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HANDBOOK of MAGNETIC MATERIALS VOLUME 15

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HANDBOOK of MAGNETIC MATERIALS

VOLUME 15 EDITED BY

K.H.J. BUSCHOW Van der Waals-Zeeman Institute University of Amsterdam Amsterdam The Netherlands

2003

Amsterdam - Boston - Heidelberg - London - New York - Oxford Paris - San Diego - San Francisco - Singapore - Sydney - Tokyo

ELSEVIER B.V. Sara Burgerhartstraat 25 P.O. Box 211, 1000 AE Amsterdam, The Netherlands © 2003 Elsevier B.V. All rights reserved This work is protected under copyright by Elsevier and the following terms and conditions apply to its use: Photocopying Single photocopies of single chapters may be made for personal use as allowed by national copyright laws. Permission of the Publisher and payment of a fee is required for all other photocopying, including multiple or systematic copying, copying for advertising or promotional purposes, resale, and all forms of document delivery. Special rates are available for educational institutions that wish to make photocopies for non-profit educational classroom use. Permissions may be sought directly from Elsevier’s Rights Department in Oxford, UK: phone: (+44) 1865 843830, fax: (+44) 1865 853333, e-mail: [email protected]. You may also complete your request on-line via the Elsevier homepage (http://www.elsevier.com), by selecting ‘Customer Support’ and then ‘Obtaining Permissions’. In the USA, users may clear permissions and make payments through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA; phone: (+1) (978) 7508400, fax: (+1) (978) 7504744, and in the UK through the Copyright Licensing Agency Rapid Clearance Service (CLARCS), 90 Tottenham Court Road, London W1P 0LP, UK; phone: (+44) 207 631 5555; fax: (+44) 207 631 5500. Other countries may have a local reprographic rights agency for payments. Derivative Works Tables of contents may be reproduced for internal circulation, but permission of Elsevier is required for external resale or distribution of such material. Permission of the Publisher is required for all other derivative works, including compilations and translations. Electronic Storage or Usage Permission of the Publisher is required to store or use electronically any material contained in this work, including any chapter or part of a chapter. Except as outlined above, no part of this work may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without prior written permission of the Publisher. Address permissions requests to: Elsevier’s Rights Department, at the phone, fax and e-mail addresses noted above. Notice No responsibility is assumed by the Publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. Because of rapid advances in the medical sciences, in particular, independent verification of diagnoses and drug dosages should be made.

First edition 2003

ISBN: 0-444-51459-7 ISSN: 1567-2719 ∞The paper used in this publication meets the requirements of ANSI/NISO Z39.48-1992 (Permanence of Paper).

Printed in The Netherlands.

PREFACE TO VOLUME 15

The Handbook series Magnetic Materials is a continuation of the Handbook series Ferromagnetic Materials. When Peter Wohlfarth started the latter series, his original aim was to combine new developments in magnetism with the achievements of earlier compilations of monographs, producing a worthy successor to Bozorth’s classical and monumental book Ferromagnetism. This is the main reason that Ferromagnetic Materials was initially chosen as title for the Handbook series, although the latter aimed at giving a more complete cross-section of magnetism than Bozorth’s book. In the last few decades magnetism has seen an enormous expansion into a variety of different areas of research, comprising the magnetism of several classes of novel materials that share with truly ferromagnetic materials only the presence of magnetic moments. For this reason the Editor and Publisher of this Handbook series have carefully reconsidered the title of the Handbook series and changed it into Magnetic Materials. It is with much pleasure that I can introduce to you now Volume 15 of this Handbook series. Advanced ultra-high vacuum deposition methods, make it possible to manufacture highly perfect artificial layered magnetic materials. The investigations performed in the last two decades on nanometer-scale thin film and artificial multilayers with well defined layer thickness and interface flatness have led to the discovery of novel and most interesting effects. A general overview of the giant magnetoresistance effect in magnetic multilayers was already presented in chapter 1 of volume 12 of this Handbook. A prominent role among the layered magnetic materials is played by the so-called exchange biased spin valves and their excellent magnetoresistive properties. The advent of the exchange biased spin valves has led to many sensor applications, including those in hard disk read heads and applications in position and velocity sensors. In chapter 1 of the present volume, an application-oriented overview is presented of the extensive research efforts made on spin valves during the last decade. This overview includes work dealing with the magnetoresistance ratio, the thermal and field stability and the micromagnetic stability. The magnetic interactions and their interplay are discussed together with theoretical understanding and modeling of the magnetoresistance. Because of the high application relevance in spin valves and spin-electronic devices and because of the involved novel physics and materials science, special attention is paid to the exchange bias effect. Special emphasis is placed also on work dealing with magnetic tunnel junctions, which are presently considered as excellent candidates for storage elements in non-volatile magnetic random access memories. A further novel field of interest in magnetism is that of transition metal nanostructures. It has largely kept pace with microelectronics, forming the core of information technology. Current research efforts include the preparation of thin films for improved data storage, the exploitation of the electron spin rather than its charge for device switching (“spintronics”), v

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and the development of new materials for lightweight and low-cost applications. Generally, there has been a need for adequate theoretical descriptions able to explain most of the experimental phenomena and results. The many-body aspect of magnetic systems makes the task of calculating low-energy configurations of spin ensembles a formidable one. Because a full quantum mechanical description is actually intractable, various approximations have been used. The concentrated effort and the enthusiasm of a large number of scientists have resulted in an impressive display of new ideas and truly new discoveries. Theoretical work has already played and still plays a most important role in the process of active feedback between theories and experiments which has helped and speeded up the occurrence of novel accomplishments. Indeed, all magnetic properties of a solid are attributable to its electrons. In a free atom, there are two contributions to the magnetic moment. First, every electron has intrinsic spin and its associated magnetic moment. Second, there is the magnetic moment associated with the electron’s orbital angular momentum. In a free atom these contributions are typically comparable in magnitude. For transition metals Hund’s rules predict the ground state configuration, but the situation is quite different for solids in which a restricted number of these atoms have condensed into low-dimensional arrangements. In chapter 2 of the present volume a survey is given of the electronic structure of low-dimensional transition metals. It comprises not only thin films and multilayers but also clusters of transition metal atoms and nanowires. Results of novel experimental techniques are discussed hand in hand with theoretical approaches proposed to describe the electronic structure of these low-dimensional systems. Diluted magnetic semiconductors (DMS) can be characterized as substitutional mixed crystals with some of the cations of the semiconductor host lattice replaced by magnetic ions such as Mn, Fe or Eu. These materials encompass a large number of different compounds. A review covering the field of bulk II–VI compounds has been presented already in chapter 4 of volume 7 of the Handbook. In the last decade many new materials (e.g., IV–VI compounds) have been investigated. This is true in particular for low-dimensional quantum structures based on diluted magnetic semiconductors. Therefore, the present chapter is a logical extension of the earlier chapter presented in volume 7. It gives an overview of the research activities on low-dimensional structures of II–VI diluted magnetic semiconductors with manganese, including new DMS materials in which the magnetic components are different from Mn. Special emphasis is put on results obtained with IV–VI materials containing a magnetic component. In a way it can be regarded as a complement to the chapter on III–V Ferromagnetic Semiconductors that has appeared in volume 14 of the Handbook in 2002. Chapter 3 of the present volume, like the chapter in volume 14, will be of use in particular to the numerous scientists who have recently been attracted to the field of DMS by the prospect of incorporating diluted magnetic semiconductors in “spintronic” devices including those for quantum information applications. The current interest in spintronics has given renewed impetus to studies of diluted magnetic materials. As a result, we are witnessing now a vast increase of the number of contributions to the field of DMS, which has led to a new type of topical conference (Physics and Applications of Spin Related Phenomena in Semiconductors, or PASPS) organized already twice (in Sendai in 2000, and in Würzburg in 2002). High-Tc superconductors are prominent examples of novel materials that are not only interesting because of their surprisingly high superconducting transition temperatures but


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also because of their unusual magnetic properties and the interplay between antiferromagnetism and superconductivity. After the discovery of the first high-Tc superconductor La2−x Bax CuO4 by Bednorz and Müller in 1986 tremendous efforts have been spent world-wide in raising Tc even further and to interpret the rich phase diagrams displayed by the cuprates and nickelates for various doping levels. A thorough discussion of the two-dimensional antiferromagnetism of the cuprates was already presented in chapter 1 of volume 10. In chapter 4 of the present volume an account is given of the enormous progress made more recently. This is in particular true with regard to statical and dynamical stripes and the collective magnetic mode, the so-called resonance peak. Results of novel experimental techniques, like ARPES, STM and μSR are presented together with results obtained from neutron scattering, NMR and NQR. These and many other experimental result are discussed in the light of the corresponding theoretical framework. Magnetotransport properties of materials have become of quite substantial importance in the competitive market of technological devices. This is true in particular for devices dealing with the storage and reading of information in magnetic recording media. In the last decade we have seen concentrated efforts to search for new giant magnetoresistive (GMR) materials and to fully uncover its origin. Nowadays, GMR based devices are already a reality in commercial hard disks, and they are responsible for a considerable increase in the recording areal density. A chapter on Giant Magnetoresistance in Magnetic Multilayers has appeared already in volume 12 of the Handbook. Of almost equal technological importance is the so-called giant magnetoimpedance effect, GMI. Initially, its observation and the concomitant research accomplishments were received with only modest enthusiasm, probably because of the envisaged modest technological expectations and an apparent lack of intrinsically new magnetic effects related to its origin. Nevertheless, it soon became clear that its interpretation requires a deep understanding of the micromagnetic characteristics of soft magnetic materials and its dependence on dynamic magnetism. With the vast increase of the number of scientists all over the world investigating GMI and its technological applications, GMI has actually opened a new branch of research linking micromagnetics of soft magnets with classical electrodynamics. From the applications perspective, there exists already a wide range of prototypes of magnetic and magnetoelastic sensors and several devices have already penetrated the market. It is worth mentioning that the GMI-based devices are not intended to oust spin-valve-based heads from the magnetic recording market. However, GMI devices have reached a development stage that is mature enough for entering the relevant area of extremely sensitive magnetic field sensoring. Indeed, in some systems, with additional advantages, the best characteristics of the wellestablished fluxgate sensors were reached. Moreover, sensitivities as high as those found in sensors based on superconducting quantum interference devices (SQUIDs) are expected to be reached, great advantages being competitive price and operation at room temperature. The present chapter summarizes and updates the increasing number of information on the giant magnetoimpedance phenomenon. Volume 15 of the Handbook on the Properties of Magnetic Materials, as the preceding volumes, has a dual purpose. As a textbook it is intended to be of assistance to those who wish to be introduced to a given topic in the field of magnetism without the need to read the vast amount of literature published. As a work of reference it is intended for scientists active in magnetism research. To this dual purpose, Volume 15 of the Handbook is

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composed of topical review articles written by leading authorities. In each of these articles an extensive description is given in graphical as well as in tabular form, much emphasis being placed on the discussion of the experimental material in the framework of physics, chemistry and material science. The task to provide the readership with novel trends and achievements in magnetism would have been extremely difficult without the professionalism of the North Holland Physics Division of Elsevier B.V., and I wish to thank Paul Penman for his great help and expertise. K.H.J. B USCHOW VAN DER WAALS -Z EEMAN I NSTITUTE U NIVERSITY OF A MSTERDAM , N ETHERLANDS

CONTENTS

Preface to Volume 15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

v

Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

ix

Contents of Volumes 1–14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

xi

List of Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

xv

1. Giant Magnetoresistance and Magnetic Interactions in Exchange-Biased SpinValves R. COEHOORN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Electronic Structure Calculations of Low-dimensional Transition Metals A. VEGA, J.C. PARLEBAS and C. DEMANGEAT . . . . . . . . . . . . . . . . 3. II–VI and IV–VI Diluted Magnetic Semiconductors – New Bulk Materials and Low-Dimensional Quantum Structures W. DOBROWOLSKI, J. KOSSUT and T. STORY . . . . . . . . . . . . . . . . . 4. Magnetic Ordering Phenomena and Dynamic Fluctuations in Cuprate Superconductors and Insulating Nickelates H.B. BROM and J. ZAANEN . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. Giant Magnetoimpedance M. KNOBEL, M. VÁZQUEZ and L. KRAUS . . . . . . . . . . . . . . . . . . .

1 199

289

379 497

Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

565

Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

649

Materials Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

657

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CONTENTS OF VOLUMES 1–14 Volume 1 1. 2. 3. 4. 5. 6. 7.

Iron, Cobalt and Nickel, by E. P. Wohlfarth . . . . . . . . . . . . . . Dilute Transition Metal Alloys: Spin Glasses, by J. A. Mydosh and G. J. Nieuwenhuys Rare Earth Metals and Alloys, by S. Legvold . . . . . . . . . . . . . Rare Earth Compounds, by K. H. J. Buschow . . . . . . . . . . . . . Actinide Elements and Compounds, by W. Trzebiatowski . . . . . . . . . Amorphous Ferromagnets, by F. E. Luborsky . . . . . . . . . . . . . Magnetostrictive Rare Earth–Fe2 Compounds, by A. E. Clark . . . . . . . .

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1 71 183 297 415 451 531

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1 55 189 243 297 345 381 509

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Volume 2 1. 2. 3. 4. 5. 6. 7. 8.

Ferromagnetic Insulators: Garnets, by M. A. Gilleo . . . . Soft Magnetic Metallic Materials, by G. Y. Chin and J. H. Wernick Ferrites for Non-Microwave Applications, by P. I. Slick . . . Microwave Ferrites, by J. Nicolas . . . . . . . . . . Crystalline Films for Bubbles, by A. H. Eschenfelder . . . . Amorphous Films for Bubbles, by A. H. Eschenfelder . . . Recording Materials, by G. Bate . . . . . . . . . . Ferromagnetic Liquids, by S. W. Charles and J. Popplewell . .

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Volume 3 1. Magnetism and Magnetic Materials: Historical Developments and Present Role in Industry and Technology, by U. Enz . . . . . . . . . . . . . . . . . . . . . 2. Permanent Magnets; Theory, by H. Zijlstra . . . . . . . . . . . . . . . . 3. The Structure and Properties of Alnico Permanent Magnet Alloys, by R. A. McCurrie . . 4. Oxide Spinels, by S. Krupiˇcka and P. Novák . . . . . . . . . . . . . . . 5. Fundamental Properties of Hexagonal Ferrites with Magnetoplumbite Structure, by H. Kojima . . . . . . . . . . . . . . . . . . . . . . . . . . 6. Properties of Ferroxplana-Type Hexagonal Ferrites, by M. Sugimoto . . . . . . . 7. Hard Ferrites and Plastoferrites, by H. Stäblein . . . . . . . . . . . . . . . 8. Sulphospinels, by R. P. van Stapele . . . . . . . . . . . . . . . . . . . 9. Transport Properties of Ferromagnets, by I. A. Campbell and A. Fert . . . . . . .

305 393 441 603 747

Volume 4 1. Permanent Magnet Materials Based on 3d-rich Ternary Compounds, by K. H. J. Buschow . . . . . 1 2. Rare Earth–Cobalt Permanent Magnets, by K. J. Strnat . . . . . . . . . . . . . . . . 131 3. Ferromagnetic Transition Metal Intermetallic Compounds, by J. G. Booth . . . . . . . . . . 211 xi

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CONTENTS OF VOLUMES 1–14

4. Intermetallic Compounds of Actinides, by V. Sechovský and L. Havela . . . . . . . . . . . 309 5. Magneto-Optical Properties of Alloys and Intermetallic Compounds, by K. H. J. Buschow . . . . 493

Volume 5 1. Quadrupolar Interactions and Magneto-Elastic Effects in Rare-Earth Intermetallic Compounds, by P. Morin and D. Schmitt . . . . . . . . . . . . . . . . . . . . . . 2. Magneto-Optical Spectroscopy of f-Electron Systems, by W. Reim and J. Schoenes . . . . 3. INVAR: Moment-Volume Instabilities in Transition Metals and Alloys, by E. F. Wasserman . 4. Strongly Enhanced Itinerant Intermetallics and Alloys, by P. E. Brommer and J. J. M. Franse . 5. First-Order Magnetic Processes, by G. Asti . . . . . . . . . . . . . . . . . 6. Magnetic Superconductors, by Ø. Fischer . . . . . . . . . . . . . . . . .

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1 133 237 323 397 465

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1 85 181 289 453 511

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Volume 6 1. Magnetic Properties of Ternary Rare-Earth Transition-Metal Compounds, by H.-S. Li and J. M. D. Coey . . . . . . . . . . . . . . . . . . . . . . . . . 2. Magnetic Properties of Ternary Intermetallic Rare-Earth Compounds, by A. Szytula . 3. Compounds of Transition Elements with Nonmetals, by O. Beckman and L. Lundgren . 4. Magnetic Amorphous Alloys, by P. Hansen . . . . . . . . . . . . . . . 5. Magnetism and Quasicrystals, by R. C. O’Handley, R. A. Dunlap and M. E. McHenry . 6. Magnetism of Hydrides, by G. Wiesinger and G. Hilscher . . . . . . . . . .

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Volume 7 1. Magnetism in Ultrathin Transition Metal Films, by U. Gradmann . . . . . . . . . . 2. Energy Band Theory of Metallic Magnetism in the Elements, by V. L. Moruzzi and P. M. Marcus . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Density Functional Theory of the Ground State Magnetic Properties of Rare Earths and Actinides, by M. S. S. Brooks and B. Johansson . . . . . . . . . . . . . . . . . . . . 4. Diluted Magnetic Semiconductors, by J. Kossut and W. Dobrowolski . . . . . . . . . 5. Magnetic Properties of Binary Rare-Earth 3d-Transition-Metal Intermetallic Compounds, by J. J. M. Franse and R. J. Radwański . . . . . . . . . . . . . . . . . . . 6. Neutron Scattering on Heavy Fermion and Valence Fluctuation 4f-systems, by M. Loewenhaupt and K. H. Fischer . . . . . . . . . . . . . . . . . . .

. . 139 . . 231 . . 307 . . 503

Volume 8 1. Magnetism in Artificial Metallic Superlattices of Rare Earth Metals, by J. J. Rhyne and R. W. Erwin . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Thermal Expansion Anomalies and Spontaneous Magnetostriction in Rare-Earth Intermetallics with Cobalt and Iron, by A. V. Andreev . . . . . . . . . . . . . . . . . . 3. Progress in Spinel Ferrite Research, by V. A. M. Brabers . . . . . . . . . . . . . 4. Anisotropy in Iron-Based Soft Magnetic Materials, by M. Soinski and A. J. Moses . . . . 5. Magnetic Properties of Rare Earth–Cu2 Compounds, by Nguyen Hoang Luong and J. J. M. Franse . . . . . . . . . . . . . . . . . . . . . . . . . .

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Volume 9 1. Heavy Fermions and Related Compounds, by G.J. Nieuwenhuys . . . . . . . . . . . . . 2. Magnetic Materials Studied by Muon Spin Rotation Spectroscopy, by A. Schenck and F.N. Gygax . .

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CONTENTS OF VOLUMES 1–14

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3. Interstitially Modified Intermetallics of Rare Earth and 3d Elements, by H. Fujii and H. Sun . . . . 303 4. Field Induced Phase Transitions in Ferrimagnets, by A.K. Zvezdin . . . . . . . . . . . . 405 5. Photon Beam Studies of Magnetic Materials, by S.W. Lovesey . . . . . . . . . . . . . . 545

Volume 10 1. Normal-State Magnetic Properties of Single-Layer Cuprate High-Temperature Superconductors and Related Materials, by D.C. Johnston . . . . . . . . . . . . . . . . . . . . . . 1 2. Magnetism of Compounds of Rare Earths with Non-Magnetic Metals, by D. Gignoux and D. Schmitt 239 3. Nanocrystalline Soft Magnetic Alloys, by G. Herzer . . . . . . . . . . . . . . . . . 415 4. Magnetism and Processing of Permanent Magnet Materials, by K.H.J. Buschow . . . . . . . . 463

Volume 11 1. Magnetism of Ternary Intermetallic Compounds of Uranium, by V. Sechovský and L. Havela . . . 1 2. Magnetic Recording Hard Disk Thin Film Media, by J.C. Lodder . . . . . . . . . . . . 291 3. Magnetism of Permanent Magnet Materials and Related Compounds as Studied by NMR, by Cz. Kapusta, P.C. Riedi and G.J. Tomka . . . . . . . . . . . . . . . . . . . . 407 4. Crystal Field Effects in Intermetallic Compounds Studied by Inelastic Neutron Scattering, by O. Moze 493

Volume 12 1. Giant Magnetoresistance in Magnetic Multilayers, by A. Barthélémy, A. Fert and F. Petroff 2. NMR of Thin Magnetic Films and Superlattices, by P.C. Riedi, T. Thomson and G.J. Tomka 3. Formation of 3d-Moments and Spin Fluctuations in Some Rare-Earth–Cobalt Compounds, by N.H. Duc and P.E. Brommer . . . . . . . . . . . . . . . . . . . . 4. Magnetocaloric Effect in the Vicinity of Phase Transitions, by A.M. Tishin . . . . .

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Volume 13 1. Interlayer Exchange Coupling in Layered Magnetic Structures, by D.E. Bürgler, P. Grünberg, S.O. Demokritov and M.T. Johnson . . . . . . . . . . . . . . . . . . 1 2. Density Functional Theory Applied to 4f and 5f Elements and Metallic Compounds, by M. Richter . 87 3. Magneto-Optical Kerr Spectra, by P.M. Oppeneer . . . . . . . . . . . . . . . . . . 229 4. Geometrical Frustration, by A.P. Ramirez . . . . . . . . . . . . . . . . . . . . 423

Volume 14 1. III-V Ferromagnetic Semiconductors, by F. Matsukura, H. Ohno and T. Dietl . . . . . . . 2. Magnetoelasticity in Nanoscale Heterogeneous Magnetic Materials, by N.H. Duc and P.E. Brommer 3. Magnetic and Superconducting Properties of Rare Earth Borocarbides of the Type RNi2 B2 C, by K.-H. Müller, G. Fuchs, S.-L. Drechsler and V.N. Narozhnyi . . . . . . . . . . . . 4. Spontaneous Magnetoelastic Effects in Gadolinium Compounds, by A. Lindbaum and M. Rotter .

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LIST OF CONTRIBUTORS

H.B. Brom, Kamerlingh Onnes Laboratory, Leiden University, NL 2300 RA, The Netherlands R. Coehoorn, Philips Research Laboratories, Prof. Holstlaan 4, 5656 AA Eindhoven, The Netherlands Eindhoven University of Technology, Department of Applied Physics, P.O. Box 513, 5600 MB Eindhoven, The Netherlands C. Demangeat, Institut de Physique et Chimie des Matériaux de Strasbourg, CNRS, 23, rue du Loess, F-67034 Strasbourg Cedex 02, France W. Dobrowolski, Institute of Physics of the Polish Academy of Sciences, Warsaw, Poland M. Knobel, Instituto de Física Gleb Wataghin (IFGW), Universidade Estadual de Campinas (UNICAMP), C.P. 6165, Campinas 13.083-970 S.P., Brazil J. Kossut, Institute of Physics of the Polish Academy of Sciences, Warsaw, Poland L. Kraus, Institute of Physics, Academy of Sciences of the Czech Republic, Prague, Czech Republic J.C. Parlebas, Institut de Physique et Chimie des Matériaux de Strasbourg, CNRS, 23, rue du Loess, F-67034 Strasbourg Cedex 02, France T. Story, Institute of Physics of the Polish Academy of Sciences, Warsaw, Poland M. Vázquez, Instituto de Ciencia de Materiales, Consejo Superior de Investigaciones Científicas (CSIC), 28049 Cantoblanco (Madrid), Spain A. Vega, Departamento de Física Teórica, Atómica, Molecular y Nuclear, Universidad de Valladolid, E-47011 Valladolid, Spain J. Zaanen, Lorentz Institute for Theoretical Physics, Leiden University, NL 2300 RA, The Netherlands

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chapter 1

GIANT MAGNETORESISTANCE AND MAGNETIC INTERACTIONS IN EXCHANGE-BIASED SPIN-VALVES

R. COEHOORN Philips Research Laboratories, Prof. Holstlaan 4, 5656 AA Eindhoven, The Netherlands e-mail: [email protected] Eindhoven University of Technology, Department of Applied Physics, P.O. Box 513, 5600 MB Eindhoven, The Netherlands

Handbook of Magnetic Materials, edited by K.H.J. Buschow Vol. 15 ISSN: 1567-2719 DOI 10.1016/S1567-2719(03)15001-9

1

© 2003 Elsevier Science B.V. All rights reserved

CONTENTS 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4

1.1. Scope of this chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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1.2. The GMR effect in magnetic multilayers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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1.3. Structure and functioning of exchange-biased spin-valves . . . . . . . . . . . . . . . . . . . . . .

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1.4. Experimental results for prototype simple spin-valves . . . . . . . . . . . . . . . . . . . . . . . .

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1.5. Dependence of the MR ratio on the layer thicknesses . . . . . . . . . . . . . . . . . . . . . . . . .

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1.6. Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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1.7. Figures of merit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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2. Structure and transport properties of conventional and advanced spin-valves . . . . . . . . . . . . . . .

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2.1. Simple spin-valves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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2.2. Dual spin-valves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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2.3. Spin-valves with improved magnetic characteristics by additional layers outside the active part . .

53

2.4. Pseudo-spin-valves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

55

2.5. Temperature dependence of the magnetoresistance . . . . . . . . . . . . . . . . . . . . . . . . . .

59

2.6. Anisotropic magnetoresistance and anisotropy of the giant magnetoresistance . . . . . . . . . . .

61

2.7. Thermoelectric power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

62

2.8. Infrared optical properties – the magnetorefractive effect . . . . . . . . . . . . . . . . . . . . . . .

63

2.9. Deposition and microstructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

64

2.10. Thermal stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

71

3. Spin-polarized transport in spin-valves: theory and modelling . . . . . . . . . . . . . . . . . . . . . . .

77

3.1. Spin-dependent conductivity in ferromagnets – spin-dependent scattering . . . . . . . . . . . . .

78

3.2. Spin-dependent conductivity in ferromagnets – effect of spin-mixing . . . . . . . . . . . . . . . .

80

3.3. Spin-dependent scattering at interfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

83

3.4. Series resistor model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

85

3.5. The Camley–Barnas semiclassical transport model . . . . . . . . . . . . . . . . . . . . . . . . . .

86

3.6. Applications of the Camley–Barnas model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

89

3.7. Extensions of the semiclassical Camley–Barnas model . . . . . . . . . . . . . . . . . . . . . . . . 103 3.8. Semiclassical models based on realistic band structures . . . . . . . . . . . . . . . . . . . . . . . 106 3.9. Quantum-mechanical models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 3.10. Trends and future prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 4. Magnetic interactions and magnetization reversal processes . . . . . . . . . . . . . . . . . . . . . . . . . 115 4.1. Applications of the Stoner–Wohlfarth model to spin-valves . . . . . . . . . . . . . . . . . . . . . 115 4.2. Deviations from the single-domain model – micromagnetics . . . . . . . . . . . . . . . . . . . . . 124 4.3. Frequency dependence of the magnetic response, magnetization fluctuations and electronic noise 2

130

GIANT MAGNETORESISTANCE AND MAGNETIC INTERACTIONS

3

4.4. Anisotropy and magnetostriction of the free layer . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 4.5. Interlayer coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 4.6. Exchange anisotropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 5. Conclusions and outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197

1. Introduction 1.1. Scope of this chapter The use of advanced ultra-high vacuum deposition methods makes it possible to fabricate highly perfect artificial layered magnetic materials. In the past two decades studies of materials with nanometer-scale layer thicknesses, made with atomic-scale control of the layer thicknesses and interface flatness, have led to the discovery of several very interesting and sometimes unanticipated effects (Bland and Heinrich, 1994). One of these developments was the discovery of the giant magnetoresistance (GMR) effect by Grünberg and co-workers (Binasch et al., 1989), and, independently, by Fert and co-workers (Baibich et al., 1988). For layered materials consisting of ferromagnetic (F) layers, separated by non-magnetic (NM) layers, a large change of the electrical resistance was observed upon the application of a magnetic field. The relative resistance change can be more than 100% at room temperature. Some examples are given in section 1.2. The GMR effect is a consequence of the spin-polarization of the electrical conduction in the layer structure. In this chapter we focus on a specific class of layered GMR materials, called exchange-biased spin-valves (SVs), which are excellently suited for sensor applications. Less than a decade after the first publication by Dieny and coworkers at IBM (Dieny et al., 1991a, 1991b, 1991c), exchange-biased SVs were already introduced as sensor materials in hard disk read heads (Tsang et al., 1998). Other (potential) applications include position, speed and velocity sensors, and electronic compasses. The purpose of this chapter is to give an overview of the extensive research on exchangebiased SVs that has taken place during the past 12 years. Section 1 contains a description of the basic structure of SVs, a phenomenological explanation of their functioning as a magnetoresistive material, and a brief overview of applications. Sections 2–4 contain indepth discussions on the various detailed subjects that have been studied in order to obtain a better understanding of the functioning of SVs and in order to improve their performance in applications. Section 2 provides an overview of the experimental results of studies of the resistance and magnetoresistance for conventional and advanced spin-valves. The theoretical understanding and modelling of the magnetoresistance is discussed in section 3. The magnetization reversal processes, the magnetic interactions and their interplay are reviewed in section 4. Section 5 contains a summary and outlook. An overall conclusion of this review is that important progress is still being made, leading, e.g., to ever larger magnetoresistances, better control of the magnetic interactions, and enhanced stability with respect to elevated temperatures and the application of large magnetic fields. Therefore, studies of SVs continue to open opportunities for novel innovative applications. Many of the developments that are described in this chapter are not only important for the advancement of SV applications, but have also an impact in the much broader field 4


5

of spin-electronics. Within this novel research field materials and devices are studied of which the conduction can be influenced by the application of a magnetic field, as a result of the spin-polarization of the electron transport in these devices. Besides devices based on GMR materials, the presently most intensively studied spin-electronic devices are magnetic tunnel junctions (MTJs, Moodera et al. (1995), Leclair (2003)). In MTJs, spin-polarized electron tunneling between two ferromagnetic electrode layers across an insulating spacer layer can give rise a high magnetoresistance, over 50% at room temperature. Apart from the presence of the insulating spacer layer, their layer structure can be quite similar to that of exchange-biased SVs (Lu et al., 1997). The physics and materials science of the magnetic interactions in SVs, discussed in section 4 of this chapter, is equally relevant for such MTJs. MTJs are presently considered as prime candidates for storage elements in nonvolatile Magnetic Random Access Memories (MRAMs) (section 1.6.3). Spin-electronic materials and devices can also be made of combinations of ferromagnetic metallic layers and semiconductors. The spin-polarized transport processes in these materials and devices, and the novel opportunities that are envisaged for applications in solid state memory, logic and sensor elements, have been reviewed by Prinz (1995), Wolf et al. (2001), Ziese and Thornton (2001), Gregg et al. (2002), and Awschalom et al. (2002). For a comprehensive review on the GMR effect we refer to chapter 1 in volume 12 of this Handbook series (Barthélémy et al., 1999). Other reviews, focused on the fundamental aspects, have been presented by Levy (1994), Fert and Bruno (1994), Parkin (1994b), Gijs and Bauer (1997), Tsymbal and Pettifor (2001), Shinjo (2002), and Levy and Mertig (2002). Earlier reviews focused on exchange-biased spin-valves and on sensor applications have been written by Dieny (1994), Kools (1996), Kools et al. (1998a, 1998b), Tsang et al. (1998), Coehoorn et al. (1998), Coehoorn (2000) and Sakakima (2002). The application of magnetoresistive materials in sensors has been reviewed by Tumanski (2001). 1.2. The GMR effect in magnetic multilayers The GMR effect in magnetic multilayers is the dependence of the resistance on the angles between the magnetization directions of the successive magnetic layers. The effect originates from the spin-dependence of the electrical conduction in ferromagnetic materials, and occurs for systems with nanometer-scale layer thicknesses. Prototype examples of thin film materials showing a large GMR effect are antiferromagnetically (AF) coupled Co/Cu and Fe/Cr multilayers.1 At zero field a strong antiferromagnetic interlayer exchange coupling (reviewed by Bürgler et al., 2001) gives rise to an antiparallel alignment of the magnetization directions of neighbouring ferromagnetic layers. The application of a magnetic field leads to a transition to a parallel state, upon which the electrical resistance decreases strongly. The magnetoresistance (MR) ratio is defined as ΔR RAP − RP ≡ , R RP

(1.1)

where RP and RAP are the resistances in the parallel and antiparallel states, respectively. 1 The notation ‘A/B multilayer’ is used to briefly indicate a periodic layered material of the type (A/B) , formed n

by n 1 repetitions of a bilayer consisting of materials A and B.

6

R. COEHOORN

Fig. 1.1. Magnetoresistance curve for a sputtered epitaxial [110] oriented AF-coupled Co/Cu multilayer for the field applied along the [011] direction in the plane of the superlattice. The insets show, schematically, the alignment of the magnetization directions in the Co95 Fe5 layers. From Parkin (2002).

At room temperature, the MR ratio can be as large as 65% for polycrystalline sputter deposited (0.8 nm Co/ 0.83 nm Cu)60 multilayers (Parkin et al., 1991a) and 42% for (0.45 nm Fe/ 1.2 nm Cr)50 superlattice structures grown by Molecular Beam Epitaxy (MBE) (Schad et al., 1994). At 4.2 K the MR ratios observed for the same systems are even larger, viz. 115% and 220%, respectively. The largest yet reported MR ratio at room temperature, 110%, has been observed for a sputter deposited epitaxial [110]-oriented AF-coupled Co95 Fe5 /Cu superlattice (Parkin, 2002). Fig. 1.1 shows the magnetoresistance curve. These experimental results were all obtained for the “Current In the Plane of the layers” (CIP) geometry. The current is then parallel to the plane of the layers. Standard four-point measurements can be carried out easily by applying needle-shaped current and voltage probes directly on the thin-film specimen. For making devices, lithographic patterning is used for defining the multilayer magnetoresistor stripes and low-resistive contact leads, as shown schematically in fig. 1.2(a). Magnetoresistance studies of “Current Perpendicular to the Planes of the layers” (CPP) devices are technically much more demanding than CIP-GMR studies, but have revealed GMR ratio up to 300% at cryogenic temperatures (Gijs and Bauer, 1997). The geometry is shown schematically in fig. 1.2(b). It is necessary to create samples with small cross-sectional areas, in order to obtain a resistance that is not unacceptably low, and to carefully consider the functioning of the contacts as proper equipotential planes. The term ‘giant’ MR effect was chosen because the MR ratio can be much larger than observed at room temperature for the magnetoresistance effects already known at the time of the discovery, the ordinary MR effect and the anisotropic (AMR) effect. The ordinary MR effect is the dependence of the resistance of a material on the magnetic induction (Bfield), due to the effect of the Lorentz force on the trajectories of the conduction electrons


7

Fig. 1.2. Schematic device structures for measurements of the GMR ratio of a multilayer in (a) the Current-In-Plane (CIP) device geometry, and (b) the Current-Perpendicular-to-the-Plane (CPP) geometry. In order to eliminate the contact resistance, four-point CIP-measurements are carried out by making use of additional voltage probing contacts in between the current contacts (not shown). For an overview of methods for eliminating contact effects in the CPP-geometry we refer to Gijs and Bauer (1997).

(Jan, 1957). It occurs already in non-magnetic materials. The AMR effect is the dependence of the resistance of ferromagnetic materials on the angle between the current and the magnetization. It is of relativistic origin (Smit, 1951; Banhard and Ebert, 1995). The effect is relatively small, typically 1.5–3% in 10–30 nm thick permalloy layers (McGuire and Potter, 1975; Miyazaki et al., 1989; Mao et al., 1999a; Dieny et al., 2000b). Permalloy (Py) is a softmagnetic Ni1−x Fex alloy with x ≈ 0.20. AMR materials are presently used extensively in sensors (Tumanski, 2001), and have been used in hard disk read heads. However, in the latter application SVs have now fully replaced AMR materials. The GMR-effect arises as a result of the spin-dependent conductance in the ferromagnetic layers, and/or as a result of spin-dependent scattering at the interfaces. As proposed first by Mott (1936, 1964), the conductance of ferromagnetic materials can be viewed as the sum of separate contributions from electrons with opposite spin directions when the spin quantum number of the conduction electrons is conserved in the most of the scattering processes. This so-called two-current model is a fair approximation for ferromagnets based on Fe, Co and Ni, at least at temperatures well below the Curie temperature. Experimental studies on these metals, and on dilute alloys based on these metals, have revealed that the conductance can be strongly spin-dependent (Campbell and Fert, 1982). Since the discovery of the GMR effect, it has become clear that also the transport through interfaces can be spin-dependent. Fig. 1.3(a) illustrates the origin of the CIP-GMR effect for a periodic F/NM multilayer. The figure depicts typical trajectories of diffusively scattered electrons with opposite spin directions.2 The conductance depends on the angles between the magnetization directions of the neighbouring magnetic layers if: (1) the conductance in the F layers is spin-dependent and/or if the scattering probability at the F/NM interfaces is spin-dependent, and if 2 When in this chapter a specific layer structure is considered the spin-directions are indicated as “+” and “−”,

as defined with respect to an absolute axis direction. When a single F layer or an F/NM interface are considered, the spin directions are indicated as “↑” and “↓” (“up” and “down”), defined as the majority and minority spin electrons, respectively, within the F layer. In fig. 1.3, the “+” spin direction points to the right for systems with (e.g.) F = Py, Co or Co90 Fe10 and NM = Cu. The “+” spin direction points to the left for, e.g., Fe/Cr systems. Scattering in the bulk of the Fe layer and at the interfaces is then strongest for the majority spin electrons.

