothness. Also Bhattacharyya and co-workers (1987) presented the comparative study of various methods of biasing – current biasing CB, shunt biasing SH, permanent magnet biasing PM, soft adjacent layer biasing SAL and dual element approach DS. A number of important design parameters have been compared. Figure 1.94 present the comparison of the transfer characteristics. The magnetic field from the medium was simulated by introducing a small current loop below the MR head (figure 1.94). The results of analysis proved

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Figure 1.93 The comparison of spectral response function Fu(k) for various magnetoresistive heads – UMR: unshielded head; SMR: shielded head; DMR: dual element head; GMR: gradiometer head; Fu(k): coefficient describing the sensitivity of the head introduced and defined by Smith (1992).

Figure 1.94 The comparison of various biasing techniques – DS: dual element; CB: current bias; SB: shunt bias; PB: permanent magnet bias; SAL: soft adjacent bias (Bhattacharyya et al 1987).

that the dual element bias scheme was the most attractive candidate for sensors, especially in the case of reading heads. Another comparison of SAL biased element and dual element magnetoresistive heads was presented by Yuan and Bertram (1993). The square wave playback pulses have been read using an unshielded SAL biased head (figure 1.95(left)), a shielded SAL biased head (figure 1.95(centre)) and a dual element head (figure 1.95(right)). The bit spacing was about 0.8 m. After comparison of various parameters Yuan and Bertram stated that the shielded MR-SAL head and dual MR head were the more advantageous AMR candidates for ultra high density read heads.

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Figure 1.95 The comparison of the head response when the square wave playback pulses are read – USAL: unshielded SAL biased head; SSAL: shielded SAL biased head; GDMR: gradiometer dual element head (Yuan and Bertram 1993).

1.2.8 AC biasing techniques Several advantages can be achieved by applying an AC stabilizing field e.g. temperature offset drift compensation, noise and hysteresis suppression or simultaneous measurement of both magnetic field components (Kwiatkowski and Tumanski 1986, Tumanski 1984, Mapps 1987, Vincent 1978, Baltes et al 1982, Veillard 1989, Ueda et al 1990, Kaplan and Paperno 1994, Paperno and Kaplan 1995, Paperno and Kaplan 1995b, Flynn 1994). Figure 1.96 presents the change of magnetization direction versus varying magnetic field along the easy axis – calculated using the single-domain Stoner–Wohlfarth model. Two values have been calculated: sin (representing the change of resistance in the case of the path along anisotropy axis, as

Rx sin2 ) and sin 2 representing the change of the resistance of the quasilinear sensors (sensors with path inclined at 45° with respect to the anisotropy axis or Barber-pole sensors).

Figure 1.96 The change of magnetization vector direction versus the longitudinal field value Hs calculated using the SW model.

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When the stabilizing field is a square wave of the amplitude larger than the switching field then the state of magnetization is flipped between two explicit (without hysteresis) positions. In the case of linear sensors the difference between these positions is dependent on the transverse magnetic field value. Figure 1.97 presents the magnetoresistive loops determined experimentally for the quasi-linear sensor. These loops are practically the same as the theoretical ones presented in figure 1.96. To tests has been used the magnetoresistor of the low dispersion of anisotropy, with precise easy axis indication and with the compensation of the earth magnetic field. Figure 1.98 presents the experimentally determined U f(Hs) characteristics for the case when the dispersion of anisotropy causes the complex transition process between the switch to two states of magnetization. Even if the stabilizing field is not exact directed along the anisotropy axis and the film is with significant dispersion of anisotropy the difference of the steady states ( U for Hs value larger than switching field – see figure 1.98) is still explicitly dependent on the transverse field value. Switching the stabilizing field can be used to diminish hysteresis because it places the operating point outside the hysteresis loop. But the most important advantage of the AC biasing method is the possibility of the offset compensation. The offset caused for example by the temperature zero drift is the

Figure 1.97 The experimentally determined response of the quasi-linear sensor versus the longitudinal field value Hs.

Figure 1.98 The experimentally determined response of the quasi-linear sensor determined for the absence of Hx field (Hx 0) (a) and for very small Hx field (Hx 5 A/m) (b).

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main problem limiting the resolution when the constant magnetic field is measured. It is not possible to separate the DC zero drift from the DC output signal. When the AC stabilizing field is used the zero drift is still a DC signal but the output signal is alternating. Figure 1.99 presents the idea of the AC biasing method proposed by Tumanski (1984). The square wave current flowing through the coil generates the magnetic field along the anisotropy axis. The amplitude of the output signal depends on the transverse field value – the carrier signal is modulated by the signal dependent on the measured field. The alternating output signal can be transformed or again rectified using phase sensitive detector. Figure 1.100 illustrates why the AC biased magnetoresistor is insensitive to zero drift. The zero drift (caused for example by a change of temperature) results in the shifting of the magnetoresistive loop. Thus the additional DC signal can be easily separated from the alternating usable signal. Figure 1.100(b) illustrates that the sensor stabilized by AC magnetic field is insensitive (to a certain limit) to the additional DC orthogonal component of the measured field. The appearance of the additional Hy field only causes change in the DC component of the AC output signal.

Figure 1.99 The principle of the AC bias method.

Figure 1.100 The influence of temperature offset drift (a) and orthogonal field component (b) on the output signal for the case of the AC bias method.

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Instead of a square wave the AC stabilizing field can be in the form of pulses flipping the sensor comparable to the chopping technique. Such a method of stabilizing the sensor and offset elimination recommends Philips for the Barberpole magnetoresistors. Figure 1.101 presents the block diagram of a flipping circuit and signals.

Figure 1.101 The principle of the flipping bias method recommended by Philips – the flipping circuit and the timing diagram of flipping signals: (a) flipping current; (b) output voltage; (c) filtered output voltage (Philips technical information).

The magnetoresistive sensor can also operate as a phase sensitive detector. This mode can be realized in the double-switching circuit proposed by Tumanski (1984) and is presented in figure 1.102. When the stabilizing field is a square wave and simultaneously the current is of the same shape the output signal is now the DC signal while the offset component is alternating. The proposed method is useful in the case of the canted easy axis sensor type but in the case of the barber-pole sensor some problems may appear because the current of this sensor is normally used to generate the additional stabilizing field. When an AC stabilizing field is used the switching process can be noisy because this process is related to domain activity and movement of the domain walls. Therefore Kaplan and Paperno (1995, 1995b, 1996) proposed another AC biasing mode which provide continuous saturation of the ferromagnetic material. The bias magnetic field is generated by two orthogonal coils producing

Figure 1.102 The dual flipping method proposed by Tumanski (1984).

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an elliptically rotating field (figure 1.103(a)). If this rotating field is sufficiently large the film is still in the mono-domain state and Barkhausen noise in the alternating output signal is significantly decreased. Figure 1.103(a,b) presents a comparison of the spectral analysis of the sensor output signal when the stabilizing field is only along the easy axis and when it is rotating. For rotating frequency of about 1 kHz the Barkhausen noise is effectively suppressed.

Figure 1.103 The elliptically biased MR sensor: the principle of the method, and the spectral analysis of the sensor output signal when stabilizing field is only along the easy axis (a) and when it is rotating (b) (Paperno and Kaplan 1996).

The sensor stabilized by the elliptically rotating field enables the simultaneous measurement of both Hx and Hy of the external DC magnetic field. If the sensor is biased by the two magnetic fields Hbx and Hby Hbx aHk cos t

and

Hby bHk sin t

(1.98)

the output signal is expressed as Hy sin t ——

Uout bH 1 k ———— cos2 arctan ——————– — —.

Uout max Hx 4 2 cos t —— aHk

(

)

(1.99)

The odd zero-crossing points of the output signal are affected exclusively by the Hx field component while the even zero-crossing points are affected exclusively by the Hy component – as illustrated in figure 1.104. The time shifts can be described as

Hx

todd ——— aHk

(1.100)

Hy

teven ————— . (a 1)Hk

(1.101)

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Figure 1.104 The calculated output signal of elliptically biased sensor: (a) various values of Hx component; (b) various values of Hy component (Paperno and Kaplan 1995).

The time shifts associated with the sensor output signal can be used to measure both components of the external magnetic field. Because the stabilizing field reduces the sensitivity of the sensor Flynn (1994) proposed the application of a unipolar stabilizing filed. This field can be periodically switched off during the time period when the magnetic field is measured. Simultaneously with the square wave stabilizing field the alternating transverse bias field ensures linearity of the sensor. This rather complicated biasing and stabilizing technique allows full sensitivity and reduction of noise and hysteresis.

1.2.9 The reverse mode of biasing In the conventional biasing mode the measured field is directed perpendicular to the anisotropy axis. Initially the magnetization is rotated by 45° with respect to the current direction. Usually the stabilizing field is applied along the anisotropy axis. As described in section 1.1.4 in the reverse mode of biasing the measured field Hx can be directed along the anisotropy axis and the bias field Hb is directed perpendicular to the anisotropy axis. Thus the change of resistance can be described as

Rx

1 —— —– ——————– Hx Rx Hb Hk Hd

(1.102)

where Hd is the demagnetizing field Theoretically if the bias field is equal to (Hk Hd) the sensitivity should be as large as infinity. Several groups (Hebbert and Schwee 1966, Gordon et al 1977, Hoffman and Birtwistle 1982, Vieth et al 1994, Hoffman et al 1983) preferred this mode of biasing. In the real structure significant limitations and obstacles may appear when the film is biased to rotate the magnetization by 90°. Due to dispersion of anisotropy and non-uniformity of magnetization it is very difficult to apply the bias field exactly perpendicular to anisotropy axis. In this

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state some parts of the film can switch their direction and the film can be partially demagnetized. This switching process may cause hysteresis and noise. Taking into consideration the above described problems the reverse bias method can give satisfying results only in the case of extremely good quality films – especially those with very low dispersion of anisotropy. Figure 1.105 presents the sensitivity characteristics of the reverse biased sensor experimentally determined by Hoffman and co-workers (1983). The optimal value of the bias field should be selected depending on the geometry of the thin film structure. Vieth and co-workers (1994) compared both modes of biasing. The examples of the results of investigations are presented in figure 1.106. The Barber-pole structure of Hk 300 A/m and Hd 250 A/m has been tested for various values of the bias field Hb. For Hb 480 A/m the sensitivity of the sensor was almost twenty times larger than for the conventional case. The small deviations of the bias field strongly affected the output signal. Therefore a larger bias field was recommended. But even for a bias field of 800 A/m the sensitivity was still five times larger in comparison with the conventional easy axis bias.

Figure 1.105 The experimentally determined dependence of the sensitivity and bias field value in the reverse biased sensor: (a) 0° 45°; (b) 0° 2°; (c) 10° 0°; (d) 80° 0° (Hoffman et al 1983).

Figure 1.106 Experimentally determined transfer characteristics biased conventionally – along easy axis of anisotropy (a) and biased in reverse mode (b) (Vieth et al 1994).

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1.3 DESIGN AND PERFORMANCES OF AMR SENSORS

1.3.1 The influence of the sample geometry on the MR effect The magnetoresistive behaviours may significantly change depending on the shape of the magnetoresistor. Usually the magnetoresistor path in the form of the stripe or small rectangular is cut from the whole film sheet. As described in previous sections the small thin film particles suffer by the domain activities generating additional noise and hysteresis. In the next section we will analyse the influence of non-uniformity of magnetization depending on the shape of the sample. In this section the influence of the sample geometry will be considered assuming the simplified homogeneous state of the film. In the case of the stripe inclined by the arbitrary angle o with respect to the material anisotropy axis (figure 1.107) an additional component representing the shape anisotropy appears in the expression describing the free energy of the system: 1 W o Ms Hx cos o Ms Hy sin —o Ms Hk sin2 ( o ) 2 1 —o NMs2 sin2 . 2

(1.103)

The component representing the shape anisotropy can be considered as the additional shape anisotropy field Hd NMs (N – the demagnetizing coefficient). As the result of the influence of a shape anisotropy the direction of the resultant anisotropy axis Lw may be changed and the resultant anisotropy field value Hk

Figure 1.107 The declination of the anisotropy axis after preparing the stripe (L: anisotropy axis of the material before preparing the shape; L: shape anisotropy axis; Lw: resultant anisotropy axis declined by the angle ).

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will also be changed. After minimization of the free energy the resultant anisotropy field can be determined as (Fluitman 1973, Sczaniecki et al 1974) —————————————– Hk √Hko2 (NMs )2 2Hko NMs cos 2o

(1.104)

where Hko is the anisotropy field of the film material (before preparing the sample). The new direction of the resultant anisotropy axis is described by the expression:

(

)

1 Hko sin 2o — arctg ———————— . 2 NMs Hko cos 2o

(1.105)

When the magnetoresistor stripe is considered as an ellipsoid then the demagnetizing coefficients depend on the dimensions of the stripe – on the thickness t, the width w and the length L. The demagnetizing coefficients in the film plane are: Nw t/(t w) for the direction perpendicular to the stripe axis and NL t/(t w) for the direction along the stripe. For the direction perpendicular to the film plane the demagnetizing coefficient is Nt w/(t w). Assuming typical values w 103 t and w L the coefficients NL and Nt can be assumed as Nt 1 and NL 0. It means that the demagnetizing field is in the film plane and can be described by the expression: t t ~ M ——— Hd Ms Nw M —. t+w w

(1.106)1

The simplest case to analyse is when the stripe is directed along the anisotropy axis of the material and the angle o is zero. Then the direction of the resultant anisotropy axis is the same as the material anisotropy axis and the resultant anisotropy field is the algebraic sum of both components Hk Hko NM Hko Hd .

(1.107)

The change of resistance in this case is described by the expression 2

( )

2

R

Hx

Hx —– —– ———–— —– ————— . Rx Hko Hd t Hko M — w

(

)

(1.108)

For typical parameters of magnetoresistor path t 50 nm, w 30 m and M 8 105 A/m the demagnetizing field is equal to Hd 1300 A/m. The typical anisotropy of material is about Hko 200–300 A/m. Thus the shape anisotropy 1

For simplicity the saturation magnetization Ms will be described by the letter M.

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may be the dominant factor influencing the parameters of the magnetoresistor. For very narrow stripes the anisotropy of the material is negligible in comparison with the shape anisotropy. Figure 1.108 presents experimentally determined transfer characteristics of magnetoresistors with various aspect ratios t/w.

Figure 1.108 The experimentally determined transfer characteristics of the single path sensor at various widths of the stripe: w 25 m; w 50 m; w 75 m.

Almasi and co-workers (1973) proposed applying the shape anisotropy as a method of improving the sensor behaviours. It was proposed to prepare the MR device having a shape anisotropy field perpendicular to the material anisotropy (figure 1.109). In fact such a method seems to be very attractive because in this case the resultant anisotropy can be expressed as:

(

)

t t Hk (Nw Nl )M Hko — — M Hko . w l

(1.109)

Thus it is possible to obtain a decrease of anisotropy (and increase of sensitivity) by the appropriate choice of the geometry of the stripe.

Figure 1.109 The magnetoresistive transducer with path perpendicular to the anisotropy axis: (a) the shape of the transducer; (b) transducer applied as the reading head (Almasi et al 1973).

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Unfortunately experiments proved (Stobiecki 1978) that the stripes cut perpendicularly to the anisotropy axis exhibit enlarged dispersion of anisotropy. It is difficult to obtain the element of such geometry with acceptable parameters. Another method of utilizing the shape anisotropy was proposed by Gebhardt and Richter (1981). Taking into account the expression (1.106) and by appropriate design (o 90° and Hko Hd) it could be possible to fulfil the condition of correct biasing 45° without any additional bias fields. Thus it could be possible to obtain the linear sensor without an additional bias field. However such a design is difficult to realize because of the inhomogeneity of demagnetizing field. Moreover in this case the small deviations of the anisotropy of the material Hko can cause a large change of the resultant anisotropy. Therefore the whole system might be very sensitive to technology conditions or operating conditions (for example temperature). In the case when the path is inclined by the angle o with respect to the anisotropy axis of the film the anisotropy value not only changes but also the direction of the resultant anisotropy axis is changed. The resultant anisotropy axis after preparing the shape is inclined by the new angle instead of o. It means that the magnetoresistor designed as a linear one (with path inclined by 45°) will exhibit quite different transfer characteristics. For example when t 20 nm and w = 100 m the resultant anisotropy axis is inclined by only 30°. Figure 1.110(a) shows the difference between expected characteristics (for 45°) obtained after etching the shape. To obtain the quasi-linear characteristic the stripe should be cut by an angle sufficiently larger than 45°. Figure 1.110(b) presents the calculated dependence of the anisotropy axis deviation on the normalized resultant anisotropy heff Hk /Hko (Sczaniecki et al 1974). From this dependence it is possible to determine the appropriate geometry of the sensor ensuring that the resultant angle is exactly as required.

Figure 1.110 The change of anisotropy axis direction after preparation of the stripe: (a) the transfer characteristic of the stripe inclined by the angle o 45° with respect to the anisotropy axis of the film; (b) the change of the angle versus the effective anisotropy heff Hk /Hko value (Sczaniecki et al 1974).

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The change of direction of the anisotropy axis means that the measured field is not exactly transversal. After deviation of the anisotropy axis by o (figure 1.107) the sensor can measure false field components Hx Hx cos Hy sin Hy Hy cos Hx sin .

(1.110)

This error can be easily eliminated in the case of a single magnetoresistor by taking into account the new direction of the resultant anisotropy axis. More complicated is the situation when both differential magnetoresistors (i.e. magnetoresistors of o1 45° and o2 45°) are etched in the same film. In such a case both axes of anisotropy are in different directions (figure 1.111(a)) and both magnetoresistors measure different magnetic field components Hx1 Hx cos Hy sin and

Hx2 Hx cos Hy sin

Hy1 Hy cos Hx sin and

Hy2 Hy cos Hx sin .

(1.111)

The transfer characteristics of both magnetoresistors are very different as shown in figure 1.111(b). Fortunately the resultant anisotropy axis of the whole sensor is the same as the primary anisotropy axis of the material. After connecting the magnetoresistors to adjacent arms of the bridge circuit according to the formula

Rx 1

Rx 2 Uout K —–— —–— Rx1 Rx2

(

)

(1.112)

Figure 1.111 The influence of the shape anisotropy in the case of two differential magnetoresistors etched on the same film: (a) the directions of anisotropy axes; (b) the transfer characteristics of both magnetoresistors and resultant characteristic of the sensor.

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all parasitic components are compensated. The sensor exhibits the resultant transfer characteristics similar to the case of a 45°. But as a consequence of the anisotropy axes deviation the sensitivity is diminished by the factor cos 2 :

1 Uout K —– sin 2o cos 2 ———–——— Hx . Hk Hy cos

(1.113)

Jeffers (1979) suggested forcing the appropriate initial direction of magnetization by cutting the magnetoresistive stripes inclined by the angle o from the thin film anisotropy axis. Such a canted easy axis technique can substitute the need of applying an additional bias field. The construction of the canted axis transducer is presented in figure 1.112(a). In the three-conductor layer design the bias angle is essentially independent of the sense current because the fields produced by this current cancel each other. Both magnetoresistors operate differentially which enables supression of Barkhausen noise, second harmonic distortion and thermal noise. It is important to find the optimal value of the angle o to ensure linearity and maximal sensitivity of the sensor. After analysis of the energy of the system the following formula for optimal value of the angle o was proposed: —————– 16 H 1 — —–d 1 . 9 Hko

(√

3Hko cos (o )opt —— 4Hd 2

)

(1.114)

The dependence (1.114) is presented in figure 1.112(b). When Hd Hko the optimal value of the canted easy axis is 45°. Typically Hd is larger than Hko and the layers should be prepared by an angle larger than 45°. In the design of the sensor presented by Jeffers the Hd value was about 3.2 kA/m and the optimal value of the angle o was 58.5°.

Figure 1.112 The magnetoresistive transducer with canted easy axis: (a) the design of the transducer; (b) the dependence of the optimal value of the angle o on the shape anisotropy Hd (Jeffers 1979).

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1.3.2 The influence of the magnetization non-uniformity on the MR effect The magnetization of the thin film element may be non-uniform, especially in the case of very narrow and thin stripes. Figure 1.113 presents the distribution of magnetization across the element width determined using a high magnification Kerr magneto-optic microscope (Collins and Jones 1979).

Figure 1.113 The distribution of magnetization across the element width using a high magnification Kerr magneto-optic microscope (Collins and Jones 1979).

The distribution of magnetization can be calculated for the simplified model presented in figure 1.114. It can be assumed that the elementary magnetic poles are located at the edge of the stripe. The point A is influenced by the sum of the magnetic field generated by these elementary poles. Thus the demagnetizing field dH in the point A placed at the distance r from the elementary pole dm can be expressed as dm dH —— r cos . r3

(1.115)

The resultant demagnetizing field is the sum of all the elementary fields and can be determined by integration for the whole sample l/2

Hd

∫

l / 2

[

]

dm dm —— r cos —— r cos dy (r)3 (r)3

(1.116)

where the parameters r, r, cos , cos are presented in figure 1.114 and can be described as

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Figure 1.114 The model of a rectangular thin film element with elementary magnetic poles located at the edges.

w w ——————— ——————— — x —x 2 2 w w 2 2 r — x y 2 , r — x y 2 , cos ——– , cos ——–. 2 2 r r

√( )

√( )

After integration the demagnetizing field can be described as

[(

]

Mtl 1 1 Hd —– —————————–—— —————–— —————————–—— —————–— . (1.117) 2 2 8 w w l2 w w l2 — x — x — —x —x — 2 2 4 2 2 4

) √( )

( ) √( )

Taking into account the condition l w the demagnetizing coefficient can be expressed as

(

)

t 1 1 N — ——— ——— . 4 w w — x —x 2 2

(1.118)

The demagnetizing factor changes across the width of the stripe. Thus the demagnetizing field is the smallest in the middle of the stripe and the largest near the edge. Knowing the value of Hd it is possible to determine the local direction of the magnetization from the equation describing the energy of the system. Figure 1.115 presents the change of N, Hd and sin determined for the narrow thin film stripe. More exact calculation of the demagnetizing field is possible using numerical methods (Anderson et al 1972). In the general case the demagnetizing field in the point A(x,y) is the sum of the elementary fields dH generated by the magnetic poles M(,). The elementary magnetic field can be expressed as

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Figure 1.115 The distribution of magnetization direction sin , demagnetizing coefficient N and demagnetizing field Hd across the stripe calculated using the simplified model presented in figure 1.114 ((a) t 20 nm, w 20 m; (b) t 20 nm, w 100 m).

1 dH M(,) — r r3

(1.119)

where r is the distance between points (x,y) and (,). The resultant magnetic field is then M(r2)(r1 r2) Hd (r1) ∫ ——————– r1 r23

(1.120)

where r1, r2 determine the position of the points (x,y) and (,) respectively. In the case of the thin film the demagnetizing field is in the film plane and can be determined as: ∞

∫

Hd (x)

∞

dM() x ——— ——– dd . d r3 w / 2 w/2

∫

(1.121)

Taking into account that ———————— r √(x )2 (y )2

and

Mx M sin

after integration the demagnetizing field is described by d sin () t ————– arctg ———— d . d 2(x ) w / 2 w/2

Hd (x) M

∫

(1.122)

After determination of Hd (x) it is possible to calculate the local direction of magnetization from the equilibrium condition – as a minimum energy of the system:

[

]

Hx sin (x) ————— cos (x) 0. Hk Hd (x)

(1.123)

The numerical model of a magnetoresistive sensor was introduced by Anderson, Bajorek and Thompson (Anderson et al 1972) and developed by

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Casselman and Hanka (1980). In the ABT model the demagnetizing field was calculated numerically from the expression: d () ——– cos () d Hd (x) tM ∫ ——————– d . x w / 2 w/2

(1.124)

Taking into account the non-uniformity of Hd (x) or (x) the output signal of the sensor was determined by integrating cos (x) dependence across the stripe width:

R

w / 2 ——x —– ∫ cos2 (x)dx. Rx w / 2

(1.125)

Figure 1.116(a) presents the calculated direction of magnetization distribution along the stripe width. The validity of the model was tested experimentally. The results are presented in figure 1.116(b). In the general case when the current path is inclined with respect to the anisotropy axis the angle is different from the angle ( – angle between magnetization direction and anisotropy axis, – angle between magnetization direction and the direction of the sense current). To calculate the change of resistance from the Voigt–Thomson formula (as max cos2 ) the distribution of the current in the stripe should also be taken into account. From this first ABT model a great number of other mathematical models have been developed (Fluitman 1978, Smith and Wachenschwanz 1987, Fredkin and Koehler 1990, Tomlinson and Hill 1990, Hill et al 1991, Koehler and Fredkin 1991, Koehler and Williams 1995, Shtrikman and Smith 1996, Jia et al 1996). The micromagnetic models are especially comprehensive and attractive. Some of them have been presented in previous sections, for example the

Figure 1.116 The numerical analysis of magnetoresistive transducer: (a) the distribution of magnetization direction across the stripe; (b) the transfer characteristics of the sensor (Anderson et al 1972).

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micromagnetic model of MR-SAL sensor proposed by Smith (1987) and described in the section 1.2.6. The micromagnetic technique introduced by Brown (Brown 1978) and Aharoni (Aharoni 1996) allows modelling of small ferromagnetic elements taking into account subtle structures, including structures within domains. As was described in section 1.2.2 by using the micromagnetic model it is possible to calculate even the dispersion of anisotropy (Shiiki et al 1996) or the condition of domain wall nucleation (Smith 1988). Micromagnetic modelling also allows analysis of the dynamic properties of thin film ferromagnetic transducers. In micromagnetic modelling after discretization the analysed element is assumed to be an array of localized magnetic moments that are allowed to take any direction. Under a given external field the metastable state of a moment array is calculated as a local minimum of the free energy. Thus all possible local energy minima fulfilling the condition W/x 0 are determined. Brown’s equation describing the stability condition is formulated as m Heff 0.

(1.126)

The effective field Heff is the sum of applied external field Ha, anisotropy field Hk, exchange field Hex, demagnetizing field Hd and the field Hi generated by the current. As an equation of motion the Landau–Lifschitz–Gilbert formula is usually used (Nakatani et al 1989): M M —– (M Heff ) —– M —– t Ms t

(

)

(1.127)

where is the gyromagnetic ratio and is the damping constant. In the case of electron spin the gyromagnetic ratio is 2.21 105 mA 1 s 1. The LLG equation is compatible with Brown’s equation for m/t 0. The solution presented above is rather complex and requires large computing power. Different mesh sizes may give different results. A small mesh size requires large storage arrays and large computing time. As stated by Tomlinson and Hill (1990) calculations of the demagnetizing fields require about 95% of the computing time. Using Fast Fourier Transform it is possible to calculate the demagnetizing field much more efficiently (Yan and Della Torre 1988, Yuan and Bertram 1992). For example a mesh of 16 000 points requires about 6 ms per iteration per cell. After applying the FFT convolution this time was diminished to about 1 ms (Tomlinson and Hill 1990). Figure 1.117 presents the results of micromagnetic calculations reported by Fujimoto et al (1997). The magnetization distribution change was determined after applying an external field of about 24 kA/m to the SAL-biased magnetoresistor with dimensions: 20 2.5 0.02 m (length, width and thickness respectively). Two cases were analysed – shielded (figure 1.117(a,b))

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Figure 1.117 The magnetization distribution in a SAL-biased MR transducer calculated by Fujimoto and co-workers (1997): (a,b) shielded magnetoresistive sensor; (c,d) unshielded magnetoresistive sensor; (a,c) Hx 0; (b,d) Hx 24 kA/m.

and unshielded (figure 1.117(c,d)) sensors. In the absence of an external magnetic field the effect of biasing (middle part of the sensor) and stabilizing (side parts of the sensor) are visible. Figure 1.118 shows the results of analysis of the much smaller (1 0.5 0.01 m) thin film element reported by Jia and co-workers (1996). The magnetoresistor was initially magnetized by the large transverse field (figure 1.118(a)) and next the magnetization distribution was determined when the field was gradually reduced to 8 kA/m (figure 1.118(b)), then to zero field (figure 1.118(c)) and finally to 8 kA/m (figure 1.118(d)). When the field was decreased a vortex near the edge was created. It was stated that the creation of the vortex was the reason for the Barkhausen jumps. This effect was explained by taking into consideration the effect of the demagnetization energy and boundary conditions. The demagnetization term tries to make the flux close while the boundary conditions forces the edge spins to be parallel to it. Thus for a certain value of magnetic field the edge spins suddenly change their directions which causes a jump in transfer characteristic. When the magnetoresistive sensor is designed as a read head one of the most important conditions is to obtain the dimensions as small as possible. In this case in order to neutralize the effect of demagnetizing field the flux closure system (for example SAL biasing) is recommended. Theoretically the sensors used to measure the magnetic field (for example earth magnetic field) can be designed with larger dimensions. But in this case the sensor path should be very narrow and long to obtain sufficiently large sensitivity (Tumanski and Stabrowski 1984). To contain the long path in a limited area the sensor in the form of a meander is usually prepared. With such a geometrical form it is possible to neutralize the effect of the demagnetizing field by reducing the gap width between paths (Pant 1996, Hoffman et al 1984).

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Figure 1.118 The magnetization distribution in small dimension permalloy film calculated by Jia and co-workers (1996).

Figure 1.119 presents the considered structure consisting of three paths of width w separated by the gap p. The demagnetizing coefficient of the path adjacent to two neighbours can be described as:

(

t 1 1 1 1 N — ——— ——— ———–— ————– 4 w w w w —x —x —px —p x 2 2 2 2

)

1 1 ————–— ———–—— 3w 3w —– p x —– p x 2 2

Figure 1.119 The model of three paths sensor with gap p between paths.

(1.128)

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and for the larger number k of the paths as: t k 1 1 N— ——————————— ————————– 4 n 1 (2n 1)c (n 1)p x (2n 2)c np x

∑

[

]

1 1 ——————————— ————————– . (2n 1)c (n 1p x) (2n 1)c np x

(1.129)

In the general case of the multipath sensor the following equations should be calculated:

{

p w / 2

w/2

p3w / 2

p 3w / 2

w / 2

pw / 2

[

t N(x) –——— sin (x)

∫G(x, )d

∫G(x, )d

]

∫G(x, )d

(1.130)

[

Hx cos (x) sin (x) ————— 0 Hk MN(x)

]

where: d sin () t G(x, ) —–——— arctg ———— d . d 2(x ) Figure 1.120(a) presents the calculated distribution of magnetization for the multipath sensor with path dimensions w 20 m and t 20 nm. As described in section 1.3.1 the shape anisotropy influences two parameters – anisotropy field Hk and anisotropy axis inclination cos 2 (see equation 1.113). Figure 1.120(b) presents the calculated dependence of the cos 2 /Hk coefficient on the gap width. The coupling between paths is effective when the gap width is smaller than 10 m. Using electron-beam lithography it is possible to prepare the multipath magnetoresistor with submicron gap width (Hoffman et al 1984).

Figure 1.120 The calculated behaviours of the multipath sensor with the gap p between paths: (a) the distribution of magnetization; (b) the coefficient cos 2 /Hk representing the influence of the shape anisotropy on the sensitivity.

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Figure 1.121 presents the sensitivity dependence of the multipath sensors prepared by Hoffman and co-workers (1984) with the gap width below 1 m. The sensitivity of the sensor with a conductor spacing of 0.2 m was three times greater than the sensor with a 2.6 m gap. Moreover the sensor with the smaller gap required a smaller value of the bias field.

Figure 1.121 The transfer characteristics of multipath sensors with extremely small gap width between paths: (a) p 0.1 m; (b) p 0.2 m; (c) p 0.5 m; (d) p 1 m (Hoffman et al 1984).

1.3.3 Technological factors affecting the performances of AMR sensors The desirable material for thin film AMR magnetoresistors should meet the following requirements: • The magnetoresistivity coefficient / should be as large as possible because the sensitivity and the output signal directly depend on this parameter. • The resistivity of the material should be large (for given value of /) – the larger the resistivity the smaller the dimensions of the sensor for the same sensitivity. Larger resistance of the sensor means smaller power consumption for the same output signal. • The anisotropy field Hk should be small, because sensitivity is inversely proportional to the anisotropy field. It is desirable to minimize the anisotropy dispersion 50. • The coercive field Hc should be small because large coercivity causes hysteresis of the transfer characteristic. • The material should be non-magnetostrictive because sensors made from magnetostrictive materials can be sensitive to stress, caused for example by a change of temperature. The magnetostriction coefficient should be small, the best if equal to zero.

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• Temperature influences the following parameters: , and Hk. For certain materials it is possible to obtain / T Hk/ T and the sensor is selfcompensating to the temperature change. • The material should be reliable – resistant to the corrosion, with parameters stable in time, etc. All the above mentioned properties depend on the following technological factors: • The material composition and structure. • The thickness of the film and dimensions of the magnetoresistor. • The conditions of deposition (for example quality of vacuum during evaporation or argon pressure during sputtering, substrate temperature, deposition rate, etc.). • Supplementary technological processes such as annealing, ageing, passivation etc. Figures 1.122 and 1.123 present the dependence of the main parameters versus material composition for the three most important magnetoresistive alloys NiFe, NiCo and NiFeCo. In table 1.2 the typical parameters of various magnetoresistive alloys are shown. The permalloy (non-magnetostrictive nickel-iron alloy NiFe 81:19) seems to be the best material for magnetoresistors and therefore it is most widely used in AMR sensors. The nickel-cobalt alloy NiCo 70:30 exhibits the largest magnetoresistivity (3.8%) (Asama et al 1973, Takahashi et al 1976, Makino and Okamoto 1978), but it suffers from large coercivity and certain magnetostriction. As a compromise between NiFe and NiCo the non-magnetostrictive NiFeCo alloys are recommended (Patel et al 1977, Collins and Sanders 1978, Sanders 1983, Hoffman et al 1986, Inagaki et al 1986). These alloys exhibit quite large magnetoresistivity (2.8–3.2%) and very small dispersion of anisotropy ( 50 0.05° for NiFeCo 60:10:30 in comparison with 50 0.3° for NiFe 82:18). The relatively large anisotropy field of NiFeCo alloys is not a

Figure 1.122 The dependence of thin film parameters (anisotropy Hk [kA/m], coercive field Hc [kA/m], magnetoresistance / [%], anisotropy dispersion [degrees], magnetostriction ) on the material composition: NiFe alloy and NiCo alloy.

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Figure 1.123 The anisotropy field [kA/m] of NiFeCo alloy is indicated by dashed line (Wilts and Humphrey 19680) (a) and dependence of its parameters on the Co contents (b).

drawback in the case of small dimensions of the sensor because the anisotropy of material is then negligible in comparison with the shape anisotropy. Table 1.2 The properties of various magnetoresistive materials. Alloy composition [%] NiFe 81:19

/ [%]

[10 8 m]

Hk [A/m]

Hc [A/m]

2.2

22

250

80

Ms [10 5 A/m] 8.7

[10 6] 0

NiFe 86:14

3.0

15

200

100

7.6

12

NiCo 70:30

3.8

26

2500

1500

7.9

20

NiCo 50:50

2.2

24

2500

1000

10.0

0

NiFeCo 60:10:30

3.2

18

1900

300

10.3

5

NiFeCo 74:10:16

2.8

23

1000

250

10.1

0

NiFeMo 87:8:5

0.7

72

490

170

5.1

0

CoFeB 65:15:20

0.07

86

2000

15

1.03

0

It is not fully clear why only several Ni-based alloys exhibit remarkably large magnetoresistivity. Experiments proved (Inagaki et al 1986, van Elst 1959, Miyazaki et al 1990) that the magnetoresistivity reaches the maximum in the neighbourhood of nB 0.9 (nB – Bohr magneton number) (figure 1.124). It corresponds to an electron concentration of 27.7 electrons per atom and may be explained using the theory of the magnetoresistance as a consequence of spinorbit interaction (Berger 1965). Addition of another component to the optimal NiFe, NiCo or NiFeCo composition does not result in improvement of parameters. In fact various potential materials for magnetoresistors have been tested without success (Miyazaki et al 1990, Sueda and Fujiwara 1971, Freitas et al

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Figure 1.124 The dependence of magnetoresistance on the number of Bohr magnetons: (a) after van Elst (1959) – bulk material Ni alloys at 20 K; (b) after Miyazaki et al (1990) – 82 Ni-Fe-M film alloys at room temperature.

1990, Tanaka et al 1990, Granberg et al 1999). New amorphous materials of attractive magnetic parameters (for example very small coercivity) exhibit rather poor magnetoresistance (Inagaki et al 1986). The third component, as for example Ti, Al, Si, V, Cr, Mn, Cu, Ge, Gd, Zr, Pd added to NiFe or NiCo alloys in general caused a decrease of the magnetoresistivity coefficient. Figure 1.125(a) presents the dependence of the magnetoresistance on the concentration of the third element added to (Ni89.5Fe10.5)100–xMx alloy determined by Tanaka and co-workers (1990). A third element, such Cr, Ir or Rh added to permalloy film, might be desirable because it may improve corrosion resistance. Unfortunately such addition causes an increase in magnetostriction. As shown by Klokholm and Aboaf (1981) it is possible to find the correct conditions to ensure that the addition of Cr or Rh does not cause the magnetostriction coefficient to change (figure 1.125(b)).

Figure 1.125 The influence of the addition of the third component to NiFe alloy: (a) the change of magnetoresistance after addition of Co, Cu, Al, Si, Nb, Gd (Tanaka et al 1990); (b) the change of magnetostriction after addition of Cr, Rh (Klokholm and Aboaf 1981).

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Figures 1.122 and 1.123 present the dependence of magnetostriction on material composition. The conditions ensuring negligible magnetostriction are very important because even domain movement during the magnetization process may locally strain the material and cause noise. As zero magnetostrictive it is assumed the permalloy of the composition NiFe 81.5:18.5 (Reekstin 1967, Klokholm and Aboaf 1981). Metzdorf (1966) investigated the magnetoelastic properties of permalloy films and proved that the magnetostriction depends not only on the material composition but also on the film structure (grain size, impurities, oxidation, lattice defects). These structure parameters depend on the deposition conditions. Unfortunately the maximal value of magnetoresistance appears at another film composition (about 86% of Ni) other than zero magnetostriction. To overcome this drawback Kitada and Shimizu (Kitada et al 1986, Kitada and Shimizu 1988) proposed using the composite material of a multilayer structure consisting of a pair of films with negative and positive magnetostriction. The magnetoresistivity ratio of such a multilayer structure increased from 2.0 (for NiFe 81/19) to 2.5% (eight layers of NiFe 17:83 and NiFe 22:78). The magnetostriction coefficient averaged the magnetostriction of both type of films exhibited small value of 3 10–7. The multilayer structures have been adapted to AMR sensor technology (Hill et al 1991, Hur et al 1988, Mitsuoka et al 1987). When the magnetoresistor is very small then a large demagnetizing field reduces sensitivity. If double layers are used the demagnetizing field can be effectively reduced due to magnetic flux closure. Hur and co-workers (1988) prepared a bilayer structure with NiFeCo 65:15:20 thin magnetoresistive films separated by a tantalum layer with a thickness of about 10 nm. After annealing, a magnetoresistive effect as high as 3% was obtained. A similar structure was investigated Hill et al (1991). The results are presented in figure 1.126. The coercivity was significantly reduced when a tantalum separator of thickness 5 nm was used.

Figure 1.126 The change of anisotropy and coercivity in permalloy–tantalum multilayer: (a) dependence on the number of layers; (b) dependence on the tantalum layer thickness (Hill et al 1991).

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Another composite structure for the magnetoresistive sensor was proposed by Mitsuoka and co-workers (Mitsuoka et al 1987, Mitsuoka et al 1987b). The alumina insulator film and two auxiliary poles from permalloy were deposited on the highly magnetoresistive NiCo film (figure 1.127(a)). With this improved design the demagnetizing field decreased by half (figure 1.127(b)). The poles also act as stabilizing elements effectively reducing hysteresis (figure 1.127(c)).

Figure 1.127 The composite material for magnetoresistive element proposed by Mitsuoka et al (1987): (a) design of the sensor; (b) dependence of anisotropy on with w; (c) dependence of hysteresis on the sensor design (A: conventional design; B: improved design).

Thin film elements, in which the mean free path is comparable with the dimensions, exhibit quite different electrical and magnetic properties compared to bulk materials. The theory of electrical transport considering size effects has been formulated by Fuchs and Sondheimer taking into account the diffused scattering of conduction electrons at the film surface (Fuchs 1938, Sondheimer 1952). This theory was experimentally analysed by Maydas and Shatzkes (Mayadas and Schatzkes 1970, Mayadas et al 1974) and many other authors (Mitchell et al 1964, Krongelb 1973, Miyazaki et al 1989, Collins et al 1981, Chapman et al 1982, Solt 1985, Yeh et al 1987, Rijks 1995)2. Figure 1.128(a) presents the dependence of the film resistivity on its thickness.

Figure 1.128 Dependence of resistivity of permalloy on the film thickness (a) and on the lo /t ratio (b) (Miyazaki et al 1989). 2

The size effects in thin films have been reviewed by Tillier and Tosser (1982)

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Taking into account formulated theories the electrical resistivity of thin film can be expressed as:

(

)

3 lo b 1 — —– 8 t

(

for t lo

1

)

4 lo l b — —– 1n —–o 0.42 8 t t

(1.131)

for t lo

(1.132)

where b is the bulk resistivity (b 18 cm) and lo is the mean free path (lo 30 nm). Figure 1.128(b) presents the dependence f(lo /t) confirming the validity of above expressions (Miyazaki et al 1989). The magnetoresistivity change is almost independent of the thickness of the film. Therefore the magnetoresistivity coefficient / decreases when the film thickness decreases. Examples of both dependencies are presented in figure 1.129. Other authors have reported similar results although small differences exist in reported values. The reason is that other technological factors influence the resistivity. The thin film is typically polycrystalline and two scattering effects exist – film boundary and grain boundary scattering. Grain size in particular depends on the technology conditions, as do deposition rate, substrate temperature and annealing. Rijks and co-workers (1995) investigated the influence of grain size on transport properties. It was found that the grain boundaries are an important source of electron scattering because grain size is typically smaller than the film thickness.

Figure 1.129 The dependence of magnetoresistivity of permalloy on the film thickness (Miyazaki et al 1989).

Also magnetic parameters, such as coercivity and anisotropy depend on the film thickness. Several authors (Collins et al 1981, Lo et al 1987) stated that coercivity increased when thickness was decreased, other authors (Solt 1985, Miyazaki et al 1989) also observed independency or increase of coercivity when the thickness was decreased (figure 1.130(a)). The differences can exist because coercivity strongly depends on grain structure, thus it depends on various other

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Figure 1.130 The dependence of the coercivity on the permalloy film thickness: (a) data reported by various authors ((a) Miyazaki et al 1989, (b) Lo et al 1987, (c) Akhter et al 1997, (d) Solt 1985, (e) Collins et al 1981); (b) data reported by Akhter et al (1997).

technological factors. In fact small values of coercivity, independent of the thickness, were reported for samples after annealing. Akhter and Mapps (Akhter et al 1997. Mapps 1997) investigated the effect of thickness and grain size on the coercivity of very thin (2.5–30 nm) permalloy films. It was found that the coercivity of films with very small grain size was much lower than those with a normal grain size (figure 1.130(b)). The lowest coercivity was observed in 7.5 nm thick films having a grain size of 4 nm. The coercivity may be caused by the domain wall movement. In thicker films the Bloch walls interact with the surfaces of the film. For such films the Neel’s ‘4/3 low’ (Hct4/3) was confirmed experimentally (Mapps et al 1991). In films with thickness below about 40 nm Neel walls dominated. These walls are mostly parallel to the film plane and have much lower energy than Bloch walls. Therefore the coercivity attributed to this wall movement is lower. Coercivity also depends on the width when very narrow stripes are prepared. This effect was observed by Fluitman (1973) and confirmed by other authors (Kryder et al 1980, Adeyeye et al 1996). The increase of Hc when the width is reduced was investigated by Kryder et al (1980) and was explained as the formation of the walls perpendicular to the stripe. The theoretical model of the buckling process in narrow stripes shows that a minimum energy occurs when the stripe buckles with the wavelength approximately equal to the width of the stripe. The coercivity of narrow stripes can be reduced by thin Si passivation as demonstrated in figure 1.131(a). The differences in coercivity of the passivated and non-passivated films were significant only after they were etched onto the stripes, not on the sheet films themselves. In the submicron range of narrow stripes the easy axis coercivity can be significantly large, with values exceeding 10 kA/m (figure 1.131(b)). Of course the anisotropy also depends on both thickness and width because the shape anisotropy (demagnetizing field) is proportional to the aspect ratio t/w. Smaller anisotropy means larger sensitivity of the sensor. One of the methods to

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Figure 1.131 The dependence of coercivity on path width: (a) after Kryder et al (1980); (b) after Adeyeye et al (1996).

reduce the demagnetizing field, which can be very large in the case of very small magnetoresistive elements, is to decrease the film thickness. In this way the sensitivity of the sensor for the given sensor area can be increased by decreasing the film thickness. On the other hand the magnetoresistivity ratio decreases significantly with decreasing thickness (figure 1.129). Eijkel and Fluitman (1990) recommended as the optimal film thickness a thickness of about 10–20 nm. Hauser and co-workers (Hauser et al 1998, Aigner et al 1998) recommended a thickness of about 50 nm. Typically the AMR magnetoresistors are fabricated with thicknesses of about 30–40 nm although magnetoresistors of thickness 10 nm are also reporteded (Pant and Krahn 1991). Experiments proved that the limit of film thickness is about 5 nm. A film thinner than 5 nm might be discontinuous with nonmagnetic holes and defects. Also thick film magnetoresistors with thickness of 20–30 m (adopting the hybrid electronics standards) are reported (Cirri et al 1992). The smallest Hko values of about 180–250 A/m are achieved in NiFe films. The anisotropy field of the material should be small because the sensitivity is inversely proportional to Hk. But experimental results presented by Yeh and Witcraft (1995) show that the noise is inversely proportional to Hk2 (figure 1.132). The increased noise level was explained by the induced instability of the magnetic domain structure and by the increase of the dispersion of anisotropy. The sensor wafers are usually fabricated using conventional semiconductor processes (Baubock et al 1996). Both deposition techniques – evaporation or sputtering – are used. Vacuum evaporation has been used successfully for quite a few years – its advantage is its relative simplicity. Recently sputtering is more favoured due to larger flexibility and good reproducibility, which is important in industrial production. The principles of the two main deposition techniques are presented in figure 1.133. In the evaporation technique the material to be deposited can be heated in a tungsten crucible by using an external tungsten wire wound around the crucible. This method of heating is now rarely used rarely because of its relatively low power level and the possibility of contamination by the crucible

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Figure 1.132 Dependence of sensitivity (a) and noise (b) on the anisotropy field of NiFe film (Yeh and Witcraft 1995).

Figure 1.133 Two main deposition techniques: (a) evaporation; (b) sputtering.

material. The preferred method is electron beam evaporation because this method enables evaporation of very pure films at almost any rate. Purity is ensured due to heating only a small amount of the source material. The electron beam is usually accelerated by a high voltage electric field and deflected by the magnetic field by 270° (figure 1.133(a)). In a vacuum environment the evaporated material is transferred to the substrate. As the substrate glasses, oxidized silicon or ceramic materials are used. The substrate should be extremely clean and smooth, it is recommended that the substrate is kept in the temperature range 200–300°C. Better adhesion to the substrate and improvement of other parameters can be obtained by pre-deposition of the buffer layer, for example from titanium or tantalum. The deposition is usually performed in an applied magnetic field to induce the uniaxial anisotropy in the preferred direction. Various values of this field have been reported – 1 kA/m (Dibbern and Petersen 1983), 5 kA/m (most often) and even 24 kA/m (Hill et al 1986). Various authors recommend various rates of deposition – from less than 5 nm/min (Dibbern 1986) to larger than 100 nm/min (Collins and Sanders 1987). Although

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Krongelb (1973) did not observe any influence of the deposition rate in the range 4–25 nm/min, the deposition rate should be chosen carefully. Collins and Sanders (1978) observed a large decrease of resistivity (and increase of magnetoresistivity ratio) with deposition rate caused by reduction of impurities in ordinary, not ultrahigh vacuum. Yang and Aboaf (1989) observed increase of stress with increased deposition rate when permalloy was sputtered. Krongelb (1973) recommended the deposition rate of about 15 nm/min. Let us follow the deposition procedure described by Collins and Sanders (1978). The alloy evaporation slugs were prepared from spectroscopically pure wire, the compositions were to give zero magnetostriction in films deposited at a substrate temperatures of 200°C. It should be pointed out that the composition of melt can be different from the expected composition of film because of the different evaporation rates of alloy components. For example from the melt composition NiFe 82:18 the film composition NiFe 80.3:19.7 has been obtained. The films were deposited by vacuum evaporation with electron beam bombardment heating at a dynamic pressure during evaporation of 1.3 mPa. The source to substrate distance was 15 cm. The substrates were Corning type 7059 glass and they were heated by a quartz-iodine lamp radiant heater. The films were deposited at rates between 30 nm/min and 150 nm/min in an aligning field of 5 kA/m. The isothermal annealing of the films was carried out under vacuum of 0.13 mPa. One of the advantages of the sputtering technique is that the composition of the film is very similar to the composition of the source. The main idea of the sputtering method is presented in figure 1.133(b). After evacuation of the deposition chamber to obtain a vacuum, a gas, typically argon, is introduced with the pressure between 1 Pa and 10 Pa. Under the electrical field between the anode (attributed to the substrate) and cathode (attributed to the source, called target) the glow discharge appears. The ionized gas ejects the atoms of the material from the target. These atoms are transferred to the substrate and condensed on it. As evaporation the external magnetic field may be applied during sputtering. Various sputtering techniques can be used (Ohring 1992, Yang and Aboaf 1989, Serikawa 1977, Pötzlberger 1984). In the DC sputtering system, also called diode or cathode sputtering, the glow discharge is caused by a DC electric field. This field is usually supported by a magnetic field in magnetron sputtering systems. The electrodes can be supplied by an AC voltage. Such a system is called the RF sputtering method because a radio frequency (15.56 MHz) supply signal is applied. The RF sputtering techniques allow sputtering of any material irrespective of its resistivity, including insulating thin films. The sputtering process may be supported by ion beams when the ion beam sputter deposition method is used (Nishimura 1987, Jahnes et al 1992, Nagai and Tashima 1986). In sputtering methods the parameters of magnetic films depend on several technological factors, such as gas pressure or additional substrate bias potential. Aigner and co-workers (1998) investigated the conditions of deposition of permalloy magnetoresistive films in the cathode sputtering technique. The

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arrangement of the analysed sputtering system is presented in figure 1.134. In this triode method the argon plasma supporting the deposition process is created by the cathode–anode setup. The target was connected to a negative potential of Ut 800 V while the substrate was biased by Us 60 V. The following parameters were varied: target and substrate materials, the distance between target and substrate and the film thickness. The best parameters (/ 3.7%) were obtained for the following conditions: temperature of target 560°C, temperature of substrate 270°C, distance between target and substrate 36 mm and film thickness 50 nm. The thin film prepared in such conditions exhibited negligible coercivity along the hard direction and an almost rectangular hysteresis loop for the easy axis of anisotropy.

Figure 1.134 The cathode sputtering system reported by Aigner et al (1998).

Figure 1.135 presents the dependence of thin film parameters on the substrate temperature in the evaporation technique. The resistivity decreases and it causes the increase of the magnetoresistivity ratio when the temperature of the substrate increases. Also the anisotropy field decreases with increase of the substrate temperature. These dependences are explained as the result of the smaller stresses and larger grain size when the substrate is heated to a temperature between 200°C and 300°C. In general the dependence of the thin film parameters on the substrate temperature is much smaller in ultrahigh vacuum than in ordinary technical vacuum (0.1–1 mPa) (Chapman et al 1982), which is interpreted as the smaller influence of oxygen impurities. The improvement of the magnetoresistor parameters as a result of the increase of the substrate temperature is limited by a simultaneous increase of coercivity and anisotropy dispersion (figure 1.135(b)). The increase of the substrate temperature above 300°C causes some surface roughening which results in anisotropy degradation, coercivity increase and magnetoresistivity reduction (figure 1.136) (Choe and Steinback 1999). The significant increase of anisotropy dispersion and coercivity for temperature of substrate above 300°C is also explained as the change of crystal structure from a columnar to a granular type.

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Figure 1.135 The dependence of film parameters on the substrate temperature during deposition: (a) resistivity and magnetoresistance (Collins and Sanders 1978); (b) dispersion of anisotropy and coercivity (Chapman et al 1981).

Figure 1.136 The dependence of thin film parameters on the roughness (Ra: average deviation of surface roughness of the mean high) (Choe and Steiback 1999).

To overcome the above described limitation Krongelb et al (1973) proposed the deposition of thin film using a moderate substrate temperature of about 200–250°C and subsequently annealing the thin film to improve its parameters. In fact annealing is now the crucial element of the technology process. Especially in the case of sputtering method, where applying the magnetic field during deposition may be limited, annealing in the magnetic field is an important process of improving the anisotropy. Figure 1.137 presents the dependence of thin film parameters on the annealing temperature determined by Ciureanu and Korony (1988). An annealing temperature of about 425°C was recommended (Ciureanu and Korony 1988). Figure 1.138 presents the time dependences of the annealing process. Thus an annealing time of several hours is recommended. Not all authors accept such a high annealing temperature. For example Hur and coworkers (1988), investigating the NiFeCo multilayer films, stated that the magnetoresistivity of the sensor annealed at various temperatures with 8 kA/m external field increased significantly: by 15% for annealing at 200°C and by 22% for annealing at 300°C. Further increase of the annealing temperature (up to 400°C) did not change the MR ratio and decreased some magnetic parameters.

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Figure 1.137 The dependence of thin film parameters on the annealing temperature (Ciureanu and Korony 1988).

Figure 1.138 The dependence of thin film parameters on the annealing time (Ciureanu and Korony 1988).

Probably the various optimal annealing temperatures depend on the annealing condition – the oxygen pressure in the vacuum. Dibbern (1989), one of the constructors of the widely used sensors of Philips, recommended annealing thin film by several hours at 300°C in a homogeneous field of several kA/m. On the other hand some technological processes, for example preparation of integrated sensors, may require temperatures above 350°C (Linke 1992, Jost et al 1993). In yoke magnetoresistive heads with a high-permeable amorphous yoke an annealing temperature above 440°C should be applied. It was tested that even a temperature of 500°C did not deteriorate the parameters of the sensor although magnetoresistivity ratio decreased by approximately 20% and coercivity increased (Fukuzawa et al 1987, Nagata et al 1987). High temperature during fabrication can influence other thin film sensor behaviours. For example the reaction between the permalloy and parts from other materials (leads, short bars in Barber-pole sensors) can be dangerous. This reaction between permalloys and different metals has been investigated (Kitada et al 1984, Chow 1979). An example of the change of coercivity due to interdiffusion between various metals and permalloys is presented in figure 1.139. Copper is particularly not recommended while molybdenum and tantalum cause very small influences on the coercivity after annealing. Unfortunately these last two materials exhibit rather large resistivity. Gold was

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Figure 1.139 Dependence of the coercivity in various pairs of materials on the annealing temperature ((a) Cu/NiFe, (b) Al/NiFe, (c) Au/NiFe, (d) Cr/NiFe, (e) Ta/NiFe, (f) NiFe, (g) Mo/NiFe) (Kitada et al 1984, Kitada 1985).

recommended as the contact material (Gangulee et al 1974) although under humidity the noble Au-and NiFeCo contacts may activate corrosion. As an alternative titan was proposed – its resistivity is only three times larger than the resistivity of the permalloy. In commercially produced Barber-pole sensors the short bars are prepared from aluminium or from gold. Figure 1.140 presents the results of investigations of the air (oxygen) influence during annealing (Gangulee et al 1974). The permalloy film annealed in the vacuum did not exhibit any changes of coercivity, but in the air condition coercivity enlarged significantly (figure 1.140). The additional passivation by SiO2, SiO, Si3N4 or Al2O3 can adequately inhibit oxidation of the permalloy film (figure 1.140). In the Barber-pole sensors it was found that such covering of the

Figure 1.140 The change of coercivity during annealing in vacuum and in air conditions (Gangulee et al 1974).

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steep slopes was incomplete. As an alternative an organic passivation layer of polyamide were found to give good results (Dibbern 1989). The problem of oxidation at higher temperatures occurred as a possible limitation of current density in permalloy small elements. To obtain a sufficiently large output signal a current density as large as 106–107 A/cm2 may be required. For such a high current density the electromigration effect (micro-segregation of the Fe and Ni atoms) leads to reduction of magnetoresistance (Moore et al 1972). Tests showed that passivated films could work reliably even at a current density of 107 A/cm2 and temperature 250°C (Gangulee et al 1974). The whole sensor consists of several different parts therefore different technological processes are required for manufacture. Figure 1.141 presents the structure of two typical AMR sensors: Barber-pole structure and SAL structure. The manufacture of MR sensors especially in the case of magnetoresistive heads can be a very complex process. Fontana (Fontana 1995, Fontana et al 1996, Fontana et al 1999) summarized the technological process steps necessary for various MR sensors. The Barber-pole device required only six steps (two photo steps, one deposition magnetic, one deposition conductor and two patterning), but the dual stripe sensor required 19 steps. The magnetoresistive sensor processing contributes approximately 20% of the total processing requirements for a full head structure.

Figure 1.141 The structure of the barber-pole sensor (a) (Linke 1992) and SAL biased magnetoresistive head (Fontana 1995).

Dibbern and Petersen (1983) specified the following major steps in the fabrication of the Barber-pole sensors of Philips: • The surface of silicon substrate (1.6 1.63 mm2) oxidation. • Sputter deposition of an adhesive layer of titanium (0.1 m thick). • Sputter deposition of the permalloy film (30 or 40 nm thick). • Formation of permalloy stripes using a substractive photolithographic process. • Annealing of the permalloy film in the magnetic field (approximately 300°C). • Sputter deposition of a titanium/tungsten adhesive layer (0.1 m thick). • Formation of gold or aluminium Barber-pole patterns. • Laser trimming of the bridge to give the zero offset voltage at 25°C.

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All these technology steps are similar and compatible to conventional semiconductor processes. More sophisticated is the technology of extremely small magnetoresistive sensors used as reading heads. To achieve better than 3 Gbit/in2 areal density in hard disk applications the trackwidth should be smaller than 1 m. Table 1.3 presents the comparison of lithography critical features for magnetoresistive heads reported today and expected in the near future and summarized by Fontana et al (1996, 1999). Table 1.3 Critical features of the magnetoresistive heads (Fontana et al 1999). Year

Density [Gbit/in2]

Trackwidth [m]

1995

1

2.0

15.0 (AMR)

Sense layer [nm]

1997

3

1.1

12.0 (AMR)

1998

5

0.7

9.0 (AMR)

2000

10

0.5

5.0 (GMR-SV)

2002

20

0.35

3.5 (GMR-SV)

2003

40

0.25

2.5 (GMR-SV)

2005

80

0.18

1.8 (GMR-SV)

The magnetoresistive sensors for reading heads and memory applications should have dimensions in the submicron range. Recently the submicron lithography allows the manufacture of thin film elements with geometrical resolution of about 0.25 m (Chen 1995, Romankiw 1996). In the classical optical lithography the minimum linewidth W is set by Fresnel diffraction between the mask and the bottom of the resist and is described by the expression (Chen 1995): —

g —–. 2

√

W 1.5

(1.133)

Assuming typical values of wavelength as about 200 nm (deep UV) and the gap between the mask and the bottom of the resist g as about 4 m the minimum linewidth is about 1 m. The resolution can be improved by using the optical projection method with numerical aperture N.A.. The minimal linewidth is then

W ————–. 1.28(N.A.)

