Introduction to magnetism and magnetic Materials

Introduction to Magnetism

and Magnetic Materials

Introduction to Magnetism

and Magnetic Materials

David Jiles

Ames Laboratory,

US Department of Energy

and

Department of Materials Science

and Engineering, Iowa State University,

Ames, Iowa, USA

SPRINGER-SCffiNCE+BUSINESS MEDIA, B.V.

First edition 1991

©1991 David Jiles

Originally published by Chapman and Hall in 1991

Typeset in 10/12 pt Times by

Thomson Press (India) Ltd, New Delhi

All rights reserved. No part of this publication may be reproduced or

transmitted, in any form or by any means, electronic, mechanical,

photocopying, recording or otherwise, or stored in any retrieval system of any

nature, without the written permission of the copyright holder and the

publisher, application for which shall be made to the publisher.

British Library Cataloguing in Publication Data

Jiles, David

Introduction to magnetism and magnetic materials.

1. Magnetic materials. Properties

I. Title

538.3

ISBN 978-0-412-38640-4 ISBN 978-1-4615-3868-4 (eBook)

DOI 10.1007/978-1-4615-3868-4

Library of Congress Cataloging-in-Publication Data

Jiles, David.

Introduction to magnetism and magnetic materials / David Jiles.—

1st ed.

p. cm.

Includes bibliographical references and index.

1. Magnetism. 2. Magnetic materials. I. Title.

QC753.2.J55 1990 90-41506

538-dc20 CIP

Few subjects in science are more difficult to understand than magnetism.

Encyclopedia Britannica, Fifteenth Edition 1989.

Preface

Over the years there have been a number of excellent textbooks on the subject

of magnetism. Among these we must include Bozorth's Ferromagnetism (1950),

Chikazumi's Physics of Magnetism (1964) and Cullity's Introduction to Magnetic

Materials (1972). However at present there is no up to date general textbook on

magnetism. This book will, I hope, satisfy this need. It is a book for the newcomer

to magnetism, and so I anticipate it will be useful as a text for final-year

undergraduate courses in magnetism and magnetic materials or for graduate

courses. I would also hope that it will be useful to the researcher who, for one

reason or another, is beginning a study of magnetism and needs an introductory

general text. In this case the extensive references to the literature of magnetism

given in the text should prove useful in enabling the reader to gain rapid access

to the most important papers on the subject. For the expert there are of course

already numerous excellent specialist works, of which the most significant is

Wohlfarth's four-volume series Ferromagnetic Materials.

The book was conceived as a whole and deals with the fundamentals of

magnetism in Chapters 1 to 11, and the principal applications in Chapters 12 to

16. The approach which I have taken is to consider magnetic phenomena first

on an everyday macroscopic scale, which should be familiar to most readers,

and then gradually to progress to smaller-scale phenomena in the search for

explanations of observations on the larger scale. In this way I hope that the

book will be of interest to a wider audience consisting of physicists, materials

scientists and electrical engineers. One advantage of this approach is that it is

possible to introduce the subject from an appeal to the reader's experience rather

than through abstract concepts. It is also easier to maintain the reader's interest

if he does not find himself immediately confronted with difficult concepts when

he first opens the book at chapter one.

Whereas physicists are likely to be mainly interested in the microscopic

phenomena discussed in Chapters 9, 10 and 11, the materials scientists and

metallurgists are more interested in the domain processes and how these are

affected by microstructure, as described in Chapters 6, 7 and 8. Electrical engineers

are probably more familiar with field calculations and modelling of magnetic

properties in Chapters 1, 2 and 5. Each of these groups should be interested in

the applications of our subject since it is the applications which sustain it. There

Vl11 Preface

is a strong demand today for scientists and engineers with skills in magnetism

because of applications in magnetic recording, permanent magnets, electrical

steels, soft magnetic materials and materials evaluation and measurements; not

because it is a deeply interesting and difficult subject - which it undoubtedly is.

The choice of units in magnetism presents a continual problem which those

not experienced in the subject will find difficult to comprehend. In research

journals papers are primarily written in CGS (Gaussian) units. This system has

the advantage that the permeability of free space is unity and that the unit of

magnetic field, the oersted, has a very convenient size for practical applications.

In electromagnetism the Sommerfeld system of units has been adopted widely.