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Fig. 1.3. (a) Electron transport in F/NM multilayers for parallel and antiparallel alignments of the magnetizations. Typical trajectories of spin “+” and spin “−” electrons are indicated by dashed lines. (b) Effective resistor scheme that gives, within a simple model, the parallel and antiparallel resistances of an F/NM multilayer (see text in sections 1.2 and 3.4). (c) Electron transport in the active part of a spin-valve for parallel and antiparallel alignment of the magnetizations. Scattering at the outer boundaries is taken to be diffusive. In the case of multilayers or spin-valves based on Co, Ni, or on fcc Co–Fe–Ni binary or ternary alloys, and with NM = Cu, the majority-spin electrons have a lower scattering probability in the bulk of the F layers and at the interfaces, than the minority-spin electrons. The spin “+” and “−” directions then correspond in this figure to “right” and “left”.

(2) in the parallel aligned magnetic state the scattering probability upon traversal of one period is significantly smaller than 1, for electrons of at least one spin-direction. In the figure the electrons for which in the parallel state the scattering probability is smallest are called the spin “+” electrons. For the parallel state the spin “+” contribution to the conductance is much larger than the spin “−” contribution. In contrast, in the antiparallel state, “+” as well as “−” electrons each scatter strongly in one of the F layers. This results in a relatively high antiparallel resistance. Each layer acts thus as a spin-selective valve: its magnetization direction determines whether it most easily transmits spin “+” or spin “−”


9

electrons. Therefore the GMR effect is sometimes, more appropriately, called the “spinvalve effect” (Dieny et al., 1991a). Within the simplest possible quantitative model of the GMR effect, the resistances RP and RAP in the parallel and antiparallel configurations can be obtained from the resistor schemes that are shown in fig. 1.3(b). R+ and R− are the resistances in the parallel configuration for spin “+” and spin “−” electrons. This series resistor model, which is further discussed in section 3.4, leads to an MR ratio equal to ΔR/R = (R+ − R− )2 /(4R+ R− ). The high relative resistance changes of the AF-coupled multilayer materials discussed above are only obtained in high magnetic fields. E.g., fig. 1.1 reveals a saturation magnetic field of approximately 2400 kA/m (corresponding to ≈ 30 kOe 3 ). For comparison, the amplitude of the earth magnetic field is only ≈ 0.05 kA/m. For sensor applications, this is a disadvantageous situation. However, AF interlayer coupling is not a necessary requirement for obtaining the GMR effect. The GMR effect is observed in many other systems within which the relative alignment of the magnetization of nearby ferromagnetic regions can be changed by the application of a magnetic field. Besides exchange-biased SVs, which are the subject of this chapter, other examples are multilayers comprising layers of which the magnetization switches via multidomain states (Dupas, 1990), granular systems (Xiao et al., 1992), so-called discontinuous layer systems (Hylton et al., 1993), and so-called hard–soft multilayers (Shinjo and Yamamoto, 1990; Yamamoto et al., 1991). Exchangebiased SVs have a layer structure in which the coupling between the F layers is very weak or even zero. The field interval (around zero field) within which the resistance change takes place can be as small as a few tenths of a kA/m (a few Oe). This is one of their advantageous properties for low-field sensor applications. 1.3. Structure and functioning of exchange-biased spin-valves The layer structures of the three basic types of exchange-biased spin-valves (SVs) are shown schematically in fig. 1.4. The structures (a) and (b) are so-called “simple SVs”. These consist essentially of a sandwich structure of two ferromagnetic (F) layers separated by a nonmagnetic (NM) spacer layer, and an antiferromagnetic (AF) layer that is in contact with one of the F layers. The magnetization of this F layer, the “pinned” or “reference” layer Fp , is held fixed in a certain direction by the strong exchange interaction with the AF layer. Use is made of the “exchange anisotropy” effect. To a first approximation, the AF/F exchange interaction acts as if a strong local magnetic field, the so-called exchange bias field, Heb , acts on the pinned layer. Therefore, the exchange anisotropy effect is also called the “exchange bias effect”. The preferred direction of the pinned layer is determined by the magnetization direction of the pinned layer during growth of the AF layer on top of it (in case of a top spin-valve), or during cooling of the system after heating the system to a temperature above the so-called “blocking temperature” (for top and bottom spinvalves). The blocking temperature, Tb , is the temperature above which Heb is zero. A more precise definition is given in section 4.6.4. The AF layer is often an antiferromagnetic Mncontaining alloy or compound, such as PtMn, or an antiferromagnetic oxide, such as NiO. 3 A magnetic field of H = 1 kA/m (S.I.) corresponds to 12.57 Oe (c.g.s.). The corresponding magnetic induction

in vacuum is B = 1.257 mT (S.I.) or 12.57 G (c.g.s.).

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Fig. 1.4. Basic layer structures of exchange-biased spin-valves.

The pinned F layer can consist, e.g., of Co or permalloy. The other ferromagnetic layer, the “free layer” Ff , is effectively magnetically soft, and can consist, e.g., of permalloy. The NM spacer layer serves to magnetically decouple the F-layers. It consists usually of a 2–3 nm Cu layer. Sometimes, the thickness is even less. The thickness should be sufficient to prevent direct ferromagnetic exchange coupling between the layers via “pinholes”. Even in the absence of pinhole coupling, indirect interlayer exchange coupling (due to a weak magnetic polarization of the NM layer by the exchange interaction with the F layers) and magnetostatic interactions contribute to a net coupling between the pinned and free F layers (see section 4.5). The AF layer can be deposited on top of the other layers (“top SV”, fig. 1.4(a)) or on the bottom of the structure (“bottom SV” or “inverted SV”, fig. 1.4(b)). The order of growth of the layers (top or bottom AF layer) affects the microstructure within the layers, the antiferromagnetic domain structure in the AF layer, and in some cases the effective field that is sensed (e.g., due to the magnetic field that is created by the sense current). However, the basic functioning of both structures is the same. Underlayers (sometimes called “buffer layers” or “seed layers”) are frequently used to influence the microstructure of the film (e.g., the grain size, the preferential crystallite orientation and the interface flatness) or to prevent interdiffusion with the substrate. For top spin-valves the underlayer must be nonmagnetic. For bottom spin-valves the underlayer may be ferromagnetic. Structures with two pinned layers are called “dual” or “symmetric” SVs (fig. 1.4(c)). A thin cap layer (sometimes called “cover layer”) is often used to protect the structure from corrosion. In the early literature the term “spin-valve” was used to indicate multilayers in which the GMR effect arises upon a reversal of the magnetization of one or more soft magnetic layers that are not coupled to the other magnetic layers. However, it has become customary


11

Fig. 1.5. Schematic curves of the magnetic moment (a) and resistance (b) versus the applied magnetic field for a simple SV. The magnetic moments per unit area of the free and pinned layers have been assumed to be equal. The top and bottom arrows indicate the magnetization directions of the pinned and free layer, respectively.

to use the term “spin-valve” more exclusively for exchange-biased spin-valves. We follow that convention. When a relatively small magnetic field is applied, the free layer reverses whereas the magnetization direction(s) of the pinned layer(s) remain unchanged. Fig. 1.5(a) shows a schematic magnetization curve. The applied magnetic field is parallel to the exchange bias field. By definition, the applied field is positive when its direction is the same as that of the exchange bias field. For sufficiently large fields the free and pinned layers have parallel magnetizations. In a small field interval around the coupling field, Hcoupl , the magnetization of the free F layer reverses, whereas the magnetization of the pinned F layer remains fixed. This definition of Hcoupl implies that it is negative or positive when the coupling is ferromagnetic or antiferromagnetic, respectively. Only upon the application of a large negative field, the exchange bias interaction is overcome, and the pinned layer switches, too. Assuming ideal conditions, i.e., |Hcoupl| Heb , this happens when H ≈ −Heb . The complications that arise otherwise are discussed in section 4.1.2. Usually, the switching of the pinned layer is not fully reversible, leading to a certain hysteresis, as indicated in fig. 1.5. For sensor applications, the magnetization of the free layer should reverse by a reversible, coherent rotation process. This can be realized by making use of a free layer

12

R. COEHOORN

Fig. 1.6. Schematic representation of the magnetization reversal processes in the F layers of a spin-valve with (a) crossed anisotropies and (b) parallel anisotropies. Ha and Heb are the anisotropy and exchange bias fields, respectively. Interlayer magnetic coupling is neglected.

with uniaxial magnetic anisotropy, with the easy magnetization axis perpendicular to the exchange bias direction. Within this crossed anisotropy (CA) configuration the applied field is along the hard axis direction of the free layer (fig. 1.6(a)). Using the Stoner– Wohlfarth model (section 4.1) one finds that the free layer reverses in the field interval [−Ha + Hcoupl, Ha + Hcoupl] (eq. (4.8)), where Ha is the magnetic anisotropy field of the free layer. The switch field range, ΔHsw , is equal to 2Ha . This is the situation that is depicted in fig. 1.5(a). In actual devices the symmetry is slightly broken, in order to make one of the two otherwise equivalent reversal modes (clockwise or anti-clockwise) more favorable than the other. That favors real single-domain reversal (see sections 2.3, 4.1 and 4.2). The parallel anisotropy (PA) configuration (easy axis of the free layer and exchange bias direction parallel) leads to hysteretic, irreversible switching of the free layer, via domain wall movement (fig. 1.6(b)). This configuration is useful when a spin-valve is to be applied as a memory element, with the two zero-field states of the free layer corresponding to a digital “0” and “1”. The resistance versus applied field (R(H )) curve, the transfer curve, is shown in fig. 1.5(b). The angular variation of the resistance due to the GMR effect is to a good approximation given by R(θ ) = R(θ = 0) +

ΔRGMR (1 − cos θ ), 2

(1.2)

where θ is the angle between the magnetization directions of the free and pinned layers (Chaiken et al., 1990; Shinjo et al., 1992). It should be remarked that a study of a multilayer structure with a relatively high GMR ratio has revealed that the conductance, instead of the resistance, varies linearly with (1 − cos θ ) (Duvail et al., 1995). The difference between the two descriptions is of second order in the GMR ratio, and is therefore small in the case of a small GMR ratio. In the limit of weak coupling (|Hcoupl| Heb ) the transfer curve for


the crossed-anisotropy configuration is then linear, and given by H − Hcoupl ΔRGMR R(H ) = R(H = ∞) + 1− 2 Ha

13

(1.3)

for |H − Hcoupl| Ha . We have used eq. (4.8) for cos θ . The resistance shows a steep slope around H = Hcoupl , where the magnetization of the free layer reverses. The linearity of the response is a very desirable property for sensors. For negative applied fields the resistance stays high until, at the exchange bias field, the pinned layer switches, too. For CIP-SVs, the AF layers and underlayers may often be regarded as simple shunt resistors. Sometimes, the sheet resistances of these layers are so large that they can be neglected. The inner part of the stack, within which the detailed current density distribution depends on the alignment of the free and pinned layers, is called the “active layer” or “active part”. It is the part of the layer stack that is responsible for the GMR effect. The trajectories of electrons with opposite spin directions in the active part of the layer stack are shown schematically in fig. 1.3(c). Spin-polarized transport through the bulk of the layer and/or spin-polarized scattering at the interfaces leads to a GMR effect when, for at least one of the spin-directions, the scattering probability upon traversal through the SV layer stack is significantly smaller than 1. In this chapter, we do not discuss CPP-GMR studies of SVs. CPP-GMR spin-valve devices have only recently been studied at room temperature, and only recently possible applications of such devices have been considered. In all present applications the CIPgeometry is used. Experimental studies of spin-valves in the CPP-geometry have been carried out by Steenwyk et al. (1997), Gu et al. (2000), Nagasaka et al. (2001a, 2001b), Slater et al. (2001), Hosomi et al. (2002), Oshima et al. (2002), and Yuasa et al. (2002). Design studies of possible CPP-GMR hard disk read heads based on spin-valves have been carried out by Tanaka et al. (2002) and Takagishi et al. (2002). 1.4. Experimental results for prototype simple spin-valves The functioning of spin-valves is illustrated by fig. 1.7. In the upper part, R(H ) curves are given for a series of (8 nm Ni80 Fe20 / tCu nm Cu/ 6 nm Ni80 Fe20 / 8 nm Fe50 Mn50) films with varying Cu layer thickness.4 Fe50 Mn50 is an antiferromagnetic alloy with a Néel temperature of 230 ◦ C. These prototype materials were grown by sputter deposition in ultrahigh vacuum on a 3 nm Ta buffer layer on a Si(100) substrate, and covered by a 3 nm Ta cap layer (Rijks et al., 1994a). For tCu > 2.2 nm, the R(H ) curves have the ideal form given in fig. 1.5. There is a well-defined high-resistance plateau in the field range in which the magnetizations of the free and pinned layers are antiparallel, as can be seen from the figures for tCu = 2.5 and 4.7 nm. The MR ratio increases with decreasing Cu thickness, to a maximum of almost 5% around tCu = 2.2 nm. Below that Cu layer thickness a perfectly antiparallel alignment is not obtained at any field, because the coupling field is then no longer much smaller than the exchange bias field. As a result, the MR ratio decreases below tCu = 2.2 nm. At tCu = 1.3 nm, the magnetization directions of both layers remain almost parallel during the switching process. We will analyse the Cu thickness dependence of the MR ratio in sections 1.5 and 3. The shapes of the R(H ) curves will be analyzed 4 Throughout this chapter, the layers are given in the order of deposition.

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Fig. 1.7. Dependence of the room temperature magnetoresistance curves and the MR ratio on the Cu spacer layer thickness, for (8 nm Py/ tCu nm Cu/ 6 nm Py/ 8 nm Fe50 Mn50 ) spin-valves. The dashed line gives a fit to the data using eq. (1.4), for the Cu thicknesses for which full antiparallel alignment is obtained. From Rijks et al. (1994a).

in more detail in section 4.1.2. The exchange-bias field of these Fe–Mn based spin-valves shows an approximately linear decrease with increasing temperature, and vanishes around the blocking temperature, Tb ≈ 140 ◦ C. Fig. 1.8 shows the dependence of the MR ratio on the thickness and composition of the F layers in (F/Cu/F/Fe50 Mn50 ) SVs (Rijks, 1996a). For all F layers a rather broad maximum is found around tF = 6–8 nm. For spin-valves based on F = (Ni80 Fe20 )1−x Cox layers the MR ratio increases with increasing x, up to 8% at room temperature for F = Co. A comparison of figs 1.8(a) and 1.8(b) shows that the thermal stability of the MR ratio of Ni–Fe–Co based spin-valves increases with increasing Co content, at least in between 4.2 and 293 K. This is also observed above room temperature. We discuss this issue in section 2.5 in more detail. Spin-valves based on spacer layers other than Cu show lower MR ratios, Ag and Au being second-best choices. Fig. 1.9 shows the dependence of the GMR ratio on the layer thickness of Cu, Ag and Au spacer layers in simple spin-valves. In fig. 1.10 we take a closer look at the transfer curves of (Py/Cu/Py/Fe50Mn50 ) SVs that are nominally equal to those discussed above (although from another batch), with tCu = 3 nm (Rijks et al., 1994b). All curves reveal a weak ferromagnetic coupling between the free and pinned layers, with Hcoupl ≈ −0.5 kA/m. Curves (a) and (b)–(d) show the transfer curves for systems with parallel and crossed-anisotropy configurations, respectively. The easy anisotropy axis of the free permalloy layer is parallel to the direction of the magnetization during its growth. This is due to a certain degree of pair ordering in the otherwise random permalloy alloy (see further section 4.4). The crossed-anisotropy configuration can be obtained in situ during the growth by a 90◦ rotation of the applied field just before the growth of the AF layer (curve (b)), or after the growth by an ex situ process of heating to 160 ◦ C and subsequent cooling in a magnetic field that is parallel to the required


15

Fig. 1.8. Dependence of the MR ratio on the free magnetic layer thickness for (F/Cu/F/Fe50 Mn50 ) spin-valves, grown on 3 nm Ta underlayers on Si(100) substrates, at (a) 293 K and (b) 5 K. Symbols: F = Co (squares), F = Ni66 Fe16 Co18 (triangles) and F = Ni80 Fe20 (plus signs). Layer thicknesses: tCu = 3 nm (but tCu = 2.5 nm for F = Ni80 Fe20 ), and tF,p = 5 nm (but tF,p = 6 nm for F = Ni66 Fe16 Co18 ). From Rijks (1996a).

bias direction (curve (c)). Both transfer curves are essentially free of hysteresis, in contrast to curve (a), as expected from the different switching processes (fig. 1.6). Interestingly, the anneal process, which took approximately 10 minutes, is seen to reduce the anisotropy field of the permalloy layer. Apparently, the degree of pair ordering is reduced. A similar effect takes place when the curve-(b) spin-valve is given an identical field-cool treatment (curve (d)). It is important to be aware of such anneal effects on the transfer curve when designing sensors for high temperature applications, or when planning fabrication using high temperature processing steps (see section 4.4.2). A spin-valve would be electronically equivalent to an AF-coupled multilayer (with Flayers that are a factor of two thinner) if the scattering of electrons at the interfaces with the AF layer and with the cap layer would be specular. However, this is certainly not the case for the prototype (8 nm Ni80 Fe20 / 2.2 nm Cu/ 6 nm Ni80 Fe20 /Fe50 Mn50 ) spin-

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Fig. 1.9. Dependence of the room temperature MR ratio on the spacer layer thickness for spin valves with the layer structure (Si/ 7 nm Co/ tNM nm NM/ 4.7 nm Py/ 7.8 nm Fe50 Mn50 / 1.5 nm NM), with NM = Cu, Ag and Au. From Dieny et al. (1991c).

Fig. 1.10. Low-field magnetoresistance curves of (8 nm Py/ 3 nm Cu/ 6 nm Py/ 8 nm Fe50 Mn50 ) SVs, with (a) parallel anisotropies of the free and pinned layer, (b)–(d) crossed anisotropy configuration, obtained by rotating the applied field during sputter deposition (b), heating the system to 160 ◦ C and subsequent cooling in a field (c), and by the combination of these procedures (d). From Rijks et al. (1994b).

valves that were discussed above. In fact, for these systems the scattering at the Ta/Py and Py/Fe50 Mn50 interfaces is considered to be (almost) completely diffusive. This explains why the MR-ratio is quite small as compared to the MR-ratio for AF-coupled multilayers that are based on the same materials. For these spin-valves, fig. 1.7 shows that ΔR/R is ≈ 5% at the optimum Cu thickness. It would not be much larger for spinvalves with smaller Cu layer thicknesses for which (hypothetically) still a full antiparallel alignment could be obtained (dashed curve, see section 1.4). In contrast, for (1.5 nm Ni80 Fe20 / 1.0 nm Cu)60 multilayers the MR ratio is approximately 20% (Inomata and Hashimoto, 1993). As can be seen from fig. 1.8, the discrepancy is even larger for spin-


17

valves with smaller permalloy-layer thicknesses. Diffusive boundary scattering limits the distance along the current direction between two consecutive scattering process of spin “+” electrons, thereby reducing the otherwise large spin “+” current in the parallel magnetization state. As a result, the GMR ratio is reduced. This situation is depicted schematically in fig. 1.3(c). The GMR ratio of spin-valves with diffusively scattering outer boundaries can be increased by the introduction of a second pinned layer (dual spin-valves (fig. 1.4(c)). The introduction of a second free layer would not be useful, because of the high spin-independent resistivity of AF layers. The GMR ratio can also be increased by modifying the structure of the outer boundaries in order to enhance the degree of specular reflection, e.g., by making use of an oxidic AF layer or of thin “nano-oxide layers” (NOLs). Both improvements have led to advanced spin-valves with GMR ratios that are larger than 20%. We discuss these technologically important developments in section 2. 1.5. Dependence of the MR ratio on the layer thicknesses For the CIP-geometry the physically relevant length scales are the spin-dependent electron mean free paths. The local current density is not proportional to the local conductivity at any point in a layer at which the distance to an interface is smaller than the local mean free path. Ohm’s law is then not applicable on a local scale. The layer thicknesses must therefore be sufficiently small. How do the resistance and magnetoresistance depend on the layer thicknesses? In section 3, we discuss a semi-classical transport model that provides an extremely useful starting point for the modelling of the CIP (magneto)conductivity of spin valves and other multilayer systems, developed by Camley and Barnas (CB) (1989). It employs the semi-classical Boltzmann transport equation, and uses the relaxation time approximation to describe scattering (Ashcroft and Mermin, 1976). The electronic structure in all layers is assumed to be identical and spin-independent, and is described within the nearly-free electron model. That implies that (superlattice) band structure effects are neglected. The GMR effect is then entirely due to spin-dependent scattering. The parameters that enter the model are the spin-dependent mean free paths in each of the layers and the probabilities for diffusive and specular scattering at the interfaces and outer boundaries. We will apply the model to spin-valves of various types, discuss its limitations, and discuss theories beyond the CB model. However, even without the application of this and other advanced models we can already learn something about the (spin-dependent) scattering in spin-valves. As shown in this section, useful insight is obtained by analyzing the layer thickness dependence of the MR ratio using some simple phenomenological expressions. 1.5.1. Spacer layer thickness dependence The GMR ratio of spin-valves decreases with increasing non-magnetic spacer layer thickness, tNM , as can be seen in figs 1.7 and 1.9. The spacer layer should ideally be thin as compared to the electron mean free path, λNM , in that layer. Otherwise the orientation of the magnetization in one of the F layers influences the current density in the other F layer only weakly, and the GMR ratio is small. The decrease of the GMR ratio with increasing spacer layer thickness is also due to the increasing current shunting by the spacer

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layer. These factors are taken into account by the following simple expression for the tNM dependence of the GMR ratio, first proposed by Speriosu et al. (1991): ΔR exp(−tNM /NM ) =A× . R 1 + tNM /a

(1.4)

A(tF ), a(tF ) and NM should be viewed as phenomenological parameters. The factor exp(−tNM /NM ) may be viewed as the effective probability of electron transmission through the NM spacer layer without scattering. Dieny (1994) suggested that NM ≈ 12 λNM , where the factor 12 takes the distribution of electron velocity directions with respect to the current direction into account (see also section 3.6.1). The denominator expresses the shunting effect by the NM layer; a is of the order of the NM layer thickness at which the current through that layer is equal to the current through the F layers. Eq. (1.4) provides a reasonable fit to the experimental data on Py/Cu/Py-based spinvalves in fig. 1.7 (dashed curve), for Cu layer thicknesses for which the MR curves show that full antiparallel alignment has been reached. The fit parameters are A = 7.7%, Cu = 15.8 nm and a = 4.6 nm (Rijks et al., 1994a). Assuming that Cu ≈ 12 λCu , it would follow that λCu ≈ 32 nm. This is close to value λCu ≈ 40 nm that is obtained from the room temperature resistivity of a single crystal using the Drude model (Ashcroft and Mermin, 1976). The small value of a as compared to the total thickness of the two permalloy layers (14 nm) indicates that the current density in the permalloy layers is small as compared to the current density in the Cu layer. This is supported by the results of model calculations within the CB-model (section 3.6.5), which further show that the current through the permalloy layers is not only small due to their large resistivity, but also to the diffusive scattering at the interfaces with the Ta and Fe50 Mn50 layers. 1.5.2. Magnetic layer thickness dependence The MR ratio of SVs, studied as a function of the F-layer thickness, shows a pronounced optimum (see fig. 1.8). When scattering at the outer boundaries is diffusive, the optimum F-layer thickness is determined by the balance between the following two factors. On the one hand, the F layers should be sufficiently thick, so that spin-dependent scattering in the interior of the layer stack, and not the diffusive scattering at the outer boundaries, determines the overall conductance. On the other hand, the F layer thickness should not be much larger than the largest of the majority and minority spin electron mean free paths in that layer, λF,> . Otherwise, the orientation of the magnetization in one of the F layers does not influence the current density in the other F layer at a distance much larger than λF,> from the F/NM interface. The current density in the outer parts of the F layers then shunts the alignment-dependent conductance of the inner part of the trilayer, and the GMR ratio decreases with increasing F layer thickness. Dieny et al. (1992a) have proposed the following phenomenological expression for the dependence of the GMR ratio on the thickness tF,1 of one of the F layers: (1 − exp(−tF,1 /F )) ΔR =B × , R 1 + tF,1 /b

(1.5)

with F ≈ 12 λF,1> (Dieny, 1994). B and b depend on tNM and tF,2 . The denominator describes the shunting effect for thick F layers; b is of the order of the F1 layer thickness


19

at which the current through that layer is equal to the current through the other layers. From room temperature studies of F/Cu/F/Fe50 Mn50 spin-valves, with F = Co, Py and Ni, Dieny et al. (1992a) obtained F = 7.2, 7.2 and 8.5 nm, respectively. For these materials, the majority-spin mean free paths are thus in the 10–20 nm range at room temperature. Mean free paths depend on the film microstructure. However, these are representative values, also obtained from other studies (see section 3.6). In section 3 we show on the basis of theoretical considerations that in Co, permalloy and Ni the mean free path is largest for the majority-spin electrons. The “+” and “−” spin directions in fig. 1.3(c) point then to the right and left, respectively. 1.6. Applications 1.6.1. Read heads The main present application of exchange biased SVs is in hard disk read heads. Fig. 1.11(a) shows the geometry of “shielded” read heads, which are commonly used in hard disks. The MR-element is present in between two soft magnetic shields that confine the length of the region along a track to which the MR element is sensitive to essentially the bit length. For that purpose, the optimal distance between the shields is approximately two times the bit length. In addition to the MR material, the read gap contains two dielectric gap layers that electrically isolate the MR material from the metallic shields. The head is mounted on a slider, which flies at a very small fixed distance above the disk (typically 10 nm) due to the formation of an air film that functions as an air bearing in between the head and the slider (Ashar, 1997). Fig. 1.12 shows the growth of the storage density since 1990. Recently, recording at an areal bit density beyond 100 Gbit/inch2 (≈ 150 bits per μm2) has been demonstrated. The bit lengths and track widths are then typically 35 nm and 200 nm, respectively (Zhang et al., 2002). An overview of selected publications on hard disk read heads containing exchange biased SVs is included in table 1.1. The ever smaller bit lengths, track widths and data rates pose a number of great challenges to the development of SV elements. (1) In order to retain a sufficient signal-to-noise ratio (SNR), obtaining SVs with ever larger MR ratios would be very helpful. SVs with nano-oxide specular reflection layers (NOLs) and MR ratios above 20% hold, in this respect, a great promise (see section 2.1.7). (2) A second development that can lead to an increase of the SNR is the reduction of the Msat,f tf -product of the free layer. This can be understood as follows. The combination of the MR element and the shields functions as a flux guide. Flux from a magnetic transition in the written track enters the head via the SV, and returns via the shields, or vice versa. The average flux Φ through the SV element (per unit track width) increases with increasing free layer thickness, tf : the head becomes then more efficient. However, the average field in the free layer is proportional to Φ/(Msat,f tf ), where Msat,f is the saturation magnetization of the free layer. The net result of these two opposing effects is an increase of the average internal field with decreasing Msat,f tf product (Bertram, 1995). The prototype SVs discussed in section 1.5, with tF,f = 8 nm, are in this respect already more advantageous than the 15–25 nm permalloy layer thickness employed in AMR read heads in the early 1990s. Important recent developments are the use of

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Fig. 1.11. Schematic views of the read principle for (a) a shielded head in a hard-disk recording system, and (b) a multitrack yoke-type head in a tape recording system. For the purpose of clarity the bit length shown in (b) is not to scale, and the MRE and contact metalization have in (b) not been drawn for one of the heads.

“spin-filter SVs” (section 2.1.3) or SVs with NOLs (section 2.1.7), within which tF,f can be as small as 1 to 3 nm, and for which at the same time the MR ratio can be large and the switch field range small. (3) The ever decreasing space that is available for the MR material in between the shields restricts the possibilities of using thick AF exchange bias layers (see section 4.6) or other additional layers (see section 2.3).


21

Fig. 1.12. Growth in the storage density for magnetic disk drives since 1990. Circles mark the areal bit densities attained in laboratory demonstrations. The target set for 2006 by the U.S. Information Storage Industry Consortium (INSIC), 1 Tbit/inch2 , is indicated by a square. In the late 1990s, commercial products with the same density were available within two years after the laboratory demonstration. In the early 1960s and 1980s, densities were less than 0.1 Mbit/inch2 and around 10 Mbit/inch2 , respectively. From Goss Levi (2002).

(4) A fourth challenge concerns the thermal stability during processing and operation. The ultimate performance of a given read head is determined by the maximum possible sense current. Element heating reduces the MR ratio (section 2.5) and reduces the lifetime as a result of thermally activated degradation processes (section 2.10). Progress on this issue is made by making use of novel exchange bias materials with function up to much higher temperatures than Fe50 Mn50 (section 4.6), by developing deposition methods that lead to an improved microstructure, and by creating an improved thermal environment around the MR element (Ju et al., 2002). The potential for further growth of the bit density, towards a projected target of 1 Tbit/inch2 for 2006 as indicated in fig. 1.12, will depend on continued improvements on the MR materials, as well as on the resolution of challenging issues concerning the magnetic media (Moser et al., 2002). Read heads for tape recording can be shielded heads or so-called “yoke-type” heads (fig. 1.11(b)). In the latter case the MR element is separated from the head-tape interface by a flux guide. This protects the MR element against the mechanical wear and the thermal fluctuations that occur due to the direct head-medium contact. In one type of tape recording, used, e.g., in the analogue Compact Cassette audio system, the tape moves linearly with respect to a stationary read head. Digital tape recording based on the same principle is generally used for backup purposes. As compared to hard-disk recording, the volume bit density is higher and the price per stored bit is lower. However, the areal density is much smaller, with track widths exceeding 10 μm, and the data rate per recording channel is generally much smaller. SV yoke-type heads for such applications have been demonstrated by Philips (see references in table 1.1), and give rise to much larger signal levels than AMRbased heads (Coehoorn, 2000). In so-called helical scan recording, used, e.g., within the analogue VHS video recording system, the tape is wound on a rotary drum on which the

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R. COEHOORN TABLE 1.1 Selected publications on applications of exchange-biased spin-valves

Application

Reference

(a) Read heads for hard disk recording Design, fabrication and testing

Head for perpendicular recording Reliability of SV deposition for read heads Process considerations of critical features Read head based on a dual SV Demonstration 1 Gbit/s head SV head technology Recording demonstration > 100 Gbit/inch2

Tsang et al. (1994, 1998, 1999), Yoda et al. (1996), Nakamoto et al. (1996) Kim et al. (1997) Gurney et al. (1997) Fontana (1999) Yan et al. (1999) Shi et al. (2000) Kanai et al. (2001) Zhang et al. (2002)

(b) Read heads for tape recording Yoke-type heads Modelling of yoke-type heads Shielded heads Shielded heads: comparison AMR and GMR Helical scan recording by shielded heads

Folkerts et al. (1994, 1995) Wei et al. (1997, 1999) Oliveira et al. (1999) Dee (2002) Ozue et al. (2002)

(c) Magnetic field sensors Bridge sensor, pinning directions opposite in alternate branches Novel sensor principle using ac bias magnetic field Linear displacement sensor Bridge sensor based on SVs with Sy-AF pinned layers with opposite layer thickness unbalance Thermally and magnetically robust bridge sensor Bridge sensor (2 elements inactive) Comparison SV and multilayer bridge sensors Bridge sensor, opposite antiparallel fields in alternate branches due to use of flux guides Sensors for automotive applications Sensors for string instruments

Spong et al. (1996) Yamane et al. (1997) Miller et al. (1997) Marrows et al. (1999) Lenssen et al. (2000b) Freitas et al. (1999, 2000) Hill (2000) Prieto et al. (2001) Treutler (2001) Lenssen et al. (2002)

(d) SV-MRAMs Submicrometer MRAM cells Differential type MRAM cell MRAM with pinned layer as the storage layer

Tang et al. (1995) Yamane and Kobayashi (1998) Beech et al. (2000)

(e) Other applications Strain sensor Scanning magnetoresistance microscopy MEMS microbridge vibration sensor Biosensors

Mamin et al. (1998) Petrov et al. (1998) Li et al. (2002a) Graham et al. (2003)

heads are present. Digital helical scan recording up to an areal density of 11.5 Gbit/inch2 , using shielded SV heads, has been demonstrated by Sony (Ozue et al., 2002). SV heads are not yet employed in commercial tape recording systems.


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Fig. 1.13. Measurement of the rotation speed of an axis using a GMR sensor. The sensor is positioned between a soft-magnetic gear wheel and a permanent magnet (top part of the figure), with its sensitivity direction in the tangential direction. A varying position of the teeth of the wheel gives rise to a varying tangential component of the field at the sensor position (lower part of the figure). The number of peaks per unit time of the approximately sinusoidal output signal is a measure for the rotation speed. From Lenssen et al. (2000b).