(1.134)

With a numerical aperture of about 0.5 it is possible to achieve resolution of about 0.3 m and this value may be assumed as a limit of optical lithography. Better resolution is possible using X-ray lithography due to shorter wavelengths (between 0.4 nm and 5 nm). In this lithography it is difficult to prepare the appropriate mask absorbing X-ray. Using gold mask lithography

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satisfying results have been reported, but to obtain such a mask E-beam lithography has been used. Much better results are possible using ion beam or electron lithography. In these techniques the diffraction effect is negligible and the de Broglie wavelength for a charged particle is described by the expression: h

———— — 2me √

(1.135)

where: h is Planck’s constant, m is the mass of particle, e is the particle the charge and is the electrical potential of the particle. The focus of the ion beam may be about 30 nm in diameter. In electron beam lithography the minimum dimensions in organic resist is about 10 nm with the beam diameter as small as 0.3 nm. Using electron beam lithography Hoffman et al (1984) prepared multipath sensors with path gap width down to 400 nm. The MR elements are usually defined by the ion beam etching (often called ion milling) technique (figure 1.142(a)). The ion beam etches all parts not covered by the resist. After removing the resist only the MR element with the desired shape remains. The leads are usually defined by the lift-off technique (figure 1.142(b)). In this method the resist covers the MR layer for the deposition of the next layer. Figure 1.143 presents the process sequences used

Figure 1.142 The ion milling (a) and lift-off (b) techniques of lithography (Fontana 1995).

Figure 1.143 The main technological sequences during the preparation of magnetoresistive heads: (a) resist exposing, trackwidth defining; (b) ion milling, junction forming; (c) longitudinal bias deposition, leads deposition; (d) material lift-off, trackwidth forming (Fontana et al 1996).

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for preparation of the magnetoresistive sensor with patterned stabilizing layers at the end of the MR stripe and with deposited leads. Xiao and Kryder (1996) proposed an improvement of the above described method of head fabrication by the application of an additional thin SiO2 mask during ion milling and by a new silicon nitride lift-off process. In a typical magnetoresistive head structure the MR sensor occupies only a very small part of the whole area. For example in the head described by Fontana (1996) the wafer had dimensions of about 1 mm by 0.75 mm. A significant portion of this area used leads connections and the virtual head was deposited on an area 150 m by 150 m (3% of the wafer area). In this head area the active magnetoresistive sensor occupies only an area of 1 m by 1 m.

1.3.4 Design and construction of AMR sensors Figure 1.144(a) presents the simplest single-path magnetoresistive sensor commonly used as a non-shielded reading head. This sensor can be biased to obtain the linear transfer characteristic. When the information is digital (for example the information in a credit card) then the linearity of the sensor is not necessarily required. In this case in order to reduce sensor costs it may be fabricated as a simple path (without biasing). If the shape anisotropy is large such a sensor may correctly operate even without a stabilizing field.

Figure 1.144 The example of single path sensor design and its transfer characteristic (Jeffers and Karsh 1984).

Despite the sophisticated micromagnetic analysis presented in previous sections the design principles of a simple single-path magnetoresistor can be analysed using the following expression: R Hb ——x —– ————– Hx2 (Hk Hy)2 Rx

(1.136)

where Hx is the measured field component perpendicular to the anisotropy axis.

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Assuming that Hy 0 and the biasing field Hb is much larger than measured field Hx the sensor can be described by the expression R 1 ——x ≅ —– 2Hb —–2 Hx . Rx Hk

(1.137)

For the user of the sensor the most interesting factor is not Rx/Rx but the output voltage signal Uout when the sensor is supplied by the current determined by the permissible current density J: 1 1 Uout 2JHb L —— —– Hx 2JHb L —————–– Hx. 2 Hk t 2 Hko M — w

(

)

(1.138)

Figure 1.144(b) presents an example of the transfer characteristic of the single path sensor indicating the experimentally determined point of inflection (Jeffers and Karsh 1984). Theoretically the inflection point appears for Hb 0.707 Hk (for 45°). Casselman and Hanka (1980) proposed calculating the optimal bias using following expression t Hb 0.26 710 —. w

(1.139)

Taking into consideration the experimental results presented by Jeffers and Karsh it is more realistic to assume that Hb Hk. Then the expression (1.138) can be rewritten as 1 Uout 2JL –—————– Hx SHx . t Hko M — w

(1.140)

The sensitivity coefficient S depends on the sensor length L and on the aspect ratio t/w. The other parameters J, Hko and M do not depend on the dimension of the sensors. Assuming typical parameters of the permalloy (table 1.2) the sensitivity S/L was calculated and is presented in figure 1.145. For a permalloy stripe the sensitivity decreases as the aspect ratio decreases below 104. The dependence of the sensitivity on thickness and width is presented in figure 1.146. Even taking into account that magnetoresistivity slightly decreases for thicknesses below 40 nm (see figure 1.129(left)) to obtain large output signal the thickness should be as small as possible and the width and length of the path should be as large as possible. Usually when the sensor is used as a reading head the dimensions are limited. The length depends on the trackwidth. The width cannot be very large because the magnetic field from the tape decreases significantly versus the distance from

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Figure 1.145 The sensitivity per unit length calculated for single-path sensor: (a) t 10 nm; (b) t 20 nm (the broken line represents the same dependence calculated for the sensor with path inclined by 45° with respect to the anisotropy axis).

Figure 1.146 The dependence of the sensitivity calculated for single path sensor: dependence on the film thickness – (a) w 10 µm, (b) w 20 µm, (c) w 50 µm; dependence on the path width – (a) t 100 nm, (b) t 50 nm, (c) t 20 nm.

the tape. It is assumed that the width should be smaller than 10 m (van Gestel et al 1977). When the magnetoresistive element is very small then the component Mt/w (demagnetizing field) is much larger than the anisotropy of material Hko. In such a case the major advantage of the permalloy – small anisotropy field Hko – is less important and other alloys might be considered. Figure 1.147(a) presents comparison of the anisotropy field of a small element prepared from two materials: NiFe and NiCo (Takahashi et al 1976). Due to smaller saturation magnetization the narrow element prepared from NiCo exhibited a smaller anisotropy field. Taking into account the larger magnetoresistivity of the NiCo alloy its advantage is more visible after calculating the ratio (/Hk) responsible for the sensitivity (figure 1.147(b)). Unfortunately the NiCo alloy suffers from magnetostriction. As the alternative material for very small

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Figure 1.147 The comparison of two materials for magnetoresistive sensors NiFe and NiCo: (a) experimentally determined dependence of anisotropy field on the path width (Takahashi et al 1976); (b) the calculated dependence of the sensitivity on the path width.

elements the non-magnetostrictive NiFeCo can be recommended – exhibiting a larger anisotropy field Hko but also larger magnetoresistivity / than the permalloy. Table 1.4 The typical design parameters of single path sensors. Parameter Material

After [a] NiFe 80:20

after [a] NiCo 70:30

after [b] NiFe 80:20

t [nm]

50

20

60

w [m]

20

20

4.6

L [m]

75

75

280

R []

18

45

230

R/R [%]

2

4

2.5

Hk [kA/m]

2.4

2.8

10.8

Hs [kA/m]

3.2

3.2

28

Hb [kA/m]

2

2

10.6

S [mv/(kA/m)]3

0.75

1.3

0.5

[a] – Bajorek et al (1974), [b] – Jeffers and Carsh (1984)

Figure 1.148 presents the typical design of the single-path sensor used as a magnetic card reader. As an example let us summarize the design parameters reported by one of the manufacturers (MR Sensors Ltd Cardiff): material NiFe 80:20 deposited on Corning 7059 glass, film thickness 40 nm, resistance 150–450 , width 45 m (spacing from front face 35 m), length 1 mm, saturation field 0.4–1.2 kA/m, current 10 mA maximum, magnetoresistive change 1.4–2.1%, adhesion layer Cr 4 nm, contact layer Au 200 nm, protection – 3

Calculated for J 5·109 A/m2.

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Figure 1.148 Examples of single-path magnetoresistive reading head: (a) the layout; (b) design of the encapsulated head; (c) the final product.

polymer coating plus ceramic overstrate. Table 1.4 presents typical parameters of single-path sensors. Figure 1.149 presents the design and transfer characteristics of the biased SAL sensor described by Fujimoto and co-workers (1997). To stabilize the sensor two antiferromagnetic films are used at the end of the stripe. The extremely small sensor with linear characteristics was designed with the following parameters: thickness of the MR film 20 nm, thickness of the SAL layer 20 nm, thickness of the spacer between layers 20 nm, width 2.5 m, length 20 m, anisotropy field of the MR film 0.4 kA/m, anisotropy field of the SAL film 0.8 kA/m, resistivity of the MR film 26 cm, resistivity of SAL film 70 cm, resistivity of the spacer 180 cm, current density 1 1011 A/m2. Figure 1.150 presents the developed sensor design proposed by Gorter et al (1974). A second magnetoresistive stripe on the same substrate but with a larger distance from the field source (for example the magnetic tape) is added to the active MR stripe. The outputs of both magnetoresistors are differentially amplified to reject common mode thermal noise, especially dynamic thermal

Figure 1.149 The design of the SAL-biased magnetoresistive head and experimentally determined transfer characteristics of the head (Fujimoto and co-workers 1997).

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Figure 1.150 The dual stripe magnetoresistive head: the principle of the sensor and an example of the layout design (Gorter et al 1974 and van Gestel et al 1977).

noise generated at the head and tape interface. Figure 1.150(right) presents the example of such a head structure. Hempstead (1975) analysed this dual stripe head geometry and concluded that the dual stripe geometry is effective for low thermal noise frequency and high thermal diffusivity substrate material. Nagata and co-workers (1987) proposed to use the yoke type geometry presented in figure 1.151(a). It is known that the largest domain activity and Barkhausen noise source is at the end parts of the stripe. The Bitter technique (Das 1991, Kools et al 1998) shows that domain walls nucleate at the ends of a long stripe and propagate into the central region as the transverse field is increased. Therefore it would be a good idea to remove the end as far as possible from the active sensing part. This can be achieved by applying the Ushape form presented for example in figure 1.151(b). The radical solution is to use the ‘endloss form’ – closed yoke type with small gap (figure 1.151(a)). Comparison of the closed yoke type MR sensor with the conventional stripe sensor revealed that both, noise level and higher harmonic distortion were about 10 dB lower in the improved design (Nagata et al 1987). Mohd Ali and Moses (1988,1989) adopted a chevron-shaped magnetoresistor (used earlier to stretch and detect bubble domains (Nelson 1977)) and designed the small magnetic field vector detector. The structure of the sensor is presented

Figure 1.151 The yoke type sensor design: (a) U-shape yoke sensor proposed by Nagata et al (1987); (b) C-shape sensor proposed by Uchida et al (1982, 1985).

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Figure 1.152 The chevron-shaped magnetoresistive sensor designed by Mohd Ali and Moses (1988, 1989): (a) design of the sensor; (b) sensor after encapsulation.

in figure 1.152. Two legs of the sensor, each of length 1.5 mm, width 20 m and thickness 40 nm are laid out at an angle of 120°. A small magnet chip was applied to bias both magnetoresistors. The encapsulated sensor is presented in figure 1.151(b). Because the measured magnetic fields of both magnetoresistors are different: H1 H sin (105°) and H2 H sin (75°) it is possible to determine the magnitude H and the direction angle from the expressions: H √cos2 75°(H1 H2)2 sin2 75°(H1 H2)2 H1 H2 tg1 ———– tg 75° . H1 H2

(

)

(1.141)

When the area of the sensor is not so strictly limited (as in the case of reading heads) then according to expression (1.140) the sensitivity may be significantly enlarged by increasing the length of the stripe. An effective method to elongate the length of the path for a given area is to use a meander shape. An example of such sensor designed by the Sony Corporation is presented in figure 1.153 (Hager 1993).

Figure 1.153 An example of multipath sensor design proposed by the Sony Corporation.

In the case of multipath sensors the length of path depends on the sensor area A, width of the path w and width p of the gap – L A/(p w). The output signal depends then on sensor parameters as follows:

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THIN FILM MAGNETORESISTIVE SENSORS 1 1 1 Uout 2JHb A –——– —— Hx ≅JA –——– –————–– Hx . (1.142) wp wp t Hko M — w

Using the relatively simple expression (1.142) it is possible to determine the dimensions of the sensor. In this case the optimal value of the sensor width for a given sensor area, film thickness and gap width can be calculated. Figure 1.154 presents the dependence of the sensitivity on the path dimensions. For example when the thickness of the film is 20 nm then the optimal width of the path is about 8 m for p 1 m and 30 m for a gap of 10 m.

Figure 1.154 The calculated dependence of the sensitivity per area unit on the path width in the case of multipath sensor design: (a) t 50 nm, p 10 m; (b) t 20 nm, p 10 m; (c) t 20 nm, p 1 m.

Figure 1.155(a) presents the dependence of the sensitivity on the aspect ratio t/w. For the permalloy the best shape configuration is about 10–3. It may be simply stated that ‘the width expressed in m should be equal to the thickness expressed in nm’. Sometimes (especially in cases when small magnetic fields are measured) resolution is more important than sensitivity. Assuming that due to appropriate choice of design and stabilizing field the Barkhausen noise is negligible (in comparison with thermal noise) the signal to noise ratio (SNR) can be expressed as —– — Jwt — J√wt √A SNR ———– (1.143) ——– —– √RHx ——————–– ————– –—–– —– Hx . 2√kTf 2Hk√kTp(p w) √f From (1.143) it may be concluded that increasing the sensor area can achieve better signal to noise ratio SNR. The dependence of the signal to noise ratio on the sensor dimensions is presented in figure 1.155(b). The SNR ratio decreases significantly when the t/w ratio is larger than 10–4.

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Figure 1.155 The dependence of the sensor sensitivity (left) and SNR (right) on the path dimensions: (a) t 20 nm, p 5 m; (b) t 50 nm, p 5 m; (c) t 50 nm, p 50 m, (P/A 1 W/cm2).

As mentioned in previous sections it is not recommended to design sensors with the path perpendicular to the anisotropy axis. Such magnetoresistors are not fully differential to magnetoresistors with the path parallel to the anisotropy axis and suffers from larger dispersion of anisotropy. The sensor presented in figure 1.153 was designed for non-contact switch applications and linearity or noise were less important than large output signals (70–80 mV for a 10 m motion of the magnet). Therefore design of the path inclination with 01 0° and 02 90° was reasonable. More often paths are inclined by 45° to the anisotropy axis – this results in a quasi-linear sensor consisting of differential magnetoresistors. Figure 1.156(a) presents a ‘herringbone’ sensor design originally described by Hebbert and Schwee (1966). The sensor presented in figure 1.156(b) was designed by the same authors to profit from the exceptionally perfect high frequency behaviours of ferromagnetic thin films. It was expected that this process should be very fast because in the single domain state thin film is magnetized by rotation of the magnetization. Indeed the sensor presented in figure 1.156(b) exhibited a flat response to the alternating magnetic field as high in frequency as 65 MHz, which was only limited by the test equipment. To improve the parameters for a

Figure 1.156 The ‘herring-bone’ multipath sensor design (a) and the sensor development for high frequency magnetic field detection (b) (Hebbert and Schwee 1966).

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high frequency field two magnetoresistors were connected to the copper halfwavelength line designed for the 300 MHz carrier. Figure 1.157 presents various designs of quasi-linear sensors proposed by Tumanski (Tumanski and Stabrowski 1984, Kwiatkowski and Tumanski 1986). The four-arm bridge circuit can be etched from one film (figure 1.157(a,b)) but to reduce the sensor area two half-bridge circuits can be glued (back to back) together (figure 1.157(c,d)).

Figure 1.157 Various designs of multipath quasi-linear sensors proposed by Tumanski (Tumanski and Stabrowski 1984).

For a sensor with the path inclined by the angle o with respect to the anisotropy axis additional complication exists due to the change of the anisotropy axis direction. This change can be taken into account by supplementing the design expression by the factor sin 2o cos 2 (see formula 1.113): 1 Uout JA –——– sin 2o cos 2(o ) —– wp 1 ————————————————–– Hx . t 2 t H 2ko M — 2Hko M — cos 2o w w

√ ( )

(1.144)

Using expression (1.144) it is possible to optimize the performance of the sensor. Figure 1.158(left) presents the calculated dependence of the sensitivity on the sensor width. The optimal value of the width of the path for given sensor area and other dimensions has been calculated. It is also possible to determine the optimal value of the angle o using expression (1.105). Figure 1.158(right) presents the calculated dependence of the angle on the aspect ratio t/w. When the aspect ratio is smaller than 10–2 the deviation of the easy axis is negligibly small, the paths are inclined by the angle 45° with respect to the anisotropy axis. In the range 10–2–5·10–1 it is possible to correct the easy axis deviation by the design of the angle o larger than 45°. The calculated corrected value of o ensuring the resultant angle 45° is presented in figure 1.158(right).

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Figure 1.158 The dependence of the sensor parameters on the path dimensions in the case of the sensor with path inclined by the angle o 45° with respect to the anisotropy axis – the dependence of the sensor sensitivity on the path dimensions: (a) t 50 nm, p 10 m; (b) t 20 nm, p 10 m; and the dependence of the resultant angle on the t/w ratio (when o 45°) and angle of o recommended to ensure the resultant angle 45°.

The geometry of the path (width of the path and gap between paths) determines the desired sensitivity of the sensor. Figure 1.159 presents the fotomask of the sensor used to test the various geometric paths. Sensors with paths inclined with respect to the anisotropy axis may be very sensitive and simple to manufacture. Unfortunately these sensors require an external stabilizing field. Therefore self-stabilized Barber-pole structures are the most frequently manufactured magnetic field sensor (Kuijk et al 1975, Feng et al 1977, Druvesteyn et al 1981, Dibbern 1983). These sensors can be made as single path, three-paths, multipath and yoke shape sensors – as shown in figure 1.160. The design of Barber-pole sensors is a rather difficult task because in addition to the above mentioned factors several new parameters should be considered: shorting bars width b, distance between shorting bars a and shorting bars

Figure 1.159 The dependence between sensor design and its transfer characteristics: (a) w 150 m, p 50 m; (b) w 300 m, p 50 m.

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Figure 1.160 The Barber-pole sensor design examples: (a) yoke sensor, yoke slanted edges sensor (Kools et al 1998), single path differential sensor (Metzdorf 1982), three-path sensor (Druvesteyn et al 1981), multipath sensor (Hauser et al 1999).

resistivity b. The main problem is that not only is the magnetization nonuniform but also that current lines are irregular. Figure 1.161 presents calculated equipotential and current flow lines in the three-segment magnetoresistor. Therefore numerical methods are indispensable in the design of the Barber-pole sensors (Haudek and Metzdorf 1980, Tumanski and Stabrowski 1985, Pant 1990, Pant 1996).

Figure 1.161 The calculated equipotential and current flow lines in the three-segment magnetoresistor.

The output signal of the Barber-pole sensor can be determined using the following expression (Tumanski and Stabrowski):

()

a a — cos 2 — w a w Uout 2JL ——— k — ———————– a b w t —— Hko — M Hyo w w w

( )

()

(1.145)

where k(a/w) and (a/w) are numerically calculated dependencies taking into account non-uniformity of the current flow and non-uniformity of the magnetization distribution respectively. Hyo is the self-stabilizing field and can be determined from the expression:

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AMR SENSORS Jt 1 Hyo — ———. 4 b 1— a

127 (1.146)

Assuming typical values J 5 106 A/m2, b/a 0.5 and t 40 nm one gets the Hyo value approximately equal to 300 A/m. In typical applications such a stabilizing field is insufficient to fully prevent the film demagnetization, especially if the paths are narrow. Therefore the sensor can operate properly only when the measured magnetic field is small. Overload should be ‘ordered’ by an additional external stabilizing field. In the extreme case for J 1011 A/m2, b/a 0.1 and t 100 nm the stabilizing field reaches a value of about 2.3 kA/m. The coefficient (a/w) takes into consideration the deviation of the current flow from 45°. This deviation is especially large in the edge part of the stripe (figure 1.162(a)). Also the boundary area between shorting bar and permalloy is an equipotential line only when the resistivity ratio p /b is extremely large. Figure 1.162(b,c) presents calculated current flow lines and potential distribution in the Barber-pole structure at various resistivity ratios.

Figure 1.162 The non-uniformity of the current flow: (a) near the edges; (b) when the resistivity ratio is p /b 10; (c) when the resistivity ratio is p /b 2000.

The resistivity ratio (strictly the ratio of the resistances per unit area) depends on the thickness of the shorting bars. The result of numerical analysis of the influence of the gold bar thickness tb on the resistivity ratio p /b is presented in figure 1.163(left) (it has been assumed that for tp tb it is p /b 10, also the contact resistance has been neglected). Thus the shorting bar boundary is practically equipotential for a gold bar of thickness larger than 10tp. The dependence of the term cos 2 on the resistivity ratio is presented in figure 1.163(right). It follows from this plot that the boundary between the permalloy and the shorting bars is approximately equipotential if p /b 100. This condition can be simply fulfilled because resistivity of the permalloy is 22 m while resistivity of aluminium is about 2.6 m. The Barber-pole segment has been divided into 100 elementary magnetoresistors with identical resistances (a division for 10 equipotential and 10 current stream lines). The relations k(a/w) and cos 2(a/w) were computed and are presented in figure 1.164. These relations can be approximated by the following expressions:

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()

()

a a k — 0.5 0.14 — w w

()

()

(1.147)

()

a a a 2 cos 2 — 1 0.08 — 0.11 — . w w w

(1.148)

Figure 1.163 The dependence of the resistivity ratio per area unit on the thickness ratio tb /tp and the dependence of the cos 2δ coefficient on the resistivity ratio ρp /ρb.

Figure 1.164 The dependence of the coefficients k and cos 2 on the a/w ratio.

Using equations (1.144–1.146 the sensitivity of the magnetoresistor was computed. The results are presented in figure 1.165. From the dependencies presented in figure 1.165 the practical design guidelines can be summarized as follows: • The width of the shorting bar b should be as small as possible. • For the assumed width b there exists an optimal value of the permalloy stripe part width a, limited by (0.5–1.5)w. Because of a plateau in the curve S/L f(a/w) the practical value of a/w may be chosen with considerable latitude. • The stripe aspect ratio t/w can be recommended as 10–3 for both single stripe and multipath sensors. Thus the ‘golden proportion design’ – width

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in m equal to thickness in nm may be recommended (see also figure 1.155).

Figure 1.165 The dependence of the Barber-pole sensor sensitivity on its dimensions. Table 1.5 The design parameters of Barber-pole sensors manufactured by Philips (Dibbern 1989). Parameter

KMZ10A

KMZ10B

KMZ10C

Sensitivity [mV/(kA/m)] for U 5 V

80

20

7.5

Sensitivity [mV/V(kA/m)]

16

4

1.5

Range [kA/m]

0.5

2.0

7.5

R [k]

1.3

1.7

1.4

Hk [kA/m]

1.2

3.8

17.6

t [nm]

33

44

130

w [m]

30

10

6

b [m]

4

4

4

a [m]

10

4

4

Number of paths

14

13

30

Recommended Hyo [kA/m]

0.5

3

3

Dibbern, a designer from Philips, has given the following guidelines (Dibbern 1989). The minimal width of shorting bars was b 4 m. To reduce the border effects, the a/w ratio was recommended as less than 0.5 and b/tb ratio larger than 2. The final design parameters of the most sensitive sensor KMZ10A are as follows: t 33 nm, w 30 m, a 10 m and b 4 m. The design parameters of Barber-pole sensors manufactured by Philips are shown in table 1.5. Figure 1.166 presents the layouts of two main sensors available on the market – Philips KMZ sensor and Honeywell HMC sensor. Pant, a designer from Honyewell Inc., considered design tradeoffs for the magnetoresistive sensors (Pant 1996). The main performance parameters – minimum detectable

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Figure 1.166 The layout of the KMZ10 barber-pole sensor designed by Philips (a) and Barber-pole sensor designed by Pant from Honeywell (Pant 1996) (b).

field, sensitivity, range of linearity of the transfer function, power dissipation, sensor area – depend on the design parameters. One cannot simultaneously optimize all the performance parameters and therefore the expected application should be firstly considered. For example when the sensor is used in an application requiring a wide range of linearity and low power dissipation (e.g. geartooth sensing in angle measurements) applying thick and narrow stripes has been suggested. For an application requiring very high sensitivity (e.g. magnetic anomaly detection) thin and wide stripes have been recommended. For devices requiring ultra low power ( 1 mW) an increasing of number of stripes to obtain a large resistance has been proposed. In an application where a small size is required (e.g. sensors used to map the magnetic field) reduction of stripe width with a sacrifice of sensitivity has been suggested. The unconventional shape of the multipath Barber-pole sensor was proposed by Hauser (figure 1.167) (Hauser et al 1998, 1999). To achieve a homogeneous and small demagnetizing field, an elliptical shape of the AMR array has been proposed, with the ellipse axes 1.76 1.00 mm.

Figure 1.167 The elliptically shaped Barber-pole sensor designed by Hauser (1998,1999).

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Thin film magnetoresistive sensors are prepared using processes similar to those of semiconductor devices. Therefore attempts to fabricate integrated MR sensors (Jost et al 1993, Konno et al 1989, Konno and Kataniwa 1991, Akiyama et al 1994) are fully reasonable. An example of an integrated circuit developed by Konno and co-workers is presented in figure 1.168. A monolithic sensor with four magnetoresistive elements and a comparator circuit have been prepared on one chip and may be used to convert the magnetic signals into digital electric signals. Figure 1.168(b) presents the transversal schematic morphology of the chip and figure 1.168(c) the equivalent circuit of the sensor. Other integrated circuits have been reported, for example a circuit including an instrumentation amplifier obtaining sensitivity of 0.5 V/(kA/m) (Jost et al 1993).

Figure 1.168 An example of an integrated circuit developed by Konno and co-workers (Konno et al 1989): (a) the sensor in encapsulation; (b) the transversal schematic morphology of the chip; (c) equivalent circuit of the sensor.

In practice the design of integrated MR sensors is not so simple and obvious. The permalloy technology is not friendly to silicon technology 4. The costs of manufacturing integrated sensors are much larger than fabrication of both parts separately. For example it has been estimated that from one wafer it was possible to obtain 300 chips instead of 1000 circuits in a typical technological process (Jost et al 1993). Therefore more often the manufacturer of MR sensors offer sensors in the simpler hybrid technology. An example of a three-axis magnetic sensor hybrid is presented in figure 1.169. The hybrid sensor presented in figure 1.169 consists of three independent bridge sensors each measuring one component of the external magnetic field. These bridge sensors are connected to instrumentation amplifiers ensuring sensitivity of 6–60 mV/(A/m) with resolution 8 10–3 A/m. The bridges are supplied by the voltage proportional to the temperature to compensate for temperature errors. Additionally each sensor is equipped with offset stripes to correct offset voltage, to cancel unwanted ambient field or to apply feedback. The hybrid sensor can be further extended to realize more complex devices, for example compasses, magnetometers or gradiometers. 4

Private information from the manufacturers of permalloy sensors.

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Figure 1.169 The three-axis hybrid sensor HMC2003 of Honeywell: (a) the sensor design; (b) the sensor equivalent electrical circuit.

1.3.5 The performances of AMR sensors Ordinary users of the sensors are not interested in the detailed physical origin of the operating conditions. They prefer information about the final performances of the sensor. These performances include magnetic field range, sensitivity, resolution, dimensions of the sensors, bandwidth and of course errors. The most widely used AMR sensor, the KMZ10B sensor of Philips, exhibits a sensitivity of about 48 mV/(kA/m) – it is the reported sensitivity of 4 mV/(V kA/m) multiplied by the largest permissible supply voltage of 12 V. The most sensitive sensor of the same manufacturer, the KMZ10A1, offered a sensitivity of 200 mV/(kA/m) – using a switched auxiliary field. Pant optimized the construction of the magnetoresistive sensor to obtain the largest possible sensitivity (Pant and Krahn 1991, Pant 1996). A sensitivity as high as 45 mV/(V kA/m) has been reported for a sensor with parameters: t 10 nm, w 30 m, R 1 k and Us 10 V. From these data the calculated sensitivity was about 450 mV/(kA/m). Reported transfer characteristics of the sensors are presented in figure 1.170. The sensitivity can be increased to 56 mV/(kA/m) by applying a smaller gap (1 m) between paths. The commercially available sensor HMC1001 of Honeywell exhibits a sensitivity of 40 mV/(kA/m) which for nominal supply voltage 5 V gives a sensitivity as high as 200 mV/(kA/m). The largest possible sensitivity of a sensor can be calculated using the simplified expression 1 1 Uout JA —– ——— —– Hx . w p Hk

(1.149)

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Figure 1.170 The experimentally determined transfer characteristics of the Barber-pole sensors: (a) t 10 nm, w 45 m, a 30 m; (b) t 11 nm, w 30 m, a 20 m (Pant and Krahn 1991).

An acceptable current density has been estimated as 1010 Am–2 (Moore 1972). Thus it can be assumed that the current density J 5 109 Am–2 ensures stable and reliable operation of the sensor. Assuming the path dimensions t 10 nm, w 10 m, p 1 m and the material parameters for the permalloy (table 1.3) using (1.149) an extremely large sensitivity of about 1000 mV/(kA/m) for the reasonable sensor area of 1 cm2 is obtained. Thus from the above considerations it can be stated that the typical sensitivity of the AMR sensor is about 40 mV/(kA/m) or 30 V/T for a special design this sensitivity may be enlarged to about 200 mV/(kA/m) or 150 V/T. For comparison the typical sensitivity of a Hall effect sensor is rarely larger than about 10 mV/(kA/m). The sensitivity can be significantly enlarged by integrating the sensor with an amplifier as described in the previous section. Another method of improving the sensitivity is to use flux concentrators (Smith et al 1991, Lao 1994). Figure 1.171(a) presents the construction of a magnetoresistive sensor with flux concentrators and bias coil designed by Smith and co-workers. The dimensions of the sensor were as follows: t 25 nm, w 35 m while the concentrators were prepared from the NiFe thin film with thickness 6 m, area 1.5 1.5 mm. The sensor was placed adjacent to the gap (33 m) between two concentrators. The concentrators provided a 20-fold magnification of the flux component perpendicular to the stripe axis, while simultaneously the orthogonal component was shielding by the factor of 10. Figure 1.171(b) presents the experimentally determined response of the sensor with concentrators. For 100 mW power a sensitivity of about 4000 mV/(kA/m) has been obtained. The sensitivity characteristic was flat from DC to 50 MHz. The resolution has been estimated as small at about 10–4 A/m or 1 nT.

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Figure 1.171 The magnetoresistive sensor with flux concentrator and its measured response for various applied magnetic field and various sensor power P (Smith et al 1991).

In fact, the resolution may be more important than the sensitivity when the sensor is used to measure extremely small magnetic fields. In magnetoresistive sensors the resolution is limited by noise and offset drift. Figure 1.172(a) presents the experimentally determined noise characteristics of the KMZ10B sensor and figure 1.172(b) presents similar characteristics of the HMC1001 sensor. For low frequency (to about 10 Hz) the slope of the noise density curve is as 1/f. For higher frequency the Johnson’s thermal noise typical for resistive sensors dominate. This thermal noise is a function of the bandwidth f, the sensor resistance R or power dissipation P: Jwt — 1 — SNR ———– —— —– √RHx ———– —— —– √PHx . 2√kTf 2√kTf

(1.150)

Figure 1.172 The experimentally determined noise characteristics of KMZ10B sensor (Ripka 1996) and similar characteristics of HMC1001 sensor (Honeywell product information).

The SNR ratio can be improved by increasing the sensor area (see equation 1.143). The power dissipation or the current density are limited by the temperature T. Figure 1.173(a) shows noise versus supply voltage when the MR reading head was placed above the tape (Jeffers et al 1987). It was estimated

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that the supply voltage should be large enough so that the magnetic noise exceeded electronic noise, but not so large that the exponentially increased thermal noise exceeded the magnetic noise. The origin of 1/f type noise is mainly magnetic. Figure 1.173(b) shows noise versus the longitudinal magnetic field (Flynn 1994). The noise has been measured as a standard deviation of the variation for a thousand magnetizing cycles. Without the stabilizing field the sensor was very noisy but by applying a relatively small value of the stabilizing field this noise was reduced significantly.

Figure 1.173 The noise versus supply voltage determined experimentally for thin film magnetoresistive head reading the signal from the tape (Jeffers et al 1987) (a) and noise versus the value of the stabilizing longitudinal magnetic field (Flynn 1994) (b).

The resolution can be determined from expression (1.150) assuming the typical parameters: t 20 nm, w 20 m, p 1 m, A 2 mm 2 mm, noise as 1% of the signal. After simple calculation the minimal resolution can be estimated as — — Hx /√f 0.15·10–3 (A/m)/√ Hz. For the HMC1001 sensor—the noise density at 1Hz — — is given as 30 nV/√Hz which corresponds to Hx /√f 0.14·10–3 (A/m)/√Hz. Considering separately 1/f noise and Johnson noise the resolution has been determined in the form: Hx 2.1 10–3 A/m (p-p) in the bandwidth 0.1–10 Hz for 1/f noise and Hx 4·10–3 A/m (p-p) for Johnson noise in the bandwidth 1 kHz. — The minimal value of noise reported by other sources is 3.7 10–6 A/m/√Hz (Hoffman and Birtwistle 1982). The second limitation of the resolution ia especially difficult to eliminate – thermal offset drift. A typical KMZ10B sensor exhibits offset drift of 15 V/K. For a temperature change of 10°C it corresponds to an offset drift of about 7 A/m and 0.35% of the full range. The offset voltage may be laser trimmed to a negligible value. Theoretically when four identical sensors are connected into the full bridge circuit the temperature change of resistance should be compensated. But in practice due to evidence of small defects various part of the sensor can be heated to different temperatures. Figure 1.174 presents the thermovision picture of the sensor presented in figure 1.157(a). It can be seen that two internal parts (figure 1.174(a)) or one

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Figure 1.174 The thermovision picture of the magnetoresistive sensors presented in figure 1.157a and supplied at various power (power increases from left to right).

internal part (figure 1.174(b)) may exhibit larger temperatures. The temperature gradient is the major source of the thermal offset drift and generally it can be stated that the offset drift is the factor of the technology quality. An effective technique which reduces the thermal offset drift is the application of an AC (flipping) stabilizing field proposed by Tumanski (1984) and described in section 1.2.8. To realize this technique sensors are available which are equipped with a special planar coil generating stabilizing field. Figure 1.175 presents a similar set–reset technique recommended by Honeywell. The transfer characteristic of the sensor (figure 1.175(a)) shows an inversion of the gain slope and a common crossover point in the zero field offset voltage. To measure the applied field Hx the sensor is first activated by a ‘set’ pulse (figure 1.175(b)). After it has settled the Vset voltage is read and stored. Next the ‘reset’ pulse is introduced and the voltage Vreset is read. Thus two readings are as follows: Vset SHx Voffset

(1.151)

Vreset SHx Voffset .

(1.152)

Figure 1.175 The set–reset technique to reduce the offset temperature drift: (a) the transfer characteristics of the sensor in set and reset state; (b) the output signal of the sensor (Honeywell product information).

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The difference between the two readings is proportional only to the applied field and offset voltage is reduced: Vset Vreset 2SHx .

(1.153)

After applying the set–reset technique the thermal offset drift in the HMC1001 sensor is reduced from 300 ppm/°C to about 10 ppm/°C. The linearity of the transfer characteristic and the magnetic field range is interdependent. The transfer characteristic is non-linear because the phenomenon of anisotropic magnetoresistance is non-linear (Dibbern 1984, Mapps 1996). In the case of quasi-linear axis or Barber-pole sensors (assumed as the linear sensors) the output signal is not directly proportional to the magnetic field but to U S · hx√1 hx2

(1.154)

where: hx Hx /Hk . Additionally the non-linearity is the result of non-uniformity of magnetization. Casselman and Hanka (1980), following numerical calculations, estimated that the range of 1% linearity around the optimal bias point (in the case of the simple single path sensor) could be expressed as t H 60 141000 — [A/m] w

(1.155)

while the end points of the range can be estimated as: t H 230 617000 — w

(1.156)

t H 290 678000 —. w

(1.157)

For Barber-pole sensors the quadratic part in the transfer characteristic appears due to non-uniformity of the current distribution. This part shows a marked dependence on the geometry and conductivity of the shorting bars (Dibbern 1984). It is not reasonable to operate on the whole transfer characteristics (up to about 0.7 Hk) because the error of non-linearity is then very large (about 12% for the best fitting with linear approximation). The error of the non-linearity depends on the magnetic field range and method of approximation. When the transfer characteristic is approximated with the line crossing the transfer characteristic at the end point (figure 1.176(a)) then the error of non-linearity can be expressed as

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138

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THIN FILM MAGNETORESISTIVE SENSORS ———– ——— hx√1 h 2max hx√1 hx2 L ———————————. hmax

(1.158)

Figure 1.176(b) presents the calculated non-linearity error for various values of the range. If the range is not larger than H 0.3 Hk (which corresponds to Uout 0.5 Umax) then the non-linearity error is less than 2% of the full range. The range can be simply enlarged by increasing Hk (for example by the change of t/w) or by increasing of the value of the stabilizing field. Apart from the above errors – limited resolution (offset drift and noise) and non-linearity – additional errors may be caused by a change of temperature, by the evidence of the orthogonal component of the measured field or by the change of frequency of the measured field.

Figure 1.176 The non-linearity error of the magnetoresistive sensor: (a) approximation of the transfer characteristic by the line with crossing point at the end of the range; (b) the non-linearity error calculated for various ranges of the sensor.

The following parameters are temperature dependent: resistivity , magnetoresistance and anisotropy field Hko. Approximately these parameters change linearly with temperature. For a permalloy the temperature coefficients were estimated as: 0.025 K–1, 0.018 K–1, Hk 0.022 K–1. When the sensor is supplied by a fixed value of the current the temperature error can be expressed as Hko i ≅ ————————– Hk . t Hko Hyo — M w

(1.159)

When the sensor is supplied by a fixed value of the voltage the error is additionally influenced by the change of resistance: Hko i ≅ ————————– Hk . t Hko Hyo — M w

(1.160)

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Because the temperature coefficients and Hk are of the similar value it is possible to obtain a magnetoresistive sensor with negligible temperature error i. The small differences in the values of and Hk can be corrected by appropriate design of the sensor, for example by changing t/w. Sensors from NiFeCo alloy have been prepared with a temperature error smaller than 0.01%/K (Kwiatkowski and Tumanski 1986). When the sensor is supplied by a fixed value of the voltage the temperature error is larger than when it is supplied by a fixed current. For example, KMZ sensors exhibit a temperature error of about 0.1%/K for a fixed current and about 0.4%/K for a fixed voltage. The sensor operates properly in the temperature range 25 to 125°C. To correct temperature errors the manufacturer recommends the circuit presented in figure 1.177(a) with additional silicon temperature sensor T (Petersen 1986).

Figure 1.177 The methods of the temperature errors compensation: (a) with temperature sensor T (Petersen 1986); (b) with microthermostat.

The temperature sensor should be placed adjacent to the MR sensor. It is possible to use the small microthermostat as presented in figure 1.177(b). The bifilar copper windings or films can be used simultaneously as a heater and temperature sensor. In general AMR sensors compare well to other sensors taking into account temperature behaviours. Therefore AMR sensors have been used as sensors in the automotive industry (for example ABS systems) working in temperatures up to 190°C (Graeger and Petersen 1992). Another advantageous behaviour of the AMR sensor (in comparison with other sensors) is its frequency bandwidth. Magnetoresistive sensors measure both constant and alternating magnetic fields. Moreover the alternating magnetic field of very high frequency can be determined – a magnetic field with frequency as high as 300 MHz was successfully measured (Hebbert and Schwee 1966). Typical market available sensors can operate in the frequency bandwidth 0–1 MHz. In comparison with inductive sensors an important advantage is that MR sensors directly measure magnetic field H (or magnetic flux density B) while inductive sensors measure the derivative dB/dt. Thus the MR sensor does not need an integrating circuit (introducing additional errors) and its sensitivity

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does not depend on the speed of flux change (a problem while reading information from moving sources, for example credit cards). Contrary to excellent frequency behaviours the directional parameters may be in some cases a significant problem to overcome. Theoretically the sensor is not sensitive to the orthogonal component when the transversal component is equal to zero. Figure 1.178 presents the experimentally determined dependence of the output signal on the field strength varied along the anisotropy axis. In fact when the orthogonal component was smaller than about 25% of the full range (2 kA/m) no change in the output signal was detected. During switching of the magnetization state (for Hy approximately 50% of the magnetic field range) only small output signal appears (0.5 mV which corresponds to about 1% of the Uoutmax).

Figure 1.178 The experimentally determined Uout = f(Hy) characteristic of the KMZ10B sensor for Hx = 0 (Hy: the component of external field perpendicular to the sensor axis; Hx: component along the sensor axis).

More difficult to interpretate is the situation when the measured magnetic field is inclined by the angle to the axis of the sensor (axis perpendicular to the anisotropy axis). The output signal of the sensor is then equal to 1 Uout S ———————— Hx cos Hk Hs Hx sin

(1.161)

while the correct output signal should be as follows: 1 Uout S ———– Hx cos . Hk Hs

(1.162)

If the Hx sin component is sufficiently small in comparison to Hk Hb the error may be small. The directional error can be described by the expression:

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AMR SENSORS Hx sin sin d ———————— ———————–. Hk Hs Hx sin Hk Hs ———– sin Hx

141 (1.163)

The dependence of the error on the Hx /(Hk Hs) value is presented in figure 1.179. Even if the measured field is relatively small i.e. Hx 0.1(Hk Hs) the error may be as large as 9%.

Figure 1.179 The error caused by the orthogonal component of the measured field: (a) DC biased sensor; (b) AC biased sensor.

The sensitivity to the orthogonal component can be significantly reduced by differently biasing both magnetoresistors (Paul et al 1970, Mapps et al 1987). As demonstrated by Hill and Birtwistle (1987) the orthogonal field error was reduced from about 3% to 0.03% after applying the differential bias of the magnetoresistors. A relatively simple method of orthogonal field rejection involves applying an AC flipping stabilizing field (equivalent to the differential biasing method) (Tumanski 1984). In one cycle of biasing the orthogonal field causes an increase of sensitivity, but in the second cycle it causes a decrease of sensitivity. Thus it might be possible to completely reduce the orthogonal field component from the output signal as described in section 1.2.8. The elimination of the influence of the orthogonal component is not complete because the characteristic Uout f(Hs) is non-linear. The output signal of the sensor biased with a flipping field can be described with the expression: hx cos Uout S —————. 1 hx2 sin2

(1.164)

Figure 1.179(b) presents the calculated error for the AC stabilized sensor. In comparison with the DC stabilized sensor such error is significantly reduced. If Hx 0.1(Hk Hs) this error is smaller than 1%, but even when Hx 0.3(Hk Hs) (typical field range of the sensor) this error is smaller than 10%.

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All the above errors: non-linearity error, temperature error (except temperature offset drift), directional error, noise, can be spectacularly reduced by applying magnetic feedback (van Niet and Vrecken 1979). In the circuit presented in figure 1.180(a) the sensor operates only as the null-field detector and therefore it can be linear and with negligible errors in a very wide field range – as demonstrated in figure 1.180(b).

Figure 1.180 The magnetoresistive sensor with magnetic feedback : (a) electrical circuit; (b) the transfer characteristic of the sensor.

Figure 1.181 presents the distortion spectrum of the output voltage before and after applying feedback. The Barkhausen noise and the distortion have been drastically reduced through magnetic feedback. The main advantages of the feedback circuit are the more complicated construction of the sensor and the possibility of disturbing the measured field by the feedback field. Both the major manufacturers of AMR magnetoresistive sensors offer the sensors with two additional planar coils – to realize the flipped biasing and to realize the magnetic feedback. Two examples of the layouts of such sensors are presented in figure 1.182.

Figure 1.181 The distortion spectrum of the output voltage of the MR sensor before and after applying feedback (de Niet and Vreeken 1979).

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Figure 1.182 The layouts of magnetoresistive sensors equipped with feedback and flipping planar coils: (a) KMZ51 sensor of Philips; (b) HMC1001 sensor of Honeywell. Table.1.6 The performances of the HMC 1001 magnetic field sensor of Honeywell. Parameter Field range [A/m] Bridge supply voltage Us [V] Sensitivity by Us 5V [mV/kAm–1]

HMC1001 160 5 200

Resistance []

600–1200

Operating temperature [°C]

40–80

Linearity error Hx 0–80 A/m [%FS] Linearity error Hx 0–160 A/m [%FS]

0.1 1

Temperature error (fixed Us) [%/K] Temperature error (fixed Is) [%/K]

0.3 0.06

Offset temperature drift (without feedback) [%/K] Offset temperature drift (with feedback) [%/K]

0.03 0.001

Orthogonal field of 80 A/m error (without feedback) [%FS] Orthogonal field of 80 A/m error (with feedback) [%FS]

3 0.5

Hysteresis for 160 A/m [%FS] — Noise density at 1 kHz [nV/ √Hz]

0.05

Resolution by 10 Hz bandwidth [A/m] Bandwidth [MHz]

30 22 10–8 0–5

Tables 1.6 and 1.7 show performance data of the two main market-available sensors. The parameters of both sensors presented in tables 1.6/1.7 and in

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THIN FILM MAGNETORESISTIVE SENSORS Table 1.7 The performances of the KMZ10 magnetic field sensor of Philips. Parameter Field range [A/m]

KMZ10A

KMZ10B

KMZ10C

500

2000

7500

Bridge supply voltage [V]

5

Sensitivity by Us 5 V [mV/kAm ] –1

Resistance [k]

80

20

7.5

0.8–1.6

1.6–2.6

1–1.8

40–150

Operating temperature [°C] Linearity error for 50% FS [%] Linearity error for FS [%] Temperature error (fixed Us) [%/K] Temperature error (fixed Is) [%/K] Offset temperature drift [V/K]

0.8 4.0

0.5 2.0

0.8 2.7

0.4 0.15

0.4 0.1

0.5 0.15

30

15

10

Hysteresis [%FS]

0.5

Bandwidth [MHz]

0–1

figures 1.183/1.184 are similar. Other sensors manufactured by Sony (Hager 1993) or HL-Planartechnik (Dettman et al 1988, Rottman and Dettman 1991) exhibit similar behaviours. It may be stated that these parameters are the result of optimized design and represent the best performances available in this class of sensors. The significant improvement of certain performances may be obtained by applying the feedback circuit, the flux concentrators or by

Figure 1.183 The construction and experimentally determined transfer characteristics of KMZ10B sensor.

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Figure 1.184 The construction and the transfer characteristics of HMC sensor.

decreasing the power dissipation (area of the sensor) – as described above. Figures 1.183 and 1.184 present the characteristics and the construction of the most frequently used, market-available AMR sensors. Beside the above parameters of the AMR sensors other important factors should be taken into consideration by the users. For example the extremely small dimensions of the sensors (especially sensors used in memory storage systems) generate a risk of electrostatic discharge (ESD) damage (Tian and Lee 1995, Wallash 1996, Wallash 1997, Himmle 1996). Two mechanisms of ESD destructive damage have been observed: electrothermal damage and dielectric breakdown (Tian and Lee 1995). Depending on expected future applications the sensors should exhibit some other special features, like vibration resistance, humidity resistance etc. Figure 1.185 presents typical performance requirements for magnetoresistive sensors summarized by Schewe and Schelter (1997).

Figure 1.185 The typical performance requirements for magnetoresistive sensors (Schewe and Schelter (1997)

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feedback IEEE Trans. Magn. 15 1625–1627 Nishimura C 1987 Magnetic properties of NiFe films prepared using ion-beam sputtering IEEE Trans. Magn. 23 2728–2730 Nonvolatile Electronics engineering and application notes or http://www.nve.com Nouchi N et al 1982 Magnetic head and method of production thereof US Patent 4 354 212 Oberg P E et al 1968 Magnetoresistive amplifier US Patent 3 382 448 O’Day R L 1973 Balanced magnetic head IBM Tech. Discl. Bull. 15 2680 O’Day R L et al 1974 Internally biased magnetoresistive magnetic transducer US Patent 3 814 863 Ohring M 1992 The Materials Science of Thin Films (London: Academic Press) Ooyen van J A C et al 1982 Magnetoresistance in laminated NiFe films J. Appl. Phys. 53 2596–2598 Ozimek E J and Paul D I 1984 Magnetization dynamics of micron size thin permalloy films J. Appl. Phys. 55 2232–2234 Panina L V 1995 Giant magnetoimpedance in Co-rich amorphous wires and films IEEE Trans. Magn. 31 1249–1260 Pant B B 1990 Scaling in thin magnetoresistive films J. Appl. Phys. 67 414–419 Pant B B and Krahn D R 1991 High sensitivity magnetoresistive transducers J. Appl. Phys. 69 5936–5938 Pant B B 1996 Design tradeoff for high sensitivity magnetoresistive transducers Electrochem. Soc. Proc. 95 62–76 Pant B B 1996b Effect of interstrip gap on the sensitivity of high sensitivity magnetoresistive transducer J. Appl. Phys. 79 6123–6125 Paperno E and Kaplan B Z 1995 Simultaneous measurement of two dc magnetic field components by a single magnetoresistor IEEE Trans. Magn. 31 2269–2273 Paperno E and Kaplan B Z 1995b Suppression of Barkhausen noise in magnetoresistive sensors employing AC bias IEEE Trans. Magn. 31 3161–3163 Paperno E and Kaplan B Z 1996 Sub-nano-tesla on plane vector magnetometer employing single magnetoresistor Proc. of 19th Conv. of Electrical and Electronics Eng. in Israel (Jerusalem) Parkin S S P 1994 Giant magnetoresistance and oscillatory interlayer coupling in polycrystalline transition metal multilayers Ultrathin Magnetic Structures II (Berlin: Springer) 148–186 Patel K et al 1997 Optimisation of overlay properties for use in magnetic bubble devices, J. Phys. D, 11 531–537 Paul M C et al 1970 Thin film magnetoresistance magnetometer sensitive to easy axis field component and biased to be insensitive to hard axis field component, US Patent 3 546 579 Petersen A 1986 The magnetoresistive sensor – a sensitive device for detecting magnetic field variations Electr. Comp. Appl. 8 222–239

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adjacent layer biased magnetoresistive sensors J. Appl Phys. 75 7993–7997 Shiiki K et al 1996 Effect of anisotropy dispersion on magnetization process in magnetoresistive sensor films J. Appl. Phys. 79 2590–2593 Shtrikman S and Smith D R 1996 Analytic and quasi-analytic formulae for MR heads IEEE Trans. Magn. 32 43–48 Siemens A G Application notes or http://www.infineon.com Smit J 1951 Magnetoresistance of ferromagnetic metals and alloys at low temperature Physica 17 612–627 Smith C H and Schneider R W 1998 Magnetic field sensing utilizing GMR materials Sensor Review 18 230–236 Smith D O 1961 Anisotropy in nickel-iron films J. Appl. Phys. 32 70S–80S Smith N and Wachenschwanz D 1987 Magnetoresistive heads and the reciprocity principle IEEE Trans. Magn. 23 2494–2496 Smith N 1987 Micromagnetic analysis of a coupled thin film self biased magnetoresistive sensor IEEE Trans. Magn. 23 259–272 Smith N 1988 A specific model for domain wall nucleation in thin film Permalloy microelements J. Appl. Phys. 63 2932–2937 Smith N et al 1990 An improved thin film permanent magnet material and novel magnet design for magnetoresistive sensor biasing IEEE Trans. Magn. 26 2409–2411 Smith N and Cain W C 1991 Micromagnetic model of an exchange coupled NiFe-TbCo bilayer J. Appl. Phys. 69 2471–2479 Smith N et al 1991b A high sensitivity magnetoresistive magnetometer J. Appl. Phys. 69 5082–5084 Smith N et al 1992 Dual magnetoresistive head for very high density recording IEEE Trans. Magn. 28 2292–2294 Smith N et al 1992b Analysis of a dual magnetoresistive head IEEE Trans. Magn. 28 2295–2297 Smith N and Yuan S 1994 Micromagnetic modeling of a narrow track dual magnetoresistive head IEEE Trans. Magn. 30 388–393 Soeya S et al 1992 Magnetic exchange coupling for bilayered Ni81Fe19/NiO and trilayered Ni81Fe19/NiFeNb/NiO films J. Appl. Phys. 74 6297–6301 Solt K 1985 Magnetic, structural and magnetoresistive properties of magnetron sputtered thin NiFe films Thin Solid Films 125 251–256 Sondheimer E H 1952 The mean free path of electrons in metals Adv Phys. 1 1–42 Stobiecki F 1978 The influence of the geometry of thin film MR elements on their parameters Doctor’s thesis, Warsaw University of Technology Stobiecki T 1972 Influence of angular dispersion of magnetization on magnetoresistance in ferromagnetic thin films Acta. Phys. Pol. A41 657–659 Stoner E C and Wohlfarth E P 1991 A mechanism of magnetic hysteresis in heterogeneous alloys Reprint in IEEE Trans. Magn. 27 3475–3518 Sueda N and Fujiwara H 1971 Magnetoresistance effects of iron-rich iron vanadium alloys J. Sc. Hiroshima Univ. A35 59–68

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Sun J Z 1998 Magnetotransport in doped manganate perovskites IBM J. Res. Dev. 42 89–102 Suzuki T et al 1996 Instability evaluation for permanent magnet biased magnetoresistive heads IEEE Trans. Magn. 32 3383–3385 Takada A et al 1997 Vertical AMR sensor with new magnetic stabilizing design IEEE Trans. Magn. 33 2932–2934 Takahashi K et al 1976 Magnetoresistive properties of NiCo film and its applications to bubble detectors Fujitsu Sc. J. 10 123–146 Tanaka T et al 1990 Anisotropic magnetoresistance and Hall effects for NiFeM alloy thin films IEEE Trans. Magn. 26 2418–2420 Tellier C R and Tosser A J 1982 Size Effects in Thin Films, Thin film science and Technology 2 (Amsterdam: Elsevier) Thomas G et al 1969 On the theory of the spin-orbit interaction in the magnetoresistivity effects in ferromagnetic metals Physica 45 407–417 Thomson W 1857 On the electrodynamic qualities of metals: effects of magnetization on the electric conductivity of nickel and iron Proc. Roy. Soc. 8 546–550 Tian H and Lee J J 1995 Electrostatic discharge damage of MR heads IEEE Trans. Magn. 31 2624–2626 Tomlinson S L and Hill E W 1990 A micromagnetic model for the study of magnetoresistive devices IEEE Trans. Magn. 26 1662–1664 Toussaint R et al 1986 Static characteristics of soft adjacent layer self biased magnetoresistive heads IEEE Trans. Magn. 22 677–679 Trindade I G and Kryder M H 1994 Comparative experimental study of exchange biased symmetric and antisymmetric dual magnetoresistive read elements IEEE Trans. Magn. 30 3852–3854 Trindade I G and Kryder M 1996 Thermal stability of TaN and TiN spacer in dual magnetoresistive read-elements Electroch. Soc. Proc. 95 42–50 Tsang C et al 1981 Exchange induced unidirectional anisotropy at FeMnNi80Fe20 interfaces J. Appl. Phys. 52 2471–2473 Tsang C and Decker S K 1981 The origin of Barkhausen noise in small permalloy magnetoresistive sensors J. Appl. Phys. 52 2465–2467 Tsang C and Lee K 1982 Temperature dependence of unidirectional anisotropy effects in the permalloy-FeMn systems J. Appl. Phys. 53 2605–2607 Tsang C and Decker S K 1982 Study of domain formation in small permalloy magnetoresistive elements J. Appl. Phys. 53 2602–2604 Tsang C and Fontana R E 1982 Fabrication and wafer testing of Barber pole and exchange biased narrow track MR sensors IEEE Trans. Magn. 18 1149–1151 Tsang C 1984 Magnetics of small magnetoresistive sensors J. Appl. Phys. 55 2226–2231 Tsang C 1987 Magnetoresistive read transducer having patterned longitudinal bias US Patent 4 663 685 Tsang C et al 1988 Magnetics of nonlaminated, bilaminated and multilaminated permalloy stripes J. Appl. Phys. 63 2938–2940

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Tsang C 1989 Unshielded MR elements with patterned exchange biasing IEEE Trans. Magn. 25 3692–3694 Tsang C et al 1996 3 Gbit/in2 recording demonstration with dual element heads and thin film disks IEEE Trans. Magn. 32 7–12 Tsang C et al 1997 5 GB/in2 recording demonstration with conventional AMR dual element heads and thin film disks IEEE Trans. Magn. 33 2866–2871 Tumanski S and Stabrowski M 1984 Optimization of the performance of a thin film permalloy magnetoresistive sensor IEEE Trans. Magn. 20 963–965 Tumanski S 1984 A new type of thin film magnetoresistive magnetometer – an analysis of circuit principles IEEE Trans. Magn. 20 1720–1722 Tumanski S and Stabrowski M 1985 The optimization and design of magnetoresistive Barber-pole sensors Sensors and Actuators 7 285–295 Uchida H et al 1982 A non-shielded MR head with improved resolution IEEE Trans. Magn. 18 1152- 1154 Uchida H et al 1985 Magnetic transducer head utilizing magnetoresistance effect with a bias field and partial saturation US Patent 4 524 401 Ueda M et al 1990 AC bias type magnetoresistive sensor IEEE Trans. Magn. 26 1572–1574 Veillard D H Self-biased magnetoresistive reproduce head utilizing second harmonic signal detection US Patent 4 796 106 Vieth M et al 1994 Magnetoresistive permalloy sensors with increased sensitivity IEEE Trans. Magn. 30 939–941 Vincent J L 1978 The development of a sinusoidal voltage in thin ferromagnetic films and the measurement of low magnetic fields, J. Phys. D. 11 L28–L30 Voegeli O 1975 Magnetoresistive read head assembly having matched elements for common mode rejection US Patent 3 860 965 Voegeli O 1986 Differential magnetoresistive sensor for vertical recording US Patent 4 589 041 Vu Dinh Ky 1967 Theory of the anisotropy of resistance in ferromagnetic metals Sov. Phys. JETP 24 995–999 Wallash A J 1996 Electrostatic modeling and ESD damage of magnetoresistive sensors IEEE Trans. Magn. 32 49–53 Wallash A J 1997 Standardized ESD test for magnetoresistive recording heads IEEE Trans. Magn. 33 2911–2913 Weiss H 1966 The ‘Feldplatte’ – a new semiconductor magnetoresistance device IEEE Trans. Magn. 2 540–542 West F G 1960 Magnetoresistive measurements on domain rotationin nickeliron alloy films, Nature, 188 129–130 West F G 1961 Magnetoresistive measurements on domain rotation and wall development in NiFe alloy films J. Appl. Phys. 32 290S–292S West F G and Simmons C L 1966 Dependence of angular dispersion on grain size in evaporated permalloy films J. Appl. Phys. 37 1283–1284 Wieder H H 1971 Hall Generators and Magnetoresistors (London: Pion) Wilts C H and Humphrey F B 1968 Magnetic anisotropy in flat ferromagnetic

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films J. Appl. Phys. 39 1191–1196 Xiao M and Kryder M H 1996 Fabrication process for very high density shielded spin valve magnetoresistive heads Electrochem. Soc. Proc. 95 51–61 Yan Y D and Della Torre E 1988 Discretization errors in numerical micromagnetic models IEEE Trans. Magn. 24 2368–2370 Yan Y D and Jurisch M 1989 Micromagnetic predictions of closure domain patterns in magnetic thin films IEEE Trans. Magn. 25 3458–3460 Yang M M and Aboaf J A 1989 RF diode sputtered permalloy films J. Appl. Phys. 66 3734–3740 Ye W et al 1996 The influence of domain activities on MR head performances J. Appl. Phys. 79 6048–6050 Yeh T et al 1987 Thickness dependence of the magnetoresistance effect in RF sputtered thin permalloy films IEEE Trans. Magn. 23 2215–2217 Yeh T and Witcraft W F 1995 Effect of magnetic anisotropy on signal and noise of NiFe magnetoresistive sensor IEEE Trans Magn. 31 3131–3133 Yelon A 1971 Interactions in multiplayer magnetic films, Physics of thin films, 6 205–300 Yuan S and Bertram H N 1992 Fast adaptive algorithms for micromagnetics IEEE Trans. Magn. 28 2031 Yuan S W and Bertram H N 1993 Magnetoresistive heads for ultra high density recording IEEE Trans. Magn. 29 3811–3816 Yuan S W 1994 Exchange biasing schemes for MR disk heads IEEE Trans. Magn. 30 3849–3851 Zhu J G and O’Connor D J 1996 Impact of microstructure on stability of permanent magnet biased magnetoresistive heads IEEE Trans. Magn. 32 54–60

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2 GMR Sensors

2.1 GIANT MAGNETORESISTIVE EFFECTS 2.1.1 An historical review and the main terms In 1998 we celebrated the tenth birthday of the giant magnetoresistive effect GMR (Baibich et al 1988). By coincidence two giants of the computer industry IBM and Philips published (January 1998) special issues of their scientific journals to commemorate this anniversary1. Parkin from IBM, one of the most important inventors of GMR, stated that “within a decade magnetic multilayers have evolved from a scientific curiosity to become materials of significant technological importance” (Parkin 1998). Indeed GMR sensors are still in vogue, partly due to the very ‘marketing’ name, but mainly due to the expectations of their future importance in the electronic industry. This anniversary is also a good opportunity to look the fascinating history of this fundamental physics and technological challenge. Several new terms will be explained. Many of these are abbreviations (GMR, SV, RKKY, MBE, CPP, CIP, MTJ, GMI) or newly created words (magnetic valves, orange peel coupling, sandwich system, superlattices) and are usually only known to a limited circle of specialists. The giant magnetoresistive effect is a benefit of technological development that allows different magnetic structures to be obtained at nanometre and even atomic scales (Himpsel et al 1998). These ultrathin structures exhibit a wide range of mysterious and surprising phenomena which do not exist in bulk materials. The typical thin film nanostructures may be created as epitaxial films (films with ordered crystal structures of good monocrystalline quality)2 prepared by using the MBE method (molecular beam epitaxy) or polycrystalline films prepared by using the sputtering method. These films are formed as multilayers, for example a ‘sandwich structure’ (figure 2.1(a)) where a third, very thin nonmagnetic film (the spacer), is placed between two magnetic films. The border between the films is called the interface. The artificially grown structure consists of periodically alternating single-crystal film layers and is called the superlattice. Small magnetic entities may be introduced into the nonmagnetic matrix and this nanocomposite system is called the granular system (figure 2.1(c)). 1 2

IBM J. Res.Develop. 42 (1998), No.1 and Philips J. of Research 51 (1998), No.1. Epitaxy is composed of two Greek words: (epi – placed) and (arrangement).