This has the advantage of being completely compatible with the SI unit system

but suffers from a serious disadvantage because the permeability of free space,

which has the cumbersome value of 12.56 x 10 - 7 henry jmetre, enters into many

of the equations. This value has no real significance, being merely the result of

the choice of our definition of units, specifically the ampere. In this book I have

nevertheless chosen the Sommerfeld unit convention because it is the unit system

recommended by the International Union of Pure and Applied Physics, and

because this is the unit system for the future. However it was not practicable to

convert every diagram taken from research journals and monographs into this

unit system. Nor was it desirable since the practitioner of magnetism must learn

to be adept in both unit systems. Therefore many of the figures given later in

the book remain in their original units. Conversion factors are given in section

1.2.6. so that the reader becomes immediately familiar with these alternative units.

Finally I would like to take this opportunity to acknowledge the advice and

assistance given to me by many friends and colleagues while writing this book.

In particular thanks go to D. L. Atherton who persuaded me to write it, S. B.

Palmer, F. J. Friedlaender and C. D. Graham Jr for reading the entire text, and

D. K. Finnemore, R. D. Greenough, K. A. Gschneidner Jr, W. Lord, B. Lograsso,

K. J. Overshott, J. Mallinson, R. W. McCallum, A. J. Moses and E. Williams for

advice on particular chapters.

DJ.

Ames, Iowa

Foreword

As you study the intricate subject of magnetism in this book you will find that

the journey begins at a familiar level with electric currents passing through wires,

compass needles rotating in magnetic fields and bar magnets attracting or

repelling each other. As the journey progresses though, in order to understand our

observations, we must soon peel back the surface and begin to delve into the

materials, to look at ever increasing magnification at smaller and smaller details

to explain what is happening. This process takes us from bulk magnets (1023_1026

atoms) down to the domain scale (1012_1018 atoms) and then down to the scale

of a domain wall (103-1 02 atoms). In critical phenomena one is often concerned

with the behaviour of even smaller numbers (10 atoms or less) in a localized

array. Then comes the question of how the magnetic moment of a single atom

arises. We must go inside the atom to find the answer by looking at the behaviour

of a single electron orbiting a nucleus. The next question is why the magnetic

moments of neighbouring atoms are aligned. In order to answer this we must

go even further and consider the quantum mechanical exchange interaction

between two electrons on neighbouring atoms. This then marks the limit of our

journey into the fundamentals of our subject. Subsequently we must ask how can

this knowledge be used to our benefit. In Chapters 12 through 16 we look at the

most significant applications of magnetism. It is no surprise that apart from

superconductors these applications deal exclusively with ferromagnetism.

Ferromagnetism is easily the most important technological branch of magnetism

and most scientific studies, even of other forms of magnetism, are ultimately

designed to help further our understanding of ferromagnetism so that we can

both fabricate new magnetic materials with improved properties and make better

use of existing materials.

Finally I have adopted an unusual format for the book in which each section

is introduced by a question, which the following discussion attempts to answer.

Many have said they found this useful in focusing attention on the subject matter

at hand since it is then clear what is the objective of each section. I have decided

therefore to retain this format from my original notes, realizing that it is unusual

in a textbook but hoping that it proves helpful to the reader.