1.6.2. Magnetic field sensors Magnetic field sensors are used to measure the size and/or direction of an unknown magnetic field, such as in electronic compasses. In another type of application, they are used to measure perturbations on a well-known magnetic field, e.g., for contactless measurements of position, velocity and acceleration (see fig. 1.13) and for non-destructive testing of magnetic materials with microcracks. Magnetic field sensors should fulfill a combination of requirements that depends on the specific application. Sensors based on various physical principles are therefore in commercial use, including sensors containing Superconducting Interference Devices (SQUIDs), flux-gate devices, Hall-elements, ordinary (semiconductor) MR-elements, AMR-elements, and GMR-elements (Lenz, 1990; Heremans, 1993; Popovic et al., 1996; Tumanski, 2001). Table 1.1 contains references to selected publications on sensors based on exchangebiased SVs. Several groups have developed sensors that consist of a Wheatstone bridge, using various methods for obtaining opposite signals in alternating branches of the bridge. One method is to use spin-valve stripes with pairwise opposite directions of the exchange bias field (Coehoorn and van de Walle, 1995; Spong et al., 1996). This can, e.g., be realized by sequentially depositing the opposite bridge elements, in antiparallel fields, or by post-deposition local heating and subsequent field cooling using integrated current leads underneath the sensor stripes. By making use of so-called synthetic AF pinned layers (see section 2.1.4). Lenssen et al. (2000a, 2000b) developed a robust sensor that can withstand high temperatures (>200 ◦ C) and large magnetic fields (>200 kA/m). Such specifications

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are relevant for applications in the commercially important market of automotive systems. Magnetic sensors provide more safety by their application in Antilock Brake Systems (ABS) and reduce fuel consumption and polluting gas emissions by their application in motor management systems. In the future they may even be used to replace mechanical by electronic connections (e.g., “steer-by-wire”, using steering actuator position sensors) (Schewe and Schelter, 1997; Treutler, 2001). 1.6.3. Magnetic Random Access Memories (MRAMs) MRAMs are non-volatile magnetoelectronic solid-state memory devices. A matrix of memory cells is deposited in a back-end process on top of a semiconductor CMOS integrated circuit, which is used for writing and readout. Advantages of MRAMs as compared to presently used semiconductor non-volatile flash memories are operation at a low voltage, practically infinite endurance, (in principle) very short (ns-scale) read and write times, and excellent radiation hardness. MRAM cells contain elements which can be reversibly switched between two (meta)stable magnetic states. Tang et al. (1995) have demonstrated MRAM cells based on exchange biased SVs. However, most work on GMR-MRAMs has been based on so-called pseudo-SV cells (Tehrani et al., 1999; Katti and Zhu, 2001). The functioning of SV and pseudo-SV MRAM cells is discussed in section 2.4. Present research on MRAMs focuses entirely on devices based on magnetic tunnel junctions (MTJs), using a matrix type architecture with at each cross point a selection transistor that is in series with a MTJ memory element. Successful demonstrators have been presented by Motorola (Durlam et al., 2002), IBM and Infineon (Reohr et al., 2002), Samsung (Motoyishi et al., 2002) and Sony (Jeong et al., 2002). A review on the present state of the technology has been given by Kim et al. (2002a). MTJs can have a higher MR ratio (typically 50%) than SVs or pseudo SVs (section 2.4), and their relatively high resistance (as compared to that of equally large CIP-GMR elements) is better matched to the openchannel resistance of the selection transistor. 1.6.4. Other applications Stimulated by the research on MRAMs, the introduction of spin-valve GMR technology as a back-end process on top of Si-devices and circuitry is giving rise to various novel applications. Examples are: (1) MEMS (Micro Electro-Mechanical System) microbridge vibration sensors, in which a SV senses the oscillatory stray field from a hard magnetic layer on a vibrating Si microbridge on a chip (Li et al., 2002a). (2) Magnetic biosensors. In magnetic biochips, SVs (Graham et al., 2003) or other GMR materials (Baselt et al., 1998; Edelstein et al., 1999; Miller et al., 2001) detect DNA or protein binding to capture molecules in a surface layer by measuring the stray field from superparamagnetic label particles. (3) Magnetocouplers (magnetoresistive isolators), which serve for contactless (galvanically isolated) signal transmission between two parts of a circuit that operate at different voltage levels, or in sensitive equipment. Presently, optoelectronic couplers are used for such applications. However, MR isolators are expected to be more easily integrateable on a chip. GMR isolators were first developed by Hermann et al. (1997), Fayfield et al. (1999) and Daughton (1999a, 1999b, 2000). Recently they were realized


25

using SVs by Ganzer et al. (2003), who used a Wheatstone bridge circuit composed of four identical GMR elements whose resistances can be modified by the magnetic fields from currents flowing in overlying strip lines that are not resistively connected. Such a bridge is insensitive to a homogeneous external field, but yields an output voltage when the fields from the strip lines are antiparallel in adjacent legs of the bridge. Such devices can also be used as a transformer with a flat frequency response down to dc. A generalized form of such a circuit, allowing for up to four independent input currents through the strip lines in the bridge, called a “transpinnor”, was made by Bae et al. (2002). Such multiterminal devices can in principle be used as logic gates (AND, OR, etc.) (Torok et al., 2002). SV read heads have been used as scanning probes in “scanning magnetoresistance microscopy” with sub-micrometer resolution of domain patterns in materials research (Petrov et al., 1998). SVs with a magnetostrictive free layer have been demonstrated to function advantageously as strain sensors (Mamin et al. (1998), see section 4.4.3). Some novel GMR device concepts which so far have only been demonstrated using other GMR materials, are expected to be feasible or even to be of more interest when SVs are used. Examples are magnetoelectronic logic (Boolean) gates (Johnson et al., 2000), contactless current detection sensors (Vieth et al., 2000), and bridge sensors for high magnetic field measurements (Mancoff et al., 2000). 1.7. Figures of merit The optimal GMR material for a given application depends on a large number of factors. There is never a single figure of merit. This is illustrated by table 1.2, which gives a (nonexhaustive) overview of property requirements for the specific case of a magnetoresistive sensor that measures the size of a magnetic field. References are given to the sections in this chapter where these properties are discussed. In this section we make a comparison between the sensitivities of various GMR materials (issue 1 in table 1.2), and introduce an “electronic” figure of merit (issue 5). From fig. 1.14, the room temperature sensitivities of various unpatterned GMR materials can be compared. The figure gives the switch field range as a function of the MR ratio. The switch field range is defined as ΔHsw ≡ ΔR/(∂R/∂H ), where ∂R/∂H is taken at the field at which it is largest. The thin dashed lines in the figure connect points of equal sensitivity, defined as S ≡ (1/R) × (∂R/∂H ). The datapoints 1–8 correspond to the following systems. (1) Conventional (Py/Cu/Py/Fe50Mn50 ) simple SVs (section 1.5). (2) State-of-the-art double specular simple SVs with Co90 Fe10 free layers in between a Cu spacer layer and a Cu back layer (section 2.1.7). The switch field ranges indicated in the figure are typical lower limits. ΔHsw depends on the induced anisotropy field, Ha , which can in principle be reduced to very low values by growth or post-deposition annealing in a rotating magnetic field, and on lateral variations of the interlayer magnetic coupling (section 4.3). However, when Ha is too low, random lateral variations of the anisotropy field lead to micromagnetic instabilities that deteriorate the sensor performance.

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TABLE 1.2 Required properties for spin-valves that are applied in sensors that measure the size of a magnetic field. References are given to sections in which these issues are discussed Required property 1. 2. 3. 4. 5. 6. 7. 8. 9.

10. 11. 12. 13. 14. 15. 16. 17.

High sensitivity S ≡ (1/R) × (∂R/∂H ) in the operating point. Good linear response in the operating point. Small coercivity. Switch field range larger than the required dynamic range.a Optimal sheet resistance.b Small temperature dependence of the output signal. Good structural and magnetic thermal stability of the layer stack (during factory processing and lifetime). Good stability upon the application of large magnetic fields.c Well-controlled effect on the magnetic interactions and (micro)magnetic stability upon lithographic patterning: • Shape anisotropy free layer • Magnetostatic interactions free and pinned layers • Current-induced field Good corrosion resistivity.d Low intrinsic electronic noise in the frequency range (bandwidth) of interest. Fast magnetic and electronic response to a change of the applied field.e Appropriate direction of the axis of field-sensitivity with respect to the sensor structure.f Industrially feasible deposition and patterning processes. Small total thickness of the layer stack.g Small effective Msat t-product of the sense layer.h Small sensitivity to electrostatic discharge (ESD).

18. Good stability under the application of a high sense current.

Reference 1.3, 1.4, sections 2–4 1.4 1.4, 4.2 1.3, 1.4 sections 2 and 3 2.5 2.10, 4.6 2.1.4, 4.1 4.2.2

table 4.7 4.3 4.3 4.1 2.9 1.6.1 1.6.1 Ohsawa et al. (1999), Inage et al. (2000) Gafron et al. (2000)

a The dynamic range is the field range around the operating point within the requirements 2 and 3 are fulfilled to a sufficient degree. b The optimal sheet resistance is determined by the balance between all factors that contribute to the signal and noise from the sensor, contact leads and amplifier, and by the performance requirements (e.g., maximum sensitivity or minimal power consumption). See table 1.3, which gives the appropriate figure of merit for some situations of practical interest. c I.e., no irreversible changes after the application of a large magnetic field. d This applies to applications where the bare sensor material cannot be sufficiently protected, such as hard disk read heads. e E.g., MR elements in future hard disk read heads should enable readout at data rates >1 Gbit/s. f For a stripe-shaped MR element the direction of sensitivity is usually transverse in-plane (as discussed in section 1.3). For certain applications, this may not be very suitable, so that spin-valves with non-standard properties are required. g This requirement applies specifically to MR materials in shielded read heads. The sensor layer, together with contact leads and insulation layers, should fit in the ever narrower read gap. In today’s heads the gap length is already smaller than 100 nm. h This requirement applies specifically to MR materials in read heads (see section 1.6.1).

(3) A 20 nm Py AMR film. (4) Weakly AF coupled (Py/Ag)n multilayers (Hylton et al., 1993), with a moderate MR ratio. An issue that hampers the application of these highly sensitive materials is that their fabrication requires extreme control of the temperature during an anneal treatment.


27

Fig. 1.14. Switch field range of various magnetoresistive materials as a function of the magnetoresistance ratio. The thin lines are contours of equal sensitivity. The materials that correspond to the numbered data points have been discussed in the text. AMR-films, AF-coupled GMR multilayers and hard–soft multilayers are found in the shaded part of the diagram.

(5) AF-coupled Fe/Cr multilayers (Schad et al., 1994). Like Co95 Fe5 /Cu multilayers (datapoint 6), these multilayers have a very high MR ratio but a relatively small sensitivity due to the high AF coupling field. (6) Co95 Fe5 /Cu multilayers (Parkin (2002); fig. 1.1). (7) AF coupled Co90 Fe10 /Cu multilayers (Wang et al., 1997a). The AF coupling is relatively weak due to the use of relatively thick (≈2.5 nm) Cu spacer layers. By varying the F and NM layer thicknesses and compositions, it is in practice possible to obtain AF-coupled multilayers with MR ratios, switch field range and sensitivity that are intermediate between those of AMR layers and those of the strongly coupled GMRmultilayer systems 5 and 6. These multilayers are an example. See also Daughton and Chen (1993). (8) (Co/Cu/Py/Cu)n “hard–soft” multilayers (Shinjo and Yamamoto, 1990; Yamamoto et al., 1991). Ideally, these materials contain alternating magnetically hard (here Co) and soft (here permalloy) layers that are not or only very weakly coupled across the non-magnetic spacer layer. However, in practical systems the coercivity of electronically suitable hard magnetic layers (such as Co) is insufficient. It is not possible to obtain sufficiently hard layers that function as a reference layer with a fully stable fixed magnetization direction. In fig. 1.14 the shaded area represents the part of the diagram within which single layer permalloy AMR films, AF coupled periodic multilayer GMR films, or hard–soft multilayers are found. It may be concluded that the sensitivity of state-of-the-art SVs is significantly higher than that of such films.

28

R. COEHOORN TABLE 1.3 Electronic figure of merit of thin film MR elements

Boundary conditions

Figure of merit, η Thermal fluctuation noise MRE dominates

Fixed sense current Fixed powera Fixed voltageb

1/2

(ΔR/R) × Rsh ΔR/R

−1/2 (ΔR/R) × Rsh

External noise dominates (ΔR/R) × Rsh

1/2

(ΔR/R) × Rsh ΔR/R

a In the case of a stripe-shaped MR element (MRE) from which the dissipated heat is transported transversely, perpendicular to the film plane, this is the condition that leads to a fixed maximum temperature rise in the element. b In the case of a stripe-shaped MRE from which the dissipated heat is transported longitudinally to the contact leads, this is the condition that leads to a fixed maximum temperature rise. The in-plane thermal conductivity of the magnetoresistive material is assumed to be proportional to 1/Rsh , as expected from the Wiedemann–Franz law (Kittel, 1996).

A useful “electronic” figure of merit of MR materials for a certain given device application is obtained by considering the signal-to-noise (SNR) ratio for the case of maximal use of the dynamic range. We consider a stripe-shaped MR element with length L and width W . When the overall system noise is equal to the Johnson–Nyquist electrical thermal fluctuation noise of the MR element (see section 4.3.3),5 the SNR ratio is given by L Isense ΔR ΔR VS Isense × = =√ Rsh , (1.6) VN 4kT W Δf R 4kRT Δf where VS and VN are the signal voltage and r.m.s. noise voltage, respectively, Δf is the band width, Isense is the sense current and Rsh is the sheet resistance. For a given element geometry and operating conditions (T , Δf ) and for a given fixed sense current, an appro1/2 priate figure of merit is then η = (ΔR/R) × Rsh . Using the same approach, expressions for η have been deduced for fixed power and fixed voltage conditions. See table 1.3. The table also gives expressions for η for the situation in which the overall system noise voltage is entirely due to external sources (e.g., amplifiers) and is independent of the properties of the MR element. It may be concluded that one must not only consider the MR ratio but also the sheet resistance when judging the appropriateness of a SV material for a certain application. The following example explains how table 1.3 can be used. For hard disk read heads, the noise is predominantly due to the Johnson–Nyquist noise of the sensor element. Suppose that the sense current should be as large as possible, in order to maximize the signal-tonoise ratio, but that a certain maximum allowed temperature rise due to the dissipated power should not be exceeded. If the heat flow is predominantly “transverse”, towards the shields, the appropriate boundary condition is that of a fixed power dissipation. On the other hand, if the heat flow is predominantly “longitudinal”, towards the contact leads, the 5 Eq. (1.6) applies only to high-frequency devices. For low-frequency devices 1/f noise is predominant (see

section 4.3.3).


29

appropriate expression for η coincides with that for the fixed voltage boundary condition (see footnote b in table 1.3). Actual hard disk read heads are intermediate between these transverse and longitudinal cooling regimes (Guo and Yu, 1997). 2. Structure and transport properties of conventional and advanced spin-valves Since the introduction of simple top and bottom exchange-biased spin-valves with the “conventional” layer structures shown in fig. 1.4 (a) and (b), several “advanced” layer structures have been introduced. We first give overviews of the structure and transport properties of simple and dual SVs, of SVs with additional layers outside the active part in order to optimize the free layer hysteresis and the offset field, and of so-called pseudospin-valves. Subsequently, specific properties are discussed, including the temperature dependence of the MR ratio, the superimposed AMR effect, the thermoelectric power and the infrared-optical properties. In the final part of this section, brief overviews are given of the deposition methods and the resulting microstructure and thermal stability. An analysis of the differences between the magnetoresistances for the various types of SVs and an assessment of the potential for obtaining higher MR ratios will be given at the end of the next section (section 3.10). 2.1. Simple spin-valves The combination of various physically different ideas for optimizing the properties by introducing additional layers has led to investigations of a very large number of different stack sequences. In this subsection we discuss simple spin-valves with various modified layer sequences within the active part of the layer stack or at its boundaries. The modifications influence the current density distribution in the layer stack, and hence the transport properties. We have chosen to base the order of the discussion on the classification scheme that is given in fig. 2.1 (a)–(i). In the sequence with letter codes (a) to (i) each structure represents a novel approach. When in a spin-valve various approaches are combined, it belongs to various classes. It will then be discussed under the class given by the highestrank letter code. An overview of representative studies of the structures and properties of simple spin-valves is given in table 2.1. In addition to the MR ratio, ΔR/R, the table gives the sheet resistance, Rsh , and the change of the sheet resistance, ΔRsh . When in the text layer compositions are not given in detail, the reader is referred to the table. Unless stated otherwise, the structures discussed are deposited by sputter deposition. Our convention concerning the notation of chemical compositions is as follows. The composition of random substitutional alloys is indicated by subscripts (e.g., Fe50 Mn50, Co90 Fe10 ) if the composition is given in the original publication or if this (approximate) composition is with great certainty implied in the original publication (which is often the case when the notations FeMn or CoFe are used). The composition of ordered (nominally) 1:1 stoichiometric compounds is given without subscripts (e.g., PtMn). If the alloy composition is not given, or if a statement is made about an entire class of alloys, the constituting elements are separated by a hyphen (e.g., Fe–Mn). The latter notation is frequently used for Ir–Mn materials, because of the difficulty to precisely control the Ir:Mn ratio in many deposition systems.

30

R. COEHOORN

Fig. 2.1. Classification scheme of conventional and advanced simple spin-valves.

2.1.1. Conventional spin-valves (fig. 2.1(a)) The prototype of a conventional exchange biased spin-valve is the structure Py/Cu/Py/ Fe50 Mn50, introduced by Dieny et al. (1991a) and discussed extensively in section 1. Sputter deposition of Py, Co or Cu on a 2–3 nm Ta underlayer, on a substrate such as Si(100), SiO2 or glass, gives rise to a strong [111] texture. Fe50 Mn50, Cu and fcc-type Fe–Co–Ni alloys have nearly the same lattice constant. In spin-valves based on these materials, the layers grow therefore coherently. Typical average grain diameters are of the order of 15– 30 nm. The microstructure is affected by the sputter deposition conditions, and by the use of appropriate underlayers, as discussed in section 2.9 in more detail. Scattering at grain boundaries is reduced by increasing the average grain size, leading to an enlarged GMR ratio.

System (a) Conventional SVs free/ 2.2 Cu/ 4.7 Py/ 7.8 Fe50 Mn50 / 1.5 Cu

ΔR/R (%)

Rp,sh ( )

ΔRp,sh ( )

14.0 17.1 14.0

3.5 Ta/ 8 Py/ 2.2 Cu/ 6 Py/ 10 Fe50 Mn50 / 3.5 Ta 3.5 Ta/ 2 Py/ 7 Fe50 Mn50 / 6 Py/ 2 Cu/ 8 Py/ 3.5 Ta 5 Ta/ 5 Py/ 2.5 Cu/ 2.4 Co/ 15 Fe50 Mn50 / 5 Ta

4.5 3.5 1.5 9.5 6.5 5 2.5 2.5 4.5 1.4 0.3 0.2 3.0 4.3 3.8 9.0 5.0 4.7 5.2

3.5 Ta/ 8 Py/ 2 Cu/ 6 Py / 8 Fe50 Mn50 / 5 Ta

5.8

Ta/ free/ Cu/ pinned/ 8 Fe50 Mn50

Ta/ Co/ spacer/ Py/ 8 Fe50 Mn50 Ta/ Py/ spacer/ Py/ 8 Fe50 Mn50 5 Hf/ 5 Ni66 Fe16 Co18 / 2 Cu/ 5 Ni66 Fe16 Co18 / 5 Fe50 Mn50 / Hf 3 Ta/ 8 Py/ 2 Cu/ 6 Py/ 8 Fe50 Mn50 / 2 Ta 5 Ta/ 9 Cox Py1−x / 2.8 Cu/ 4 Cox Py1−x / 8 Fe50 Mn50 / 10 Ta

Remarks

Reference

0.63 0.60 0.21

free = 9 Co free = 9 Py free = 9 Ni free, pinned = Co, Co free, pinned = Co, Ni free, pinned = Py, Py free, pinned = Ni, Ni free, pinned = Fe, Py spacer = Au spacer = Ag spacer = Pt spacer = Pd

Dieny et al. (1991c)

14.6

0.63

22.0

1.1

17.5

0.91

12.5

0.72

See figs. 1.7 and 1.8 x = 0.0 x = 0.95 (full x-dependence) Study sputter conditions Study inverted structure Study thickness tolerances for read-head fabrication Study industrial scale deposition

Dieny (1994)a

Hoshino et al. (1994) Rijks et al. (1996a) Kitade et al. (1995) Kools (1995) Lenssen et al. (1996) Gurney et al. (1997)


TABLE 2.1 Magnetoresistance and sheet resistance Rp,sh (in the parallel state) of conventional and advanced simple spin valves. The entries in the table are a selection from the literature. Within each category, they are given in chronological order. All materials have been made by sputter deposition, unless indicated otherwise. More details concerning the preparation and properties are given in section 2. Notation: UL = underlayer, BL = non-magnetic “back layer”, NOL = nano-oxide layer. “Ox” indicates than an oxidation step has taken place, A-B-C = binary (ternary) alloy containing elements A, B (and C) with an unspecified composition. Py = permalloy = Ni80 Fe20 (or an alloy with at most 3 at.% more or less Ni). When in a publication the non-scientific notations NiFe, CoFe, FeMn or IrMn have been used, these have been replaced by Py, Co90 Fe10 , Fe50 Mn50 and Ir–Mn, respectively (see also introduction to section 2.1). The composition of AF Ir–Mn alloys is generally close to Ir20 Mn80 . Details concerning an anneal treatment have been given if this treatment is not strictly necessary for obtaining the proper exchange bias field (see section 4). The resulting properties are then given within square brackets. When for reference purposes structures have been made that deviate from the main structure, the corresponding data are given in between parentheses. It is likely that the experimental accuracy of Rp,sh and ΔRp is in some cases less than is suggested by the notation used. In part, this is due the possible inaccuracies involved when extracting these data from figures in the original publications. Also, it is likely that the experimental procedures used have in some cases not been optimized for determining these quantities with the precision that is suggested in the table

Schwartz et al. (1998) 31

(continued on next page)

32

TABLE 2.1 (continued) System 5 Ta/ 3.7 Co/ 2 Cu/ 3.2 Co/ 10 Fe50 Mn50 /5 Ta/ 0.5 Cu 5.2 Ta/ 4.4 Co/ 2.5 Cu/ 4.4 Co/ 10 Fe50 Mn50 / 5.2 Ta

ΔR/R (%) Rp,sh ( ) ΔRp,sh ( ) Remarks 11.2 10.0

11.3

1.13

Reference

Study sputter conditions Comparison sputter methods

Stobiecki et al. (2000) Langer et al. (2001)

x = 0.25 (x = 0) BL = Py, Co, Feb [After anneal at 250 ◦ C; low Hc , high sensitivity] F = Co90 Fe10 (F = Co) F = Co90 Fe10 [After 3 h anneal at 250 ◦ C]. F = (Co90 Fe10 )0.9 B0.1 [After 3 h anneal at 250 ◦ C].

Parkin et al. (1993)

(b) SVs with composite F layers (5.3 – x) Py/x Co/ 3.2 Cu/ x Co/ (2.2 – x) Py/ 9 Fe50 Mn50 / 1 Cu 5 Ta/ 4 Cu/ 8 Fe50 Mn50 / 5 Py/ 2.3 Cu/ 2 Py/BL/ 5 Ta SiO2 / 10 Co–Nb–Zr/2 Py/ 4.9 Co90 Fe10 / 2.8 Cu/ 4.9 Co90 Fe10 / 8 Fe50 Mn50 5 Ta/ 2 Py/5.5 F/ 3.2 Cu/ 5.5 F/15 Fe50 Mn50 / Ta

10 Co–Zr–Nb/2 Py/3 Co90 Fe10 / 3 Cu/ 2 Co90 Fe10 / 9 Ir–Mn/ 5 Ta 2 Ta/ 2 Py/2 Co90 Fe10 / 2.2 Cu/ 2.5 Co90 Fe10 / 5 Ir–Mn/ 2 Ta 5 Ta/ 5 F/2.5 Co90 Fe10 / 2.8 Cu/ 2.5 Co90 Fe10 /6 Ir–Mn/ 5 Ta 5 Ta/ 4 Ni–Fe–Ta/1 Py/1 Co/ 2.4 Cu/ 2 Co /20 PtMn/ 5 Ta 5 Ta/ 5 Py/1 Co/ 2.5 Cu/ 2 Co/20 PtMn/ 5 Ta Ta/ 4.5 Py/0.6 Co90 Fe10 / 2.4 Cu/ 3.2 Co/ AF

Ta/ 20 NiMn/ 2.4 Co90 Fe10 /2.4 Cu/ 1.2 Co90 Fe10 /2 Py/ Ta UL/ 3 Py/1 Co90 Fe10 / 2 Cu/ 2 Co90 Fe10 / 20 PtMn UL/ 2.5 Py/1.5 Co90 Fe10 / 2.8 Cu/ 2.5 Co90 Fe10 / 20 PtMn/ cap UL / 3.2 Py/0.5 Co90 Fe10 / 2.5 Cu/ 1 Co90 Fe10 / 1.9 Co60 Fe40 / 8 Ir–Mn/ 5 Ta

8.0 7.9 (6.2) 7.2 [4.8] 3.0 [4.9] 6.8 [8.5] 9.0 12.3 [9.5] (9.5) 7.5 (7.3) 10.9 9.4 8.9

23.3 18.7 [23.1] (14.7) 16.0 (15.1) 22.9 17.0 16.8

2.1 2.3 [2.2] (1.4) 1.2 (1.1) 2.5 1.6 1.5

9.2 12.0 14.7 11.5 8.0

16.7 16.3 17.4 18.7

2.0 2.4 2.0 1.5

[After 1 h anneal at 250 ◦ C]

Gurney et al. (1993) Kamiguchi et al. (1996) Kanai et al. (1996) Kanai et al. (1997)

Fuke et al. (1997)

Mao et al. (1999b) F = Py89 Ta11 Mizuguchi and Miauchi (1999) [After 5 h anneal at 280 ◦ C] (F = Py) Ni–Fe–Ta contains less Araki et al. (2000) than 15 at.% Ta. AF = 6 Ir–Mn Lin et al. (2000) AF = 25 NiMn AF = 25 PtMn Anneal treatment dependence Chen et al. (2000) Dieny et al. (2000a, 2000b) AlTiC/Al2 O3 substratesa , e Mao and Gao (2000a) UL = 4 Py60 Cr40 Childress et al. (2001) UL = 5 Ta (continued on next page)

R. COEHOORN

5 Ta/ 3.5 Py/4 F/ 3.2 Cu/ 4 F/ 10 Fe50 Mn50 / 10 Ta

5.5 (2.8)

TABLE 2.1 (continued) System

Reference

X = transition metal element; Marrows and Hickey (2001) δ < 0.1 nm; see fig. 2.4.

4.5 for δ = 0

(c) SVs with NM back layer (“Spin-filter SVs”) 5 Ta/ 4 Cu/ 8 Fe50 Mn50 / 5 Py/ 2.3 Cu/ 2 Py/ BL / 5 Ta 5 Ta/ 2 Cu/ free/ 2 Cu/ 2 Co90 Fe10 / 7 Ir22 Mn78 / 5 Ta t1 Si/ 1.5 Cu/ 4 Py/ 0.5 Co/ 2.5 Cu/ 3 Co90 Fe10 / 8 Ir–Mn/ 3 Ru t2 Si/ 4 Py/0.5 Co90 Fe10 / 2.5 Cu/ 3 Co90 Fe10 / 8 Ir–Mn/ 3 Ru

9.3 8.4 9.8 (8.8) (7.1)

21.5 20.2 15.6 (18.2) (21.8)

2.0 1.7 1.5 (1.6) (1.5)

10.3

0.65

BL = Cu, Cu50 Au50 b Gurney et al. (1993) free = 1.6 Co90 Fe10 Fukuzawa et al. (1998, 2001a) free = 2 Py / 0.5 Co Study effect Si UL; t1 = 3 nm Carey et al. (2002) (t2 = 3 nm) (t2 = 1 nm)

(d) SVs with synthetic antiferromagnetic (Sy-AF) pinned layer 3.5 Ta/ 2 Py/ 10 Ir–Mn/ 4 Co90 Fe10 / 0.8 Ru/ 4 Co90 Fe10 / t Cu/ 0.8 Co90 Fe10 /5 Py/ 4 Ta 50 Fe2 O3 / 2 Co/ 0.7 Ru/ 3 Co/ 2 Cu/ 1 Co/5 Py/ 3 Ta 5 Ta/ 5 Py/ 1 Co/ 2.5 Cu/ 2 Co/ 0.8 Ru/ 2 Co/ 30 Cr45 Mn45 Pt10 / 5 Ta 5 Ta/ 2 Py/ 1.5 Co–Fe–B/ 3 Cu/ 2.5 Co–Fe–B/ 0.8 Ru/ 1.5 Co–Fe–B/ 10 Pt–Pd–Mn/ 6 Ta 5 Ta/ 2 Py/1.5 F/ 3 Cu/ 2.5 F/ 0.8 Ru/ 1.5 F/ 15 Pt32 Pd17 Mn51 / 6 Ta 2 Ta/ 2 Py/2 Co90 Fe10 / 2.2 Cu/ 2.5 Co90 Fe10 / 0.5 Ru/ 2.2 Co90 Fe10 / 5 Ir–Mn/ 2 Ta 3 Ta/ 5 Py/5 Co90 Fe10 / 2.6 Cu/ 2.3 Co90 Fe10 / 0.7 Ru/ 2 Co90 Fe10 / 5 Ir–Mn/ 2 Ta 5 Ta/ 5 Py/1 Co/ 2.5 Cu/ t Co/ 0.9 Ru/ 1.5 Co/20 PtMn/ 5 Ta 9.3 PtMn/ 1.5 Co/ 0.8 Ru/ 2.5 Co/ 2.2 Cu/ 0.3 Co/t Py/ 3 Ta Ta/ 20 NiMn/ 2.2 Co90 Fe10 / 0.9 Ru/ 2.2 Co90 Fe10 / 2.4 Cu/ 1.2 Co90 Fe10 /2 Py/ Ta Ta/ Py/ Co90 Fe10 / Cu/ 2 Co90 Fe10 / 0.6 Ru/ 2 Co90 Fe10 / Ir–Mn/ Ta UL/ 3 Py/1 Co90 Fe10 / 2 Cu/ 2 Co90 Fe10 / 0.8 Ru/ 2.3 Co90 Fe10 / 20 PtMn

7.2 6.3 9.0 6.9 4.0 7.3 8.1 8.5 6.9 6.2 7.6 8.8 6.0 7.7 7.9 9.0

17.8 19.7

1.3 1.6

16.1 14.5

1.0 1.1

15.5

1.4

t = 2.5 nm t = 3 nm Study magnetization reversal

Lenssen et al. (1999a) Lenssen et al. (2000a) Sugita et al. (1999) Meguro et al. (1999)

Study magnetization reversal

Noma et al. (1999)

F = Co–Fe–B Ion beam sputtering

Kanai et al. (1999) Mao et al. (1999b)

Huai et al. (1999) [After 10 h anneal at 250 ◦ C] t = 1.5 nm Araki et al. (2000) t = 3.0 nm t = 2.5 nm Saito et al. (1999), t = 1.3 nm Hasegawa et al. (2000) Chen et al. (2000) Study reversal processes Partial specular reflection at the Co90 Fe10 / Ru interface


5 Ta/ (2.5 – x) Co/δX/x Co/ 3 Cu/ x Co/ δ X/ (2.5 − x) Co/ 8 Fe50 Mn50 / 2.5 Ta

ΔR/R (%) Rp,sh ( ) ΔRp,sh ( ) Remarks

Tong et al. (2000) Dieny et al. (2000a, 2000b) 33


System 20 Fe2 O3 / 2 Co90 Fe10 / 0.7 Ru/ 2 Co90 Fe10 / 2 Cu/ 0.5 Co90 Fe10 /3 Py/ 3 Ta 1.5 Ta/ 2.5 Py/5 Ir22 Mn78 / 2 Co90 Fe10 / 0.8 Ru/ 2.3 Co90 Fe10 / 2.3 Cu/ 1 Co90 Fe10 /BL/ 3 Ta Ta/ UL/ PtMn/ F/ Ru/ F/ Cu/ F/ Py/ BL/ Ta 5.5 UL/ 1 Py/ 1 Co90 Fe10 / t Cu/ 1.3 Co90 Fe10 / 0.4 Ru/ 1.1 Co90 Fe10 / 7 Ir–Mn / 5 Ta 5.5 UL/ 1 Py/ 7 Ir–Mn/ 1 Co90 Fe10 / 0.4 Ru/ 1.3 Co90 Fe10 / t Cu/ 1 Co90 Fe10 /1 Py/ 5 Ta 3 Ta/ 3.2 Py/ 1.6 Co90 Fe10 / 2.8 Cu/ 3 Co90 Fe10 / 0.7 Ru/ 1.5 Co90 Fe10 /9 Ir–Mn

34

TABLE 2.1 (continued) ΔR/R (%) Rp,sh ( ) ΔRp,sh ( ) Remarks 9.4

25.5

2.4

7.9 (4.2) 9.5 9.5 9.6 11.9 11.7 9.0

22.8 (26.2) 15.7 28.4 22.9 35.3 26.5

1.8 (1.1) 1.5 2.7 2.2 4.2 3.1

Reference Kawawake et al. (2000)

BL = 1 Cu (no BL) F = Co-alloy Ultrathin Cu: t = 0.95 nm t = 1.6 nm Ultrathin Cu: t = 1.04 nm t = 1.8 nm Study magnetization reversal

Huai et al. (2000) Ueno et al. (2000) Jo and Seigler (2002a) Jo and Seigler (2002b) Park et al. (2002)

55 NiO/ 2.5 Co82 Fe18 / 0.6 Re/ 2.2 Co82 Fe18 / 2.2 Cu/ 3.7 Py/0.6 Re/1 Co82 Fe18 / 2 Ta 1.5 Ta/ 2.2 Py/0.6 Ru/2.5 Py/ 0.5 Co82 Fe18 / 2.5 Cu/ 2.5 Co82 Fe18 / 0.6 Ru/ 2.0 Co82 Fe18 / (4–10) Ir22 Mn78 / cap layer Al2 O3 / 9.3 PtMn/ 1.5 Co/ 0.8 Ru/ 2.5 Co/ 2.2 Cu/ 0.3 Co/3 Py/0.8 Ru/2 Py/ 3 Ta 5 Ta/ 2 Py/0.8 Ru/2 Py/1 Co/ 2.5 Cu/ 2 Co/ 20 PtMn/ 5 Ta 9.3 PtMn/ 1.5 Co/0.8 Ru/2.5 Co/ 2.2 Cu/ 0.3 Co/3 Py/0.8 Ru/2 Py/ 3 Ta

7.3

Veloso et al. (1999)

4.9

Veloso and Freitas (2000)

8.1 7.5 8.0

17.3

1.3

Study Sy-AF and Sy-F coupling Saito et al. (2000) field and thermal stability Araki et al. (2000) Hasegawa et al. (2000), Saito et al. (2000)

(f) SVs with an oxidic AF 50 NiO/ 5 Py/ 2 Cu/ 5 Py 50 NiO/ 1 Py/ 4 Co/ 2 Cu/ 0.3 Co/5 Py 30 Ni50 Co50 O/ 3 Py/ 1.5 Co/ 2.2 Cu/ 1.5 Co/6 Py 75 NiO/ 3 Py/ 2 Co/ 1.7 Cu/ 2 Co/5 Py 50 NiO/ 2.5 Co/ 1.9 Cu/ 3 Co 50 NiO/ 2 Co/ 2 Cu/ 3 Co/ 1.2 Cu/ 10 NiO 50 NiO/ 2 Py/ 2 Cu/ 3 Py/ 1.2 Cu/ 10 NiO 50 NiO/ 5 Co/ 2.2 Cu/ 5 Co

4.3 7.5 6.0 13.5 16.2 (19.0) 15.0 5.5 15.0

Study coupling across Cu, interface “dusting” with Co

≈ 33 ≈ 36

≈ 4.9 ≈ 2.0

(O2 in chamber during growth) ΔR/R = 27% at 10 K ΔR/R = 14% at 10 K

Hoshiya et al. (1994) Lin et al. (1994a) Anthony et al. (1994) Egelhoff et al. (1996a, 1997a, 1997b) Swagten et al. (1996, 1998) Kitakami et al. (1996) (continued on next page)

R. COEHOORN

(e) SVs with synthetic ferromagnetic (Sy-F) free layer


50 NiO/ 4 F / 3.2 Cu/ 2 F/5.5 Py/ 10 Ta 50 NiO/ 3 Co90 Fe10 / 2 Cu/ 0.8 Co90 Fe10 /4.2 Ni66 Fe16 Co18 / 1.5 Ta 50 Fe2 O3 / 2 Co/ 2 Cu/ 5 Co/ 0.4 Cu 50 NiO/2.5 Co/ 2 Cu/ 3 Co/ CL NiO/ 2.4 Co/ 2.5 Cu/ 4 Co/ 1 Ta NiO/ 2 F/ 2.6 Cu/ 1.6 F/ 5 nm Si–N 50 Fe2 O3 / 3 F/ 2.3 Cu/ 3.1 F/ 5 Au

7.6 10.0 4.5 6.0 [8.2] 14.0 18.0 16.0 16.7 (16.0) (14.0) 9.7 7.9 5.8 3.6 16.1 5.0

11.8 12.0

1.9 0.6

t = 1 nm t = 0 nm F = (Co90 Fe10 )0.9 B0.1 [After 3 h anneal at 250 ◦ C] Small free layer coercivity α-Al2 O3 (110) substrateg glass substrate CL = 0.5 ML oxygenc (CL = 0.4 nm Au) (no CLc ) Ion Beam Deposition F = Co90 Fe10 F = (Co90 Fe10 )0.95 B0.05 F = (Co90 Fe10 )0.90 B0.10 F = Cog F = Ni80 Fe20 g

Reference Hasegawa et al. (1996) Kanai et al. (1997) Kools et al. (1998b) Sugita et al. (1998), Kawawake et al. (1999) Egelhoff et al. (1999) Slaughter et al. (1999) Shirota et al. (1999) Bae et al. (2000a)

(g)–(i) SV with NOL in pinned layer and/or near free layer 5 Ta/ 1.5 Ru/ 1 Cu/ NOL1/ 1 Cu/ 2 Co90 Fe10 / 2 Cu/ 2 Co90 Fe10 / NOL1/ 1.5 Co90 Fe10 / 7 Ir–Mn/ 5 Ta 5 Ta/ 2 Py/ 7 Ir–Mn/ 1 Co90 Fe10 F/ NOL1/ 1 Co90 Fe10 / 2 Cu/ 2 Co90 Fe10 / 1 Cu/ NOL2/ 2 Ta 3 Ta/ 1.5 Ru/ 1 Cu/ NOL1/ 1 Cu/ 2 Py/ 1 Co/ 2 Cu/ 2 Co / NOL3/ 1 Co/ 0.9 Ru/ 3 Co–Cr/ 10 PtMn/ 5 Ta 5 Ta/ 2 Py/ 7 Ir–Mn/ pinned layer + NOL1/ 2 Cu/ 2 Co90 Fe10 / 0.4 Co–Fe–O/ 0.4 Ta 7 Ta/ 5 Py/ 9 Ir–Mn/ 1.4 Co90 Fe10 // Ox// 2.5 Co90 Fe10 / 2 Cu/ 2.6 Co90 Fe10 // Ox// 2 Ta 3 Ta/ 15 PtMn/ 1–2 Co90 Fe10 / NOL/ 1–2 Co90 Fe10 / 2 Cu/ 1–2 Co90 Fe10 / NOL/ 3 Ta 3 Ta/ 15 PtMn/ 1–2 Co/ 0.7 Ru/ 1–2 Co/ NOL/ 1–2 Co/ 2 Cu/ 2 (Co90 Fe10 /Py)/ NOL/ 3 Ta