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Figure 2.1 Various types of GMR structures: (a) multilayer; (b) spin valve and (c) granular films.

The important phenomenon utilized in many GMR structures is the exchange magnetic coupling between the magnetic films in the sandwich system. In 1986 Grünberg and co-workers (Grünberg et al 1986) discovered that for some thickness of nonmagnetic spacer (0.9 nm in their case) antiferromagnetic exchange coupling3 occured in the sandwich multilayer structure of the magnetic films (Fe–Cr–Fe). Antiferromagnetic coupling means that two magnetic films are magnetized antiparallel to each other (figure 2.2). In 1990 (Parkin et al 1990) discovered that magnetoresistance oscillated with some period when the thickness of the interlayer was varied. These oscillations (figure 2.2) indicate that the character of coupling changes with the change of thickness of the spacer – as a periodic sequence from magnetizations of the films aligned parallel to antiparallel.

Figure 2.2 Evidence of oscillatory exchange coupling in thin film multilayers.

3 In 1986 Majkrzak and co-workers (Majkrzak et al 1986) also discovered antiferromagnetic coupling in the Gd-Y superlattice.

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Figure 2.3 The first announcement of GMR effects – results obtained by Baibich and co-workers (1988).

The first announcement of the GMR effect was reported in 1988 by Baibich and co-workers (1988). They discovered that the resistance of a sandwich type multilayer with magnetizations aligned initially (in the magnetic field H 0) antiparallel decreased more than 50% after applying an external magnetic field. Because this decrease of resistance was very large they called this effect giant magnetoresistance (GMR) and this nomenclature is still in use today.4 Figure 2.3 shows the original results obtained by Baibich and co-workers. The (001)Fe/(001)Cr bcc superlattices were grown by the MBE method. The magnetoresistance was measured at 4.2 K for different thicknesses of the Cr spacer. The authors explained the GMR effect as follows. The resistivity drops when the magnetic external field overcomes the antiferromagnetic coupling and the alignment of magnetizations becomes a parallel arrangement. It was supposed that the spin-dependent scattering of the conduction electrons in the magnetic layers or at their interfaces was responsible for the GMR effect. The scattering in antiparallel alignment is much larger than in the parallel case. At the same time as Baibich another team (Binasch, Grünberg and coworkers 1989) described similar results for the Fe/Cr/Fe multilayer system. Figure 2.4(b) shows the results obtained by Grünberg. They compared GMR and AMR effects – it was assumed that GMR disappeared for large thicknesses of the spacer and that only AMR remained. Although the change of resistance was not very big ( R/R about 1.5%) comparison with the AMR effect for the same material ( R/R about 0.13%) justified the name ‘giant’.

The term ‘giant magnetoresistance’ is very good for marketing but it is a bit misleading. In many exchange coupled sandwich structures the magnetoresistance is small (less than 1%) and the name ‘giant’ is extravagant. 4

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Figure 2.4 The exchange coupled multilayer structure and results reported by Binasch and coworkers (1989) for Fe–Cr–Fe structure (the anisotropic magnetoresistive effect (AMR) in the same structure is also shown).

Many other authors later described evidence of GMR effects in various exchange-coupled multilayer structures. The best result was reported by Parkin – more than 60% of magnetoresistance in Co/Cu/Co multilayers at room temperature (Parkin 1991). (Unpublished work of this author announced results better than 110% at room temperature in Co/Cu multilayers (Parkin 1998).) Recently the typical value of magnetoresistance in GMR systems at room temperature is 10–20% (Brown 1994), but R/R 220% at low temperatures has even been reported (Schad et al 1994). Parkin (1991) also reported another remarkable achievement. He proved that it was not necessary to produce epitaxial films to obtain the GMR effect. He obtained large magnetoresistance in polycrystalline samples manufactured using the faster sputtering method. The main disadvantage of exchange-coupled GMR sensors, compared to AMR sensors, is that a much larger magnetic field is necessary to obtain the change of resistance. In the original experiment of Baibich the magnetic field was about 160 kA/m, and typically to obtain about 20% magnetoresistance a magnetic field of more than 10 kA/m is necessary. Therefore despite large magnetoresistance the sensitivity of these sensors is smaller than AMR sensors. An effective method of improving of the sensitivity of GMR sensors was introduced in 1991 by Dieny and co-workers (Dieny et al 1991). They proposed a new type of GMR sandwich structure termed a spin-valve (SV) sensor. In the spin-valve structure the antiferromagnetic alignment is obtained not by exchange coupling between two ferromagnetic films (figure 2.4(a)) but by exchange biasing one of the films (figure 2.5(left)). This biased layer (called the fixed or pinned layer) is separated by a nonferromagnetic spacer from the second ferromagnetic layer (free or unpinned layer). Because the coupling between layers is now much smaller than in exchange-coupling structures a much lower magnetic field is necessary to change the alignment of

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Figure 2.5 The spin-valve structure and results reported by Dieny and co-workers (Dieny et al 1991) for NiFe/Cu/NiFe/FeMn structure.

magnetizations. The term ‘spin-valve’ followed from the term ‘magnetic valve’ introduced by Slonczewski (1989) for the tunnelling effect in ferromagnetic layers. Spin-valve means that the magnetizations of the layers act as a sort of valve for conduction electrons. In an experiment described by Dieny (1991) magnetoresistance of about 4% at room temperature was obtained for a field not larger than 800 A/m (figure 2.5(right)). Recently spin-valve sensors have exhibited magnetoresistance of 8–20% in a field not exceeding several kA/m. Therefore they are now the most frequently used type of GMR sensor and have practically replaced exchangecoupled structures. The pinning of one of the layers is realized by different methods. The most popular is biasing one of the films by the adjacent additional film from antiferromagnetic material, for example Fe50Mn50. In 1992 another GMR system was introduced by Xiao (Xiao et al 1992) and Berkowitz (Berkowitz et al 1992). Instead of thin layers they used granular magnetic composites – small magnetic particles precipitated in the nonmagnetic matrix (figure 2.6(left)). The sensor constructed from these

Figure 2.6 The granular structure and results reported by Berkowitz and co-workers (1992) for Cu–Co granular structure.

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granular films exhibited magnetoresistance of about 7% at room temperature (30% at 4.2 K) (figure 2.6(right)). Unfortunately application of a large magnetic field (about 20–100 kA/m) is necessary to obtain such a change of resistance. These limitations (Hylton 1993) restricted the application of granular GMR sensors. Another more promising GMR structure was proposed by Slonczewski (1989) and investigated by Moodera and co-workers (1995) and Miyzaki and Tezuka (1995). In this structure the magnetic layers are separated by a thin insulator barrier. It was expected that by using this magnetic tunnel junction (MTJ) sensors with magnetoresistivity of about 10–20% for very low magnetic fields (about 10–100 A/m) could be obtained. Recently the tunnel junction sensor has been reported with magnetoresistance values of 30% at room temperature and magnetic field 400–800 A/m (Parkin 1997).

Figure 2.7 The tunnelling junction structure and results reported by Miyazaki and Tezuka (1995) for Fe/Al2O3/Fe junction.

In a typical GMR sensor the current flows in the plane of the film (figure 2.8(left)). This system is called a CIP system (current in plane). Taking into consideration that the scattering process mainly acts in the interfaces it may be expected that a system with current flowing through superlattice films (CPP mode – current perpendicular to the plane – figure 2.8(left)) would be the most effective. In fact experiments performed at Michigan State University (Pratt et al 1991) proved that the same material working in CPP mode exhibited much larger magnetoresistivity than in CPI mode (figure 2.8(right)). Unfortunately it is very difficult to measure the change of resistance in the CPP system due to very low sensor resistance. Various models of CPP sensors developed by Gijs and Bauer with improved performances have been described (Gijs and Bauer 1997). An interesting proposition for fast and cheap preparation of CPP sensors is to manufacture nanowire structures by the electrodeposition method (Piraux et al 1994, Blondel et al 1994).

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Figure 2.8 The CPP structure and results reported by Pratt and co-workers (1991) for the Ag/Co multilayer.

In the race to achieve larger and larger magnetoresistivity several groups (Jin et al 1994, Jin et al 1994b, von Helmolt et al 1993, Sun 1998, Gong 1995, McCormack et al 1994) proclaimed the colossal magnetoresistive effect exhibited by doped manganate perovskites materials (figure 2.9). Indeed a spectacular change in the resistance from the insulator to metallic state was reported, with the highest magnetoresistance values exceeding 108% (Chen et al 1996). Only one ‘small’ problem remains to be overcome – colossal effect requires low temperatures (below 100 K) and large magnetic fields (above 2000 kA/m). And there is another ‘giant’ effect – giant magnetoimpedance effect. It was natural to expect that thin film magnetic materials should exhibit changes in their magnetic parameters, for example permeability, with applied magnetic

Figure 2.9 The structure of mangate perovskites and results reported by McCormack and coworkers (1994) for La0.67Ca0.33MnO3 structure.

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Figure 2.10 The design of thin film magnetoimpedance sensor and results reported by Uchiyama and co-workers (1995) for amorphous (CoFe)80B20 thin film structure.

fields. Several groups (Vazguez et al 1997, Chiriac et al 1997, Panina 1995, Hika et al 1996) investigated the magnetoimpedance effect in various magnetic structures, firstly in wires and ribbons, and lately in thin films. They reported remarkable results, thin film magnetoimpedance sensors may compete with fluxgate sensors due to their large sensitivity and simplicity of design. Table 2.1 Comparison of various types of GMR structures (after Daughton 1996, 1999) GMR structure

GMR [%]

Saturation field [kA/m]

Sensitivity %/kAm 1

Sensitivity %/Oe

Exchange coupled multilayer

10–80

8–200

1.0

0.1

Spin-valve

5–10

0.4–4

10

1.0

Granular

8–40

60–600

0.1

0.01

Tunnelling

10–25

0.4–2

25

2.0

Colossal

100

80

1.0

0.1

Magnetoimpedance

50

1

50

4

AMR

2.2

0.25

10

0.8

Table 2.1 compares the typical parameters of various GMR structures. The importance of GMR sensors compared to AMR sensors consists in much larger magnetoresistance values. This allows the construction of much smaller read heads. It should be remarked that sensitivity is an important parameter when the magnetoresistor is used as a magnetic field sensor. When used as a read head in data storage systems the detected field is not very small and therefore the output signal is more important than sensitivity for assumed dimensions (depending on R/R). Spin-valve heads obtain almost fourfold larger signals than MR heads for the

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Figure 2.11 Comparison of the output signals of AMR and GMR reading heads (Grochowski and Thompson 1994).

same sensing layer thickness (figure 2.11). Also the read cycle time decreases approximately as the inverse square of the magnetoresistance (Egelhoff et al 1998). Recently GMR heads for over 5 Gbit/in2 density recording have been reported (Kanai et al 1997). GMR heads for density recording of 100 Gbit/in2 have also been considered (Khizroev et al 1997). Introduction of GMR read heads in the microcomputer industry has created new perspectives to high density information storage.

2.1.2 Oscillatory exchange coupling in the magnetic multilayers To obtain the GMR effect in the magnetic multilayer structure an initial antiferromagnetic alignment is required. This alignment is possible due to exchange coupling of two magnetic layers separated by a very thin nonmagnetic layer.5 The precise study performed by Parkin and co-workers (1990) surprisingly indicated that the GMR effect exists only for selected values of the thickness of the nonmagnetic layer. Moreover these values of thickness repeat with a certain period. These results have been confirmed by other investigations of different multilayer structures (Parkin et al 1991, Parkin 1991, Mosca et al 5 As far back as the seventies and eighties several designers of AMR structures have tried to apply multilayer coupled films to such sensors. In most cases additional films were (permanent magnet or antiferromagnetic) used to bias the MR film (Hempstead et al 1978, Tsang and Lee 1982, Kitada et al 1985, Hill et al 1986, Cain et al 1988). The exchange coupled films were also tested to improve the performance of AMR sensors (Ooyen et al 1982, Wieberdink and Eijkel 1989, Yoo et al 1989). The main difference between exchange coupling described here and that presented in section one is the scale of dimensions. In AMR structures the films were coupled by exchange anisotropy (or by magnetostatic field). In GMR structures two films are separated by a much thinner non-magnetic layer. Therefore this exchange coupling arises from the atomic interaction.

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Figure 2.12 Changes in oscillations of the MR ratio with the thickness of non-magnetic layers (experiments reported by Parkin 1991).

1991, Petroff et al 1991, Parkin 1992, Fert et al 1992, Okuno and Inomata 1994, Parkin et al 1994, Fullerton et al 1993, Inomata and Saito 1993, Mattheis et al 1993, Farrow 1998, Okuno and Inomata 1993, Sakakima and Satomi 1993, Kataoka 1993). Figure 2.12 presents two examples of the oscillatory behaviour of magnetoresistance. It was obvious that the oscillations were due to the change of exchange coupling when the thickness of the spacer was varied. The exchange coupling may be determined from the saturation field of magnetizing curve. The interlayer coupling areal energy density W1 is described by: M1 · M2 W1 J1 ———— J1 cos

M 1

M 2

(2.1)

where: M1, M2 – magnetizations of both layers, – angle between the magnetizations, J1 – coupling coefficient. The coefficient J1 of the magnetic layer with thickness tFe may be determined from the saturation field Hs of the magnetisation curve6: o H sMt Fe J1 ————–. 2

(2.2)

Thus the value of the saturation field provides information about the coupling. Figure 2.13 presents the results of the saturation field for the NiFe/Au structure versus the thickness of Au (Parkin 1994). Very good correlation may be observed between variation of magnetoresistance and saturation field (coupling). Direct measurement of coupling in magnetic multilayers is rather complicated (Allenspach and Weber 1998, Fert and Bruno 1994, Parkin 1994, 6 Expression (2.2) describes the sandwich structure. For a multilayer structure with many layers the coefficient 12 should be replaced by 14.

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Figure 2.13 Changes in oscillations of magnetoresistivity and saturation field in NiFe/Au multilayer structure (experiments reported by Parkin 1994).

Pierce et al 1994). The most widely used are the magneto-optical Kerr effect (MOKE) or the magnetometric method (Johnson et al 1992, Qiu et al 1992, Bloemen et al 1994, Coehoorn and Duchateau 1993, Celinski and Heinrich 1991, Purcell et al 1991, Purcell et al 1992). Using a wedge-shaped spacer and the Kerr method it is possible to investigate the local value of coupling for a precise determined thickness of the spacer. Figure 2.14 presents an example of magnetizing curves determined by the magnetometric method and figure 2.15 presents results obtained using the Kerr method (Czapkiewicz 1999). Various other methods have been used, for example Brillouin light scattering (BLS) (Cochran 1994, Hillebrands and Günterodt 1994, Cochran et al 1990), ferromagnetic resonance (FMR) (Heinrich 1994, Heinrich et al 1990), spin polarized low energy electron diffraction (SPLEED) (Carbone and Alvarad 1987, Pescia 1990), scanning electron microscopy with polarization analysis (SEMPA) (Unguris et al 1991, Weber et al 1995).

Figure 2.14 The magnetizing curves determined for Fe/Cr multilayer structure by the magnetometric method: (a) antiferromagnetic coupling; (b) ferromagnetic coupling (Czapkiewicz 1999).

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Figure 2.15 The magnetizing curves determined for Fe/Cr multilayer structure by the Kerr method: (a) antiferromagnetic coupling; (b) ferromagnetic coupling (Czapkiewicz 1999).

Figure 2.16(a) presents the results of investigations of interlayer coupling performed by Demokritov and co-workers (Demokritov et al 1991, Grünberg et al 1992). They used two methods: M(H) curve analysis (by MOKE) for antiferromagnetic coupling and spinwave analysis (BLS) for ferromagnetic coupling. Another method called ‘spin engineering’ was proposed by Parkin (Parkin and Mauri 1991). In this method one of the layers is pinned to an additional Co layer. This allows analysis of ferromagnetic exchange coupling. The results obtained by Parkin for NiCo/Ru/NiCo structure are shown in figure 2.16(b). Both experiments confirmed that coupling periodically changed from antiferromagnetic to ferromagnetic. The positive value of the coupling coefficient J1 means that coupling is ferromagnetic, a negative valve means that it is antiferromagnetic (the reverse convention also can be found in the literature). Various sandwich structures have been tested, for example Fe/Cu, Fe/Cr (Petroff et al 1991), Fe/Ag (Celinski and Heinrich 1991), Fe/Au (Shintaku et al 1993, Fullerton et al 1993), Ni/Ag (dos Santos et al 1991), Mo/Ni (Zheng et al

Figure 2.16 Experimentally determined coupling coefficient: (a) by Demokritov et al (1991) and (b) by Parkin et al 1994.

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1993), Co/Cu (Honda et al 1993, Cebollada et al 1989), Co/Ag (Tosin et al 1993), NiFe/Cu (Holody et al 1998, Parkin 1992, Nakatani et al 1993), NiFe/Cr (Chubing et al 1993), NiCo/Cu (Kubota et al 1993), FeCoNi/Cu (Coehoorn and Duchateau 1993), CoFe/Cu (Kataoka et al 1993), Co/Cr (Metoki et al 1993), Co/CuNi (Okuno and Inomata 1993), NiFe/Au (Parkin 1996), Co/Ru, Co/Mo, Co/V, Co/Ir (Parkin 1991), Gd/Y (Freitas 1991). Table 2.2 presents experimentally determined thicknesses of nonferromagnetic layers corresponding with the first antiferromagnetic peak and the period of oscillation. Table 2.2 Experimentally determined thickness of nonferromagnetic layer corresponding with the first AF peak (t1max) and period of oscillation ( t) in selected typical sandwich structures. t1max [nm]

t [nm]

Reference

Co/Cr

0.7

1.8

Parkin et al 1990

Co/Cu

0.8

1.0

Parkin et al 1991

Co1.5/Mo

0.52

1.1

Parkin 1991

Co/Ru

0.3

1.2

Parkin et al 1990

Co/Rh

0.79

0.9

Parkin 1991

Co/Ir

0.4

0.9

Parkin 1991

Fe/Cu

1.4

1.2

Petroff et al 1991

Fe/Cr

0.9

1.8

Parkin et al 1990

Structure

NiFe/Cu

0.9

1.1

Czapkiewicz 1999

NiFe/Au

1.2

1.0

Parkin 1996

Figure 2.17 Experimentally determined variation of the MR ratio as a function of the thickness of Cu layer (T 4.2 K) (Petroff et al 1991).

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The period of oscillation depends on the material of the spacer and for most materials it is equal to 0.9–1.1 nm, with the exception of Cr (1.8 nm). Moreover it depends on the crystal structure and growth direction of both ferromagnetic and nonferromagnetic layers (Coehoorn 1991). For example for fcc Co/Cu(111) multilayers the period of oscillation is between 1.2 and 1.5 nm, but for fcc Co/Cu(100) this period is between 5.5 and 7.2 nm. Figure 2.17 presents the experimentally determined dependence of the magnetoresistance on the thickness of the nonferromagnetic layers for two typical multilayers (Fe 1.5/Cu tx) 507 and (Co 1.5/Cu tx) 30. Although the period of oscillation is similar in both cases the oscillations have opposite phases. Designers of GMR multilayer sensors need to calculate the nonmagnetic layer thickness as identical to the maximum value of magnetoresistance (peak values of thickness corresponding with antiferromagnetic coupling). Due to the oscillatory behaviour of the spacer thickness a small deviation from tmax may cause quite a large decrease of magnetoresistance. The magnetoresistance

Figure 2.18 Dependence of the saturation field Hs, magnetoresistance R/R and sensitivity S on the spacer thickness determined for NiFe/Cu multilayer structure (Czapkiewicz 1999).

7 The notation of the multilayer structure should be understood as follows: Si(111)/Cr10/[Fe 2/ Cr tcr]N/Ta 5 means that a layer of Cr with thickness 10 nm was deposited on the silicon (111) surface, next was deposited a multilayer structure consisting of N double layers 2 nm Fe and tcr nm Cr and finally a Ta 5 nm capping layer was deposited.

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for the second peak t2max is smaller than for the first peak t1max. However, at the same time exchange coupling diminishes (faster than magnetoresistance) with decrease of the thickness of the spacer. This may result in a larger sensitivity of the sensor obtained for the second peak than the first peak. Figure 2.18 illustrates the experimentally determined dependence of magnetoresistivity on the thickness of copper layer R/R f(tcu) and the same dependence of the magnetic saturation field Hs f(tcu) for the NiFe/Cu sandwich structure. The sensitivity R/R:Hs f(tcu) has also been calculated. The sensitivity for the second peak was two times larger than for the first peak. More precise investigations of exchange interlayer coupling have indicated that besides the oscillations presented above (long-term oscillations) oscillations with higher frequency (short-term oscillations) also existed. Figure 2.19 presents the results of investigations of the Fe/Cr/Fe structure using scanning electron microscopy with polarization analysis (SEMPA) reported by Unguris and co-workers (1991). The two different periods of oscillation were revealed. This observation was confirmed by other authors. Figure 2.19(b) presents results reported by Fuss and co-workers (1992). Only the antiferromagnetic part of the oscillations could be analysed. In the sandwich Fe/Au/Fe structure apart from long period oscillations with 1 1.6 nm short period oscillations with the period 2 0.4 nm were detected. Short period oscillations are not always detectable because they strongly depend on the roughness of the layer (Bruno and Chappert 1991). Moreover evidence of varying oscillation with the thickness of the ferromagnetic layer has also been detected (Okuno and Inomata 1994). Taking into account the two periods of oscillations the total coupling coefficient J1 is a superposition of two sine waves:

[ (

)

(

)]

1 2 · t 2 · t J1(t) — J11 sin ——– 1 J12 sin ——– 2 t2 1 2

.

(2.3)

Figure 2.19 Results of the experiments confirming the short period oscillations of coupling: (a) by Unguris et al 1991 and (b) by Fuss et al 1992.

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The following parameters of oscillation have been determined for the Cu interlayer: long period oscillations 1 2.6 ML, short period osillations 2 8 ML (ML – thickness of the atomic monolayer, in the case of Cu 1 ML 0.18 nm). The ratio of amplitudes J11/J12 was about 1.2. The phases of both oscillations was determined as 1 14.2 and 2 14.5 (Bloemen et al 1993, Allenspach and Weber 1998). The experimentally determined large value of exchange coupling indicates that its origin must be electronic. Equation (2.3) is similar to the formula describing the oscillatory interaction between magnetic impurities given by the RKKY 8 theory. This resemblance suggested that the origin of both effects might be the same. Therefore the RKKY theory is very often adapted to describe exchange coupling in multilayers (Bruno and Chappert 1991, Baltensperger and Helman 1990, Bruno and Chappert 1992, Mathon et al 1992, Yafet 1990, Bruno 1993, Chappert and Renard 1991, Bruno 1994, Bruno 1995). The RKKY theory analyses indirect exchange coupling between isolated spins mediated by the spin polarization of the conduction electrons. Adaptation of this theory was based on the assumption of a uniform continuous spin distribution within the ferromagnetic layers (Baltensperger and Helman 1990). The period of oscillation depends on the properties of the Fermi surface curvature in the spacer layer. For layers consisting of spins Si located at atomic positions Ri the RKKY interaction is described by Hij J(Rij )Si · Sj

(2.4)

where the exchange integral J(R) for the free electron approximation is given by the expression (Bruno and Chappert 1992): 4 4A2mk 4F J(R) ———— F(2kF R) (2)3h– 2

(2.5)

x cos x sin x cos x F(x) ——————– ——– 4 x x3

(2.6)

and the range function is

where: kF – Fermi wave vector. For two layers separated by distance D and with uniform distributions Ns of spins formula (2.5) may be rearranged to the following form

8 RKKY is an abbreviation derived from the names: Ruderman, Kittel (1954), Kasuya (1956) and Yosida (1957).

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mA2S 2Ns2 kF2 J1 ————— Y(2kF D) 42h– 2

(2.7)

sin x Y(x) ——–. x2

(2.8)

This means that the coupling coefficient oscillates as sin(2k F D)/D 2 and the period of oscillation is /k F (decay of oscillations is 1/D 2). Assuming a spherical Fermi surface for Cu the theoretical value of the period of oscillation is F /k F 0.231 nm (Coehoorn 1991), whereas the experimental results reveal a much larger value, about 1 nm (see table 2.2). As noted by Coehoorn (1991) the discrete nature of the interlayer thickness D should be taken into account. The thickness can only be equal to the multiple of thickness d of the atomic monolayer – D (n 1)d. The oscillations of the coupling can only be sampled at discrete planes of the crystal lattice (aliasing). The resultant period after taking into account the reciprocal lattice vector q is given by (Bruno and Chappert 1992): 2 —————. 2 q n —– d

(2.9)

Figure 2.20 illustrates the effect of aliasing between the Fermi wavelength and lattice periodicity. The long beat frequency corresponds to the wavelength of the envelope wavefunction. But even by considering the lattice periodicity the proposed RKKY model is still not complete because it does not take into account all the topological properties of the Fermi surface. Such a complex

Figure 2.20 Oscillations of exchange coupling calculated by Bruno and Chappert (1992) using the RKKY model.

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system has been considered by Bruno and Chapert (1992). They proposed the following expression describing interlayer coupling

∑—–m sin(q

A 2 m d2 J1(z) —– S 2 ———– —– Vo 162h– 2 z 2

( )

m*

z

)F(z,T)

(2.10)

where: m*,qz, – parameters connected to the Fermi surface and Vo is the atomic volume. This rather complicated model allowed the authors to analyse various structural influences, in more detail, for example influence of misfit dislocations, strain and interfacial roughness. Especially important are conclusions devoted to the roughness. The roughness may drastically influence the period and magnitude of the oscillations. Figure 2.21 presents the results of calculation of the interlayer coupling determined for smooth and rough interfaces.

Figure 2.21 Effect of roughness on interlayer coupling – calculated by Bruno and Chappert (1991) using the RKKY model.

The above model has been tested using noble metals, because they possess relatively simple Fermi surfaces known from de Haas–van Alphen experiments (Halse 1969). Table 2.3 presents the reported results. Table 2.3 The period of oscillations obtained experimentally and from RKKY theory (Bruno and Chappert 1992) Spacer

System

RKKY model

Experiment

Cu(111)

Co/Cu/Co

4.5 ML

5 ML

Cu(001)

Co/Cu/Co

12.6 ML 25.9 ML

12.6 ML 28 ML

Au(001)

Fe/Au/Fe

12.6 ML 28.6 ML

12 ML 27–8 ML

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The theoretical results correspond fairly well with experimental ones. But this relates only to the periods of oscillation. Results of modelling the magnitude of oscillations are not so satisfactory. The reason is that the RKKY model mainly describes effects in the spacer, which are responsible for the period of oscillation. The magnitude of the oscillations depends on effects in the ferromagnetic layer. The RKKY model is not appropriate for ferromagnetic 3d transition metals and this is its main disadvantage. A variety of other theoretical models have been proposed to explain exchange coupling. The comparative review of these models is given in Jones (1998). For example the tight-binding model based on the Haas–van Alphen effect has been used to describe exchange coupling in multilayers (Mathon et al 1992, Edwards 1991, Itoh et al 1993, Nakanishi et al 1993). The s–d mixing model (Wang et al 1990, Levy et al 1993) has also been used in this context. Significant progress in modelling exchange coupling was made when quantum well states were used to explain oscillatory coupling (Ortega and Himpsel 1992, Ortega et al 1993, Himpsel 1991, Himpsel et al 1998). Quantum well states are the effect of tailoring electronic properties when the material is in the nanometre scale. The wavefunctions of electrons change when they are confined to dimensions comparable with their wavelength. Figure 2.22 presents a comparison of the density of states in bulk material and multilayer structure. The continuous bulk band breaks into discrete states. The wavefunction for the quantum well state consists of a fast oscillating Bloch wave modulated by an envelope function. The period of the envelope env depends on the inverse of the distance between the Fermi wave vector kF and the Brillouin zone boundary kZB (Ortega and Himpsel 1992): env ————. kZB kF

(2.11)

Figure 2.22 A band calculation for an 11-layer slab – quantum well states in a thin film (Himpsel 1998).

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Figure 2.23 The model of the quantum well states formed by reflection of electrons at the interfaces (Himpsel and Rader 1995).

This modulation resembles the above described aliasing of two waves dependent on kF vector and on the reciprocal-lattice vector q /kZB as applied in the RKKY model. The quantum well states are formed by reflection of electrons at the interfaces. This reflection is spin-dependent as illustrated in figure 2.23. Several authors have proposed more precise models of exchange coupling effects in multilayers using the quantum well theory (Bruno 1994, Stiles 1993, Mathon 1995, Jones and Hanna 1993). The most comprehensive model proposed by Bruno (1995) will now be described. The quantum interference model proposed by Bruno describes exchange coupling as spin-dependent reflections of Bloch waves at the multilayer interface. This model can be compared to an optical interferometer (for example Fabry–Perot) (see figure 2.23). The conduction electrons represented by a Bloch wave travel across the nonmagnetic spacer. At the boundary of the spacer (at the interface) they are partially reflected. The reflected Bloch wave interferes with the incoming wave and a standing wave may arise depending on the thickness of the spacer. The part of the wave that was not reflected at the interface may interfere with the magnetic layer. As the reflection is spin–dependent, reflection can be described by the coefficients: r↑ r↓ –r ——— 2

and

r↑ r↓ r ———. 2

(2.12)

The exchange coupling coefficient J1 can be described by the following expression: 1 h– 2k 2 r↓2 2ik D J1 ——– ——–F Im —– e F 1 2 1 r↓2 42D 2 2m 2

{

[

(

)(

kF L 2 2ik ↓L 1— — e F kF↓ D

) ]}

(2.13)

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where: r↓ – coefficient for the semi-infinite layer. Using formula (2.13) it is possible to calculate the oscillation as the dependence on the thickness of the nonferromagnetic layer (figure 2.24(left)). Several experiments have reported evidence of the dependence of oscillations with the thickness of the ferromagnetic layer (Okuno and Inomata 1994, Bloemen et al 1994). This may be confirmed using the quantum interference model as illustrated in figure 2.24(right). This approach can also be used to calculate coupling effects in various spacer materials, including the insulating layer in tunneling GMR sensors.

Figure 2.24 The oscillations of the coupling coefficient as a function of nonmagnetic layer thickness and ferromagnetic layer thickness (calculated by Bruno using the quantum interference model – Bruno 1994).

Similarly to the RKKY model parameters describing the Fermi surface have been introduced to expression (2.13). Expression (2.13) is enhanced to the following formula – ⊥ hv

r r e ∑———– 4 D

J1 Im

2

2

A

(

)

2kBTD F ———– . – ⊥ hv

iq⊥D B

(2.14)

A special concept of a complex Fermi surface has been proposed to describe the Fermi surface applicable to the quantum well state model (Bruno 1995). The parameters describing this complex Fermi surface can be introduced in formula (2.14). As Bruno proved the proposed quantum interference model can be treated as an enhancement of earlier existing models.

2.1.3 Other coupling effects in multilayer structures Oscillatory exchange coupling is crucial in the sandwich type structure of GMR sensors. But it is not an exclusive condition to obtain the GMR effect. Exchange coupling is just one way of ensuring initial antiparallel magnetizing of the ferromagnetic layers. In some systems, for example in spin-valve structures,

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oscillatory exchange coupling is not necessary. These systems are sometimes called uncoupled systems (Velu et al 1992, Speriosu et al 1991). In fact they are coupled but by other mechanisms and the coupling field is much smaller than in exchange-coupled structures. Figure 2.25 presents the results of investigations into the relation between the coupling field and magnetoresistance in spin-valve structures reported by Speriosu and co-workers (1991). Although the coupling field oscillated according to the RKKY model, surprisingly the magnetoresistance decreased monotonically with increasing thickness of the non-magnetic layer. The authors concluded with a rather extreme suggestion that both behaviours, coupling and GMR, had entirely different origins.

Figure 2.25 The coupling field and magnetoresistance as a dependence on the spacer thickness (determined by Speriosu et al 1991) for Ru2/Cu 1.2/Co 3/Cu tcu/Co 3/FeMn 15 spin-valve structure.

Similar results for spin-valve structures were reported a few years later by Anthony and co-workers (1994). As presented in figure 2.26 the coupling field oscillates with a typical period for Cu. Above a thickness of about 2 nm the coupling is only ferromagnetic. These effects can be explained by taking into account the results of investigations of interlayer coupling reported by Kools et al (1995).

Figure 2.26 The coupling field and magnetoresistance as a dependence on the spacer thickness (determined by Anthony et al (1994) for NiFe 10/Co 2/Cu 2.4/Co 2/NiFe 3/MnFe 15 spin-valve structure.

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Figure 2.27 The coupling fields in spin-valve structures determined by Kools et al (1995) (a) and Leal and Kryder (1996) (b).

The real spin-valve structure is much more complex than a relatively simple multilayer structure. The coupling field in spin-valve structures is the result of several components. Figure 2.27 presents the results of investigations of the coupling field in spin-valve structures reported by two groups – Kools et al (1995) and Leal and Kryder (1996).

Figure 2.28 The coupling effect caused by ‘pin holes’ (a) and roughness of the multilayer structure (b).

The origin of the very large coupling field for very thin (below 1 nm) nonmagnetic layers is obvious. In this range of thickness the effect of bridging sites (defects) causing direct contact between ferromagnetic layers (figure 2.28(a)) may be expected. This mechanism is sometimes called the ‘pin holes’ effect. For larger thicknesses of nonmagnetic layers the shift of the coupling value from antiferromagnetic to ferromagnetic is caused by an additional ferromagnetic component. The origin of this effect was described by Neel (1962) as the influence of magnetostatic coupling caused by correlated waviness of non-ideal flat layers (figure 2.28(b)). This coupling depends on the roughness of the layers and is sometimes called ‘orange peel coupling’ or ‘Neel coupling’. The resultant coupling coefficient is the sum of both RKKY-like and ‘orange peel’ components:

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THIN FILM MAGNETORESISTIVE SENSORS –— Jo 2 · tcu 2 h 2

2√2tcu J —– sin ——— —– — ( M · M) exp ————– (2.15) – o 2 t cu √2

(

)

where: h and are the magnitude and wavelength of the waviness.

Figure 2.29 Coupling energy determined by Leal and Kryder (1996) for two samples with different roughness.

Leal and Cryder (1996) demonstrated experimentally the dependence of interlayer coupling on roughness. The coupling energy was determined for two samples with different roughnesses (figure 2.29). After determination of the parameters of roughness (h and ) the Neel coupling energy was calculated. The results confirmed the analytical model of coupling consisting of both components. Because roughness is not an intrinsic parameter of the structure, but depends on the technology, the problems of roughness will be described in more detail in the sections devoted to technological factors.

Figure 2.30 The magnetizing curve of Fe/Ag/Fe multilayer determined for two thicknesses of Ag layer: (a) 1.6 nm; (b) 2.5 nm. For t 1.6 nm the antiparallel coupling is not perfect and biquadratic coupling effects are visible (Leng et al 1993).

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The experiments revealed the existence of an additional second-order coupling effect – biquadratic coupling (90° coupling). For example domain observation (using the Kerr effect) of wedged interlayer structures (Leng et al 1993, Fert et al 1995) indicated that for certain thicknesses of the spacer areas appeared with domains of 90° alignment. Figure 2.30 presents the results of investigations showing the magnetizing curve with fragments corresponding to 90° coupling (Leng et al 1993). The biquadratic coupling may significantly deform the resultant transfer characteristic R/R f(H). Figure 2.31 presents the R/R f(H) dependence determined for two thicknesses of interlayers. For small deviations from antiferromagnetic coupling, biquadratic coupling occurred and consequently the transfer characteristic was deformed.

Figure 2.31 The transfer characteristics of the NiFe/Cu/NiFe multilayer determined for two thicknesses of the Cu layer For t 1 nm the antiparallel coupling is not perfect and the biquadratic coupling effect is visible (Pettit et al 1997).

Taking into account the evidence of biquadratic coupling the coupling energy per unit area can be described by the expression:

(

)

M1 · M2 M1 · M2 2 W J1 ———–

J2 ———– J1 cos J2 cos2 . (2.16) M1 M2 M1 M2 The origin of the biquadratic coupling is not fully clear. From the theory of coupling the biquadratic component is not surprising. Taking into consideration that energy may be expanded by powers of cos (equation 2.16) Bruno (1995) developed the expression describing the coupling coefficient (2.13) to the following formula 2n r2n e2nikFD h– 2kF2 Jn ———– Im —————— . 82mD 2 n3

(

)

(2.17)

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Figure 2.32 The bilinear J1 and biquadratic J2 coefficients determined theoretically by Barnas and Grünberg (1993).

Calculated values of biquadratic coupling coefficients are much smaller than those derived from experiments. Other theoretical models (Barnas and Grünberg 1993, Edwards et al 1993) also reported smaller calculated values of J2. Figure 2.32 presents the results obtained by Barnas and Grünberg. Thus biquadratic coupling is not the only intrinsic behaviour of multilayer structures and extrinsic factors should be considered. Slonczewski (1991) using the periodic terraces mode demonstrated biquadratic exchange coupling in an epitaxial trilayer with non-magnetic layer of changing thickness. He concluded that the biquadratic coupling arises from the spatial fluctuations of macroscopically bilinear coupling. These microfluctuations were caused by local thickness fluctuations. In fact other analyses and experiments confirmed that the main reasons of biquadratic coupling were various kinds of surface defects, like pinholes, roughness or impurities (Ribas and Dieny 1992, Pettit et al 1997, Azevedo et al 1996, Chesman et al 1997, Azevedo et al 1998, Chesman et al 1998). Slonczewski (1995) proposed the following expression to describe the coupling coefficient 4( J1)2 L ·t J2 ———— coth —— 3 A L

( )

(2.18)

where: A is the exchange stiffness constant of the Fe layer, L is the terrace width and t is the Fe layer thickness. A comprehensive analysis of biquadratic coupling in magnetic thin-film trilayers was reported by Rezende and co-workers (Rezende 1999, Rezende et al 1998). They used various independent techniques, such as the magneto-optic Kerr effect (MOKE), Brillouin light scattering (BLS) and ferromagnetic resonance (FMR). Figure 2.33 presents an example of their results. After analysis they concluded that biquadratic coupling could not be attributed to intrinsic mechanisms. But also that

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Figure 2.33 The results of analysis of bilinear and biquadratic coefficients reported by Rezende et al (1999): (a) the dependence of the exchange coupling constants on spacer thickness; (b) the dependence of the exchange coupling constants on temperature.

the exchange fluctuation mechanism did not fully explain all the effects, especially the dependence of J2 on temperature (Gutierrrez et al 1992).

2.1.4 Theoretical models of giant magnetoresistance The effect of enormous changes of resistance in ultrathin magnetic film multilayers is called the giant magnetoresistive (GMR) effect. The GMR multilayer consists of at least two ferromagnetic films separated by a third film of non-ferromagnetic material. The resistance of this sandwich structure depends on the relative alignment of magnetizations in the ferromagnetic films. This resistance is largest when the films are magnetized antiparallel and smallest when they are magnetized in a parallel manner. The change of alignment of magnetizations (and of course the change of the resistance) is caused by applying an external magnetic field. Experimentally it has been shown (Dieny 1995) that the GMR effect is nearly the same for the current flowing parallel or perpendicular to the magnetization in the layer. Compared to the anisotropic magnetoresistive (AMR) effect the giant magnetoresistive effect is isotropic. As the GMR effect arises in ultrathin films with dimensions comparable to the atomic scale it is a very attractive target for fundamental physics. The analysis of the phenomenon of giant magnetoresistance may help to develop knowledge about atomic structures and interactions. No wonder that a huge number of papers devoted to the theory of magnetoresistance has appeared. Several scientific workshops and conferences devoted to this subject have also been organized, for example ‘The International Workshop on Spin Polarized Electron Transport’ held in Miami in 19959. The theoretical model of GMR effects might be the subject of a special book. More details can be found in several comprehensive reviews on the 9

Spin polarized electron transport, Special issue of J. Magn. Magn. Mat., 151 (1995), 315–432.

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theory of giant magnetoresistance (Levy 1994, Nesbet 1998, Levy and Zhang 1995). In this section only the most important milestones in development of the theory of GMR will be presented. Almost all models utilize the classical two-current model introduced by Mott (Mott and Wills 1936). The resistor network model proposed by Edwards and coworkers (Edwards et al 1991) and the model of scattering in superlattices proposed by White (1992) are commonly used to explain the physical origin of magnetoresistance. Two main approaches are used – the semiclassical model (based on Fuchs–Sondheimer theory) introduced by Camley and Barnas (1989) and the quantum model (based on Kubo formula) developed by Levy and co-workers (Levy 1994, Levy and Zhang 1995, Levy and Zhang 1991, Levy et al 1990, Zhang et al 1992, Zhang and Levy 1993). Two current Mott mechanisms can be explained on the schematic diagram of the density of states presented in figure 2.34. The energy bands for noble metals are the same for electrons with different spins. But the energy bands for ferromagnetic materials split into two sub-bands, one in which electrons have their spin parallel to the magnetization (spin-up electrons) and the other in which spin is antiparallel to the magnetization (spin-down electrons). The difference in the density of states at the Fermi level for spin-up and spin-down d electrons leads to different scattering rates. For example in ferromagnetic metals the spin-up band is full and s-d scattering is not possible. On the contrary for the spin-down band s-d scattering is possible. Consequently scattering of the spin-down electrons is more effective than spin-up electrons. In the two-current model proposed by Mott it is assumed that there are two independent conduction channels, corresponding to the spin-up and spin-down electrons. These two channels are characterized by different mean free paths and resistivities. The spin-up electrons (with spin parallel to magnetization) are scattered very weakly in comparison with the spin-down electrons. It has been estimated that the mean free path of spin-up electrons may be five times longer than for spin-down electrons (Dieny 1994).

Figure 2.34 The density of states N(E) in non-magnetic and ferromagnetic metals.

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Figure 2.35 The density of states in cobalt–copper–cobalt trilayer calculated by Butler et al (1995).

The spin-dependent scattering has been analysed using first principle calculations by Butler and co-workers (1995). Figure 2.35 presents the calculated Fermi energy density of states for each atomic layer in the Co/Cu/Co trilayer. The density of states in the minority channel (in the spin-down channel) is approximately seven times greater than in the majority channel (in spin-up channel). Because the scattering rate is proportional to the density of states at the Fermi energy it means that for spin-down electrons scattering is much larger than for spin-up electrons. As spin-dependent scattering of conduction electrons is the primary source of the GMR effect it is important to establish the location and sources of the scattering. Two locations of the scattering may be considered – bulk scattering (inside the layer) and interface scattering (at the interface between layers). Experimental studies (Parkin 1993) and theoretical calculations (Butler et al 1995) emphasize the importance of scattering at the interfaces. It has been established that to obtain the GMR effect the thickness of the layer should be smaller than the mean free path of an electron. This condition is

Figure 2.36 The spin-dependent scattering of electrons in the multilayer with magnetization aligned parallel (a) and antiparallel (b) (White 1992).

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normally fulfilled, as the typical mean free path is about 20–40 nm. (for Cu mfp 40 nm, for NiFe mfp 20 nm). The heuristic model of scattering in the multilayers introduced by White (1992) is presented in figure 2.36. From the model presented in figure 2.36 it appears that for the antiparallel alignment of magnetizations probability of scattering is equal for both classes of electrons. But for parallel alignment spin-up electrons are privileged – they can traverse the layers without scattering over much larger distances. A longer mean free path lo of an electron in the material means smaller resistance, because resistivity depends on lo: mv —— nq2lo

(2.19)

where: m – mass of an electron, v – average velocity of an electron in the material, n – number of conduction electrons, q – charge of an electron. From figure 2.36 it is evident that in the case of parallel alignment spin-up electrons twice cross the layer of small resistivity M↑, while spin-down current twice cross the layer of large resistivity M↓. This situation is represented as the resistor network presented in figure 2.37(a), as it can be assumed that these two currents flow independently. In the case of antiparallel alignment both spin-up and spin-down electrons cross small M↑ and large M↓ resistivity. This situation corresponds to the network presented in figure 2.37(b).

Figure 2.37 Network model of spin-dependent scattering presented in figure 2.36.

Thus parallel alignment can be described by the following expression: 2↑↓ F —————— ↑ ↓

(2.20)

and antiparallel alignment by the expression: ↑ ↓ AF ——————. 2

(2.21)

Taking into account equations (2.20) and (2.21) the coefficient of magnetoresistivity may be described as:

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AF F 1 —— ————— ——— AF 1

(

2

)

(2.22)

where: M↓/M↑. Butler and co-workers (1995) calculated values of the resistivities M↓ and M↑ and obtained the following results for the Co/Cu multilayer structure: M↓ 80 cm and M↑ 5 cm. These results led to / 78%. Taking into account the resistivity of the non-ferromagnetic layer N↑ N↓ N (eight-resistor network) Edward and co-workers (1991) obtained the following expression: (↑ ↓)2 —— ————————— d d 4 ↑ – ↓ – t t

(

)(

)

(2.23)

where: ↑ M↑/N, ↓ M↓/N, d – thickness of the spacer, t – thickness of the ferromagnetic layer. The magnitude of / depends on the scattering asymmetry. It decreases with increasing thickness of spacer layer. In the semiclassical model introduced by Camley and Barnas (1989) two spin-up and spin-down currents are described by relaxation times ↑ and ↓ and transmission coefficients T↑ and T↓ corresponding to the fraction of electrons that coherently pass across the layer. For each sub-layer the Boltzman equation can be written in the form (Barnas et al 1990): g↑(↓)(z,v) g↑(↓)(z,v) eE fo(v) ———— ———— —– ——– z ↑(↓)vz mvz vx

(2.24)

where: E – electric field, v – velocity of the electron, fo – equilibrium distribution function, g – correction to the distribution function due to scattering: g↑(↓)(z,v) f ↑(↓)(z,v) fo (v).

(2.25)

The general solution of (2.24) for each sub-layer takes the form eE ↑(↓) fo (v) z g↑(↓)(z,v) ——— —–— 1 F↑(↓)(v) exp ———– m vx ↑(↓) vz

[

(

)]

(2.26)

where: corresponds to vz0 and vz0 and function F(v) can be determined from the boundary conditions. After computation of the g↑(↓)(v,z) in each sub-layer it is possible to determine the current I (per unit length along the y axis) from the formula:

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THIN FILM MAGNETORESISTIVE SENSORS I edzdv[g↑(v, z) g↓(v, z)]vx.

(2.27)

Knowing the current it is possible to find the resistance for both parallel and antiparallel configurations and hence the magnetoresistivity coefficient. Camley and Barnas tested their theoretical model for Fe 12/Cr 1/Fe 12. A comparison of calculated results with experimental results is presented in figure 2.38.

Figure 2.38 The comparison of results calculated by means of the theoretical semiclassical model with experimental data (Camley and Barnas 1989).

Many groups have enhanced the theoretical model of Camley and Barnas (Barnas 1994, Johnson and Camley 1991, Trigui et al 1991, Vischer 1994, Berhelemy and Fert 1991, Inoue and Maekawa 1991, Dieny 1992, Hood and Falicov 1992). For example, Barthelemy and Fert (1991) developed the semiclassical approach in order to analyse the influence of various parameters, such as layer thickness and mean free path lo, on the magnetoresistivity coefficient. In the case of Fe/Cr multilayers this coefficient can be calculated from the equation

tcr exp —— R 3 lo —– – (T↓ T↑)2 ————— . RAF 2 tfe tcr 2 —– —– lo lo

( ) ( )( )

(2.28)

The graphical solution of an equation (2.28) is presented in figure 2.39. The semiclassical models are not adequate for very thin films because they omit quantum size effects. A comparison of semiclassical and quantum models indicated that the quantum model better agrees with experimental results when the layer thickness is much smaller than the mean free path.

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Figure 2.39 Dependence of the magnetoresistivity on the thickness of the layers in the multilayer structure, calculated by Barthelemey and Fert (1991).

Quantum models allow better analysis of spin-dependent bulk scattering and transmission at the interfaces especially for t lo and high resistivity of the film material. The quantum theory of transport and surface scattering was introduced by Tesanovic and co-workers (Tesanovic et al 1986). Levy and co-workers developed this theory for multilayer structures (Levy 1994). The analysis of conductivity and magnetoresistance in ferromagnetic multilayers starts from the determination of the Hamiltonian HM and current-field relation jf(E) as follows (Levy 1994): p2 p2 ^ ^ HM —– VMpot (r,) Vscat —– VMpot (r,) ∑(va jM a · )!(r ra) (2.29) 2m 2m a j(r) d3r (r,r ) · E(r )

(2.30)

where: j(r) is the two-point conductivity at a point r related to the electric field E at r; (r,r) is the microscopic conductivity given by Kubo’s linear response formalism, !(r-ra) represents a short-range impurity potential. The dependence of the scattering potential V(r,s) on magnetization M, interface roughness f() in the zl position of the lth interface is described by (Fert and Bruno 1994): ^ ^ ^ ^ ^ V(r, s) ∑(v jsM · )fl()!(z zl ) ∑(vb jb Mi · !(r rj ) ∑vb ! (r rj ) l

l

s

(2.31) ^

where: represents the Pauli spin matrix.

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Figure 2.40 Position-dependent conductivity (a), and magnetoresistance as a function of the spacer thickness (b) (determined by Zhang, Levy and Fert by means of the quantum model of magnetoresistivity (Levy et al 1990, Zhang et al 1992)).

After rather sophisticated calculations it is possible to determine the positiondependent conductivity as well as the dependence of the magnetoresistance on the thickness of the layers. Two examples of such calculations are presented in figure 2.40. Figure 2.40(a) presents the results of calculations of the conductivity as a function of the position in the Fe/Cr multilayer structure. Figure 2.40(b) presents the results of calculations of magnetoresistivity as a function of the thickness of the layer in the multilayer structure. For the spinvalve structure, calculations by means of the quantum theory have been described by Vadyayev and co-workers (1992). As the problem of modelling magnetoresistance is very complex all theoretical models are of rather a qualitative nature, although some results are very close to experimental ones (for example the results presented in figure 2.41

Figure 2.41 The comparison of theoretical (quantum model) and experimental data reported by Levy and Zhang (1991) (L and T – longitudinal and transversal resistivity respectively).

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and reported by Levy and Zhang). It is not realistic to expect that the theoretical model could help in the design of magnetoresistive sensors, but the models are very useful in understanding the origin of the GMR phenomenon. Methods of modelling the transport properties of ferromagnetic multilayers are still in progress. Lately several groups have used the Korring–Kohn–Rostocker (KRK) Green’s function in numerical methods to calculate ab initio parameters of electrical transport in ferromagnetic multilayers (Butler et al 1995, Zahn et al 1995, Mertig et al 1995). These models may be used to optimize the material composition and dimensions of GMR sensors. Butler and co-workers (1999) have demonstrated first principles methods of modelling GMR devices – random access memory structure.

2.1.5 Ferromagnetic multilayers as magnetic field sensors For users of GMR sensors the most important feature is the dependence of the output signal R/R on the applied measured magnetic field strength or flux density – R/R f(H) or R/R f(B). Figure 2.42 presents typical characteristics of GMR sensors with antiferromagnetic exchange coupling.

Figure 2.42 The typical transfer characteristic of the GMR multilayer structure: (Co 1.5/Cu 0.9) 30 multilayer at 4.2 K (Fert et al 1992).

It may be assumed that the dependence R/R f(H) for GMR sensors with antiferromagnetic exchange coupling is near-parabolic (sometimes it is bellshaped, sometimes it is more pyramid-like shaped). From experiments it is known that the resistance of multilayer varies as cos("1–"2) (Dieny et al 1991, Bertram 1995), where "1, "2 are the angles of magnetization of the two magnetic layers, as shown in figure 2.43. Thus the resistance of the multilayer can be calculated as

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THIN FILM MAGNETORESISTIVE SENSORS (Rap Rp ) R(H) Rp ————– [1 cos("1 "2)] 2

(2.32)

where: Rp and Rap represent the resistance in the parallel and antiparallel magnetic configurations. The values of the angles "1 and "2 can be determined by minimizing the total energy per unit area W. This energy for the structure is presented in figure 2.43(a) and describes the following expression (Fujiwara and Parker 1994): W o MHt [cos ( "1) cos ( "2)] o Kt (sin2 "1 sin2 "2) o J1 cos ("1 "2)

(2.33)

where: H – applied measured field, K – anisotropy constant, J1 – exchange coupling constant, t – thickness of magnetic layers, M – magnetization of the layers (it is assumed that both magnetic layers are identical and M1 M2).

Figure 2.43 The exchange couple multilayer sensor: structure (a) and orientations of the magnetization vectors (b) in the calculated model (Fujiwara and Parker 1994).

In expression (2.33) the dimensional effects (shape anisotropy, current induced fields) are neglected – they will be considered later. Taking into account that: 2K Hk —– M

and

4J1 H1 ——— lo Mt

(2.34)

and assuming that the measured field in the hard axis direction ( /2) equation (2.33) may be rewritten as 1 W o MtH(sin "1 sin "2) – o MtHk (sin2 "1 sin2 "2) 2 1

– o MtH1 cos("1 "2). 4

(2.35)

Taking into account symmetry and "1 "2 " equation (2.35) can be simplified to:

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1 W o MtH sin o MtHk sin2 – o MtH1 cos 2. 4

(2.36)

Differentiating W with respect to and setting the derivative to zero yields H sin ————. Hk H1

(2.37)

Inserting this expression into (2.32) leads to

[

]

H2 R(H) Rp (Rap Rp) · 1 ————– (H1 Hk )2

for H Hk H1.

(2.38)

Because the anisotropy field is much smaller than the exchange coupling field the sensitivity of the sensor depends mainly on the H1 value. The exchange coupling field is practically equal to the saturation field. The R(H) characteristic calculated from expression (2.38) is shown in figure 2.44(a). Its shape is too convex in comparison with that presented in figure 2.42. More complex models have been developed (Fujiwara and Parker 1994, Andrieu 1996, Dieny et al 1990, Dieny and Gavigan 1990, Fujiwara 1995). Fujiwara and Parker also have included the biquadratic component Wbq in the energy aggregate Wbq J2 cos2 (1 2).

(2.39)

The total energy sum can be expressed in the form: H (,) Hk sin2 – cos2 cos2 – sin2 —–1 cos 2 2 2 H —–2 cos2 2H cos – cos( ) 2 2

[ ()

() ]

()

(2.40)

Figure 2.44 The results of calculations of the transfer characteristic of multilayer sensors: simplified model (a) and Fujiwara and Parker model (b) (Fujiwara and Parker 1994).

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where: 2E/M, the angles and are presented in figure 2.43(b), and the coupling field bilinear (Heisenberg) H1 and biquadratic H2 for 2N magnetic layers are described by the expressions 2(2N 1) J H1 ———–— —1 ; Nt M

2(2N 1) J2 H2 ————– —. Nt M

(2.41)

Equation (2.32) may be substituted by Rap Rp R(H) Rp ———— (1 cos ). 2

(2.42)

The value of the angle can be determined from the equilibrium conditions:

—– 0;

—– 0;

2 2

2 2 —— —— ——– ≥ 0.

2 2

( )

(2.43)

Fujiwara and Parker (1994) found the solution of this problem for various conditions of the sensor work. When the field is applied in the hard direction ( /2 and /2) the solution is in the form h cos – c cos – cos 2 2

(2.44)

where h and c are the fields in the reduced terms: H h ———— ; Hk H1

2H2 c ————. Hk H1

The calculated R/R f(h) dependence for various biquadratic coupling field values is presented in figure 2.44(b). Taking into account the biquadratic exchange term it is possible to describe the transfer characteristics that better match the real ones. It is also possible to analysis hysteresis which sometimes appears when H is in the easy direction ( 0). The spin-valve sensor is more complicated to analyse because both ferromagnetic layers work in different ways (Coehoorn et al 1998, Kools 1996). Figure 2.45 presents typical characteristics of spin-valve sensors. The sensor consists of two hysteresis loops (the second loop in the magnificationfigure 2.45(right)) – one corresponding to the pinned layer and the second corresponding to the free (unpinned) layer (figure 2.46(left)). Usually only the second, small-hysteresis loop is used. In spin-valve sensors it is possible to obtain hysteresis-free quasi-linear dependence R/R f(H) by applying the pinning field perpendicular to the easy axis of the free layer (transverse biasing).

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Figure 2.45 Typical characteristics of the spin-valve sensor (Kools 1996).

In comparison with antiferromagnetic coupling multilayers the expression describing the total energy density should be supplemented by a new term – exchange anisotropy: 1 Wp – o MtHp sin2(p p ) 2

(2.45)

where: p – the angle describing the direction of magnetization vector of pinned layer, p – the direction of the pinning field Hp: Jp Hp ———

o Mt

(2.46)

where : Jp – exchange biasing coefficient. The component representing the coupling energy H1 is now not oscillatory exchange energy (RKKY like) but the much smaller magnetostatic Neel coupling energy (Lin et al 1994). To determine the dependence R(H) in a first rough estimation it can be assumed that the angle p of the pinned layer is fixed and only the angle f of the

Figure 2.46 The spin-valve sensor: structure (a) and orientations of the magnetization vectors (b) in the calculated model.