Contents

Preface VB

Foreword ix

1 Magnetic Fields 1

1.1 The Magnetic Field 1

1.2 Magnetic Induction 6

1.3 Magnetic Field Calculations 12

Examples and Exercises 26

2 Magnetization and Magnetic Moment 27

2.1 Magnetic Moment and Magnetization 27

2.2 Permeability and Susceptibility of Various Materials 32

2.3 Magnetic Circuits and Demagnetizing Field 36

Examples and Exercises 44

3 Magnetic Measurements 47

3.1 Induction Methods 47

3.2 Methods Depending on Changes in Material Properties 53

3.3 Other Methods 60

Examples and Exercises 67

4 Magnetic Materials 69

4.1 Important Magnetic Properties of Ferromagnets 69

4.2 Different Types of Ferromagnets Materials

for Applications 74

4.3 Paramagnetism and Diamagnetism 81

Examples and Exercises 86

5 Magnetic Properties 89

5.1 Hysteresis and Related Properties 89

5.2 The Barkhausen Effect and Related Phenomena 97

5.3 Magnetostriction 98

Examples and Exercises 105

XlI Contents

6 Magnetic Domains 107

6.1 Development of Domain Theory 107

6.2 Energy Considerations and Domain Patterns 118

Examples and Exercises 125

7 Domain Walls 127

7.1 Properties of Domain Boundaries 127

7.2 Domain-Wall Motion 137

Examples and Exercises 144

8 Domain Processes 147

8.1 Reversible and Irreversible Domain Processes 147

8.2 Determination of Magnetization Curves from Pinning Models 156

8.3 Theory of Ferromagnetic Hysteresis 165

Examples and Exercises 174

9 Magnetic Order and Critical Phenomena 177

9.1 Theories of Diamagnetism and Paramagnetism 177

9.2 Theories of Ordered Magnetism 188

9.3 Magnetic Structure 197

Examples and Exercises 217

10 Electronic Magnetic Moments 219

10.1 The Classical Model of Electronic Magnetic Moments 219

10.2 The Quantum Mechanical Model of Electronic Magnetic

Moments 221

10.3 Magnetic Properties of Free Atoms 237

Examples and Exercises 245

11 Quantum Theory of Magnetism 247

11.1 Electron-Electron Interactions 247

11.2 The Localized Electron Theory 254

11.3 The Itinerant Electron Theory 261

Examples and Exercises 268

12 Soft Magnetic Materials 269

12.1 Properties and Uses of Soft Magnetic Materials 269

12.2 Materials for a.c. Applications 272

12.3 Materials for d.c. Applications 290

13 Hard Magnetic Materials 299

13.1 Properties and Applications 299

13.2 Permanent Magnet Materials 311

Contents Xlll

14 Magnetic Recording 323

14.1 Magnetic Recording Media 323

14.2 The Recording Process and Applications of Magnetic

Recording 334

15 Superconductivity 345

15.1 Basic Properties of Superconductors 345

15.2 Applications of Superconductors 358

16 Magnetic Methods for Materials Evaluation 365

16.1 Methods for Evaluation of Intrinsic Properties 365

16.2 Methods for Detection of Flaws and other Inhomogeneities 377

16.3 Conclusions 394

Solutions 399

Index 425

Acknowledgements

I am grateful to the authors and publishers for permission to reproduce the

following figures which appear in this book.

1.2

1.7

2.3

2.5

3.1

P. Ruth (1969) Introduction to Field and Particle, Butterworths, London.

G. V. Brown and L. Flax (1964) Journal of Applied Physics, 35, 1764.

F. W. Sears (1951) Electricity and Magnetism, Addison Wesley, Reading,

Mass.

1. A. Osborne (1945) Physical Review, 67, 351.

D. O. Smith (1956) Review of Scientific Instruments, 27, 261.

3.2, 3.6, 3. 7

3.5

3.9

4.4

4.5

T. R. McGuire and P. 1. Flanders (1969) in Magnetism and Metallurgy (eds

A. E. Berkowitz and E. Kneller), Academic Press, New York.

S. Chikazumi (1964) Physics of Magnetism" John Wiley, New York.

B. I. Bleaney and B. Bleaney (1976) Electricity and Magnetism, Oxford

University Press, Oxford.

J. Fidler, J. Bernardi and P. Skalicky (1987) High Performance Permanent

Magnet Materials, (eds S. G. Sankar, 1. F. Herbst and N. C. Koon),

Materials Research Society.

C. Kittel (1986) Introduction to Solid State Physics, 6th edn, Wiley, New

York. R. 1. Elliott and A. F. Gibson (1974), An Introduction to Solid State

Physics and its Applications, MacMillan, London.

4.7,5.1

A. E. E. McKenzie (1971) A Second Course of Electricity, 2nd edn,

Cambridge University Press.

XVI Acknowledgements

5.7

6.4

6.6

6.7

6.8

7.1

7.4

7.6

8.2

8.5

E. W. Lee (1955) Rep. Prog. Phys. 18, 184. A. E. Clark and H. T. Savage

(1983) Journal of Magnetism and Magnetics Materials, 31,849.

H. J. Williams, R. J. Bozorth and W. Shockley (1940) Physical Review,

75, 155.

C. Kittel (1986) Introduction to Solid State Physics, 6th edn, Wiley,

New York.

R. M. Bozorth (1951) Ferromagnetism, Van Nostrand, New York.

C. Kittel and J. K. Galt (1956) Solid State Physics, 3, 437.

C. Kittel (1949) Reviews of Modern Physics, 21, 541.

R. W. Deblois and C. D. Graham (1958) Journal of Applied Physics, 29, 931.

S. Chikazumi (1964) Physics of Magnetism, Wiley, New York.

M. Kersten (1938) Probleme der Technische Magnetisierungs Kurve, Springer￾Verlag, Berlin.

K. Hosclitz (1951) Ferromagnetic Properties of Metals and Alloys, Oxford

University Press, Oxford.

8.8,8.9

8.10

8.12

J. Degaugue, B. Astie, J. L. Porteseil and R. Vergne (1982) Journal of

Magnetism and M agnetic Material, 26, 261.

A Globus, P. Duplex and M. Guyot (1971) IEEE Transactions on Magnetics,

7,617. A. Globus and P. Duplex (1966) IEEE Transactions on Magnetics, 2,

441.