NOL1 = 1 nm Co–Fe–O

18.0 17.0

Kamiguchi et al. (1999a)

NOL2 = 1 nm Cu–Ta–O

17.0

NOL3 = 1 nm CoO Pinned layer and NOL1 not specified

16.0 13.0

14.6

1.9

14.5

17.9

2.6

thickness NOL = 1.4 nmd

11.3

25.7

2.9

thickness NOL = 1 nmd

Kamiguchi et al. (1999b) Veloso et al. (2000)


50 NiO/ 5 Co/ 2.2 Cu/ 5 Py 100 Fe2 O3 / 6 − t Py/ t Co/ 2.2 Cu/ t Co/ 9 – t Py/ 5 Ta


Sakakima et al. (2000a, 2000b)

35


36


UL/ Pd–Pt–Mn/ F/ Ru/ F/NOL/ F/ Cu/ 1.5 F/ Cu/ Al2 O3 UL/ Pd–Pt–Mn/ F/ Ru/ F/ 2 Cu/ 1.5 F/ Cu/ Al2 O3 60 NiO/ 5 Py/ 0.7 Co/ 2 Cu/ 7 Py// Ox 2 Ta/ 3 Py/ 7 Ir–Mn/ 2 Co90 Fe10 // Ox // 2 Co90 Fe10 / 2 Cu/ 2 Co90 Fe10 / 1 Cu/ 1 TaOx 2 Ta/ NOL/ 2.5 Py/1 Co90 Fe10 / 2 Cu/ 3 Co90 Fe10 / 7 Ir–Mn/ 2 TaOx

Rp,sh ( )

ΔRp,sh ( )

12.0 (8.0) 11.8 (8.2) 13.0

14.2 (15.0) 15.2 (14.6) 37.0

1.7 (1.2) 1.8 (1.2) 4.8

10.0 (8.1) 13.8 (10.5) (7.7)

42.0 (40.0) 15.9 (16.2) (20.8)

4.2 3.2 2.2 (1.7) (1.6)

11.0 (8.0) 13.0

13.1

1.7

12.1

18.2

2.2

9.8 12.2

27.0 19.5

2.6 2.4

12.2 (8.5) 11.9

27.9 (29.4) 21.8

3.4 (2.5) 2.6

9.0 (5.6) 7.3 (4.9) 13.3

26.7

2.4

22.6

3.0

12.0 (8.6)

28.5 (29.5)

3.4 2.5

Remarks thickness NOL = 1.0 nmd (no NOL) NOL not specified. (No NOL)

Reference

Araki et al. (2000), Tsuchiya et al. (2000) Gillies et al. (2001)

Lin and Mauri (2001) (no Al2 O3 layers) F = 2.5 Py/ 1.5 Co90 Fe10 (No oxidation, F = 4 Py) Study thermal stability due to Ta/Ni–Fe–Cr underlayer. Ru–O functions as AF coupling layer and as NOL Ion Beam Deposition. Various oxidation methods. NOL = Co–Fe–O or Fe–O NOL = 1–2 nm Co90 Fe10 -O (no NOL) F = Co–Fe–B;a NOL not specified. (cap = Cu/Taa ) 80 days natural oxidation

Li et al. (2001a) Sugita et al. (2001)

Sant et al. (2001) Uhlig et al. (2001) Hong et al. (2001)

Kim et al. (2001) Gibbons et al. (2001)

NOL = 1–2 nm Co90 Fe10 -O (continued on next page)

R. COEHOORN

3 Ta/ 15 PtMn/ 2 Co90 Fe10 / NOL/ 2 Co90 Fe10 / 2 Cu/ 5 Co90 Fe10 / 3 Ta 5 Ta/ 2 Py/ NOL / 1 Py/2 Co90 Fe10 / 2.5 Cu/ 2 Co90 Fe10 / NOL/ 1 Co90 Fe10 / 10 Ru–Rh–Mn/ 5 Ta 3.5 Ta/ 2 Py/ 8 Ir–Mn/ 3 Co90 Fe10 // Ox// 3 Co90 Fe10 / 2.5 Cu/ 4 Co90 Fe10 // Ox 3.5 Ta/ 2 Py/ 8 Ir–Mn/ 3 Co90 Fe10 / 2.5 Cu/ 4 Co90 Fe10 // Ox (3.5 Ta/ 2 Py/ 8 Ir–Mn/ 3 Co90 Fe10 / 2.5 Cu/ 4 Co90 Fe10 / 3.5 Ta) 3 Al2 O3 / 3 Ni–Fe–Cr/ 1 Py/ 20 PtMn/ 2 Co90 Fe10 / 0.8 Ru/ 2.2 Co90 Fe10 / 2.2 Cu/ 0.9 Co90 Fe10 /2.7 Py/ 0.8 Cu/ 1 Al2 O3 / 6 Tah 3 Ta/ 20 PtMn/ 2 Co90 Fe10 / 0.8 Ru/ 2.2 Co90 Fe10 / 2.2 Cu/ 0.9 Co90 Fe10 /2.7 Py/ 0.8 Cu/ 6 Tah 2 Ta/ 3 Py/ 6 Ir–Mn/ 1.5 Co90 Fe10 // Ox// 2 Co90 Fe10 / 2.2 Cu/ 2 Co90 Fe10 /F// Ox// 4 Ta UL/ 15 PtMn/ 2 Co90 Fe10 / 0.7 Ru/ 2.5 Co90 Fe10 / 2.5 Cu/ 1 Co90 Fe10 /1 Py/ NOL/ 1 Cu/ 3 Ta UL/ 15 PtMn/ 2 Co90 Fe10 / 0.7 Ru// Ox// 3 Co90 Fe10 / 2.5 Cu/ 2 Co90 Fe10 / 1 Cu/ 3 Ta 2 Ta/ NOL/ 1 Py/2 Co90 Fe10 / 2.4 Cu/ 2 Co90 Fe10 / 6 Ir–Mn/ 2 Ta 5 Ta/ 2 Py/ 7 Ir–Mn/ 2 Co90 Fe10 // Ox// 2 Co90 Fe10 / 2 Cu/ 2 Co90 Fe10 / 1 Cu / 1 Ta 2 Ta/ NOL/ 2.5 Py/1 Co90 Fe10 / 2 Cu/ 3 Co90 Fe10 / 7 Ir–Mn/ 2 TaOx

ΔR/R (%)


3.5 Ta/ 2 Py/ 8 Ir–Mn/ 3 Co90 Fe10 // Ox // 3 Co90 Fe10 / 2.5 Cu/ 4 Co90 Fe10 // Ox // Al 3 Ta/ 2 Py/ 10 PtMn/ 1.5 Co90 Fe10 / 0.8 Ru// Ox// 2 Co90 Fe10 / 2 Cu/ 2 Co90 Fe10 / 1 Cu/ 1 TaOx 5 Ta/ 2 Py/ 7 Ir–Mn/ 2 Co90 Fe10 // Ox // 2 Co90 Fe10 / 2 Cu/ 2 Co90 Fe10 / 1 Cu/ 1 Ta UL/ 7 Ir–Mn/ Co90 Fe10 // Ox // 2 Co90 Fe10 / 2.2 Cu/ 2 Co90 Fe10 / 1 Cu/ 1 Ta// Ox//

3 Ta/ 2 Py/ 6 Ir–Mn/ 1.5 Co90 Fe10 // Ox // 1.5 Co90 Fe10 / 2 Cu/ Co90 Fe10 // Ox // 1 Ta 3 Ta/ 2 Py/ 6 Ir–Mn/ 1.5 Co90 Fe10 // Ox // 1.5 Co90 Fe10 / 2 Cu/ 1 Co90 Fe10 /2 Py/1.2 Co90 Fe10 // Ox // 1 Cu/ 1 Ta 3 Ta/ 2 Py/ 6 Ir–Mn/ 3 Co90 Fe10 / 2 Cu/ 1 Co90 Fe10 /2 Py/1 Co90 Fe10 / 1 Cu/ 1 Ta 25 Fe2 O3 / 3 Co/ 2.3 Cu/ 3.1 Co/ 2.5 Ta2 O5 3.5 Ta/ 2 Py/ 6 Ir–Mn/ 1.5 Co90 Fe10 // Ox // 2 Co90 Fe10 / 2.2 Cu/ 1 Co90 Fe10 / 1 Cu/ Co90 Fe10 // Ox// 3 Ta 3.5 Ta/ 2 Py/ 6 Ir–Mn/ 3.5 Co90 Fe10 / 2.2 Cu/ 4 Co90 Fe10 / 3 Ta 2 Ta/ 2 Py1−x Crx / 12 PtMn/ 1.9 Co90 Fe10 / 0.8 Ru/ 1 Co90 Fe10 // Ox// 2 Co90 Fe10 / 2.1 Cu/ 2 Co90 Fe10 / 1 Cu/ 1 Ta–O 6.7 Ta/ 4.2 Py/ 9 Ir–Mn/ 1.4 Co90 Fe10 // Ox // 1.5 Co90 Fe10 / 2.2 Cu/ 4 Co90 Fe10 // Ox // 3 Ta UL/ Co90 Fe10 // Ox // 2.5 Py/1 Co90 Fe10 / 1.9 Cu/ 3 Co90 Fe10/ 7 Ir–Mn/ 2 Ta Ta/ 2.5 Py/1 Co90 Fe10 / 1.9 Cu/ 3 Co90 Fe10 / 7 Ir–Mn/ 2 Ta

10.4 13.1 (6.5) (8.6) 14.0

23.1 (24.6)

14.9

22.1

15.5 (12.0) 17.0 (13.0) (12.9) (9.4) 15.3∗ 13.1∗ 14.2∗∗ (9.0)∗

2.4 (1.6)

20.0 (21.5) (20.2) (22.3)

32.0∗

3.3

3.4 (2.8) (2.6) (2.1)

4.5∗

16.0 14.5 (8.0) 16.1 15.0 (12.5)

22.7 20.1 (21.8)

3.7 3.0 (2.7)

12.5 (5.9) 12.5

28.3

3.5

(8.4)

(30.2)

(2.5)

Reference

Ion-beam sputtered, IBS Magnetron sputtered, MS (no oxygen exposure, IBS) (no oxygen exposure, MS) Al–O via solid state reaction; low-coercivity free layer. very low Hc

Lee et al. (2001)

Study oxidation methods. (No oxidation)

Kools et al. (2001)

Gillies et al. (2001) Mizoguchi and Kano (2001)

Fukuzawa et al. (2001b) (no NOL near free layerf ) (no NOL in pinned layer) (no NOLs)f * From fig. 1 in reference.

Li et al. (2001b)

** From fig. 2 in reference.

High coercivity. MRAM cell.g Study effect of variation thicknesses free layer and Cu back layer Plasma oxidation Natural oxidation No NOL in pinned layer. Study read heads. Study temperature dependence MR Study oxides of Ta, Co90 Fe10 , Py, Py1−x Crx , Cr, Cu, Ta, Nb, Al as NOL; varying Cu layer thickness

Bae et al. (2001a, 2001b) Lu et al. (2002a) Huai et al. (2002)

Sousa et al. (2002)


3 Ta/ 1 Cu/ 8.5 Ir–Mn/ 1 Co90 Fe10 // Ox // 2.3 Co90 Fe10 / 2.4 Cu/ 1.6 Co90 Fe10 /2.2 Py/ 3.5 Ta


Mao et al. (2002)

37


38

TABLE 2.1 (continued) System 3 Ta/ Co90 Fe10 // Ox// 1.5 Co90 Fe10 / 2.2 Cu/ 3 Co90 Fe10 / 8 Ir–Mn/ 2 Ta 3 Ta/ 2 Py/ 6 Ir–Mn/ 2.5 Co90 Fe10 / 2.2 Cu/ 1.5 Co90 Fe10 /3 Py/ 2 Cu/ Al–O/ 1 Ta 2 Ta/ 2 Py–Cr/ 12 PtMn/ 1.9 Co80 Fe20 / 0.8 Ru/ 1 Co90 Fe10 / NOL/ 2 Co90 Fe10 / 2.1 Cu/ 2 Co90 Fe10 / 1 Cu/ 1 TaOx UL/ 10 PtMn/ (Sy-AF+NOL)/ Cu/ Co90 Fe10 / Cu/ Ta–O

PtMn/ F/ Ru/ F/ Cu/ F/ Cu/ NOL 3.2 Ni–Fe–Cr/ 0.8 Py/ 8 PtMn/ 1.6 Co90 Fe10 / 0.8 Ru/ NOL1/ 2.2 Co90 Fe10 / 1.9 Cu/ 2.2 Co90 Fe10 / 0.6 Cu/ NOL2/ 1 Ta UL/ 10 PtMn/ F/ 0.8 Ru/ 1.8 Co90 Fe10 / 1.9 Cu/ 2 Co90 Fe10 / NOL

10.8

33.3

3.6

8.4

27.4

2.3

16.0

23.1

3.7

17.8

18.5

3.3

15.0 (8.0) 10.1 10.4 14.2 (11.8) 20.5 20.5 20.0

20.1 17.6

4.1 3.6

Reference

Comparison oxides of Py, Al, Ta, Co90 Fe10 , Ta as NOL

Li et al. (2002b)

Plasma oxidation. Study thermal stability. Study head performance and reliability t = 1.5–4 nm. Study structure NOLs. Top NOL: Al–O via solid state reaction. Study NOL as a Mn diffusion barrier Study oxidation in mixed gasses NOL = 1.5 nm FeOx . MR from 0–300 K (No NOL)

Diao et al. (2002)

NOL1 = 0.6 nm air oxidized Co90 Fe10 . NOL2 = 1 nm plasma oxidized Al F layer (high resistivity) and NOL not specified

Hasegawa et al. (2002) Shen et al. (2002) Jang et al. (2002a) Jang et al. (2002b) Kato et al. (2002) Hong et al. (2002) Tsunekawa et al. (2002) Li et al. (2002c)

a No layer thicknesses given in paper. b Study spin-dependent electron mean free paths. Only ΔG given. sh c Submonolayer oxygen coverage results from partial oxygen pressure p(O ) = 5 × 10−9 Torr during sputter deposition. Reference system (“no cap”) produced in 2 p(O2 ) < 2 × 10−10 Torr. d NOL sputtered from magnetic oxide target. e No comments given in paper on possible role of Al O . 2 3 f 3 nm Ta cap layer. g α-Fe O does not give rise to an exchange bias, but to a large coercivity of the pinned layer. 2 3 h In the publication the thickness of the Cu back-layer is given as “8 nm”. It is assumed that 8 Å (0.8 nm) is the actual thickness.

R. COEHOORN

3.5 Ta/ 2 Py/ 6 Ir–Mn/ 1.5 Co90 Fe10 // Ox // 2 Co90 Fe10 / 2.2 Cu/ t Co90 Fe10 // Ox // 3 Ta 3.5 Ta/ 2 Py/ 6 Ir–Mn/ 3.5 Co90 Fe10 / 2.2 Cu/ 4 Co90 Fe10 / 3 Ta 5.0 Ta/ 2 Py/ 8 Fe50 Mn50 / 2 Co90 Fe10 // Ox // 2 Co90 Fe10 / 2.6 Cu/ 1.5 Co90 Fe10 /4.5 Py/ 5 Ta 5.0 Ta/ 2.5 Py/ 7 Fe50 Mn50 / 2.5 Co90 Fe10 // Ox // 1.5 Co90 Fe10 / 2.6 Cu/ 1.6 Co90 Fe10 / 4.5 Py/ 5 Ta 3.0 Ta/ NOL/ 2 Py/ 1 Co/ 2.2 Cu/ 2 Co/ 15 PtMn/ 3 Ta



39

If grown with a strong [111] texture, the exchange bias field by Fe50 Mn50 is optimal. Bottom spin-valves based on (111) Fe50 Mn50 can be made by making use of a thin Ta/Py buffer layer (Lenssen et al., 1996). A disadvantage of Fe50 Mn50 as an exchange biasing material is the relatively strong decrease with increasing temperature of the exchange bias field. Heb becomes zero at blocking temperatures in the range Tb = 140–190 ◦ C (table 4.3). Several other AF materials show higher blocking temperatures. E.g., Ir20Mn80 random substitutional AF alloys give rise to Tb = 240–290 ◦ C. An advantageous property of this alloy is that, like Fe50 Mn50 , the exchange bias field can already be obtained by deposition in a field at room temperature. Ordered PtMn compounds, obtained after annealing the asdeposited SVs during 5–20 hours at typically 260 ◦ C, give rise to blocking temperatures in the range 350–400 ◦ C. The use of oxidic AF materials can give rise to an enhanced GMR ratio due to partially specular scattering, as discussed in section 2.1.6. An overview of the preparation and properties of AF exchange bias layers that are suitable for applications in spin-valves is given in section 4.6. A summary is provided by table 4.7. For Py pinned and free layers, the MR ratio obtained at the optimal layer thicknesses is about 5% at room temperature. Early studies in which Py was replaced by Co led to MR ratios around 9% (see table 2.1), however, at the expense of an increased coercivity. The larger MR ratio for Co-based systems, at room temperature and at 4.2 K (fig. 1.8), results from the larger majority-spin mean free path in Co and the larger spin-dependence of the interface scattering (see section 3.6.5). Optimization of the sputter deposition conditions for each of the layers separately has led to an MR ratio above 11% for Co/Cu/Co/Fe50 Mn50 spin-valves (Stobiecki et al., 2000). The magnetoresistance of simple spin-valves in which the same basic structure is repeated is essentially equal to that of a single sequence (Dieny et al., 1991c), because the high resistivity of antiferromagnets such as Fe50 Mn50 (see table 4.7) leads to a very large probability of diffusive scattering of electrons in that layer. 2.1.2. Spin-valves with composite ferromagnetic layers (fig. 2.1(b)) It is often advantageous to make use of composite F layers that are made of two or more strongly ferromagnetically exchange coupled F layers with different compositions. The most important example is the use of composite free layers that consist of a combination of a permalloy sublayer, in order to improve its magnetic softness, and a Co or Co90 Fe10 sublayer at the interface with the Cu spacer layer, in order to obtain an enhanced MR ratio and thermal stability. As demonstrated by Parkin (1993), a very thin Co “dusting” layer at the Py/Cu interfaces in Py/Cu/Py/Fe50Mn50 spin-valves can already lead to a drastic increase of the MR ratio. Fig. 2.2 shows that the MR ratio for spin-valves with the basic structure (5.3 nm Py/ 3.2 nm Cu/ 2.2 nm Py/ 9.0 nm Fe50 Mn50/ 1 nm Cu) can be increased from 2.9% at room temperature, without dusting layers, to 6.4% when only 0.6 nm Co replaces Py at the interfaces. Anthony et al. (1994) found that Co dusting of Py layers can even lead to ΔR/R = 9%, as high as the ratio observed for similar Co/Cu/Co/Fe50 Mn50 spin-valves. Adding Py dusting layers of only 0.4 nm to the Co/Cu interfaces of Co/Cu/Co/Fe50 Mn50 spin-valves was found to decrease the MR ratio from 6.8% to 3.9% (see Parkin (1993) for details of the layer structures). The beneficial effect of Co was seen to be strongly localized at the interfaces. Upon varying the position of 0.5 nm Co layers that were buried in

40

R. COEHOORN

Fig. 2.2. Dependence of the room temperature MR ratio on the thickness of Co “dusting” layer at the interfaces between the F and NM layers, for SVs with the layer structure (Si/ (5.3 – tCo ) nm Py/ tCo nm Co/ 3.2 nm Cu/ tCo nm Co/ (2.2 – tCo ) nm Py/ 9 nm Fe50 Mn50 / 1 nm Cu). From Parkin (1993).

the Py layers no significant increase of the MR ratio was found for distances to the Py/Cu interface larger than 0.6 nm. This experiment nicely demonstrated the crucial role played by the interfaces. The effect of Co is twofold (Coehoorn, 1993; Nicholson et al., 1994; Butler et al., 1995; see also sections 3.1 and 3.2). First, the diffusive minority spin scattering at imperfect Co/Cu interfaces is stronger than at equally rough Py/Cu interfaces, due to the larger mismatch of the minority spin d bands. The minority spin 3d-band-filling for Py and Co is 1.1 and 1.6 electron, respectively, less than for Cu. The scattering potential at Co/Cu interfaces is then larger, leading to a larger scattering probability. Second, one should take into account that magnetic moments at interfaces are not always equal to those in the bulk of the layers. As discussed in section 3.2, Ni magnetic moments at Ni/Cu interfaces are, already for sharp interfaces at T = 0, more strongly decreased by the presence of non-magnetic Cu neighbours than Co moments at Co/Cu interfaces. The negative effect of Cu neighbours on the Ni moments is enhanced by the relatively diffuse character of the interfaces, resulting from the good miscibility of Ni and Cu. Co and Cu are immiscible. In addition, at finite temperatures thermal fluctuations are larger for Ni moments, reflecting the lower magnetic ordering temperature. Consistent with these considerations, Speriosu et al. (1993) observed a substantial decrease of the room temperature magnetization of permalloy near the interface with Cu, effectively corresponding to a “dead layer thickness” of 0.2 ± 0.016 nm. For Co/Cu interfaces, a dead layer thickness of only 0.1 ± 0.02 nm was observed. Theoretical and experimental evidence for a significant moment reduction at the Py/Cu interface has also been given by Nicholson et al. (1994). The majority spin partial density of states of magnetic atoms at the interface has then 3d-character at the Fermi level, resulting in enhanced scattering of majority spin electrons at the interface. That reduces the GMR ratio. Gurney et al. (1993) used spin-valves with composite F layers to derive the spindependent mean free paths in Py and Co “back layers” (B) in structures of the type Fe50 Mn50/Py/Cu/Py/B. The Py part of the free layer fulfills the role of a spin-filter layer. The results and the analysis are given in section 3.6.6. The method was also used for studying non-magnetic back layers. The presence of Co layers at the interface improves the thermal stability. Although that effect is enhanced by making the dusting layer thicker, one is limited by the increase of


41

Fig. 2.3. Magnetoresistance curves of (5 nm Ta/ 2 nm Py/ 5.5 nm F/ 3.2 nm Cu/ 5.5 nm F/ 15 nm Fe50 Mn50 ) SVs, with F = Co90 Fe10 (a) or F = Co (b). From Kanai et al. (1996).

the coercivity with increasing Co layer thickness. Kanai et al. (1996) showed that it is more favorable to use Co90 Fe10 instead of Co. As shown in fig. 2.3, the resulting MR ratio is higher for an otherwise similar structure and, even more importantly, the coercivity is much smaller. The authors attributed the effect to the much smaller magnetostriction of Co90 Fe10 , and proved that it was essential that the Py part of the free layer induced a strong [111] texture in the Co90 Fe10 layer. (Co90 Fe10 )1−x Bx boron-containing alloys with x 0.2 are amorphous, and are therefore expected to be magnetically very soft. Attempts to obtain high MR ratios in spinvalves based on such alloys, or on other B-rich amorphous alloys, were unsuccessful (Wu et al., 1998; Feng and Childress, 1999). This is due to the high resistivity for both spin directions. A different approach was introduced by Kamiguchi et al. (1996), who used an amorphous Co–Nb–Zr alloy as a very soft but high resistive underlayer for enhancing the [111] texture of a composite Py/Co90 Fe10 /Cu/Co90 Fe10 /Fe50 Mn50 spin-valve, leading to a low-coercivity (0.01 kA/m) and high-sensitivity (17.8%/kA/m, or 1.4%/Oe). The highest MR ratios within this class of layer-stacks were obtained by Dieny et al. (2000a, 2000a) and Mao and Gao (2000a), viz. 12.0% and 14.7% for PtMn-based SVs. From a modeling study Dieny et al. explained the high MR ratio as the result of partial specular reflection (instead of diffusive scattering) at the Co90 Fe10 /PtMn interface (see section 3.6.5). The use of composite pinned layers can be of interest for enhancing the exchange bias field, e.g., in the combinations (Co90Fe10 )80 B20 /Py/Fe50 Mn50 (Fujita et al., 1997) or Co90 Fe10 /Co60 Fe40 /Ir–Mn (Childress et al., 2001). 2.1.3. Spin-valves with a non-magnetic back layer (“spin-filter spin-valves”, fig. 2.1(c)) Spin-valves of the type AF/F/NM/F/B with magnetic and non-magnetic “back layers” (B) were introduced by Gurney et al. (1993), with the purpose to derive the spin-dependent mean free paths in the back layer (see section 3.6.6). Replacement of a part of the free layer with an optimal layer thickness by a thin NM back layer does not lead to a decrease of the GMR ratio, provided that the scattering probability of minority-spin electrons that have crossed the spacer layer is 100% (due to strong interface scattering or due to bulk

42

R. COEHOORN

scattering when the layer thickness is larger than the minority spin mean free path). The F layer acts then as a perfect spin-filter for electrons that finally enter the back layer. This has led to the alternative term “spin-filter spin-valves” (SFSVs). In order to prevent an adverse effect on the GMR ratio by current shunting, typical Cu back layers have a thickness of only 1–1.5 nm. It has been recognized that the use of a NM back layer in spin-valves for sensor applications can give rise to several advantages (Fukuzawa et al., 1998, 2001a; Huai et al., 2000; Ueno et al., 2000): • SFSVs can show a large GMR effect at a very small effective magnetic thickness of the free layer (F layer thicknesses that would be suboptimal when no back layer is used), a property which is advantageous for read head applications (see section 1.6.1). • A very thin Co90 Fe10 free layer in between the Cu spacer layer and a Cu back layer is magnetically relatively soft. Making use of composite Py/Co90 Fe10 free layers for enhancing the softness would then not be necessary, leading to an enlarged thermal stability. • The presence of the Cu back layer shifts the center of the current density distribution away from spacer layer towards the center of the free layer, thereby reducing the sensecurrent induced field that acts on the free layer. • When an oxidic specular reflection layer is used at the outer boundary (see section 2.1.7) the presence of a Cu back layer prevents oxidation of the free layer. NM back-layers have been studied in combination with a number of other modifications of conventional simple spin-valves. The experimental data can be found in parts (c), (d), (f), (g) and (h) of table 2.1. Several authors have interpreted observed increases of the MR ratio due to the presence of noble metal cap layers on the free layer in a bottom SV (Egelhoff et al., 1997a) or on an F/NM/F trilayer (Sakakima et al., 1998) as the result of specular reflection at these cap layers. However, Wang et al. (2000) criticized this point of view, based on in situ studies of the magnetoconductance of Co/Cu layer systems, and have explained the increase of the MR ratio as a back layer effect. 2.1.4. Spin-valves with a synthetic antiferromagnetic (Sy-AF) pinned layer (fig. 2.1(d)) The magnetic stability of the pinned layer can be enhanced strongly by replacing the pinned layer by an antiferromagnetically coupled F/X/F bilayer, where X is a very thin interlayer that gives rise to strong antiferromagnetic interlayer exchange coupling. Van den Berg et al. (1996, 1997) proposed to replace the F/AF part of a spin-valve by a F/X/F trilayer, which they called “artificial antiferromagnet” (AAF). We will use the term “synthetic antiferromagnet” (Sy-AF), which has become more common. If the uniaxial magnetic anisotropy of at least one of the layers is strong, the magnetization of a Sy-AF is relatively stable against the application of a magnetic field (Zhu, 1999). However, a sufficiently large field can always be used to induce an irreversible switch between the two equivalent magnetic states of a Sy-AF with uniaxial anisotropy. Such a switch reverses the slope of the R(H ) curve near H = 0. As proposed by Heim and Parkin (1993) and others (see table 2.1), that problem can be solved by combining the Sy-AF with an AF exchange bias layer. In the remainder of this subsection we focus on such Sy-AF + AF spin-valves.


43

Fig. 2.4. Layer stack of a SV with a Sy-AF pinned layer (a), its magnetoresistance curve at 298 K (b) and the temperature dependence of the effective exchange bias field Heb,eff as compared to the exchange bias field of an otherwise identical conventional SV with a single 4 nm Co90 Fe10 pinned layer (c). Figures (b) and (c) are taken from Lenssen et al. (1999b) and Lenssen et al. (2000a), respectively. (Although the pinned layer structures are nominally identical, the effective exchange bias fields from both publications are slightly different.)

F1 /NM/F2 trilayers in which the two F layers have different coercivities, e.g., by making use of a Sy-AF, are called pseudo-spin-valves. These are discussed in section 2.4. Fig. 2.4 shows some of the results obtained by Lenssen et al. (1999a, 1999b, 2000a). The layer stack is given in fig. 2.4(a). The magnetoresistance curve (fig. 2.4(b)) shows a sharp increase near zero field, where the free layer reverses, followed at positive fields by a plateau where the 4 nm indirectly pinned Co90 Fe10 layer is antiparallel aligned with respect to the free layer. Above H ≈ 25 kA/m there is a wide field interval in which the AF coupling across the Ru layer is gradually broken. The magnetization directions of the indirectly pinned “reference layer” and the directly pinned “keeper layer” (following the terminology used by Lin and Mauri (2001)) rotate towards the direction of the applied field. The temperature dependence of the effective exchange bias field, Heb,eff is given in fig. 2.4(c). Heb,eff is defined as the field at which the resistance change has dropped to half the maximum value. For comparison, the figure also shows the exchange bias field Heb,CSV for conventional SVs with a single 4 nm Co90 Fe10 pinned layer. Heb,CSV decreases approximately linearly with temperature to the blocking temperature Tb ≈ 280 ◦ C of the Ir–Mn exchange

44

R. COEHOORN

bias layer. Evidently, the use of the Sy-AF strongly increases the effective exchange bias field at room temperature and even more at elevated temperatures. The enhanced field and thermal stability make these spin-valves excellent candidates for robust magnetic field and rotation sensors in, e.g., automotive systems (Lenssen et al., 2000b). A full analysis of the magnetization and transfer curves is given in section 4.1, where fig. 4.6 provides the definitions of the various critical fields that can be distinguished. A qualitative explanation of the experimentally observed enhanced thermal stability follows already from the results that are obtained for the limiting case of a large AF interlayer exchange coupling energy, J , as compared to the exchange bias interaction energy, Jeb . J is by definition equal to half of the energy (per unit area) that is required to change the relative alignment of the magnetization directions of the coupled layers from parallel to antiparallel (eq. (4.6)). The coupling between the directly and indirectly pinned layers is antiferromagnetic, so J < 0. Jeb is equal to half of the energy (per unit area) that is required to change the relative alignment of the pinned layer magnetization and the exchange bias field from parallel to antiparallel (eq. (4.4)). By definition, Jeb > 0. For a system with a fully compensated Sy-AF (two layers with equal Msat t products) and with negligible coupling across the Cu layer, one finds √ Heb,eff ∼ 2|J | 2/3 1 if |J | Jeb , − (2.1) = Heb,CSV Jeb 2 where Heb,CSV is the exchange bias field for a conventional SV with a pinned layer that has the same Msat t product as that of the layers forming the Sy-AF. The enhancement of the width of the high resistance plateau (indicated in fig. 2.4(b)) is in the strong coupling limit given by Hplat ∼ |J | 1/2 1 if |J | Jeb . − (2.2) = Heb,CSV Jeb 2 For the system studied by Lenssen et al. |J |/Jeb increases from ≈7 at room temperature to ≈20 at 200 ◦ C, because the decrease with temperature of Jeb (Co/Ir–Mn) is much stronger than that of J (Co/Ru/Co). The enhancement of the effective exchange bias field is therefore even larger at elevated temperatures than at room temperature. In the usual “crossed anisotropy configuration” (section 1.3) the magnetization direction of the pinned layer in a sensor stripe is perpendicular to the long axis. In conventional SVs, this gives rise to a demagnetizing field that destabilizes the pinning and that gives rise to a shift of the transfer curve. In contrast, for SVs with a fully compensated Sy-AF pinned layer the demagnetizing field is zero. Alternatively, the degree of compensation can be tuned by choosing directly and indirectly pinned layers with different Msat t products. For sufficiently narrow stripes this method can be used to obtain a certain desired positive or negative demagnetizing field in order to compensate for the interlayer magnetic coupling with the free layer. In a SV with a Sy-AF pinned layer the current density through the directly pinned F layer is usually not determined by the magnetic alignment, because diffusive scattering in AF coupling layers such as Ru is very strong. If the microstructure of the active part is the same as that of a reference conventional spin-valve, the use of a Sy-AF leads thus to a slight decrease of the MR ratio. However, the comparison becomes less straightforward if


45

specular scattering occurs at the AF bias layer in a CSV or at the AF coupling layer in the spin-valve with Sy-AF. Dieny et al. (2000a, 2000b) have found indications for both effects (see section 3.6.5). If required, the shunt conduction through the directly pinned F layer can be reduced by making use of an alloy layer with a higher resistivity than that of the reference layer (Li et al., 2002b). An intriguing novel opportunity for enhancing the change of the sheet resistance, ΔRsh , was demonstrated by Jo and Seigler (2002a, 2002b). They were able to fabricate SVs with a Sy-AF pinned layer in which down to Cu thicknesses well below 1 nm the coupling across the Cu spacer layer was predominantly due to the oscillatory interlayer exchange coupling. For bottom SVs with a Cu spacer layer thickness around 1.04 nm, where the coupling is weakly antiferromagnetic, they obtained an MR ratio of almost 12%, and ΔRsh = 4.2 . The results were obtained after an anneal treatment in a magnetic field at 220 ◦ C for 2 hours. Excellent control of the layer thickness uniformity and a small interface roughness are likely explanations for the relatively small contributions of the ferromagnetic pin-hole and “orange-peel” coupling (see section 4.5). However, the growth conditions and underlayer structure that have made it possible to realize this result have not yet been disclosed. The AF coupling layer is selected on the basis of the coupling strength (see Parkin et al., 1990; Parkin, 1991b; Saito et al., 2000; Beach et al., 2000) and the thermal stability upon annealing. Most groups consider Ru layers with thicknesses in the range 0.7–0.9 nm as most suitable for the coupling of Co layers or Co90 Fe10 alloy layers. The interlayer coupling parameter J for a (Co90 Fe10 / 0.8 nm Ru/ Co90 Fe10 ) Sy-AF can be as large as −1.5 to −1.7 mJ/m2 (Nagai et al., 1999; Park et al., 2002), although most groups find slightly lower values (e.g., J ≈ −0.95 mJ/m2 for (Co/0.8 nm Ru)n multilayers, Bloemen and van Kesteren, 1994). Jeb is typically 0.1 to 0.5 mJ/m2 (see table 4.7). The thermal stability of J has been investigated by Saito et al. (2000). Rh interlayers with a thickness of ≈0.8 nm give rise to large coupling (Parkin, 1991b; Saito et al., 2000), but the good miscibility of Co and Rh leads to a poor thermal stability (Manders et al. 1998). Re coupling layers have been used by Veloso et al. (1999) and Ir coupling has been investigated by Colis and Dinia (2002). 2.1.5. Spin-valves with a synthetic ferromagnetic (Sy-F) free layer (fig. 2.1(e)) Speriosu et al. (1996) proposed to realize more sensitive read heads by using spin-valves with a free layer that consists of an “synthetic ferromagnet” of the form of a F/X/F trilayer. As in a Sy-AF, X is a thin layer such as Ru that couples the two F layers antiferromagnetically. Of course, the trilayer must be ferromagnetic, not antiferromagnetic, so that the free layer remains sensitive to the externally applied field. However, by using a Sy-F the Msat t product can be reduced without reducing the physical thickness of the layer that is in contact with the spacer layer, i.e., without a large concurrent decrease of the MR ratio. This provides an alternative for the use of a non-magnetic back layer as a means to reduce the Msat t product (section 2.1.3). A second advantage is the possibility to completely compensate for the shape anisotropy of the free layer in a narrow stripe-shaped SV-element. This is accomplished by using a Sy-F free layer that is formed by F layers with a uniaxial in-plane anisotropy with the easy axes perpendicular to the stripe length (“transverse easy axes”, Coehoorn, 1999).