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free layer changes. By neglecting components that do not change with the magnetic field the expression describing energy may be written as W H cos( f ) –1 Hk sin2 f cos(f p) H1 cos (f p ). 2

(2.47)

In the quasi-linear case the pinned layer is magnetized perpendicularly to the unpinned layer and p /2 and /2. Thus expression (2.47) is now W H sin f –1 Hk sin2 f Hp sin f H1 sin f . 2

(2.48)

The angular dependence f f(H) can be obtained from the equilibrium condition W/ f 0 as H Hp H1 sin ——————. Hk

(2.49)

Inserting this expression into (2.32) leads to Rap Rp H Hp H1 R Rp ———— 1 —————— . 2 Hk

(

)

(2.50)

The R(H) characteristics calculated from expression (2.50) are shown in figure 2.47(a). Sensitivity now depends mainly on the anisotropy of the free layer Hk, which is relatively small. The characteristic R/R f(H) is shifted from zero field due to the influence of the coupling field and the exchange field. In real spin-valve structures the magnetizing process is more complex. Both pinned and free layers may have different thicknesses. The pinned layer also changes the direction of magnetization with magnetic field. Several models more

Figure 2.47 The results of calculations of the transfer characteristics of spin-valve sensors: simplified model (a) and Fujiwara and co-workers’ model (b) (Fujiwara et al 1996).

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exactly describing the transfer characteristics of spin-valve sensors have been proposed (Dieny 1992, Everitt and Pohm 1997, Rijks 1994, Mauri et al 1987, Rijks et al 1997, Parker et al 1995, Folkerts et al 1994). Nishioka et al (1995) have calculated the R(H) dependence by differentiating the energy expressed as: W H[Mtf cos( f ) Mtp cos( p )] K(tf sin2 f tp sin2 p ) J1 cos(f p ) Jp cos(p p ). (2.51) Figure 2.47(b) presents the results of calculations of spin-valve sensors with transverse bias fields (Fujiwara et al 1996). Figure 2.48 presents a comparison of calculated and experimental results (Nishioka et al 1995). In the experiments the coupling field has been varied by changing the non-magnetic layer thickness. By appropriate choice of coupling field it is possible to obtain almost linear, transfer characteristics of the sensor without hysteresis.

Figure 2.48 A comparison of experimental and calculated results of spin-valve sensors: (a) determined experimentally for various thickness of spacer; (b) calculated for various coupling fields (Nashioka and co-workers 1995).

In some applications, for example in memory elements, switching conditions are more important than linearity. Parker and co-workers (1995) developed the analytical model by considering the energy densities of free and pinned layers separately. They differentiated two energy equations in form: 1 1 1 H sin( 1) – Hk1 sin 21 – H11 sin(1 2) – H21 sin 2(1 2) 0 2 2 2 1 1 H sin( 2) – Hk2 sin 22 – H12 sin(1 2) 2 2 1 1 – H22 sin 2(1 2) – Hp sin 2 0 2 2

(2.52)

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where: 2J1 H11 —— ; M1t1

2J1 2J2 H12 —— ; H21 —— ; M2t2 M1t1

2J2 H22 —— ; M2t2

2Kp Hp ——. M2t2

Figure 2.49(a) presents the calculated results of easy-axis switching field characteristics of the spin-valve sensor with pinning direction parallel to the easy axis. Other cases (applied field or biasing field along various axes) can be analysed using this model. An example of hard-axis switching characteristics is presented in figure 2.49(b).

Figure 2.49 The easy-axis (a) and hard-axis (b) switching characteristics of spin-valve sensors (calculated by Parker and co-workers 1995).

When GMR sensors are described in the literature there are no standard parameters reported – various authors use the terms sensitivity, magnetoresistivity ratio and saturation field in different ways. Figure 2.50 presents two typical characteristics GMR sensors – in multilayer and spin-valve structures. The magnetoresistivity coefficient may be described using different definitions, for example a) max min —– ————— ; max

b) max min —– ————— ; min

c) (H 0) min —– ——————— ; (H 0)

d) max min —– 2 —————. max min

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Figure 2.50 Methods of determination of the parameters of GMR magnetoresistive sensors.

In conventional situations when / is relatively small differences between the above described formulas are negligible and usually the change of resistance is related to R(H 0). When the change is ‘giant’ then from the definitions with respect to the maximal value (formula (a) or (c) the maximal magnetoresistance can never be larger than 100%. Meanwhile magnetoresistances as great as 220% or 150% have been reported (Schad et al 1994). From the definitions with respect to the minimal value (formula (b) infinite magnetoresistance is possible. In fact using formula (b) a magnetoresistivity ratio of 108% is reported (Chen et al 1996). Assuming that the sensor is connected into a bridge circuit the output signal is proportional to the relative change of resistance: Uout S·Usupl · R/R. The definition (a) or (c) (with respect to the larger value of resistance) is physically more correct because output voltage cannot be larger than the supply voltage. However, both definitions: (H 0) (H Hs ) —— —————————– (H Hs )

(2.53)

(H 0) (H Hs ) —— —————————– (H 0)

(2.54)

or

are in use. The formula (2.54) is used most often in various reports (probably to emphasize that the effect is really giant). More complicated is the problem of the determination of the sensitivity (and Hs value). Formally sensitivity should be determined as:

—— SH ———

H

(2.55)

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but due to non-linearity of the transfer characteristic the formula is usually substituted by —— max SH ————. H

( )

(2.56)

It is reasonable to determine Hs using the method presented in figure 2.50 – as a prolongation of the tangent to a curve in the operating point. Such a definition will be used in the next sections. In some papers the term FWHM (full width at half maximum) is also used to describe the magnetic field range.

Figure 2.51 Various methods determine the resistance of thin film structure: (a) thin film stripe; (b) four-point method; (c) van der Pauw method (Ohring 1992).

Real sensor structures are rarely used to describe the magnetoresistivity effect in the literature, for example as presented in figure 2.51(a). Usually the resistance is measured on the whole film by means of the four-point method presented in figure 2.51(b). In the four-point method, if the film surface is much larger than the probe assembly and the probe spacing is large compared with film thickness, the resistance can be determined from the expression U U R K — 4.53 —. I I

(2.57)

Sometimes the van der Pauw method is used to determine the resistance (figure 2.51(c)). After alternate contacts of the supply and of the output the resistivity in the van der Pauw method can be calculated from · t UCD · t UDA exp —— —— exp —— —— 1. IAB IBC

(2.58)

After patterning the sensor the resistance may be different than that determined by the four-point method due to the influence of the demagnetizing field.

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2.2 VARIOUS TYPES OF GMR STRUCTURES

2.2.1 Structures with antiferromagnetic coupling GMR structures with antiferromagnetic coupling recently lost the competition to the more sensitive spin-valve structures. But due to the relative simplicity of manufacturing (no need to apply additional exchange pinning layer) they may be attractive for various applications, for example as reading heads for ultrahigh density magnetic recording (Smith et al 1996, Freitas et al 1997). Many combinations of the ferromagnetic/nonferromagnetic layers have been investigated. But only the several most important materials are now in use – Co, Fe, NieFe or NiFeCo alloys separated by Cr, Cu, Ag or Au. Figure 2.52 presents room temperature R/R f(H) characteristics of two typical magnetoresistors with antiferromagnetic coupling – Co/Cu/Co and NiFe/Cu/NiFe. The Co/Cu structure exhibits larger magnetoresistivity than the NiFe/Cu structure but for larger saturation field Hs. The transfer characteristic is usually bell-shaped although almost perfect parabolic shapes or triangular-shapes have been reported. As discussed in previous sections the shape of the transfer characteristic depends on the quality of the coupling. It is very difficult to compare and evaluate the various reported structures, because results are obtained for different conditions: both manufacture and work. The layers are produced using molecular beam epitaxial growth (Farrow 1998, Kamijo 1993), various kinds of sputtering, electron beam evaporation and even the electrodeposition method (Zaman et al 1997, Schwarzacher and Lashmore 1996). Parameters of multilayer systems may change dramatically after annealing (Tosin 1993, Satomi and Sakakima 1993). Magnetoresistance depends on design

Figure 2.52 Typical room temperature transfer characteristics for Co/Cu and NiFe/Cu multilayers: (a) Si/Fe 5/[Co 1/Cu 0.9] 16/Fe 5; (b) Si/NiFe 5/[NiFe 1.5/Cu 0.8] 14 (Parkin 1991, 1992).

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parameters (chemical composition of the layers, thickness of the layers, buffer layer, number of layers) and structure (interface sharpness, crystallization). Various authors have reported the magnetoresistive ratio determined at different temperatures. Table 2.4 and 2.5 show some typical parameters of antiferromagnetic coupled magnetoresistors. Table 2.4 Selected parameters of antiferromagnetic coupled magnetoresistors (T 4.2°K). Structure

R/R [%]

Hs [kA/m]

R/R:Hs [%:kA/m]

Ref

(Co1.5/Cr0.4) 30

2.5

480

0.005

[a]

(Fe0.5/Cr1.2) 50

2201

8000

0.03

[b]

(Fe3.0/Cr0.9) 40

90

1600

0.06

[c]

(Fe1.5/Cu1.5) 60

12

150

0.08

[d]

(Fe1.4/Cr0.8) 50

150

1600

0.09

[e]

(Fe4.2/Cr1.2) 50

70

800

0.09

[f]

(Co0.8/Cu0.8) 60

115

1040

0.11

[g]

(Co0.7/Cu0.9) 16

80

640

0.12

[h]

(Co1.5/Cu0.9) 30

80

480

0.17

[i]

(NiFe1.5/Cu0.8) 14

25

140

0.18

[j]

NiFe1.5/Cu2.0) 14

25

64

0.39

[k]

(CoFe0.4/Ag1.5)

100

240

0.41

[l]

(NiFe2.0/Ag1.0)

50

80

0.62

[m]

a – Parkin 1990, b – Schad et al 1994, c – Baibich et al 1988, d – Petroff et al 1991, e – Fullerton et al 1993, f – Schad et al 1994, g – Parkin et al 1991, h – Parkin et al 1991, i – Fert et al 1992, j – Parkin 1992, k – Parkin – 1992, l – Dieny 1994, m – Rodmacq et al 1993.

The largest magnetoresistive effect was shown in Fe/Cr structures – 220% at 1.5 K (Schad et al 1994). But this large effect is only obtained for large magnetic fields and the sensitivity of the system is rather small. The most frequently used are Co/Cu multilayers2 (with room temperature sensitivity about 0.08) and NiFe/Cu multilayers (Sato et al 1993, Kitada and Nakatani 1993, Nakatani et al 1992, Dei et al 1993) (with sensitivity about 0.3). The largest room temperature sensitivity was obtained in NiFe/Ag multilayer structures. A sensitivity of 7.5%/kAm1 (0.6%/Oe) has been reported (Andrieu 1996). Unfortunately this structure is not thermally stable after annealing at high temperature (above 300°C) (Parker 1996). It may be an important Measured at 1.5 K. For example: Grundy et al 1993, Mosca et al 1991, Mao et al 1997, Kobayashi et al 1993, Kano et al 1993, Suzuki et al 1993, Rupp and Schuster 1993, Howson et al 1993.

1 2

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Table 2.5 Selected parameters of antiferromagnetic coupled magnetoresistors (T 300°K). Structure

R/R [%]

Hs [kA/m]

R/R:Hs [%:kA/m]

Ref

(Fe0.5/Cr1.2) 50

42

6400

0.06

[a]

(Fe 0.9/Au 3.3) 19

2

32

0.06

[b]

(Co1.0/Cu0.8) 30

38

450

0.08

[c]

(Co0.8/Cu0.8) 60

70

880

0.08

[d]

(FeCo1.5/Cu0.9) 30

32

160

0.20

[e]

(NiFe1.5/Cu0.8) 14

16

56

0.28

[f]

(NiFe2.0/Cu1.0) 30

18

56

0.32

[g]

(NiFe3.0/Au1.2) 12

10

32

0.31

[h]

(NiFe1.2/Ag1.0)

13

16

0.81

[i]

NiFe/Cu sensor

6.1

17

0.36

[j]

AMR sensor

1.6

1

1.6

a – Schad et al 1994, b – Fullerton et al 1993, c – Grundy et al 1993, d – Parkin 1991, e – Jimbo et al 1993, f – Parkin 1992, g – Sato et al 1993, h – Parkin et al 1994, i – Rodmacq et al 1993, j – Kitada and Nakatani 1993.

drawback because integrated circuit technology requires annealing at a minimum temperature of 285°C for a few hours. Wang and co-workers (1997) reported that this requirement was fulfilled by the CoFe/Cu multilayer structure. The data presented in tables 2.4 and 2.5 were obtained by the four-probe method for the whole sample. In real structures these parameters may be reduced due to the influence of demagnetizing fields and non-uniformity of magnetization. The (NiFe1.6/Cu2.2) 8 element with dimensions 20 400 m exhibited magnetoresistivity of 6% (Kitada and Nakatani 1993). It is interesting that only privileged pairs of metals are suitable for the GMR effect. In general a high GMR ratio is observed when both metals possess similar crystal and electronic structures. They should have especially similar scattering features. These requirements are fulfilled by pairs NiFe/Cu and Co/Cu (Coehoorn et al 1998). Parkin (1991) investigated the coupling effect for various combinations of magnetic and nonmagnetic metals. The exchange coupling strength increased systematically from the 5d to 4d to 3d metals and exponentially with increasing number of d electrons along each period. Thus for Co the best were Cu, Rh, Ru and Ir and for Fe the best was Cr. Composition dependence of the magnetoresistance in FeCoNi/Cu multilayer structure was investigated by Coehoorn and Duchateau (1993). The MR ratio showed a maximum for the Co/Cu structure. Magnetoresistivity increases with decrease of the spacer thickness (figure 2.53(left)) As discussed in the previous section only selected critical values of

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Figure 2.53 Dependence of the magnetoresistivity ratio on the thickness of the nonmagnetic layer (Parkin 1994, Coehoorn and Duchateau 1993).

thickness (corresponding to antiferromagnetic coupling) can be chosen. Due to the sharp selectivity of oscillations (figure 2.53(right)) the thickness of the nonferromagnetic layer should be controlled precisely. The saturation filed Hs decreases with the spacer thickness faster than R/R. Therefore the sensitivity obtained for the second peak of the oscillation period may be larger than for the first peak. Figure 2.54 presents the transfer characteristics determined by Parkin and co-workers (1994) for four succeeding antiferromagnetic couplings in the NiFe/Au multilayer structure. The parameters

Figure 2.54 The ∆R/R=f(H) characteristics determined for four succeeding antiferromagnetic coupling periods (NiFe/Au multilayer – AF1: t 1.17 nm; AF2: t 2.15 nm; AF3: t 2.98 nm; AF4: t 4.1 nm) (Parkin et al 1994).

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determined from these characteristics are presented in table 2.6. Even the fourth antiferromagnetic peak exhibits larger sensitivity than the first. But for larger thicknesses of nonmagnetic layers significant hysteresis appeared as a result of imperfect coupling. Therefore the best parameters were obtained for the second peak. Table 2.6 Sensitivity of the NIFe/Au multilayer structure determined for four periods of the succeeding antiferromagnetic coupling (Parkin et al 1994). Structure

R/R [%]

Hs [kA/m]

R/R:Hs [%:kA/m]

(NiFe 3.0/Au 1.2) 12

10

32

0.31

(NiFe 3.0/Au 2.1) 12

12

8

1.5

(NiFe 3.0/Au 3.0) 12

7

3.2

2.18

(NiFe 3.0/Au 4.1) 12

5

1.6

3.1

The ferromagnetic layer should be as thin as possible to eliminate shunting of the current in the inner part of the layer. But for certain values of this thickness further decreasing of the ferromagnet layer leads to deterioration of the magnetoresistive effect (figure 2.55). Below certain values of thickness the scattering is insufficient and appears to influence the outer surface (Dieny 1994). The optimal value of thickness depends on the ferromagnetic material and the type of multilayer (three-layer or superlattice) and is about 2–10 nm.

Figure 2.55 Dependence of magnetoresistivity parameters on the thickness of ferromagnetic layers determined for NiFe 5/Cu 1/[NiFe tFe/Cu 1] 30 multilayer structure (Sato et al 1993).

By increasing the number of layers (number of periods in a superlattice structure) it is possible to increase the magnetoresistivity and improve exchange coupling (Parkin et al 1991). Various sources report different optimal numbers of bilayers, for example about 60 (Parkin et al 1991) or about 20 (Freitas et al 1997). Figure 2.56 presents the results of investigations made by Sato and coworkers. Above about 100 nm of the total thickness of the superlattice structure further increases of thickness do not change the MR ratio and the saturation field.

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Figure 2.56 Dependence of magnetoresistivity parameters on the number of the layers (determined for NiFe/Cu multilayer structure with tNiFe 1.5 nm) (Sato et al 1993).

To obtain a good quality multilayer structure it is necessary to introduce a buffer layer between the substrate and magnetoresistor layers. Figure 2.57 presents the results of investigations of the magnetoresistive effect for various buffers. Without buffer R/R was about 2% while with Fe buffer R/R increased to about 40% for the Co/Cu multilayer. Investigations (Dei et al 1993, Jimbo et al 1993, Martinez-Albertos et al 1993, Dieny et al 1992) have shown that the material and thickness of the buffer layer is crucial to the growth of the superlattice. The buffer changes the preferred orientations, texture and interfacial roughness of the layer. Suzuki and co-workers (1993) found that the buffer layer determined the number of grain nuclei and initiated the growth of texture, grains and crystallographic orientation. It has been proved that too thin a buffer layer (below 3 nm) did not guarantee a good quality interface. Because too thick a buffer layer decreases magnetoresistivity due to the shunting effect, reasonable buffer thickness is about 5 nm. Various buffer materials have been tested (Dei et al 1993). For NiFe/Cu the best parameters were obtained when the Fe buffer layer was used.

Figure 2.57 The change in the magnetoresistance due to introduction of the Fe buffer layer (Grundy et al 1993).

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Figure 2.58 Improvement of sensitivity due to the introduction of a thin Co layer: (a) structure – Si/Ru 3.1/NiFe 1/Co 0.5/[Cu 1.9/Co 0.5/NiFe 1.2/Co 0.5] x 19/Ru (Parkin 1992); (b) change of magnetoresistance and saturation field as a function of thickness of inserted Co layer (Hwang et al 1996).

However, the Fe buffer layer causes an increase in both parameters – the magnetoresistivity and the saturation field Hs (Jimbo et al 1993). For example in the CoFe/Cu structure the MR ratio increased from 11% (without buffer) to 20% (with Fe buffer). Simultaneously the saturation field increased sixfold (Gangopadhyay et al 1995). Other materials, for example NiFe, Cu or Cr also reported similar effects. Various methods of spin engineering to improve the properties of antiferromagnetic coupled structures have been tested. Parkin (1992) found that introducing a very thin (about 0.3 nm) additional Co layer to the NiFe/Cu multilayer remarkably increases the magnetoresistivity ratio (figure 2.58). It was revealed that this thin Co layer enhanced interlayer antiferromagnetic coupling and changed the roughness of the interface (Hwang et al 1996, Hosoe et al 1992). A similar method of insertion of other very thin films to improve the characteristics of the structure (for example Fe to Co/Cu multilayer or NiFe to Ni/Cu multilayer) has been reported (Song and Joo 1996). Kouchiyama and co-workers (1994) reported that in NiFe/(Ni/Fe/Cu) 8/NiFe multilayer structure high sensitivity (FWHM 800 A/m) was achieved. By alternating thicknesses of Co layers in the Co/Cu multilayer structure it is possible to reduce hysteresis (Holoway and Kubinski 1996). Mao and coworkers (1997) found that by appropriate design of the thickness of the Co layer in the Co/Cu structure the hysteresis could be eliminated. Figure 2.59 presents the dependence of hysteresis on the Co layer thickness in the structure: Si/[Co 3/Cu 2/Co tco/Cu 2] 15/Cu 2. Hylton and co-workers (Hylton et al 1993, 1994, 1995) introduced a new type of multilayer structure called the ‘discontinuous multilayer – DML’. The discontinuous multilayer was produced by controlled annealing of the multilayer to break up the layers into islands. Another technique was patterning the layer into arrays of dots or other geometries with submicron scale. A sensitivity as high as 15%/kAm1 has been reported.

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Figure 2.59 The decrease of hysteresis due to the introduction of the thin Co layer in [Co 3/Cu 2/Co tco /Cu 2] 15 multilayer structure (Mao et al 1997).

Figure 2.60 presents the change of magnetoresistance with annealing of the Ta 10/Ag 2/[NiFe 2/Ag 4] 4/NiFe 2/Ag 2/Ta 4/SiO2 70 multilayer structure. For an annealing temperature of 315°C the formation of Ag intrusions into the NiFe layer was observed. Although this structure exhibits high sensitivity and is simple in preparation it suffers from noise. The discontinuous structures may be treated as a transition between continuous structures and granular ones – the subject of the next section.

Figure 2.60 The improvement of parameters of the multilayer Ta 10/Ag 2/[NiFe 2/Ag 4] 4/NiFe 2/Ag 2/Ta 4/SiO2 70 by annealing to obtain the discontinuous structure (Hylton et al 1994).

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2.2.2 Granular GMR structures The granular GMR structure consists of nanometre-size granules of magnetic material dispersed in a nonmagnetic host material (Xiao et al 1992, Berkowitz et al 1992, Xiao et al 1993, Berkowitz et al 1994, Chien et al 1993, Teixeira et al 1994, Dieny et al 1994). This structure is usually prepared by codeposition of magnetic and nonmagnetic metals. Because of the immiscibility of some transition metals with noble metals it is possible to obtain a mixture of a nonmagnetic matrix with precipitated magnetic entities. It is also possible to obtain the granular structure straight away by sputtering deposition from the composite material target (Wang and Xiao 1994). Directly after the sputtering process a large saturation field is necessary to exhibit the full value of magnetoresistance – about 4000 kA/m. But after annealing, when the granular structure stabilizes it is possible to obtain magnetoresistance for a saturation field smaller than 1000 A/m. Another method of manufacturing the granular structure was proposed by Parkin and co-workers (1993). The granular structure was obtained by appropriate molecular beam epitaxial growth of Co/Cu and Co/Ag films. It was possible to prepare the granular structure by slow co-evaporation under UHV conditions and at moderate (below 400°C) substrate temperature. Such a process led to spontaneous phase separation. Depending on the substrate temperature the next step of annealing may change the magnetoresistance in different ways. Even without annealing a large magnetoresistance ratio was obtained, exceeding 70% at 4.2 K for the CoAg alloy. In (111)-oriented Co-Ag film Co particles with diameter of 2.5 nm separated from each other by a distance of 8 nm were created. Figure 2.61 presents the typical transfer characteristics R/R f(H) determined for the CoFe/Ag composition. Characteristics R/R f(H) are similar to the transfer characteristics describing the GMR effect in multilayers with antiferromagnetic coupling. The granular structure may be interpreted as a special form of nanometric entities with the resistance changed by spin-dependent scattering. After applying an external magnetic field the particles are aligned parallel to each other. Thus the GMR effect in multilayer structures and in granular alloys has a common origin. Several theoretical models of magnetotransport in granular structures have been proposed (Berkowitz et al 1992, Wang and Xiao 1994, Sheng et al 1996, Zhang 1992, Xing and Chang 1993, Rubinstein 1994). Assuming random distribution of magnetic M particles with average radius rM in a nonmagnetic NM matrix and adopting spin-dependent scattering theory Berkowitz formulated the following formula describing magnetoresistivity: 4ps2 —— —————————————–— o (1 ps2)2 2(1 ps2) · rM 2rM2

(2.59)

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Figure 2.61 An example of the transfer characteristics of granular structure (Co70Fe30)36/Ag64 after annealing at 300°C at room temperature (Teixeira et al 1994).

where: 1c c ——— —— MN M —————– 3c and: c – concentration of M particles, M, MN – mean free paths, – scattering strength on surfaces, ps – spin-dependent ratio of scattering. The magnetoresistivity depends on the size of particles, mean free paths of both components, the ratio of spin-dependent to spin-independent scattering potentials. The magnetoresistivity ratio is inversely proportional to the granule size. In granular structures appropriate thermal annealing that induces phase separation and generates granular solid is very important. Figure 2.62 illustrates the effect of annealing two typical granular structures NiFe/Ag and Fe/Ag. Although magnetoresistivity decreased a little after annealing it was very advantageous that after annealing the saturation field significantly decreased. The annealing reduces structural disorder but increases the size of particles and interparticle separation. Thus the electron mean free path increases. The change of grain size and mean free path length with annealing determined by Wang and Xiao (1994) is presented in figure 2.63. The annealing causes the change of magnetoresistivity ratio as is shown in figure 2.64. To obtain the best sensitivity the annealing should be performed at a temperature about 400–600°C. Figure 2.65 presents X-ray diffraction patterns determined by Jiang and co-workers (1992) for the NiFe/Ag structure. It is

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Figure 2.62 The change of the transfer characteristics with annealing: Fe30Ag70 at 5 K (Xiao et al 1993).

Figure 2.63 The change of grain sizes d and mean free path eff of granular structure Fe20Ag80 versus annealing temperature (determined by Wang and Xiao (1994) using transmission electron microscopy).

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Figure 2.64 The magnetoresistance of various granular alloys as a function of annealing temperature (Xiao et al 1993).

clearly visualized that the phase separation fully appears above 500°C. Further annealing does not improve phase separation and is not recommended (Teixera et al 1994). Various compositions of material for granular systems have been tested. Only immiscible pairs of metals can be taken into consideration. Mutually insoluble ones are for example the pairs Co/Cu, Co/Ag, Fe/Ag, NiFe/Ag, CoFe/Cu, CoFe/Ag. Figure 2.66 presents the transfer characteristics of four typical granular structures determined by Wang and Xiao (1994). Table 2.7 shows the parameters of the most often reported granular structures.

Figure 2.65 X-ray diffraction patterns of NiFe/Ag alloy as deposited and after annealing (Jiang et al 1992).

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Figure 2.66 Magnetoresistivity of various granular structures (determined at 4.2 K) (Wang and Xiao 1994). Table 2.7 The parameters of typical granular GMR structures. Structure

R/R [%]

Hs [kA/m]

R/R:Hs [%:kA/m]

T [K]

Ref

Co20Cu80

9

800

0.011

5

[a]

Fe30Ag70

15

550

0.027

5

[b]

Co26Ag74

70

800

0.087

4

[c]

NiFe20Ag80

40

800

0.05

5

[d]

Co20Ag80

22

800

0.027

5

[e]

Co32Ag68

5

1600

0.003

300

[f]

Co26Ag74

25

800

0.031

300

[g]

Co20Ag80

4

5600

0.0007

250

[h]

CoFe36Ag64

20

1000

0.02

300

[i]

a – Xiao et al 1992, b – Xiao et al 1993, c – Parkin et al 1993, d – Jiang et al 1992, e – Chien et al 1993, f – Zaman et al 1997, g – Parkin et al 1993, h – Fert et al 1997, Teixeira et al 1994.

The granular structures are prepared with a thickness of several m (typical 1 m). Malkinski and co-workers (1999) found limitations in decreasing the thickness of granular layer. The magnetoresistivity significantly dropped when the thickness diminished below several dozen nanometres. Granular CoAg films can also be prepared by the electrodeposition method (Zaman et al 1997). The simplest method of deposition is to use an electrolyte containing both components and maintain the substrate in the potential at which both metals deposit. The fabrication of Co/Ag or Co/Cu granular layers with parameters comparable to sputtered ones has been reported.

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Figure 2.67 The granular structures obtained by: (a) electrodeposition method (Co32Ag68 at various deposition current density) (Zaman et al 1997); (b) melt-spun ribbon (Co20Cu80 as cast and after annealing) (Dieny et al 1993).

The granular layers have also been prepared by melt-spinning (Dieny et al 1993, Tiberto et al 1995, Wecker et al 1993). For example a rapidly solidified granular Co/Cu structure was obtained by planar flow casting in a He atmosphere on a CuZr wheel. The melt-spun ribbons with dimensions 5 mm wide, 50 m thick and length tens of metres have been fabricated (Dieny et al 1993). Granular structures have many advantages, for example simple and low-cost preparation. But from the data presented in table 2.7 it is difficult to describe these structures as ‘giant magnetoresistance’. The sensitivity at room temperature (not published in the most cases) is very small. Hylton (1993) in the analysis of the properties of the granular sensors has shown that it is difficult to overcome these limitations in preparation of granular films competitive to other GMR structures. Therefore the application of these structures as sensors or reading heads to date is not reported.

2.2.3 Spin-valve structures with asymmetric magnetic layers (uncoupled structures) The main obstacle in the application of multilayer GMR magnetoresistors is the relative small sensitivity resulting from the strong exchange coupling field between layers. To overcome this coupling field a large external magnetic field is required. It would be a good idea to keep the sandwich structure which is necessary for the GMR effect but to remove coupling between layers. The coupling should be replaced by another way of antiparallel alignment of the layers. It is possible to obtain the difference of directions of magnetization in ferromagnetic layers by fixing (pinning) the state of magnetization of one of the layers. In spin-valve structures the pinning of one of the layers is realized

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by applying an additional exchange biasing film, for example an adjacent antiferromagnetic one. The second ferromagnetic layer is left free (unpinned) and can change its alignment with respect to the pinned one when an external field is applied. This is the main idea behind exchange biased spin-valve sensors described in the next section. Another type of spin-valve sensors is described in this section – spin-valve sensors with asymmetric ferromagnetic layers and without a biasing layer. Such sensors are sometimes called uncoupled GMR sensors (Chaiken et al 1991, Velu et al 1992, Yamamoto et al 1993). The uncoupled sandwich structure can be switched between parallel and antiparallel configuration if both ferromagnetic layers have different coercivities (figure 2.68(a)) or different thicknesses (figure 2.68(b)). Figure 2.68(c) explains the principle of operation of such a system using the model proposed by White (1992). For large magnetic field strength H both layers are magnetized similarly – parallel. When H decreases, the layer of smaller coercivity Hc1 at first switches its state of magnetization. The second layer is magnetized antiparallel with respect to the first layer until H is sufficient to reverse its magnetization (when the field exceeds the high-coercivity Hc2). For H value between Hc1 and Hc2 the uncoupled multilayer is magnetized antiparallel. The resistance correspondingly follows these changes of magnetization alignment as shown in figure 2.68. The whole system acts as a valve system and hence was probably named ‘spin valve’ by its inventors Dieny et al (1991, 1991b).

Figure 2.68 The asymmetric spin-valve structure: (a) structure of different materials of magnetic layers; (b) structure of different thickness of magnetic layers; (c) the principle of the asymmetric spin-valve mechanism (White 1992).

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Figure 2.69 The characteristics of the asymmetric spin-valve sensor with different coercivity of the magnetic layer – structure Co/Ag/Co (Barnas et al 1990).

Figure 2.69 presents the realization of the above described idea performed by Barnas and co-workers (1990). In the Co/Au/Co sandwich structure the first Co layer was evaporated on [110]-oriented GaAs, whereas the second layer was grown on the Au interlayer. Thus, due to differences in the microcrystalline structure (one epitaxial and the second polycrystalline) both Co films exhibited different coercivities. Another realization of the same idea was proposed by Dupas and co-workers (1990). It is known that the coercivity of the film depends on its thickness (Beauvillain et al 1988). An example of such a relation is presented in figure 2.70. Thus by using two magnetic layers with different thicknesses (figure 2.68(b)) the desirable difference of coercivity can be obtained. Figure 2.71 presents the characteristics of Au/Co/Au/Co/Au structure with cobalt layers of thickness 0.3nm and 0.65 nm. The coercivities of both layers were 80kA/m and 560 kA/m respectively.

Figure 2.70 The change of the coercive force versus thickness of the layer (Allenspach and Weber 1998).

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Figure 2.71 The characteristics of the asymmetric spin-valve sensor with different thickness of magnetic layers – structure Au/Co/Au/Co/Au (Dupas et al 1990).

Yamamoto and co-workers (1991) have used two different materials Co and NiFe. The characteristic of the [Cu 5/Co 3/Cu 5/NiFe 3] 15 structure is presented in figure 2.72(a). The influence of both components on the resultant curve is presented on the graph estimated by Shinjo and Yamamoto (1990) – figure 2.72(b). Similar results for other pairs of ferromagnetic materials (for example Fe/Cu/Co or NiFe/Cu/NiCo) have been reported (Dieny et al 1991, Chaiken et al 1991). The difference of the coercivity of ferromagnetic films has also been obtained by applying different magnetic fields during deposition (Dieny et al 1991, Matsuyama et al 1996). The nonmagnetic layer in the uncoupled spin-valve structure should be thick enough to diminish the exchange coupling between ferromagnetic layers to a negligible value. However, to obtain the giant magnetoresistive effect the layers should be very thin. Too thick a nonmagnetic layer may also shunt the whole

Figure 2.72 The characteristics of the asymmetric spin-valve structure with different materials of the magnetic layer – structure Co/Cu/NiFe (Shinjo and Yamamoto 1990).

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Figure 2.73 The dependence of the magnetoresistivity on the thickness of the nonmagnetic layer ((a) after Yamamoto et al 1991; (b) after Matsuyama et al 1996).

structure. Therefore the optimal value of the spacer thickness can be determined. Figure 2.73 presents a comparison of the results reported for the Co/Cu/NiFe structure (Yamamoto et al 1991, Matsuyama et al 1996). Both investigations determine the optimal thickness as 5–6 nm. There are about five periods of oscillation in exchange coupling for the Cu layer. For five periods this coupling is very small indeed. Also the dependence of magnetoresistivity on the thickness of magnetic layers has been investigated (Chaiken et al 1991, Mapps 1994). An example of the results is presented in figure 2.74. A thickness of about 4–6 nm seems to be a good choice. Table 2.8 presents parameters of selected uncoupled structures.

Figure 2.74 The dependence of the magnetoresistivity on the thickness of magnetic layers in the NiFe/Cu/Co asymmetric spin-valve structure (Mapps 1994).

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Table 2.8 The parameters of selected uncoupled structures (at room temperature). Structure

R/R [%]

Hs [kA/m]

R/R:Hs [%:kA/m]

Ref

Cr/NiFe/Cu/Co/Cu

14

8

1.75

[a]

NiFe/Cu/Co/Cu

9

8

1.12

[b]

Au/Co/Au/Co/Au

1.5

8

0.19

[c]

Fe/Cu/Co/Cu

3

8

0.37

[d]

NiFe/Cu/NiCo

1.5

0.4

3.7

[e]

(Co/Cu)3/(Fe/Pd)3

1.7

0.3

5.7

[f]

NiFe/Co/Cu/Co

0.5

0.08

3.1

[g]

3

a – Yamamoto et al 1993, b – Yamamoto et al 1991, c – Dupas et al 1990, d – Chaiken et al 1991, e – Dieny et al 1991, f – Schul et al 1994, g – Matsuyama et al 1996.

Figure 2.75 presents the characteristics of the real patterned sensor designed by Matsuyama and co-workers (1996). The asymmetry of magnetic layers has been ensured by applying different magnetic layers – NiFe and Co. During the evaporation of the Co top layer the magnetic field was applied to induce the uniaxial anisotropy parallel to the length of the strip. Experimentally it was determined that insertion of an additional Co thin layer improved the parameters of the sensor. Following the experiments the structure NiFe 3/Co 1/Cu 5/Co 3 was chosen. The sensor with width w 120 m and length l 600 m and external bias field of 1.5 kA/m exhibited linear response sensitivity 3%/kAm1.

Figure 2.75 The characteristics of the asymmetric patterned spin-valve sensor (Matsuyama et al 1996).

A new spin-valve like system has been proposed by Schul and co-workers (1994). It utilized the exceptionally small coercivity of the Fe/Pd bilayers grown by molecular beam epitaxy. Thus by co-operation with the conventional large coercivity bilayer it is possible to obtain a similar structure to other asymmetric spin-valve structures. Although the magnetoresistivity of such a system was not 3

Measured for strip with dimensions w 120 and l 600 m.

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Figure 2.76 The low-field epitaxial (Fe/Pb)/(Co/Cu) spin-valve type structure (Schul et al 1994).

very large (about 2% at 4.2 K) the very small Hs was promising for low field applications. By increasing the number of bilayers to three, Schul and coworkers obtained spin-valve like structures appropriate for low field applications at room temperatures. An example of the characteristics of the structure [Fe/(Fe/Pd) 3]/Cu/Co) 3/Cu] is shown in figure 2.76. The spin-valve structure with asymmetry of the magnetic layer is an interesting alternative for other GMR structures. Its sensitivity is quite large and manufacture relatively simple because an additional biasing layer is not required (as in the case of the exchange-biased spin-valve structure). Its switching parameters are acceptable for digital applications. Therefore this structure is used in the design of magnetoresistive random access memory (MRAM) elements (Pohm et al 1997, Zheng and Zhu 1997, Everitt et al 1998, Tehreni et al 1999). In this application spin-valve structure with asymmetry is often called the pseudo-spin valve in order to differentiate it from exchange-biased spinvalve structures. In pseudo-spin valve structures the asymmetry of magnetic

Figure 2.77 The design and switching characteristics of the pseudo-spin valve memory element (Pohm et al 1997).

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layers is usually realized by designing ferromagnetic layers of different thicknesses. Figure 2.77 presents the structure and switching characteristics of the MRAM memory element prepared from CoFe 1.5/NiFeCo 5.5/Cu 2.8/NiFeCo 4.5/CoFe 1.5 as the pseudo-spin valve structure.

2.2.4 Spin valve structures with exchange-biased layer The exchange-biased spin-valve sensors are widely investigated GMR sensors because of their expected application in next-generation reading heads. Therefore these structures have also been well documented (Dieny 1994, Coehoorn et al 1998, Kools 1996).

Figure 2.78 The hysteresis loop of permalloy biased by: FeMn and NiO antiferromagnetic layer (Lin et al 1995).

The exchange biasing of ferromagnetic film by an antiferromagnetic film has been known for many years4 (Hempstead et al 1978, Meiklejohn and Bean 1956. Tsang et al 1981). This kind of coupling produces the unidirectional anisotropy resulting in a shift by Hp of the BH loop and achieves the desired anisotropy and coercivity in biased film (Lin et al 1995, Jungblut et al 1994). Figure 2.78 presents the resultant BH loop of permalloy biased by the two most frequently used biasing antiferromagnetic materials – FeMn and NiO. The origin of this interaction between ferromagnetic and antiferromagnetic films is complicated and not fully understood (Nogues and Schuller 1999). Many theoretical models of exchange anisotropy have been proposed (Malozemoff 1988, Nogues and Schuller 1999). The exchange bias field of a pinned layer with thickness t is described by the expression Jp Hp ——–.

o Mt

(2.60)

The exchange AFM/FM anisotropy was discovered in 1956 by Meiklejohn and Bean (Meiklejohn and Bean 1956). 4

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The exchange bias coefficient Jp for Fe50Mn50 is about 0.1 mJ/m2. For example in the configuration 25 nm FeMn and 40 nm NiFe the HB loop with coercivity Hcp360 A/m is shifted by Hp 2000 A/m (Tsang and Lee 1982). The spin-valve structure is composed of two magnetic layers separated by a nonmagnetic layer. One of the magnetic layers is free (unbiased) and changes the direction of magnetization after applying the external magnetic field. The second layer is biased and a large magnetic field is required to change the direction of its magnetization. Thus it can be assumed that this layer is ‘pinned’. The resultant hysteresis of such a spin-valve system is composed of two loops – a hysteresis loop corresponding with the pinned layer (shifted by Hp field and with coercivity Hcp) and a hysteresis loop corresponding with the unpinned layer. This second hysteresis is shifted by a small field representing the coupling field and may have modest coercivity. Figure 2.79(a) presents a model of such a two-hysteresis system and figure 2.79(b) presents an example of the hysteresis of a real spin-valve system (for structure: NiFe 6.2/Cu 2.2/NiFe 4/FeMn 7).

Figure 2.79 The hysteresis loop of the spin-valve structure biased by an antiferromagnetic layer: (a) model; (b) curve determined for NiFe 6.2/Cu 2.2/NiFe 4/FeMn 7 by Dieny (1991).

Figure 2.80 illustrates the main idea of a spin-valve sensor. For large magnetic fields both magnetic layers are magnetized parallel. When the magnetic field is decreased at first only the free layer changes the direction of magnetization and both layers are then magnetized antiparallel. Further decreasing the magnetic field leads to the change (with significant hysteresis) of direction of magnetization in the second (pinned) layer. Resistance of the whole system follows the changes of magnetization. Between changes of the direction of magnetization when the layers are magnetized antiparallel resistance of the structure is maximal (plateau on the characteristic R(H)). Figure 2.81 presents the characteristic R(H) of the same structure as presented in figure 2.79. Usually only a part of the whole characteristic is utilized –

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Figure 2.80 The principle of operation of the spin-valve sensor (White 1992).

corresponding with low field (and low hysteresis) switching. This part of the whole characteristic used for a sensor is presented in expanded scale in figure 2.81(right). It is shifted about 500 A/m and exhibits coercivity of less then 100 A/m. The second hysteresis loop is shifted about 34 kA/m and exhibits coercivity of about 8 kA/m. Comparing the transfer characteristic presented in figure 2.81(right) with similar characteristics determined for multilayer structures it can be appreciated that there are two important advantages of spin-valve sensors. Their transfer characteristic is almost linear while for exchange coupling it is parabolic. Moreover the sensitivity of spin-valve sensors is much larger and the sensor needs lower fields. But in comparison with exchange-coupled structures the magnetoresistivity ratio is much smaller, typically several percent while with exchange coupling it is several tens of percent. The characteristics presented in

Figure 2.81 The characteristic ∆R/R = f(H) of the structure NiFe 6.2/Cu 2.2/NiFe 4/FeMn 7 (Dieny 1991).

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Figure 2.82 The characteristic ∆R/R = f(H) of the structure NiO/NiFe/Co/Cu/Co/NiFe (Han et al 1997).

figure 2.81 are close to the theoretical ones presented in figure 2.80. Figure 2.82 presents an example of other characteristics determined for the NiO/NiFe/Co/Cu/Co/NiFe spin-valve structure. In this case the biasing field Hp is of modest value and both R(H) loops are not separated significantly from each other. Three typical characteristics of from spin-valve structures are presented in figure 2.83 (Parkin 1994). Only the low-field loop is shown. Co/Cu/Co/FeMn structure exhibits the largest magnetoresistivity ratio of 7% but it suffers from large coercivity. The most frequently used structure NiFe/Cu/NiFe/FeMn,

Figure 2.83 The low field characteristics of the most frequently used spin-valve structures (Parkin 1994).

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exhibits a smaller magnetoresistivity ratio than the Co/Cu structure but a lower magnetic field is required. Similarly as in the other GMR structures inserting an additional very thin Co layer increases the magnetoresistivity ratio (Parkin 1993). Magnetoresistivity of about 3% has been determined for an NiFe/Cu/NiFe/FeMn structure, which increased to about 6% after adding a 0.2 nm Co layer. The usually used slope of the R/R f(H) characteristic in expanded scale indicates hysteresis (figure 2.83). As proved by Rijks and co-workers (1994) applying exchange anisotropy perpendicular to anisotropy in the unpinned layer (termed crossed anisotropies or transverse scheme) significantly reduced hysteresis and improved linearity (figure 2.84). This effect appears because in the spin valve with crossed anisotropies the free layer is magnetized by coherent rotation, and by domain wall movement with parallel anisotropies. The crossed anisotropy configuration has been obtained by applying the perpendicular magnetic field during deposition of the films or by appropriate annealing of the film. A similar effect has been obtained by tilting the pinning field direction of the pinned layer from the easy axis of the soft magnetic layer (Fujiwara et al 1996).

Figure 2.84 The low field characteristics of the spin-valve structure with parallel easy axis (a) and crossed easy axis (b) (Folkerts et al 1994).

The thickness of the nonmagnetic layer is especially important for the proper work of spin-valve structure. If this layer is too thin we come back to exchange coupling (with oscillatory behaviours and low sensitivity). If the spacer is too thick we come back to the anisotropic magnetoresistivity effect additionally reduced by a shunting effect. As a compromise it is usually assumed that the spacer layer must be large enough to provide decoupling of the ferromagnetic layers. Assuming the minimal coupling field as 1 kA/m the minimum values of this thickness has been determined as about 2 nm for Cu, 1 nm for Au and 5 nm for Ag (Dieny 1994). Figure 2.85 presents R(H) curves determined by Rijks (Rijks et al 1994) for different thicknesses of Cu layer in the Ta 3/NiFe 8/Cu/NiFe 8/FeMn 8/Ta 2 structure. When the thickness of the copper layer tcu is about 1.5 nm the

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Figure 2.85 The low field characteristics of the NiFe/Cu/NiFe/FeMn structure determined for various values of copper thickness (Rijks et al 1994).

characteristic R(H) resembles the transfer characteristic of the oscillatory coupling multilayer. The maximum value of the magnetoresistivity ratio has been obtained for tcu 2.2 nm. Figure 2.86 presents the example of the experimentally determined dependence of the magnetoresistance on the thickness of the nonmagnetic layer (Coehoorn et al 1998). An optimal value of thickness exists also for the ferromagnetic layer. When this layer is too thin ineffective scattering on the border of the layer (interfaces between the magnetic layer and buffer layer or exchange-biasing layer respectively) influences the resultant magnetoresistance. When this layer is too thick the shunting effect diminishes the magnetoresistance. As a compromise it

Figure 2.86 The dependence of magnetoresistance on the thickness of the nonmagnetic layer (Coehoorn 1998).

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Figure 2.87 The dependence of magnetoresistance on the thickness of the magnetic layer (Coehoorn et al 1998).

is usually assumed that the thickness of the ferromagnetic layer should be about one half of the mean free path in this material (Coehoorn et al 1998). As the mean free path is roughly 10–20 nm in typical ferromagnetic materials the optimal thickness of this layer is 6–10 nm. Figure 2.87 presents the experimentally determined dependence of the magnetoresistance on the thickness of the magnetic layer. The exchange-biasing parameters are crucial for correct functioning of spinvalve sensors. The correct choice of the exchange biasing layer is very important. A large biasing field Hp with a small coercive field Hcp is the preferred choice. These parameters depend on the material of the layers, their thicknesses and crystal orientation (Jungblut et al 1994, Kim et al 1995). The most frequently used material for the biasing layer is the antiferromagnetic metallic alloy Fe50Mn50. Figure 2.88 presents the dependence of Hp and Hcp on the thickness of the layers in the (111) NiFe/FeMn biased structure.

Figure 2.88 The main parameters of the FeMn biasing structure as a function of the thickness of the biasing layer (Jungblut et al 1994).

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Figure 2.89 The corrosion tests of various spin-valve structures (corrosion was determined after immersing the samples into pure water) (Hasegawa et al 1996).

Assuming a typical thickness of the NiFe layer tFe 7 nm then the thickness of the biasing layer should be larger than 5 nm. As this thickness increases, the coercive field decreases and the biasing field does not change. Thus it is advisable to apply a rather thick FeMn layer. Because FeMn is a conductor ( 74 108 m) the optimal thickness of this layer is usually chosen as 5–10 nm to avoid the shunting effect. Exchange bias is sensitive to the crystal orientation of NiFe (Jungblut et al 1994, Wang et al 1996). The most favourable is the [111] texture where the coercive field is significantly small and exchange biasing is strong. This texture is also advantageous for other spin-valve parameters (Coehoorn et al 1998). The Fe50Mn50 alloy is recommended for exchange biasing due to the relative simplicity of deposition and flexibility in choice of parameters. But it is not without drawbacks. It corrodes easily as shown in figure 2.89. Investigations of corrosion effects indicated that humidity is catastrophic to FeMn spin valves even with protective Ta capping layers (Burkett 1997). An important parameter of exchange biasing is the blocking temperature. It is the temperature at which the biasing field disappears (figure 2.90). The FeMn alloy exhibits a low blocking temperature (about 140°C) and therefore during the manufacturing of the sensor the exchange biasing may deteriorate. Fortunately this feature may be restored by appropriate temperature treatment. Another drawback of FeMn is the shunting effect. It would be better to use a biasing layer of much higher resistivity. Sometimes NiO is used as a biasing material (Lee et al 1996, Lai et al 1997, Carey and Berkowitz 1992, Shen and Kief 1996, Cheng et al 1996). It is an insulator and its blocking temperature is about 200°C. NiO for spin-valve sensors shows remarkable resistance to corrosion (Burkett 1997). The disadvantages of NiO are a poor exchange field and large coercivity (in comparison with FeMn). Other candidates for exchange

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Figure 2.90 The exchange fields of various spin-valve structures as a function of the temperature (Deasahayam and Kryder 1996).

biasing layers have been tested, for example NiMn (Devasahayam and Kryder 1996), TbCo (Leal et al 1994, Freitas et al 1994), CoNiO, IrMn (Devasahayam and Kryder 1999), -Fe2O3 (Hasegawa et al 1996), NiO/CoO (Fujikata et al 1995,1996) or NiO/CuO (Lee et al 1997). A comparison of these materials is presented in figures 2.89 and 2.90. The spin-valve structure is composed of at least six layers: buffer layer, feromagnetic ‘unpinned’ layer, nonmagnetic layer, ferromagnetic exchange biased (‘pinned’) layer, antiferromagnetic biasing layer and capping layer (figure 2.91(a)). The buffer layer significantly influences the quality of the deposited layer, particularly its texture. The capping layer mainly protects the structure against corrosion. Tantalum is usually used for these layers (Lenssen et al 1996). The 2–3 nm thick Ta layer is sufficient to improve the texture of the following layer and to protect the layers. Its relatively large resistivity ( 160 108 m) means that the shunting effect is negligible. Egelhoff and

Figure 2.91 The various layouts of spin-valve structures : (a) top spin valve; (b) bottom spin valve; (c) symmetrical spin valve (Coehoorn et al 1998).

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co-workers (1995) found that in the Co/Cu/Co spin-valve structure a capping of only 0.4 nm Ta layer, oxidized by exposure to air, not only protects the spin valve but also increases the GMR. Other materials for the buffer layer have been tested (Nakatani et al 1994). Usually the exchange-biasing layer is at the top of spin-valve structure (figure 2.91(a)). Lenssen et al (1997) proposed an ‘inverted spin-valve’ structure with the biasing layer at the bottom (figure 2.91(b)). This structure decreases the large corrosion sensitivity of this layer and is most suitable for certain head applications. In such a structure it is necessary to introduce an additional buffer layer (for example NiFe) to obtain the required texture. In spin-valve structures it is not possible to increase magnetoresistivity by multiple sandwich layers, as in exchange-coupled structures. But it is possible to increase the R/R ratio by approximately 50% in ‘symmetrical spin valve’ structures (two spin valves – bottom and top composed together) as introduced by Anthony and Brug (1994) (figure 2.91(c)). In the symmetrical structure the largest reported magnetoresistance ratio was 24.8% (Egelhoff et al 1995,1996). Although various materials for spin-valve structures are still being tested practically only two materials, cobalt and NiFe (or NiFeCo) alloy combined with copper, are in use. They fulfil the main requirements for spin-valve materials: matching of crystal structures, similarity of electron structures (Coehoorn et al 1998). Table 2.9 presents the main parameters of spin-valve structures. It is difficult to compare and evaluate the various kinds of spin-valve sensors from reported data. Many authors are fascinated by the MR ratio but show little interest in the second important parameter – the range of the magnetic field Hs. Various authors have estimated the Hs value in different ways. In general it can be stated that the Co/Cu/CO structure exhibits the largest MR ratio – Table 2.9 The parameters of selected spin-valve structures (at room temperature). Structure

R/R [%]

Hs [kA/m]

R/R: Hs [%:kA/m]

Ref

Co/Cu/Co

9.5

1.2

7.92

[a]

NiFe/Cu/NiFe

3.1

0.17

18.0

[b]

Ni/Cu/Ni

2.5

0.48

5.2

[c]

Co/Cu/NiFe

6.5

1.2

5.4

[d]

NiFe/Ag/NiFe

1.2

0.32

3.7

[e]

NiO/Co/Cu/Co/Cu/Co/NiO

24.8

3.3

7.51

[f]

Ta/NiFe/Cu/NiFe/FeMn/Ta

4.2

0.8

5.2

[g]

Co/Cu/Co/FeMn/Cu

6.9

0.8

8.6

[h]

NiFe/Cu/NiFe/FeMn/Cu

2.7

0.4

6.7

[i]

a – Dieny 1994, b – Choe et al 1998, c,d,e, – Dieny 1994, f – Egelhoff et al 1997, g,h,i – Dieny et al 1995).

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typically 6–10%. For the NiFe/Cu/NiFe structure it is possible to obtain an MR ratio 2.5–5%. Because the Hs value of NiFe/Cu/NiFe structure is smaller than for Co/Cu/Co (typically 400 A/m for NiFe and 1200 A/m for Co) the resultant sensitivity is better for the NiFe/Cu/NiFe structure. Moreover structures with a permalloy exhibit significantly lower hysteresis. The largest magnetoresistive ratio of 25% (Egelhoff et al 1997) reported for the symmetric structure is still far from the 110% at room temperature reported for exchange-coupling GMR structures. Egelhoff and co-workers (1998) have performed further analysis and estimated that it is reasonable to expect for spin-valve sensors of 50% at room temperature within a decade. Hs in table 2.9 should be as small as possible in order to obtain large sensitivity. It is also concerned with quality of switching in digital applications. Comprehensive analysis of this parameter was presented by Rijks and coworkers (1997). The switching field Hs may be interpreted as the field interval between antiparallel and parallel states. If magnetic coupling between layers is negligible the field interval Hs depends on the induced anisotropy field Hk of the unpinned layer Hs 2Hk. The induced anisotropy field for permalloy Ni80Fe20 is about 400 A/m and decreases almost by a half when the thickness of the ferromagnetic layer decreases from 10 nm to 3 nm. The switching field is additionally enlarged by the component dependent on the exchange-biased field Hp: 2H 21 tf Hs 2Hk —— — Hp tp

(2.61)

where: H1 – offset field resulting from coupling between layers, tf, tp – thickness of unpinned and exchange biased layers, respectively. The switching field interval depends on the alloy composition and on the thickness of both layers. Figure 2.92 presents this dependence determined for the NiFeCo/Cu/NiFeCo/FeMn structure. This switching field is very sensitive to heat treatments.

Figure 2.92 The dependence of the switching field interval on the thickness of magnetic and nonmagnetic layers (Rijks et al 1997).

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In weakly coupled structures, such as spin valves, besides the GMR effect the AMR effect may also influence parameters of the sensor. In general the AMR component is undesirable because it deteriorates linearity and introduces asymmetry. The resultant resistance of the spin-valve structure with AMR component is described in the following expression (Rijks et al 1994): RGMR RAMR R Ro ——— [1 cos(1 2)] ——— (cos2 1 cos2 2). 2 2

(2.62)

The AMR effect in spin-valve structures was investigated by Uehara and coworkers (1996). In the sample structure of NiFe/CoFe/Cu/CoFe/FeMn with a relatively thick Cu layer (3.6 nm) an AMR effect as large as 16% of GMR effect has been detected. The shortcoming of exchange-biased structures is the choice of the antiferromagnetic biasing layer (low blocking temperature, temperature dependence, corrosion effects, shunting effects). Therefore other candidates for the pinning of one layer should be considered. Recently another method of pinning one of the magnetic layers in the spin-valve structure has been tested. It is the application of the so-called ‘synthetic antiferromagnetic structure’ – SAF (or artificial antiferromagnetic structure) (Zhu and Zheng 1998, van Berg et al 1996, Zhu 1999). Instead of the magnetic layer biased by the antiferromagnetic material an exchange-coupled sandwich can be used. For example the Co/Ru/Co trilayer has been considered. When Ru layer thickness is around 0.6 nm the interlayer coupling is antiferromagnetic and an exchange-coupling coefficient as large as 1 mJ/m2 has been reported. The main reason for substituting the exchange-biased layer with the artificial antiferromagnetic system is the need to eliminate the magnetostatic interaction in conventional structures. Especially at the submicrometre scale the non-uniform

Figure 2.93 Spin-valve structures with the synthetic antiferromagnetic bias system.

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magnetostatic field deteriorates switching parameters (Zhu and Zheng 1998). In the new system the interlayer magnetostatic fields may be neglected due to the strong exchange coupling and the flux closure in the structure. The SAF-biased spin-valve structure is presented in figure 2.93. The synthetic antiferromagnet applied in the spin-valve structures can be influenced by the magnetostatic field from the free layer. This leads to irreversible magnetization flipping (Zhu and Zheng 1998). Pinning of the SAF structure by a conventional antiferromagnetic can ensure proper operation of the whole structure.

2.2.5 Current perpendicular to plane (CPP) structures In a structure with the current flowing perpendicular to the film plane (CPP) all of the current must undergo spin scattering at every interface and therefore a larger magnetoresistive effect may be expected than in a classical CIP (current in plane) structure. The first experiments were made by a group from Michigan State University (Pratt et al 1991, Lee et al 1992) and confirmed this hypothesis – magnetoresistance as large as 170% at 4.2 K has been obtained. Another advantage of the CPP structure in comparison with a CIP structure is the elimination of shunting effects caused by buffers, capping or biasing layers. However, there is one drawback of the CPP system. The resistance is extremely small – typically 10–1000 n for 1 mm2 area at 4.2 K (Gijs et al 1995). Such a small resistance is practically not possible to measure by conventional methods. The output signal from the CPP sensor is inversely proportional to the sensor area. Therefore small resistivity may not be a large disadvantage in the manufacture of submicron-size devices in integrated applications and in ultra-high density reading of information (Rottmayer and Zhu 1995). To detect very small changes of resistance the dimensions of the sensor should be as small as possible, fewer than parts of m. Structures with current flowing perpendicularly to the plane are very attractive for fundamental physics. They enable analysis of new aspects of the transport problem at atomic scale and provide information that cannot easily be obtained in any other way (Pratt et al 1993). For example more precise analysis of bulk and interface scattering and transparency is possible in this structure compared to the more complex CIP structure (Camblong et al 1993, Valet and Fert 1993, Zhang and Levy 1991, Lee at al 1993, Bauer 1992, Bauer et al 1993, Gijs et al 1993, Chui 1995). The CPP configuration raised new fundamental questions, for example the role of spin accumulation effects at the interface or the role of spin-flip electron scattering. A comprehensive analysis of the perpendicular giant magnetoresistance is presented in a study published by Gijs and Bauer (1997). The analytical expression describing perpendicular giant magnetoresistance has been formulated by Valet and Fert (1993) in the form:

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t

F F* t 2 · *b M √(R(AP) R(P))R(AP) ———– t t F

(2.63)

N

where coefficient describes the difference between bulk resistivities ↑F and ↓F (bulk spin-dependent scattering) ↑F 2*F (1 ),

↓F 2*F (1 )

and coefficient describes the difference between interface resistances r↑b and r↓b (interface spin-dependent scattering) r↑b 2r*b (1 ),

r↓b 2r*b (1 ).

The other symbols in (2.63) describe: R(P), R(AP) – resistance in parallel and antiparallel configurations of magnetization; M – number of bilayers; tF, tN – thickness of ferromagnetic and nonmagnetic layers respectively; t – thickness of the whole structure (t M(tFtN)). Thus bulk and interface scattering can be described by F and FN coefficients ↓F 1 F —– ———, ↑F 1

r↓b 1 FN —– ———. r↑b 1

By investigating CPP structures with different numbers of bilayers M and different ratio tF/tN it is possible to determine the scattering coefficients used in formula (2.63). In table 2.10 experimentally determined scattering parameters are given. Comparing the presented data leads to the conclusion that both types of scattering (bulk and interface) are important, although interface scattering is much the strongest.