S. Chikazumi (1964) Physics of Magnetism, Wiley, New York.

9.2,9.3

9.5

9.6

C. Kittel (1986) Introduction to Solid State Physics, 6th edn, Wiley,

New York.

P. Weiss and R. Forrer (1929) Annalen der Physik, 12, 279.

D. H. Martin (1967) Magnetism in Solids, Illife Books, London.

9.7,9.9,9.10

G. E. Bacon (1975) Neutron Diffraction, 3rd edn, Clarendon Press,

Oxford.

Acknowledgements XVll

9.8

J. Crangle (1977) The Magnetic Properties of Solids, Edward Arnold, London.

9.11

G. L. Squires (1954) Proceedings of the Physical Society of London, A67, 248.

9.12

D. Cribier, B. Jacrot and G. Parette (1962) Journal of the Physical Society of

Japan, 17-BIII, 67.

9.14,9.15,9.16

9.17

9.19

9.20

9.21

9.22

B. D. Cullity (1972) Introduction to Magnetic Materials, Addison-Wesley,

Reading, Mass.

C. Kittel (1986) Introduction to Solid State Physics, 6th edn, Wiley,

New York.

J. A. Hofman, A. Pashkin, K. J. Tauer and R. J. Weiss (1956) Journal of

Physics and Chemistry of Solids, 1, 45.

D. H. Martin (1967) Magnetism in Solids, Illife Books, London.

S.B. Palmer and C. Isci (1978) Journal of Physics F. Metal Physics, 8, 247.

D. C. Jiles and S. B. Palmer (1980) Journal of Physics F. Metal Physics, 10,

2857.

R. D. Greenough and C. Isci (1978) Journal of Magnetism and Magnetic

Materials, 8, 43.

10.7,10.8

11.1

H. Semat (1972) Introduction to Atomic and Nuclear Physics, 5th edn, Holt,

Rinehart and Winston, New York.

D. H. Martin (1967) Magnetism in Solids, Illife Books, London.

11.3

11.4

J. Crangle (1977) The Magnetic Properties of Solids, Edwards Arnold,

London.

W. E. Henry (1952) Physical Review, 88, 559.

11.8

B. D. Cullity (1972) Introduction to Magnetic Materials, Addison-Wesley,

Reading, Mass.

11.9,12.1

R. M. Bozorth (1951) Ferromagnetism, Van Nostrand, New York.

12.2,12.3,12.13,12.19

G. Y. Chin and J. H. Wernick (1980) in Ferromagnetic Materials, Vol. 2,

(ed. E. P. Wohlfarth), North Holland.

xviii Acknowledgements

12.4

M. F. Litmann (1971) IEEE Transactions on Magnetics, 7, 48.

12.5,12.6

M. F. Litmann (1967) Journal of Applied Physics, 38, 1104.

12.7

E. Adams (1962) Journal of Applied Physics, 33,1214.

12.8,12.9,12.10,12.11

C. Heck (1972) Magnetic Materials and their Applications, Crane, Russak

and Company, New York.

12.14,12.16,12.1

F. E. Luborsky (1980) in Ferromagnetic Materials, Vol. 1, (ed. E. P. Woh￾lfarth), North Holland.

12.15,12.17

Reproduced by permission of Allied Signal Company, Morristown, New

Jersey.

12.20,12.21

1. H. Swisher and E. O. Fuchs (1970) Journal of the Iron and Steel Institute,

August.

12.24

G. W. Elman (1935) Electrical Engineering, 54, 1292.

13.5,13.6,13.7,13.8,13.9

D.1. Craik (1971) Structure and Properties of Magnetic Materials, Pion,

London.

13.10,13.11

R. J. Parker and R. J. Studders (1962) Permanent Magnets and their

Applications, Wiley, New York.

13.12,13.13,13.14

R. A. McCurrie (1982) in Ferromagnetic Materials, Vol. 3 (ed. E. P.

Wohlfarth), North Holland.

13.16,13.17

M. McCaig and A. G. Clegg (1987) Permanent Magnets in Theory and

Practice, 2nd edn, Pen tech Press, London.

14.1,14.2,14.3,14.4,14.8

14.5

R. M. White (1985) Introduction to Magnetic Recording, IEEE Press,

New York.

C. D. Mee (1964) The Physics of Magnetic Recording, North Holland.

15.2

H. Kamerlingh-Onnes Akad (1911) Wertenschappen, 14, 113.

15.3

15.4

C. Kittel (1986) Introduction to Solid State Physics, 6th edn, Wiley,

New York.

U. Essmann and H. Trauble (1968) Journal of Applied Physics, 39, 4052.