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2.1.6. Spin-valves with an oxidic antiferromagnet (fig. 2.1(f)) Studies of the magnetoresistance of spin-valves that are based on an oxidic antiferromagnet, such as NiO or Fe2 O3 , have led to the insight that scattering at the outer boundaries is not necessarily diffusive, but can be (partially) specular. Full specular reflection at both outer boundaries would make a spin-valve effectively equivalent to a multilayer. The reduction of diffusive boundary scattering leads to an increase of the GMR ratio and to a shift of the optimal F layer thicknesses to lower values. Results of model calculations of these effects are discussed in section 3.6.3. The first observations of a shift of the optimal F layer thickness to very low values, in combination with relatively high MR ratios, were obtained from studies by Anthony et al. (1994) of simple and dual NiO-based spin-valves. Egelhoff and coworkers were the first to suggest that specular reflection could play a role. When studying the optimal F layer thicknesses for NiO/Co/Cu/Co bottom SVs, they found that the optimum GMR ratio was obtained for a slightly thinner bottom Co layer (see table 2.1). Such an effect is expected when scattering at the NiO is partially specular. Strong support for this hypothesis was provided by experimental and modelling studies by Swagten et al. (1996, 1998). They investigated back-layer spin-valves of the type NiO/Co/Cu/Co/Cu/NiO and made a comparison with “standard” all-metal Fe50 Mn50 based spin-valves. The Cu back layer had the function to magnetically separate the top NiO layer from the free Co layer. The NiO layer directly on top of the substrate was deposited at 200 ◦ C to ensure a [111] texture of the layer stack. The remainder of the stack was grown at room temperature to avoid interdiffusion between the separate layers. Fig. 2.5 shows the free layer thickness dependence of the GMR ratio for NiO based and Fe50 Mn50 -based spin-valves, measured at 10 K. Results of a calculation using the Camley–Barnas model (section 3.5), assuming fully reflective and fully diffusive scattering at the outer boundaries, are in fair agreement with the experimental data. The highest GMR ratio in this class, 18% at room temperature, has been reported by Sugita et al. (1998) for (Fe2 O3 /Co/Cu/Co/Cu) spin-valves. The 50 nm α-Fe2 O3 AF layer was epitaxially grown on a flat polished (110) α-Al2 O3 single crystal substrate, which was argued to give rise to a very flat Fe2 O3 /Co interface and a high probability of specular scattering. This work strongly emphasizes the potential benefits of improving specular boundary scattering. As observed already by Hasegawa et al. (1996), Fe2 O3 layers do not give rise to an exchange bias. Instead, they induced a high coercivity of the pinned layer: Hc ≈ 100 kA/m in the experiments by Sugita et al. The magnetic structure is thus not stable with respect to high magnetic fields. Bae et al. (2000a, 2001b, 2001b) proposed to use the coercivity of the pinned layer in α-Fe2 O3 -based spin-valves for applications in magnetoelectronic devices, including an MRAM cell. The functioning of actual devices was demonstrated. Sakakima et al. (1999a) studied spin-valves based on AF perovskites of the type MFeO3 , with M = Y, La, Pr, Nd and Sm. Like α-Fe2 O3 , the perovskites induce coercivity, but no exchange bias. MFeO3 /Co/Cu/Co show MR ratios up to 11.4%. A disadvantage is the high substrate temperature (350 ◦ C) required during the deposition of the perovskite layers. CoO gives rise to a strong exchange bias field at temperatures well below the Néel temperature, TN = 18 ◦ C. However, this precludes practical applications at and above room temperature. In principle, the use of an oxidic antiferromagnet is also advantageous because of the absence of current shunting by the AF layer. The advantage can be derived from the ratio


47

Fig. 2.5. Closed circles: measured MR ratios of (50 nm NiO/ 2 nm Co/ 2 nm Cu/ tF2 nm Co/ 1.2 nm Cu/ 10 nm NiO) SVs, at 10 K. Closed squares: measured MR ratios of (10 nm Fe50 Mn50 / 2 nm Co/ 2 nm Cu/ tF2 nm Co/ 2 nm Cu) all-metal SVs, at 10 K. Solid curves: MR ratios calculated using the CB model for the system (oxide/ 2 nm Co/ 2 nm Cu/ 2 nm Co/oxide), as a function of the thickness of layer F2 , for specular reflection coefficients R = 0, 0.5 and 1 at the interfaces between the F layers and the oxide layers. Dashed-dotted curve: MR ratios calculated using the CB model for the system (10 nm Fe50 Mn/ 2 nm Co/ 2 nm Cu/ tF2 nm Co/ 2 nm Cu), with diffusive scattering at the outer boundaries (R = 0). The mean free paths used in the calculations are λ↑ (Co) = 8 nm, λ↓ (Co) = 2 nm, λ(Cu) = 20 nm and λ(Fe50 Mn50 ) = 1.2 nm, and the interface transmission coefficients ↑ ↓ used are TCo/Cu = 1 and TCo/Cu = 0.2. From Swagten et al. (1996).

of the sheet resistance of the total layer stack, which is usually in the range 15–25 (table 2.1), and the sheet resistance of the AF layer (see table 4.7). Let us assume that the sheet resistance of the active part is 20 , and that the sheet resistance of the AF layer is equal to the value RAF,sh,min = ρAF /tAF,min , given in table 4.7, for an AF layer with the minimal possible thickness for obtaining the exchange bias effect. It follows that shunting by, e.g., Ir–Mn, Fe50 Mn50 and NiMn decreases the MR ratio by typically 3, 11 and 21%, respectively. Early studies of spin-valves based on NiO were primarily motivated by the expected higher thermal stability of the exchange bias field as compared that of Fe50 Mn50, in view of the higher Néel temperature (252 ◦ C versus 230 ◦ C, respectively). Indeed, the blocking temperature of NiO based systems was found to be higher than for Fe50 Mn50 based systems (180–230 ◦ C versus 140–190 ◦ C, see table 4.7). The excellent corrosion resistance is another advantage. Kools et al. (1998b) developed NiO based spin-valves with an optimized combination of a high MR ratio (14%), a high sensitivity of 11%/ (kA/m) and a small coercivity (Hc ≈ 0.1 kA/m) by making use of a compound free layer. Several groups have demonstrated hard disk read-heads based on NiO spin-valves (Hamakawa et al., 1996; Nakamoto et al., 1996; Pinarbasi et al., 2000). However, at present AF materials that are thermally even more stable, such as PtMn or Ir20Mn80 , are regarded as more suitable for that application.

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2.1.7. Spin-valves with nano-oxide layers (NOLs) in the pinned layer and/or near the free layer (fig. 2.1(g)–(i)) An extremely fruitful novel concept was developed by Kamiguchi et al. (1999a, 1999b). They introduced very thin specularly reflecting oxide layers (“nano-oxide layers”, NOLs) inside the pinned layer and near the free layer of SVs and obtained for such “double specular” SVs enhanced MR ratios up to 18%. NOLs are formed by the oxidation of an already deposited magnetic layer, by the deposition of a (magnetic) oxide layer, or by a solid-state reaction (see below). Across NOLs in the pinned layer a strong exchange coupling should be retained, in order to retain a large effective exchange bias field. NOLs near the free layer should preferably be not magnetic, or they should be separated from the free layer by making use of a non-magnetic back layer (fig. 2.1(h)). Non-magnetic NOLs near the free layer can be made of non-magnetic oxides such as the oxides of Cu, Ta or Al. Table 2.1 gives an overview of the structures investigated, and references. A systematic investigation of the effect of NOLs on the MR ratio has been carried out by Fukuzawa et al. (2001b), for spin-valves with the structure underlayer/ Ir–Mn/ Co90 Fe10 / (Co–Fe–O)/ Co90 Fe10 / Cu/ Co90 Fe10 / Cu/ TaOx . The MR ratio for these double specular SVs was 17%. A reference system without NOLs showed an MR ratio of only 9.4%, and reference systems containing only a NOL in the pinned layer or near the free layer showed an MR ratio of only about 13%. Several authors have analysed the experimental resistance and magnetoresistance of SVs with NOLs using the semiclassical Camley–Barnas transport model (Sakakima et al., 2000a; Uhlig et al., 2001; Gibbons et al., 2001 and Lu et al., 2002a). From these analyses the probabilities of specular reflection at the NOLs used are found to be typically 0.6–0.85. One of these analyses is discussed in section 3.6.7. MR ratios in the range 17.8 to 20.5% have been reported by Hasegawa et al. (2002) in a regular scientific publication and by Kamiguchi et al. (1999a), Li et al. (2002c) and Tsunekawa et al. (2002) in a patent application and in conference digests and abstracts. The high value of 20% reported by Li et al. (2002c) for a SV with the structure (PtMn/ F/ Ru/ Co90 Fe10 / 1.9 Cu/ Co90 Fe10 / NOL), with F an unspecified high resistivity ferromagnetic layer, is remarkable. The system contains only one NOL. Its composition was not disclosed. At the time of writing this chapter, progress in the field is fast and may be expected to lead to even higher MR ratios. Spin-valves based on NOLs can provide the combined advantages of the (partially) specular boundary scattering at the interface with an oxide, the high thermal stability of metallic antiferromagnets such as PtMn or Ir20Mn80 , the enhanced magnetic and thermal stability of a SV with a Sy-AF pinned layer and the very small effective free magnetic layer thickness and low free layer coercivity of SVs with a non-magnetic back layer. Moreover, NOLs improve the thermal stability in two additional ways. Firstly, NOLs give rise to a certain planarization of the grain structure, thereby slowing down the high-temperature diffusion of atoms along grain-boundaries (Kamiguchi et al., 1999a, 1999b). A decreased interface roughness of SVs containing NOLs has been observed by Veloso et al. (2000) and by Mizuguchi and Kano (2001). Secondly, NOLs act as a Mn diffusion barrier, as it effectively blocks Mn that diffuses out of Mn-containing AF layers (Kamiguchi et al., 1999a; Gillies et al., 2001; Jang et al., 2002a). That hinders diffusion of Mn atoms into the Cu spacer layer where Mn gives rise to strong diffusive scattering which reduces the GMR ratio. The use of NOLs affects the microstructure of the layer stack in a way that depends on


49

the detailed composition and preparation method of the NOL (see, e.g., Mao et al., 2002). This affects the scattering in the bulk of the F layers, the coercivity of the free layer, and the interlayer magnetic coupling across the spacer layer (see, e.g., Lin and Mauri, 2001 and Li et al., 2001b). NOLs in the pinned layer are frequently made by the oxidation of a Co90 Fe10 layer. The preparation process that is used most often is thermal oxidation at room temperature, in highly pure oxygen, an oxygen/noble gas mixture, or in air. At a given exposure time, the end result is determined by the pressure. Oxidation by radicals (Kamiguchi et al., 1999a), by neutral atoms (remote plasma oxidation or atom beam oxidation, Veloso et al., 2000, Kools et al., 2001, Sant et al., 2001, Diao et al., 2002) and by ions (ion beam oxidation, Kools et al., 2001, Sant et al., 2001) have also been used. Alternatively, NOLs have been deposited by sputtering from a magnetic oxide target (Sakakima et al., 2000a). In contrast to results reported by Kamiguchi et al. (1999a), Gillies and Kuiper (2000) found that (at room temperature) oxides formed from pure Co do not couple the F layers in between which they are sandwiched. Oxidation of Co90 Fe10 layers was found to lead to more oxidized Fe than would be expected from the Co:Fe ratio in this alloy, suggesting that Fe segregates to the surface during oxidation. On the other hand, Vanhelmont (2003) found from an XPS study no significant preferential oxidation for Co90 Fe10 -based NOLs. The precise composition and crystal structure of Co–Fe–O NOLs is not known. However, Gillies and Kuiper (2000), Uhlig et al. (2001) and Ventura et al. (2002) concluded from the observation of an exchange bias effect that such NOLs are antiferromagnetic below 100–200 K. In almost all cases deposition is followed by an anneal step. Information on the anneal process is not included in table 2.1. The reader is referred to the original publications. In general, the purpose of annealing is to induce crystallographic ordering in the AF layer (PtMn, e.g.), to set the direction of the exchange bias field, to modify the microstructure by inducing grain growth, and/or to induce a solid state reaction involving the oxidized layers. An example of the latter situation has been described by Gillies et al. (2001), who created a NOL on top of a Co90 Fe10 sense layer in a bottom SV by first oxidizing the Co90 Fe10 layer in air, by subsequently depositing 1.5 nm Al on top of the oxide, and by finally carrying out a 120 s anneal step at 300 ◦ C. Already upon deposition near room temperature, the Co–Fe–O layer is almost completely reduced by the Al layer. The anneal step was used to ensure that all oxygen is transferred into Al, forming Al2 O3 . Similarly, Shen et al. (2002) observed that a Ta layer on top of Co–Fe–O reduces that layer, giving rise to a Ta2 O5 -NOL. The optimal thickness of a NOL in the pinned layer is determined by a sometimes delicate balance between an increase of the probability of specular scattering with increasing thickness and the concurrent decrease of the effective exchange bias field (Gillies et al., 2001; Li et al., 2001b; Huai et al., 2002). Co–Fe–O NOLs give already rise to a significant specular reflection for ≈0.5–1 nm layer thicknesses. The exchange coupling between the metallic F layers at both sides of the oxide is then still sufficient for obtaining a high resistance plateau in the R(H ) transfer curve. This trade-off is visible in fig. 2.6, taken from Li et al. (2001b). For a double-specular spin-valve containing two NOLs the width of the high-resistance plateau is much smaller than that of a reference SV without NOLs. In this study, the largest MR ratios were found after in situ oxidation at room temperature in pure oxygen during one minute at a pressure of 10−1 Pa. Oxidation at a higher O2

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Fig. 2.6. Magnetoresistance curves for bottom SVs with the structure (3 nm Ta/ 2 nm Py/ 6 nm Ir–Mn/ 3 nm Co90 Fe10 , 2 nm Cu/ 1 nm Co90 Fe10 / 1 nm Cu/ 1 nm Ta) (curve (1)) and a double specular SV with a NOL with the structure (3 nm Ta/ 2 nm Py/ 6 nm Ir–Mn/ 1 nm Co90 Fe10 // Ox // 1.5 nm Co90 Fe10 / 2 nm Cu/ 4 nm Co90 Fe10 // Ox // 2 nm Ta) (curve (2)). From Li et al. (2001b).

pressure, for the same time, was observed to lead to a decrease of the MR ratio. A plateau region with full antiparallel alignment is then not anymore present. The insertion of NOLs is expected to be most effective for stack structures which have a high effective exchange bias field in the absence of the NOL, e.g., for SVs with Sy-AF pinned layers. However, also for such SVs the plateau width decreases by the use of a NOL (see, e.g., Huai et al., 2001). For sensor applications, it is important that the free layer has a strong [111] texture to reduce the adverse effect of the cubic magnetocrystalline anisotropy on the coercivity. Gillies and Kuiper (2000) observed from Transmission Electron Microscopy (TEM) that 0.2–0.5 nm NOLs, prepared by thermal oxidation of Co90 Fe10 , do not interrupt the grain structure and thus preserve the crystallite texture. From CPP conduction experiments, Gillies and Kuiper found that such NOLs were incompletely closed discontinuous layers, containing metallic pinholes. A TEM study by Diao et al. (2002) of SVs with a NOL made by thermal oxidation confirmed that such a NOL is indeed discontinuous, and further showed that NOLs made by plasma oxidation are much more continuous. 2.2. Dual spin-valves Dual (or symmetric) spin-valves consist of essentially three F layers, separated by two non-magnetic spacer layers (fig. 1.4(c)). The magnetization of the two outer F layers is pinned by an AF exchange bias layer, whereas the inner F layer is free. In dual SVs diffusive scattering at the outer boundaries plays a less important role than in simple spin-valve with equal layer thicknesses. When scattering at the outer boundaries is (partially) diffusive, dual SVs will thus show a higher MR ratio than otherwise similar simple SVs (see section 3.6.2). This picture is confirmed by the outcome of experimental studies. Table 2.2 gives an overview of selected results from the literature. Noguchi et al. (1994) were the first to demonstrate that dual SVs can indeed give rise to a higher MR ratio than otherwise similar simple SVs. However, the MR ra-

GIANT MAGNETORESISTANCE AND MAGNETIC INTERACTIONS 51

TABLE 2.2 Magnetoresistance and sheet resistance (in the parallel state) of dual spin valves. The entries in the table are a selection from the literature. The notation is identical to that used in table 2.1 ΔR/R (%)Rp,sh ( )ΔRp,sh ( ) Remarks System Reference 5 Hf/ 5 Cu/ 5 Fe50 Mn50 / 5 Ni–Fe–Co/ 2.5 Cu/ 5 Ni–Fe–Co/ 3.7 Noguchi et al. (1994) 2.5 Cu/ 5 Ni–Fe–Co/ 5 Fe50 Mn50 / 5 Cu 50 NiO/ 5 Ni–Fe–Co/ 2.5 Cu/ 5 Ni–Fe–Co/ 2.5 Cu/ 5.6 5 Ni–Fe–Co/ 5 Fe50 Mn50 / 5 Cu (2.2) 5 Hf/ 5 Cu/ 5 Fe50 Mn50 / 5 Ni–Fe–Co/ 2.5 Cu/ 5 Ni–Fe–Co/ 5 Cu Hoshiya et al. (1994) 50 NiO/ 4 Py/ 2 Cu/ 4 Py/ 2 Cu/ 4 Py/ NiO 7.0 ΔHsw = 0.8 kA/m Anthony et al. (1994) 75 NiO/ 3 Py/ 2 Co/ 3.4 Cu/ 4 Co/ 2.4 Cu/ 2 Co/ 3 Py/ 15 Fe50 Mn50 / 2 Py 13.3 50 NiO/ 2.5 Co/ 1.8 Cu/ 4 Co/ 1.8 Cu/ 2.5 Co/ 50 NiO 21.5 Large hysteresis Egelhoff et al. (1995) 50 NiO/ 2.5 Co/ 1.9 Cu/ 4 Co/ 1.9 Cu/ 2.5 Co/ 50 NiO 23.4 21.4 5.0 Egelhoff et al. (1996a, 1997a, 1997b) 24.8 O2 in chamber during 50 NiO/ 2.5 Co/ 3 Cu/ 4 Co/ 3 Cu/ 2.5 Co/ 50 NiO 16.0 22.0 Ff = Co Egelhoff et al. (1996d) 50 NiO/ 2.5 Co/ 1.9 Cu/ 4 Ff / 1.9 Cu/ 2.5 Co/ 50 NiO 17.0 Ff = Co95 Fe5 15.0 Ff = Co90 Fe10 12.0 Ff = Py 15.0 Ff = Co86 Fe10.5 Ni3.5 5.0 Ff = Co85 B15 5 Ta/ 5 Py/ 25 Pt–Pd–Mn/ 2.5 Co90 Fe10 / 2.5 Cu/2.5 Co90 Fe10 / 10.3 Tanaka et al. (1997, 1999) 2 Py/2.5 Co90 Fe10 / 2.5 Cu/ 2.5 Co90 Fe10 / 25 Pd–Pt–Mn 27.8 α-Al2 O3 (110) substrate Sugita et al. (1998), 50 α-Fe2 O3 / 2 Co/ 2 Cu/ 5 Co/ 2 Cu/ 2 Co/ 50 α-Fe2 O3 Sakakima et al. (1999b) UL/ Ir–Mn/ Sy-AF/ Cu/ free/ Cu/ Sy-AF/Ir–Mn/ Ta 13.0 13.8 1.8 UL = Ta/Py/Cu Tong et al. (1999) Sy-AF = Co90 Fe10 /Ru/Co90 Fe10 free = Co90 Fe10 /Py/Co90 Fe10 NiO/ 2.5 Co/ 2.5 Cu/ 4 Co/ 2.5 Cu/ 2.5 Co/ 10 Fe50 Mn50 / 1 Ta 12.1 Ion Beam Deposition Slaughter et al. (1999) 11.8 Lenssen et al. (2000a) 3.5 Ta/ 2 Py/ 6 Ir–Mn/ 4 Co90 Fe10 / 0.8 Ru/ 4 Co90 Fe10 / 2.5 Cu/ 1.6 Co90 Fe10 / 2.5 Cu/ 4 Co90 Fe10 / 0.8 Ru/ 4 Co90 Fe10 / 6 Ir–Mn/ 3.5 Ta 2 Ta/ 2 Py/ 6 Ir–Mn/ 1.5 Co90 Fe10 // Ox // 2 Co90 Fe10 / 2 Cu/ 18.5 Sant et al. (2001) 2.5 Co90 Fe10 / 2 Cu/ 2 Co90 Fe10 // Ox // 1.5 Co90 Fe10 / 6 Ir–Mn/ 2 Ta 20.5 Lee et al. (2001) 4 Ta/ 1.2 Cu/ 8.5 Ir–Mn/ 1 Co90 Fe10 // Ox // 2.3 Co90 Fe10 / 2.4 Cu/ (10.6) (no oxygen exposure) 3.0 Co90 Fe10 / 2.7 Cu/ 3 Co90 Fe10 / 7 Ir–Mn/ 3.5 Ta 21.8 19.3 4.2 Li et al. (2002a) 3 Ta/ 2 Py/ 6 Ir–Mn/ 1.5 Co90 Fe10 // Ox // 1.5 Co90 Fe10 / 2.2 Cu/ 1.0 Co90 Fe10 / 2.0 Cu/ 2 Co90 Fe10 // Ox// 1 Co90 Fe10 / 6 Ir–Mn/ 2 Ta 2.0 Dual SV read head. Tong et al. (2002) UL/ Ir–Mn/ t Co90 Fe10 / 0.6–0.8 Ru/ t Co90 Fe10 / 2–2.3 Cu/ t Co90 Fe10 / t = 1.5–2.0 nm 2–2.3 Cu/ t Co90 Fe10 / 0.6–0.8 Ru/ t Co90 Fe10 / Ir–Mn/ CL UL = CL = Ni–Fe–Cr.

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Fig. 2.7. Magnetoresistance curve of dual SVs with the layer structure α-Al2 O3 (110)/ 50 nm α-Fe2 O3 / 2 nm Co/ 2 nm Cu/ 5 nm Co/ 2 nm Cu/ 2 nm Co/ 50 nm α-Fe2 O3 . From Sugita et al. (1998).

tios obtained (at most 5.6%) were lower than for state-of-the-art (at that time) simple spin-valves, probably as a result of the use of relatively thick Cu underlayers and cap layers. For NiO-biased Co/Cu/Co/Cu/Co systems Egelhoff et al. (1995, 1996a) found MR ratios up to 23.4%, versus 17% for reference simple SVs. Growth in a 5 × 10−9 Torr partial oxygen pressure, even led to MR ratios up to 24.8% for dual SVs and 19.0% for reference simple SVs (Egelhoff et al., 1997b). Oxygen was argued to act as a surfactant, suppressing the formation of defects. As mentioned already in section 2.1.6 when discussing simple SVs, Swagten et al. (1996) provided support for the suggestion by Egelhoff et al. that the high observed MR ratio in NiO-biased systems is in part the result of specular scattering at the Co/NiO interfaces. The highest MR ratio reported so far for a simple or dual SV, 27.8%, has been obtained by Sugita et al. (1998) for α-Fe2 O3 -based Co/Cu/Co/Cu/Co systems. For comparable simple SVs the MR ratio was only 18% (see section 2.1.6). Fig. 2.7 shows the magnetoresistance curve. The α-Fe2 O3 layers do not give rise to an exchange bias field, but to an enlarged coercivity. No analysis was made of the magnetoconductance. The authors emphasized the possible role of strong specular scattering at the very flat interfaces that were observed from a TEM study. The specific growth method, sputter deposition on a saphire single crystal (see section 2.1.6), is regarded as being of crucial importance. Double specular dual SVs with two NOLs, with Ir–Mn exchange biased F layers and grown on a technologically relevant substrate, have so far been prepared with MR ratios up to 21.8% (Li et al., 2002a). Hard disk read heads based on dual SVs, with Ir–Mn AF layers and using Sy-AF pinned layers to obtain an enhanced exchange bias field and thermal stability, have been demonstrated by Tong et al. (2002).


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Fig. 2.8. Overview of various types of SVs with improved magnetic characteristics by additional layers outside the active part. Dashed lines in figures (e)–(g) indicate the current stripes in which these materials are used. The current direction is not relevant for structures (a)–(d). Curved arrows in figs (f) and (g) indicate schematically the direction of the external magnetostatic field. IEC = interlayer exchange coupling.

2.3. Spin-valves with improved magnetic characteristics by additional layers outside the active part In the two previous subsections we have discussed various methods for improving the GMR ratio and magnetic characteristics by making use of advanced layer structures that affect the current density distribution within the active part of the layer stack. In this subsection we focus on the application of additional layers outside the active part. Such layers can improve the magnetic characteristics by shifting the offset field to zero, or by reducing the coercivity of the free layer. The offset field, Hoffset , is the field around which the free layer reverses. For a patterned micrometer or nanometer scale device structure Hoffset is equal to the macroscopic coupling field, Hcoupl , plus the field due to the sample-size dependent magnetostatic interactions with the other layers (see section 4.2.2). Various additional layer stacks have been proposed. An overview is given in fig. 2.8, where for clarity the additional layers have been drawn separately from the basic structure. In the stacks

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Fig. 2.9. Full line: magnetoresistance curve of a SV with the layer structure (3.5 nm Ta/ 2 nm Py/ 10 nm Ir–Mn/ 4.5 nm Co90 Fe10 / 0.8 nm Ru/ 3.5 nm Co90 Fe10 / 3 nm Cu/ 1 nm Co90 Fe10 / 1 nm Py/ 1.6 nm Ta / 2 nm Co90 Fe10 / 0.8 nm Ru/ 1.5 nm Co90 Fe10 / 10 nm Ir–Mn/ 4 nm Ta). Dashed line: magnetoresistance curve for the same layer structure, but without the stabilizing top structure indicated by the italic font. From Lenssen et al. (2001).

shown in figures (a)–(e) use is made of exchange interactions, and in the stacks shown in figures (f) and (g) use is made of magnetostatic interactions (as indicated by the schematic flux lines). In all cases, apart from the case shown by fig. 2.8(e), the applied field is parallel to the bias direction of the pinned layer in the active part. Compensation for the offset field due to a coupling with the pinned layer can be realized by making use of an additional AF exchange bias layer (Lu et al., 2000). The AF layer is set to give rise to a “transverse” exchange bias field, i.e., a field perpendicular to the easy axis of the free layer (fig. 2.8(a)). A problem is that the exchange bias field must be very small, but still reproducible and temperature independent. It is difficult to realize that combination of requirements. Lenssen et al. (2001) proposed to make use of weak interlayer exchange coupling between an exchange biased F layer and the free layer, across an interlayer such as Ta (fig. 2.8(b)). As an even more stable alternative, they proposed to use a pinned Sy-AF (fig. 2.8(c)). The coupling across 2 nm Ta between a (0.8 nm Co90 Fe10 / 3.5 nm Py/ 0.8 nm Co90 Fe10 ) free layer and a pinned Co90 Fe10 layer was shown to give rise to a reproducible offset compensation field of about 1 kA/m. Identical layer stacks, but with the additional AF layer set to give rise to a “longitudinal” exchange bias field, can be used to reduce the coercivity of the free layer (Lu et al., 2000; Lenssen et al., 2001). Without the effective longitudinal field that is applied to the free layer, that layer could reverse upon a reversal of the applied field by clockwise or counter-clockwise rotations of the magnetization. Both processes are equivalent, giving rise to the formation of domain walls. Already a small longitudinal field is sufficient for elimination of one of these processes, giving rise to perfect single-domain reversal processes. Barkhausen noise is thus suppressed. Fig. 2.9 shows the effect on the hysteresis of the use of a structure such as given in fig. 2.8(d), taken from Lenssen et al. (2001). The authors also showed that hysteresis elimination and offset elimination can be realized simultaneously by setting the exchange bias direction of the top AF layer to an intermediate angle. It should be remarked that a longitudinal bias has also been obtained for conventional SVs in which the exchange bias field had a certain longitudinal component (“canted pinning field”, Suzuki and Matsutera (1998), Lu et al. (2002b)).


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In these cases the magnetostatic and interlayer coupling between the pinned and free layer was used, respectively. The use of an additional AF layer has the advantage that its functioning is independent of the presence of coupling between the pinned and free layer. Sankar et al. (1999) proposed a novel type of SV of the type AF/F/NM/F/AF, in which the two AF and F layers are identical. The AF-F exchange bias fields are weak, and directed under ±45◦ angles with respect to the field that is to be sensed (fig. 2.8(e)). This is accomplished by cooling from a temperature above the blocking temperature while a current flows through the device, in the presence of an additional external field parallel to the current direction. The current gives rise to opposite local fields in the two F layers, perpendicular to the current direction (see also section 4.2.2). The additional common external field makes it possible to obtain the required ±45◦ angles of the local bias field direction. The authors only demonstrated a system with ±90◦ angles of the two pinning directions with respect to the external field, obtained by cooling in the presence of a current, but without an external field. A ±90◦ doubly-biased spin-valve was also discussed by Ambrose et al. (1999). As for the structure given in fig. 2.8(a), the difficulties to precisely control the size of the exchange bias field seem to limit the applicability of this design. The offset field due to the magnetization of the pinned layer can, in a patterned structure, be compensated by using the magnetostatic field from an additional ferromagnetic “bias compensation layer”. That layer can be pinned by an AF layer, as show in fig. 2.8(f). Opposite bias directions due to the two AF layers in the stack can be obtained by using AF materials with different blocking temperatures (Mao et al., 2000a). Alternatively, a soft magnetic layer can be used with the easy axis parallel to the longitudinal direction (Kanai et al., 1998; Tong et al., 1999). Such a layer can compensate at the same time for the flux from the pinned layer and for the field from the sense current. Childress et al. (2002) proposed to make use of magnetostatic biasing by a longitudinally pinned F layer on top of the element (fig. 2.8(g)). This provides an alternative to the novel options discussed above for longitudinal biasing in order to reduce the coercivity and Barkhausen noise. In present submicrometer sensor elements in a hard disk read head longitudinal biasing is usually accomplished by adding hard magnet layers in the tail regions of the element, outside the track width and shunted by the current leads. 2.4. Pseudo-spin-valves Pseudo-spin-valves are F1 /NM/F2 trilayers within which the magnetic coupling across the NM spacer layer is small as compared to the effective magnetic anisotropy of at least one of the F layers. The F-layers can consist of a single material with different thicknesses in order to realize a different shape anisotropy in a patterned device, or can be composite stacks of strongly exchange coupled magnetic layers. There is no AF exchange bias layer, so that these SVs are outside the scope of this chapter. However, we include a brief discussion on their properties, in order to be able to make it possible to compare their suitability for sensor and memory applications with that of exchange biased SVs. A perfectly antiparallel state can be obtained by using the combination of a hard and a soft magnetic F layer. Such pseudo-SVs may be viewed as the n = 1 version of the hard–soft (Fhard /NM/Fsoft /NM)n multilayers introduced by Shinjo and Yamamoto (1990). Fig. 2.10 shows results of a study by Hütten et al. (2002) of such pseudo-SVs, with the layer structure (glass/ 3.6 nm Py/ 3.5 nm Co/ t Cu/ 3.9 nm Co). The permalloy-containing

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Fig. 2.10. Dependence of the room temperature magnetoresistance curves and the MR ratio on the Cu spacer layer thickness, for (3.6 nm Py/ 3.5 nm Co/ tCu nm Cu/ 3.9 nm Co) pseudo spin-valves. The dashed line gives a fit to the data using eq. (1.4), assuming that for Cu thicknesses at which the MR ratio is peaked a full antiparallel alignment is reached. From Hütten et al. (2002).

bottom F-layer is magnetically softer than the Co F-layer on top of the structure. The MR ratio is maximal at Cu thicknesses t at which the oscillatory interlayer exchange coupling across the Cu layer is most strongly antiferromagnetic, i.e., near t = 1.1, 2.2 and 3.3 nm. Below t ≈ 3.3 nm, the interlayer exchange coupling is the dominant interaction. The MR ratio is only large when the coupling is antiferromagnetic. For t > 3.3 nm, the interlayer coupling is relatively weak as compared to the coercive field of the Co layer, so that the MR ratio does not oscillate anymore with t. The trilayers may then be called pseudo-SVs. The MR ratio of approximately 11% for the t = 2.2 nm system is comparable with that of similar exchange-biased spin-valves. Mao et al. (2000b) reported MR ratios up to 14% for double specular pseudo-SVs with the layer structure 3 Cr/ Co–Fe–O/ 3 Co90 Fe10 / 2.3 Cu/ 1 Co90 Fe10 / 3 Ni–Co–Fe/ 1 Co90 Fe10 / TaOx containing two NOLs. The growth on a (110) bcc-Cr underlayer was used to induce a coercive field of ≈10 kA/m in the hard bottom Co90 Fe10 layer. The pseudo-SVs discussed above would not be suitable for sensor applications. Firstly, a very moderate field of only a 3–10 kA/m would already reverse the slope of the transfer curve near zero field. Secondly, Hütten and co-workers found that minor R(H ) loops taken in a small field range around H = 0 show a distinct coercivity, and that after repeated cycling through such loops the resistance change decreases irreversibly. This indicates that very stable 360◦ domain walls (walls within which the magnetization vector rotates over 360◦ , between domains with parallel magnetizations) had been formed. It is in practice not possible to obtain a uniaxial anisotropy and coercivity in electronically suitable com-


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positionally homogeneous reference layers that is sufficiently high for sensor applications. That would require the presence of a large defect density in order to pin domain walls, whereas at the same time the defect density should be small in order to obtain a large spindependence of the scattering. Obvious candidate materials would be Co1−x Ptx alloys with x ≈ 0.25, as Pt addition to Co is known to give rise to magnetic hardening. However, Irie et al. (1995) found that the coercive field of such layers in (Co–Fe–Ni/Cu/Co0.75Pt0.25 /Cu)9 hard–soft multilayers is only 10 kA/m, and that the MR ratio of such multilayers is only about 3%. As discussed already in section 2.1.6, the magnetization of F-layers can be stabilized by making use of a synthetic antiferromagnet (Sy-AF) of the type F/X/F. At least one of the F layers that form the Sy-AF should have a large uniaxial in-plane anisotropy. Leal and Kryder (1998a, 1998b, 1999) studied pseudo-SVs of the type Co/Ru/Co/Cu/Co/Py, where Co/Ru/Co is the Sy-AF, and showed that uniaxial anisotropy in the bottom Co layers can be obtained by growth on a Cr underlayer. Seigler et al. (2002) and Wu et al. (2002) used Co– Cr–Pt permanent magnet underlayers to enhance the magnetic anisotropy of the adjacent magnetic layers in the Sy-AF, and Boeve et al. (2002) used Tb–Co underlayers for the same purpose. Seigler and coworkers pointed out that for some sensor applications the use of pseudo-SVs containing a Sy-AF pinned layer and permanent magnet layers such as Co–Pt–Cr can have the following advantages over an exchange biased SV with an AF bias material such as PtMn: better corrosion resistance, large switching field at relatively high temperatures and no high temperature anneal to obtain the ordering that gives rise to the exchange bias field. Hard–soft pseudo-SVs can also be used in non-volatile Magnetic Random Access Memories (MRAMs) cells (Tehrani et al., 1999; Katti and Zhu, 2001). The hard and soft layers have the functions of a storage and sense layer, respectively. The status of the bit (“0” or “1”) is determined by the magnetic state of the hard layer, and can be probed by measuring the element resistance as a function of the applied magnetic field. As the fields that are generated by realistic write currents on a chip are small, the coercivity of the hard layer should be small but well defined. A first approach would be to make use of pseudo-SVs with a small intrinsic hard layer coercivity, i.e., the coercivity that is measured in an unpatterned sample and that is only determined by the composition and microstructure of the layers. Such pseudo-spin valves were developed by, e.g., Irie et al. (1995), Sakakima et al. (1996, 1997), Tsunashima et al. (1997) and Shirota et al. (1999). A second approach is to make use of pseudo-SV memory elements containing two F layers that are intrinsically soft, but that switch at different fields due to different shape anisotropies (Everitt et al., 1997). Let us suppose that the elements are smaller than a domain wall width, and that the magnetization reverses like a single domain. For permalloy, the Néel wall width is approximately 0.5–1 μm. For infinitely long 5 nm thick and 1 μm wide permalloy stripes the shape anisotropy field is already one order of magnitude larger than the ≈0.4 kA/m intrinsic uniaxial anisotropy field. In stripe-shaped memory elements, with widths of a few tenths of a μm or less, the shape anisotropy is thus dominant. A schematic picture of a memory element that functions on the basis of this concept is shown in fig. 2.11(a). Fig. 2.11(b) shows the transfer curve for a memory element based on a (5 nm Ta/ 6.5 nm Py/ 1.5 nm Co90 Fe10 / 3.7 nm Cu/ 1.5 nm Co90 Fe10 / 4.5 nm Py/ 20 nm Ta) pseudo-SV, patterned in the form of a 0.6 μm wide and approximately 2 μm long stripe with tapered ends (Katti et al., 2001).

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Fig. 2.11. (a) Device principle of a memory element based on a pseudo-SV. The full and dashed arrows indicate the magnetization directions in the two binary states. (b) Magnetoresistance curve of a (5 nm Ta/ 6.5 nm Py/ 1.5 nm Co90 Fe10 / 3.7 nm Cu/ 1.5 nm Co90 Fe10 / 4.5 nm Py/ 2 nm Ta) pseudo-SV 0.6 μm wide element. The element length is much longer than the width. The field is parallel to the long axis. From Katti et al. (2001). (c) Device principle of a memory element based on an exchange-biased SV. The full and dashed arrows indicate the magnetization directions in the two binary states. (d) Magnetoresistance curves of 6 μm long exchange-biased SV elements with various widths. The SVs contain 9 nm F layers (composition not disclosed) and 2.2–2.5 nm Cu spacer layers. From Tang et al. (1995).