Table 2.10 Experimentally determined scattering parameters in the CPP structure (Pratt et al 1991). Parameter

Co/Ag

Co/Cu

NiFe/Cu

F [nm]

107

86

122

10

7

5

ARFN [fm ]

0.56

0.50

0.50

0.48

0.50

0.50

0.85

0.76

0.81

F

2.9

3.0

3.0

FN

12

7.5

9.5

N [nm] 2

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In table 2.10 letter A denotes the area of the structure. The parameters given in the table 2.10 were determined using special measuring equipment, developed at Michigan State University (Slaughter et al 1989). To measure very small resistances with n resolution the ultrasensitive SQUID voltmeter technique was used. Figure 2.94 presents the main idea of the superconducting measuring circuit used to investigate CPP structures at 4.2 K. In the measuring system presented in figure 2.94 the tested multilayer sample is sputtered between two contacts strips from Nb. The measured area is in the square (about 1 mm2) between the two Nb legs. The output signal for applied current 50 mA was about 10 nV. To measure such a small voltage value the SQUID based null-detector technique was adapted. Measured resistance and reference resistance Rref are connected in a bridge circuit. After applying a magnetic field the bridge is not in equilibrium and SQUID detects the flowing unbalanced current. The feedback circuit changes Iref to balance the bridge. Thus Iref is the output signal proportional to measured resistance.

Figure 2.94 The geometry of the sample and the measuring method of the CPP magnetoresistive effect (Gijs and Bauer 1997).

Using a similar measuring system to that presented in figure 2.94 various CPP structures have been tested, for example NiFe/Cu (Holody et al 1998), Co/Cu (Pratt et al 1993), Fe/Cr (Gijs et al 1994), Co/Ag (Pratt et al 1993, Lee et al 1995), Co/Cu/NiFe/Cu (Yang et al 1995, Vavra et al 1995). Figure 2.95 presents an example of the dependence of the MR ratio on nonmagnetic layer thickness determined for the NiFe/Cu CPP structure. Similar to exchange-coupled CIP structures oscillations with period 1.1 nm can be observed. Figure 2.96 presents the transfer characteristics of the Co/Cu structure for both cases – antiferromagnetic exchange coupling (tcu 0.9 nm) and the uncoupled state (tcu 4 nm). Superconducting measuring systems are very useful for investigating CPP effects, but are not acceptable for routine applications becauce of their cost and

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Figure 2.95 The dependence of CPP magnetoresistance on the thickness of the nonmagnetic layer (NiFe 5 {NiFe 1.5/Cu] 14 structure) (Holody et al 1998).

Figure 2.96 The transfer characteristics AR f(H) determined for the CPP Co/Cu structure (A: area of the structure) (Pratt et al 1993).

complication. Investigations at the room temperature are important for the eventual applications of the CPP structure. Extremely small ‘pillar’ shape CPP structures have been obtained using microfabrication techniques and sophisticated lithographic methods (Vavra et al 1995, Spallas et al 1996,1997, Gijs et al 1994, Krebs et al 1996). Typical dimensions of the pillar do not exceed several m, and a sensor of 0.4 m diameter has been obtained using electron beam lithography (Spallas et al 1997). The main problems in using pillar-like structures occurs in the contacts preparation. Even carefully prepared contacts using the best conducting materials introduced interface resistance comparable to the measured one. Additionally the specific contact geometry needs to be chosen to ensure uniform distribution of the current. Figure 2.97 presents the transfer characteristics of the 0.4 m diameter device developed by Spallas and co-workers. Table 2.11 presents the main parameters of CPP devices (including a comparison with the CIP effect of the same geometry). Although the magnetoresistivity ratio of

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Figure 2.97 The comparison of the transfer characteristics determined for pillar-like (Cu 2/Co 1.2) 30 structure. The dimensions of the structure: diameter of 1.5 m, high 1.1 m) (Spallas et al 1997).

39% is remarkably large the output signal (several V) and sensitivity (1.6%:kA/m) are still too small to think about large-scale manufacture. Gijs and co-workers (1995) developed a novel technique to solve the problem of contact manufacturing. The layers were deposited on the grooved substrate (figure 2.98). By using holographic laser interference lithography and anisotropic etching techniques the pillars connected in series were obtained in a grooved shape structure. Figure 2.99 presents the magnetoresistance curve of such a structure in the form of a Cu 2 (Co 1.5/Cu 6) 32 Cu 2 structure. A magnetoresistivity ratio of 17% at room temperature was reported. Another method used to obtain CPP structures at room temperature is the manufacture of the multilayer wires by electrodeposition into a template of nanometre-scale pores created by nuclear track etching in a polycarbonate Table 2.11 The parameters of submicron scale CPP devices. Parameter

(Cu 3/Co 20 18

(Cu 2/Co 1.2) 30

Diameter [ m]

0.43

1.5

Thickness [nm]

90

97

R []

8.7

0.54

(Cu 2/Co 1.2) 30 CIP

I [mA]

0.7

2.1

Uout [ V]

12.7

8.4

R/R [%]

20

39

18

Hs [kA/m]

20

24

20

R/R:Hs[%:kA/m]

1.0

1.6

0.9

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Figure 2.98 The method of deposition of the CPP structure on the grooved substrate (Gijs et al 1995).

Figure 2.99 The transfer characteristic of the CPP structure (Co 1.5 Cu 6) 32 deposited on the grooved substrate (Gijs et al 1995).

Figure 2.100 The method of preparation of the nanowires by electrodeposition in a membrane and the transfer characteristic of the Cu/Co nanowire (Piraux et al 1994, Blondel et al 1994).

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membrane (Whitney et al 1993, Liu et al 1995, Blondel et al 1995, Voegeli et al 1995) (figure 2.100(left)). The wires of diameter about 80 nm and length 6 m were electrolytically grown. Figure 2.100(right) presents the transfer characteristic determined for the Cu 5/NiFe 5 nanowire structure. A magnetoresistance ratio of 10% at room temperature has been measured. The advantage of electrodeposition of the wires in nanoporous membranes is the relative simplicity of manufacturing. However, the sensitivity of about 0.02%:kA/m is rather small. To date experiments with CPP structures are not satisfactory because the results are modest compared to the efforts involved in preparing the samples.

2.2.6 Magnetic tunnel junction (MTJ) structures In the ferromagnetic tunnelling structure two magnetic layers are separated by an insulator thin film and current flows through this barrier. From classical physics this structure is not possible because resistance should be of infinity. But at nanometric scale the tunnelling current caused by the external magnetic field may flow in such a structure. The current in the tunnelling junction is dependent of the density of states of the two electrodes. If both ferromagnetic electrodes are magnetized parallel to each other then there is a best match between the density of states of majority and minority energy bands. Hence the tunnelling probability is large and the resistance is at a minimum. In the antiparallel configuration the maximal mismatch between the density of states occurs. Thus the resistance is at a maximum. The tunnelling probability of electrons is controlled by the state of magnetization of both ferromagnetic layers. Slonczewski (Slonczewski 1989) theoretically analysed this structure and termed it the ‘magnetic valve’ (‘spin filter’ is used as well). As described by Julliere (1975) the tunnelling conductance G varies with the angle between the magnetizations of both layers: G Go (1 cos )

(2.64)

where: Go, – constants. Figure 2.101 presents the dependence of the tunnelling conductance on the angle determined experimentally by Miyazaki and Tezuka (1995). The constants in the expression (2.64) have been calculated as: Go 96 1, 0.09. The magnetic tunnelling phenomenon was theoretically predicted many years ago but it was not possible to manufacture thin enough uniform insulating layers to test it experimentally. The first successful spin-polarized tunnelling experiment was reported in 1975 by Julliere (1975). A change of nearly 14% at 4.2 K was observed in the Co/Ge/Fe junction. Many other experimental works at room temperature and for various tunnel junctions have also been reported (Maekawa and Gäfwert 1982, Gallagher et al 1997, Moodera and Kinder 1996,

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Figure 2.101 The dependence of the tunnelling conductance on the angle between the magnetizations of two magnetic electrodes (Miyazaki and Tezeuka 1995).

Moodera et al 1996, Sato and Kobayashi 1997, Miyzaki and Tezuka 1995, Yaoi et al 1993, Tiusan et al 1999). The junction structure is usually manufactured by deposition on the ferromagnetic layer – 1–2 nm thick film of Al or Mg. This film is then oxidized to obtain the Al2O3 or MgO insulator layer. Various techniques of oxidation have been used, for example plasma oxidation, thermal oxidation, oxygen glow discharge or deposition of Al2O3 from the target (Beech et al 1996). Ferromagnetic layers are uncoupled therefore to obtain switching behaviour between parallel and antiparallel configurations exchange biasing similar to that employed in spin valves is necessary. Two ferromagnetic layers with different coercivities may be used, exchange biasing one of the layers by MnFe or an artificial Co/Ru/Co layer (Tiusan et al 1999). In comparison with spin-valve structures the exchange biasing layer must be an electrical conductor because current flows perpendicular to the plane. Figure 2.102 presents the R/R f(H) characteristics determined for two examples of submicron tunnelling junction structures: MnFe/NiFe/I/Co and

Figure 2.102 The dependence of the resistance on the magnetic field determined for tunnelling junction structures: MnFe/NiFe/I/Co and MnFe/Co/I/NiFe (Gallagher et al 1997).

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MnFe/Co/I/NiFe. In the first structure (figure 2.102(left)) the permalloy layer is biased, and the Co-layer is free. This structure consists of [Pt 20/NiFe 4/MnFe 10/NiFe 8]/ [Al2O3 2]/[Co 8/Pt 20]. In the second structure (figure 2.102(right)) the Co layer is biased, and the permalloy layer is free. It consists of [Co 20/NiFe 4/MnFe 10/Co 10]/[Al2O3 2]/[NiFe 20/Pt 20]. The hysteresis is much smaller when the permalloy layer is free. Because the switching field interval is very small it is expected that magnetic tunnel junctions may be used as very sensitive magnetic field sensors. The magnetoresistivity ratio depends on the material of the magnetic layers. The theory of the magnetic tunnel junction including the analysis of the choice of material have been developed by Juliere, Slonczewski and others (Slonczewski 1989, Juliere 1975, Maekawa et al 1996, Meservey and Tedrow 1994, Meservey et al 1983). The tunnel junction magnetoresistance may be described by the expression (Julliere 1975) R 2P1P2 —— ———— R 1 P1P2

(2.65)

where P is the spin polarization n↑ n↓ P ———–. n↑ n↓

(2.66)

The spin polarization was determined as 44% for iron, 34% for cobalt and 11% for nickel (Meservey and Tedrow 1994). By substituting these data into equation (2.65) a magnetoresistance of 32% for Fe/I/Fe tunnel junction is obtained. The experimentally determined magnetoresistance for such a structure

Figure 2.103 Theoretically determined expected values of the magnetoresistivity of various electrodes in the tunnelling junction structures (Miyazaki and Tezuka 1995).

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was equal to 30% at 4.2 K and 18% at 300 K. Figure 2.103 presents the expected values of magnetoresistivity calculated from equation (2.65). The experimental data in some cases may be very close to the model described by equation (2.65). For example a value of 25.6% at 4.2 K for CoFe/I/Co junction has been reported while the theoretical value is 27.6% (Moodera and Kinder 1996). In the model developed by Slonczewski (1989) the effective spin polarization also depends on the barrier. Assuming a rectangular barrier potential between the ferromagnetic layers the conductance is described by the expression G —— G

( )

2P1P2A12A21

(2.67)

max

where polarization factor P is described as: k↑ k↓ P ———– k↑ k↓ and interfacial factor A is described as: 2 k↑k↓ A ———— 2 k↑k↓ where: k – majority and minority spin Fermi wave vectors, 2/2 and is the magnitude of the potential barrier. The largest value of magnetoresistivity ratio at room temperature has been reported as 42% for the CoFe/I/CoFe junction (Parkin et al 1999). Various tunnel junction FM/I/FM materials have been tested, for example Co, Fe, Ni, CoCr, CoFe, FePb, NiFe. The typical value of maximal resistivity changes is 14–17 at room temperature. It corresponds to a sensitivity of 60%/kAm1 (Moodera and Kinder 1996). The spin-dependent tunnelling sensors with resolution of picotesla have been reported (Tondra et al 1998). The tunnelling magnetoresistance effect has also been reported in granular films (Fujimori et al 1995, Furubayashi and Nakatani 1995, Huang et al 1997). In these films the ultrafine magnetic particles are embedded in the insulator matrix. Figure 2.104(left) presents the dependence of the magnetoresistivity on the thickness of the insulator layer determined experimentally for the structure NiFe/Co/Al2O3/Co/NiFe/FeMn/NiFe. The magnetoresistivity ratio was almost constant for different thicknesses, but above 1.5 nm the tendency to decrease is observed. The thickness of an insulator layer is of the order 1–2 nm. Technologically it is difficult to prepare thin and smooth insulator layers free from pinholes. The magnetoresistivity depends on the bias voltage, probably due to the influence on the potential barrier (Yaoi et al 1993). It was experimentally determined that the bias voltage should be not larger than 10 mV because above this value the magnetoresistivity significantly decreases, as shown in figure 2.104(right).

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Figure 2.104 The dependence of the magnetoresistivity on the thickness of the insulator layer and the bias voltage (Sato and Kobayashi 1997).

Figure 2.105 The switching characteristic determined for the MnFe/CoFe/I/CoFe structure (Parkin et al 1999).

Due to a very sharp change of resistance with magnetic field obtained for a small area of the sensor tunnel junction structures are attractive candidates for use in nonvolatile random access memory (Daughton 1997). Figure 2.105 presents the room temperature switching characteristics of the MnFe/CoFe/Al2O3/CoFe structure with dimensions 40 40 m. To obtain very large sensitivity several sensors may be connected in one chip. This type of very sensitive sensor has been developed by the Nonvolatile Electronics team (Beech et al 1996, Tondra et al 1998) and is described in the next sections.

2.2.7 Colossal magnetoresistance (CMR) thin film structures Extraordinary large magnetoresistance (for example almost 108% at 60 K (Chen et al 1996)5 appears in doped manganate perovskite-like thin films. This effect The authors describing the CMR effect use the definition of MR ratio as MR [R(H 0)–R(H Hs)]/R(H Hs), where Hs – saturation field. Assuming another definition MR [R(H 0)–R(H Hs)]/R(H 0) the reported MR ratio 108% corresponds to 99.999%. 5

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is often called colossal magnetoresistance (von Helmolt et al 1995, Ramirez et al 1997). In the oxide of lanthanum manganite, LaMnO3, the La3 ions are partially replaced with 2 valence ions such as Ba, Ca, Cd, Sr, Pb and the structure of the material changes from orthorhombic to rhombohedral (Urushibara et al 1995). Simultaneously the material exhibits strong ferromagnetism and the resistance significantly decreases (Jonkwer and van Santen 1950). After appropriate heat treatment huge negative, isotropic magnetoresistance can be achieved in this material. The mechanism of magnetoresistance in doped manganate perovskites is not yet fully understood. Several theoretical models have been proposed to explain CMR effects in magnetic oxides. Usually the analysis starts with the doubleexchange interaction model (Zener–Gennes model – Zener 1951, de Gennes 1960, Anderson and Hasegawa 1955) assuming mixing of Mn3/Mn4 valence and creating mobile charge carriers (Zener carriers), which increase conductivity. The double-exchange interaction model is not sufficient to fully explain the colossal magnetoresistance (Millis et al 1995). Therefore the importance of electron-lattice coupling is considered (Jahn–Teller effect of electron–phonon coupling) resulting in conduction via polarons (Millis et al 1996, Hwang et al 1995, Jaime et al 1996). It is suggested that the change in resistance is caused by current carrier density collapse due to the formation of immobile pairs of polarons in the vicinity of Tc temperature (Alexandrov and Bratkovsky 1999). Other models assume that spin-dependent electronic transport across local magnetic clusters is the origin of the very large magnetoresistive effect (Zhang 1996, Zhang and Yang 1996, Sun et al 1996). Also the intergrain tunnelling effect has been taken into account (Hwang et al 1996, Lu et al 1996). Figure 2.106 presents typical transfer characteristics of the LaCaMnO film structure. In this case applying a magnetic field causes the transition from 1.3 M resistance to 1 k. From figure 2.106 it is evident that the manganate CPR structures suffer from two main drawbacks. The first is that to obtain a very large change of resistance, applying a very large magnetic field is required (2000–5000 kA/m). The second drawback is that the CMR effect occurs only in

Figure 2.106 The transfer characteristic of CMR and the dependence of CMR effect on the temperature determined for LaCaMnO film (Jin et al 1994, 1994b).

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a small region of temperatures in the vicinity of the Curie temperature as illustrated in figure 2.106. Because the Tc temperature is relatively low the colossal magnetoresistive effect is limited to very low temperatures and high fields. Various material compositions have been tested in the structure R1–xAxMnO3, where R are rare-earth components and A alkaline-earth components. The most frequently investigated is the La-Ca-MnO3 structure6, but also La-Ba-MnO3 (van Helmolt et al 1993), La-Sr-MnO3 (Lu et al 1996), La-Pb-MnO3 (Searle and Wang 1970), Nd-Sr-MO3 (Xiong et al 1995), Nd-Pb-MnO3 (Kusters et al 1989) have been considered. Table 2.12 presents the parameters of selected CMR structures. Table 2.12 The parameters of selected CMR structures. Structure

Tp [K]

Hs [kA/m]

R/R [%]

Ref

La0.67Ca0.33MnO3

77

4800

127 000

[a]

La0.67Ca0.33MnO3

100

4800

125 000

[b]

La0.67Ca0.33MnO3

226

660

130

[c]

La0.7Ba0.3MnO3

300

5600

150

[d]

La0.74Pb0.24MnO3

325

1600

30

[e]

La0.80Sr0.20MnO3

290

60

[f]

L0.55Ca0.25Sr0.08MnO3

313

2400

51

[g]

La0.6Y0.07Ca0.33MnO3

60

5600

100 000 000

[h]

a – Jin et al 1994, b – McCormack et al 1994, c – Zeng and Wong 1995, d – von Helmolt 1993, e – Srinivasan et al 1995, f – Ju et al 1994, g – Jin et al 1994, h – Chen et al 1996.

The La-Ca-MnO3 structures exhibit the largest magnetoresistivity ratios but their transition temperature Tp is low. The highest transition temperature was observed in La0.7Sr0.3MnO3 – 380 K (Ju et al 1994) and LaPbO3, but with a smaller magnetoresistivity than La-Ca-MnO3 alloys. The magnetoresistive effect depends on the composition of the alloy and is largest in the ferromagnetic region below a ferromagnetic transition. Figure 2.107 presents the dependence of the Curie temperature on the composition La1–xRxMnO3 for the most frequently used CMR materials. Although dc, rf and ion beam sputtering are reported as the methods enabling the deposition of oxide films, some problems may arise in non-stoichiometric transfer from the target. The most widely used technique is pulsed laser deposition on perovskite single crystal LaAlO3 or SrTiO3. Let us follow the typical technological process of manufacturing La-Co-MnO3 thin film reported 6 For example: Jin et al 1994, 1994b, Gong 1995, McCormack 1994, Mathur et al 1997, Snyder et al 1996, Schiffer et al 1995, Chahara 1993, Chen et al 1995.

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Figure 2.107 The dependence of the transition temperature on the material composition determined for various manganese oxide materials (Ju et al 1994).

by Jin and co-workers (1994). Thin film was deposited on (100) LaAlO3 substrate by pulsed laser deposition to the thickness 100 nm. The substrate was heated to 650–700 °C. After deposition the film exhibited the same composition La0.67Ca0.33MnOx as target. The deposited film exhibited an MR ratio about 500% at temperature range 50–300 K. After heat treatment at 900 °C/30 min in an oxygen atmosphere magnetoresistance increases to 127 000% at 77 K. Further annealing at 900 °C/3 h caused the MR value to decrease (to 11 000%) but at a higher temperature of 100 K. Figure 2.108 presents the characteristics of the structure with the largest reported magnetoresistance. It was obtained by partially substituting La3 ions with smaller Y3 ions in the structure La0.6Y0.07Ca0.33MnO3. The deposited film exhibited an MR ratio of 370% at 85 K. But after heat treatment at 850 °C/2 h in oxygen the MR ration improves to 2.3 107%. After applying the magnetic field, the resistance of about 1450 M drops to 6.1 k. The optimal thickness of the film was determined as 100 nm.

Figure 2.108 The transfer characteristic and temperature influence determined for the structure LaYCaMnO (Chen et al 1996).

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The large field and low transition temperature are the fundamental limit of the potential applications of CMR structures. Therefore the main research efforts concentrate on the materials and technology of the CMR effect at room temperature and at low field (Manoharan et al 1994, Hwang et al 1996, Sun et al 1996). The results are rather modest. Figure 2.109 presents two room temperature characteristics of CMR sensors. Although some materials were found with transition temperature of up to about 380 K a very large magnetic field was still required to change resistance. For example the La0.6Pb0.4MNO3 structure can operate at 300 K but has a resistance change of 40% in a large magnetic field of 5000 kA/m (figure 2.109).

Figure 2.109 The room temperature CMR effect in La-Pb-Mn-O film (Manoharan et al 1994).

The decrease of magnetic field to about 16 kA/m was possible in the current perpendicular to plane construction (CPP), but only at low temperatures (Sun et al 1996). One of the methods of increasing the transition temperature is heat treatment of the sample in oxygen or deposition with a higher oxygen partial pressure (Jin et al 1994). In this way a structure with magnetoresistivity ratio of about 470% at 280 K has been obtained. However, the strong dependence of the magnetoresistivity on temperature is not acceptable – after decreasing the temperature from 280 K to 260 K magnetoresisitvity increases from 470% to 1300%. Sensors with the resistance change from the insulator to metal might be very attractive, especially in switching applications. But it is questionable whether this class of the material will be useful at room temperature and low field. Several new materials exhibit the colossal effect, for example chalcogenite spinels (Ramirez et al 1997) or pyrochlore structures (Subramanian et al 1996).

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2.2.8 Giant magnetoimpedance (GMI) structures The giant magnetoimpedance effect was first developed in very thin nanowires and ribbons7. In wires made from amorphous or nanocrystaline material with diameters of several m the magnetoimpedance effect was as large as 400%. These wires supplied by a high frequency current may achieve sensitivity better than 100%/kAm1 for a magnetic field not exceeding 1 kA/m. The magnetoimpedance effect in wires arises from the change of permeability with external magnetic field and consequently the change of depth of the skin effect. Due to the skin effect both resistance and inductance change with the applied magnetic field. Figure 2.110 presents the dependence of the skin depth and the permeability on the external magnetic field H.

Figure 2.110 The dependence of the skin depth and permeability on the external magnetic field in the amorphous nanowire (Velazquez et al 1994).

The skin depth depends on the permeability and current frequency f

——–

——. f

√

(2.68)

The impedance Z of wire with diameter a and length l depends on skin depth as described in the following expression (Mohri et al 1997) l 1 l 2 Z — —— j —– —. a 2 8 a

(2.69)

Figure 2.111 presents typical experimentally determined transfer characteristics of Co68.15Fe4.35Si12.5B15 amorphous glass-covered wire with diameter 14.5 m and 5 cm long. The dc magnetic field for which GMI reaches its maximum corresponds approximately to the anisotropy field. For example: Makino et al 1989, Squire et al 1994, Mohri et al 1992, 1995, 1997, Panina and Mori 1994, Panina 1994, Beach and Berkowitz 1994, Rao et al 1994, Tejedor et al 1996, Knobel et al 1996, 1997, Chiriac et al 1997. 7

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Figure 2.111 The transfer characteristic Z = f(H) and the dependence of the magnetoimpedance on the frequency determined for Co68.15Fe4.35Si12.5B15 glass-coated nanowire (Chiriac et al 1997).

The idea of a magnetoimpedance effect has been transferred to thin film technology (Sommer and Chien 1995, Senda et al 1994, Xiao et al 1998, 1999, Morikawa et al 1996, 1997, Panina et al 1997, Liu et al 1996, Takezawa et al 1998). The adoption of a thin film structure decreases the dimensions of the sensor and increases current frequency. These parameters are important for applications such as read heads (Senda et al 1995, 1996). The impedance of thin film structure with thickness d, width w and length l may be described by the expression (Panina 1995).

√

l d Z — ——– — w √ 2

———————– d d cosh — cos — —

l —— √ —————–—— —— √ d d 2w cosh — cos —

(2.70)

where: is a transverse permeability for the circumferential field H, which is generated by a high frequency current flowing through the film. An example of the transfer characteristics determined for the (CoFe)80B20 amorphous film with dimensions: thickness 4 m, width 300 m and length 10 mm is presented in figure 2.112. The twin peaks correspond to the anisotropy field. The induced anisotropy is a crucial parameter, which influences the shape of Z/Z f(H) characteristics (Sommer and Chien 1995, Tejedor et al 1996). The anisotropy depends on the materials’ composition, shape of the structure and deposition conditions. An appropriate annealing process must be chosen (Takemura et al 1996, Knobel et al 1995). It is advantageous that after annealing the characteristic Z/Z f(H) does not change with temperature. Thin film structures require much higher current frequencies (for a wire of thickness 4 m this frequency is 10 MHz while in the film it is 80 MHz). With decreasing film thickness (which is necessary for high density reading of information) a frequency higher than GHz is necessary to induce the skin

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Figure 2.112 The transfer characteristic Z f(H) and the dependence of the magnetoimpedance on the frequency determined for the (CoFe)80B20 amporphous film sample (Uchiyama 1995).

effect. Therefore other sandwich-type GMI structures have been developed (Senda et al 1994, Xiao et al 1999). To obtain the GMI effect in sandwich-type structures a significant skin effect is not required. The main contribution to impedance is the inductance of the coil, which depends on permeability (H). An example of such a structure and its characteristic is presented in figure 2.113. The magnetic layers of thickness 50 nm form a closed loop around a copper layer with thickness 100 nm and width 4 m. The impedance of a sandwich structure with length l may be described by the expression (Hika et al 1996) dm l dm Z R j —– l(H) ———– j —– l(H) 2b 2bdcc 2b

(2.71)

where: dm, dc, b – dimensions as in figure 2.113. Morikawa and co-workers (1996) proposed further enhancement of the layered structure by introducing an additional insulator separation (figure 2.114). An example of the transfer characteristic determined for the CoSiB/SiO2/Cu/SiO2/CoSiB structure is presented in figure 2.114. The driving current only flows in the Cu layer (due to SiO2 separation) and the giant magnetoimpedance effect (Z/Z)max 700%

Figure 2.113 The sandwich magnetoimpedance structure and its transfer characteristic Z f(H) determined for the NiFe/Cu/NiFe sensor (Hika et al 1996).

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Figure 2.114 The construction and the transfer characteristic CoSiB/SiO2/Cu/SiO2/CoSiB sandwich structure (Morikawa et al 1996).

259

Z f(H)

of

the

for Hmax 0.9 kA/m and f 20 MHz has been obtained. A comparison of different structures: single-layer CoSiB, sandwich layer CoSiB/Cu/CoSiB and sandwich isolated layer CoSiB/SiO2/Cu/SiO2/CoSiB with the same dimensions is presented in figure 2.115. Senda and co-workers (Senda et al 1994, 1995, 1996) proposed another GMI structure. A magnetic strip composed of a multilayer film (NiFe/SiO2 50/50 nm 10) formed a closed magnetic circuit around the Cu layer. This structure exhibits magnetoimpedance of 70% for frequencies 600–1000 MHz. In high density storage systems a large current frequency may be advisable, because it is able to detect signals with a broad bandwidth. Jiang

Figure 2.115 The dependence of the impedance change ratio on the driving frequency determined for various thin film sensors: CoSiB, CoSiB/Cu/CoSiB and CoSiB/SiO2/Cu/SiO2/CoSiB (Morikawa et al 1996).

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Figure 2.116 The impedance sensor in the Colpitts oscillator circuit and the output characteristic of the circuit (Uchiyama et al 1995).

and co-workers designed a GMI structure composed of a 3 m thick Cu ground plane layer, 0.5 mm thick dielectric layer and 1 m thick amorphous Co85.6Zr5.2Nb9.2 magnetic strip (5 by 20 m). Due to the appropriate geometry a bandwidth of 300 MHz with sensitivity 75 mV/kAm1 has been obtained. The giant magnetoimpedance sensors are attractive alternatives to existing sensors. Due to large sensitivity they are competitive with fluxgate sensors. Small dimensions, large magnetoimpedance ratio and wide frequency bandwidth mean that they can be used as reading heads (Senda et al 1996). The electronic circuit may directly transform the output signal into the voltage. An example of such a circuit is presented in figure 2.116. The sensor is connected into the Colpitts oscillator circuit. The oscillation frequency as a dependence on the impedance of the sensors may be expressed as follows ————————– 1 r(H) 1 — 1 —— — C2 R C1 f —————————– — 2 √ L(H)

√ (

)

(2.72)

where: r(H), L(H) – resistance and inductance of the sensor, R – input resistance of a transistor. The oscillator circuit amplifies the signal of the sensor. The output characteristic of the oscillator circuit is presented in figure 2.116.

2.3 PREPARATION, DESIGN AND PROPERTIES OF GMR SENSORS

2.3.1 The deposition of thin film GMR structures The most frequently used method of GMR preparation is sputtering deposition of the layers (Chapman 1980). Two techniques – DC magnetron sputtering and

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RF diode sputtering – have been reported. However, by looking at the data reported in the literature, it can be concluded that all typical thin film deposition techniques (Glocker 1995, Ohring 1992, Westwood 1989) can be adapted to manufacture GMR sensors. Exchange-coupled structures are very often prepared using the molecular beam epitaxy (MBE) method (Herman and Sitter 1996), colossal magnetoresistance structures are prepared by the pulsed laser deposition (PLD) method. Eectron beam evaporation or ion beam sputtering are often used. Even chemical vapour deposition (CVD) and electrodeposition have been reported. High quality films grown by molecular beam epitaxy (MBE) is a fundamental method of thin film physics research. It is able to obtain films with almost perfect crystallinity. Therefore it yields valuable information which is essential to the understanding of exchange coupling and giant magnetoresistance processes. The use of the MBE method does not automatically mean that the best magnetoresistor is obtained. Experiments did not prove that multilayers prepared by the MBE method exhibited better parameters than sputtered ones. Often the MR ratio is smaller and the saturation field is larger when film is grown by the MBE method (Kobayashi et al 1993). It may be concluded that the MBE method is preferable for research but the sputtering method is recommended in the production of GMR sensors. Modern sputtering equipment also obtains films of very good crystalline quality (experiments proved that highly oriented or single crystalline multilayers could be manufactured) (Harp and Parkin 1994, Mattson et al 1995). In his study on the MBE method in magnetoresistance and exchange coupling Farrow (1998) stated that both techniques are complementary. Figure 2.117 presents the main idea of the molecular beam epitaxy technique. The evaporated beams of atoms or molecules are transferred from the source to the rotating (and eventually heated) substrate. An important feature of epitaxial film growth is that the deposited film mimics the crystallographic orientation of the substrate. Therefore usually a crystal with the desired crystallographic

Figure 2.117 The principle of operation of the MBE deposition system.

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orientation is used as a substrate, for example sapphire Al2O3, GaAs, MgO. An ultrahigh vacuum (UHV) with pressures lower than 107 Pa is required. The rate of deposition is rather slow at 0.005–0.1 nm/s. The important advantage of MBE equipment is the possibility of monitoring the film structure and composition during growth in situ (in sputtering this is impossible due to the background pressure precluding the use of an electron beam). Some apparatus may also control the growth by the feedback technique – the results of analysis are transferred to a process control computer (figure 2.117). Practically all MBE apparatus are equipped with RHEED (Reflection High Energy Electron Diffraction) analysers. In the RHEED method the electron beam is incident to the film surface and after reflection it is presented on the screen. The pattern representing lattice planes, roughness or number of multilayers is visible on the screen. Figure 2.118(a) presents an example of the RHEED picture of the NiFe/NiO bilayer when NiFe was deposited on the NiO layer (Han et al 1997). Figure 2.118(b) presents a method of counting the number of monolayers during growth of the superlattice structure (one cycle of oscillations corresponds to one monolayer growth). Sometimes the MBE apparatus is equipped with other analysing instruments, for example an Auger electron spectrometer or X-ray photoelectron spectrometer. The first GMR structure described by Baibich and co-workers (1988) was prepared by molecular beam epitaxy. The (001)Fe/(001) Cr bcc superlattices were grown on (001) GaAs substrate with deposition rates of 0.06 nm/s and 0.1 nm/s respectively. The residual pressure of the MBE chamber was 6.6 109 Pa (5 1011 Torr) and the substrate temperature was around 20°C. The crucible of molybdenum was heated by electron bombardment. A similar technique was reported by Schad and co-workers, who achieved the largest 220% GMR effect (Schad 1994). The Fe/Cr superlattices were grown on MgO (100) substrate held at 50°C with a deposition rate of 0.1 nm/s. The deposition chamber was equipped with two E-beam evaporators. The pressure was 2 109 Pa (2 1011 mbar).

Figure 2.118 The method of analysis: (a) composition and crystal structure; (b) number of layers by means of RHEED method (Han et al 1997, Herman and Sitter 1996).

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Figure 2.119 The principle of operation of sputtering deposition: (a) DC sputtering method; (b) RF sputtering method (Ohring 1992).

In the sputtering method atoms are dislodged from the solid target surface by impact of gaseous ions. Figure 2.119 presents the idea of two systems: DC and RF sputtering. In these systems after preparing a low-pressure vacuum environment (typically 106–107 Pa) a gas, usually argon, is introduced (typically pressure 0.1–0.5 Pa) to the sputtering chamber. The gas is required to ensure a glow discharge in order to transfer the ions as plasma from the target (cathode) to the substrate (anode) after applying power. One of the advantages of sputtering compared to the evaporation method is that film composition is very close to the target composition (for example when alloys are deposited). To enhance the speed and quality of deposition an additional magnetic field is introduced – such a system is known as magnetron sputtering. For insulator and poor conductive targets DC sputtering must be substituted by RF (radio-frequency) sputtering. Sometimes the combination of both systems is used simultaneously, especially in the case of many different layers, for example spin-valve structures. The target may be heated or biased, usually it is rotated to ensure homogeneity of the film. A magnetic field of 10–20 kA/m is often applied to improve the magnetic properties (Ichihara et al 1996) and/or induce magnetic anisotropy (Coehoorn et al 1998, Rijks et al 1994). Several manufacturers of thin film deposition equipment offer fully automated multi-target systems especially adapted to the preparation of GMR multilayers or spin-valve structures. An example of such a system is presented in figure 2.120. Let us follow the example of a typical process of deposition reported by Rijks and co-workers (1994) for the spin-valve structure. The NiFe 8/Co 2/NiFe 6/Fe50Mn50 8 structure was prepared by DC magnetron sputtering with 0.6 Pa argon pressure during deposition. The base pressure of the system was 106 Pa. The components were deposited at room temperature on a 4 12 mm Si(100) substrate with a deposition rate of 0.2 nm/s. A buffer layer of 3 nm Ta was deposited on the substrate, which was precleaned ex situ by a 2% HF dip.

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Figure 2.120 Multi-target sputtering system (system EMERAL of Balzers Process Systems).

During the deposition an external magnetic field of 10 kA/m was applied. Finally a 2 nm Ta capping layer was prepared. The ion beam deposition (IBD) method has been applied in many thin film technologies to produce films with enhanced physical properties. Therefore several groups have adapted this method to prepare magnetic structures 1. Figure 2.121 presents the idea of the IBD technique. The ion beam from the beam gun bombards the target and a flux of atoms is transferred for deposition on the substrate. The second ion gun may be used to stimulate the deposition process, for example to enhance the growth of crystallites. The main advantage of the IBD technique compared to conventional DC sputtering is that deposition conditions are much more controllable. Furthermore the background pressure may be quite low (for example 10 2 Pa – Wang et al 1997) resulting in better purity of atmosphere. Moreover the ion-beam sputtering rate is 3–5 times higher than conventional sputtering rates (Lo et al 1987). The results obtained by the IBD technique are satisfactory (for example Mao et al 1999, Slaughter et al 1999, Miyamato et al 1995, Naoe et al 1994) although significant improvements of GMR parameters have not been obtained to date. In the evaporation method the material heated by the electron-beam in the crucible is evaporated in vacuum to the substrate. This traditional technique is often substituted by sputtering methods because of better repeatability and suitability to industrial-scale manufacturing. The evaporation method is sometimes chosen because of its relative simplicity and physical For example: Wang et al 1997, Bailey et al 1996, Mao et al 1999, Russak et al 1992, Slaughter et al 1999, Lo et al 1987, Miyamato et al 1995, Naoe et al 1994.

1

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Figure 2.121 The dual ion-beam sputtering system.

transparency. Film formation and growth occur in a better vacuum and thus in a cleaner environment than during sputtering. Smith and co-workers (1996) have reported the following conditions of E-beam evaporation used to prepare a GMR sensor: background pressure 2 106 Pa, substrate temperature 200°C, evaporation rate 0.2 nm/s. The layers were evaporated in a field of 12 kA/m on 3 in oxidized Si wafers using a graphite crucible with Ni83Fe17 (at.%) and 99.95% pure Cu. The wafer was post-annealed for 2 or 4 hours in purified Ar at temperatures of 250–350°C in a magnetic field of 15 kA/m. Matsuyama and co-workers (1996) reported the preparation of highly sensitive and hysteresis free spin-valve sensors using conventional electron beam evaporation. More details about evaporation deposition are in the first part of this book devoted to AMR sensors. In the pulsed laser deposition (PLD) method a high-powered pulsed laser is focused on the target material to be ablated (figure 2.122). For example McGrath (1992) used a pulsed Quantel Nd:YAG laser with a pulse duration of 9 ns and a pulse frequency of 10 Hz. The radiation wavelength was 532 nm (frequency doubling of the Nd:YAG fundamental) with a maximum energy per pulse of 0.3 J. The absorption of the laser beam results in the formation of a plasma, which is the main difference compared to thermal evaporation. The laser ablation is frequently used for deposition of complex oxides because it is easy to obtain stoichiometric transfer of material from the target to the surface. Omitting many specific problems related to each deposition method the main difference between them is in the energy distribution of the atoms arriving at the film surface (figure 2.123). During MBE deposition atoms arrive with similar thermal energies and they can grow in a well-ordered way. Atoms arriving during the sputtering process may have different energies and angular variations depending on gas pressure, acceleration voltage, bias voltage, distance between the target and the substrate. The film morphology

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Figure 2.122 The principle of operation of the pulsed laser deposition system.

Figure 2.123 Kinetic energy distribution of Cu atoms arriving at the substrate – calculated by Kools (1995).

(crystallity, grain size, roughness, interdiffusion mixing) strongly depends on the deposition conditions.

2.3.2 Technological factors affecting the performances of GMR sensors GMR sensors are rather complex systems and therefore various parameters influence their performances. The composition of the material or the thickness of the layers are specific for different GMR structures and have been analysed in previous chapters. Common to all structures are the technology dependent problems of the quality of deposited structures. The technological conditions affecting spin-valve performances as an example

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will be analysed in more detail because this structure is the most promising candidate for sensors or reading heads. A good quality sensor should exhibit following features: • a large value of magnetoresistivity ratio (R/R)max, (Rmax Rmin)/Rmax, • large sensitivity S (R/R)max/Hs, • small hysteresis usually described by coercive field Hc, • small anisotropy field Hk of the unpinned layer (sensitivity depends on Hk), • large exchange biasing field Hex, • small changes of parameters with temperature, • good repeatability and reliability. These features depend on the technological parameters: interface quality (roughness, interfacial mixing), crystal quality (texture, grain size) and material quality (purity of composition and structure). These technological parameters also depend on the deposition conditions: sputter gas pressure, base gas pressure, type of sputter gas, quality of the substrate, substrate temperature or biasing, sputtering power. In ‘normal’ thin film magnetic devices these relations are obvious – better deposition parameters (or technological parameters) mean better performances of the device. For example deposition of AMR structures in ultrahigh vacuum has resulted in lower dispersion of anisotropy compared to using an ordinary vacuum (Chapman et al 1981). But in the case of GMR structures quite surprising inverse relations have been reported (Miura and co-workers 1998, 1999). Improving the base pressure from 9.3 106 Pa to 4.0 106 Pa resulted in a magnetoresistivity deterioration from 48% to 14% in the Co/Cu multilayer structure (figure 2.124). It has been determined that the probable reason for this puzzling effect was the change of interfacial roughness. Bailey and co-workers (1996) developed an ion beam deposition technology and obtained an almost perfect (111) texture, which is very desirable. They also obtained a decrease of the magnetoresistivity ratio from 6.7% to 2.8% in the spin-valve structure.

Figure 2.124 The deterioration of magnetoresistivity after decreasing residual impurities (oxygen) in sputtering atmosphere and after preparation in an ultra-clean vacuum (Egelhoff et al 1997, Miura et al 1998, 1999).

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Egelhoff and co-workers (1997) tested the influence of the purity of the base vacuum on the GMR effect. By removing p(H2O) below 107 Pa an increase of the GMR ratio has been observed. But further reduction of p(H2O) to 108 Pa resulted in a sharply lower GMR effect (23% to 17% decrease). It was found that the oxygen in the gas was a surfactant on the growth suppressing the Cu/Co intermixing and influencing the surface roughness. Indeed, it is evident that GMR prefers some kind of controllable disorder. These examples show how the precise choice of deposition conditions is important. One of the most important problems is the influence of interface roughness on the GMR effect (Park and Shin 1997, Yang and Scheinfein 1995, Suzuki and Taga 1995, Doherty et al 1998, Choe and Steinback 1999, Nakanishi et al 1993). Many groups have investigated the effects of the interfacial roughness in exchange-couple multilayers (Fullerton 1992, Rensing et al 1993) and in spin-valve structures (Park et al 1996, 1996b, Lai et al 1996). It was observed that changing the sputtering gas pressure or the sputtering power resulted in changes of roughness, and correspondingly changes of magnetoresistivity. Also annealing significantly changes roughness. Figure 2.125 presents the results of investigations of the Fe/Cr multilayer reported by Rensing and co-workers (1993). From X-ray diffraction spectra (figure 2.125(left)) it is evident that decreasing gas pressure results in the decrease of layer roughness – the supperlattice Bragg peaks are more differentiated. Correspondingly the magnetoresistance appeared as roughness dependent. The structure with the larger roughness exhibited a lower magnitude of MR ratio and the oscillations vanished (figure 2.125(right)).

Figure 2.125 X-ray diffraction data and magnetoresistance dependence versus Cr-layer thickness determined for different values of gas pressure (investigated structure Fe/Cr/Fe) (Rensing et al 1993).

Park and co-workers (1996, 1997) investigated roughness and magnetoresistivity for different gas pressures during preparation of the FeMn/NiFe/Cu/NiFe spin-valve structure. Figure 2.126(left) presents the dependence of the roughness on the gas pressure and figure 2.126(right)

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Figure 2.126 Roughness and transfer characteristic determined for different values of gas pressure (investigated spin-valve FeMn/NiFe/Cu/NiFe structure – curve a and b collected from two sources) (Park and Shin 1997, Park et al 1996).

presents the transfer characteristics of the sensor. Most of the experiments indicated an increase of roughness with an increase of gas pressure. The dependence of the MR ratio on the roughness is presented in figure 2.127. For the Si/FeMn 5/NiFe 8/Cu 2.8/NiFe 4/FeMn 15 structure the optimal value of the gas pressure (and roughness) has been determined (Park et al 1996, 1997). It was found that the largest magnetoresistivity occured for the gas pressure of about 0.7 Pa. It is interesting that the ideal flatness of the interface is not necessary to obtain the largest magnetoresistivity and the magnetoresistance is enhanced by the presence of roughness. The optimal deposition conditions determined by Park were as follows: argon pressure 0.6–0.9 Pa, sputtering power 40–50 W, roughness Rrms 1.1–1.3 nm. Han and co-workers (1997) differentiated the roughness by changing the deposition conditions for the same run of the sputtering process. It has also been found that the magnetoresistivity increased with increasing of roughness. Park and co-workers also tested the relation between roughness and the coupling or exchange fields. It was found that the coupling field decreased and the exchange field increased with decrease of roughness (figure 2.127).

Figure 2.127 Dependence of magnetoresistivity ratio and coupling field on roughness (curve a and b collected from two sources) (Han et al 1997, Park and Shin 1997).

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The influence of roughness can be explained by taking into account coupling fields (Zhang and White 1996, 1996b, Moran et al 1995, Choe and Gupta (1997), Bobo et al 1993). The coupling field is the sum of three contributions: oscillatory exchange coupling, ‘orange peel’ magnetostatic coupling and direct exchange ‘pin hole’ coupling. Roughness is dependent on the magnetostatic coupling caused by correlated waviness of non-ideal flat films. This coupling depends on the roughness parameters: amplitude h and wavelength (as described in the section 2.1.3). The magnetostatic coupling induced by interfacial roughness was calculated and tested by Zhang and White (1996). Dan Wei and Bertram (1996) presented the numerical simulation of the interlayer coupling dependence on the roughness. The three-dimensional model with ‘pyramid-shape’ roughness was calculated with the discretization of magnetic spins at an atomic scale. The position of the spin was calculated from the minimum energy state by numerically integrating the complete Landau–Lifshitz equation. The results (figure 2.128) proved that for smooth surfaces exchange coupling dominated. When surface has roughness the coupling becomes less antiferromagnetic because spins remain approximately parallel to the topological shape. Thus the roughness reduces the exchange coupling and creates magnetostatic coupling. The technology conditions also influence the interfacial mixing of neighbouring layers (Speriosu et al 1993, Nozieres et al 1993). Petroff and coworkers (1991) introduced artificial mixing by short-time codeposition of the second material. The structure with a mixed interface exhibited larger magnetoresistance. Saito and co-workers (1993) indicated a strong dependence of the magnetoresistivity effect on the argon acceleration voltage VB (figure 2.129). The analysis of the interface structure using the 59Co NMR technique elucidated this effect as the large mixing ratio of Co and Cu at the interface

Figure 2.128 The results of calculation of spins in the spin-valve structure with roughness: (a) the initial conditions; (b) after calculation of the minimum energy state (Dan Wei and Bertram 1996).

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Figure 2.129 The transfer characteristics and NMR spectra of the Co/Cu superlattice deposited using different acceleration voltages (Saito et al 1993).

region. Figure 2.129 presents the NMR spectra of superlattices as a function of the acceleration voltage. The largest magnetoresistive effect corresponded with the sharpest interface. At the interface mixing of different phases of fcc and bcc components may also exist (Meny et al 1993) or the ultrathin layer with a nonmagnetic moment (dead layer) (Kools 1995, Speriosu et al 1993, Nozieres et al 1993). The interfacial mixing is very important because it is the main reason for thermal instability. During annealing (Meny et al 1993, Huang et al 1992) interdiffusion of mixed components appears causing a large, permanent change of magnetoresistivity. Iwasaki and co-workers (1997) investigated the interdiffusion effect by Auger spectroscopy. The results are presented in figure 2.130. After annealing the diffusion of Co atoms in the FeMn layer and Mn atoms to the Cu layer has been observed. In general the magnetoresistance decreases monotonically with temperature (Dieny et al 1991, 1992, 1998, McMichael 1995). Dieny and co-workers

Figure 2.130 The Auger depth-profiles for the FeMn/Co/Cu spin-valve structure: as deposited and after annealing (Iwasaki et al 1997).

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Figure 2.131 The temperature influence on magnetoresistivity in spin-valve sensors – for various AF layers and for various thicknesses of magnetic layer (Dieny et al 1992).

investigated the temperature properties of various spin-valve sensors. It was found that the magnetoresistivity ratio decreases monotonically with temperature to a certain temperature correlated with the Curie temperature of the magnetic layers (figure 2.131(left)). This temperature did not depend on the nonmagnetic layer and is the same for all thicknesses of magnetic layers (figure 2.131(right)). The decrease of the MR ratio with temperature was explained as the spin↑ and spin↓ intermixing due to magnon scattering. Iwasaki and co-workers (1997) found that the best thermal reliability was exhibited by a spin valve with an IrMn biasing layer. In the spin-valve structure of CoZrNb 10/NiFe 2/CoFe 3/Cu 3/CoFe 2.3/IrMn 8 the magnetoresitivity ratio decreased from 8% to 5% with a temperature change from 20°C to 160°C. It gives the temperature coefficient of about 2.5%/10°C. Figure 2.132 presents the temperature characteristics of spin-valve sensors. The exchange biasing field, anisotropy field and coercive field are strongly influenced by the crystal orientation. The most desirable situation is when the Hex/Hc ratio and the blocking temperature are large. Many investigations have proved that the most favourable is a [111] texture

Figure 2.132 The dependence of the spin-valve parameters on the temperature (Hp: exchange bias field, Hc: coercive field of pinned layer) determined for CoFe-IrMn spin-valve structure (Iwasaki et al 1997).

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Figure 2.133 The change of X-ray diffraction patterns and the change of exchange bias field Hp after applying a buffer layer and a bias voltage during sputtering (Choe and Gupta 1997, 1997b, 1998).

because it ensures maximum biasing field and minimum coercive field (Jerome et al 1994, Lubitz et al 1999, Choe et al 1998). When the NiFe layer is textured in the (111) direction only the uniaxial in-plane anisotropy remains. The texture can be introduced by an appropriate choice of the buffer layer. The thin Ta layer is almost ideal—it is effective in suppressing grain growth and maintaining the [111] texture. Choe and Gupta (1997, 1998) reported excellent parameters of spin-valve structures by enhancing the [111] texture of NiFe and FeMn. The layers were deposited in a DC magnetron sputtering system with a permanent magnet field used to induce uniaxial anisotropy. By applying an additional RF substrate bias at about 200 V it was possible to improve the texture, as shown in figure 2.133(left) and to improve the Hex/Hc ratio as shown in figure 2.133(right). Similarly Devasahayama and Kryder (1995) reported an improvement of the exchange field and coercivity of the spin-valve sensor by optimizing the deposition conditions, gas pressure and bias voltage.

Figure 2.134 The grain size distribution for different thicknesses of Cu underlayer (a) and the dependence of Hp f(T) determined for different grain sizes (Nishioka et al 1996(b)).

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Nishioka and co-workers (1996) analysed the dependence between grain size and coupling field in the spin-valve structure. The grain size was varied by changing the thickness of the Cu underlayer. The grain size distribution for different thicknesses of the Cu underlayer is presented in figure 2.134(a). By increasing the thickness of the Cu underlayer from zero to 30 nm the mean value of the grain size was varied from 2 nm to 6 nm. The coupling field decreased almost linearly with increasing temperature for larger grains. Concave curves were obtained for smaller grains. The coercive fields also decreased with the temperature but remained the same for different grain sizes. Various other technological methods to improve the performances of spinvalve structures have been reported, for example another gas (Kr or Xe) in the sputtering system (Donnet et al 1996) or using ion beam deposition (Wang et al 1997). Egelhoff and co-workers (1997) found that after deposition of 0.4 nm Au, Ag or Cu layer on a bottom spin valve the magnetoresistivity increased from 13.5% to 15%. Park and Shin (1998) enhanced the magnetoresistance characteristics of the spin-valve structure by two-step sputter deposition. This invention utilizes the effect that the parameters of spin-valve sensors depend on the argon sputtering pressure (Park and Shin 1997). A comparison of spin-valve characteristics obtained for different pressures shows that increasing the gas pressure from 0.1 Pa to 0.8 Pa results in an increase of the coupling field from 40 A/m to 1100 A/m (figure 2.135). Unfortunately the magnetoresistance decreases from 3.4% to 1.5% with decreasing gas pressure. It is possible to lower the coupling field without sacrificing the magnetoresistivity by applying a smaller argon pressure for only the bottom part of the structure. For example by deposition of the buffer layer at 0.1 Pa and the rest at 0.9 Pa an effective decrease of the coupling field can be obtained without effectively changing the magnetoresistivity (figure 2.136(c)). Interesting results

Figure 2.135 The dependence of the coupling field and magnetoresistivity on the gas pressure during deposition (Park and Shin 1997).

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Figure 2.136 The change of the coupling field and magnetoresistivity by optimizing deposition conditions: (a) p 0.7 Pa; (b) p 0.1 Pa; (c) FeMn 5 – buffer layer p 0.1 Pa and NiFeCo 8/Cu 2.8/NiFeCo 4/FeMn 15 p 0.7 Pa; (d) FeMn 5/NiCo 2 p 0.1 Pa and NiFeCo 6/Cu 2.8/NiFeCo 4/FeMn 15 (Park and Shin 1998).

have been obtained by separating the deposition of the pinned layer (part at 0.1 Pa and part at 0.7 Pa) as shown in figure 2.136(d). Analysis of the relations between technological conditions and obtained parameters of GMR structures emphasizes the need of very exact preservation of the process parameters. Even a small deviation might result in a large change of product quality. Fortunately it is possible to ensure good repeatability of most of the technological factors. The valuable analysis of the toleration of spin-valve parameters to variations of processing conditions in a production environment were presented by a group from IBM (Gurney et al 1997). They try to answer the question: can spin valves be reliably deposited for use as magnetic recording applications? From their experiences the spin-valve sensor should exhibit the following parameters: • magnetoresistance : 3.5% • resistance: 15 / , • coupling field: 0.45–1 kA/m • exchange bias field: 16 kA/m • uniaxial anisotropy field: 0.4 kA/m • magnetostriction: 2 10–6. The magnetostriction depends mainly on the correct choice of material composition. The rest of the parameters depend on geometrical factors. The dependence of the properties on the thickness of the layers P(t1,t2,…tn) allows the output voltage of the sensor to be expressed as a multivariate function F: V F[P1(t1,t2 ...tn ), P2(t1,t2 ...tn )....Pn (t1,t2 . . . tn )]. The gradient has been calculated as follows:

(2.73)

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∑ ki

P —–k tn

( V) —–— Pk

( )( ) 0

0

∑T

S

kn k

(2.74)

k

where: Sk – the sensitivity to the relative property Pk, Tkn – describes how much of a change in a relative property results from a given change of process parameter. If the distribution of process parameters tn is Gaussian with standard deviation tn the overall distribution of signal amplitude coming from the manufacturing line is

( V)

——————— ( V) —–— (tn )2. tn n

√∑( )

(2.75)

Sophisticated calculations have been performed taking into account micromagnetic modelling of the magnetization process and assuming that modern equipment enables deposition with a uniformity better than 3% and resolution better than 0.2 nm. Taking as a quality criterion that a 10% deviation from the mean signal amplitude might be considered. Gurney and co-workers have found that over 99.7% of the spin-valve depositions fulfilled design criteria. This means that spin-valve sensors can be manufactured in large scale production processes, as for example reading heads in magnetic recording devices.

2.3.3 The shape effects in thin film GMR devices In previous sections GMR devices were considered without taking into account the influence of the shape (therefore they were called structures to differentiate them from sensors). The performances of patterned sensors may be different from the ‘as deposited’ structure. Figure 2.137 presents a comparison of the transfer characteristic of a spin valve as deposited and after patterning the shape – the rectangular 2 5 m element of MRAM memory investigated by Matsuyama and co-workers (1997). The change of the R/R f(H) curve (and in general of the performances) is caused by the influence of demagnetizing fields. Besides the demagnetizing field in the real sensor an additional influence may appear – the magnetic field Hj created by the current flowing through the structure (Smith 1994, Kos et al 1997, Cross et al 1994). Thus in the expression describing the total energy (see section 2.1.5) two additional components should be taken into account, energy connected with shape anisotropy:

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Figure 2.137 The characteristics of the NiFe/Cu/Co spin-valve structure after deposition (a) and after patterning to a 2 5 m stripe (Matsuyama et al 1997).

t Ws NM 2 cos2 Hd M 2 cos2 — M 2 cos2 w

(2.76)

and energy connected with the field Hj created by the current of the current density J: I ~ 1 —M— 1 MJt. Wj MHj sin ~ = = 3 3 w

(2.77)

Minimizing the total energy leads to the following simplified expression Rap Rp H Hp Hj R Rp ———— 1 ——————– . 2 Hk Hd

(

)

(2.78)

In expression (2.78) should be added an additional component – the magnetic field resulting from the magnetostatic interaction between the free and pinned layers Hd2. Therefore two components of the demagnetizing field should be taken into account and expression (2.78) is as follows Rap Rp H Hp Hd2 Hj R Rp ———— 1 ——————–——– 2 Hk Hd1

(

where: t free t pinned Hd1 M —— and Hd2 M ——–. w w

)

(2.78)

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From expression (2.78) it is possible to decrease the R/R(H 0) shift by appropriate choice of the current and by balancing of the fields Hp Hj Hd2. When the aspect ratio t/w is large then the sensitivity may be limited by the shape anisotropy. One of the methods of reducing the demagnetizing field may be to decrease the thickness of the magnetic films (Wang et al 1998). Expression (2.78) is extremely simplified because in the real sensor structure all fields are non-uniform. The non-uniform demagnetizing field causes curling of the magnetization at the edges and the layers are magnetized nonuniformly. Figure 2.138 presents the typical shape of a GMR spin-valve sensor. In general this shape is not very complicated (in comparison for example with the AMR barber-pole sensor). But GMR sensors are mainly predestined for use in high density storage devices (heads or memory elements), therefore they should be extremely small. In order to compete with semiconductors the GMR memory cells should be in the submicron range of dimensions – it is planned to produce elements of width between 0.05 and 0.1 m (Everitt et al 1997, Pohm et al 1994). In such a small element the process of magnetization may be very complex.

Figure 2.138 The typical design of a GMR spin-valve sensor.

For the memory element a square hysteresis loop is desirable with very sharp switching between parallel and antiparallel alignment. The switching parameters are the most important – the switch magnitude (R/R)max and switching field Hs. A switch time in the nanosecond range or less is required. This means that the element should be in the one-domain state and magnetized only by rotation of the magnetization vector. Figure 2.139 presents the change of the sensor switching parameters when the element is diminished from 1.5 1 5 m to 0.25 4.25 m. The GMR ratio decreases from 5.3% to 0.3% (for H 0) and the switching field increases from 6 kA/m to 20 kA/m. The squareness of the hysteresis is destroyed. The behaviours of submicrometre GMR devices due to large nonuniformity of magnetization cannot be described by simplified analytical

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Figure 2.139 The dependence of the magnetoresistive hysteresis on the dimensions of spin valve element (Chen et al 1997).

expression – for example (2.78). It is necessary to compute the parameters by micromagnetic simulations. Figure 2.140 presents the results of such simulations determined by Zheng and Zhu (1996). They computed the distribution of magnetization in the spin-valve elements using the Landau–Lifshitz–Gilbert equation after discretization of the cell into 10 10 nm elements. Figure 2.140 also shows the magnetization distributions in two layers with a different aspect ratio L/w. It can be seen that part of the layer is not magnetized parallel to the pinned layer due to the curling effect at the end of the edges. Similar results were reported by Oti and Russek (1997).

Figure 2.140 The magnetoresistive hysteresis and the magnetization distribution in the free layer calculated by Zheng and Zhu (1996) for the spin valve structure.

Assuming a single-domain state for the strip with length L much larger than width w and thickness t this switching field can be determined from the following expression (Chen et al 1997):

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(2.79)

where: M – magnetization in tesla. Figure 2.141 presents the dependence of the switching field and GMR ratio on the width of magnetic layer w determined for a film thickness of 8.5 nm. The decrease of the width of the element from 1 m to 0.5 m causes an increase of the switching field from about 4 kA/m to 10 kA/m with simultaneous decrease of the GMR ratio from 5% to 2%.

Figure 2.141 The dependence of the switching field and the GMR ratio on the width of the spinvalve element (Chen et al 1997).

Various methods have been proposed to overcome this degradation of switching properties caused by the demagnetizing field. Zheng and Zhu (1996) proved that by preparing the pinned layer slightly longer than the free layer demagnetization effect on the edges might be greatly reduced. Figure 2.142(a) presents two hysteresis loops calculated for an element with dimensions 0.5 0.25 m and for an element with the pinned layer longer than the free

Figure 2.142 The improvement of the switching parameters of the GMR sensor by: (a) prolongation of the pinned layer; (b) applying the bias field (Pohm et al 1997, Zheng and Zhu 1996).