The field is parallel to the stripe axis. The thicker bottom and thinner top (Co90 Fe10 /Py) layers function as storage layer and sense layer, respectively. The change of the resistance near H = 0 is due to a switch of the sense layer. The antiparallel state is stabilized by the magnetostatic interaction between both layers, due to the finite stripe length. The switching of sub-100 nm pseudo-SV elements was studied by Castaño et al. (2001). Micromagnetic modelling studies showed that precise control of the shape of the tapered ends is of crucial importance for obtaining reproducible switch fields and for preventing nonrepeatable switching by the formation of end domains (Gadbois et al., 1998; Fang and Zhu, 2000). For practical applications, the minimum element size will therefore be significantly larger than the minimum feature size of the lithographic process. Alternatively, MRAM cells can be based on exchange-biased spin-valves. Fig. 2.11(c) shows the concept, which was first proposed by Tang et al. (1995). The free layer functions as the storage layer. Bistability is obtained by making use of the shape anisotropy of stripeshaped elements width submicrometer widths. The magnetization of the pinned F layer is not changed during the write process. As shown in fig. 2.11(d), the switch fields become more well defined if the elements become smaller, i.e., when single-domain switching


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Fig. 2.12. Temperature dependence of the MR ratio of SVs biased by Fe50 Mn50 with different combinations of F layer compositions. The active parts of the SVs are: (9 nm Co/ 3 nm Cu/ 3.5 nm Co) (), (8 nm Co/ 3 nm Cu/ 5 nm Py) (), (7.5 nm Py/ 2.2 nm Cu/ 5 nm Py) () and (9 nm Ni/ 2.2 nm Cu/ 5 nm Py) (•). From Dieny et al. (1991d).

instead of switching via domain wall movement becomes dominant. At present, storage elements based on this magnetic concept, but made from magnetic tunnel junctions, are considered as the most promising candidates for MRAM applications (see references in section 1.6.3). 2.5. Temperature dependence of the magnetoresistance Extensive studies of the temperature dependence of the MR ratio of spin-valves have been carried out by Dieny et al. (1991d, 1992a). A very striking result is that for a variety of systems of the type F1 /NM/F2 /Fe50 Mn50 the MR ratio decreases (around room temperature) approximately linearly with increasing temperature. Fig. 2.12 shows some of their results for spin-valves with Cu spacer layers and with F = Ni, Py or Co. The MR ratio was found to extrapolate to zero at a temperature T0 that depends on the composition of the F materials at both sides of the interfaces, but not (or only weakly) on the thicknesses of the layers. T0 is smallest when one of the F layers is Ni, which has the lowest Curie temperature (627 K), and is highest when both F layers consist of Co, which has the highest Curie temperature (1388 K). This general picture has been confirmed by later studies (see table 2.3). Szucs et al. (1997) observed that a 0.8 nm Co “dusting” layer in a Py/Co/Cu/Co/Py/ Fe50 Mn50 spin-valve enhances T0 from 470–500 K (for Py/Cu/Py systems) by approximately 100 K. Thicker (1.5 nm) Co dusting layers led rise to the same value of T0 as that of Co/Cu/Co systems, viz. approximately 700 K. Similarly, Lenssen et al. (2000a) observed for (Ir–Mn/ 4 nm Co90 Fe10 / 5 nm Cu/0.8 nm Co90 Fe10 /5 nm Py) SVs that the 0.8 nm Co90 Fe10 dusting layer led only to T0 ≈ 635 K, which is still significantly smaller

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TABLE 2.3 Temperature dependence of the MR-ratio of spin-valves with Cu spacer layers. T0 is the temperature at which, from a linear fit of the (ΔR/R)(T ) curve in the indicated temperature interval [Tmin − Tmax ], the MR ratio would become zero. The systems are ordered according to the combination of materials that is present at the interfaces with the Cu spacer layer. Only the active parts of the SVs are given. The layer thicknesses are in nm System

T0 (K)

Ni/Py 9 Ni/ 2.2 Cu/ 5 Py 420 2.5 Ni/ 2.2 Cu/ 5 Py 375 4.7–20 Ni/ 2.2 Cu/ 5 Py 430–445a Py/Py 7.5 Py/ 2.2 Cu/ 5 Py 470 12.5–41.5 Py/ 2.2 Cu/ 5 Py 500–515a 5 Py/ 3.3 Cu/ 2.5 Py 500 Py/Co 8 Co/ 3 Cu/ 5 Py 600 7.5–43 Co/ 2.2 Cu/ 5 Py 510–540 Py/Co90 Fe10 4–8 Py/2.2 Cu/2 Co90 Fe10 640–690 Co90 Fe10 /Co90 Fe10 2 Py/ 3 Co90 Fe10 / 3 Cu/ 2 Co90 Fe10 690 660 3 Py/ 1.5 Co90 Fe10 / 2.3 Cu/ 2.5 Co90 Fe10 635 4 Co90 Fe10 / 5 Cu/ 0.8 Co90 Fe10 / 5 Py 695 4 Py/ 1.5 Co90 Fe10 / 2.8 Cu/ 2 Co90 Fe10 /1.5 Py Co/Co 9 Co/ 3 Cu/ 3.5 Co 700 5 Py/ 8 Co/ 3.3 Cu/ 8 Co/ 2.5 Py 570 6 Py/ 1.5 Co/ 3.3 Cu/ 1.5 Co/ 3 Py 700 6 Co/ 2.2 Cu/ 5 Co 640 2.5 Py/ 1.5 Co/ 3 Cu/ 1.5 Co/ 5.5 Py 720 4.4 Co/ 2.2 Cu/ 4.4 Co 550(I), 685(II)b

Tmin (K)–Tmax (K) Reference 225–320 80–320 80–320

Dieny et al. (1991d) Dieny et al. (1992a)

200–320 80–320 150–300

Dieny et al. (1991d) Dieny et al. (1992a) Szucs et al. (1997)

80–320 80–320

Dieny et al. (1991d) Dieny et al. (1992a)

300–550

Tanoue and Tabuchi (2001)

300–430 300–450 300–500 300–570

Iwasaki et al. (1997) Mao et al. (2000c) Lenssen et al. (2000a) Zhang et al. (2000)

77–320 50–300 50–300 50–350 300–450 175–325

Dieny et al. (1991d) Szucs et al. (1997) Dieny et al. (1998) Mao et al. (1998) Stobiecki et al. (2000)

a From a second-order polynomial fit. b Samples (I) and (II): different RF-power used for RF-magnetron sputter deposition of the Cu layers.

than the value of T0 ≈ 660–700 K that is commonly observed for SVs that contain thick Co90 Fe10 free and pinned layers. The value of T0 depends on the preparational conditions, as is evident from results obtained by Stobiecki et al. (2000). The approximately linear temperature dependence of the MR ratio around room temperature results from the combined effects an approximately linearly increasing sheet resistance, and a linearly decreasing change of the sheet resistance. See, e.g., Mao et al. (1998). In the limit to 0 K, the temperature dependence of the MR ratio goes to zero (Dieny et al., 1992c). A similar temperature dependence is observed for AFcoupled multilayers. For Co/Cu multilayers, e.g., Suzuki and Taga (1995) observed that below 100 K the temperature dependence of the resistivity is well described by a T 2 power law, as is expected when electron–electron and electron–magnon scattering dominate, and that the temperature dependence of the MR ratio is proportional to T 3/2 . Dieny et al. (1991d) proposed that the relatively small values of T0 as compared to the bulk Curie temperatures may be understood as a result of enhanced spin-flip scattering at


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the interfaces due to the reduced Curie temperature of alloyed interface regions. It should be noted that even in the case of perfectly flat interfaces thermal fluctuations reduce the magnetization in the first monolayers more strongly than in the bulk, due to the smaller number of magnetic nearest and next nearest neighbours. The effect of the temperature dependent scattering probabilities and of spin-mixing in the bulk of the layers and at the interfaces has been modelled by Duvail et al. (1995), and has been applied successfully to spin-valves by Dieny (1998) (see section 3.7.2). 2.6. Anisotropic magnetoresistance and anisotropy of the giant magnetoresistance Precise measurements show a small deviation from the cos θ angular response that would be expected from eq. (1.2), and from the linear response that would be expected from eq. (1.3) (Rijks et al., 1994a; Uehara et al., 1996; Sugawara et al., 1997; Johnson et al., 2002). This is due to a small contribution from the anisotropic magnetoresistance (AMR) of the free layer, whose magnetization direction changes with respect to the current direction. For stripe-shaped sensor elements, in which the direction of the magnetization of the pinned layer is perpendicular to the current direction, the resistance can to a good approximation be expressed as ΔRGMR (1 − cos θ ) + ΔRAMR × sin2 θ, (2.3) 2 with θ the angle between the pinned and free layer magnetization directions. For |H − Hcoupl| Ha the transfer curve is then given by: H − Hcoupl ΔRGMR R(H ) = R(H = ∞) + 1− 2 Ha 2 H − Hcoupl + ΔRAMR 1 − (2.4) . Ha R(θ ) = R(θ = 0) +

Schematic transfer curves for different ratios r ≡ ΔRAMR /ΔRGMR are given in fig. 2.13. The AMR effect gives rise to a higher sensitivity when a sensor is used around an operating point Hcoupl < Hop < Hcoupl + Ha than when Hop = Hcoupl. However, it has the adverse effect of spoiling the linearity of the response. Typical GMR and AMR ratios for (8 nm Py/ 2.5 nm Cu/ 6 nm Py/ 8 nm Fe50 Mn50) spin-valves are 4.5% and 1.1%, respectively (Rijks et al., 1994a). It follows from fig. 2.13 that the sensitivity of such spin-valves, as calculated for Hop = Hcoupl + 0.5Ha , is almost 50% higher than expected from the GMR effect only. The AMR/GMR ratio can be reduced to less then 10% by making use of thinner free layers and by replacing Py by Co90 Fe10 (Li et al., 2001c). Specular scattering at oxide layers increases the GMR ratio but also the AMR ratio (Dieny et al., 2000b). As far as I know, no reports are yet available on the AMR contribution to the transfer curves of double specular SVs. Rijks et al. (1993, 1995b) studied the interplay between the GMR and AMR effect in SVs on the basis of the semiclassical Camley–Barnas transport model (see section 3.5). The model was extended to include a microscopic model for the AMR effect in terms of spin and angle dependent electron mean free paths. Within a description using the twocurrent model the AMR effect in Ni-rich Ni–Fe alloys such as permalloy is predominantly

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Fig. 2.13. Dependence on the ratio r ≡ ΔRAMR /ΔRGMR of the magnetoresistance curves for an exchange-biased SV with crossed anisotropies.

due to a dependence of the mean free path of majority-spin electrons on the angle between the electron velocity vector and the local magnetization direction: λ⊥ > λ . The authors predicted that the GMR ratios that are obtained when the pinned layer magnetizations are perpendicular and parallel to the current direction, (ΔRGMR /R)⊥ and (ΔRGMR /R) , respectively, are then, in general slightly different. Eq. (2.3) is thus not entirely correct. Granovskii et al. (1995) arrived at the same conclusion using a less rigorous model. In view of the larger perpendicular mean free path, one would expect a negative anisotropy: (ΔRGMR /R) < (ΔRGMR /R)⊥ . For Py/Cu/Py-based spin-valves with small F and NM layer thicknesses Rijks et al. predicted indeed that (ΔRGMR, − ΔRGMR,⊥ )/RGMR,⊥ can be in the range −0.1 to −0.2%. Experimental observations by Dieny et al. (1996) for Ni/Cu/Py-based SVs provided support for this prediction, and for the predicted trends in the layer thickness dependence of the effect. A positive anisotropy that was predicted for large Py thicknesses was not observed. Miller et al. (1999) found a negative anisotropy for all systems in a large set of different SVs with Py and Co magnetic layers, studied at 4.2 K. The anisotropy of the sheet conductance change, (ΔGsh,GMR,⊥ − ΔGsh,GMR, ), was found to show a strong positive correlation with the sheet conductance change, ΔGsh,GMR, . From an analysis using the semiclassical transport model for the combined GMR and AMR effects that was introduced by Rijks et al. (1995b), Miller and coworkers concluded that the data provided support for a strong spin-dependence of the scattering in the bulk of the magnetic layers. 2.7. Thermoelectric power The thermoelectric power (TEP) of spin-valves is a property of fundamental interest, because its study can lead to further insight in the transport mechanism. It is also of practical interest, because a (time-dependent) temperature gradient over a device can give rise to an offset voltage and to additional noise. As far as is known to the author, there is only one report of a study of the TEP for spin-valves. Sato et al. (1998) studied the TEP of (50 nm NiO/ 3 nm Py/ 2.5 nm Cu/ 6 nm Py/ 1 nm Cu) bottom SVs (type I) and of (3 nm Ta/ 6 nm Py/ 2.5 nm Cu/ 3 nm Py/ 10 nm Fe50 Mn50 / 3 nm Ta) top SVs (type II), with


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MR ratios at room temperature of ≈4% and ≈2.5%, respectively. The TEP was found to vary approximately linearly with temperature T , and was at 300 K approximately equal to S = −10 μV/K for both systems. A magnetothermoelectric power (MTEP) effect was found when reversing the relative alignment of the free and pinned layers. The relative change of the TEP, defined as ΔS = (SP − SAP )/SAP , was −4.5 and −8% for systems I and II, respectively. A temperature difference of 10 K along the sample would thus give rise to a thermoelectric voltage of 0.1 mV, and to a voltage change by the application of a field that is one order of magnitude less. In devices that are operated using a small sense current, this contribution to the output voltage can be dominant. It is of interest to remark that qualitatively similar results have been obtained for AFcoupled Co/Cu multilayers, which have a negative thermoelectric power and a negative magnetothermoelectric power (Nishimura et al. (1994) and Shi et al. (1996)). Tsymbal et al. (1999) were able to successfully explain the experimental results for Co/Cu multilayers from first principles electronic structure calculations, using the Mott formula: π 2 kB2 T ∂ ln σ . S =− (2.5) 3e ∂E E=EF Here EF is the Fermi energy and σ the conductivity. The elemental charge e is taken positive. Their method for calculating the conductivity is discussed in some detail in section 3.9. No analysis has yet been given for the TEP and MTEP of spin-valves. 2.8. Infrared optical properties – the magnetorefractive effect The spin-dependent conductivity that gives rise to the GMR effect gives also rise to an interesting magnetic field effect on the infrared (IR) optical properties. The effect was discovered by Jacquet and Valet (1995), who observed that for hard–soft multilayers the IR transmission depends on the relative alignment of the magnetization directions of the layers. This was found to be a magnetorefractive effect, caused by a dependence of the complex refractive indices (or, equivalently, the εxx and εyy diagonal elements of the dielectric tensor, where x and y are the in-plane directions6 ) on the alignment. Van Driel et al. (2000a) observed the same effect for exchange-biased spin-valves. The relative transmission change for (Si(100)/ 40 nm NiO/ 4.5 nm Py/ t nm Cu/ 8 nm Py) spin-valves is shown in fig. 2.14. The effect shows an interesting wavelength dependence with a layer thickness dependent minimum and a zero-crossing. The magnetorefractive effect can be understood as the result of a spin-dependence of the relaxation times in the F layers. The experimental results are well described within a semiquantitative two-current Drude model for the optical conductivity, introduced by Jacquet and Valet. The model predicts that in the limit of very long wavelengths, the relative transmission change will be positive, and equal to the CIP-GMR ratio. However, long wavelength experiments are very difficult due to the small absolute transmission. In the limit of small wavelengths the intraband (Drude) contribution to the dielectric tensor becomes small, and is dominated by the larger contribution due to interband excitations. From the analysis, van Driel and coworkers obtained a spin asymmetry ratio α = τ↑ /τ↓ = 1.9 ± 0.15 6 The tensor elements ε xx and εyy are, independent of the alignment of the magnetic layers, equal when the

film is isotropic in the film plane.

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Fig. 2.14. Relative change of the infrared light transmission through (40 nm NiO/ 4.5 nm Py/ tCu nm Cu/ 8 nm Py) spin-valves, for various Cu thicknesses. The room temperature MR ratios are 6.4, 5.0, 4.1 and 2.7% for SVs with 1.6, 2.6, 3.6 and 6.0 nm Cu spacer layers, respectively. The lines are guides to the eye. From van Driel et al. (1999a, 2000b).

for the spin-dependent relaxation times in the permalloy layers. It may be expected that the IR relaxation times depend in a different way on the extrinsic scattering at, e.g., grain boundaries than the ratio of mean free paths that is deduced from the analyses of the CIPGMR effect of spin-valves (section 3.6), or than the ratio of resistivities that is deduced from CPP-GMR experiments (section 3.1). Studies of the IR magnetorefractive effect might therefore be used to provide complementary information about the spin-dependent scattering processes. Just as the magnetorefractive effect is related to the GMR effect, there is a linear magnetic dichroism effect that is related to the AMR effect. This was discovered by van Driel et al. (1999a, 2000a), who found that the transmission of linearly polarized IR light through spin-valves or single ferromagnetic layers depends on the polarization direction with respect to the magnetization direction of the layer(s). When the magnetization is along the x-axis, the εxx and εyy dielectric tensor elements are different. Like the AMR effect, this results from the anisotropy of the relaxation times. The effect depends also on the spin-dependence of the relaxation times. An analysis by van Driel and coworkers of the wavelength dependence of the transmission change for permalloy films with variable layer thicknesses led to a spin-asymmetry ratio in the range α = 1.5–2.5. This is consistent with the result that was obtained independently from the magnetorefractive effect. 2.9. Deposition and microstructure Ideally, the microstructure of spin-valves should give rise to (1) A long mean free path for electrons of one type of spin (majority spin electrons for the commonly used fcc-type Ni–Co–Fe based SVs). (2) Strong scattering in the bulk of the F layers or at the interfaces for electrons with opposite spins.


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Fig. 2.15. Transmission Electron Microscopy cross-sectional image of a (Si(100)/ 3 nm Ta/ 8 nm Py/ 2.8 nm Cu/ 6 nm Py/ 10 nm Fe50 Mn50 / 5 nm Ta) spin-valve. From Rijks (1996a).

(3) Strongly specular scattering if specular reflection layers are present. (4) Optimized and well-controlled magnetic interactions. (5) A high thermal stability. The presence of defects in the bulk of the layers, such as vacancies, dislocations and grain boundaries, reduces the electron mean free paths, and gives potentially rise to a reduction of the energy barriers for processes that contribute to the thermally activated diffusion of atoms. The interface structure (flat, rough or interdiffused) also influences the mean free paths, and moreover determines in part the strength of magnetostatic and exchange interactions between the layers. We discuss in this section various factors which influence the microstructure. 2.9.1. Lattice matching It is a fortunate situation that the F and NM materials that are most suitable from the point of view of their electronic properties, such as Co, fcc-type binary or ternary Co– Fe–Ni alloys, and Cu are very well lattice matched. The lattice constants are very similar, leading to coherent growth. This can be seen from the cross-sectional Transmission Electron Microscopy (TEM) micrograph shown in fig. 2.15 for a Py/Cu/Py/Fe50 Mn50 spinvalve. The columnar grains extend through the Py, Cu and Fe50 Mn50 layers. The average grain size is 15–30 nm. The Si substrate and the Ta layers can be clearly distinguished, but the other layers are indistinguishable due to the small atomic number difference of the elements concerned. Grain-to-grain epitaxy in Py/Fe50 Mn50 bilayers had been observed earlier in a TEM study by Hwang et al. (1988). Lattice mismatch results in defects such as dislocations, at which scattering can take place. If in a structurally perfect system scattering (e.g., electron–phonon scattering) is already very strong for electrons of one spin, additional scattering at defects will (also) shorten the mean free path of the electrons of the opposite spin. The GMR ratio is then reduced, irrespective of the spin-dependence of the additional scattering (e.g., as a result of a spin-dependent density of final states). Better lattice matching can therefore explain the observation that the GMR ratio of Co/Cu/Ni80 Fe20 -based spin-valves is larger than that of spin-valves containing the electronically very similar noble metals Ag or Au (fig. 1.8).

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The mismatch between the cubic lattice constants of Ni80 Fe20 or Co with that of Cu is only approximately 1 and 2%, respectively. In contrast, the mismatch with Ag or Au is approximately 15%. However, also for spin-valves with Cu spacer layers scattering at grain boundaries cannot be neglected, as was concluded already by Dieny (1992b) and Dieny et al. (1993) (see section 3.6.5). 2.9.2. Layer thickness effect on the grain size The average grain size in thin films tends to increase with increasing film thickness. Grains with an energetically more favorable orientation tend to grow faster, at the expense of other grains. If that is the case, the effective mean free path increases with increasing film thickness. Rijks et al. (1995a) studied this effect for Cu and permalloy films, deposited on a Si(100) substrate covered by a 3 nm Ta underlayer. The sputter deposition conditions were typical for those used for fabricating spin-valves. The dependence of the conductance on the layer thickness was analysed within the semiclassical Boltzmann transport theory (see section 3.5). The results were analysed in terms of a layer thickness dependent mean −1 −1 free path, λ = (λ−1 i + λe ) . Here λi is the (temperature dependent) intrinsic mean free path and λe is the (temperature independent) extrinsic mean free path for defect scattering. For both materials, experiments carried out at 4.2 K and 300 K consistently revealed a monotonic increase of λe with increasing film thickness, with λe proportional to the grains size as observed using TEM. This suggests that grain boundary scattering might be a major cause of the defect scattering (in the paper, the notation λgr , instead of λe , was therefore used). For Cu films, λi (300 K) ≈33 nm was obtained, which is close to the value λi (300 K) ≈40 nm that would follow within the free electron Drude model. For films in the 5–20 nm ↑ ↓ range, λe varied from 10 to 30 nm. For permalloy films, (λi + λi ) ≈ 36 nm was obtained ↑ ↓ at 4.2 K, where λi and λi are the majority spin and minority spin intrinsic mean free paths, respectively. For film thicknesses in the 5–20 nm range, the analysis yielded λe ≈ 3–10 nm. In conclusion, defect scattering can strongly affect the mean free paths in thin films such as spin-valves. These results also imply that in studies of the layer thickness dependence of the transport properties of spin-valves, the possibility that the scattering parameters vary with the layer thickness should be considered (Rijks et al. 1996a). 2.9.3. Underlayers Underlayers are used for several purposes. They can act as a planarization layer or as a diffusion barrier between the spin-valve and the substrate (“buffer layer”). They can also be used as a specular reflection layer (see section 2.1). Here we focus on their effects on the microstructure. One of the most frequently used underlayers is a Ta layer with a thickness of a few nanometers. Its presence on top of various substrates such as Si(100), SiO2 , Si3 N4 or glass gives rise to a strong [111] texture of Cu and fcc-type Co–Fe–Ni alloys. X-ray diffraction of Ta/Py layers shows that a Ta layer thickness of only 3 nm is sufficient to obtain the full effect (Duchateau et al. 1994). A strong [111] texture is often advantageous for the following reasons: (1) The [111] texture promotes magnetic softness of the free layer, because the magnetocrystalline energy of a cubic crystal such as permalloy, Co or Co90 Fe10 does not


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depend on the magnetization direction within the (111) planes, if the K2 anisotropy constant can be neglected (Jérome et al., 1994). The preferred in-plane magnetization direction is then fully determined by the uniaxial anisotropy that is induced by growth in a magnetic field or by the shape anisotropy, and there are no grains with deviating easy-axis orientations that can act as nucleation or pinning centers of domain walls. (2) Growth on a 2 to 3 nm Ta underlayer is found to lead to a 10–15% larger MR ratio of Py/Cu/Py/Fe50Mn50 conventional spin-valves and a typically 20% lower sheet resistance (Duchateau et al. 1994). This may be attributed to a decreased defect scattering. The high sheet resistance of the thin Ta layer (resistivity typically 160 × 10−8 m) leads to negligible shunting. Gong et al. (2000) observed even a 20% increase of the AMR ratio of single permalloy layers by using 2–3 nm Ta underlayers. (3) The exchange bias field due to AF layers such as Ir20Mn80 or Fe50 Mn50 is highest for [111] oriented systems. See section 4.1. However, for PtMn a strong [111] texture may not be ideal (Lee et al., 2002a). The Ta layer is amorphous or nanocrystalline (Holloway and Fryer, 1990; Galtier et al., 1994; Lefakis et al., 1996; Lenssen et al., 1996). Lenssen and coworkers concluded from transmission electron diffraction of MBE-grown and sputter-deposited permalloy layers on Ta underlayers that the [111] texture is correlated with a Ta layer consisting of nanometersize randomly oriented grains in a metastable cubic phase which is different from the stable bulk bcc-type α-Ta structure or from earlier-reported metastable β-Ta or fcc-Ta phases. The detailed crystallographic structure was not determined. For sputter-deposited films the desired phase is observed up to tens of nanometers underlayer thickness, but for MBEgrown films it is only present up to a thickness of 1 nm. Thicker underlayers have then the stable α-Ta structure which does not induce a [111] structure. These results suggest that the initial Ta structure gives rise to a larger mobility of the Ni and Fe atoms to form the energetically favorable [111] texture. Nakatani et al. (1994) studied the effect of other underlayer materials for Fe50 Mn50based SVs on Si(100) substrates. Strong [111] textures, relatively high exchange bias fields and relatively high MR ratios were found using Ta, Hf, Nb, Ti or Zr underlayers. Cu, Ag, Au and Cr underlayers, grown directly on the Si substrate, did not cause a significant texture. Carey et al. (2002) studied the effect of thin Si underlayers. Several authors developed further improved SVs by making use of non-magnetic highresistivity fcc-type underlayers that give rise to an increased grain size in the active part of the layer stack, in order to enhance the GMR ratio and the thermal stability. Mizuguchi and Miauchi (1999) and Araki et al. (2000) found that the MR ratio of top SVs can be enhanced by making use of Ta/Py100−x Tax underlayers, with x < 15, instead of using only a Ta underlayer. For Ta/ 5 nm Py89 Ta11 / 2.5 nm Co90 Fe10 / 2.8 nm Cu/ 2.5 nm Co90 Fe10 / 6 nm Ir–Mn/ Ta spin-valves, Mizuguchu and Miyauchi obtained a very large GMR ratio (ΔR/R = 12.3%) and a change of the sheet resistance change that is about a factor of four larger than for conventional Py/Cu/Py/Fe50 Mn50 spin-valves (see table 2.1). Childress et al. (2001) studied Ta/ 4 nm Py60 Cr40 / 3.2 nm Py/ 0.5 nm Co90 Fe10 / 2.5 nm Cu/ 1 nm Co90 Fe10 / 1.9 nm Co60 Fe40 / 8 nm Ir–Mn/ 5 nm Ta

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spin-valves. The use of the Py60 Cr40 underlayer, instead of only Ta, was found to lead to an increase of the MR ratio from 8% to 11.5%. The observation of a decrease of the exchange bias field upon inclusion of the Py–Cr underlayer was considered to be consistent with the assumed larger average grain size, because within some models for the exchange anisotropy effect Heb is expected to decrease with increasing grain size in the AF layer (see section 4.6.2). 2.9.4. Deposition methods Magnetron sputtering or ion beam deposition are found to be the most suitable techniques for depositing spin-valves with a high MR ratio and optimal magnetic properties and thermal stability. In a dc magnetron sputter deposition chamber ions from a noble gas plasma (usually Ar) that is present in between the sputter target and the sample substrate are accelerated towards the target. The atoms that are sputtered from the target have initially a high kinetic energy, but lose part of that energy due to collisions with the noble gas atoms in the chamber. The degree of thermalisation of the atoms that arrive at the substrate depends on the massmismatch between the sputtered atoms and the noble gas atoms, and on the (substrate-target distance) × (sputter gas pressure) product. The substrate-target distance is typically fixed at 5 to 10 cm. The sputter gas pressure can be used to optimize the properties of the thin film. The deposition rate is typically 0.1–0.3 nm/s. Kools (1995) investigated experimentally how the microstructure and MR ratio of Py/Cu/Py/Fe50Mn50 spin-valves depend on the Ar sputter pressure, and used the results of Monte Carlo calculations of the kinetic-energy distribution of atoms arriving at the substrate to interpret the observations. Fig. 2.16 shows the measured dependence of the MR ratio on the Cu thickness, for various sputter pressures. The full curves are a fit using eq. (1.4) to the data above the critical Cu thickness below which there is no more a

Fig. 2.16. Dependence of the MR ratio on the Cu layer thickness and Ar sputter pressure, for SVs with the layer structure (Si(100)/ 3.5 nm Ta/ 8 nm Py/ tCu nm Cu/ 6 nm Py/ 10 nm Fe50 Mn50 / 3.5 nm Ta). The full lines represent a fit to the data using eq. (1.4), for the Cu thicknesses for which a full antiparallel alignment is obtained. 1 mTorr corresponds to 0.131 Pa. From Kools (1995).


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high-resistance plateau in the transfer curve. The use of a higher Ar pressure has a positive effect on the parameter A (the MR ratio in the limit tCu = 0), which shows a gradual increase from 5.8% at 1.5 mTorr to 6.9% at 10 mTorr. (Note: in fig. 2.16 the tCu scale starts at 1 nm, so this is not directly visible from the figure.) On the other hand, a high Ar pressure has a negative effect on the interlayer magnetic coupling across the Cu layer. Its increase with increasing pressure is evident from the larger decrease of the MR ratio at small Cu thicknesses. Deposition at intermediate pressures (3 to 5 mTorr) was found to be most optimal. These results were explained as follows. For low Ar pressures, a significant fraction of the atoms arriving at the target was calculated to have a kinetic energy above 15 eV, which is a few times the atomic binding energy. This leads to atomic displacements from one layer to another over typically 2 to 3 atomic planes. The resulting large atomic mobility during the growth leads to a low probability of the formation of voids between the grains and to relatively flat but strongly intermixed interfaces. For high Ar pressures, such collisional mixing occurs less frequently, leading to less intermixed interfaces. This explains the trend in (ΔR/R)0 , which is apparently quite sensitive to the interface quality. On the other hand, the small collisional mixing at high pressures gives rise to a large interface corrugation, and thereby to a strong magnetostatic interlayer coupling (“orange peel coupling”, see section 4.5.2). This picture was confirmed by the observations that the 1.5 mTorr samples showed a smaller sheet resistance, smaller surface roughness (from atomic force microscopy) and larger effective magnetically “dead” Py/Cu interface layer thickness (from magnetization experiments) than the 10 mTorr samples. Park and Shin (1998) and Lu et al. (1999) confirmed the trends observed by Kools, and showed that more optimal SV microstructures can be made by making use of a two-step sputter deposition process. The lower layers are deposited using a relatively low pressure, giving rise to dense layers with relatively large grains, whereas the upper layers are deposited at a much higher pressure in order to obtain less interdiffused interfaces. These studies were only carried out for SVs with permalloy or Ni66 Fe16 Co18 F-layers, resulting in fairly low MR ratios up to 5%. The benefits of this approach to state-of-the-art SVs with much higher MR ratios, containing, e.g., Co or Co90 Fe10 F-layers, have yet to be demonstrated. Zhou and Wadley (1998) carried out a theoretical study of the deposition process, and concluded that a combination of sharp interfaces and dense bulk layers can best be obtained by a flux of low energy adatoms at the beginning of each new layer, followed by a flux of higher energy adatoms during the deposition of the remainder of the layer. The effect of the background pressure in the sputter chamber was studied by Mao et al. (2000d). They found that the MR ratio and magnetic properties of Ni–Fe– Co/Co/Cu/F/Fe50 Mn50 conventional SVs, with F = Co or Ni–Fe–Co, are suboptimal when the background pressure is larger than 5 × 10−7 Torr (≈ 7 × 10−5 Pa). However, in some cases pumping down to a lower background pressure is advantageous. Takahashi et al. (2000a, 2000b) found a beneficial effect of a decrease of the background pressure in the chamber from 10−7 Torr to less than 10−10 Torr on the exchange bias interaction between Ir41 Mn59 and permalloy. Egelhoff et al. (1997b) found that the MR ratio of NiO/Co/Cu/Co bottom spin-valves is optimal at a partial O2 pressure of 5 × 10−9 Torr (5 × 10−7 Pa). The presence of such a small amount of oxygen gives rise to a relatively small ferromagnetic interlayer coupling and a decreased sheet resistance. It was argued that oxygen acts as a surfactant, leading to a decreased defect concentration, and that it enhanced the MR ratio

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by the formation of a specularly reflecting top layer. The effect of other surfactants, such as In, Pb and Ag was studied by Egelhoff et al. (1996b, 1996c) and Chopra et al. (2000a). The use of surfactants can give rise to smoother interfaces and hence to a reduced interlayer coupling (see section 4.5). It should be noted that in practice the partial pressure of contaminants such as water vapor can be less during deposition than just before deposition, as a result of the getting effect of deposited material (especially Ta). It can also be higher, when during the sputtering process contaminants are released from the chamber walls and from the targets by the impact of high energy atoms or ions, or when the sputter gas is insufficiently pure. Schwartz et al. (1998) investigated industrial scale dc magnetron sputter deposition, in order to assess the feasibility for applications such as read heads. They found that the thickness of nominally 2–3 nm Cu layers can be controlled within 0.05 nm. Variations of the sheet resistance and the MR ratio for a Py/Cu/Py/Fe50Mn50 top SVs over a 100 mm wafer were found to be only approximately ±1%, and the coupling field Hcoupl was found to vary by ±0.04 kA/m (±0.5 Oe). DC magnetron sputtering led to a substantially larger MR ratio than rf diode sputtering using the same chamber and magnetron sources (5.5% versus 3.8% for layer stacks with tCu = 2.0 nm). Similarly, Langer et al. (2001) found that the MR ratio of dc magnetron sputtered Co/Cu/Co/Fe50 Mn50 top SVs is larger than that of rf sputtered samples (10.0% versus 7.1% for layer stacks with tCu = 2.5 nm). The interface roughness that results from dc magnetron sputter deposition has been studied using low-angle X-ray diffraction (XRD) by Huang et al. (1992) and Langer et al. (2001), and using High Resolution Transmission Electron Microscopy (HRTEM) by Bayle-Guillemaud et al. (1996). For F/Cu/F/Fe50 Mn50 top SVs with F = Py and Co, low angle XRD revealed a root-mean-square roughnesses of the bottom (top) Py/Cu and Co/Cu interfaces of 0.74 (0.62) nm (Huang and coworkers) and 0.41 (0.48) nm (Langer and coworkers). The HRTEM study by Bayle-Guillemaud and coworkers of similar SVs with F = Co revealed that the interfaces are locally diffuse or rough over two monolayers (≈0.42 nm). It should be noted that the lateral scale over which low-angle XRD averages the interface roughness is of the order of 100 nm, whereas the HRTEM result is an average over a 3–5 nm length scale. The latter length scale is more relevant when assessing the effect of the interface structure on the scattering probability. It should also be noted that neither of the two methods can make a distinction between compositionally sharp, but stepped interfaces, and interdiffused interfaces. The larger roughness for the Py/Cu interfaces may be due to the much larger miscibility of Ni and Cu than of Co and Cu. The different interface qualities can in part explain the much higher MR ratio for Co-based SVs (see also section 3.3). In an ion beam deposition (IBD) chamber, a separate ion source is used to sputter atoms from a target. For the deposition of spin-valves, IBD has a number of advantages and disadvantages as compared to magnetron sputtering (Slaughter et al., 1999; Hegde et al., 1999; Hylton et al., 2000). One of the most important differences is the low pressure in the deposition chamber. On the one hand, that makes deposition under cleaner conditions possible. On the other hand, the kinetic energy of ions that are reflected from the target as neutral atoms is less strongly reduced by collisions at the gas molecules in the chamber. They can arrive at the sample with a very large kinetic energy, which gives rise to strong collisional mixing and hence to a poor interface quality. The flux of reflected neutrals decreases with increasing mass of the ions. IBD of spin-valves using Ar-ions led to


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disappointingly low MR ratios (Joo and Atwater, 1995; Wang et al., 1997b). The use of Xe-ions, which are heavier, has led to higher MR ratios due to less collisional mixing. However, the MR ratios still tend to be smaller than obtained by sputter deposition (Wang et al., 1997b; Slaughter et al., 1999; Hegde et al., 1999; Sant et al., 2001; Kools et al., 2001; Lee et al., 2001). E.g., Kools et al. (2001) studied Ta/Py/Ir–Mn/Co90Fe10 /NOL/Co90 Fe10 / Cu/Co90 Fe10 /Cu/Ta specular spin-valves. For samples made by sputter deposition and IBD, they obtained MR ratios up to 15.5% and 12%, respectively. Whereas for magnetron sputtering the kinetic energy of the arriving atoms can thus be chosen to be an optimal compromise between two extremes, that degree of freedom is not available for evaporation deposition. For the growth on single crystalline substrates, such as AF-coupled Fe/Cr multilayers with a high GMR ratio on GaAs or Ge, MBE is well suited, because a superlattice with a very small density of bulk defects can already be obtained as a result of the coherence with the substrate. However, there are no suitable and industrially feasible insulating single crystal substrates for the coherent MBE growth of the fcc-type materials of which spin-valves are composed. Lenssen et al. (1996) studied MBE grown Si(100)/Ta/Py/Cu/Py/Fe50Mn50 conventional SVs, and obtained MR ratios up to 4%. Sputter deposition yields typically 4.5% to 5%. The authors ascribed the slightly smaller MR ratio to the relatively small degree of [111] texture that could be obtained on the Ta underlayers. A later study of similar SVs by Huang et al. (1999) led to even lower MR ratios and a large coercivity of the free layer. The MBE deposition rate is typically one order of magnitude smaller than for sputter deposition and an ultralow (UHV) pressure is required. For all these reasons, MBE is not of interest for the industrial production of SV devices. 2.10. Thermal stability The thermal stability of spin-valves is determined by (i) the stability of the structure of the active part of the layer stack with respect to irreversible changes due to transformation or diffusion processes, and (ii) the stability of the exchange bias field with respect to structural and magnetic changes of the AF layer. It is not always possible to strictly separate both aspects, e.g., because of diffusion of atoms from the AF layer into the active part. Here we focus on the stability of the active part. The thermal stability of the exchange bias field is discussed in section 4.6. Irreversible thermal degradation of the structure can take place during the lithographic processing, or during the lifetime. In a read head fabrication process, SVs are exposed to 250–280 ◦ C for 2–10 hours. The working temperature of a hard disk read head during practical use is 120–150 ◦ C (Saito et al., 1998). Operational lifetimes are usually specified as >10 years. Automotive applications of SV sensors require stability during the lifetime up to 175–200 ◦ C. SVs that have been deposited in a back-end process on top of a CMOS semiconductor structure should be able to withstand short thermal treatments up to 400–450 ◦ C during processing. The diffusion processes that have been identified as most relevant are interface mixing and grain boundary diffusion. At the temperatures and timescales of interest, bulk diffusion is expected to play a less important role. We focus on the initial stages of degradation, before grain growth starts to give rise to a more drastic change of the microstructure (Meny et al., 1993).