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layer (0.25 m greater at each end). The switching threshold can also be improved by introducing an additional bias field across an element – as shown in figure 2.142(b). The switching parameters in the spin-valve element can also be improved by introducing the uniaxial transverse anisotropy to the pinned layer in the pseudo spin-valve element (for example by in-field deposition). Figure 2.143 presents the results of the computation of the GMR transfer curve for the trilayer structure with dimensions 1 0.2 m (figure 2.143(left)) and after applying a transverse anisotropy field of 2 kA/m in the soft layer (figure 2.143(right)).

Figure 2.143 The calculated switching characteristic of the spin-valve sensor and the change of characteristic after introducing the transverse anisotropy field (Chen et al 1997).

Extremely small GMR elements may be narrower than the magnetic domain wall width. At this juncture the element is in a single-domain state. In such a state the switching time should be very short. Tang and co-workers (1995) prepared very small spin-valve RAM cells and found switching times better than 2 ns. When GMR sensors are used as tape heads or disk heads it is recommended that their design is as narrow as possible. To read the data in small rigid disks with densities over 1 Gbit/in2 (about 0.2 Gbit/cm2) the trackwidth W should be smaller than 2 m (Tsang et al 1993) and for densities over 1 Gbit/cm2 a trackwidth below 1 m is expected. For other data storage devices, such as QIC tape drivers and cassette systems a trackwidth below 20 m is required (O’Kane and Kroes 1994, Zieren et al 1993). Figure 2.144 presents examples of transfer characteristics determined experimentally by ten Berge and coworkers (1995). The characteristics of spin-valve sensors for two different aspect ratios L/w are shown. In the sensor with aspect ratio L/w 20 (L 80 m, w 4 m) the maximal output signal was as large as 200 mV. For the sensor with aspect ratio L/w 1 (L w 2 m) only 1.2 mV of the output signal was obtained when a similar current density was used. Table 2.12 presents the results reported by ten Berge and co-workers for different aspect ratios of the sensors.

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Figure 2.144 Examples of transfer characteristics determined for spin-valve read heads (ten Berge et al 1995). Table 2.12 The parameters of the spin-valve head of various dimensions L/w (after ten Berge et al 1995). Lw [m]

MRmax [%]

H [kA/m]

MR/H [%:/kAm–1]

I [mA]

Umax [mV]

U/H [mV/kAm–1]

R []

80 4

6.5

6.4

1.0

9.7

60 4

5.4

6.4

0.8

4.0

200

31

294

60

9.3

274

63

4.0

6.4

0.6

2.0

2.5

0.4

37

22

2.0

8.0

0.2

2.0

1.2

0.1

32

When length L of the sensor (trackwidth W for the sensor used as a head) is diminished the output signal also decreases. Figure 2.145 presents the dependence of the MR ratio on the aspect ratio L/w experimentally determined by Leal and co-workers (1994) for sensors of various widths. It is clear that the GMR ratio mainly depends on the L/W ratio independent of the sensor width.

Figure 2.145 The dependence of the magnetoresistivity ratio on the aspect ratio L/w of the GMR structure (grey line – calculated taking into account the resistance of the contacts) (Leal et al 1994).

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For very small sensors the contact resistance significantly influences the parameters as shown in figure 2.145. In the spin-valve sensor all layers are magnetized non-uniformly, both bilinear and biquadratic exchange interaction exists, the current in the stripe produces an additional non-uniform field biasing the unpinned layer, the magnetostatic coupling influences the performances. Such a complex assembly may be analysed using the numerical micromagnetic model. Several numerical models of spin-valve or multilayer sensors have been proposed2. The micromagnetic model of the GMR multilayer resembles a similar model describing dual-coupled film AMR heads developed by Smith (1987, 1992, 1992b). After appropriate discretization the output signal of the multilayer sensor in the model proposed by Smith may be computed from the formula R

1 —– —– ———– R

2N 1

∑ 2 [1 – m 1

n

· mn1]

(2.80)

n

where: 2N – number of layers, mn – magnetization vector in nth layer. The free energy W of the multilayer is expressed as:

w

W ∫

{

∑

0 n

1 mn tn Km2ny – Hd(xn ,y) · Mn (y) A —— 2 y

[

2

( )

Kafc (mn · mn1) Kbqc (mn · mn1)2

Ha (xn ,y) · Mn (y)

]

}

dy

(2.81) where: W – height of the stripe (width), tn – thickness of the layer, K – anisotropy constant, Kafc – antiferromagnetic coupling constant, Kbqc – biquadratic coupling constant, A – interlayer exchange constant, Ha – applied field, Hd – demagnetizing field calculated for example from the formula (Smith 1987) Hd (x,y) My (x,y) — x

L

t/2

ln[(x x)2 (y y)2]. ∫0 dyt∫/ 2dx · My (x,y) —– x (2.82)

The value of mn (y,H) in equation (2.80) may be obtained from the torque equation: W mni ——– 0 mni

(2.83)

For example: Bertram 1995, Fujiwara and Parker 1994, Nishioka et al 1995, Parker et al 1995, Smith et al 1996, Leal et al 1994, Freitas et al 1998, Russek et al 1995, Oti and Russek 1997, Miles and Parker 1996, Koehler and Williams 1997. 2

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after computing equation (2.81). This rather sophisticated micromagnetic model (presented above with maximum simplification) can analyse self-biased effects caused by sensor current or the influence of biquadratic exchange coupling. Figure 2.146 presents the results of computations of the NiFeCo/Cu multilayer sensor and a comparison with the experimental results.

Figure 2.146 The results of micromagnetic computations of the multilayer GMR structure (black line: experiment; grey lines: calculated without consideration of biquadratic coupling (right) and including the biquadratic coupling (left) – calculated by Smith (1994).

An enhanced micromagnetic model to analyse both spin-valve and multilayer sensors has been proposed by Miles and Parker (1996). Figure 2.147 presents the results of calculations of the magnetization distribution in the layers for different applied field values. These graphs illustrate excellently the change of magnetization alignment of both free and pinned layers (from Ms to Ms respectively). The change of the magnetization is asymmetric for Ha and Ha increase. The layers are practically always magnetized non-uniformly due to the influence of the demagnetizing field at the edge of the stripe.

Figure 2.147 The results of calculations of the magnetization distribution in free and pinned layers of the spin-valve structure – calculated by Miles and Parker (1996).

To achieve a large output signal and small signal-to-noise ratio GMR sensors usually operate at high current densities (greater than 107 A/cm2). In a correctly designed sensor the bias field produced by the current may be used to

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Figure 2.148 The magnetoresistive hysteresis of the spin valve sensor determined for different values of sensor current (Russek et al 1995).

compensate for the demagnetizing field (Gurney et al 1997). Too large a current density may be dangerous not only because of thermal effects but also because of the influence of an additional magnetic field. Cross and co-workers (1994) determined that a field from the current with density 1.1 107 A/cm2 reduces the output signal by 30%. Figure 2.148 presents the results of investigations of the effects caused by too large a current of the sensor (Russek et al 1995). Another disadvantageous effect that appears in very small GMR elements is the formation of microdomains resulting in the increase of noise (Kirschenbaum et al 1997, Harner et al 1996, Stokes et al 1999, Gijs et al 1996, Wan et al 1997). Figure 2.149 presents the dependence of low frequency noise on the stripe width determined by Kirschenbaum and co-workers (1997).

Figure 2.149 The 10 Hz noise amplitude per square of the material as a function of the GMR stripe width (Kirschenbaum et al 1997).

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The smaller the sensor dimensions the larger the influence of the contact resistance. The analysis presented by Devasahayam and co-workers (1999) proved that contact resistance was the major contribution to the reduction of the MR ratio for very small spin-valve read heads (see figure 2.145). The shape-preparing techniques (lithography, etching) are similar to those described in the first part of this book devoted to AMR sensors (Fontana et al 1995, 1995b, 1999, Xiao and Kryder 1996, Daughton 1992). The integration of a GMR structure to a silicon wafer is rather difficult (Daughton 1996). The GMR structures require a substrate with very good smoothness and crystallity. The temperature of deposition and annealing may damage the semiconductor elements and the high temperature necessary for some processes of semiconductor technology may be detrimental to magnetic properties, especially antiferromagnetic materials heated above the blocking temperature.

2.3.4 Design and construction of GMR sensors Practically all efforts in the investigations of GMR effects are concentrated on the construction of read heads and memory elements (described in the next part of the book). Only a few groups reported achievements in the construction of the ‘pure’ sensor i.e. transducer of the magnetic field to the voltage output (Tondra et al 1996, Hill et al 1997, Spong et al 1996, Daughton et al 1994). At the moment there are two groups of market available GMR sensors – manufactured by Nonvolatile Electronics Inc. and by Siemens AG. Applications of the GMR sensors other than data storage systems have only just been realized. GMR sensors may be used as displacement control devices (Miller et al 1997, Freitas 1999), new electronic elements (potentiometer, isolator, gate) (Clemens et al 1997, Hermann 1997, Hassoun et al 1997). In the design of thin film structures it is useful to operate at the resistivity determined for the condition w L (w – width, L –length)3:

Rsq —. t

(2.84)

This resistance ‘ohms per square’ is the same for any square irrespective of size. It depends only on the thickness of the film. The dependence of the output signal on the aspect ratio L/w may be described by the following expression (Gurney et al 1997): In the description of the dimensions of the sensor various nomenclature is used. Because the main application is in read heads the length of the sensor is called w (width) to find an easy relation with trackwidth. Width of the sensor is usually called h (high) and thickness is denoted by t or d. In this book the following notation is used: length (L), width (w), thickness (t), trackwidth (W). Of course L W and h w. The maximal value of the magnetoresistivity ratio is described as / . 3

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GMR SENSORS L cos( free1 pinned ) Uout IRsq — —– ————–————. w

2

( )

287 (2.85)

For the multilayer (exchange coupling) sensor expression (2.38) can be rewritten as: L

1

1 Uout IRsq — —– ——————— H 2x J L —– ——————— H 2x 2 w (H1 Hk Hd )

(H1 Hk Hd )2 1 J L —– —— H 2x

H 2s

(2.86)

where: I – bias current, J – current density, Hs – saturation field, H1 – coupling field, Hk – anisotropy field, Hd – demagnetizing field. In the rough estimations for the typical NiFe/Cu structure the following parameters may be assumed: Rsq 15 ; / 7%; 20 108 m; J 106–107 A/cm2 ; Hk 0.25 kA/m; H1 6 kA/m. The desired resistance of the sensor can be easily determined as a dependence on the aspect ratio L/w (R Rsq L/w). For a limited value of current density J and for a given material ( / , , Hk) the output signal can be increased by lengthening the sensor. If the width of the sensor w is too small it influences the sensitivity because the demagnetizing field depends on the aspect ratio t/w:4 t Hd M —. w

(2.87)

Assuming typical values M 8 105 A/m and thickness t 4 nm from equation (2.87) it can be calculated that if the width of the sensor is decreased to 1 m, the demagnetizing field Hd is about 3 kA/m and the output signal is diminished to a half. In many applications resolution of the sensor is also very important. This resolution is limited by the noise. Nor and co-workers (1998) estimated that signal-to-noise ratio is proportional to the square root of the device area: — SNR c√ Lw where : c – constants. Thus although the width of the sensor w does not appear in expression (2.86) it should be considered in the design. It is not clear which thickness t should be considered in the sandwich (or multilayer) structure. It is not correct to analyse the magnetic layers independently because they influence each other. Only the numerical micromagnetic model (or experiments) may give the correct answer. 4

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Figure 2.150 The construction of the (NiFe/Cu/NiFe) GMR sensor and its transfer characteristic (Kitada and Nakatani 1993).

Figure 2.150 presents the design and transfer characteristic of a multilayer sensor prepared by Kitada and Nakatani (1993). The sensor structure consists of 8 bilayers of NiFe 1.6/Cu 2.2 and before patterning a saturation field of 8 kA/m and magnetoresistivity of 5.7% was determined. Next the stripe with dimensions 20 400 m was patterned by photolithography and ion milling. Three-layer electrodes, Cr 50/Cu 300/Cr 50, with distance between electrodes of 150 m were formed on both ends. By supplying the sensor with a current of density 106 A/cm2 the maximal output signal of 10 mV was obtained. The rest of the parameters were as follows: maximum magnetoresistivity 6.1%, half width of transfer curve FWHM 8.5 kA/m and sensitivity 1.2 mV/kAm–1. The transfer characteristic was with hysteresis. After applying an additional biasing field (4 kA/m) the transfer curve can be shifted to the linear part for H 0. The permalloy ARM sensor with the same dimensions exhibited sensitivity which is two times larger. The multilayer sensors exhibit smaller sensitivities than AMR sensors and spin-valve sensors. But multilayer sensors display the largest magnetoresistivity. To profit from the large magnetoresistivity and overcome the small sensitivity several groups have reported the use of the thin film flux concentrator (Daughton et al 1994, Smith et al 1997, Jardine et al

Figure 2.151 The GMR device with soft adjacent layer and the characteristics of the sensor without and with the flux concentrator (Jardine et al 1998).

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1998). Figure 2.151 presents an example of such a sensor designed by Jardine and co-workers (1998). The multilayer stripe of Fe 5(Co 1.5.Cu 2.2) 30 was placed between the poles of the integrated soft adjacent layer made from amorphous material Co 66Si16B12Fe4Mo2. The stripe was 4 m wide while the distance between poles was only 5 m. After applying the flux concentrator sensitivity increased from 0.4%/kAm –1 to 75%/kAm–1 (figure 2.151).

Figure 2.152 GMR bridge sensor with shielding and flux concentrators (Daughton et al 1994).

The flux concentrator plays a double role in the sensors designed by Nonvolatile Electronics Inc. (Brown 1994, Daughton et al 1994). These devices are commercially available. The main idea of these sensors is presented in figure 2.152. Two magnetoresistors R1, R4 are placed in a gap of two co-planar rectangular flux concentrators made from high permeability material. A high permeability material covers the other two magnetoresistors R2, R3. Thus they are shielded from the external applied magnetic field. Non-active magnetoresistors are used in the bridge circuit and serve as a temperature compensator to cancel thermal drift. Figure 2.153 presents the construction of

Figure 2.153 The construction and sample of the transfer characteristic of the NVE GMR sensor.

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the sensor and its typical transfer characteristic. The device supplied by 5 V voltage (bridge resistance is 5 k) exhibits a sensitivity of 62 mV/kAm–1. Figure 2.154 presents the sensor layout. The whole chip is very small (1.2 0.3 mm) and the GMR resistors occupy less than 10% of the chip area. After removing the shield all four magnetoresistors can be active. Such a sensor (presented in figure 2.154(bottom)) may be used as a gradiometer bridge sensor (for example for gear tooth detection by angle measurements). The magnetoresistor is patterned to the meander form to obtain a large length of the path. Figure 2.155(left) shows a resistor of the resistance 5 k, prepared using 2 m lithography in an area 80 100 m. The material composition reported by NVE (Daughton 1996) is presented in figure 2.155(right). Table 2.13 presents the parameters of NVE sensors.

Figure 2.154 The layout of the magnetic field sensor and gradiometer (NVE).

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Figure 2.155 The multipath magnetoresistor and its structure (product of NVE). Table 2.13 The parameters of GMR sensors produced by Nonvolatile Electronics Inc. Type

Sensitivity [mV/V Oe]

Sensitivity [mV/V kAm–1]

Field range [kA/m]

Comments

AA002

4.2

52

1.2

Standard sensor 5k/1 mA

AA003

3.2

40

1.6

Standard sensor 5k/1 mA

AA004

1.3

16

4.0

Standard sensor 5k/1 mA

AA005

0.6

8

8.0

Standard sensor 5k/1 mA

AA006

3.2

40

1.6

Low power sensor 30k/0.3 mA

AC004

3.2

40

1.6

Current sensor for PCB

20

Gradient sensor with 0.5 mm active element separation

AB001

It would be a good idea to use all four magnetoresistors connected to the bridge circuit. Two pairs of magnetoresistors should then be differential to each other. It is possible to realize the differential magnetoresistors by biasing them with magnetic fields of opposite direction as shown in figure 2.156 (Hill et al 1997, Daughton et al 1994). The bridge sensor with four magnetoresistors obtains large sensitivities (Uout Usupl R/R while with two magnetoresistors Uout 0.5 Usupl R/R in the best case). And importantantly such a configuration indicates the polarity of the applied field. The idea of the four-magnetoresistors bridge sensor has been realized by Hill and co-workers (1997). A permanent magnet array (thin film platinum cobalt) was placed above the magnetoresistors as illustrated in figure 2.157. The whole layout of the sensor is presented in figure 2.158. The constructed sensor exhibited sensitivity of 20 mV/V kAm–1 (150 mV/kAm–1)5 for a field range of 800 A/m. The determined noise level was 0.28 10–6 Am–1Hz1/2 for the 5

Deduced from the reported data: R 1.5 k and I 5 mA.

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Figure 2.156 The idea of preparation of the differential sensors by additional biasing of two pairs of magnetoresistors.

Figure 2.157 The GMR sensor with differentially biased magnetoresistors (Hill et al 1997).

bandwith 10 Hz–10 kHz. Sensor output as a function of applied field is presented in figure 2.158.

Figure 2.158 The layout of a differentially biased sensor (presented in figure 2.157) and its transfer characteristic (Hill et al 1997).

The design of the spin-valve sensor is slightly different from that of the multilayer exchange-coupled sensor. The coupling field is much smaller – for example about 1.2 kA/m (Spong 1997). Therefore the demagnetizing fields and the field produced by the current may significantly influence the parameters of the sensor. The expression describing the output signal can be rewritten as:

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GMR SENSORS L Hx Hp Hd2 Hj Hx Hp Hd2 Hj Uout IRsq — —– ————————– J L ————————–. w

Hk Hd1 Hk Hd1

293 (2.88)

The transfer characteristic is shifted by the coupling and magnetostatic field and it is possible to eliminate this shift by appropriate design, i.e. from the condition: t 1 Hp M — – Jt 0. w 3 Assuming typical values: Hp 0.8–1.2 A/m; t 3 nm and w 1 m we obtain Hd2 3.3 kA/m. Thus to compensate 2 kA/m applying a bias current of about 6 mA is required. It means that a current density of about 0.7 108 A/cm2 is required. The demagnetizing field Hd1 in the spin-valve sensors may be much larger than the anisotropy field Hk (typically Hk 0.25 kA/m) and may determine the sensor sensitivity and operating range because t Hs Hk M —. (2.89) w Taking into account the above described relations Spong and co-workers (1996) proposed using the relationship between the design parameters shown in figure 2.159. For an assumed supply voltage and sensor resistance the optimal width and length of the path can be determined. For example for U 5 V and R 2.2 k a width of 3.25 m and length of 500 m were chosen.

Figure 2.159 The relationship between design parameters of the spin-valve sensor (Spong et al 1996).

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Smith and co-workers (1997) described the design of a very sensitive GMR spin-valve sensor with flux concentrator. Figure 2.160 presents the construction of this sensor. Two identical end-connected spin-valve magnetoresistors are placed above the flux concentrator. One of the magnetoresistors is active – it is placed in the flux concentrator gap. The second one is insensitive (it is shielded from the applied field) and serves as a temperature compensator. The sensor consists of the following layers: Ta 5/NiFe 7/Co 1/Cu 2.3/Co 1/NiFe 6/FeMn9/Ta 5. Its parameters before patterning were as follows: / 6.8%, Hk 0.32 kA/m, Hp 0.88 kA/m, Hex 13.6 kA/m. The transfer characteristic of this structure is presented in figure 2.161

Figure 2.160 The construction of the spin-valve sensor with flux concentrator (Smith et al 1997).

After micromagnetic computations the following optimal dimensions were determined: magnetoresistor—width w 15 m, length L 750 m; concentrator—area 2 (750 750 m), gap 9 m and thickness 2 m. The sensor area was not larger than 1 mm2. Figure 2.161 presents the transfer characteristics of the sensor – with and without the flux concentrator. With the flux concentrator a sensitivity of 140%/kAm–1 and resolution (noise level) of 1.6 10–4 Am–1 Hz1/2 were reported.

Figure 2.161 The transfer characteristic of the spin-valve sensor: without and with flux concentrator (Smith et al 1997).

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The spin-valve bridge sensor with four active magnetoresistors has been designed and fabricated by Spong and co-workers (1996). The structure of the magnetoresistors consisted of the following layers: Si/Al2O3 100/Ta 5/NiFe 4.2/Co 0.7/Cu 2.5/Co 0.9/NiFe 3.2/FeMn 15/Ta 5. By photolithography and ionmilling four magnetoresistors have been obtained with parameters: w 3.25 m, l 500 m, Hp 1.2 kA/m, Hs 2 kA/m, / 5.8%, R 2.2 k. For a supply voltage 5 V a sensitivity of 50 mV/kAm–1 and resolution 2 104 Am–1 Hz1/2 has been reported. The transfer characteristic of the sensor is presented in figure 2.162(bottom) (for comparison the typical transfer characteristic of an AMR sensor is also shown). To obtain differential behaviours of two pairs of magnetoresistors a clever magnetizing procedure has been applied. The free layers are magnetized along the strip. In the first pair of magnetoresistors the pinned layer is magnetized by the angle 1 3 90° and in the second pair by the angle 2 4 90° (as shown in figure 2.162(top)). Above the magnetoresistors is placed a conducting loop supplied in such a way that the current corresponding with neighbouring magnetoresistors is in the opposite direction (see figure 2.162(top)). After preparation of the sensor the current was passed through the loop to heat the biasing layers above the blocking temperature (about 180°C by I 140 mA).

Figure 2.162 The bridge spin-valve sensor (top) and its transfer characteristic (bottom) (Spong et al 1996).

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This current was then reduced to such a value that the temperature dropped below the blocking temperature (about 100°C by a 115 mA current). The dimensions of the loop were designed in such a way that this low-temperature current was enough to produce the magnetic field capable of magnetizing each biasing layer (about 6 kA/m by a current 115 mA). After such a procedure the current could be switched off and the sensor was ready to work. The largest sensitivity is expected from the spin-dependent tunnelling devices. The design of such sensors is reported by a group from Nonvolatile Electronics Inc. (Beech et al 1996, Tondra et al 1998). The construction of the sensor is presented in figure 2.163(top). The whole structure consists of the following layers: NiFeCo 12.5/Al2O3 2.5/CoFe 7Ru 0.9/CoFe 7/FeMn 12.5. The barrier is created by the thin insulator film of Al2O3. The artificial antiferromagnetic material (CoFe/Ru/CoFe) was used as the pinned electrode. To obtain stable, hysteresis-free transfer characteristics application of the orthogonal to the easy axis bias field was required. The transfer characteristic of the biased sensor is presented in figure 2.163(bottom). The sensitivity at the region of near zero field was about 40%/kAm–1.

Figure 2.163 The spin-dependent tunnelling sensor: construction (top) and its transfer characteristic (bottom) (Beech et al 1996, Tondra et al 1998).

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The sensor was optimized with respect to the signal-to-noise ratio. This parameter was determined as: S AH — —— N C

— N — R

√

(2.90)

where: A – sensitivity of the element, ———— H – magnetic field value, N – number of elements, R – resistance, C√4k T f. Because decreasing the resistance is limited by technology and A,C,H, are constant there remains only one effective way to improve the resolution – increasing the number of elements. Therefore the bridge circuit was designed with 16 tunnel junctions in each leg – a total number of 64 elements. In such sensors resolution of picotesla (10–6 A/m) is achievable. In 1999 Siemens AG introduced into the market magnetic sensors based on the GMR principle. Although not all details of this sensor are published it is described in the product information that this structure consists of 11 layers with a total thickness of 25 nm. The magnetic cobalt layers are antiferromagnetic coupled with thin copper layers used as separation. Soft magnetic iron layers covers the antiferromagnet at the bottom and top (figure 2.164(left)). To obtain relatively large resistance of the sensor (more than 700 ) the current paths are etched in the form of a meander (figure 2.164(right)).

Figure 2.164 The structure (left) and sensor layout (right) of the GMR B6 sensor developed by Siemens AG (after Siemens product information).

The sensors are in principle designed as the switching or position sensing devices. Therefore the sensor characteristics exhibit a large range of saturation (H 5 15 kA/m) and it operates practically independently of the magnetic field strength as the angle transducer. An example of the transfer characteristic of the transducer sensing the rotation of the magnet is presented in figure 2.165. The GMR B6 and GMR C6 sensors of Siemens are prepared as integrated bridge chips (with dimensions 3 mm 1.3 mm 1 mm and active area 0.3 mm 0.3 mm). The GMR B6 sensor consists of two antiparallel half bridges or one full bridge. The sensor GMR C6 consists of two half bridges with crossed directions of sensor axis.

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Figure 2.165 The GMR sensor as the angle transducer and its transfer characteristic (Siemens product information).

The magnetoresistive effect of the presented GMR B6 or GMR C6 sensors is rather modest and does not exceed 5%. But for supply current of 10 mA it is possible to obtain an output voltage as high as 250 mV which is sufficient for application as rotational sensors, non-contacting potentiometers or noncontacting switches. It is expected that in the future GMR read heads will substitute AMR heads (Lenssen et al 1997). The results of a comparison of GMR sensors and AMR sensors (Kools et al 1998) are not so obvious. GMR sensors exhibit a larger range of detected fields and much larger maximal output signal for the same area and power supply. But sensitivity, linearity, temperature and time stability of the AMR sensors are still competitive (if not better) than GMR sensors. It would not be fair to compare AMR sensors usually produced without the flux concentrator and GMR sensors produced with the flux concentrator. The technology of fabrication of GMR sensors is much more sophisticated and probably much more expensive. GMR sensors are not suitable at high temperature while AMR sensors can work without problems at temperatures up to 190°C. It is easy to obtain differential AMR sensors. In the case of GMR sensors special tricks must be used to obtain differential pairs in the bridge circuit (Hill et al 1997, Spong et al 1996). However, research into GMR sensors is still in progress.

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Rev. 100 675–681 Andrieu O 1996 Magnetoresistance of NiFe/Ag multilayers: modelling of the effects IEEE Trans. Magn. 32 4734–4736 Anthony T C 1994 Magnetoresistance of symmetric spin valve structure IEEE Trans. Magn. 30 3819–3821 Azevedo A 1996 Biquadratic exchange coupling in sputtered (100) Fe/Cr/Fe Phys. Rev. Lett. 76 4837–4840 Azavedo A 1998 Biquadratic coupling dependence on spacer thickness for Fe/Cr/Fe J. Magn. Magn. Mat. 177–181 1177–1178 Baibich M N 1988 Giant magnetoresistance of (001)Fe/(001)Cr magnetic superlattices Phys. Rev. Lett. 61 2472–2475 Bailey W E 1996 Structural comparison of ion-beam and dc magnetron sputtered GMR spin valves by high resolution TEM J. Appl. Phys. 79 6393–6395 Baltensperger W and Helman J S 1990 Ruderman-Kittel coupling between ferromagnets separated by a nonmagnetic layer Appl. Phys. Lett. 57 2954–2955 Barnas J 1990 Novel magnetoresistance effect in layered magnetic structures: theory and experiment Phys. Rev. B42 8110–8120 Barnas J and Grünberg P 1993 On the biquadratic interlayer coupling in layered magnetic structures J. Magn. Magn. Mat. 121 326–29 Barnas J 1994 Transport in magnetic layered structures: giant magnetoresistance Act. Phys. Polon. 85 165–177 Beauvillain P 1988 Magnetoresistance and magnetization studies of ultrathin Co-Au sandwiches and bilayers, J. Phys. Colloq. 49 1703–1704 Berg van H A M 1996 GMR sensor scheme with artificial antiferromagnetic subsystem IEEE Trans. Magn. 32 4624–4626 Berkowitz J A E 1992 Giant magnetoresistance in heterogenous alloys Phys. Rev. Lett. 68 3745–3748 Berkowitz A E 1994 Giant magnetoresistance in heterogeneous alloy films IEEE Trans. Magn. 30 353–357 Barthelemy A and Fert 1991 A Theory of the magnetoresistance in magnetic multilayers: analytical expressions from a semiclassical approach Phys. Rev. B43 13124–13129 Bauer G E W 1992 Perpendicular transport through magnetic multilayers Phys. Rev. Lett. 69 1676–1679 Bauer G E W 1993 Perpendicular magnetoresistance of magnetic multilayers: theory and experiments J. Magn. Magn. Mat. 126 454–456 Beach R S and Berkowitz A E 1994 Giant magnetic field dependent impedance in amorphous FeCoSiB wire Appl. Phys. Lett. 64 3652–3654 Beach R S and Berkowitz A E 1994b Sensitive field and frequency dependent impedance spectra of amorphous FeCoSiB wire and ribbon J. Appl. Phys. 76 6209–6213 Beech R S 1994 Current distribution in spin valve structures IEEE Trans. Magn.

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Vavra W 1995 Perpendicular current magnetoresistance in Co/Cu/NiFe/Cu multilayered structures Appl. Phys. Lett. 66 2579–2581 Vazquez M 1997 Giant magnetoimpedance effect in soft magnetic wires for sensor applications Sensors and Actuators A59 20–29 Velazquez J 1994 Giant magnetoimpedance in non-magnetostrictive amorphous wires Phys. Rev. B50 16737–16740 Velu E 1992 Strong magnetoresistance reduction at the coercive-field crossover of two uncoupled magnetic films J. Appl. Phys. 71 503–505 Vischer P B 1994 Transport in magnetic multilayers from the quantum Boltzman equation Phys. Rev. B49 3907–3915 Voegeli B 1995 Electron transport in multilayered Co/Cu nanowires J. Magn. Magn. Mat. 151 388–395 Wan H 1997 Comparison of flicker noise in single layer, AMR and GMR sandwich magnetic film devices IEEE Trans. Magn. 33 3409–3411 Wang Y 1990 Interlayer magnetic coupling in Fe/Cr multilayered structures Phys. Rev. Lett. 65 2732–2735 Wang J Q and Xiao G 1994 Transition-metal granular solids: microstructure, magnetic properties and giant magnetoresistance Phys. Rev. B49 3982–3986 Wang G 1996 Structure and properties of sputtered FeMn/NiFe bilayer thin films IEEE Trans. Magn. 32 4660–4662 Wang D 1997 Thermally stable, low saturation field, low hysteresis, high GMR Co/Fe/Cu multilayers IEEE Trans. Magn. 33 3520–3522 Wang D 1998 Magnetic properties of very thin single and multilayer NiFeCo and CoFe films deposited by sputtering J. Appl. Phys. 83 7034–7036 Wang S X 1997 Ion beam deposition and structural characterization of GMR spin valves IEEE Trans. Magn. 33 2369–2374 Weber W 1995 Exchange coupling across Cu(100): a high-precision study Europhys. Lett. 31 491–496 Wecker J 1993 Giant magnetoresistance in melt-spun Cu-Co alloys Appl. Phys. Lett. 62 1985–1987 Westwood W D 1989 Microelectronic Materials and Processes (Dordrecht: Kluwer Academic) White R L 1992 Giant magnetoresistance: a primer IEEE Trans. Magn. 28 2482–2486 Whitney T M 1993 Fabrication and magnetic properties of arrays of metallic nanowires Science 261 1316–1319 Wieberdink J W and Eijkel K J M 1989 Permalloy multilayers to reduce the effect of uniaxial anisotropy IEEE Trans. Magn. 25 4278–4282 Wolf J A 1993 Interlayer coupling of Fe film across Cr interlayers and its relation to growth and structure J. Magn. Magn. Mat. 121 253–258 Xiao J Q 1992 Giant magnetoresistance in nonmultilayer magnetic systems Phys. Rev. Lett. 68 3749–3752 Xiao J Q 1993 Giant magnetoresistive properties in granular transition metals IEEE Trans. Magn. 29 2688–2693

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Xiao M and Kryder M H 1996 Fabrication process for very high density shielded spin valve magnetoresistive heads Electrochem. Soc. Proc. 95 51–61 Xiao S Q 1998 Magnetic properties and giant magnetoimpedance in amorphous FeNiCrSiB film J. Phys. Cond. Mat. 10 3651–3658 Xiao S Q 1999 Giant magnetoimpedance effect in sandwiched films J. Appl. Phys. 85 4127–4130 Xing L and Chang Y C 1993 Theory of giant magnetoresistance in magnetic granular systems Phys. Rev. B48 4156–4159 Xiong G C 1995 Giant magnetoresistance in epitaxial Nd0.7Sr0.3MnO3 thin films Appl. Phys. Lett. 66 1427–1429 Yafet Y Ruderman-Kittel-Yosida range function of a no-dimensional freeelectron gas Phys. Rev. B36 3948–3949 Yamamoto H 1991 Magnetoresistance of multilayers with two magnetic components J. Magn. Magn. Mat. 99 243–252 Yamamoto H 1993 Magnetoresistance of non-coupled NiFe/Cu/Co/Cu multilayers J. Magn. Magn. Mat. 126 437–439 Yang Z J and Scheinfein M R 1995 Interfacial-roughness effects on giant magnetoresistance and interlayer coupling in Co/Cu superlattices Phys. Rev. B52 4263–4274 Yang Q 1995 Prediction and measurement of perpendicular giant magnetoresistances of Co/Cu/Ni84/Fe16/Cu multilayers Phys. Rev. B51 3226–3229 Yaoi T 1993 Dependence of magnetoresistance on temperature and applied voltage in a 82NiFe/Al.-Al2O3/Co tunneling junction J. Magn. Magn. Mat. 126 430–432 Yoo H Y 1989 Dynamic switching process of sandwich-structured MR elements IEEE Trans. Magn. 25 4269–4271 Yosida K 1957 Magnetic properties of Cu-Mn alloys Phys. Rev. 106 893–898 Zahn P 1995 Ab initio calculations of the giant magnetoresistance Phys. Rev. Lett. 75 2996–2999 Zaman H 1997 Magnetoresistance in Co-Ag multilayers and granular films produced by electrodeposition method IEEE Trans. Magn. 33 3517–3519 Zener C 1951 Interaction between the d-shell in the transition metals. II. Ferromagnetic compounds of manganese with perovskite structure Phys. Rev. 82 403–405 Zeng X T and Wong H K 1995 Annealing effect on the giant magnetoresistance of La-Ca-Mn-O thin film IEEE Trans. Magn. 31 3910–3911 Zhang S and Levy P M 1991 Conductivity perpendicular to the plane of multilayered structures J. Appl. Phys. 69 4786–4788 Zhang S 1992 Theory of giant magnetoresistance in magnetic granular films Appl. Phys. Lett. 61 1855–1857 Zhang S 1992 Conductivity and magnetoresistance of magnetic multilayer structures Phys. Rev. B45 8689–8702 Zhang S and Levy P M 1993 Interpretation of the magnetoresistance in

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multilayered structures Phys. Rev. B47 6776–6779 Zhang S 1996 Electrical conductivity in ferromagnetic perovskite structures J. Appl. Phys. 79 4542–4544 Zhang S and Yang J 1996 On the origin of the magnetoresistance in ferromagnetic perovskite structures J. Appl. Phys. 79 7398–7400 Zhang J and White R M 1996 Topological coupling in magnetic multilayer films J. Appl. Phys. 79 5113–5115 Zhang J and White R M 1996b Topological coupling in spin valve type multilayers IEEE Trans. Magn. 32 4630–4635 Zheng G G 1993 Magnetotransport in Mo/Ni superlattices J. Magn. Magn. Mat. 126 498–500 Zheng Y and Zhu J G 1996 Micromagnetics of spin valve memory cells IEEE Trans. Magn. 32 4237–4239 Zheng Y and Zhu J G 1997 Micromagnetic principles in pseudo spin valve memory element design IEEE Trans. Magn. 33 3286–3288 Zhu J G and Zheng Y 1998 Characteristics of AP bias in spin valve memory elements IEEE Trans. Magn. 34 1063–1065 Zhu J G 1999 Spin valve and dual spin valve heads with synthetic antiferromagnets IEEE Trans. Magn. 35 655–660 Zieren V 1993 Design and fabrication of thin film heads for the digital compact cassette audio system IEEE Trans. Magn. 29 3064–3066

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3 Applications of Magnetoresistive Sensors

3.1 MAGNETIC MEASUREMENTS 3.1.1 Magnetometers and compasses In the previous sections the magnetic field was usually described as the magnetic field strength H and the unit the A/m was used. In magnetometry applications induction B (magnetic flux density B) with the unit tesla 1T 1 Vs/Am2) is usually used to describe the magnetic field. For vacuum and free air both unit systems can be used because the relation between B and H is explicit: B o H

(3.1)

where permeability o 4 10–7 Vs/Am. The International Association of Geomagnetism and Aeronomy has recommended the induction B (flux density) as the preferred quantity to describe the magnetic field in free air (Lowes 1974). Table 3.1 Conversion factors for common magnetic units. Tesla [T]

[A/m]

Gauss [G]

Oersted [Oe]

12.56 10

12.56 10–3

A/m

1.256 10

Oe

10–4

79.6

1

1

T

1

7.96 105

104

104

10–9

7.96 10–5

10–5

10–5

G

10

79.6

1

1

–6

–4

1

–3

The use of the units of both quantities is more complicated. Table 3.1 presents the conversion factors for common magnetic units. In many countries SI units (SI – ‘systeme internationale’) are legally prescribed and the use of the old units Gauss (1 G 10–4 T) and Oersted (1 Oe 103/4 A/m) is prohibited. Nevertheless the old units (Gauss, Oersted and 10–5 Oe) are still in use in several countries, especially in the US. In fact the old units are very convenient

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because in free air a field strength of 1Oe corresponded with an induction of 1G. For simple conversion the following dependence may be used: 1 Oe →1 Gs→100 T→0.1 mT→0.796 A/cm→79.6 A/m;

1 1 nT.

In comparison with other sensors magnetoresistive sensors offer some very competitive behaviours (Gordon et al 1972, Lenz 1990, Popovic et al 1996, Bratland et al 1996, Caruso 1998). First of all they exhibit practically the largest sensitivity per area unit. This means that it is possible to design extremely small sensors whilst retaining good sensitivity (or output signal level). This advantage has been appreciated in storage reading applications (reading heads, memory etc) (Thompson et al 1975, Shelledy and Nix 1992). Due to the small dimensions of the sensor it is also possible to map magnetic fields with extremely small resolution (Fluitman and Krabbe 1972, Groenland and Fluitman 1981, O’Barr et al 1996, Yamamoto et al 1996, Indeck and Judy 1984). The mapping of magnetic field distribution on an investigated surface is facilitated because thin film magnetoresistive sensors detect the magnetic field component in the film plane (in the case of the Hall-effect sensor the magnetic field component perpendicular to the sensor plane is detected). Thus it is possible to place the sensor very near the investigated area. Hall-effect sensors typically measure magnetic fields above 10 mT. Simple and effective sensors do not exist for measurements in the range below 10 mT. For measurement of small fields (below 10 mT) the flux-gate sensors are typically used (Ripka 1992, Tumanski 1986). In fact flux-gate sensors are able to measure magnetic fields in the range 100 nT – 100 T with a sensitivity of about 10 V/nT. The output signal of flux-gate sensors is alternating when the direct magnetic field is measured. It is relatively easy to separate the DC offset drift signal from the useful AC signal. Thus flux-gate sensors may be recommended for very small (1n T–100 nT) direct magnetic fields. Integrated, extremely small constructions of flux-gate sensors have been reported (Choi et al 1996). In general flux-gate sensors are more complicated in preparation (and of higher costs) than magnetoresistive sensors. Moreover flux-gate sensors have limited frequency bandwidth. Usually such sensors operate in the frequency bandwidth up to 10 Hz and for higher frequencies search coils are preferred. The search coil (Tumanski 1986) measures only alternating magnetic fields and with the rather significant obstacles that this sensor does not measure magnetic field H but only a derivative of this field dH/dt. Thus to determine the value of magnetic field strength an integrating circuit must be used which introduces an additional error of conversion. To conclude the rough comparison the following attributes of MR sensors can be emphasized: • Small dimensions • High reliability and simplicity, low cost • Exceptionally wide frequency bandwidth including DC fields

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• Output signal proportional to the H value • Recommended magnetic field range of 1 T – 1000 T. The typical range of MR sensors is similar to the Earth’s magnetic field range. And although the Earth’s magnetic field is typically measured using nuclear precession proton magnetometers (Stuart 1972, Grivet and Molnar 1967, Hine 1968) the simplicity, and most importantly vector value detection, favour MR sensors as the Earth’s field sensor for navigation and compassing (Petersen 1986, Wellhausen 1989, Mapps et al 1987, Irons and Schwee 1972). Figure 3.1 presents a map of the horizontal component of the Earth’s magnetic field. This field is about 10–30 T – for example, in London it is 18.8 T. The main problem in measurement of the Earth’s magnetic field is that the horizontal component is often only a small part of the total magnetic field. For example, the Earth’s magnetic field in Berlin is characterized by the horizontal component H 18.6 T, the vertical component Z 45.1 T, the total field T 48.8 T, the declination V 0.4° and the inclination D 67.6°.

Figure 3.1 Lines of equal horizontal field component in T.

The magnetic field is not constant in time. It changes about 30 nT a year and 2–20 nT a day. Figure 3.2 presents an example of the daily changes of magnetic field components determined at the Geophysical Laboratory in Poland. During a magnetic storm changes of as high as several T are possible. The non-uniformity of the Earth’s magnetic field is approximately 10 pT/m. To precisely determine the Earth’s magnetic field all three components should be measured. Figures 3.3 and 3.4 present a map of the declination angle V and inclination angle D.

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Figure 3.2 An example of the components of the Earth’s magnetic field and its daily changes.

Figure 3.3 Lines of the declination angle of the Earth’s magnetic field.

Figure 3.4 Lines of the inclination angle of the Earth’s magnetic field.

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There is a need for a simple and reliable electronic compass for automotive and aircraft navigation. Such a compass integrated with the GPS system (‘Global Positioning System’) might be a very effective tool for vehicles, aircraft or marine craft. Taking into consideration the complicated nature of the Earth’s magnetic field such a device is much more complicated than a simple needle compass. The errors that occur when the sensor plane is not parallel to the Earth’s surface need to be considered– for example when a car is going up or downhill. When the sensor is not placed horizontally the Earth’s false field direction is detected. The sensor in a compass system may operate in the presence of the orthogonal component, which is very often significantly larger than the measured field. Therefore the longitudinal flipping field should practically always be used, because such a stabilizing technique ensures insensitivity to the orthogonal component (as described in previous sections). Figure 3.5(left) shows the KMZ10A1 sensor especially designed by Philips for compass application. For easier placement of the sensor in the external flipping coil the anisotropy axis is directed parallel to the leads connectors. Sensors equipped with the internal flipping planar coil (for example the KMZ51 sensor) may be connected to the microprocessor circuit, as shown in figure 3.5(right). The market-available magnetoresistive compasses (for example the HMR3000 device of Honeywell) include quite complicated electronic circuits, A/D converters and a microprocessor.

Figure 3.5 The KMZ10A1 sensor of Philips placed inside the flipping and compensation coils and recommended microprocessor circuit to realize the weak magnetic field transducer (Philips Technical Information).

When the sensor is rotated in the Earth’s magnetic field a pure sinusoidal output signal versus the angle of rotation is expected. For a single sensor compass it is not possible to determine the compass heading. At least two sensors are required as shown in figure 3.6. According to the diagram in figure 3.6(b) the compass heading can be calculated after determination of both Hx and Hy using the following set of equations (Caruso 1996):

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Figure 3.6 The principle operation of the electronic compass: (a) two-sensor arrangement; (b) the output signal of two sensors versus the direction of external magnetic field.

0

when Hy 0, Hx 0

H 90 arctg —–x Hy

when Hy 0

180

when Hy 0, Hx 0

H 270 arctg —–x Hy

when Hy 0.

(3.2)

Equipped with three sensors, three 16-bit A/D converters and a microprocessor the HMR3000 electronic compass of Honeywell is able to determine the heading with resolution of 0.1° while the tilt axis can be changed in the range 40°. The HMR2300 compass was especially designed for the avionics industry and exhibits improved resolution better than 0.02° in any direction. In vehicle navigation often it is not necessary to know the direction with such high resolution. It may be sufficient to know the direction with 45° resolution, for example to know N, NE, NW, W, SW etc. Figure 3.7 presents a simple two-

Figure 3.7 The two-sensor electronic compass design and the method of the simple determination of eight magnetic field directions (Philips Technical Information).

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sensor system designed for compass application. In this system eight major compass directions can be detected. Typical comparators can be used to obtain eight different signals transferred to the display. Figure 3.8 presents a similar compass circuit using three sensors able to detect the direction with 30° resolution.

Figure 3.8 The principle operation of the three-sensor electronic compass with 30° resolution (Wellhausen 1989).

All magnetoresistive sensors might be directly used as a magnetometer device because their output signal is proportional to magnetic field strength. Several authors have described magnetoresistive sensors designed as magnetic field sensors1. But the magnetometer, as an instrument for measuring the magnetic field, should be equipped with many additional circuits to perform calibration, compensation of the parasitic fields, correction of errors, calculation of the vectorial components etc. Actually apart from the HMR2300 digital magnetometer of Honeywell there are no other available magnetoresistive magnetometers (unlike for example the numerous models of Hall-sensor magnetometers). All manufacturers of MR sensors offer many application notes allowing users to construct such instruments. Tumanski (1984) analysed and tested various circuit principles of the magnetoresistive magnetometers. The four main ideas of such magnetometers are presented in figure 3.9. The simplest one is the circuit with a DC supply voltage of the sensor and a direct longitudinal stabilizing field. The major drawbacks of such circuit are difficult to overcome – temperature offset drift and small immunity from the orthogonal field component. This last disadvantage may be reduced by applying the magnetic feedback technique. Thus the magnetometer presented in figure 3.9(a) may be recommended as a simple device, with modest sensitivity and resolution, but of large frequency bandwidth. 1 For example: Gebhard and Richter 1982, Smith et al 1991, de Ridder and Fluitman 1990, Hebbert and Schwee 1966, Dibbern 1986, Hoffman and Birtwistle 1982, Hoffman et al 1983, Hoffman et al 1984, Pant and Krahn 1991, Kwiatkowski and Tumanski 1986, Kwiatkowski and Tumanski 1983, Tumanski 1984, Tumanski and Stabrowski 1984, Hill 1997, Smith et al 1997, Spong et al 1996, Daughton 1994, Caruso et al 1999, Dibbern and Petersen 1983, Groenland et al 1992.

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Figure 3.9 The four main magnetometer circuit concepts analysed by Tumanski (PD: phase detector, F: filter) (Tumanski 1984).

The circuit presented in figure 3.9(b) adopted the principle utilized in the strain gauge technique, where extremely small changes of resistance are commonly detected. A selective or even homodyne nanovoltmeter can be used to improve the sensitivity. The selective amplification of the measured voltage might be possible by supplying the bridge circuit with alternating voltage which is then utilized as the carrier signal. The improvement of sensitivity does not mean an improvement in resolution because this circuit suffers from offset drift. Therefore it can be recommended as a very sensitive device for mainly alternating magnetic fields. Lately the most frequently circuit recommended by manufacturers is that presented in figure 3.9(c). In fact this circuit radically reduces offset drift and errors caused by the orthogonal component. Its main drawbacks are the need of applying an additional coil to produce the flipping field and a more complicated electronic circuit. More simple is the circuit presented in figure 3.9(d) where supply voltage and longitudinal magnetic field are switched simultaneously. The alternating offset drift can be simply filtered from the DC output signal. The circuit presented in figure 3.9(d) has been successfully used as a direct current transformer (linear isolation transformer) (Kwiatkowski et al 1984) but it has not yet been used as a magnetometer. Figure 3.10 presents the magnetometer circuit adopting the principle presented in figure 3.9(a) and constructed at Warsaw University of Technology. The main assumptions were to design the portable instrument relatively simply and with modest accuracy of 2%. The magnetic field can be measured in four ranges (2 T, 20 T, 200 T, 2000 T or 2 A/m, 20 A/m, 200 A/m, 2000 A/m). For A/m units the gain of the instrumental preamplifier was fixed as 25, while for T units this gain can be changed to 31.4. The unbalance of the bridge circuit for H 0 is eliminated by the potentiometer to avoid saturation of the amplifier when the smallest range is used. For the smallest ranges the other disturbing fields (for example Earth’s magnetic field) should be compensated.

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Figure 3.10 An example of a magnetic field measuring instrument.

This is realized by introducing an additional voltage to one of the inputs of the differential amplifier. Two amplifier blocks are then used to change the range (switched gain 1 V/V, 10 V/V and 100 V/V) and for calibration (changed gain 0.8–1.2 V/V). The measured magnetic field can be determined from the fourdigit display unit (true RMS in the case of alternating fields) or from analog output (200 mV full-range voltage). The magnetometer, utilizing the KMZ10B sensor as a probe was tested successfully in various applications. Figure 3.11 presents the magnetometer circuit adopting the flipping circuit with the compensation technique (presented in figure 3.9(c)) and recommended by Philips. The sensor can be switched by the positive and negative pulse of the flipping current from the flipping generator (pulse of approximately 0.7 A/10 s and frequency 1 kHz). If the sensor is stabilized by a direct magnetic field (for example by a magnet) the flipping generator can be used to periodically reset the sensor (in such a mode only the positive pulse may be sent to the flipping coil). The flipped output signal of the sensor bridge is amplified in the preamplifier circuit by a factor of 100 to approximately 300 mVpp (corresponding with about 15 A/m). The offset voltage is removed in the preamplifier block by applying

Figure 3.11 The magnetometer circuit recommended by Philips for the KMZ51-type sensor (Philips Technical Information).

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negative feedback from the offset compensation block. Such a solution has two advantages – it ensures against overload of the amplifier by DC components and it compensates for the offset of the amplifier. The output signal is sent to the compensation coil after synchronous rectification and filtration. Figure 3.12 presents a relatively simple magnetometer circuit proposed by Petersen (1986). Two potentiometers can be used to set the bridge offset and sensitivity. The output signal from the bridge circuit is sent to the comparator. When the magnetic field appears the sensor will cause the comparator to switch and current to pass through the feedback coil. The simplest way to obtain the magnetometer instrument is to use the typical instrumentation amplifier that assures offset reduction and precise gain adjust.

Figure 3.12 The simplified magnetometer circuit utilizing KMZ10B sensor – designed by Petersen (1986).

The most developed magnetoresistive instrument for magnetic field measurements is the HMR2300 three-axis digital magnetometer offered by Honeywell. The magnetometer consists of three independent bridge sensors connected to 16-bit delta-sigma A/D converters and an internal microprocessor circuit. The output digital signals representing the three components of the measured field are sent to the computer in RS232 standard. The magnetometer determines the magnetic field in the range of 200 T with resolution of 7 nT and accuracy 1% of full scale. Another concept of thin film magnetoresistive magnetometer was proposed by de Ridder and Fluitman (1984, 1987, 1988). The alternating biasing field directed perpendicular to the anisotropy axis saturates the sensor in the positive and negative directions along the hard anisotropy axis. In the absence of the measured field (directed along the anisotropy axis) due to the dispersion of anisotropy equal parts of the film are magnetized by clockwise or anticlockwise rotation of magnetization. Thus the output signal is zero. When the external magnetic field appears clockwise or anticlockwise rotation may dominate – depending on the direction of the external field. The magnitude of the

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periodically changing output signal is proportional to the value of the measured magnetic field and the phase depends on the direction of this field (figure 3.13(a)). The dependence between output signal and measured magnetic field was determined as: Jl Hx Uout ——– —– √2 Hk

(3.3)

where is a standard deviation of the angular dispersion of anisotropy. The third harmonic may be separated as the output signal. A sensitivity of about 3 10–5 V/Am-1 (2.4 10–7 V/T) has been reported.

Figure 3.13 The output signals of AC-biased sensor magnetometers: (a) orthogonal magnetometer proposed by de Ridder and Fluitman (1984) (curve 1: bias field, curves 2,3,4 corresponding to external fields 2 A/m, 0.5 A/m and 2 A/m respectively); (b) the elliptically rotating field biased sensor proposed by Paperno and Kaplan (1995, 1995b, 1996) (curves 1,2: components of bias field, curves 3,4,5 corresponding to external field 630 A/m, 0 A/m and 630 A/m respectively).

The output signal obtained after applying the periodic change of direction of magnetizations may be noisy. This problem can be omitted when the thin film is still saturated – by applying an elliptically changed bias field with a value larger than Hk. Such a method was proposed by Paperno and Kaplan (1995, 1995b, 1996) and is described in section 1.2.8. It not only reduces Barkhausen noise but also allows simultaneous measurement of both components of the magnetic field. Figure 3.13(b) presents the experimentally detected output signal of the elliptically biased sensor. After applying a lock-in amplifier a resolution as high as 10–10 T/Hz1/2 has been reported. In typical applications of magnetic field measurements it is not always necessary to use extremely small sensors. By increasing sensor area both sensitivity and resolution (signal-to-noise ratio) can be effectively increased. The KMZ sensors exhibit sensitivities of: KMZ10A – 64 V/T, KMZ10B – 16 V/T, KMZ10C – 6 V/T for a sensor area of approximately 1 mm 1 mm. Assuming a reasonable sensor area of 10 mm 10 mm for the same path dimensions as the KMZ10A sensor a sensitivity as high as 6400 V/T is attainable, but with a supply

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voltage of 500 V and power consumption of 2.5 W. When the sensor paths are very small applying a large supply voltage may result in electrostatic discharge damage (Tian and Lee 1995, Wallash 1996). Analysis of large area sensors with respect to attainable sensitivity leads to the conclusion that for a reasonable sensor area of 10 mm 10 mm and supply parameters U 25 V and P 1 W a sensitivity of 500–1000 V/T can be realistically obtained. Further significant improvement of the sensitivity can be obtained by applying flux concentrators. Such a technique is typically used in GMR sensors (Smith et al 1997, Daughton 1994, Smith and Schneider 1998). Why not apply this method to AMR sensors? Gebhard and Richter (1982) placed the sensor between two external permalloy rods (figure 3.14(left)). A resolution better than 1 nT/Hz1/2 and sensitivity of about 1000 V/T was reported. Smith et al (1991) constructed a sensor with integrated flux concentrators (see figure 1.170). Magnetic fields as small as parts of nT have been detected (figure 1.170(b)) and a sensitivity of about 3000 V/T can be estimated from presented results. This is the largest sensitivity reported for magnetoresistive sensors.

Figure 3.14 The magnetic field sensor with flux concentrators and its output signal (Gebhardt and Richter 1982).

3.1.2 Gradiometers, magnetic anomaly detection For detecting the non-uniformity of a magnetic field, caused for example by the presence of ferromagnetic objects, a gradient sensor might be more useful than a magnetic field sensor. Due to the small dimensions of MR elements it is relatively easy to design gradient sensors. Dibbern (1983) proposed a simple change of the spatial arrangement of magnetoresistors to obtain the gradient sensor. Similarly the Nonvolatile company designed a gradiometer sensor (sensor AB001 – see figure 2.170(b)) with spatially distanced magnetoresistors in one chip (Smith and Schneider 1998). Also the double-element magnetoresistive head works in gradiometer mode (figure 3.15(b)) (Indeck et al 1988). Figure 3.15(c) presents the gradiometer sensor designed by Dettmann and Loreit (1993) for detection of the magnetic field around the current conductor. In this sensor two pairs of magnetoresistor are placed at both edge sides of the chip.

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Figure 3.15 The gradient field sensor: (a,b) two modes of operation; (c) sensor with distanced elements proposed by Dettmann and Loreit (1993).

Magnetic anomaly may be caused by stable objects, like mineral deposits, bridges or by mobile objects, like vehicles (cars, vans, trucks and even bicycles), ships or submarines. These last objects are not detectable in water by other conventional methods, for example by radar. The magnetic signature of a submarine may be caused by various sources. One of them is effected from magnetized hard iron parts – the whole object acts like a bar magnet. This effect can be reduced by ‘de-perming’ procedures. There also exists another effect when magnetic parts perturb the Earth’s ambient magnetic field. The total magnetic field is the superposition of the uniform magnetic field and the induced dipole perturbance, as demonstrated in figure 3.16. To avoid the possibility of detecting the magnetic anomaly the ships are constructed from non-magnetic materials and typically have onboard ‘de-gaussing’ coils. Also the alternating magnetic field from engines etc may create a detectable magnetic signature.

Figure 3.16 The magnetic field anomaly as result of superposition of a uniform magnetic field and dipole disturbance (Lenz 1990).

Magnetic anomalies from detected ferromagnetic objects decrease very fast with the distance from the source. Figure 3.17 presents the magnetic signatures of various magnetic anomalies (Lenz 1990). For large distances these signatures are very small (below 1 nT) and can be detected by extremely sensitive methods such as SQUID, optically pumped magnetometers or fibre-optic magnetometers. But for small distances, of several dozen metres, MR sensors may be recommended because of their low price and simplicity.

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Figure 3.17 The magnetic signatures of various magnetic anomalies (Lenz 1990). Table 3.2. Typical magnetic anomalies (after Breiner 1973). Object

Distance [m]

Anomaly [nT]

Ship (1000 tons)

300

0.5–1

DC train

300

1–50

Light aircraft

150

0.5–2

Automobile (1 ton)

30

1

Pipeline ( 30 cm)

15

12–50

Screwdriver

3

0,5–1

Revolver

3

1–2

Figure 3.18 presents an example of magnetic fields generated by a moving vehicle. Magnetic fields as high as 5–50 A/m can be easily used for traffic

Figure 3.18 The magnetic field disturbance caused by a moving car (Philips Technical Information).

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control, to anticipate traffic jams or indicate possible incidents. MR sensors are advantageous also for airport ground traffic control systems. The very small magnetic field disturbances are usually detected in the presence of a relatively large external field (for example the Earth’s magnetic field). Nakamura (1986) proposed an active external magnetic field compensation system consisting of two sensors. The output signal of one sensor exposed only to the external magnetic field is used to cancel an effect of this field using the magnetic feedback technique (figure 3.19).

Figure 3.19 The principle of operation of the sensor with compensation of external stray fields (Nakamura 1986).

Another method of using magnetoresistive sensors to detect objects was proposed by Collins (Collins 1989, McClelland 1989). The magnetic field generated by an eddy current induced in a conducting plate passing through the magnetic field can be used to recognize coins (figure 3.20). The phase difference between the applied magnetic field and that due to the coin is applied as the electromagnetic fingerprint. The microprocessor circuit helps to compare and differentiate signals independently of the velocity and acceleration of the coin passing over the sensor. Figure 3.20(right) presents a comparison of detected phase shifts of various coins.

Figure 3.20 The principle operation of the magnetic coin detector and magnetic signatures of two different coins.

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Okabe and Wakaumi (1990) described a magnetic system using MR sensors for the recognition of grooved bar codes. A magnetic encoding system may substitute widespread optical bar code systems when there is a risk of blots or slight scratches in e.g. an industrial environment. Figure 3.21 presents a comparison of the output signal from dirty bar codes detected by optical and magnetic encoders.

Figure 3.21 A comparison of the output signal from dirty bar codes detected by optical and magnetic encoders (Miyashita et al 1987).

The grooved bar codes are practically indestructible and difficult to falsify. The idea of the system is presented in figure 3.22(left). The magnetic field generated by the magnet placed near the grooved plate is distributed dependently over the shape of the groove. By moving the sensor–magnet set directly above the coded plate it is possible to recognize the bar code pattern

Figure 3.22 The grooved bar-code pattern recognition system: principle operation (left) and the output signal detected above various bar-code pattern configurations (right) (Okabe and Wakaumi 1990).

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with a high resolution (figure 3.22(right)). The 1.3 mm wide and 0.1 mm deep grooves have been reliably detected. The gradiometer sensors are an attractive alternative for magnetic field detection when this field is of large non-uniformity. Figure 3.23 presents the magnetic field measured by the gradiometer sensor for ferrous gear tooth detection. Two easy-to-detect pulses correspond with the slope of the tooth while the conventional magnetic field sensor measures the sinusoidal signal only approximately.