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Fig. 2.17. Results of a study of the thermal stability of (Si(100)/ 5 nm Ta/ tf nm Py/ tCu nm Cu/ tp nm Py/ 11 nm Fe50 Mn50 / 5 nm Ta) SVs. Four consecutive anneal steps were performed at the temperatures given in (a), each lasting 6.5 hours. (a) Variation with the annealing temperature of the MR ratio, as a function of the Py free layer thickness tf , for tCu = 2.25 nm and tp = 5 nm. (b) Variation with the annealing temperature of the MR ratio, as a function of the Cu spacer layer thickness tCu , for tf = 7.5 nm and tp = 5 nm. (c) Variation with the annealing temperature of the effective interface roughness, δXRD , as determined from X-ray Diffraction, and of the effective “non-ferromagnetic layer thickness”, δNF , as determined from magnetization measurements. From Nozières et al. (1993).

2.10.1. Interface mixing Thermal deterioration by interface mixing occurs when the F and NM layers are miscible. Speriosu et al. (1993) and Nozières et al. (1993) concluded that this is the predominant initial degradation mechanism for Py/Cu/Py/Fe50Mn50 spin-valves. They studied (7.5 nm Py/ 2.2 nm Cu/ 5 nm Py/ 11 nm Fe50 Mn50) structures and observed a tenfold reduction of the GMR ratio after four sequential annealing steps at 240, 280, 320 and 360 ◦ C, each step lasting 6.5 hours. Fig. 2.17 (a), (b) shows the measured Py and Cu layer thickness dependences of the MR ratio after these annealing steps. From an analysis of the curves using eqs (1.4) and (1.5) it was argued that the MR ratio is mainly decreased due to enlarged scattering at the interfaces, and much less to enhanced scattering in the bulk of the layers. Evidence for the presence of an intermixed zone at the interfaces that increases with increasing anneal temperature was obtained from low-angle X-ray diffraction (XRD), which yielded the root-mean-square interface roughness, δXRD , and from magnetization measurements, which yielded the effective “non-ferromagnetic layer thickness” per interface, δNF . Both quantities are given in fig. 2.17(c). As expected, δXRD is larger than δNF , because also the non-magnetic Cu atoms contribute to δXRD . A detailed low-angle XRD study of the annealing effects on all interfaces was carried out by Huang et al. (1993). The deterioration of the MR ratio that results from interface mixing can be avoided or reduced when no Ni, but only Co or Fe are present at the interface with the Cu spacer layers. Majority-spin scattering at rough or intermixed Co/Cu or Co–Fe/Cu interfaces is expected to be weaker than at Py/Cu interfaces (see section 3.3). In addition, Co and Fe are, at low temperatures, immiscible with Cu. It is not sufficient to use Ni-containing alloys with a lower Ni-concentration than in permalloy. Kitade et al. (1995) observed a similarly strong thermal decrease of the MR ratio after annealing at 200–300 ◦ C for (F/Cu/F/Fe50 Mn50 ) spin-valves with Co-rich Py25 Co75 F-layers (as deposited ΔR/R = 7.5%), as for F = Py


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(as-deposited ΔR/R = 3.2%). The immiscibility of Co and Cu leads even to demixing upon a heat treatment, as was shown by Menyhard et al. (2000) from an Auger depth profiling study of a spin-valve. An as-deposited 4–5 monolayer thick intermixed Co/Cu interface layer was seen to be reduced to 2 monolayers after annealing during 2 hours at 260 ◦ C. The use of a composite free layer, consisting of a softmagnetic permalloy layer and a thin Co or Co90 Fe10 layer at the interface with the Cu spacer layer does not only enhance the MR ratio (section 2.1.2). It also gives rise to a significant improvement of the thermal stability, as shown by Hwang et al. (1996) for (F/Cu)n multilayers and by Hamakawa et al. (1996) and Saito et al. (1998) for SVs. Hamakawa and coworkers concluded that insertion of a δ = 0.5 nm thick Co layer in (NiO/Py/ δ Co/Cu/Py) SVs was already sufficient to obtain the full effect of that layer as a diffusion barrier (at 230 ◦ C). Zeltser et al. (1998) found that Co90 Fe10 interface layers, in combination with Py, give rise to a slightly better thermal stability than Co interface layers. Saito et al. (1998) investigated the structural changes that occur upon annealing using low-angle XRD, and found that, like Py/Cu interfaces, also Co90 Fe10 /Cu interfaces show a certain thermally induced interface roughening. Apparently, this is then less detrimental than in the case of Py/Cu interfaces. We note that, as remarked before, from low-angle XRD no distinction can be made between intermixing and an increase of the corrugation. Moreover, the technique averages over a lateral length scale as large as ≈100 nm. Portier et al. (1998) carried out a high-resolution TEM (HRTEM) study of annealed Ti/Co/Cu/Fe50 Mn50 /Ti SVs. The authors concluded that the observed decrease of the MR ratio, from 7.5% for as-deposited samples to 5.2% after 1 hour of annealing at 290 ◦ C, is not accompanied by a significant change of the sharpness of the Co/Cu and Cu/Co interfaces. On a lateral scale of 3–5 nm, the interface remains mixed or corrugated over a thickness of only ≈2 monolayers. The decrease of the GMR effect was ascribed to alloying between the Ti underlayer and the Co layer directly on top of it, giving rise to a decrease of the effective free layer thickness. 2.10.2. Grain boundary diffusion of manganese from the AF layer Grain boundary diffusion affects the properties of SVs in various ways. Grain boundary diffusion of magnetic atoms into the Cu spacer layer can give rise to a change of the ferromagnetic magnetostatic and pin-hole coupling (Zeltser et al., 1998; Lin and Mauri et al., 2001). Grain boundary diffusion of Cu into the magnetic layers can lead to a decoupling of the grains, which for, e.g., Cu/Co/Cu trilayers has been shown to lead to an enhanced coercivity (Bensmina et al. 1999). We focus here on a third effect, viz. the reduction of the MR ratio due to diffusion of Mn from the AF layer into the active part of the layer. Mn-diffusion can give rise to a decrease of the GMR ratio because the presence of Mn impurities in Co, Co90 Fe10 or Cu layers gives rise to enhanced majority-spin electron scattering (see also section 3.6.9). The importance of Mn diffusion was discovered by Iwasaki et al. (1997), who observed that Ir–Mn based SVs are thermally more stable than otherwise identical Fe50 Mn50-based SVs. The different thermal stabilities of Ir–Mn and Fe50 Mn50 -based SVs, with the structure 10 nm Co–Nb–Zr/ 2 nm Py/ 3 nm Co90 Fe10 / 3 nm Cu/ 2.3 nm Co90 Fe10 / AF/ 5 nm Ta can be seen from fig. 2.18, taken from Saito et al. (1998). The AF layers consisted of

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Fig. 2.18. Annealing time dependence of the normalized MR ratio at various temperatures for (10 nm Co–Nb–Zr/ 2 nm Py/ 3 nm Co90 Fe10 / 3 nm Cu/ 2.3 nm Co90 Fe10 / tAF AF/ 5 nm Ta) SVs, for (a) SVs with a 15 nm Fe50 Mn50 exchange bias layer, and (b) SVs with a 7 nm Ir22 Mn78 exchange bias layer. From Saito et al. (1998).

15 nm Fe50 Mn50 or 7 nm Ir–Mn, and the as-deposited MR ratios were 6–7% and 7.5– 8%, respectively. Takiguchi et al. (2000) found that Ir–Mn based SVs are also more stable than Rh17 Mn83 -based SVs. PtMn-based SVs, in turn, were found to be thermally more stable than otherwise identical Ir–Mn based SVs (Takiguchi et al., 2000; Anderson et al. 2000c). Furthermore, SVs based on (ordered) Pd29 Pt18 Mn53 are thermally more stable than Fe50 Mn50-based SVs (Aoshima et al., 1999). An explicit proof of the occurrence of a high concentration of Mn at grain boundaries after annealing was provided by Maesaka et al. (1998) from a HRTEM and energy dispersive X-ray spectroscopy (EDXS) with a resolution of 1 nm. Fig. 2.19 shows HRTEM crosssections of a Si(100)/ SiO2 / 5.2 nm Ta/ 3.8 Py/ 2 Co90 Fe10 / 2.4 nm Cu/ 3 nm Co90 Fe10 / 7.6 nm Ir–Mn/ 8 Ta SV, as-deposited (left) and after 1 hour annealing at 275 ◦ C (right).


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Fig. 2.19. High-resolution TEM images of (Ta/ 3.8 nm Py/ 2 nm Co90 Fe10 / 2.4 nm Cu/ 3 nm Co90 Fe10 / 7.6 nm Ir20 Mn80 / 8 nm Ta) SVs, (a) as-deposited, and (b) annealed at 275 ◦ C for 1 hour. The layer compositions at points A–D are discussed in the text. From Maesaka et al. (1998).

After the anneal, the resistance change had decreased by approximately 15%. The layer stack shows a strong [111] texture. The average grain size of 15 nm had not changed after annealing. The grain boundaries were seen to extend from bumps on the Ta surface, suggesting that the roughness of that layer determines the grain nucleation. The EDXS analysis revealed that before annealing only Co and Fe are present in the Co90 Fe10 layer and near a grain boundary in that layer, in points A and B, respectively, However, after annealing Ta, Ir and Mn were found to be present in that layer, with in particular a large Mn concentration at point D in the grain boundary. Takiguchi et al. (2000) came to similar conclusions from EDXS studies of the composition of the Cu spacer layer in annealed Rh17 Mn83 -based SVs. Results on PtMn and NiMn based systems are given in figs 2.20 and 2.21, respectively. Fig. 2.20 was taken from Lin and Mauri (2001), who studied PtMn based SVs with the layer structure as given in the figure caption, containing a Sy-AF pinned layer that can act as a Mn diffusion barrier. At short anneal times, the MR ratio increases as a result of the increase of the exchange bias field when the PtMn structure orders. After an anneal of 2 hours at 280 ◦ C, the MR ratio was 13.8%. Longer annealing at higher temperatures leads to irreversible degradation of the layer stack. Up to 260 ◦ C no degradation of the MR ratio was observed until the end of the experiments after 14 hours, but changes of the coupling

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Fig. 2.20. Dependence of the MR ratio on the annealing time and temperature for (3 Al2 O3 / 3 Ni–Fe–Cr/ 1 Py/ 20 PtMn/ 2 Co90 Fe10 / 0.8 Ru/ 2.2 Co90 Fe10 / 2.2 Cu/ 0.9 Co90 Fe10 /2.7 Py/ 0.8 Cu/ 1 Al2 O3 / 6 Ta) SVs. From Lin and Mauri (2001).

Fig. 2.21. Dependence of the MR ratio on the annealing time and temperature for (Ta/ 4 nm Py/ 1.5 nm Co90 Fe10 / 2.8 nm Cu/ 2 nm Co90 Fe10 / 1.5 nm Py/ 25 nm NiMn/ Ta) SVs. From Zhang et al. (2000).

field were already noticed at lower anneal temperatures. Other studies on the thermal stability of PtMn based SVs were carried out by Cool et al. (2000) and Kim et al. (2001a). Fig. 2.21 shows results reported by Zhang et al. (2000) on the thermal stability of the MR ratio of NiMn-based systems with the layer structure given in the figure caption, measured over a 10-day period. The samples had already been given a 7.5 hour postdeposition anneal at 275 ◦ C in order to obtain the exchange bias field, after which the MR ratio was 6%. No systematic comparison of the stability of all relevant Mn-containing AF materials with respect to diffusion out of that layer has been made so far. If the thermodynamic sta-


77

bility of the AF layer would be the determining factor, one would expect an increase of the stability of relevant AF materials in the order Fe50 Mn50 – Cr0.46 Mn0.46Pt0.08 – (Ru– Rh)20 Mn80 – NiMn – Ir20 Mn80 – Pd0.6Pt0.4 Mn – PtMn. This follows from the heats of formation for materials with these compositions as predicted from the Miedema model (de Boer et al., 1988). We have included the calculated heats of formation in table 4.7. An experimental indication that the thermodynamic stability is of importance was found by Anderson et al. (2000c), who observed a significant slowing down of thermal degradation of PtMn based SVs after the occurrence of the fcc-fct disorder-order phase transition in PtMn. The observed increases of the stability in the series Fe50 Mn50 – Ir20Mn80 – PtMn, Rh17 Mn83 – Ir–Mn and Fe50 Mn50 – Pd29 Pt18 Mn53 are all consistent with the prediction given above. It is at present not possible to make further meaningful comparisons between the results from different groups, e.g., between Ir–Mn and NiMn or between NiMn and PtMn based systems, because of the sensitivity of the thermal stability on the layer thicknesses and film microstructure. There are several ways for improving the thermal stability of SVs with respect to Mn diffusion. A first possibility is to use a deposition process or an underlayer that leads to a microstructure for which grain boundary diffusion is slow. E.g., Maesaka et al. (1998) showed that growth on a MgO(111) substrate, or on a Co–Zr–Ta underlayer, leads to larger and smaller average grain sizes with respect to growth on Ta, respectively, leading to a better and worse thermal stability. A second option is to make use of a NOL in the pinned layer. NOLs act as a diffusion barrier, and give rise to planarization of the layer structure which makes grain boundary diffusion less fast (Kamiguchi et al., 1999a; Gillies et al., 2001; Jang et al., 2002a; see section 2.1.7). Thirdly, also a Ru layer acts as a diffusion barrier. Mn or Ni diffusion into the active part of the spin-valve can be slowed down by making use of a Sy-AF pinned layer of the form Co90 Fe10 /Ru/Co90 Fe10 , as shown by Anderson et al. (2000c) for Ir–Mn based SVs and by Huang et al. (2001) for NiMn based SVs. A fourth approach is to make use of ternary crystalline ferromagnetic (Co90 Fe10 )1−x Bx alloys (Kanai et al., 1997, 1999). Spin valves of the type Py/Co–Fe– B/Cu/(Co90 Fe10 )1−x Bx /Py/Fe50 Mn50 were found to show for x = 0 a considerable decrease of the MR ratio after annealing to 250–300 ◦ C during wafer fabrication. In contrast, the MR ratio of systems with x = 0.05 and x = 0.10 (see table 2.1(b)) was found to increase. An optimal MR ratio of 8.2% after annealing was found for NiO biased systems using (Co90 Fe10 )0.95B0.05 (table 2.1(f)). The B-containing layer may act as a barrier against Ni or Mn diffusion towards the Cu layer. B decreases the majority spin mean free path in the alloy, so the optimal composition is a compromise that depends on the required thermal stability. 3. Spin-polarized transport in spin-valves: theory and modelling In this section we first discuss the microscopic origin of spin-dependent scattering in spinvalves, in the bulk of the layers and at the interfaces. Subsequently, we present analyses of the (magneto)conductance of various types of spin valves in terms of the semi-classical Camley–Barnas (CB) transport model, for the current-in-the-plane of the layers (CIP) geometry. Finally, we discuss briefly some limitations of the CB model, some proposed extensions, and theories beyond the model.

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R. COEHOORN

3.1. Spin-dependent conductivity in ferromagnets – spin-dependent scattering The spin-dependence of the conductivity in the bulk of the F layers is related to the spindependence of the electronic structure of the layers, and/or to the spin-dependence of the scattering potential. When the two-current model (already introduced in section 1.2) is applicable, the conductivity is given by σ = σ ↑ + σ ↓,

(3.1)

where σ↑ and σ↓ are the conductivities for the two spin-channels. The scattering spin asymmetry ratio α, defined as, α≡

σ ↑ ρ↓ = σ ↓ ρ↑

(3.2)

is frequently used as a measure of the spin-dependence of the conductivity. Making the free-electron approximation, σ↑ and σ↓ are given by the Drude formula (Ashcroft and Mermin, 1976): e2 n↑(↓) τ ↑(↓) (3.3) m where e is the electron charge, n is the conduction electron density, τ is the electron momentum relaxation time and m is the electron mass. From the Fermi golden rule, the spindependent scattering rate is given by σ ↑(↓) =

2π ↑(↓) 2 ↑(↓) 1 = N (EF ), V h¯ sc τ ↑(↓) ↑(↓)

(3.4)

where |Vsc |2 is the (average) scattering potential and N ↑(↓) (EF ) is the density of states at the Fermi level. The spin-dependence of the conductivity is thus determined by factors that follow directly from the band structure of the unperturbed lattice (n, N(EF ) and m), and by the scattering potential, which arises from perturbations of the lattice periodicity. The spin-dependence of scattering in the elementary 3d-transition metals Fe, Co and Ni can be understood from the spin-dependent density of states (DOS), given in fig. 3.1 (a)–(c). To a first approximation, the DOS can be viewed as a superposition of a wide spband and a narrow d-band. The conductivity, which is determined predominantly by the contribution from the light sp-electrons, is decreased when d-states (to which scattering can take place) are present at the Fermi level. For Co and Ni the majority spin d-band is fully occupied, and is situated well below the Fermi level, whereas the minority spin 3d-band is only partially occupied. So when the scattering potential is spin-independent, the majority spin conductivity of Co and Ni is expected to be larger than the minority spin conductivity. Qualitatively, this picture is supported by analyses of the temperature dependence of the conductivity of dilute binary alloys (Loegel and Gautier, 1971; Fert and Campbell, 1976). For Co, analyses of the CPP magnetoresistance at 4.2 K of magnetic multilayers have yielded αCo = 3.1 (Yang et al., 1995; Pratt et al., 1996). For Fe, dilute alloy experiments have led to the conclusion that α is very close to 1 (Campbell and Fert, 1982). The much smaller polarization of the conductance for Fe, than for Co and Ni, can be understood from DOS, which shows that majority and minority spin


79

Fig. 3.1. Densities of states (DOS) of the elemental metals Fe, hcp-Co, Ni and Cu, obtained from self-consistent band structure calculations using the Augmented Spherical Wave (ASW) method. The DOS of fcc-Co is well approximated by that of fcc-Ni, with the minority-spin DOS shifted upwards such that the arrow coincides with the Fermi-level. From Coehoorn (2000).

3d-states are both present at the Fermi level. Therefore, sp-type electrons with both spins can scatter to 3d-type final states. Indeed, a study of the Fe layer thickness dependence of the GMR ratio of Fe/Cr multilayers has indicated that the spin-dependence of scattering in the bulk of the Fe layers is very weak, and that the high GMR ratio is mainly due to spin-dependent interface scattering (Schad et al., 1994). Much experimental work has been done on the spin-dependence of the conductivity of dilute Fe, Co or Ni based magnetic alloys. Using the two-current model, their residual resistivities have been obtained from the residual resistivities of ternary alloys (Dorleijn 1976; Campbell and Fert, 1982). The spin-dependence of the scattering potential due to impurities in a given host varies widely, giving rise to a wide range of observed spin asymmetry ratios. For dilute Co–Fe, Co–Ni, Ni–Fe or Ni–Co alloys, e.g., α 1, whereas for dilute Co–Cr, Co–V, Ni–Cr and Ni–V alloys, α 1 (Dorleijn 1976; Campbell and Fert, 1982). (The host metal is indicated by bold symbols.) We will use these results in section 3.6.9, where the magnetoresistance of SVs containing Co layers with transition metal impurity layers is discussed. For that purpose, the spin-polarized residual resistivities of transition metal impurities in Co are included in fig. 3.11.

80

R. COEHOORN

Good qualitative understanding of these results has been obtained from Virtual Bound State theories (Campbell and Fert, 1982; Coehoorn, 1993). The spin-dependent residual resistivities are then considered to be related to the differences in the spin-dependent filling of the host metal and impurity atom 3d densities of states. Recently, results obtained from scalar-relativistic7 first principles calculations of the spin-dependent residual resistivity of dilute magnetic alloys were for many alloys found to be in good quantitative agreement with experiment (Mertig, 1999). An important exception is the residual resistivity calculated for strong ferromagnets, such as Ni–Co and Ni–Fe alloys. In these alloys the filling of the majority-spin host and guest 3d-DOS is essentially 100%, reflecting that there is almost no difference between the host and guest electronic potentials. Majority-spin scattering is therefore calculated to be very weak, leading to spin-asymmetry ratios larger than 100 or even 1000. Experimentally, much lower values are found, e.g., αeff,exp = 13–30 for Ni–Co and αeff,exp = 7.3–20 for Ni–Fe (Campbell and Fert, 1982). A similar discrepancy is found for concentrated alloys that are more relevant to spin-valves, such as permalloy. In the next section, it is shown that a fully relativistic theory is required for explaining these results. 3.2. Spin-dependent conductivity in ferromagnets – effect of spin-mixing due to the spin-orbit interaction The picture that we have sketched in section 3.1 can be used to understand trends in the spin-dependence of the conductance. However, it has been found to be quantitatively incorrect for 3d-transition metal alloys in which the conductivity is strongly spin-dependent (Mertig, 1993; Butler et al., 1995; Banhart et al., 1997). The problem is that in such cases the spin-mixing due to the spin-orbit interaction (SOI) cannot be neglected. In the simple form presented above, the two-current model therefore fails, e.g., for bulk permalloy, which is frequently used in spin-valves. We consider the situation for permalloy in some detail. In permalloy, the Ni and Fe atoms are randomly or almost randomly distributed on the sites of an fcc lattice. The site disorder results in a finite bulk resistivity at 4.2 K of ρ = 4.7 × 10−8 m. Analyses of the CPP-GMR ratio at 4.2 K of magnetic multilayers have yielded ρ = 11.9 × 10−8 m, and αexp,CPP = 7 ± 2 (Steenwyk et al., 1997). Note that the resistivity of thin films is generally larger than the bulk resistivity due to defect scattering. Scalar-relativistic calculations, which neglect the spin-orbit interaction (SOI), yield resistivities that are more than one order of magnitude smaller than the experimental value. Results reported by Butler et al. (1995) and Nicholson et al. (1997) are ρ↑ ≈ (0.18–0.3) × 10−8 m and ρ↓ ≈ 100 × 10−8 m. The conductivity would then be almost completely carried by the majority spin electrons, with an extremely large scattering spin-asymmetry ratio: α 100. Nicholson et al. (1997) found that the introduction of the SOI raised the resistivity to about 2.5 × 10−8 m. More recently, Blaas et al. (2001) obtained ρ ≈ 7 × 10−8 m for permalloy. These drastically increased values are in much better agreement with experiment. Banhart et al. (1997) performed calculations for 7 In scalar relativistic electronic structure calculations the relativistic mass-velocity and Darwin terms are taken into account, but the spin-orbit interaction is neglected.


81

Fig. 3.2. Resistor scheme that represents the total resistivity (eq. (3.5)) after spin-mixing.

Ni1−x Fex and Ni1−x Cox alloys in wide concentration ranges, and found similarly large increases of the resistivity when the SOI was included. The introduction of the SOI has two effects: it mixes majority and minority spin states, and it leads to a spin-dependent energy shift of states. Ebert et al. (2000) showed explicitly that it is the mixing effect that is responsible for the increase of the resistivity. The majority spin electron states acquire some minority spin character, so that they can be scattered into the minority spin sub-band. In spite of the low degree of intermixing of spin character for light atoms such as Fe, Co and Ni, the additional scattering is strong because of the large minority spin density of final states. The majority spin resistivity is then strongly increased. The enhancement of the resistivity by spin mixing due to the SOI can be treated in the same way as that by spin-mixing due to electron–magnon scattering. The resistivity is given by (Fert and Campbell, 1976; see also section 3.7.2) ↑ ↓

ρ=

↑

↓

ρ0 ρ0 + ρ ↑↓ (ρ0 + ρ0 ) ↑

↓

ρ0 + ρ0 + 4ρ ↑↓

,

(3.5)

where the indices “0” indicate the resistivities that would be obtained in the absence of the SOI and where ρ ↑↓ is called the spin-mixing resistivity. The total resistivity can be represented by the resistor scheme shown in fig. 3.2. When discussing the resistivity enhance↓ ↑ ment for materials with α0 ≡ ρ0 /ρ0 > 1, it is convenient to make use of the dimensionless ↓ parameter x ≡ ρ ↑↓ /ρ0 . We show below that for the 3d-transition metal alloys and multilayers that are of interest for applications in spin-valves, x 1. It follows from eq. (3.5) that a significant enhancement of the resistivity will only occur if the product α0 x is of the order of 1, or larger. In order to gain some understanding of the physical meaning of the parameter x, we consider the effect of spin mixing due to the SOI using a more microscopic model, in the limit α0 1. Due to the SOI, wavefunctions that have predominantly majority or minority spin character have the general form φ1 = aφ ↑ + bφ ↓ and φ2 = bφ ↑ + aφ ↓ , respectively, with b2 < a 2 . The normalized wavefunctions φ ↑ and φ ↓ and the parameters b and a = (1 − b2) are assumed to be representative for all electron states that contribute to the conduction. Neglecting terms containing V ↑ and N ↑ (EF ) (because α0 1), the scattering

82

R. COEHOORN

rates of electrons in states |φ1 are from eq. (3.4) proportional to |bφ ↓ |V ↓ |aφ ↓ |2 . The ↓ resistivity for transport via the |φ1 channel is then equal to ρ1 = a 2b2 ρ0 . Similarly, the ↓ resistivity for transport via the |φ2 channel is equal to ρ2 = a 4 ρ0 . When the SOI is weak ↓ ↑ (b2 1) the total resistivity ρ ≈ ρ1 ≈ b2 ρ0 . Using eq. (3.5), with ρ0 = 0, it follows that ρ ↑↓ ↓

ρ0

≡x ∼ = b2

if α0−1 x 1.

(3.6)

This shows that x is determined by the degree to which the SOI induces wavefunction mixing. For a given material, x is proportional to the square of the relevant SOI parameter. In the case of 3d-transition metal systems, this is the spin-orbit parameter for the 3d states. The effect of the SOI parameter on the resistivity of permalloy has been studied by Banhart et al. (1996). Spin-mixing invalidates the two-current model. However, as suggested by the formal theory of spin-mixing (section 3.7.2) one may define a modified version of the two-current model, based on the effective resistivities ↑ ↓

↑

ρeff =

↑

↓

ρ0 ρ0 + ρ ↑↓ (ρ0 + ρ0 ) ↓

ρ0 + 2ρ ↑↓

,

(3.7)

.

(3.8)

and ↓ ρeff

↑ ↓

=

↑

↓

ρ0 ρ0 + ρ ↑↓ (ρ0 + ρ0 ) ↑

ρ0 + 2ρ ↑↓

These effective resistivities are physically meaningful quantities in following sense. Suppose that the resistivity is increased by adding a low concentration of additional scat↑ ↑ ↑ tering centers, giving rise to modified spin-dependent resistivities ρ0 = ρ0 + Δρ0 and ↓ ↓ ↓ ↑ ρ0 = ρ0 + Δρ0 , whereas ρ ↑↓ remains unchanged. For sufficiently small values of Δρ0 ↓ and Δρ0 an excellent approximation to the exact value of the modified overall resistivity, ↑ ↓ ↑ ↑ ↑ ρ , is then given by the resistivity ρ = (1/ρeff + 1/ρeff )−1 , with ρeff = ρeff + Δρ0 and ↓ ↓ ↓ ρeff = ρeff + Δρ0 , as if spin-mixing would play no role. The relative error, (ρ − ρ )/ρ , ↑ ↓ is to first order in Δρ0 or Δρ0 equal to zero. It is thus possible to successfully predict the effect on the resistivity due to (sufficiently small) additional spin-polarized resistivities ↑ ↓ ↑ ↓ from a modified form of the two-current model that uses ρeff and ρeff instead of ρ0 and ρ0 . ↓ ↑ The effective scattering spin asymmetry ratio, αeff ≡ ρeff /ρeff , can be obtained from eqs (3.7) and (3.8). When α0−1 x 1, αeff is given by 1 1 +1∼ αeff ∼ (3.9) = = 2 + 1. 2x 2b It is then not determined by the ratio of spin-dependent conductivities that would follow from eqs (3.3) and (3.4), which depend on the (spin-dependent) scattering potentials, but by the degree to which the SOI mixes majority and minority states, an intrinsic property of the material. The detailed scattering mechanism then does not affect αeff , provided that it does not affect x.


83

The application of this formalism to the theoretical results obtained for permalloy (see ↑↓ ↓ ↓ above) yields ρth ≈ ρth ρth,0 /(4ρth + ρth,0 ) ≈ 2.3 × 10−8 m, xth ≈ 0.023 and αeff,th ≈ 22. As expected from the low atomic masses of Ni and Fe, x is much smaller than 1. Application to the results obtained by Banhart et al. (1997) yields xth ≈ 0.018 for Ni– Co and Ni–Fe alloys in the Ni-rich limit, and a monotonous decrease to xth ≈ 0.004 and xth ≈ 0.002 in the Co and Fe-rich limits, respectively. This reflects, in part, the effect of the ≈25% and ≈50% decrease of the 3d-spin orbit parameter when replacing Ni by Co or Fe, respectively. Results obtained by analysing the CIP-magnetoresistance of spin-valves (section 3.6.5) and the CPP-magnetoresistance of multilayers (Steenwyk et al., 1997) yield values for αeff in the range 6 to 20. The (rough) theoretical estimate thus coincides with the upper limit of this range of experimental values. When making a comparison between theory and experiments at T = 0 it should be realized that in realistic alloy films extrinsic scattering due to defects may be larger than the intrinsic scattering. Spin-mixing that is induced by the SOI will be less relevant when these additional scattering processes are dominant and relatively weakly spin-dependent, i.e., if for these processes α0 x 1. Effects of the microstructure of spin-valves on the effective mean free paths are discussed in section 3.6.5. However, a full understanding of ↑ ↓ microstructural effects on ρ0 , ρ0 and ρ ↑↓ is presently not available for the materials that are of interest in spin-valves. Binder et al. (2001) calculated the resistivity due to scattering at Cu impurities in Co, and obtained α ≈ 23. For fcc and hcp Co, Schulthess et al. (1997) have theoretically studied the effect of introducing structural defects on the spin-dependent conductivity. While neglecting the SOI, they found that stacking faults and twin boundaries lead to a resistivity rise which is largest for the minority spin channel. A qualitatively similar effect is expected for permalloy, which has a similar electronic structure. At finite temperatures, electron–phonon scattering may become dominant, and spin-mixing due to electron–magnon scattering may become more important than spin-mixing due to the SOI. 3.3. Spin-dependent scattering at interfaces The spin-dependence of the scattering potential plays an important role when considering scattering at the F/NM interfaces. Interfaces can be atomically flat, rough but nonintermixed, or diffuse (forming an intermixed boundary layer). At atomically flat interfaces, only specular reflection can take place. This occurs when, effectively, the potentials within the F and NM layers are different. At rough or diffuse interfaces diffuse scattering can take place. Both effects are relevant to the GMR effect in spin-valves. Fig. 3.3 shows a schematic picture of the “potential landscape” in the active layer of a simple spin-valve, indicating the different origins of scattering. Only deviations from the periodic atomic potentials are shown, as no scattering takes place in a regular periodic lattice. The size of the potential step and of the scattering potentials at imperfections of the interfaces depends on the degree of matching of the electronic structures of the F and NM materials in the bulk of the layers and near the interface (Itoh et al., 1993; Butler et al., 1995). In order to obtain a large GMR effect, good electronic structure matching is required for one spin direction, and bad matching for the opposite spin direction. Ideally, this is true for the electronic structures in the bulk of the layers, at atomically flat parts of the interfaces, and even near imperfections of the interfaces.

84

R. COEHOORN

Fig. 3.3. “Potential landscape” inside the F/NM/F active part of a spin-valve, for the two spin channels in the parallel state (a), (b) and in the antiparallel state (c), indicating the different origins of scattering. Adapted from Vouille et al. (1999).

Excellent electronic structure matching explains, in part, the large GMR ratios for Fe/Cr and Co/Cu and systems. For Fe and Cr, matching is good for the minority spin electronic structures (Butler et al., 1995), also for atomically rough interfaces (Inoue and Maekawa, 1991; Coehoorn, 1995). For Co and Cu, good matching occurs for the majority-spin electronic structures in the bulk of the layers, as can be seen from the density of states given in fig. 3.1. Also for binary and ternary Co–Fe–Ni alloys with a fully occupied majority spin 3d-band (such as Ni80 Fe20 ) matching of the bulk electronic structures with the band structure of Cu is excellent. Near Co/Cu interfaces, the magnetic moment of Co is hardly changed by the presence of Cu nearest neighbour atoms. The filling of the 3d-partial density of states of Co atoms near the interface is therefore not essentially different from that in bulk Co. The majority-spin 3d band is fully occupied, so that no or only very weak scattering of majority-spin electrons will occur at imperfections of the interface. In contrast, the local minority-spin electronic potential on a Co-atom at a rough interface is quite different from that on its Cu neighbours in the same atomic layer, giving rise to strongly diffusive scattering. Indeed, Binder et al. (2001) calculated the additional resistivity due to scattering at Cu impurities on an interface site, and found a scattering spin anisotropy ratio α ≈ 17. Quantifying the “spin-dependence of scattering at the interfaces” cannot be done without defining the experiment that is used to probe the effect. CPP-GMR experiments can be analysed in terms of a series resistor model of spin-dependent bulk and interface resistances. For Co/Cu and Py/Cu interfaces, e.g., such analyses have led to interfacial spin-


85

asymmetry ratios r↓ /r↑ = 7.3 and r↓ /r↑ = 5.7, respectively, at 4.2 K (Pratt et al., 1996, Steenwyk et al., 1997). Here r↑ and r↓ are the majority and minority spin interface resistances, respectively. These high ratios confirm the remarks concerning electronic structure matching given above. However, in CIP-experiments the potential step at the interface plays a different role then in CPP-experiments. Within the semi-classical Camley–Barnas model (section 3.5), two spin-dependent parameters (the probabilities for diffusive scattering and for specular reflection) are introduced, which bear no formal relationship with the interfacial resistances measured in a CPP experiment. Nevertheless, the trends are generally the same: analyses of CIP-experiments on systems containing Co/Cu interfaces reveal a high (low) probability of minority (majority) spin-scattering at the interfaces (see section 3.6). For bulk Ni and Cu, electronic structure matching is very good for the majority spinelectrons (see fig. 3.1). However, Ni-moments at interfaces with Cu are more sensitive to the presence of Cu neighbours than Co moments. Already at a perfect Ni/Cu interface, and even more at an imperfect interface, the Ni magnetic moments are smaller than the bulk value of approximately 0.6μB (Coehoorn, 1993; Nicholson et al., 1994). As a result, the majority-spin 3d-density of states is no longer zero at the Fermi level, so that there is no good majority spin electronic structure matching with the Cu spacer layer. This contributes to the decrease of the GMR ratio of spin-valves based on Ni–Co–Fe alloys with increasing Ni concentration, as shown in fig. 1.8. For Ni/Cu/Ni/Fe50 Mn50 spin-valves the GMR ratio is only at most 2% at room temperature (see table 2.1). It should be noted that the solubility of Ni in Cu is larger than that of Fe or Co in Cu, giving rise to more diffuse interfaces, and that the thermal stability of Ni moments at interfaces with non-magnetic metals such as Cu is expected to be relatively small, in view of the relatively low Curie temperature of Ni. Both effects contribute to the low room-temperature GMR ratio of Ni/Cu/Ni/AF spinvalves. The role played by scattering at the interfaces in SVs containing Ni-rich F layers became very clear when studying the effect of thin Co “dusting” layers at the interfaces (see fig. 2.2). A complicating effect is the possibility that the F moments near the interfaces are noncollinear. Oparin et al. (1999) have shown from first-principles band structure calculations that this is expected to be the case for the Ni and Fe moments near interdiffused Py/Cu interfaces. The non-collinearity enhances the scattering for both spin-directions, thereby reducing the magnetoresistance. 3.4. Series resistor model A strongly simplified model of GMR effect in magnetic multilayers is obtained by making the (implicit) assumption that the current densities are homogeneous for both spin directions. If the resistances for the “+” and “−” channels in the parallel configuration are R+ and R− , the resistances of the “+” and “−” channels in the antiparallel configuration are equal to 12 (R+ + R− ). The parallel and antiparallel resistances are then given by Fert (1990) RP =

R+ R− R+ + R−

(3.10)

86

R. COEHOORN

and R+ + R− , 4 and the giant magnetoresistance ratio is given by RAP =

(3.11)

ΔR (R+ − R− )2 (1 − α)2 = , = R 4R+ R− 4α

(3.12)

where α ≡ R− /R+ can be viewed as the effective scattering spin-asymmetry ratio for the multilayer. Effective resistor schemes that correspond to eqs (3.10) and (3.11) were already given in fig. 1.3(b). The MR ratio is thus expected to be positive, as is observed indeed without exception for AF-coupled F/NM systems.8 As shown by Valet and Fert (1993), this series resistor model is valid for the CPP geometry, if spin-flip can be neglected. It is then possible to express α in terms of the F and NM layer thicknesses, spin-polarized bulk resistivities and interface resistances. In spin-valves and other layered materials, the scattering probability when traversing a layer is usually close to 1 for electrons of at least one spin-direction. In the CIP-geometry, the current density is thus in general a non-uniform function of the position in the layer stack. Also diffusive scattering at the outer boundaries makes the current density nonuniform. Therefore, the series resistor model (eqs (3.10)–(3.12)) is generally not valid for the CIP-geometry (although it still has a certain didactical value). It would only be valid for CIP-systems in the weak scattering limit, when for both types of electrons the scattering probabilities upon traversal of one multilayer period is much smaller than one. In that case, the CIP and CPP-GMR ratios are equal. A semiclassical transport model for the CIPgeometry, within which the non-uniform current density is calculated, is discussed in the next section. 3.5. The Camley–Barnas semiclassical transport model A very useful model for describing the spin-polarized, inhomogeneous current densities in magnetic multilayers, studied in the CIP-geometry, is the semi-classical transport model proposed by Camley and Barnas (1989). Within this model, electrons are essentially regarded as pointlike particles (hence ‘classical’) although some consequences of quantum mechanics are taken into account, such as the use of quantum-mechanics to calculate the relation between the energy and momentum, Fermi–Dirac statistics and quantummechanically evaluated scattering probabilities (hence ‘semi’). Within the CB model the electronic structure in each of the layers is treated as a free-electron gas. The spin-dependent scattering probabilities in the bulk of the layers, at the interfaces, and at the outer boundaries, are free parameters. They can be varied in order to obtain good agreement with the observed (layer thickness dependent) (magneto)conductivities, or can be held fixed if additional information is available. The conductivity is obtained from the electron distribution function f ↑(↓) (v, r), which gives the spin dependent probability that a state at position r with velocity v is occupied. A convenient 8 For (F /NM/F /NM) systems, with F layers having opposite signs of the spin-polarisations of the conducn 1 2

tance, an inverse GMR effect can be obtained (George et al., 1994; Renard et al., 1995).


87

notation is ↑(↓)

f ↑(↓) ( v , r) = f0

( v , r) + g ↑(↓) ( v , r).

(3.13)

Here g ↑(↓) (v, r) is the deviation from the Fermi–Dirac equilibrium distribution function ↑(↓) f0 (v, r), in the presence of an electric field E, for spin up (↑) and spin down (↓) electrons, at energy ε = 12 mv 2 . The electron distribution function is obtained by solving the Boltzmann transport equation in the relaxation time approximation: ↑(↓)

v ·

∂f (ε) g ↑(↓) ( v , r) v , r) ∂g ↑(↓) ( − eE · v 0 =− , ↑(↓) ∂ r ∂ε τ

(3.14)

in which e is the electron charge, m is the electron mass, and τ ↑(↓) is a spin-dependent and layer-dependent isotropic relaxation time. The spin-dependent current density follows from an integral over velocity space of the electron distribution function: 3 m j↑(↓) (r ) = e (3.15) v , r), d3 v vg ↑(↓) ( h where h is Planck’s constant. Solutions of the Boltzmann transport equation for a multilayer consisting of N layers, with the planes perpendicular to the z-axis and with the interfaces at positions {z0 , z1 , . . . , zN } have, in layer i, the following form: −(z − zi−1 ) ∂f0 (ε) v , z) = −eτi Ex vx g+,i ( (3.16) , 1 − F+,i exp ∂ε τi vz for vz > 0, and

∂f0 (ε) −(zi − z) g−,i ( v , z) = −eτi Ex vx 1 − F−,i exp , ∂ε τi |vz |

(3.17)

for vz < 0. The electric field is along the x-direction. The spin (↑ and ↓) labels have been omitted from the relaxation time τ and the coefficient A. The coefficients F are determined from the boundary conditions at the interfaces or outer boundaries (transmission, reflection, diffusive scattering, see below). For the case of bulk metals, this model is discussed in many textbooks (see, e.g., Ashcroft and Mermin, 1976). It leads to the Drude formula (eq. (3.3)). The relaxation time τ can be expressed in terms of the electron mean free path λ and Fermi velocity vF as τ = λvF . Fuchs (1938) and Sondheimer (1952) have first applied this model to the conductivity of homogeneous thin films. For a film with thickness t in between z = 0 and z = t, the coefficients F in the g-functions, from which the current density follows via eq. (3.15), are obtained by the application of the boundary conditions g+ (z = 0) = pg− (z = 0) and g− (z = t) = pg+ (z = t). Here p is the probability for specular scattering at the outer surfaces. When p = 1, diffusive scattering at the outer boundaries leads to a decrease of the effective conductivity σ with decreasing t. The effect is significant for t close to and smaller than λ. The ratio of the conductivity of the film with respect to the bulk conductivity σ0 is given by (Fuchs, 1938; Fert, 1990) 3 ∞ 1 1

σ = 1 − (1 − p) − 5 1 − exp(−kx) dx, (3.18a) 3 σ0 2k 1 x x

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R. COEHOORN

where k = t/λ. A good approximation in the thick film limit (t λ) is λ σ ∼ 3 = 1 − (1 − p) . σ0 8 t

(3.18b)

In that limit, the current density is close to the bulk value in the center of the film, but lowered in a zone with thickness of the order λ near the outer boundaries. These two boundary zones overlap when the condition t λ is not satisfied, resulting in the more complicated general expression (3.18a). The current density in magnetic layered structures can be obtained after the introduction of two types boundary conditions (in addition to the specularity parameters p at the outer surfaces), which relate the g-functions at the interfaces. First, at the interfaces three possible processes are distinguished: transmission (probability Ti,s ), specular reflection (probability Ri,s ), or diffusive scattering (probability Di,s ). Specular reflection could arise in the case of a potential step at the interface between two layers (as depicted schematically in fig. 3.3). These probabilities depend on the interface i and the spin s; T + R + D = 1. At the interface between two layers A and B the boundary conditions are: σ σ σ g± (B) = T σ g± (A) + R σ g∓ (B).

(3.19)

Second, systems with different magnetization directions in the different layers are dealt with using spin-transmission coefficients T ↑↑ , T ↑↓ , T ↓↑ , and T ↓↓ , through a plane situated within the non-magnetic spacer layer between the magnetic layers (the precise position of this plane in the non-magnetic spacer layer does not affect the final results). These transmission coefficients determine the probability of an electron which has spin up or down with respect to the magnetization direction (quantization axis) in one magnetic layer to continue in the other magnetic layer as an electron with spin up or down with respect to the new quantization axis. The transmission coefficients are given by T ↑↑ = T ↓↓ = cos2 (θ/2) and T ↑↓ = T ↓↑ = sin2 (θ/2),

(3.20)

where θ is the angle between both magnetization directions. For example, in the case of an antiparallel arrangement of the magnetization directions T ↑↑ = T ↓↓ = 0 and T ↓↑ = T ↑↓ = 1. A majority spin electron in one magnetic layer becomes then a minority spin electron in the other magnetic layer, after traversing a nonmagnetic layer in between. If the interfaces at which the spin-boundary conditions are applied are taken to coincide with interfaces between layers, the determination of the 2N coefficients F∓ for N layers (and for each spin) involves solving a set of 2N linear equations, obtained by applying the boundary conditions. From the resulting g-functions, the z-dependent current densities in layer i can be calculated using eq. (3.15): e2 Ex m2 vF2 ↑(↓) π/2 −(z − zi−1 ) ↑(↓) ↑(↓) λ exp ji,x (z) = 2 − F i +,i ↑(↓) 8π 2 h¯ 3 β=0 λi cos β −(zi − z) ↑(↓) sin3 β dβ − F−,i exp ↑(↓) λi cos β


3 π/2 −(z − zi−1 ) ↑(↓) ↑(↓) = σ0 Ex × 2 − F+,i exp ↑(↓) 4 β=0 λi cos β −(zi − z) ↑(↓) sin3 β dβ. − F−,i exp ↑(↓) λi cos β

89

(3.21)

The second part of the equation is obtained by using the well-known relationship between the Fermi-velocity and the electron density (Kittel, 1996). The Drude formula is retained ↑(↓) for bulk systems, when F∓ = 0. For a layered system, the contribution from each spin current to the conductance follows after integration over the entire thickness of each layer, and summation of the contributions from all layers. The occurrence of the angular integral in eq. (3.21) prohibits the formulation of simple but physically transparent expressions for the sheet conductance. It is therefore sometimes useful to make an approximation, by replacing the cos(β) factor in the argument of the exponential functions by a fixed, representative, average value, γ . The current density in each layer is then given by ↑(↓)

↑(↓)

ji,x (z) = σ0

↑(↓) F+,i −(z − zi−1 ) exp Ex × 1 − ↑(↓) 2 γλ i

↑(↓)

−

F−,i 2

−(zi − z) exp , ↑(↓) γ λi

and the contribution from layer i to the sheet conductance is zi 1 ↑(↓) Gi,sh ≡ j ↑(↓) (z) dz Ex zi−1 x γ λ↑(↓) ↑(↓) ti ↑(↓) ↑(↓) ∼ F+,i + F−,i 1− , 1 − exp − ↑(↓) = ti σ0 2 ti γλ

(3.22)

(3.23)

where ti = (zi − zi−1 ) is the thickness of the layer. Willekens (1997) has found that for realistic spin-valves quite an accurate approximation to eq. (3.21) is obtained when choosing γ = 1/2.9 3.6. Applications of the Camley–Barnas model 3.6.1. Model calculations for conventional simple spin-valves As a first illustration of the use of the CB-model, we show in fig. 3.4 the results of a calculation of the current density in a simple F/NM/F spin valve (Coehoorn, 2000). A similar result was presented by Prados et al. (1999). The current density distribution cannot be obtained directly by experiment, but is of practical importance for applications. In the case of a stripe-shaped magnetoresistive conductor the current leads to an effective magnetic field in the magnetic layers, directed perpendicular to the current direction (section 4.2.2). 9 For a single layer with t/λ 1, the Fuch–Sondheimer formula, eq. (3.18b), is retained by taking γ = 3/8 (Willekens, 1997).

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Fig. 3.4. Results of a model calculation of the current density per unit electric field, in a (8 nm F/ 2 nm NM/ 8 nm F) sandwich system, using the Camley–Barnas model. The magnetization of the left layer is in all figures up, whereas the right layer is up (down) for parallel (antiparallel) alignment. Model parameters: λNM = 20 nm, ↑ ↓ ↑ ↓ λF = 12 nm, λF = 0.6 nm, TCo/Cu = TCo/Cu = 1, diffusive scattering at the outer boundaries for both spin

directions. Electron density: 8.45 × 1028 m−3 in all layers (as in bulk Cu). The calculated parallel and antiparallel sheet resistances are 6.82 and 7.57 , and the calculated GMR ratio is 11.0%. (a)–(b) Contributions to the current density by electrons with vz > 0 for parallel and antiparallel configurations. The contributions from electrons with vz < 0 follow from a reflection in the z = 9 nm plane. (c) Total current densities for the parallel and antiparallel configurations, for spin up and spin down electrons. (d) Total current density, after summation of the contributions from both spin directions. From Coehoorn (2000).

In the calculations, scattering is assumed to be diffusive at the outer boundaries. The NM spacer layer thickness is 2 nm and the F layer thicknesses are 8 nm. The conductivity ↑ ↓ is spin-dependent in the F layers, with mean free paths λF = 12 nm and λF = 0.6 nm; λNM = 20 nm. These are realistic values for, e.g., Co/Cu/Co spin-valves (section 3.6.2). For both spins the interface transmission coefficients are equal to T = 1, and scattering is diffusive at the outer boundaries. For this specific example the calculated parallel and antiparallel sheet resistances are 6.8 and 7.5 , and the calculated GMR ratio is 11.0%. As remarked already by Dieny (1992b), the current density in the NM layers is, for the model assumptions used, the same for both alignments. This may be understood by noting that contributions to the current density for a given electron direction (positive or negative vz ) are the same in the first F layer that is traversed, and in the NM layer. Only the current density in the second F layer depends on the relative alignment (see fig. 3.4 (a), (b)). Upon


91

switching from the parallel to the antiparallel alignment, the only change of the current density occurs in a thin region in the F layers, close to the interface with the NM layers. From these observations, it is not difficult to understand the size of the change of the total sheet conductance. Let us first consider an extreme case, with a vanishing spacer layer ↓ thickness, infinite F layer thicknesses, and negligible λF . The thickness of the regions close to the interfaces in which the current density depends on the alignment is then expected to ↑ be of the order 12 λF . The factor 12 takes into account that electrons with a wide distribution of velocity directions contribute to the current. Only half of the spin ↑ electrons, viz. only those with a velocity direction away from the spacer layer, contribute to the change of the current density near a given interface. Effectively, each interface therefore contributes a ↑ change of the sheet conductance that is equal to 14 λF σ0,F , so that the total effect is ΔGsh ≈ ↑ ↓ 1 2 λF σ0,F . For systems with finite layer thicknesses and λF = 0, the change of the sheet conductance is (from eq. (3.23) with γ = 1/2) approximately equal to (Willekens, 1997): ∼ ΔGbulk sh =

↑ 2tNM 1 σ0,F × exp − 2 λ↑ λNM F

×

↑ λF

2 2tF 2tF ↓ . 1 − exp − ↑ − λF 1 − exp − ↓ λF λF

(3.24)

The label “bulk” indicates that only spin-dependent scattering (SDS) in the bulk of the ↓ F-layers has been considered. For tNM = 0, λF = 0 and tF → ∞, eq. (3.23) yields indeed ↑ ΔGsh → 12 λF σ0,F , in agreement with the estimate given above. The exponential NM layer thickness dependence agrees with the simple expression for the MR ratio given already in section 1 (eq. (1.4)). When the conductivity in the F layers is strongly spin-polarized, the F layer thickness dependence is proportional to [1 − exp(−2tF /λ> )]2 , where λ> is the larger of the two mean free paths in the F layer. This quadratic form reflects the dual polarizer/analyzer role played by the two F layers. It is of interest to investigate the sheet conductance change for the case of interface SDS. We consider (otherwise identical) spin-valves in which the transmission probability through the interfaces is spin-dependent (T ↑ = T ↓ ), but in which the F-layer conductivity ↑ ↓ is spin-independent. Taking λF = λF = λNM = λ, and assuming no specular reflection at the interfaces, Willekens (1997) has shown that the application of eq. (3.21) (again with γ = 1/2) leads to 2

↑ −2tNM −2tF int ∼ 1 ↓ 2 × exp . ΔGsh = σ0 λ T − T (3.25) × 1 − exp 4 λ λ Here σ0 is the total F (or NM) layer conductivity. For multilayers, a similar expression has been derived by Barthélémy and Fert (1991). It may be concluded from a comparison of eqs (3.24) and (3.25) that different mechanisms can give rise to layer thickness dependences of the magnetoconductance that are not very dissimilar. Studies of the layer thickness dependence of the magnetoconductance and the conductance are necessary to distinguish interface from bulk contributions to the CIP-magnetoconductance.

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Fig. 3.5. Results of a model calculations of the MR ratio of (F/NM)N /F multilayers with tNM = 1 nm versus the F layer thickness, for various periods N . The model parameters used were identical to those given in the caption of fig. 3.4. From Dieny (1992b).

3.6.2. Model calculations for dual and multilayer structures Dieny (1992b) have applied the CB model in order to investigate the effect on the GMR ratio of increasing the number of repetitions in a multilayer. For this purpose they considered (F/NM)N /F multilayers, with an NM layer thickness equal to 1 nm, and with variable F layer thicknesses. For N = 2, the calculations describe a dual spin valve. The same set of scattering conditions are used as employed in the example given in section 3.6.1 (fig. 3.4). As shown in fig. 3.5, the maximum GMR ratio increases with increasing number of repetitions, due to the decreasing importance of diffusive scattering at the outer boundaries. The shift with N of the maximum in the MR curves to lower F layer thicknesses reflects the strongly spin-dependent mean free paths in the F layers. For N = 1 (a simple spin-valve) the F layers should be relatively thick in order to make it possible for the spin ↑ electrons to contribute to the conduction before scattering diffusively at the outer boundaries. On the other hand, in the case of a large number of repetitions, scattering at the outer boundaries becomes relatively unimportant, and the F layer should simply be just thick enough ↓ to scatter the spin ↓ electrons (i.e., of the order of λF = 0.6 nm), without giving rise to appreciable scattering of spin ↑ electrons. 3.6.3. Model calculations of the effect of specular boundary scattering From the point of view of its magnetoresistance, a multilayer with an infinite number of repetitions is equivalent to a simple spin valve with perfectly specular scattering at the outer boundaries (and with F layer thicknesses that are half as large). The effect on the F-layer thickness dependence of the GMR ratio, upon an increase of the probability of specular scattering at the outer boundaries, is thus (qualitatively) the same as the effect of increasing N . Swagten et al. (1996, 1998), Dieny (1998), Bailey (2000a) and Li et al. (2000a) employed the CB model to investigate the effect of variations of the specular reflection coefficient R at the outer boundaries. This work was motivated by successful experimental


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Fig. 3.6. Results of model calculations of the MR ratio of (tF1 nm F1/ 2.5 nm NM/ tF2 nm F2) layer structures, for the case of a variable specular reflection coefficient R at the top outer boundary (a)–(c) or at both outer boundaries (d)–(f). In figures (a)–(c), scattering at the bottom outer boundary is diffusive. Model parameters: ↑ ↓ ↑ ↑ ↓ ↓ λNM = λNM = λF = 10 nm, TF/NM = 1; λF and TF/NM are obtained by the expressions given in the top part of the figure. From Swagten et al. (1998).

demonstrations of enhanced GMR ratios in systems including NiO layers (Anthony et al., 1994; Egelhoff et al., 1995; Swagten et al., 1996) (see section 2.1.6). Fig. 3.6 shows the results of calculations by Swagten et al. (1998) of the GMR ratio for (8 nm F1 / 2.5 nm NM/ tF2 F2 ) spin-valves. The results shown in fig. 3.6 (a)–(c) were obtained for the case of diffusive scattering at the “bottom” outer boundary (with the F1 layer), and variable reflectivity R at the “top” outer boundary. The mean free path in the NM layer, and λ↑ in the F layers are both equal to 10 nm. The other parameters used are given in the top part of the figure. It is seen that already partial reflection at the top boundary enhances the GMR effect strongly, in particular for low F2 layer thicknesses (well below the largest mean free path). The F2 layer thickness at which the GMR ratio is maximal, tmax , shifts to lower values. The precise effect depends on the origin of the spin-dependent scattering (interface (a), bulk (b) or both (c)). For these parameter values, the largest possible enhancement of the GMR ratio is slightly less than a factor of two. For specular scattering at both outer inter-

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faces (fig. 3.6 (d)–(f)), the trends are analogous to the effects obtained in figs. 3.6 (a)–(c). However, a much larger enhancement and a much larger shift of tmax are predicted. 3.6.4. Angular dependence of the conductance For a simple spin-valve of the type F/NM/F, in which scattering at the outer boundaries is diffusive, and in which no specular scattering takes place at the interfaces, the assumptions made within the CB model lead to a conductance that is proportional to (1 − cos θ ) (de Jong, 1995). This result is only to first order in the GMR ratio equivalent to the expression given by eq. (1.2), within which the resistance varies linearly with (1 − cos θ ). The difference will be only significant for systems with relatively large GMR ratios. The resistance was found to be proportional to (1 − cos θ ) for exchange-biased Py/Cu/Py/Fe50 Mn50 systems (Dieny et al., 1991a)and for an AF-coupled Fe/Cr/Fe system (Chaiken et al., 1990), with GMR ratios of about 3 and 0.4%, respectively. So far, only for a certain multilayer system, with a relatively large MR ratio, a linear variation of the conductance with (1 − cos θ ) has been observed (Duvail et al., 1995). For simple spin valves a non-linear angular variation of the conductance with (1 − cos θ ) is expected in the case of non-zero specular reflection at the interfaces between the magnetic and non-magnetic layers (Vedyaev et al., 1994; Barnas et al., 1997; Sheng et al., 1997). Xu and Mai (1999) showed that a significant non-linearity can also arise within the CB model, for the case of a very high probability of specular scattering at the outer boundaries. This indicates that the successful development of specularly reflecting layers (such as NOLs) at the outer boundaries, leading to a high GMR ratio, could have a disadvantageous effect on the linearity of the response of a sensor. 3.6.5. Determination of scattering parameters Pioneering studies, aimed at analyzing the conductance and magnetoconductance of simple spin valves in terms of the parameters that enter the CB model, have been carried out by Dieny (1992b), Dieny et al. (1993). They studied F/Cu/F/Fe50 Mn50 spin-valves at 1.5 K, with F = Fe, Co and Ni80 Fe20 . From preliminary analyses, they concluded that no satisfactory description of the resistance and the magnetoresistance was possible using the same set of parameters. Parameter sets describing correctly the layer thickness dependence of the conductivities were found to underestimate the MR ratio by about 20% in relative value. This was ascribed to anisotropic scattering due to the presence of grain boundaries (see also section 2.9.2). In the case of a columnar grain structure, stronger scattering is expected for electrons with velocities nearly parallel to the layers (which predominantly determine the resistivity), as compared to scattering for electrons with a substantial perpendicular velocity component (whose contribution to the magnetoresistance is larger). In order to incorporate anisotropic scattering, Dieny made use of an ad hoc extension of the semiclassical model, by using the following expression for the anisotropic mean free path for scattering in the bulk of the layers: λ(θ ) = λ sin2 θ + λ⊥ cos2 θ,

(3.26)

in which θ is the angle between the velocity vector and the film-normal, and in which the parallel and perpendicular mean free paths are related by 1 1 1 = + . λ λ⊥ λgr

(3.27)


95

TABLE 3.1 Resistivities and scattering parameters for (F/Cu/F/Fe50 Mn50 ) spin-valves at 1.5 K, as obtained by Dieny et al. (1992a, 1993) using the CB model. The parallel and perpendicular mean free paths are related to each other by eq. (3.27), with λgr = 40 nm ↑

↑

↓

↓

↑

Materials

ρ (10−8 m)

λ (nm)

λ⊥ (nm)

λ (nm)

λ⊥ (nm)

TF/Cu

Cu Ni80 Fe20 Co Fe

4.7 15.4 10.7 10.5

13 11 14 7

20 15 21 8.5

13 0.6 1 7

20 0.6 1 8.5

1 1 1

↓

TF/Cu 1 0.2 0.6

The parameter λgr is expected to be of the order of the grain diameter. Satisfactory fits to the layer thickness dependent conductance and magnetoconductance were obtained when diffusive scattering was assumed at the outer boundaries, and taking λgr = 40 nm for the F as well as the Cu layer. For minority-spin electrons in Ni80 Fe20 or Co layers no anisotropy of the mean free path was taken into account. In view of the small values of their mean free paths, the fit would be very unsensitive to such an effect. An overview of the scattering parameters that were obtained is given in table 3.1. The results indicate that for permalloybased systems spin-dependent bulk scattering is the predominant origin of the GMR effect, whereas for Co/Cu and Fe/Cu systems spin-dependent scattering at the interfaces plays an important role. For Fe, bulk scattering is seen to be almost spin-independent. An excellent example of the application of the CB model to the room temperature magnetoconductance of state-of-the-art spin-valves that are relevant to sensor applications has been presented by Dieny et al. (2000a). They studied simple PtMn-based spin-valves with a composite free layer: UL/ 3.0 nm Ni80 Fe20 / 1.0 nm Co90 Fe10 / 2.0 nm Cu/ x nm Co90 Fe10 /20 nm PtMn/Ta. The composition of the underlayer (UL) was not specified. For x = 2.0 nm, the GMR ratio is surprisingly high, viz. 12.0% (see also table 2.1). Note that the free and pinned layers are quite thin, as compared to the optimal F layer thicknesses for Fe50 Mn50 -based spin valves (fig. 1.8). Based on numerous studies of a wide variety of spin-valve structures, the authors concluded that the effect must be due to a certain degree of specular scattering of electrons at the underlayer/Ni80Fe20 and Co90 Fe10 /PtMn interfaces. The final results of their fits are given in table 3.2. As compared to the mean free paths given in table 3.1 from a low-temperature study, the mean free paths in Cu and Ni80 Fe20 are somewhat smaller. Neglecting differences of the microstructure, this could be ascribed to increased electron– phonon scattering and (in the permalloy layers) electron–magnon scattering. Fig. 3.7 shows the effect of “switching on” specular scattering at the interface with the PtMn layer. Consistent with the results shown in fig. 3.6, it leads to a high GMR ratio, even for small thicknesses of the pinned layer. The sheet resistance is slightly lowered. Analyses by the same authors of spin-valves with a synthetic AF pinned layer (Co90 Fe10 /Ru/Co90 Fe10 replaces the single Co90 Fe10 pinned layer in the structures studied above) led to the conclusion that specular reflection occurs also at Co90 Fe10 /Ru interfaces. The reflection coefficient for the Co90 Fe10 /Ru interface is R = 0.3. Upon analysing the

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TABLE 3.2 Scattering parameters for (buffer/ 3.0 nm Ni80 Fe20 / 1.0 nm Co90 Fe10 / 2.0 nm Cu/ x nm Co90 Fe10 / 20 nm PtMn/Ta) spin valves at room temperature, obtained by Dieny et al. (2000a, 2000b) using the CB model. The composition of the high-resistivity buffer layer is not specified. The (spin-dependent) transmission coefficients T and the (spin-independent) specular reflection coefficient R correspond to the interfaces between the indicated layer and the previous layer in the stack. Specular reflection occurs only at the buffer/Ni80 Fe20 and Co90 Fe10 /PtMn interfaces Materials

λ↑ (nm)

λ↓ (nm)

T↑

T↓

R

buffer Ni80 Fe20 Co90 Fe10 Cu Co90 Fe10 PtMn Ta

0.2 7 9 12 9 0.2 0.4

0.2 0.7 0.9 12 0.9 0.2 0.4

0.6 1 1 1 0.5 1

0.6 1 0.5 0.5 0.5 1

0.3

0.3

Fig. 3.7. Experimental and theoretical sheet resistance (a) and MR ratio (b) of a SV with the composition (underlayer/ 3 nm Py/ 1 nm Co90 Fe10 / 2 nm Cu/ tp nm Co90 Fe10 / 20 nm PtMn), versus the thickness tp of the Co90 Fe10 pinned layer. Full line: model calculation using the CB model (table 3.2) assuming specular reflection at the Co90 Fe10 /PtMn interface (reflection coefficient R = 0.3). Dashed line: model calculation assuming R = 0. From Dieny et al. (2000a).

CIP-magnetoconductance, the possibility that specular reflection occurs at metal/metal interfaces thus cannot always be disregarded. We emphasize that the mean free paths that are given in tables 3.1 and 3.2 should be considered as effective values, which could differ considerably from the values that would have been obtained in the absence of spin-mixing due to the spin-orbit interaction and/or due to electron–magnon interactions (see sections 3.1 and 3.7).


97

3.6.6. Spin-valves with a back layer Spin-valves with a back layer (or “spin-filter spin-valves”) with the structure B/F/NM/F/ AF (with B the back layer, see fig. 2.1(c)) have been studied in order to extract the scattering parameters in an alternative manner, as well as for their favorable combination of properties for applications in, e.g., read heads (section 2.1.3). They were introduced by Gurney et al. (1994), in order to study the spin-polarized mean free paths in the back layer. The authors observed that the variation of the sheet magnetoconductance as a function of the thickness tB of the back layer is to a very good approximation given by tB ΔGsh = ΔGsh,0 + ΔGsh,B 1 − exp − (3.28) . LB From room temperature experiments the following values were found for the fit parameter LB : 19 nm (Cu), 2.2 nm (Au50Cu50 ), 4.6 nm (Ni80 Fe20 ), 5.5 nm (Co) and 1.5 nm (Fe). Gurney et al. associated this length scale to λ> , the largest of the two mean free paths in the back layer. An analysis using the CB model, using the approximation made in eq. (3.23) with γ = 1/2, has later revealed that for non-magnetic back layers the change of the sheet resistance is indeed expected to have the form given by eq. (3.28), but that LB is approximately equal to half the mean free path (Willekens, 1997). For Cu, the resulting value λ = 38 nm is in fair agreement with the “intrinsic” value λi ≈ 33 nm obtained by Rijks et al. (1995a) from single thin film studies in the thick film limit (see section 3.6.5). For ferromagnetic back layers in which λ↑ λ↓ , Rijks (1996a) has found from model studies using the CB-model that to a very good approximation ↓ T 1 ↑ λ↓ . LB ∼ (3.29) λ + = 2 T↑ In view of the parameter values given in table 3.1, a further approximation, LB ≈ 12 λ↑ , is expected to be very good. This leads for Ni80 Fe20 and Co to λ↑ ≈ 9 and 11 nm, respectively. These values are quite close to the results given in table 3.2 for Ni80 Fe20 and Co90 Fe10 . Less direct estimates of the mean free paths for the other spin direction yielded λ↓ 0.6 nm (Ni80 Fe20 ), λ↓ 1 nm (Co), and λ↓ = 2.1 ± 0.5 nm (Fe). Also these data thus provide evidence for a strong spin-dependence of the scattering in permalloy and Co, and a much weaker spin-dependence of the scattering in Fe. A different type of study of spin-valves with a back layer was carried out by Swagten et al. (1997) (see also Strijkers et al., 1997). Their aim was to investigate the importance of the interfacial contribution to the spin-polarized scattering that gives rise to the GMR effect. They noted that making a distinction between bulk and interface spin-dependent scattering (SDS) is difficult when conventional spin-valves are used, because of the very similar forms of the F layer thickness dependences of the conductance change (within the approximation leading to eqs (3.24) and (3.25), these become even identical for bulk SDS with λ↑ λ↓ ). In contrast, for samples of the type F1 /NM/F2 /B, with a thick back layer, the F2 layer thickness dependences of the conductance change are expected to be very different for bulk and interface SDS. In the case of interface SDS a large magnetoconductance effect will even occur in the limit of a vanishing thickness of layer F2 , which is called the “probe layer”. In contrast, in the case of bulk SDS an F layer thickness of the order of the smallest of the mean free paths will be required to obtain an effect. Thinner layers are

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Fig. 3.8. Sheet conductance change from model calculations (a), (b) and experiment (c) for F/NM/F/B spin-valves (d), where B is a non-magnetic back layer. The CB model calculations (from Willekens (1997) are for (2.5 nm F/ ↑ ↓ ↑ ↑ 2.5 nm NM/ dPR nm F/ dB nm NM) films, and were carried out for λNM = λNM = λF = 20 nm and TF/NM = 1. Figure (a) gives the sheet conductance change ΔGint assuming only interface spin dependent scattering (SDS), ↓ ↑ ↓ with λF = λF and with TF/NM = 0.4. Figure (b) gives the sheet conductance change ΔGbulk assuming only ↓

↓

bulk SDS, with λF = 2 nm and with TF/NM = 1. Figure (c) gives experimental results for (2.5 nm Co/ 3 nm Cu/ dPR nm Co/ dB nm Cu) SVs, from Swagten et al. (1997).

then not efficient as a spin-filter. In fig. 3.8 (a) and (b) results of model calculations are given for the change of ΔGsh for the cases of interface SDS and bulk SDS, respectively. In fig. 3.8(c) experimental data, taken at 10 K, are given for a (7.5 nm Co/ 0.6 nm Ru/ 2.5 nm Co/ 3.0 nm Cu/ dpr nm Co/ dB nm Cu) spin-valve. The 2.5 nm reference Co layer is pinned by employing a synthetic AF structure. The finite ΔGsh at extremely small dpr is consistent with the occurrence of interfacial SDS. The dependence on the back layer thickness agrees, at least qualitatively, with the prediction given in fig. 3.8(a). For permalloy, similar results were obtained. For Co and permalloy, the probe layer thickness required to obtain the full conductance change (called ξ ) was observed to be 0.1 to 0.3 nm at 10 K, and to increase to 0.2–0.7 at room temperature, depending on the details of the sample structure. This length scale was interpreted as the thickness which is required to form a (magnetically) continuous layer. A possible alternative explanation of the results, in terms of bulk SDS characterized by an extremely small minority spin mean free path, was argued to be less likely. In that case, ξ would be of the order of λ↓ . However, in contrast to the


99

Fig. 3.9. Room temperature Cu layer thickness dependence of the MR ratio for (Ta/ 2 nm Ta/ NOL/ 2.5 nm Py/ 1 nm Co90 Fe10 / t nm Cu/ 3 nm Co90 Fe10 / 7 nm Ir–Mn/ 2 nm Ta) SVs with a NOL near the free layer, and for a non-oxide reference sample. The solid and dashed lines represent results of calculations using the CB model. The inset gives the results of sheet resistance measurements. For the model parameters, see the text of section 3.6.7. From Gibbons et al. (2001).

observations, it would then be expected to decrease with increasing temperature. For Co, the observed interface SDS agrees with the analysis by Dieny et al. (1992a, 1993) of data for conventional spin valves (table 3.1), but for permalloy, Dieny et al. did not detect any significant interface SDS. 3.6.7. Spin-valves with a NOL near the free layer Gibbons et al. (2001) have analysed the effect of including a nano-oxide layer (NOL) near the free layer of spin-valves with the layer structure Substrate/ 2 Ta/ NOL/ 2.5 Py/ 1 Co90 Fe10 / t Cu/ 3 Co90 Fe10 / 7 Ir–Mn/ 2 TaOx . The experimental Cu layer thickness dependence of the MR ratio could be described within the CB model using the following mean free paths: λ↑ (Py) = 5.9 nm, λ↓ (Py) = 0.6 nm, λ↑ (Co90 Fe10 ) = 9 nm, λ↓ (Co90 Fe10 ) = 0.6 nm, λ↑ (Cu) = λ↓ (Cu) = 30 nm and λ↑ (Ta) = λ↓ (Ta) = 0.6 nm. For the non-oxide reference sample T = 0.5 and D = 0.5 are assumed at the Ta/Py interface. For the oxide sample fully specular reflection is assumed at the NOL/Py boundary. As shown in fig. 3.9, the model provides a good description of the sheet resistance and magnetoresistance as a function of the Cu layer thickness. The discrepancy at small Cu thicknesses for the non-oxide sample can be attributed to the absence of a proper plateau region in the R(H ) transfer curve due to strong ferromagnetic coupling across the Cu layer (as in fig. 1.7). Apparently, the use of a NOL suppresses this effect. Indeed, it has been observed that NOLs give rise to planarisation of the layer structure, so that ferromagnetic pin–hole coupling and “orange–peel” coupling are reduced (see section 2.1.7).

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