Figure 3.23 The magnetic field measured by the gradiometer sensor for ferrous gear tooth detection.

3.2 ELECTRICAL MEASUREMENTS

3.2.1 Current transducers Conventional methods of current measurements utilize the resistor shunt technique. However, this technique exhibits several serious drawbacks. The most important disadvantage is the lack of a galvanic separation between the source (very often of high voltage) and measuring equipment. Another disadvantage of the shunt is the necessity of breaking the conductor, which is not always possible, for example in printed circuit boards (PCB) or high voltage circuits. Another conventional method of current measurement is the use of measuring transformers. This method introduces additional errors (for example hysteresis) and is typically limited to large AC currents.2 Therefore the shunts or the measuring transformers are often substituted by Hall-sensor current transducers (Hencke 1984). Due to better sensitivity, linearity and temperature behaviours the permalloy magnetoresistive current transducers can be substituted for similar Hall-sensor transducers. Moreover thin film permalloy sensors are very convenient to prepare as integrated current transducers (Bajorek et al 1976, Gordon et al 1977, Rühl and Walther 1993, Andrä 1992, Dettman and Loreit 1992, Doberschütz 1992, Rühl 1992). 2 DC measuring transformers also exist, but they are rather complicated and have modest accuracy.

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The simplest way to convert the current into the output signal of the sensor is to measure the magnetic field around the current conducting layer (figure 3.24(a)), above the current conducting track (figure 3.24(b)) or inside the coil (figure 3.24(c)). The magnetic field around the current conducting layer (figure 3.25) can be calculated from the expression: Ix H ——. 2x

(3.4)

Figure 3.24 The detection of the electrical current: (a) around the current conducting wire; (b) above the printed circuit board; (c) as a field produced by a coil.

Figure 3.25 The magnetic field around the current conducting wire.

When the KMZ10A sensor is used as the current transducer then at the full range of the sensor (about 500 A/m) at a distance of 10 cm from the wire a current of magnitude larger than 300 A can be sensed. Thus the measurements of the current by the remote mode (at a distance larger than 10 cm) can be recommended only for quite large values of the current. For shorter distances from the wire (not more than several mm) much smaller values of the current may be measured. Figure 3.26 presents the transfer characteristic of the set-up when the KM110B sensor of Philips was used.3 3 The KM110B sensor is designed for current and linear position measurements. The typical KMZ10B sensor is additionally equipped with the magnet mounted on the back of the sensor package. Due to the existence of an additional stabilizing field the sensor is more immune to overloads caused by large magnetic fields.

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Figure 3.26 The recommended application of the KMZ10B sensor for current measurements: arrangement of the sensor and typical transfer characteristics (Philips Technical Information).

In the case of printed circuit boards the sensor may be placed directly above the track. The magnetic field above the track of width w can be determined from the approximated expression (Loreit et al 1985): Ix H —–. 2w

(3.5)

Figure 3.27 presents the experimentally determined transfer characteristic of the GMR AC004 sensor placed above the track with dimensions 1.5 mm width and 0.05 mm thickness.

Figure 3.27 The recommended application of the AC004 sensor for current measurements: arrangement of the sensor and typical transfer characteristics (Honeywell Technical Information).

The measurements of the current by the determination of the magnetic field around the wire are interfered with by the external magnetic field, for example the Earth’s magnetic field when the DC current is detected. It is recommended to use the dual-sensor system in such a case, as demonstrated in figure 3.28(a). Figure 3.28(b) presents an example of dual-sensor current transducer.

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Figure 3.28 Dual-sensor current transducer: (a) principle of operation and (b) design of the transducer (Philips Technical Information).

Operation in the mA current range is possible by using the coil system to generate the magnetic field. The magnetic field inside the air coil of length L, diameter D and n turns can be determined from the expression nlx H ———––. 2 √D L2

(3.6)

It is easy to calculate that more than 5000 turns are necessary to obtain the magnetic field equal to the range of the KMZ10A sensor when D is 5 mm, L is 10 mm and measured current is 1 mA. For small currents the yoke systems are recommended. Figure 3.29 presents two examples of such systems. It may be a ferrite yoke with wounded coil or clamp-on meter. The sensor located in the air gap between the ends of the yoke operates as a nullpoint detector. Because of magnetic feedback the transducer is free of many errors existing in open circuit methods (temperature, non-linearity). The magnetic field inside the gap of width g can be determined from the expression Ixn H ≅ —–. g

Figure 3.29 The yoke systems of current transducers.

(3.7)

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The gap width of the yoke system cannot be very small because magnetoresistive thin film sensors detect the magnetic field component in the film plane. The sensor can be placed outside the small gap—see figure 3.66(c). It is possible to place the current conducting layer close to the sensor in the integrated transducer design. Figure 3.30 presents an example of the current transducer designed by Bajorek et al (1976). The transducer consists of two permalloy films of unequal thickness separated by a titanium spacer. The upper film serves as the current conducting layer. The sense currents in the adjacent arms of the bridge circuit are of opposite directions and bias the magnetoresistors differentially. The transducer converts the current up to 20 MHz in the range 0 to 50 mA into the voltage output signal 0 to 30 mV.

Figure 3.30 The current transducers with planar current conducting layers (Bajorek et al 1976).

A similar current transducer designed for measuring superconducting currents was proposed by Gebhardt and Richter (1982, 1982a). In this transducer four current conductors separated by an insulator film of SiO magnetize four magnetoresistors of canted easy axes. Other current transducers applying Barber-pole magnetoresistors and additional feedback layers have been designed by Andrä (1992) and Dettman and Loreit (1992). For example the transducer described by Dettman and Loreit (1992) converts the current in the range 10 A into the output current with a sensitivity of 3 mA/A with the insulation between output and input circuits better than 20 M. Figure 3.31 presents two other integrated current transducers with gradiometer sensors placed above the current conducting layers. The transducer designed by Dettman et al (1992, 1993) (figure 3.31(a)) converts the current of various ranges (1 A to 250 A) into the output current (0 to 50 mA) with an accuracy better than 0.5% and bandwidth from DC to 20 kHz. The KMC sensor designed by Doberschütz (1992) (figure 3.31(b)) exhibits similar performances.

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Figure 3.31 The integrated current transducer with gradient magnetoresistive sensors. (a) Dettman et al 1992, 1993 and (b) Doberschütz 1992.

Rühl (1992) investigated the integrated magnetoresistive current transducer. The linearity of the transducer was better than 0.3%. Figure 3.32(left) presents the results of bandwidth investigations. The frequency characteristic was flat up to 5 kHz and with a 3 dB drop up to 100 kHz. Figure 3.32(right) shows the comparison of the input and output signal of the transducer. Both signals are identical in value and phase.

Figure 3.32 The performances of the MR current transducer tested by Rühl (1992) – frequency characteristics of the transducer (left) and comparison of output and input signals (right).

Figure 3.33 presents an application of the current sensor in the automotive industry (Rottman 1992). Two currents of the headlamp create flux of opposite directions in the yoke. Thus bulb failure can be easily detected and is indicated as the non-balance flux in the yoke.

Figure 3.33 Device for continuous testing of automobile headlamps (Rottman 1992).

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3.2.2 Electrical transducers, switching and logic elements A valuable behaviour of magnetoresistive sensors – galvanic separation between input and output – is useful not only in current transducers, but also for converting other electrical quantities into standardized output. The various electrical measurement converters include: multipliers, dividers, adders, current transformers, power converters, electrical energy metres have been described by Kwiatkowski et al (1984). Other groups also reported the application of thin magnetoresistive sensors as power converters (Yoda et al 1989, Vountesmeri 1998), isolation devices (Hermann et al 1997, Daughton 1999), logic devices (Hassoun et al 1997), amplifiers (Gordon et al 1977, Oberg et al 1968), switching devices, contactless potentiometers (Clemens et al 1997, Schewe and Schelter 1997), square devices (Patel and Aly 1977) or digital to analog converters (Tolman 1968).

Figure 3.34 Galvanic separation circuits (DC current transformers).

Figure 3.34 presents various techniques used for galvanic separation of the input and output circuits. The sensor acts as a current transformer by detecting the magnetic field generated by the current conducting layer or coil (figure 3.34(a)). In comparison with conventional transformers the magnetoresistive transformer also converts DC current and AC current with a much higher frequency bandwidth. It is possible to convert the sum of the currents into the output signal – the transformer may additionally serve as the adder (figure 3.34(b)). If magnetic feedback is used (figure 3.34(c)) and the gain of the amplifier is sufficiently large the output current practically does not depend on the sensor sensitivity changes (for example caused by the temperature) and depends only on the ratio of the winding turns: n Iout —1 Ix. n2

(3.8)

To eliminate the offset drift in the DC operation mode the flipping biasing field is recommended. Figure 3.35(a) presents the integrated galvanic isolation device developed by Nonvolatile Electronics Inc. The input current in the planar coil generates the magnetic field. Thus the input signal is transmitted through the thin

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insulator film by the magnetic flux. This magnetic flux is sensed by a serpentine GMR sensor. The isolation voltage has been determined as high as 1–3 kV. In comparison with opto-isolators the GMR one-chip device is smaller, easy to integrate with silicon circuits and of high speed, faster than 1 GBaud. A similar isolator structure designed for analog applications, for example to connect various circuits to eliminate source ground potentials, is presented in figure 3.35(b). With a feedback circuit a non-linearity less than 1% was achieved.

Figure 3.35 The integrated galvanic isolation device: (a) principle of operation; (b) device with magnetic feedback for analog applications (Hermann et al 1997).

Figure 3.36 presents another important application of the magnetoresistive sensor. When the sensor is linear it can operate as a multiplier device because the output signal can be expressed as: 1 Uout —– ———– RI1xcI2x S(I1x · I2x)

Hk Hyo

(3.9)

where: c is the coil constant.

Figure 3.36 The magnetoresistive sensor as multiplier (a) and divider (b) device.

Assuming distorted current and voltage waveform at the multiplier input: i Io Ilm sin(t li) I2m sin(2t 2i) ···

(3.10)

u Uo Ulm sin(t lu) U2m sin(2t 2u) ···

(3.11)

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the average output signal is expressed as T

Uout ∫ uidt IoUo I1U1 cos(lu li) I2U2 cos(2u 2u) ··· .

(3.12)

0

Thus it is possible to determine the electrical power and due to the excellent frequency behaviours of the magnetoresistive sensor such a transducer can correctly operate with distorted waveforms signals. The bandwidth is limited only by the coil inductance. The inductance of the coil can also introduce an additional phase shift between measured signals. Therefore the best choice is to use a single planar line as the magnetic field generating part, or to use a coil of a limited number of turns. In the power transducer it is easy to eliminate the AC offset drift by filtering the DC output signal. The circuit implementing reciprocal function, i.e. also the division of the signals is shown in figure 3.36(b). The output current of the transducer can be expressed as: 1 U1x Iout — —–. S I1x

(3.13)

Figure 3.37 presents the power converter constructed by Kwiatkowski et al (1984). The thin film multiplier is located inside a four-turn coil. Input voltage feeds the bridge circuit. Some inconvenience arises due to the necessity of using the voltage transformer at the input. The whole transducer is placed inside the permalloy shield box (figure 3.37(a)). To stabilize the sensor two magnets elements were used. The constructed power transducer correctly measures the power for the input current (5 or 10 A) and input voltage (200 or 400 V) with accuracy better than 0.5%. The transducer is able to convert power independently of the power factor cos value and at tenfold current overloads. It may be fed from the voltage input due to the relatively small power consumption (less than 3 VA).

Figure 3.37 Electrical power transducer: (a) design; (b) application circuit (Kwiatkowski et al 1984).

Figure 3.38 presents a three-phase version of the power converter. Two thin film multipliers are used for a basic conversion while a third thin film sensor is

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used as an adder. Further development of the described transducer yielded the design of an electrical energy meter (figure 3.39) (Kwiatkowski et al 1984). The output signal of a multiplier is converted into a frequency using a typical integrating converter (1 kHz at 100% of nominal power). After stepping down the frequency the output signal drives a relay counting system using one-shot flip-flop for pulse shaping. The errors of the watt-hour-meter were below 1% in the power range 10–200% of nominal power and below 5% in the power range up to 10% of nominal power.

Figure 3.38 Three-phase power converter.

Figure 3.39 Applying a MR power converter in an electrical energy meter (watt-hour meter).

The large change of resistance in the case of GMR sensors leads to the idea of contactless potentiometers (Clemens et al 1997, Schewe and Schelter 1997). The performances of such potentiometers are presented in figure 3.40. The rotating magnet causes a change of resistance. The potentiometer is constructed from the multilayer GMR sensor with an artificial antiferromagnetic subsystem. With two sensors in the planar setup the whole 360° angle range can be covered. The sensor gives a sinusoidal signal dependence on the direction of the rotating magnetic field and the amplitude of the change of resistance does not depend on the magnetic field value within a field range of about 4–28 kA/m. The whole change of resistance is not very large (about 5%) but it is sufficient for use in electronic circuits or angle measurements. Larger changes of resistance, practically from the insulator state to the conductor state, are possible using the colossal magnetoresistive element.

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Figure 3.40 The performances of the contactless potentiometer: the transfer characteristic of the potentiometer and the dependence of the output signal on the magnetic field value (Clemens et al 1997).

The switching behaviours of GMR sensors may be used for logic elements, like gates or comparators. The solid-state switching device has been developed by Nonvolatile Electronics (figure 3.41). One chip comprises the GMR sensor and semiconductor electronics. The schematic and logic output characteristic of a commercial integrated digital GMR sensor is presented in figure 3.41.

Figure 3.41 The GMR element as a switching device (Daughton 1999).

Using pseudo spin-valve GMR sensors Hassoun and co-workers (1997) developed GMR sensors as field programmable logic gates. The switching characteristic of the pseudo spin-valve logic element is presented in figure 3.42. The magnetoresistive sensor placed above the current conducting word line can

Figure 3.42 The programmable spin-valve logic element (Hassoun et al 1997).

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be switched between two well-defined ‘logic 0’ and ‘logic 1’ states. The switching time can be no longer then a few nanoseconds. A device is programmed high or low by simply applying a negative or positive word current. Figure 3.43 presents two examples of logic programmable gates. The basic circuit consists of a 4-input gate (a circuit of up to 60 inputs is possible). The bottom bit of each pair is the evaluation bit while the top bit is the reference bit. The device can by described be the equation

[

v v

({B1 ⊕ X1}{B2 ⊕ X2}{B3 ⊕ X3}{B4 ⊕ X4}) ·—- Isens ({Br1 ⊕ Xr1}{Br2 ⊕ Xr2}{Br3 ⊕ Xr3}{Br4 ⊕ Xr4}

]

(3.14) where: B and Br are the programmed values of the evaluation and reference bits respectively (1 or 0 for high or low), X and Xr are the logic value of the inputs to the evaluation and reference bits respectively (1 or 0). For the NOR configuration (figure 3.43(a)) equation (3.14) is reduced to v v [({B1 ⊕ X1}{B2 ⊕ X2}{B3 ⊕ X3}{B4 ⊕ X4}) 4] · —– Isens (3.15) and since the B values are high: — — — — v v [( X1 X2 X3 X4 ) 4]· —– Isen.

(3.16)

Figure 3.43 The NOR (a) and NAND (b) gate configuration (Hassoun et al 1997).

To develop competitive MR logic elements it is necessary to solve the problem of offset voltage compensation. The reduction of the evaluation and programming currents is also necessary. In the described construction this current was about 1–5 mA per gate. Further reduction of these currents is possible by applying multi-turn planar coils.

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3.3 MAGNETORESISTIVE ELEMENTS IN DATA STORAGE APPLICATIONS

3.3.1 Magnetic Random Access Memory (MRAM) devices The idea of using thin film magnetoresistive elements in memory devices appeared very early. Because a thin film element is in a quasi single-domain state the magnetization process is very fast (by rotation of magnetization). The hysteresis loop for the easy direction is a rectangle and switching threshold is very fast. Therefore magnetoresistive memory might be considered an alternative for other memory technologies. In the seventies and eighties large efforts were made in the preparation of magnetic bubble memory elements. In these devices various magnetoresistive domain detectors were tested. The bubble memory lost the competition to semiconductors because of preparation costs and the performances. This technique is described elsewhere (Almasi 1973, Eschenfelder et al 1980) and is now of little importance. The existing semiconductor random access memories SRAM (static random access memory), DRAM (dynamic random access memory) or FLASH are not without drawbacks (Tehrani et al l999). For example SRAM memory is volatile. Also DRAM is volatile and requires refreshing the storage capacitor. FLASH memory exhibits poor write endurance of about 106 cycles. Therefore magnetoresistive memory may be an attractive alternative (Tehrani et al 1999, Gau 1989, Daughton 1992), because it is nonvolatile (state of memory is maintained even when power is switched off), with unlimited read/write endurance. Moreover this memory is radiation immune and compatible with semiconductor technology. It can be very simple and relatively low price to manufacture. The individual cells can be very small, in the submicron range and very fast, with a switching time of several nanoseconds. The concept of magnetoresistive memory is presented in figure 3.44. Two well-defined states of magnetization of the thin film cell exist representing

Figure 3.44 The principle of operation of magnetoresistive random access memory: (a) memory cell structure (Gau 1989); (b) an example of the signals in the memory lines (Pohm et al 1987).

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stored ‘0’ or ‘1’ signals. Each cell is driven by the sense current supplied by the sense line. The change of magnetization can be caused by the magnetic field generated by the current in a word line. A ‘1’ or ‘0’ can be written into a 2D array of the cells by the word current in combination with a sense current of appropriate polarity (figure 3.44(b)). Neither the sense current alone nor the word current alone can switch the magnetizations. The first results of devices utilizing AMR elements4 were not fully satisfactory. The devices were not competitive with semiconductor devices and their applications were rather limited. But after introducing the GMR technique the manufacture of magnetoresistive random access memories MRAM is now more realistic. The main drawback of AMR-MRAM is a small output signal. Therefore to ensure an adequate signal-to-noise ratio the cell cannot be very small. Moreover the time required to read the state of magnetization of a cell depends on the difference is in signals between the two states representing ‘0’ and ‘1’. For AMR-MRAMs this time is not smaller than hundreds of nanoseconds. For a given SNR the read access time decreases as the inverse square of the sense signal (Daughton 1992). Thus an enlargement of the output signal by a factor of 10 may result in an improvement of the access time to several nanoseconds. Figures 3.45 and 3.46 present the switching behaviours of various magnetoresistive elements. The AMR sandwich film structure (Berchier et al 1984), typically used in AMR memory elements, exhibits an output signal of several millivolts and the switching field is less than 1 kA/m (figure 3.45(a)). The output signal of the antiferromagnetically coupled multilayer structure (Pohm et al 1994, 1995, 1996) is much larger but for a switching field not smaller than 10 kA/m. This is unacceptable because it means applying a large word current.

Figure 3.45 The switching behaviours of AMR multilayer memory cell (a) (Pohm et al 1987, [96] and antiferromagnetic coupled multilayer memory cell (b) (Tehrani et al 1999). 4 For example: Pohm et al 1987, 1987a, 1988, 1989, Granley et al 1991, Ranmuthu et al 1990, Yoo et al 1989, Pohm and Comstock 1991, Comstock et al 1988.

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Figure 3.46 The switching behaviours of spin valve memory cell (a) (Tehrani et al 1999) and tunnel junction memory cell (b) (Daughton 1997).

The spin-valve structure can be applied in the GMR memory (Tang et al 1995, Oti and Russek 1997, Chen et al 1997, Melo et al 1997). It exhibits a relatively large output signal for an acceptable value of the switching field – smaller than 5 kA/m (figure 3.46(a)). The most widely utilized are the pseudo-spin-valve structures (Matsuyama et al 1997, Everitt and Pohm 1997, Pohm et al 1997, Zheng and Zhu 1997, Everitt et al 1998, Gadbois et al 1998). Recently magnetic tunnel junctions have been considered as memory structures (Daughton 1997, Gallagher et al 1997, Parkin et al 1999). Figure 3.46(b) presents an example of the tunnel junction characteristic. The change of resistance may be larger than in spin-valve structures and can be obtained for a switching filed smaller than 2 kA/m. Figure 3.47(left) presents a prototype of an MRAM cell with pseudo-spin-valve elements (designed by Tehrani and co-workers 1999). This element consists of two ferromagnetic layers of different thicknesses separated by a Cu layer (figure 3.47(left)). The cell was diminished to the sub-micrometres dimensions of 0.25 m 2.5 m. A comparison of the characteristic of the cell (figure

Figure 3.47 The pseudo-spin-valve memory element: memory cell design with wraparound word line and an example of the switching characteristic of a cell with dimensions 0.25 m 2.5 m (Tehrani et al 1999).

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3.47(right)) with the other one prepared from the same material but of larger dimensions (1 m 10 m) shows an improvement in the switching behaviours. The characteristic was refashioned from a triangular shape to a rectangular shape. This improvement of abruptness of the shape for a very small thin film element is attributed to nearly single-domain formation. As demonstrated by Tang et al (1995) when the film stripe is narrower than the magnetic domain width then the cell becomes a quasi single-domain state. Such elements exhibit a rectangle shape of the characteristic and the switches states in sub-nanoseconds. The memory cell presented in figure 3.47 is wrapped on the top and bottom by the three word lines. This wraparound mode decreases the word current by half in comparison with a conventional single word line. The cells are connected in series and only one transistor is required for several cells, which helps in the design of higher density memories. The memory states are written by applying a word current large enough to switch the state of magnetization. The direction of the current depends on the ‘0’ or ‘1’ states of the memory cell. A non-destructive read is realized by applying a sense current together with first a negative, and second a positive word current. The magnitude of a word current is such that the magnetic field generated by the word current and sense current is enough to switch the thin magnetic layer without switching the thick magnetic layer. Although the change of resistance is about 6% the effective change of the output signal is about 12% because the signal of ‘1’ corresponds to plus 6% and the signal of ‘0’ corresponds to minus 6%. The use of tunnel junctions with MRAM devices may achieve devices of further improved memory performances. In fact tunnel junctions with dimensions in the submicron range can exhibit the change of resistance at room temperature of about 40% for a relatively small magnetic field. Because the current flows perpendicular to the layers the cells can be arranged along the common word line at the cross points with the corresponding upper bit lines. Thus it is possible to obtain the larger output signal in comparison with the spin-valve cells connected in-series (when the output signal is U/N). A comparison of the memory architecture for the spin valve and tunnel junction cells is presented in figure 3.48.

Figure 3.48 The design of spin-valve memory with cells connected in series (a) and the design of magnetic tunnel junction memory with cells arranged at the cross points of word and bit lines (b) (Parkin et al 1999).

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Promising results in the construction of the MRAM with tunnel junction cells arranged in the cross-point architecture was reported by Parkin et al (1999). The design of the cell is presented in figure 3.49(a). The tunnel junction consists of a bottom FM electrode and top FM electrode separated by a tunnel barrier of 0.7 nm oxidized Al. The bottom electrode was in the form: Ta 5/Al 25/Ni60Fe40 4/Mn54Fe46 10/Co 4/Ru 0.7/Co 3. FeMn layer and Co/Ru/Co artificial antiferromagnetic layer were used as the exchange biased layers. The top electrode consisted of Ni60Fe40 7.5/Al 25/Ta 7.5. The transfer characteristic of the tunnel junction with dimensions 0.6 m 1.2 m is presented in figure 3.49(b). Each tunnel junction cell was integrated with a silicon diode allowing every element of the memory array to be switched.

Figure 3.49 The tunnel junction memory element: (a) the cross-section of a single cell; (b) an example of the switching characteristic of the cell with dimensions 0.6 m 1.2 m (Parkin et al 1999).

It was concluded that the exchange-biased magnetic tunnel junction devices might be attractive candidates for magnetic non-volatile storage elements. Because the specific resistance was as little as 60 (m)2 memory chips of gigabit range could be designed. But as analysed by Daughton (1997) to date there are many problems to overcome to obtain a competitive commercially available product. For example the signal-to-noise ratio should be improved. Because the tunnel junction with nonmagnetic barrier is a capacitor the dielectric should be thin enough, and the specific resistance should be sufficiently small to ensure that the RC time constant does not limit the speed of memory.

3.3.2 Magnetic card readers Magnetoresistive heads can be considered as sensors capable of detecting the magnetic field above the magnetic medium (tape, disc or magnetically encoded credit card). In comparison with conventional inductive heads magnetoresistive

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heads exhibit several significant advantages such as independence of the medium speed, smaller dimensions, larger sensitivity, simpler design and lower costs of manufacturing. The main disadvantage of MR heads is that they are not able to write the signal. This disadvantage is unimportant when this head is used as a card reader. Moreover another drawback of MR heads – non-linearity and bias necessity – is also of little importance because these heads are used only to detect relatively large magnetic flux changes and can operate properly even without biasing. Figure 3.50 presents the operating principle of magnetic card readers. On the magnetic stripe are recorded magnetic flux lines corresponding with bytes ‘0’ or ‘1’. The density of the pulse train is not very high – typically 50–100 recorded transitions per cm.1 These recorded pulses are detected as magnetic field changes from H to H. In conventional magnetic tape the field magnitude is about 4–8 kA/m, but when the head is distanced from the medium by 30–50 m this field can be no larger than 1.5 kA/m. Usually the head is placed 20–50 m from the medium to protect it from wear and lapping effects. Figure 3.51 presents the dependence of the output signal of the head on the distance to the medium and recorded density (determined experimentally by Jones et al 1982).

Figure 3.50 The principle of operation of magnetic card readers.

The magnetic card can be moved with various speeds. When this speed is lower than 10 cm/sec the reading capability of the conventional inductive head is impaired. The MR head can operate properly for the speed range 2.5–160 cm/sec (McClelland 1989). The information recorded on the magnetic cards is usually encoded to allow reproduction independently of the speed. Commonly the self-clocking code is used from which, after decoding, it is possible to obtain clock and data signals. For example in the Aiken code the information is recorded without space intervals and each data cell is defined by a magnetic line charge at the beginning and end of 1 The density of recorded information is often determined as fc/cm – flux changes per cm or fci – flux changes per inch or bpi – bits per inch.

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Figure 3.51 The dependence of the output signal of the head on the distance to the medium and recorded density – head dimensions: width 49 m, thickness 34 nm, length 2 mm, sense current 0.9 1010 A/m2 (Jones et al 1982).

the cell. If the bit is ‘1’ the additional magnetic flux line is recorded at the centre of the cell. If the bit is ‘0’ there is no additional flux line (Moore and Cote 1976). An example of recorded information is presented in figure 3.52. The inductive magnetic card reader is usually connected to the conditioning electronic circuits consisting of an automatic gain controlled amplifier and a decoding circuit. The amplifier is necessary to compensate for changes in the amplitude of the head signal, which is a function of the speed at which the encoded data passes the head. In the case of the MR head the electronic circuit can be much simpler. The automatic gain amplifier is not necessary and the decoding system can be less complicated. Moore and Cote (1976) proposed using the dual magnetoresistive card reader with two detectors spaced at one-half of the data cell width. The design of the sensor is presented in figure 3.52. Such an MR head connected to very simple decoding electronics (figure 3.53) generates two resultant output signals – clock signal (strobe signal) and data single pulse train.

Figure 3.52 A dual detector card reading system proposed by Moore and Cote (1976) – design of the sensor and principle of operation.

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Figure 3.53 Electronics for detecting the output of the dual detector read head and the main signals (Moore and Cote 1976).

An even simpler electronics circuit processing the data from the MR head was proposed by Collins (1989). As demonstrated in figure 3.54 a logic ‘0’ signal corresponds with one pulse output signal from the MR head, while a logic ‘1’ with two pulses. Relatively simple electronics can be employed to convert these pulses into standard magnetic card reader output. Typical MR card readers produced by MR Sensors Ltd company include electronics for transmitting the output data via an RS232 interface directly to the serial port of the PC. Transmitted data may then be decoded into ASCII format.

Figure 3.54 The input and output signals in single stripe magnetic card reader (Collins 1989).

Figure 3.55 presents a comparison of the conventional inductive head and magnetoresistive head, reported by Desserre and Helle (1978). The output signal obtained after sensing one isolated bar was in the case of the MR head more than two times higher compared to 1800 coil turns of the inductive head. The signalto-noise ratio was 56 dB for the MR head and 28 dB for the inductive head.

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Figure 3.55 A comparison of the performances of the conventional inductive head and MR head: output signals and dependence of the output signal on the head-to-medium distance (Desserre and Helle 1978).

The magnetoresistive head is much less sensitive to the distance change from the medium or to the skew of the head with respect to the card track (Desserre and Helle 1978).

3.3.3 Magnetoresistive heads for tape and disk applications Magnetoresistive heads (Mallinson 1996, Gorter et al 1974, Druyvesteyn et al 1981, van Gestel et al 1977, Metzdorf et al 1980) are the main and most important application area of magnetoresistive sensors. It may be stated that other applications of MR sensors are byproducts of magnetoresistive heads. The importance of data storage applications results from their market size. It is estimated (Greidanus 1998) that the market size for tape and disk-based systems is about $70 billion per year. The introduction of magnetoresistive heads in 1970 by Hunt (1970, 1971) caused the revolution in high-density recording. After the introduction of the first commercial magnetoresistive reading head to data storage systems in the nineties the yearly growth rate of the areal bit density has increased from about 30% per year to about 60% per year (see figure 3.56) (Grochowski and Thompson 1994, Luitjens et al 1998, Coehoorn 1999). Conventionally the areal recording density is expressed in terms of the number of bits stored per unit area [Gb/in2].2 Recently magnetoresistive heads capable of operating with 1 Gb/in2 density (Tsang et al 1990, 1993, Tsang 1991, Hsu et al 1995), 2 Gb/in2 (Suzuki et al 1991, Shi et al 1997, Takano et al 1991), 3 Gb/in2 (Tsang et al 1996), 5 Gb/in2 (Yoda et al 1996, Kanai et al 1996, Nakamoto et al 1996, Tsang et al 1997, Hu et al 1999, Arnett et al 1997, Mutoh et al 1996), 10 Gb/in2 (Kryder et al 1996, Koganezawa et al 1996, Tong et al Because inch-based parameters are used to describe the recording parameters conventionally in this section these terms will be used. The conversion to SI units can be simply performed using the following expressions: 1 Gb/in2 0.155 Gb/cm2 1.55 Mb/mm2, 1 ktpi 39.3 t/mm and 1 kbpi 39.3 bit/mm. 2

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Figure 3.56 The development of areal density recording in hard-disk applications (a) and tape applications (b) (Luitjens et al 1998, Coehoorn 1999).

1999, Liu et al 1999) and 12 Gb/in2 (Tsang et al 1999) have been reported. It is assumed that the physics of magnetic storage layers limits the storage density to about 40 Gb/in2. Nevertheless further increase of the recording density as high as 100 Gb/in2 has been considered (Grochowski and Thompson 1994, Khizroev et al 1997). Note that the compact disk (CD) exhibits a recording density of 0.65 Gb/in2, and the DVD-ROM disk exhibits a recording density of 3.28 Gb/in2.

Figure 3.57 The fringing magnetic field above the recording medium (Mallinson 1996).

The information recorded on the disk or tape is represented by the magnetic field above the medium (figure 3.57). When this information is written as a sinusoidal change of magnetization: 2 Mx(x) Mr sin —– x

(3.17)

the magnetic field above the medium is represented by two components of magnetic field Hx and Hy expressed by the Wallace equations (Wallace 1951) Hx (x, y) 2 Mr (l ek )eky sin kx (3.18) Hy (x, y) 2 Mr (l ek )eky cos kx

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where: k 2 / is the wave vector, is the wavelength, is the medium thickness (for example tape coating thickness). The frequency of recorded information is V f—

(3.19)

where V is the head-to-medium relative velocity. Usually the frequency characteristic of a reading head is presented as a dependence of the output signal on the frequency or the wavelength. This characteristic can be determined by measuring the output signal of the head placed above the tape at a given speed. An example of such a characteristic determined by Hunt (1971) is presented in figure 3.58. The magnetoresistive element (12 m high) placed 0.6 m above the tape was used to read data from the tape with a coating thickness of 7.5 m, track width 1.25 mm and speed of 18.7 cm/s. Also shown is the characteristic determined for the ringtype inductive head with gap length 1 m, gap depth of 175 m and 62 turns.

Figure 3.58 A comparison of frequency characteristics of the MR vertical head and conventional inductive head (Hunt 1971).

Digital information is stored by writing the magnetization changes (flux changes) at the magnetic track separated by a transitions area a (figure 3.59(a)). There are two transitions in one wavelength . The length density of storage is usually determined as kilo flux changes per inch (kfci) or kilo-bits per inch (kbpi). Typical values of the linear resolution corresponding with areal density of 1 Gb/in2 is a bit length of 0.16 m (160 kfci). To obtain areal density of 10 Gb/in2 it is necessary to ensure a bit length of 0.1 m (250 kfci). Figure 3.59(b) presents

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Figure 3.59 The digital information recorded on the magnetic medium: (a) recording and reading the information on the tape; (b) microscopy image of several recorded bits (Luitjens et al 1998, Kryder and Jayasekara 1996).

an example of the magnetic force microscopy image of a 160 kfci pattern written with 1 m trackwidth head (reported by Kryder and Jayasekara 1996). The bit length is limited by the length of the transitions. This length can be determined using the Williams–Compstock model of the writing process (Williams and Comstock 1972). For the transition form presented in figure 3.59(a) the magnetization transition is expressed as:

()

2 x M(x) — Mr tan1 — a

(3.20)

where a is the so-called transition slope. The transition slope is expressed by the Williams–Compstock formula:

√

a2

2Mr d — 2 —————— √3Hc

( )

(3.21)

where d is the distance between the head and the medium, Hc is the coercivity of the medium. The typical values of these parameters are coercivity of 140–160 kA/m and media thickness of 20–50 nm. From expression (3.21) it results that the distance between the head and the disk significantly influences the recording density. Therefore this distance should be reduced depending on the shape of the slider and the roughness of the disk. Recently all hard disk drives employ a slider that flies over the disk on a self-pressurized air bearing (ABS) and the distance between head and the disk is lowered to values close to 30–50 nm.

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Figure 3.60(a) presents the typical readback waveform obtained by Tsang et al (1996) for a 3 Gb/in2 magnetic storage system. Figure 3.60(b) presents the typical dependence of the normalized output signal on the linear density (roll-off characteristic). In the readback waveform presented in figure 3.60(a) the width of the transition pulse PW50 can be determined as about 0.3 m (PW50 is expressed as a pulse width corresponding to 50% of the peak amplitude). From the Williams–Compstock model the 50% pulse width can be expressed as (Mallinson 1996):

√[

PW50 2

]

g2 (d a )(d a) —– 4

(3.22)

where g is the read-head gap length.

Figure 3.60 The readback waveform signal (a) and frequency characteristic (b) determined for 3 Gb/in2 storage system (Tsang et al 1996).

The areal density can be considered as the multiplication of the linear density expressed as kilobits per inch kbpi and the track density expressed as kilo tracks per inch (ktpi). The track density depends on the head trackwidth, recorded offtrack profile, signal-to-noise ratio and the head positioning system performances (Kryder et al 1996, Yoshikawa et al 1996). Tomiyama et al (1998) considered the optimal trackwidth design of MR heads for high-trackdensity disk drives. The results of this analysis are presented in the table 3.5. Table 3.5 The optimal values of recording densities (after Tomiyama et al 1998). Areal density [Gb/in2]

Linear density [kbpi]

Track density [ktpi]

Write trackwidth [m]

Read trackwidth [m]

3

197

15

1.35

1.15

10

316

32

0.66

0.56

20

400

50

0.41

0.36

40

530

75

0.27

0.24

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The track profile depends on the head geometry (Heim 1994, Wallash et al 1991, Partee and Lansky 1997). For example non-linearity of the track profiles reported by Anthony and co-workers (Anthony et al 1994) (figure 3.61(a)) could be significantly reduced by appropriate shared-pole planarization, as confirmed by Hsu and co-workers (Hsu et al 1995) (figure 3.61(b)).

Figure 3.61 Two examples of the cross-track profile determined for various linear densities (Anthony et al 1994, (a) and after Hsu et al 1995 (b)).

To estimate the acceptable track density tests are usually performed with the output signal of the head processed by the digital readback electronics. The PRML digital data channel is the most widely applied (Partial Response-with Maximum Likelihood sequence detection) (Cideciyan et al 1992, Huber et al 1996, Howell 1990, Eleftheriou and Hirt 1996). The error rate curve (so-called bathtub curve) is determined as a function of the offtrack displacement. An example of such a test (reported by Tsang et al (1996) is presented in figure 3.62(a). The performance of the 3 Gb/in2 head/disk system has been tested using a class IV PRML channel at a data

Figure 3.62 The examples of typical ‘bathtub curve’ (a) and ‘747 curve’ describing the performances of read heads in digital applications.

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rate of about 5 MB/s. From the error rate bathtub curve off-track capability as the width for a given error can be determined. An example of such dependence (called ‘747’ curve) determined for 3 10–5 error rate is presented in figure 3.62(b). The offtrack tolerances attain maxima around 0.35 m at track pitches of 1.5 m (which corresponds with a track density of about 16.5 ktpi). The performance depends on the linear density and tape or disk speed. In compact cassette systems this speed is relatively small, only 4.76 cm/s. But in DCC audio systems the total bit rate is 768 kbit/s and the tape speed is 25 cm/s (Zieren et al 1993). In the first commercially available 0.5 inch digital tape drive with an MR head (IBM 3480 model) the tape speed was about 250 cm/s (Cannon et al 1986). The DigaMax high density tape recording system of Philips utilizing the multitrack eight-channel magnetoresistive head is designed for a tape speed of 100 cm/s and bit rate of 2 MB/s (Luitjens et al 1998). The rigid disk systems operate with disk speed of about 1000–2000 cm/s and bit rate of 5–10 MB/s. Taking into account the Wallace equations (3.18) and assuming that the sensor is linear the output voltage signal of the MR head can be roughly estimated from (Druyvesteyn 1981) M 1 ek 1 ekh Umr IR —– —–r k · ekd ———– ———– 2Hk k

kh

(3.23)

where I is the current of the sensor, R is the resistance of the sensor, Hk is the resultant anisotropy field (including shape anisotropy), h is the height of the sensor, d is the distance between the head and the tape. The output signal obtained from the inductive head of N turns can be determined as N(d /dt) NV(d /dx). While the flux from the tape is (Mallinson 1996) kg 2 sin — (1 ek )ekd 2

(x) oMrw —————— ———– sin kx k kg

(3.24)

the output voltage signal from the inductive head can be estimated from (Druyvesteyn 1981) kg 2 sin — 2 Uind oMrVNw(1 ek )ekd ———– kg

(3.25)

where g is the gap length and w is the track width. Thus the ratio of the output signals of the MR head and inductive head can be expressed as

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(3.26)

From (3.26) it is clear that the MR head is especially advantageous when the head-to-medium velocity V is small, when track width w is small and when the wavelength is large. Druyvesteyn (1981) assumed the following parameters: I 10 mA, R 100 , / 2%, V 5 cm/s, h 40 m, N 1000, w 0.6 mm and obtained the Umr /Uind ratio as about 130. The comparison of AMR and GMR heads was presented by Coehoorn and Folkerts et al (Coehoorn 1999, Folkerts et al 1994, 1997). Assuming a linear response the output voltage change can be expressed as: 1 R w w U ——— — —– — Rsq Io ——— S —Rsq Io or tw R H h or tw h

( )( )

( )

(3.27)

where t, w, h are thickness, width (length) and height of a sensor respectively, S is the sensitivity, Rsq is the resistance per area unit. The coefficient is a head efficiency factor and indicates which part of the total medium flux is entering the head. The head efficiency depends on the relative permeability of the flux-guide and the thickness t (this dependency calculated numerically using a finite element method is presented in figure 3.63(left)). The factor /(ortw) is the change of the average internal magnetic field in the magnetoresistive element per unit of incoming flux. The dependence of this factor on the film thickness was calculated numerically by Folkerts and Ruigrok (Coehoorn 1999) and is presented in figure 3.63(right). Table 3.6 Comparison of the GMR and AMR yoke-type head parameters (after Coehoorn 1999). Parameter

AMR

GMR

t [nm]

30

8

/ [%]

1.5

4.0

H [kA/m]

0.56

0.53

S [%/(kA/m)]

2.7

7.5

r

2000

3000

/(or tw)

1

1.75

R []

90

160

U

1

8.7

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Figure 3.63 The dependence of the head efficiency factor on the flux-guide parameters and on the sensor film thickness (calculated by Folkerts et al 1994).

Typical data for the AMR (30 nm Ni80Fe20) and spin-valve GMR (8 nm Ni80Fe20/2.5 nm Cu/6 nm Ni80Fe20/8 nm Fe50Mn50) yoke type heads are presented in table 3.6. The output signal obtained from the GMR head is almost 10 times greater than from similar AMR heads, which was confirmed experimentally (Coehoorn 1999). The greater output voltage of GMR heads results not only from the higher MR ratio, but also from higher permeability, higher stripe resistance and lower shape permeability (lower thickness of the sensitive layer). The magnetoresistive heads can be placed vertically or horizontally with respect to the medium (figure 3.64(a,b)). Practically almost exclusively vertical configuration is used because the horizontal configuration exhibits worse bit resolution and is more subjected to wear. Moreover (in horizontal configuration for wavelength equal to the width of the stripe interference occurs causing zero response for such a frequency and limiting bandwidth of the whole head. Because the horizontal heads can be simply manufactured and at lower cost several attempts at the preparation of such heads have been reported (Chapman 1989, Chapman et al 1989, Jones et al 1991).

Figure 3.64 Various configurations of magnetoresistive heads: (a) horizontal head; (b) vertical head; (c) orthogonal head; (c) gradiometer head.

The sensitivity of the MR sensor depends on the length of the stripe. In the vertical configuration this length is limited by the trackwidth and for high density recording the output signal from the sensor can be very small. Suyama et al (1988) proposed a reversed head configuration – an orthogonal laminated film sensor presented in figure 3.64(c). In such head design only one lead is

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exposed to the ABS and the sensor is immune to mechanical damage from the head-disk interface. Moreover the sensitivity is independent of the track width (Wang et al 1993). Unfortunately only a small portion of the sensor close to the ABS is active and the dynamic range of the sensor is reduced compared to a conventional head design (Wang et al 1993). Currently for high density AMR heads the dual-stripe is the most widely used configuration (figure 3.64(d)). The unshielded dual stripe head exhibits better performances than the shielded single layer head (figure 3.65). Figure 3.65 presents a comparison of roll-off curves (on-track voltage versus linear density) determined by Yuan and Bertram (1993) for three main AMR head designs: unshielded head, shielded head and dual-stripe head.

Figure 3.65 Comparison of the performances of various heads: unshielded head, shielded head and symmetrical dual-stripe head (Juan and Bertram 1993).

The unshielded head exhibits poor performances when the linear density is large (see also figures 1.93–1.95). Several groups have reported successful application of the unshielded heads for high density recorded data (Jeffers and Carsh 1984, Carr and Wachenschwanz 1988, Edelman et al 1990) (a linear density as high as 100 kbpi has been obtained). Recently for very high density disk applications the shielded heads are used practically exclusively (figure 3.66(b)). For tape applications the yoke head systems are preferred (Luithjens et al 1998, Ruigrok et al 1998, van de Zaag et al 1998) (figure 3.66(c)). Due to rubbing the MR element in the tape recorders is subjected to heat and wear which results in thermal spikes, noise, corrosion and a higher sensitivity to electrostatic damage. The ferromagnetic yoke acts as the flux-guide and the sensor can be positioned sufficiently far from the medium. Thin film magnetoresistive heads can also be used for new recording media. Iwasaki (1980, 1984, 1996) proposed to use new recording material in which

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Figure 3.66 Unshielded (a), shielded (b) and yoke (c) magnetoresistive heads.

the magnetic domains are oriented with magnetization normal to the plane of the medium. This ‘perpendicular recording’ medium offers potential for higher recording density than conventional ‘longitudinal’ media. To profit from performances of such media a special design of reading head is necessary. Several attempts to apply the magnetoresistive head to this recording technique have been reported (Sonobe et al 1995, Ikeda et al 1996). Another recording material ‘keepered layer’ consists of typical hard magnetic media coated with high permeability, low coercivity film (Gooch et al 1991, Coughlin 1996, Reed et al 1996). Such material exhibits improved high density performances and stabilize recorded data. The keepered media system requires a small bias field during read operation. Wang et al (1998) proved that the dual magnetoresistive head could be applied to read the keepered media in both, longitudinal and perpendicular recording systems. The keeper layer may be biased by the stray flux from the dual stripe head. Magnetoresistive heads in comparison with conventional inductive heads exhibit several significant advantages such as higher sensitivity especially for low speed applications, independence of the medium speed, which may be important in credit card readers and disk applications (each track is moving with various speeds depending on the diameter for fixed rotational speed). In disk applications the main important behaviour of the MR head is the possibility of miniaturization allowing the data to be read with very high density. In tape recorders applications the main advantage of MR sensors is the possibility of simple manufacturing of multitrack heads. The first commercial applications of MR heads were the Computer Coded Search (CCS) system introduced in 1979 by Philips in cassette deck model N 2554 and the Pulse Code Quick Refind PCQR system introduced in 1980 in compact cassette recorders (Druyvesteyn et al 1981). Both systems profit from the advantageous MR head performances for very small signal frequencies (long wavelength) beyond the normal operating range of inductive heads. The HiFi audio information on the tape was reproduced with a conventional inductive head. The long wavelength 5 Hz code signal insensitive to the

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reproducing head was used to automatically search preselected music passages. The multitrack heads were first introduced in 1985 by IBM with its commercial data recorder model IBM 3480 (Cannon et al 1986). This model utilized 18 track heads and was followed by IBM 3490 E tape drive with 36 track heads. In 1987 Philips introduced its CLS (Communication Logging System) applied multitrack 32 channel MR head and 12 inch tape (Dohmen et al 1990). Introduced in 1992 by Philips and Matsushita the Digital Compact Cassette (DCC) audio system applied the first multitrack MR head offered for a wide consumer market (Luitjens et al 1998, Zieren et al 1993, Lokhoff 1991). The DCC head contains 18 tracks – 16 for audio data and 2 auxiliary tracks for text and search information. Depending on the tape direction the upper or lower nine channels are connected to the channel electronics. The first hard disk system with an MR head was announced in 1991 by IBM (Shelledy and Nix 1992, Scaranton 1991). The head, called Corsair was designed for 2.2 ktpi and 60 kbpi with a density of 130 Mb/in2 (Hannon et al 1994). The read track was about 5.5 m wide and the SAL biasing system was used. A year later the next generation head, called Allicat was introduced (Hannon et al 1994). The Allicat heads have read trackwidth of about 3 m and areal density 355 Mb/in2.

3.3.4 Unshielded magnetoresistive reading heads Figure 3.67 presents the operating principle of the unshielded vertical-type head. The head in the form of a stripe detects the magnetic field above the moving media (disks or tapes). The transitions of the magnetizations in the media represent previously recorded information, for example ‘0’ or ‘1’ bits.

Figure 3.67 The principle of operation of the unshielded vertical magnetoresistive head (Ciureaniu 1992).

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The output signal from the vertical magnetoresistive head can be described by expression (3.23) resulting from the Wallace equations (3.18). Similarly the output signal from the horizontal heads can be expressed as (Hunt 1971) 1 sin —– M 2kh Umrh IR —– ——r ekd (1–2 ek ) ———– sin kVt. 2Hk kh An example of the frequency characteristic of the unshielded vertical head is presented in figure 3.58. Figure 3.68 presents a similar characteristic determined by Hunt (1971) for the horizontal head. The horizontal head exhibits an interference phenomenon depending on the stripe height h. In vertical heads this interference depends on the film thickness and because the film is very thin it is far from the operating bandwidth.

Figure 3.68 An example of the frequency characteristic determined for the horizontal unshielded head (Hunt 1970).

Jones et al (1991) proposed to improve the horizontal MR head by applying two elements separated by a gap (figure 3.69(a)). For a very small gap, of about 0.2 m, the response signal from the transition has a distinctly isolated maximum. But the undershoots beside each peak are large and wear of the head surface is enlarged in comparison with vertical design. This is why the horizontal design has been abandoned. Figure 3.70 presents the dependence of the head performances on the stripe height in the vertical head design. The sensitivity is a function of the stripe height h and to obtain a sufficiently large output signal this height should be of an appropriate size. The frequency response is determined by the stripe height. The PW50 parameter of the output signal was found to be about 70% of the head height (Jeffers and Karsh 1984). When the recorded bit length was less than h,

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Figure 3.69 Dual element unshielded horizontal head and response for the recorded magnetic transition (A: single element sensor, B: dual element sensor with gap g 0.2 m, C: dual element sensor with gap g 0.6 m). After (Jones et al 1991).

the alternating adjacent pulses superimposed and reduced the signal. Therefore for high resolution the height of the stripe should be as small as possible (stripe height as small as 3–4 m is reported by Jeffers and Carsh 1984). Table 3.7 Parameters of typical unshielded vertical type MR heads. Head references

[a]

[b]

[c]

[d]

Length (trackwidth) [m]

280

16

38

100

Height [m]

4.6

4

3

10

Thickness [nm]

58

35

45

35

80 kbpi

107 kbpi

80 kbpi

0.25 ktpi

PM

PM

PM

Barber-pole

Resolution Biasing technique

a – Jeffers and Carsh 1984, b – Carr and Wachenschwanz 1988, c – Edelman et al 1990, Collins and Jones 1979.

Figure 3.70 The dependence of the unshielded head performances on the stripe height: (a) dependence of the head sensitivity on the stripe height; (b) frequency characteristics for various stripe heights (determined by Collins and Jones 1979).

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In spite of the above limitations several successful realizations of unshielded one-track (Jeffers and Carsh 1984, Carr and Wachenschwanz 1988) or multitrack (Edelman et al 1990, Collins and Jones 1979) heads have been reported. Table 3.7 presents a comparison of the essential parameters of these heads. The multitrack head designed by Metzdorf et al (1982) consisted of 32 symmetrical Barber-pole sensors. It suited parallel reproduction of information, recorded with 250 tpi and 20 m guard band on a normal cassette tape. The whole chip had dimensions of 3.9 mm 8.8 mm. Edelman et al (1990) designed multitrack heads which consisted of two eightchannel inductive write heads and nine-channel unshielded MR read heads (figure 3.71(left)). It was possible to write and read 40 data tracks (five positions of the head) on the 6.27 mm wide tape and to save two Gbytes of user data on 220 metres of tape. The single path MR elements were biased by the L-shaped permanent magnet (PM) stripe located above the elements, away from the medium (figure 3.71(right)).

Figure 3.71 The eight-track combined inductive/magnetoresistive magnetic tape head designed by Edelman et al (1990) and the structure of the read head.

Carr and Wachenschwanz (1988) tested the practical upper limits of areal storage density in magnetic recording data channel using a 16 m trackwidth unshielded MR head and S-VHS tape. At a tape speed of 9.525 cm/s the data rate was 401 kbit/s. For a linear density of 107 kbpi, areal density of about 170 Mbits/in2 has been reported. Poor performances of the unshielded heads for high-density recordings could be improved by applying sophisticated electronic equalization techniques and appropriate data channel design. The requirements of higher resolution, areal density and data transfer speed mean that unshielded heads are currently only used for long-wavelength signals, for example in magnetic card readers. The unshielded dual-element horizontal MR heads (Guzman et al 1994, Smith et al 1992) may exhibit better performances than shielded magnetoresistive head (see figure 3.65). But usually these heads are integrated with inductive writing heads requiring a shield. Thus dual element heads used for very high density recording

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applications (Kelley et al 1981, Dee and Cates 1998) are usually prepared as shielded heads.

3.3.5 Shielded magnetoresistive heads The shields on each side of an MR element can significantly improve the spatial resolution of a magnetoresistive head (Brock et al 1975). The operation principle of the shielded magnetoresistive head is illustrated in figure 3.72. For the unshielded vertical head it is assumed that the ferromagnetic thin film of the sensor practically does not disturb the fringing magnetic field above the medium (figure 3.72(a)). The horizontal component of this field depends on the wavelength of the recorded signal. The shields change the distribution of the magnetic field above the medium. The flux is concentrated in the gap when this gap is over the magnetic transition (figure 3.72(b)). Practically all flux is then directed along the magnetoresistive stripe. The spatial resolution depends mainly on the gap length, sensor height and sensor permeability (Potter 1974, Shelledy and Brock 1975, Kelley and Ketchman 1978, Schwarz and Decker 1979).

Figure 3.72 A comparison of the flux distribution in the unshielded (a) and shielded (b) head (Mallinson 1996).

The performances of the shielded magnetoresistive head have been analysed by Potter (1974). For an isolated pulse the magnetization is expressed by equation (3.20). The flux entering the MR element is t t x– g — x– — 2 M

w d a 2 2 o r – ———––

(x) ——– f ————— f —–—— g da da

{( ) ( ) ( ) ( )} t x– g — 2 f ————— f da

where

t x– — 2 ——— da

(3.28)

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APPLICATIONS OF THE MAGNETORESISTIVE SENSORS 1 f(x) x tan1 x — ln(1 x2). 2

377 (3.29)

For the sinusoidal magnetized medium the magnetization is described by equation (3.17). The flux entering the MR element is then expressed as (g t) 2 / 1 en / sin g/ 2 x– – 2 M w sin ——–—

(x) e ————– ———–– sin ——. o r 2 / g/ (3.30) Knowing the flux entering the MR stripe it is possible to determine the output signal of the head from –

(x) – ≅ Jw√2 ——— e(x) IR(x) o Ms tw

(3.31)

where Ms is the saturation magnetization of the stripe. The flux in the stripe is non-uniform and decreases as the exponential function of the distance x from the medium. In the case of the unshielded head the flux entering the MR element is decreasing depending on the recorded wavelength

(x) (0)e2nx/

(3.32)

where (0) is the flux near the medium surface. In the case of the shielded head the decay of flux entering the MR element can be determined using the transmission line theory by the model proposed by Potter (1974). For an unlimited height of the MR element the flux entering the stripe is:

(x) (0)ex/

(3.33)

√

(3.34)

where

tgr ——. 2

When the MR element is of height h the flux within the stripe decreases in essentially linear fashion, and the average flux is 12 (x–). The output signal of the linear shielded MR head can be expressed as kg 2 sin — Mr k 1 ek

(g t) 2 U IR —– —— e ———– sin ———– ———–. Mst k

kg/2

(3.35)

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In comparison with a similar expression for the unshielded magnetoresistive head (3.23) two additional components depending on the gap length appear in expression (3.35). Thus the shielded MR head has two interference terms – one is due to the half-gap g and the other to the (gt) component. Figure 3.73 presents the roll-off characteristic of the shielded MR head calculated by Schwarz and Decker (1979).

Figure 3.73 The density response of the shielded magnetoresistive head calculated by Schwarz and Decker (1979).

Two interference zero outputs exist in calculated density response. If asymmetry is assumed (g1g2) the flux through the stripe is determined as follows: ————————————––

e

o Mr w · e2 d/ 1———— 2 / 2 /

√

f 2 (g1) f 2 (g2) 2f (g1) f (g2)

———————————————————————– sin ———–– sin ———–– – cos ———–– cos ———–– (g1 t) (g2 t) (g1 t) (g2 t)

(

(3.36) where: sin x/ f (x) ————. x/ Figure 3.73 shows the roll-off characteristics calculated and determined experimentally for small asymmetry (g1 0.4 m and g2 0.6 m). For two different gaps the nulls will be washed out. Thus small asymmetry can be advisable in some cases. Figure 3.74 presents the typical roll-off characteristic of the dual stripe shielded head.

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Figure 3.74 Experimentally determined roll-off characteristic of the dual stripe shielded head (Shi et al 1997).

When almost the whole flux enters the MR element the thickness of the thin film should be designed to avoid saturation. To obtain large linear and areal density the gap should be sufficiently small. Table 3.8 presents typical parameters of shielded heads. The expected parameters of future 40 Gb/in2 heads are extremely small (column 5 in table 3.8 (Fontana et al 1999)). These requirements can be realized only by GMR sensors (Tsang et al 1994, Tsang et al 1998). For example a sensor height less than one micrometre can be obtained in the spin-valve structure (figure 3.75) (Brug et al 1996). Also submicron wide GMR read heads are reported (Chen et al 1994, Pohm et al 1998). Table 3.8 Parameters of shielded read heads. Parameter Read trackwidth [m]

[a]

[b]

[c]

[d] 0.25

2

1.4

1.15

MR element height [m]

1.8

1.1

1

MR element thickness [nm]

25

17.5

12.5

2.5

Gap length 2g [m]

0.28

0.18

0.16

0.07

Density [kbpi]

150

200

320

530

1

2

5

40

Density [Gb/in2]

a – Hsu et al 1995, Shi et al 1997, Hu et al 199, Fontana et al 1999.

In the first shielded head constructions the yoke of the writing head served as the shields for the read head (single gap design). Those heads did not work properly and were therefore substituted by two separate structures – shields for

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Figure 3.75 A comparison of the output signal as a dependence on the stripe width: (a) AMR head; (b) spin-valve head (Brug et al 1996).

read head and yoke for writing head. Such design called a ‘piggy-back’ was used in the first Corsair heads of IBM (Hannon et al 1994). The distance between read gap and write gap was about 10 m. Recently the most widely used is the ‘merged’ design in which the top shield of the read head serves as the pole for the writing head. In merged heads the separation between read and writing head is reduced to 1–3 m. Figure 3.76 presents the operating principle of the merged MR head (Kelley et al 1981). This head consists of two heads – MR read and inductive writing. In application of the head in rigid disks (Bonyhard 1990) the whole head is distanced from the medium by an air bearing system (ABS – air bearing surface). In tape applications (O’Kane and Kroes 1994) the head profile should ensure good contact for variations in tape tension and speed. Figure 3.77 presents the typical design of the shielded head. The top write yoke pole is usually narrower than the bottom yoke/top shield layer and defines the write trackwidth. The read trackwidth is usually defined by the distance between leads.

Figure 3.76 An example of the merged MR head (Kelley et al 1981).

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Figure 3.77 The typical design of the shielded magnetoresistive head.

Between the shields can be placed various magnetoresistive structures, for example AMR-biased structures (Kelley et al 1981, Dee and Cates 1998, Shibata et al 1994), Barber-pole structures (van Lier et al 1976, Mowry et al 1986) or spin-valve structures (Tsang et al 1994, ten Berge et al 1995). Figure 3.78(a) presents the structure of a SAL-biased AMR, hard magnet stabilized configuration used for example in the ‘Allicat’ or ‘Starfire’ designs of IBM (Mallinson 1996). Figure 3.78(b) presents the structure of a spin-valve head designed, fabricated and tested by a group from Hitashi Ltd (Nakamoto et al 1996).

Figure 3.78 Air-bearing surface view of a SAL-biased AMR head (a) and spin-valve head (b) (Mallinson 1996 and Nakamoto et al 1996).

Figure 3.79 presents the extremely small head designed by a group from IBM (Fontana et al 1999). The magnetoresistive sensor is less than 1 m 1 m. Typical thickness ranges for the coils, shields and yokes are 2 m to 3 m. In shielded heads it is important to design the appropriate shape of the shields, especially the ABS part. This part may be trimmed by a focused ion beam (Partee and Lansky 1997, Guo et al 1997). Partee and Lansky (1997) determined that the minimum shield width at the ABS is six gap lengths greater than the width of the MR sensor. Shi and Ju (1997) tested the magnetostatic coupling between shield and MR elements. By appropriate design of the shield shape it is possible to reduce this coupling and improve the track profiles.

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Figure 3.79 An example of the thin film head structure3 (Fontana et al 1999).

3.3.6 Yoke-type magnetoresistive heads The typical yoke-type structure of the merged head is presented in figure 3.80. The main reason for using the yoke is the need to protect the sensor from direct contact with the moving medium. Especially dangerous to the conductive recording medium are fractional heating effects and electrical shorting. Therefore yoke-type MR heads are widely used in tape recording systems, as for example the digital compact cassette DCC system.

Figure 3.80 The structure of the merged yoke-type magnetoresistive head.

The yoke serves as the flux-guide transferring the flux from the medium to the sensor. In yoke-type heads protection of the sensor is obtained by the sacrifice of the head efficiency . The efficiency is defined as the ratio between the flux encompassed by the sensor and the flux entering the read head. In practice the typical value of the efficiency is only 5–15% (Ruigrok et al 1998, van der Zaag et al 1998). The efficiency of the yoke-type head depends on the geometry and material of the yoke. The analysis of the yoke-type head is rather complicated, because both yoke and sensor area are magnetized non-uniformly. Therefore only numerical methods can be used to design the head. Analytic description of the yoke head 3

Not all details of the head are shown and the proportions are not maintained.

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by means of the transmission model have been proposed by Ruigrok, Gillies and van der Zaag (Ruigrok 1981, 1982, 1998). The most critical points determining the efficiency of the head are the gap oxide g and the electrically insulating separation oxide layer gfm between the upper flux-guide and the sensor. To prevent any flux crossing in the gap region without passing through the sensor the gap g should be large. But a small gap, of about 0.25 m is required for high-density recording. Figure 3.81 presents the influence of the head efficiency on several geometrical and material parameters of the yoke calculated by van der Zaag et al (1998). The permeability of the yoke should be sufficiently large to ensure large efficiency. To obtain significant improvement of this efficiency the gap height hg and gap gfm should be as small as possible. Due to technological limitations hg cannot be smaller than a few micrometres and gfm is about 0.5 micrometres thick. Figure 3.82 presents the design of yoke-type magnetoresistive heads used in the DCC system developed by Philips (Zieren et al 1993, Ruigrok et al 1998). The read gap is 0.4 m and the Barber-pole magnetoresistive sensor is placed about 12 m from the tape-bearing surface (TBS). The sensor is about 10 m

Figure 3.81 The yoke-type design parameters and an example of a design plot calculated for hm 5 m, tMRE 50 nm, g 0,4 m (van der Zaag et al 1998).

Figure 3.82 The design of the yoke magnetoresistive head used in the DCC system (Ruigrok et al 1998).

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long and 35 nm thick. The efficiency of the head is 10.6%. Because the DCC system must be compatible with the old analog cassette system the whole 18track head is supported by two analog playback channels. In the new design the analog track on the tape can be read by two digital read channels. To ensure sufficient linearity of the analog playback in these heads a feedback system is used (de Niet and Vreeken 1979). Figure 3.83 presents the design of yoke-type magnetoresistive heads used in the professional DigaMax digital recording system developed by Philips (Ruigrok et al 1998). Because only pure digital signals are used the Barber-pole sensor could be substituted by less linear simple AMR sensors. These sensors are biased by special current conducting layers. The distance of the sensor from the TBS was reduced to about 7 m, the separation oxide to 0.3 m and the sensor thickness to 30 nm. As a consequence of these improvements the efficiency increased to 18.6%. Further improvement of these parameters is expected by introduction of GMR sensors instead of AMR sensors (Folkerts et al 1994, 1997).

Figure 3.83 The design of yoke-type magnetoresistive heads used in the DigaMax digital recording system developed by Philips (Ruigrok et al 1998).

Recently the yoke-type magnetoresistive heads have been used as heads for tape recorders. But the application of yoke-type heads for disk recorders has also been considered (Griffith 1986, Nagata et al 1987, Maruyama et al 1987). In these yoke-type heads the trackwidth was not limited by the dimensions of the sensor but only by the gap of the yoke. Yoke-type heads are also suitable for the perpendicular media (Sawada et al 1984).

3.4 TRANSDUCERS OF MECHANICAL VALUES

3.4.1 Transducers of linear displacement Magnetoresistive sensors are widely used to detect linear or angular displacements – as position, speed, acceleration, proximity or tactile

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transducers. As linear displacement transducers1 the magnetoresistive sensor can detect the position of a moving magnet or, the moving sensor can change position with respect to the fixed magnet. Figure 3.84 presents the typical concepts of linear displacement sensors. The sensor can be moved parallel to the magnet (figure 3.84(a)) or can be moved to one of the magnet poles (figure 3.84(b)). Instead of one magnet a two-magnet system can be used (figure 3.84(c)). The sensor can also detect the magnetic pattern recorded on the hard magnetic information layer (figure 3.84d). De facto in all HDD mechanisms the head positioning system detects the position of the track, even with resolution as small as nanometre range (Yoshikawa et al 1996).

Figure 3.84 The methods of linear displacement sensing by means of MR sensors.

In comparison with other competitive techniques of the measurement of displacement the use of MR sensors offers several important advantages. The methods using MR sensors are immune to dirt and lighting conditions, which is the main problem for optical methods. MR sensors can operate even when the movement is very slow, which is the limitation of inductive methods. The sensitivity of MR sensors is much larger than the sensitivity of Hall sensors and therefore the transducer can be located at a large distance from the moving body. The dimensions of the sensor can be extremely small, thus the spatial resolution even in nanometre range is possible (Loreit and Detttman 1993). The sensor can operate in a heavy industrial environment, for example at temperatures up to 190°C (Graeger and Petersen 1992). Also taking into account low manufacturing and implementation costs it is no wonder that MR sensors are used in many application areas, including the automobile industry for ABS/ASC systems (Petersen 1985, Graeger et al 1992). The Philips data handbook offers a wide range of position, angle or speed transducers utilizing MR sensors. When the sensor is moved parallel to the magnet then both components of magnetic field influence the output characteristic (figure 3.85(a)). To obtain the linear transfer characteristic of the transducer the component Hy of the magnetic field is most often measured. Figure 3.85(b) presents the typical transfer characteristics of the linear position transducer. 1 For example: Ali and Patel 1978, Groenland 1984, Baik et al 1985, Moygha et al 1985, Nakamura 1986, Nelson et al 1986, Miller et al 1987, Dettman and Loreit 1992, Rottman 1992, Graeger and Petersen 1993, Loreit and Dettman 1993, Gatzen 1996, Valenzuela et al 1996, Miller et al 1997.

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Figure 3.85 The change of magnetic field versus the magnet position and the typical transfer characteristics of the displacement transducer (Philips Technical Information).

Transducers with the magnet placed at the back of the sensor (or above it) (figure 3.84(b)) can be used for high-resolution measurements. An example of the transfer characteristics of such a sensor is presented in figure 3.86(left). For detection of rather larger distances a long magnetic rod is required. Instead of the long magnet a two-magnet system (figure 3.84(c)), with a very linear response characteristic (figure 3.86(right)), can be used.

Figure 3.86 The transfer characteristics of the linear displacement transducers presented in figure 3.84 (Philips Technical Information).

The magnet-sensor system as the position detector can be multiplied for large distance measurement with high resolution. Such a measuring system called POMUX (Positionsmultiplexer) was designed by Baik et al (1985) (figure 3.87). The magnet is moved above the line of the sensors. Each sensor is connected to the microprocessor chip by the multiplexer. This way it is possible to determine the absolute position of the magnet with resolution of 30 m and maximal range of 1.6 m.

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Figure 3.87 The linear displacement POMUX transducer with a line of multiplexed sensors (Baik et al 1985).

Practically unlimited range with very high resolution can be realized using one- or multi-sensor systems reading the position information recorded serially onto the track of a magnetic medium (figure 3.84(d)). Usually in such an encoding system digital detection of the position is based on an incremental principle. An example of an incremental method of length determination is presented in figure 3.88. The magnetization transitions on both tracks are shifted by half the pitch (figure 3.88(left)). Then in the output signal the recorded period is represented by four impulses (figure 3.88(right)).

Figure 3.88 The incremental system of displacement detecting.

In another system presented in figure 3.89 four MR elements (connected in a bridge circuit) are spaced by a (3/2) distance (Moyhga et al 1985). As a whole, a bridge sensor senses the length by a period of /2. The resolution can be improved by using several bridge circuits. For example using a four-bridge MR sensor it is possible to detect /8 length. Figure 3.90 presents an eight-element system proposed by Nakamura (1986). Each element is spaced by a distance of /4 (figure 3.90(left)). By appropriately connecting such elements into the bridge circuits (figure 3.90(right)) it is possible

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Figure 3.89 Four-element displacement measuring system proposed by Myohga et al (1985).

Figure 3.90 Eight-element displacement sensing transducer (Nakamura 1986).

to determine not only the length but also the direction of movement in a one-track system. Loreit and Dettman (1993) designed a sensor chip of area 1.8 2.2 mm consisting of 128 Barber-pole stripes of width 5 m. The sensor supplied by a 5 V voltage exhibited a sensitivity of 0.7 mV/m and resolution as small as 10 nm. Using the length transducer it is possible to design a scale device where the slider with MR sensors can substitute commonly used rack systems. Two examples of such scale devices are presented in figure 3.91. In the scale device designed by Dettmar et al (Gatzen 1996) the slider is riding above the recorded magnetic pattern (figure 3.91(a)). Myohga et al (1985) tested various hard magnetic materials for the scale device. They proposed the (Fe40Co40Mn20)98.2C0.4Si1.4 alloy as an excellent material for preparing the wire on which the slider with MR sensors can be moved. The 22 cm long magnetic scale with a 10 m resolution has been designed and tested. The resolution of the length measurement systems using recorded patterns depends on the dimensions of the reading sensor and the gap between the sensor

Figure 3.91 Two examples of the scale device (Moyhga et al 1985 and Gatzen 1996).

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and recorded medium. Figure 3.92 presents the dependence of the output signal on the gap spacing determined by Myohga et al (1985). The sensitivity significantly decreases when the gap spacing increases. On the other hand a too small gap causes a deterioration of the sensor output, because the magnetic field from the adjacent transition disturbs the resolution. Sei et al (1987) determined experimentally the optimal gap value as 0.7 of the pitch length.

Figure 3.92 The influence of the gap spacing between recorded pattern and the head on the sensitivity of the sensor (Myohga et al 1985).

The information recorded on the hard magnetic medium enables not only the length but also the absolute position to be detected. Figure 3.93(a) presents an encoding system with 20 tracks representing 12 bit information about the position. To read this information a 52-element sensor is necessary. Figure 3.93(b) presents another system designed as a zero reference detector. The magnetoresistive elements R1–R8 can be used as an incremental detector, while elements Rz1–Rz4 can be used to obtain a zero reference signal.

Figure 3.93 The absolute position decoding system (a) and zero reference detector (b) (Miyashita et al 1987).

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The magnetoresistive sensor used as the null detector for control equipment may use the one-point position transducers presented in figure 3.94. At a defined position the output signal of the sensor is zero. Any movement of the sensor or the object causes an imbalance of the field component and results in an output signal from the sensor. The zero crossing point (figure 3.94(right)) is independent of the temperature and the distance between sensor and object.

Figure 3.94 One-point position detectors using MR sensors (Philips Technical Information).

For robotic applications position sensors can be used as very sensitive manipulators (joysticks) (Nelson et al 1986, Rottman 1992). An example of a robotic tactile sensor designed by Nelson et al (1986) is presented in figure 3.95. A magnetic rod is fastened into a hole in a sheet of stainless steel (figure 3.95(a)). The rod can pivot about its axis in response to shear forces. Also the pressure can be detected. The movement of the magnetized rod is sensed by a multi-element sensor presented in figure 3.95(b).

Figure 3.95 The position sensor used as manipulator (joystick): (a) principle of operation; (b) arrangement of the sensing elements (Nelson et al 1986).

Figure 3.96(a) presents the cross-section of a MR tactile sensor detecting local pressure. The areal network of rubber sensing elements transfers the pressure by movement of the current conducting layers with respect to the sensor network. A pressure as small as 40 Nm–2 was detected using 0.2 mm thick

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Figure 3.96 The MR displacement sensors used for local pressure detecting (a) (Vranish 1986) or for gas pressure measurements (b).

sponge-rubber between the flat conductors and the MR elements. By multiplexing the MR elements and copper conductors it is possible to scan the pressure in each element. Another pressure sensor is presented in figure 3.96(b). The movement of the magnet joined with a pressure-sensing membrane can be detected by the magnetoresistive sensor.

3.4.2 Transducers of angular position Radial displacement detection can be used as a method to determine the angle (Eijkel and Fluitman 1986, Reiniger 1986, Eijkel 1988, Eijkel et al 1990, Petersen 1991, Hager 1993, Petersen and Rinschede 1994). To measure the angle two main operating principles may be applied. The first one is a simple measurement of the field component of the external magnetic field Ho: Rx ≅ SHo sin x.

(3.37)

The main drawback of this method is the dependence of the output signal on the magnetic field strength Ho. Thus the temperature influencing the field of the magnet can decrease the accuracy of the method. Moreover when the magnetic field is too strong the switching effects can deteriorate the operation of the sensor. Too weak a magnetic field of the magnet results that the transducer is sensitive to the external magnetic field (for example the Earth’s magnetic field). The measured angle is limited to 90°, but due to nonlinearity and imperfect operation of the sensor with the magnetic field along the anisotropy axis (danger of flipping) the measured angle should be smaller than 90°. The second method utilizes the anisotropic magnetoresistive effect. The change of resistance depends on the angle x between current direction and the direction of magnetization. When the magnetic field is sufficiently large then the

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direction of magnetization is the same as direction of the external field and the change of resistance can be expressed as Rx ≅ So sin 2x.

(3.38)

The output signal of the transducer does not depend on the magnetic field strength and the measured angle range is unlimited. Figure 3.97 presents the sensor response determined for both the above described cases.

Figure 3.97 The output signal of the magnetoresistive sensor as a dependence on the direction of magnetic field determined for small magnetic field (HxHk).

Figure 3.98 presents an example of the angle transducers operating at a relatively weak magnetic field. Two magnets placed on a rotatable frame are moved around the sensor. The shield reduces the influence of external field. By using the output electronic circuit with a temperature compensation feedback loop it is possible to obtain a simple contactless potentiometer.

Figure 3.98 The angle transducer (contactless potentiometer) (Petersen 1986).

Figure 3.99 presents an example of the angle transducer operating at a strong magnetic field. The output characteristic is non-linear because the change of resistance depends on sin 2x value. Depending on the amplification of the electronic circuit (and the range of the detected field) the transducer can measure

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an angle range of 15° with good linearity or the larger angle range up to 45° when the output signal is proportional to sin instead of the angle (figure 3.99(b)).

Figure 3.99 The angle transducer operating at strong magnetic field: (a) principle of operation; (b) transfer characteristics (Philips Technical Information).

Figure 3.100 presents the hybrid angle transducer KM110BH type designed by Philips. The hybrid transducer presented in figure 3.100 consists of the sensor and conditioning electronics. The electronics ensure stabilization of the supplied voltage, temperature compensation and conversion of the sensor output signal into the DC current. The transfer characteristic of the transducer is shown in figure 3.100. The main specifications of the transducer are as follows: angle range 35°, output current 4 to 20 mA, sensitivity 0.3 mA/°, resolution better than 0.001°, DC supply voltage 8–11 V, operating temperature range 40–100°C, maximum angular speed 20°/sec.

Figure 3.100 The hybrid angle transducer KM110BH type of Philips and its transfer characteristic (Philips Technical Information).

The operating angle range can be extended by applying two magnetic field sensors positioned at 45° to one another mechanically, as shown in figure 3.101. The output signals from the two sensors represent sin 2 and cos 2 respectively, and the more linear dependence on the angle can be easily calculated.

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Figure 3.101 The two-sensor angle detection principle (Philips Technical Information).

Figure 3.102 presents the layout of the KMZ41 type sensor designed by Philips for angle measurements. This sensor consists of two independent sensors shifted by 45°. The special integrated circuit UZZ9000 has been designed to convert the two output signals of the KMZ41 sensor into the linear dependence Uout f() with accuracy better than 1° for 100° angle range.

Figure 3.102 The layout of the KMZ41 angle sensor designed for precise angle measurements (Philips Technical Information).

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For precise determination of the angle magnetic rotary encoders can also be used (Miyashita et al 1987, Sei et al 1987, Kikuchi et al 1997, Campbell et al 1990). An example of a rotary encoder is shown in figure 3.103(a). It consists of two components – a magnetic drum with recorded pattern and a magnetic sensor composed of several MR elements. Typically the drum with diameter of 30–40 mm is covered by plastic magnetic material on which are recorded magnetic poles with pitch 0.07–0.25 mm. The resolution of such encoders is 500–2500 ppr (pulses per revolution).

Figure 3.103 The rotary encoder as angle transducer (a) and two rotary encoders as torque transducer (b).

Two magnetic encoders separated by the distance L (figure 3.103(b)) may be used to measure the torque (Miyashita et al 1990). A difference angle between the drive shaft and load shaft depends on the torque T applied in the load shaft 32L ——– T GD4

(3.39)

where: G is the modulus of transverse elasticity, D is the diameter of the torsion bar, L is the length of the torsion bar. The torque can be expressed by the phase shift between two sinusoidal signals from magnetic encoders. Miyashita et al (1990) designed a torque transducer with maximum torque 200 kg cm and resolution 0.7%. Maximum torsion at the torsion bar with dimensions 7 75 mm corresponded with the 4.5° torsion angle. Knowing the torque T and rotational speed it is possible to calculate the shaft power P from the expression P 1.065Tn 104

(3.40)

where n is the rotational speed [rpm], T is the torque [Nm] and P is the shaft power [kW].

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3.4.3 Measurements of rotational speed The rotary encoders can also be used to detect rotational speed. Figure 3.104 presents other typical methods of measurements of rotational speed. Similar to magnetic rotary encoders the magnetic poles in form of magnets may be used to detect the wheel movement (figure 3.104(b)). The MR sensor in such systems counts the magnetic transitions caused by the rotating magnets.

Figure 3.104 The main methods of rotational speed measurements.

Systems with the sensor counting the magnetic field disturbances caused by rotating teeth of ferrous gear are used more often (figure 3.104(a)). Instead of toothed wheel the magnetic field may be periodically disturbed by a rotating slotted wheel. When the non-ferrous wheel is rotating the sensor can measure the magnetic field produced by eddy currents, induced in the wheel by the auxiliary magnet (figure 3.104(c)). The magnetic field is generated by the magnet positioned behind the sensor. This magnet can bias the sensor at zero point and as the wheel rotates, the teeth or slots periodically perturb the magnetic field. Manufacturers of magnetoresistive sensors offer sensors adapted to rotation sensing by mounting the magnet to the sensor encapsulation. The operating principle of such sensors is illustrated in figure 3.105.

Figure 3.105 The principle of operation of the rotational speed sensor counting the magnetic field disturbances caused by rotating ferrous gear teeth (Philips Technical Information).

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Philips designed the integrated sensor type KMI 15 especially for rotational speed measurements (figure 3.106(a)). This sensor consists of a magnetoresistive sensor, a signal conditioning circuit in bipolar technology and a ferrite magnet. The output signal from the sensor is amplified, temperature compensated and passed to the Schmitt trigger. The sensing distance from the wheel d can be changed over a large range without changing the output signal from the conditioning circuit. As an output signal a pulse current of 7/14 mA is used. The integrated circuit housing is separated from the sensor element housing to optimize sensor behaviour at high temperature.

Figure 3.106 The integrated KMI 15 sensor for rotational speed measurements: (a) design of the sensor; (b) electronics connected to the sensor (Philips Technical Information).

The output signal from the sensor (with no signal conditioning electronics) depends on the distance d between the sensor and gear wheel and on the wheel module m D/z (D – wheel diameter, z – number of teeth). This dependence determined for the KMZ10B sensor is presented in figure 3.107(b). Because a sensor signal of about 5 mV is recommended for the conditioning circuit when module m 2 the optimal value of distance d is 3 mm.

Figure 3.107 The dependence of the output signal of the KMZ10B sensor on the distance between sensor and the gear wheel (Philips Technical Information).

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GMR sensors can operate without additional electronics due to the large output signal. Freitas et al (1999) designed-spin-valve sensor for rotational speed control. The layout of the sensor is presented in figure 3.108(a). The sensor consists of four SV elements connected into a bridge circuit. Two elements R1 and R3 are active and are placed between amorphous CoZrNb flux-guide poles. The elements R2 and R4 are inactive. The inactivation of these elements was obtained by roughening the surface of the underlying oxide layer. Both characteristics, of active and ‘inactive’ spin-valve elements are presented in figure 3.108(b).

Figure 3.108 GMR sensor for rotational speed control designed by Freitas et al (1999): (a) the sensor layout; (b) the transfer characteristics of active and inactive sensor elements (I 7 mA).

The resultant transfer characteristic of the whole bridge sensor is presented in figure 3.109(a). The sensor operates as a digital one with the output signal independent of the magnetic field for a large range of H. The sensor was tested for a magnetized wheel with 60 pairs of N-S poles. The obtained square wave 400 mV pp output signal is presented in figure 3.109(b,c). The amplitude of the sensor output was independent of rotating speed (0–3000 rpm) and wheel to sensor separation (0.5–2 mm) without the need of further electronics.

Figure 3.109 The performances of the GMR rotational speed sensor: (a) transfer characteristic of the sensor; (b) the output signal for n 360 rpm, d 1 mm; (c) the output signal for n 2400 rpm, d 0.5 mm (Freitas et al 1999).

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A simple and reliable method of rotational speed measurement is required in the automobile industry for the ABS (Anti-lock Braking System) or the ASC (Anti-Slip Control). Inductive tachometers are disappointing at low speeds. An example of an ABS system utilizing magnetoresistive sensors to control the speed of each individual wheel is presented in figure 3.110. The output signal from the wheels is analysed by the electronic control unit. When it detects one or more wheels tending to lock, control signals switch the relevant magnetic valves in the hydraulic system. The information from the sensors may also be used for tachometers, odometers or in navigation systems.

Figure 3.110 The ABS system utilizing MR sensors for rotational speed control (Graeger et al 1992).

Figure 3.111 presents an example of the use of thin film MR sensors to sense the acceleration a. The MR sensors detect the movement of the magnet used as seismic mass m – thus the force of inertia F ma is measured.

Figure 3.111 Thin film acceleration transducer.

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3.5 MATERIAL TESTING AND MAGNETIC FIELD IMAGING

3.5.1 Material testing by means of thin film magnetoresistors The magnetoresistive head in HDD applications measures the magnetic field existing directly above the disk plate. Instead of reading the digital information from the disk a similar system can be used to measure a magnetic field. This field may be the source of information about tested material and the whole device may be used as a diagnostic tool. Therefore magnetoresistive heads with appropriate positioning systems have been adapted as Magneto-Resistance Microscopy (MRM) (O’Barr et al 1996, Yamamoto et al 1996). First of all these devices have been used to test recording media (Indeck and Judy 1984, Lin et al 1985). Figure 3.112(top left) presents the image of the magnetization patterns prerecorded on the commercial hard disk platter. This image was determined using magnetic force microscopy (MFM). The same disk was then tested using

Figure 3.112 The image of bits recorded on the hard disk platter: image obtained by magnetic force microscopy MFM, image obtained by magnetoresistance microscopy MRM and the cross-track section of the bit determined by a magnetoresistive sensor (O’Barr et al 1996).

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magneto-resistance microscopy with a 5 m wide sensor and with a 250 nm distance between disk and slider. The signal obtained from the sensor was too small with respect to noise. Therefore a piezoelectric bimorph oscillator was glued to the MR head with an oscillating frequency of about 1.85 kHz. Although the output signal from the sensor was still very small (about 4 V for vibrating amplitude of 50 nm) after applying the lock-in detection technique a quite clear image of the scanned area was obtained (figure 3.112(top right)). Figure 3.112(bottom) presents the cross-track section taken through one of the bits. Thus the track profile for various materials can be investigated. The magnetoresistance microscope system was further improved by Yamamoto et al (1996). To obtain a larger output signal from the sensor the slider was placed in physical contact with the investigated media. The magnetoresistive head (0.25 m read gap and 2 m track width) was positioned with a resolution of about 1 nm. Figure 3.113(left) presents the 4 m 10 m image of an isolated transition. This image consist of 50 200 points, with scan steps of 200 20 nm in the horizontal and vertical direction, respectively.

Figure 3.113 The image of one bit obtained using the magnetoresistive sensor (Yamamoto et al 1996).

Figure 3.113(right) presents a track cut through the same transition. The obtained signal of about 200 V is sufficient to obtain a precise image of the recorded bit. Figure 3.114 presents the example of the 7 80 m image of recorded transitions.

Figure 3.114 The image of recorded transitions and down track cut of the transitions (Yamamoto et al 1996).

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The stray magnetic field measured above the electrical steel sheet may be used to test the properties of this material. It can be assumed that the tangential field component directly above the steel sheet is the same as in the sheet. Above the sheet surface the normal field component also exists. There are three main sources of this normal component of the magnetic field (Pfützner et al 1983). A stray field Hs is generated by the 180° Bloch domain walls (figure 3.115(a)). The grain boundaries can be a source of the stray magnetic field Hb (figure 3.115(b)). The magnetic field generated by the grain boundaries is significant when grains exhibit different angles of misorientation. The last source of the stray field is the domain surface of misoriented grain (figure 3.115(b)). This field H may be larger than the others, especially when the sensor is positioned close to the steel surface.

Figure 3.115 The stray fields generated by a domain Bloch walls and grain boundaries: (a) demagnetized sheet; (b) magnetized sheet (Pfützner et al 1983).

Figure 3.116(left) presents the colloid pattern of domains in a demagnetized sheet and figure 3.116(right) presents the change of magnetic field strength determined using small (245 m 245 m) Hall sensors (results reported by Pfützner et al 1983, 1985). The magnetic picture obtained using the Hall sensor is not exactly the same as the colloidal picture (mainly due to the relatively large dimensions of the sensor). Nevertheless applications of magnetic field sensors may be an attractive technique due to the possibility of computer-controlled automatic detection of the domain picture (which is rather complicated in Bitter, Kerr-effect or scanning electron microscope methods).

Figure 3.116 The colloid pattern of domain structure and corresponding change of stray magnetic field detected using a miniature magnetic field sensor by Pfützner et al (1983, 1985).

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An improved method of domain imaging by means of magnetoresistive sensors was proposed by a group from Cardiff (Nicholson et al 1996, So et al 1995, Nicholson 2000). The magnetoresistive sensor (with dimensions 1 mm 40 m) was scanned about 35 m above a steel sheet magnetized by a coil placed underneath the sample. The signal profile for a single scan consisted of a series of varying peaks and troughs. These maxima and minima points indicated the centre of domains. Figure 3.117 presents a comparison of the image obtained using the MR sensor with the domain image obtained using the Bitter technique.

Figure 3.117 The image of the domain structure obtained using Bitter technique (a) and using thin film magnetoresistive sensor scanning apparatus (b) (Nicholson et al 1996, 2000).

The stray magnetic field above the steel sheet can be used to investigate the grain structure. The magnetic field should be uniformly distributed within an area of the grain and should exhibit a jump of magnitude above the grain boundary. First experiments with a magnetic pickup coil or Hall sensors confirmed that magnetic sensors might be used as a grain detector (Mohri and Fujimoto 1977, Normann and Mende 1980). Pfützner using small tangential Hall sensors found that the direction of the stray magnetic field might also provide valuable information about the grain structure. Figure 3.118 presents the magnetic field measured by Pfützner above the grain-oriented steel sheet (Pfützner 1980).

Figure 3.118 The magnetic field above the grain-oriented steel sheet determined using small tangential Hall sensors and corresponding picture of grain structure (Pfützner 1980).

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Similar results obtained using thin film magnetoresistive sensor have been reported by Mohd Ali and Moses (1985, 1988, 1988a, 1989). The chevron shaped magnetoresistive head was moved over the surface of an AC magnetized sample. An example of the map of the localized field vector distribution on the surface of the sample (dimensioned 25 mm 25 mm) is presented in figure 3.119. By observing sharp changes in the magnitude or direction of the vectors more than 90% of the grains were identified. Grains as small as 2 mm in length could be discerned.

Figure 3.119 The magnetic field detected above the grain oriented steel sheet using thin film magnetoresistive sensors and corresponding picture of grain structure (Mohd Ali 1985).

By measuring the tangential component of magnetic field above the sheet it is possible to determine the local value of magnetic field strength and the local value of one of the most important electrical steel parameter – the power losses P because fT dB P — ∫ H —– dt 0 dt

(3.41)

where is the density of material Moghaddam and Moses (1992, 1993) investigated the localized power loss using a remote search coil (for detection of dB/dt) and a magnetoresistive sensor (for detection of H). Because the sensing area was very small (1.5 mm 10 m) calculation of the localized power loss even over an individual grain was possible. Figure 3.120 presents an example of loss variation along the grain. In the area with spike domains significant lowering of local losses was detected. Thin film magnetoresistive sensors can be used to analyse the properties of electrical steel (Tumanski 1988,1989). Tumanski and Winek (1997) investigated local values of losses and other steel parameters such as permeability or coercivity. Almost all the important characteristics of electrical steel, such as magnetizing curve, hysteresis loop, losses, permeability determined for a small 1 mm2 area could be tested. Figure 3.121 presents the magnetizing curves determined at 16 points of investigated toroidal steel sample.

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Figure 3.120 The domain structure detected in an individual grain of steel and corresponding local values of power loss determined using a magnetoresistive sensor (Moghaddam and Moses 1992, 1993).

Figure 3.121 The magnetizing curves determined using a magnetoresistive sensor at 16 randomly selected points of electrical steel (thick line represents similar averaged curve determined using conventional method for the whole sample) (Tumanski and Winek 1997).

Knowing the magnetic field strength above the steel sheet it is possible to determine two-dimensional steel parameters, for example anisotropy (Tumanski and Fryskowski 1998, 1998a, Tumanski and Stabrowski 1998). Figure 3.122(a) presents the measuring device designed for anisotropy and texture analysis. In the measuring system presented in figure 3.122 the yoke-sensor set is rotated by means of the stepper motor. For a fixed value of the flux density it is possible to measure the magnetic field strength versus the angle with respect to the rolling direction. An example of the dependence H f() determined for grain-oriented electrical steel is presented in figure 3.122(right). It is possible to analyse other steel parameters which are dependent on the magnetizing direction, for example permeability or losses versus the angle .

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Figure 3.122 The method of investigation of two-dimensional properties of electrical steel by means of a MR sensor and dependence of magnetic field strength on the magnetizing direction (Tumanski and Fryskowski 1998,1998a).

3.5.2 Magnetic imaging systems Tumanski and Stabrowski (Tumanski and Stabrowski 1996, 1998, Tumanski 1999) developed an automatic measuring system for mapping of the magnetic field measured by means of the magnetoresistive sensor. Although this system was primarily designed for electrical steel testing it proved to be a versatile device for magnetic field imaging, for example for non-destructive testing of various materials or for analysing magnetic field distribution. Because of some similarities with the thermovision method the whole system was called the ‘magnetovision’ system. An example of the magnetovision system is presented in figure 3.123. Two computer-controlled stepper motors move the sensor along a meandering path over the sheet. A third stepper motor (not shown in the figure) can be used to move the sensor in the vertical direction. The primary signal from the sensor is converted into a digital voltage signal. The table of the voltage data corresponding with every test point is saved as a numerical data file. It allows further mathematical manipulations with the data, for example computations of root-mean-square value (rms value), maximal value or Fast-Fourier-Transform (FFT) analysis. As a final result the file is converted into a colour map presented on the screen or saved as a graphic file. The investigated steel sheet can be magnetized using the double C-yoke system (not shown in the figure). Figure 3.124 presents the typical magnetovision map of the steel sheet placed over the yoke. In the obtained map the magnetized part of the sheet is clearly visible, in the form of a lane between the poles. The imaged area is magnetized non-uniformly. The main reason for such heterogeneity is the crystalline structure of the sheet, but also defects may result in local enlargement of magnetic field strength. The large non-uniformity of magnetization is especially large in the case of grain-oriented steel (Tumanski 1998).

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Figure 3.123 An example of the magnetovision system (B coil: coil for measurements of the magnetic flux density, M coil: coil used for magnetizing the sheet). The yoke system closing the magnetic circuit is not shown in the figure.

Figure 3.124 The yoke used to magnetize the investigated steel stripe and an example of the magnetic field map determined for grain-oriented steel stripe.

The commercially available KMZ10B sensor with sensitivity of 20 V/(A/m) was typically used in the magnetovision system. This sensor with a field range of 2 kA/m is very convenient for electrical steel testing. It is possible to apply the smaller sensors, with dimensions of several m, but better resolution of such transducers is obtained for smaller sensitivity. Therefore for most applications sensors with active area of 1 mm2 are chosen as a reasonable compromise between resolution and sensitivity. The software system constructs the field map using 20 colours. The user may

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freely select the values of the scale start Hxo and the scale increment Hx.2 The mean value of field strength is shown in the upper right-hand corner of each map. Figure 3.125 presents a comparison of the magnetovision maps obtained for the same area (dimensions 1 cm 1 cm) but with various measurement point densities. It seems that for the considered sensor the lower limits of measurement node distance is about 0.5 mm. Further reduction of the node distance (e.g. to 0.125 mm) only increases the measurement time and blurs the information about the field distribution.

Figure 3.125 The maps of field distribution for various measurement points densities: (a) 1 mm; (b) 0.5 mm; (c) 0.25 mm; (d) 0.125 mm.

It is recommended that the sensor is placed as close to the investigated sheet surface as possible. The only limitation is the sensor case construction. A distance of 0.3 mm is practically attainable. The influence of the distance between the sheet and the sensor on the output signal value and the field map coarseness is presented in figure 3.126. The sensor output signal decreases by approximately 5% if the sheet-sensor separation increases by 1 mm. For distance greater than 1 mm the resolution of the map is distinctly impaired. Figure 3.127 presents the results of the test of repeatability of the system. The same sheet area (dimensions 3 cm 3 cm) was tested in two different measurement runs. Both maps are almost identical. This means that the measuring system is reliable, as disassembly and assembly of the yokesheet-sensor set-up does not impair the results. 2 All maps presented in this chapter use the scale shown in figure 3.125, i.e. H 0 and xo Hx 2 A/m.

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Figure 3.126 The maps of magnetic field for various distances between the sensor and the sheet surface: (a) 0.3 mm; (b) 0.5 mm; (c) 1 mm; (d) 2 mm.

Figure 3.127 The maps of the same sheet area determined in two different measurement runs.

Figure 3.128 presents the results of another test. The investigated area is limited by the construction of the magnetizing circuit. The enlargement of the magnetizing yoke may expand this area, but there is a limit to such expansion. The representative assessment of steel sheet quality needs really large measurement areas, beyond the reach of the largest yokes. The solution might be to test several sub-regions and merge them numerically as a whole. Figure 3.128 presents four maps of neighbouring sheet areas. The coincidence of the separate map patterns along the boundaries is excellent. By merging several tested sub-regions the map of an area as large as 1 m 1 m was possible.

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Figure 3.128 The maps of the field distribution determined for neighbouring sheet areas.

The main disadvantage of the scanning system discussed above is the relatively long time required for the analysis of the magnetic field distribution. For example testing an area of 5 cm2 with a 0.5 mm step takes about 30 minutes. Therefore only a static (not varying in time) magnetic field can be analysed. In order to reduce the measurement time the sensor positioning system can be replaced with a static array of sensors. Progress in the design of magnetoresistive heads allows the manufacture of multisensors composed of several hundreds of elementary magnetoresistive elements on an area not larger than several square millimetres. But there are some difficulties with the assembly of densely packed sensors. The sensitivity of a magnetoresistive sensor depends directly on the sensor area and problems can arise in multiplexing the low-level signals obtained from microscopic sensors. The solution to this problem is to combine scanning and multiplexing methods. Instead of one sensor a line of sensors may be moved. The magnetic field necessary to obtain an assumed value of the flux density depends on the steel quality – the poorer quality of steel the larger magnetic field strength is in the steel. Therefore the magnetic field detected above the sheet for a fixed flux density can be used to assess the steel quality. Figure 3.129 present four maps determined for sheets of various losses. In a colour picture the areas of low magnetic field strength (below 20 A/m) are represented by cool colours – various shades of blue and green. The areas of higher field strength (above 20 A/m) are indicated by the warmer colours of yellow and red. This colour scale quite closely resembles that used in geographical maps. The ‘colour temperature’ of the maps presented in figure 3.129 is closely correlated with the

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Figure 3.129 The maps of four materials with different power loss: (a) P1 0.231 W/kg; (b) P1 0.37 W/kg; (c) P1 0.45 W/kg; (d) P1 0.51 W/kg.

sheet quality (determined by specific power loss). Thus a map of magnetic field strength determined for the steel sample enables a quick visual assessment of steel quality – too many warm colours means that the steel is of poor quality. The maps presented in figure 3.129 have been determined for the rather small area of 3 cm 3 cm. Figure 3.130 presents two examples of maps determined for the stripe conventionally used in the Epstein apparatus. The analysis of the map of the stripes with dimensions 18 cm 3 cm confirms that the sheets with

Figure 3.130 Two maps of the stripes (dimensions 18 cm 3 cm) with different specific loss measured by the Epstein method: (a) P1 0.35 W/kg; (b) P1 0.45 W/kg.

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higher power losses exhibit a higher mean value of field strength and a wider spread of these values (at the same peak induction values). Map preparation can be substituted by numerical statistical processing. Figure 3.131 presents two histograms of magnetic field strength obtained after numerical processing over 25 000 test points from the map shown in figure 3.130. The average value of magnetic field strength and the standard deviation may be used as the quality criteria for electrical steels (Tumanski 1998).

Figure 3.131 The histograms of the magnetic field strength distribution above the stripes presented in figure 3.130.

Quite spectacular results have been obtained in tests of material heterogeneity performed for large steel sheet areas (Tumanski and Lampa 1999). The various steel sheets were tested with conventional methods – the losses were determined using the Epstein method and single stripe testers. The grain structures were determined by means of chemical etching techniques. After these tests several interesting samples were selected. Figure 3.132 presents the grain structures of selected samples. Sample (a) had the grain structure tolerably uniform – typical for most grain oriented steel. Sample (b) was composed of very large grains with inclusions of very small grains (defects). In sample (c) the grains were gradually diminished.

Figure 3.132 Three stripes of various grain structures tested by the magnetovision method.

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Figure 3.133 presents the magnetovision maps of these samples (each picture represents 9 stripes with dimensions 9 cm 3 cm). The results of investigations presented in figure 3.133 show that with some experience in the interpretation of magnetovision maps it is possible to say almost everything about tested steel – size of grains, losses, heterogeneity, localization of defects etc.

Figure 3.133 The magnetovision maps of the samples presented in figure 3.132.

The existence of defects is especially visible in the map presented in figure 3.133(b). Indeed the magnetovision method may be used as a powerful technique of non-destructive testing. Figure 3.134 presents two examples of maps determined for defected samples of electrical steel. The field map of a sheet with diversified grain structure is presented in figure 3.134(a). An inclusion consisting of small grains with dimensions less than 1 mm has been detected. This small-grain area was characterized by distinctly higher values of the mean field strength. Figure 3.134(b) presents a map with a high spread of field strength values. A spread between 4 A/m and 60 A/m for a flux density of 1 T was observed in an area of 2 cm2. The grain responsible for such deterioration of steel heterogeneity could be easily detected.

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Figure 3.134 The magnetovision maps of defected steel samples.

Electrical steel is very sensitive to surface stresses which is often underestimated by many users of SiFe electrical steel. Figure 1.135(a) presents the effect caused by writing on the steel surface the letter A with a ball-point pen. The pressure of the pen was typical – as writing on paper. Figure 3.135(b) presents the effect caused by artificial micro-cracks scribed on grain-oriented steel.

Figure 3.135 The effect of surface stress detected using the magnetovision technique: (a) the effect caused by writing on the steel surface a letter A with a ball-point pen; (b) the effect caused by artificial micro-cracks scribed on the grain-oriented steel sample.

Many routine technological processes, such as cutting or stamping the shape can destroy steel quality. Also other events, for example mishandling the product by poorly qualified workers, may also destroy the device made from electrical steel. It is assumed that the annealing process may recover the original properties. But practically it is very difficult to verify if the annealing process was performed correctly. The magnetovision method can help in the experimental verification of the condition of the magnetic material caused by different technological processes (Tumanski 2000). Figure 3.136 presents the change of electrical steel properties after cutting or laser scribing.

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Figure 3.136 The magnetovision map of a steel sample: (a) cut into the stripe (black line: the edge, in the middle of the edge is visible the effect caused by microcrack); (b) improved by laser scribing.

Modern numerical methods allow the calculation of extremely complex magnetic fields. But there are still many limitations to the exact determination of magnetic field distribution, especially when it is necessary to take into account all the parameters of magnetic materials (such as hysteresis, eddy currents, losses, material heterogeneity, domain or crystal structure). Moreover computation of three-dimensional magnetic fields is very time consuming. Therefore experimental determination of the magnetic field distribution is very useful. To investigate the magnetic field around the parts of a permanent magnet the Redcliffe Magtronics Company developed a scanning system called Magscan (figure 3.137). This scanning system enables experimental analysis of a 200 mm 200 mm area at 0.2 mm resolution in about 18 minutes. All three components of the magnetic field can be measured simultaneously using a set of three sensors. Typically a head with three Hall sensors is used, but this head can be replaced by an MR sensor head.

Figure 3.137 The scanning system Magscan of Redcliffe Magtronics.

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The magnetovision method allows the magnetic field distribution to be scanned in the 2D plane. Using a third stepper motor it is possible to reconstruct the magnetic field distribution in 3D-space. Figure 3.138 presents an example of the scanning system designed for three-dimensional testing of magnetic field distribution. An example of a 3D magnetic field map is presented in figure 3.139. Figure 3.139 presents the results of investigations of the magnetic field distribution around the magnetic circuit presented in figure 3.124 (Tumanski 2000). Although such a circuit is relatively simply it is rather difficult to numerically calculate magnetic field distributiion due to differences in thicknesses of the various parts of the magnetic circuit (very thin steel sheet in comparison with the yoke).

Figure 3.138 The scanning system designed for three-dimensional testing of magnetic field distribution.

Figure 3.139 The magnetic field distribution in 3D-space determined around the magnetic circuit presented in figure 3.124(b) (left picture describes the magnetic field distribution above the sheet, right picture describes the magnetic field distribution in the plane of the sheet).

The above presented scanning system can be used as a versatile device for material investigation and for non-destructive material testing. Experimental determinations of magnetic field distribution can effectively support numerical field calculations.

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List of Symbols

a

The width of the shorting bar in Barber-pole structure (see figure 1.67). b The distance between shorting bars in the Barberpole structure (see figure 1.67). B (Bx,By,Bz) Magnetic induction, magnetic flux density. D Grain size (diameter). g Length of the gap. H (Hx,Hy,Hz) Magnetic field strength (intensity). Hb Bias field. Hc Coercive field. Hd Demagnetizing field. Hex Exchange field. Hk Anisotropy field. Hs Stabilizing field. Hs Saturation field. Hx Measured magnetic field. hxHx/Hk Relative value of magnetic field. J Current density. J1 Exchange coupling coefficient. J2 Biquadratic coupling coefficient. Jp Exchange coupling coefficient. Ku Anisotropy coefficient. L Anisotropy axis. L Length of the sensor path. M (Mx,My,Mz) Magnetization. Ms Saturation magnetization. N Demagnetizing factor.

p P R Ra S t T Uo Uout V w W W or 50

ε

Gap between paths. Power dissipation. Resistance. Roughness. Sensitivity. Thickness of the film. Temperature. Supply voltage of the sensor. Output voltage of the sensor. Speed. Width of the magnetoresistor path (stripe). Energy. Trackwidth. Angular dispersion of the anisotropy. Thickness of the recording medium. The direction of current path with respect to the anisotropy axis (see figure 1.13). The angle between anisotropy axis and the direction of magnetization (see figure 1.13). The angle describing the direction of magnetization in the multilayer structures. The angle between the current direction and direction of magnetization (see fig.1.13). Magnetostriction coefficient. Wavelength of recorded information.

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THIN FILM MAGNETORESISTIVE SENSORS Magnetoresistivity coefficient. Resistivity. Resistivity tensor.

l Longitudinal resistivity. t Transversal resistivity. l t Change of resistivity.

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List of Abbreviations

ABS ABS ABT

anti-lock braking sustem. air bearing surface. Anderson, Bajorek and Thompson model. ACS anti-slip control system. AMR anisotropic magnetoresistance. BLS Brillouin light scattering method. bpi bits per inch. CIP current in plane. CMR colossal magnetoresistance. CPP current perpendicular to plane. DCC digital compact cassette system. DML discontinous multilayer. DMR dual element head. fci flux changes per inch. FMR ferromagnetic resonance method. FWHM full width at half maximum. GMI giant magnetoimpedance. GMR giant magnetoresistance. GPS global positioning system. IBD ion beam deposition. kbpi kilo-bits per inch. kfci kilo flux changes per inch. ktpi kilo tracks per inch. LLG Landau–Lifshitz–Gilbert equation. MBE molecular beam epitaxy. MFM magnetic force microscopy. ML thickness of atomic monolayer. MOKE magnetooptical Kerr effect.

MRAM magnetic random access memory. MRM magnetoresistance microscopy. MTJ magnetic tunnel junction. MR magnetoresistance. NDT non-destructive testing. PCB printed circuit boards. PLD pulsed lased deposition. PM permanent magnet. ppr pulses per revolution. PRML partial response with maximum likelihood. PW50 pulse width corresponding to 50% of the peak amplitude. RHEED reflection high-energy electron diffraction. RKKY Ruderman, Kittel, Kasuya and Yosida theory. rpm revolutions per minute. SAF synthetic antiferromagnetic structure. SAL soft adjacent layer method. SEMPA scanning electron microscopy. SMR shielded magnetoresistive head. SNR signal-to-noise ratio. SPLEEDspin-polarized low energy electron diffraction. SV spin valve magnetoresistor. SW Stoner–Wohlfart model. TBS tape bearing surface. UMR unshielded magnetoresistive head.

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Index

‘747’ curve, 367 Absolute position detector, 389 Abutted leads, 51 AC bias field, 33,76–81,136,141,335 Acceleration transducer, 399 Acceleration voltage, 270 Adding device, 347,350 Aiken code, 358 Air bearing surface (ABS), 364,380 Aliasing, 181 Allicat type MR head, 372,381 Anderson, Bajorek and Thompson model (ABT model), 90–91 Angle transducer, see angular position transducer Angular position transducers, 391–395 Anisotropic magnetoresistance (AMR), 4,8,9–29 Anisotropy field, 18,97,103,105,275 Anisotropy axis, 17,86 Anisotropy axis deviation, 87,96,124 Anisotropy of electrical steel measurement, 405 Annealing of thin films, 40,109–111,112,209,216,217, 218,254,265 Anomalous magnetoresistance, see anisotropic magnetoresistance Antiferromagnetic bias layer, 58–62,169,229,235–237 Antiferromagnetic coupled structures, see multilayer structures Antiferromagnetic materials, 60,235–237

Anti-lock braking system (ABS), 385,399 Anti-slip control system (ACS), 385,399 Antisymmetrical biasing, 73–74, Areal bit density, see recording density Artificial antiferromagnetic structure, see synthetic antiferromagnetic structure Asymmetry of shielded head, 378 Barber-pole sensor, 22, 28,51,55,125–129 Bar-code rocognition, see pattern recognition Barkhausen noise, 30,34,43,80,94 Bathtub curve, 366 Biasing field, 27,33,48,280,288 Biquadratic coupling, 189–191,202,284 Bit length, 363 Bit rate, 367 Bitter technique, see colloid pattern technique Blocking temperature, 59–60,236 Brillouin light scattering method (BLS), 175,190 Bohr magneton, 99 Brown’s equation, 93 Bubble memory devices, 353 Buffer layer, 106,214,237,263,273 Bulb failure detector, 346 Canted easy axis, 88 Capping layer, 237,264

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Cathode sputtering, see sputtering techniques DC sputtering Chalcogenite spinels, 255 Chevron type senor, 121 Co additional layer, 215,227,233 Coercive field, 97,98, 103,104,111,224 Coil current transducer, 344 Coin recognition, 339 Colloid pattern technique, 402 Colossal magnetoresistance (CMR), 7,171,251–255 Colpitts oscillator circuit, 260 Communication Logging System (CLS), 372 Compass application, 329–331 Composite structures, 101, 102 Computer Coded Search (CCS) system, 371 Contactless potentiometer, 350,392 CoPt bias film, 46 Corbino disk, 3 Corrosion of the layer, 59,100,236 Corsair type MR head, 372,380 Coupling fields, 187,202,274,275 Cross-track profile, see track profile Crossed anisotropy, 233 Crystal orientation, 236,272 Curie temperature, 253,272 Current conducting layer 52–58 Current density, 112,127,133,284–285 Current in plane (CIP), 170 Current measurements, see current transducers Current perpendicular to plane, 170,241–246,255 Current transducers, 341–346,347 Current transformers, see current transducers Demagnetizing fields, 38,83,85,89–91,105,276–277 Demagnetizing coefficient, 84,90,95 Density of recording, 173

De-gaussing procedure, 337 De-perming procedure, 337 Deposition pressure, 107,262,263,264,265, 267,268,274 rate 106–107,262,264,265 target, 107,108 Differential magnetoresistors, 20,31–32,49,54,57,68,70,88,291, 295 DigaMax system, 367,384 Digital Compact Cassette (DCC) system, 372,382,383 Diode sputtering, see DC sputtering Discontinuous multilayer (DML), 215 Dispersion of anisotropy, 28,33,39–44,86,97,98 Displacement transducers, see linear displacement transducers Distribution of magnetization, 36,38,43,68,89,92,94,96,279,284 Divider device, 348 Domain imaging, 403 Domain structure of thin film, 34–37 Domain walls detection, see domain imaging Döring formula, 14 Double exchange interaction, 252 Dual element bias, 63, 70–76 Dual element head (DMR), 74,370 Dual element horizontal MR head, 373 Dual sensor current transducer, 344 Dual stripe MR head, 119 Earth’s magnetic field, 327–328 Electrical steel testing, 405–415 Electrostatic discharge, 145 Electrodeposition method, 209,221,247,261 Electron–phonon coupling, 252 Encoders, 340 Energy meter, 350 Epitaxial film, 165

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INDEX Evaporation method, see vacuum evaporation Exchange anisotropy, see exchange coupling Exchange biasing layer, see antiferromagnetic bias layer Exchange coupling, 58,62,166,173–185,229,270 Exchange coupled structures, 168 Feedback technique, 142,344 Feldplatte magnetoresistor, 3 Ferromagnetic resonance method (FMR), 175,190 Fixed layer, see pinned layer Flipping bias field, 79,136,141 First principle modelling, 193,199 Flux concentrator, 133,288,294,336 Flux-gate sensors, 326 Four-point method, 208 Frequency bandwidth, 123,133,139 Fuchs and Sondheimer theory, 102 Full width at half maximum (FWHM), 208 Galvanic separation, 347,348 Gap between paths, 95–96,114 Gate device, see logic elements Gear tooth detection, 290,341,396 Geometry influence, 83–89,97, 102,104,276–286 Giant magnetoimpedance (GMI), 7,171,256–260 Giant magnetoresistance (GMR), 6,167,172,191 Global positioning system, 329 Gradiometer, 70,72,290,336–337,341,345 Grain structure imaging, 402,403 Grain size, 40,103,104,274 Granular structures, 165,169,217–222,250 Grooved bar-codes, 340 Grooved substrate, 245

437

Hall effect, 1,13,341 Hard magnetic layer, 45–51 Head efficiency factor, 368 Head positioning system, 385 Herringbone shape of the sensor, 123 Horizontal MR head, 369,373 Incremental method, 387 Insulated shunt biasing layer, 53 Integrated current transducer, 345–346 Integrated MR sensors, 131 Interface, 165,184 Interfacial mixing, 270–271 Inverted spin-valve, 238 Ion beam etching technique, see ion milling technique Ion milling technique, 114 Isolation devices, see galvanic separation Jahn–Teller effect, see electron–phonon coupling Joystick, 390 Keepered media, 371 Kerr effect, 175,176,190,402 Kohler diagram, 4 Landau–Lifshitz–Gilbert equation (LLG equation), 43,93,270 Layout of the sensor, 143,290,292,297,394,398 Lift-off technique, 114 Linear displacement transducers, 384–391 Linearity of the sensor, 137–139 Linearization methods, 22,31,68 Lithography methods electron-beam lithography, 96,114 ion beam lithography, 114 optical lithography, 113 X-ray lithography, 113

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Logic element, 351–352 Long-period oscillations, see period of oscillations Magnetic anomaly, 337–338 Magnetic card readers, 358–360 Magnetic field compensation, 339 Magnetic field during deposition, 106,263,265 Magnetic field measurements,331–336 Magnetic field units, 325 Magnetic field sensors (comparison), 7 Magnetic imaging, 406–416 Magnetic random access memory (MRAM), 228,251,353–357 Magnetic signature, 337 Magnetic tunnel junction (MTJ), 7, 170,185,247–251,296,355,356 Magnetic valve, see magnetic tunnel junction Magnetometers, see magnetic field measurements Magnetometric method, 175 Magneto-optical effect (MOKE), see Kerr effect Magnetoresistance in bismuth, 3 in metals, 3 in semiconductors, 2 Magnetoresistance microscopy, 400 Magnetoresistive effects, 1–8 Magnetoresistive heads, 357,361–384 Magnetoresistive materials, see material composition Magnetoresistive sensors (comparison), 8 Magnetoresistivity coefficient, 5,12, 16,97,98, 103,105,195,206,239, 250,254,275 Magnetoresistivity tensor, 14,15 Magnetostatic coupling, see orange peel coupling Magnetostriction, 97,98,100–101,275

Magnetovision system, 406 Manganate perovskites, 171,251 Magnetization patterns, 400 Market available MR sensors Honeywell, 8,130,131,143,145, 329,334,343 Nonvolatile Electronics, 8,289–291 Philips, 8,57,129,130,144,329, 342,393,397 Siemens, 8,297–298 Material composition, 39,98,99–101, 107,211,220,237,253 Material testing methods, 400–405 Meander shape of the path, 94,121,291 Mean free path, 102,103,192,218,235 Mechanical values transducers, 384–399 Melt-spinning, 222 Merged MR head, 380,382 Microfiber magnetoresistors, 7 Micromagnetic analysis,93,279,283 Microscopy, see magnetoresistance microscopy Molecular beam epitaxy method (MBE), 165,209,261 Mott’s two current model, see two current model Multidomain structure of thin film, 33 Multilayer structures, 101,209–216 Multipath sensor, 121,124 Multiplier device, 348 Multitrack MR head, 372,375 Nanowires, 7,170,246–247 Neel coupling, see orange peel coupling Neel’s ‘4/3 low’, 104 NiCo alloy, 98,102,117 NiFe, see permalloy NiFeCo alloy, 98,117 Noise of the sensor, 105,122,134–135,285,287,291

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INDEX Non-destructive testing, 406,413 Non-shielded read head, 115 Number of layers, 213 Odometer system, 399 Off-track capability, 367 Ohm per square resistance, 286 One-point position detector, 390 Orange peel coupling, 187,270 Orthogonal field influence, 49,78,140–141,329 Orthogonal MR head, 369 Oscillatory exchange coupling, see exchange coupling Overload of the sensor, 56 Oxidation of insulator films, 248 Passivation of thin film, 104,111 Pattern recognition, 340 Period of oscillation, 178,179,182 Permalloy, 5,98,107,117,239 Perpendicular recording, 371,384 ‘Piggy-back’ design, 380 Pillar shape structure, 244 Pin holes coupling, 187,270 Pinned layer, 168,229,230 Pitch of the recorded bits, 387,395 Planar coil, 58,136 Polarons, 252 POMUX, see positionsmultiplexer Positionsmultiplexer (POMUX), 386 Potentiometer, see contactless potentiometer Potter model of digital recording, 377 Power loss assessment, 404,411 Power transducer, 349–350 Pressure sensor, 390 Printed circuit board (PTB) current, 343 Pseudo spin-valve, 228 Pulse Code Quick Refind (PCQR) system, 371 Pulsed laser deposition (PLD), 253,261,265

439

Pyrochlore structures, 255 Quantum model of GMR effect, 192,197–198 Quantum well states, 183–185 Quasi-linear magnetoresistive sensor, 21,28 Range of measured fields, 137–139,293 Readback waveform, 365 Recording density, 281,358,361,363,365,375 Reflection high energy electron diffraction,262 Resistivity of the material, 97 Resolution of the sensor, 133–135,297 Reverse mode of biasing, 22,81–82 Ripple structure, 40 Roll-off characteristic, 365,378 Rotary encoders, 395,396 Rotational speed transducers, 396–398 Roughness of the film, 109,179,182,187,267,268–270 Ruderman, Kittel, Kasuya and Yosida theory, 180 Saturation field, 207,212,218,239 Sandwich structure, 165,176,258 Scale device, 388 Scanning electron microscopy (SEMPA), 175,179 Search coil sensors, 326 Seismic mass, 399 Semiconductor magnetoresistors, 2–3, 8 Semiclassical model of GMR effect, 192,195–196 Sensitivity of the sensor, 116,122,128, 132–133,207,212,239,335 Shaft power transducer, 395 Shape anisotropy, see demagnetizing fields

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Shape effects, see geometrical influence Shielded bias effect, 69 Shielded magnetoresistive head (SMR), 75,370,376–381 Short period oscillations, see period of oscillations Shunt biasing see current conducting layer Single path MR sensor, 115,118 Smit’s model of magnetoresistance, 9 Soft adjacent layer biasing (SAL), 33, 63–70, Spacer, 165 Speed of the disk or tape, 367,375 Spin dependent scattering, 167,193, 242 Spin engineering method, 176 Spin filter, see magnetic tunnel junction Spin-orbit interaction, 9,10,99 Spin polarized low energy electron diffraction (SPLEED), 175 Spin valve magnetoresistor (SV), 6, 168,202,229–241,263,278,295 Sputtering techniques DC sputtering, 107,261,263 ion beam deposition (IBD), 107,261,264,274 magnetron sputtering, 107,263 RF sputtering, 107,261,263 Stabilizing field, 27,29–30,49–50,55, 56,65 Starfire design, 381 Stoner–Wohlfart model, 22–26,40,76 Stoner–Wohfart asteroid (critical curve), 23,24,41 Substrate material,106,107,112,118,262 temperature, 40,106,107,108,254, 265 Superconducting measuring system, 243 Superlattice, 165,262

Switching device, 351 Switching field, 239,278–281 Symmetrical spin-valve, 238 Synthetic antiferromagnetic structure (SAF), 240 Tactile sensor, 390 Tangential field component, 402 Tape bearing surface (TBS), 383 Temperature influence, 98,110,138–139, 271–272,289,294 zero drift, 32,73,76,78, 135–136 Texture, see crystal orientation Thickness of antiferromagnetic layer, 236 atomic monolayer (ML), 180 the film, 105,112,117,118,127, 221 an insulator layer, 250 the magnetic layer, 213,226,234, 239 the spacer, 212,225,233,239 Thick film magnetoresistors, 105 Tight-binding model, 183 Torque transducer, 395 Track profile, 366,401 Trackwidth, 113,281,282,365,380 Transition slope, 364 Two current model, 8–10,192 Uncoupled structures, 186,222–228 Unshielded magnetoresistive head (UMR),75,370,372–375 Van de Pauw method, 208 Vacuum evaporation, 105,264 Vertical MR head, 369,373–374 Voigt–Thomson formula, 15 Wallace equation, 362 West’s multidomain model, 28 Wheel module, 397

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INDEX White’s model of GMR effect, 194, 223,230 Williams–Compstock model, 364 X-ray diffraction, 220,268 Yoke type current transducer, 344

Yoke-type sensor, 29,120 Yoke MR head, 370,382–384 Zero reference detector, 389 Zenner carriers, 252 Zener–Gennes model, see double exchange interaction

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