Introduction to magnetic materials

INTRODUCTION TO

MAGNETIC MATERIALS

IEEE Press

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Lajos Hanzo, Editor in Chief

R. Abari T. Chen O. Malik

J. Anderson T. G. Croda S. Nahavandi

S. Basu S. Farshchi M. S. Newman

A. Chatterjee B. M. Hammerli W. Reeve

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Steve Welch, Acquisitions Editor

Jeanne Audino, Project Editor

IEEE Magnetics Society, Sponsor

IEEE Magnetics Society Liaisons to IEEE Press, Liesl Folks and John T. Scott

Technical Reviewers

Stanley H. Charap, Emeritus Professor, Carnegie Mellon University

John T. Scott, American Institute of Physics, Retired

INTRODUCTION TO

MAGNETIC MATERIALS

Second Edition

B. D. CULLITY

University of Notre Dame

C. D. GRAHAM

University of Pennsylvania

Copyright # 2009 by the Institute of Electrical and Electronics Engineers, Inc.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey. All rights reserved.

Published simultaneously in Canada

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Library of Congress Cataloging-in-Publication Data is available:

ISBN 978-0-471-47741-9

Printed in the United States of America

10 9 8 7 6 5 4 3 2 1

CONTENTS

PREFACE TO THE FIRST EDITION xiii

PREFACE TO THE SECOND EDITION xvi

1 DEFINITIONS AND UNITS 1

1.1 Introduction / 1

1.2 The cgs–emu System of Units / 2

1.2.1 Magnetic Poles / 2

1.3 Magnetic Moment / 5

1.4 Intensity of Magnetization / 6

1.5 Magnetic Dipoles / 7

1.6 Magnetic Effects of Currents / 8

1.7 Magnetic Materials / 10

1.8 SI Units / 16

1.9 Magnetization Curves and Hysteresis Loops / 18

2 EXPERIMENTAL METHODS 23

2.1 Introduction / 23

2.2 Field Production By Solenoids / 24

2.2.1 Normal Solenoids / 24

2.2.2 High Field Solenoids / 28

2.2.3 Superconducting Solenoids / 31

2.3 Field Production by Electromagnets / 33

2.4 Field Production by Permanent Magnets / 36

v

2.5 Measurement of Field Strength / 38

2.5.1 Hall Effect / 38

2.5.2 Electronic Integrator or Fluxmeter / 39

2.5.3 Other Methods / 41

2.6 Magnetic Measurements in Closed Circuits / 44

2.7 Demagnetizing Fields / 48

2.8 Magnetic Shielding / 51

2.9 Demagnetizing Factors / 52

2.10 Magnetic Measurements in Open Circuits / 62

2.11 Instruments for Measuring Magnetization / 66

2.11.1 Extraction Method / 66

2.11.2 Vibrating-Sample Magnetometer / 67

2.11.3 Alternating (Field) Gradient Magnetometer—AFGM or AGM

(also called Vibrating Reed Magnetometer) / 70

2.11.4 Image Effect / 70

2.11.5 SQUID Magnetometer / 73

2.11.6 Standard Samples / 73

2.11.7 Background Fields / 73

2.12 Magnetic Circuits and Permeameters / 73

2.12.1 Permeameter / 77

2.12.2 Permanent Magnet Materials / 79

2.13 Susceptibility Measurements / 80

Problems / 85

3 DIAMAGNETISM AND PARAMAGNETISM 87

3.1 Introduction / 87

3.2 Magnetic Moments of Electrons / 87

3.3 Magnetic Moments of Atoms / 89

3.4 Theory of Diamagnetism / 90

3.5 Diamagnetic Substances / 90

3.6 Classical Theory of Paramagnetism / 91

3.7 Quantum Theory of Paramagnetism / 99

3.7.1 Gyromagnetic Effect / 102

3.7.2 Magnetic Resonance / 103

3.8 Paramagnetic Substances / 110

3.8.1 Salts of the Transition Elements / 110

3.8.2 Salts and Oxides of the Rare Earths / 110

3.8.3 Rare-Earth Elements / 110

3.8.4 Metals / 111

3.8.5 General / 111

Problems / 113

vi CONTENTS

4 FERROMAGNETISM 115

4.1 Introduction / 115

4.2 Molecular Field Theory / 117

4.3 Exchange Forces / 129

4.4 Band Theory / 133

4.5 Ferromagnetic Alloys / 141

4.6 Thermal Effects / 145

4.7 Theories of Ferromagnetism / 146

4.8 Magnetic Analysis / 147

Problems / 149

5 ANTIFERROMAGNETISM 151

5.1 Introduction / 151

5.2 Molecular Field Theory / 154

5.2.1 Above TN / 154

5.2.2 Below TN / 156

5.2.3 Comparison with Experiment / 161

5.3 Neutron Diffraction / 163

5.3.1 Antiferromagnetic / 171

5.3.2 Ferromagnetic / 171

5.4 Rare Earths / 171

5.5 Antiferromagnetic Alloys / 172

Problems / 173

6 FERRIMAGNETISM 175

6.1 Introduction / 175

6.2 Structure of Cubic Ferrites / 178

6.3 Saturation Magnetization / 180

6.4 Molecular Field Theory / 183

6.4.1 Above Tc / 184

6.4.2 Below Tc / 186

6.4.3 General Conclusions / 189

6.5 Hexagonal Ferrites / 190

6.6 Other Ferrimagnetic Substances / 192

6.6.1 g-Fe2O3 / 192

6.6.2 Garnets / 193

6.6.3 Alloys / 193

6.7 Summary: Kinds of Magnetism / 194

Problems / 195

CONTENTS vii

7 MAGNETIC ANISOTROPY 197

7.1 Introduction / 197

7.2 Anisotropy in Cubic Crystals / 198

7.3 Anisotropy in Hexagonal Crystals / 202

7.4 Physical Origin of Crystal Anisotropy / 204

7.5 Anisotropy Measurement / 205

7.5.1 Torque Curves / 206

7.5.2 Torque Magnetometers / 212

7.5.3 Calibration / 215

7.5.4 Torsion-Pendulum Method / 217

7.6 Anisotropy Measurement (from Magnetization Curves) / 218

7.6.1 Fitted Magnetization Curve / 218

7.6.2 Area Method / 222

7.6.3 Anisotropy Field / 226

7.7 Anisotropy Constants / 227

7.8 Polycrystalline Materials / 229

7.9 Anisotropy in Antiferromagnetics / 232

7.10 Shape Anisotropy / 234

7.11 Mixed Anisotropies / 237

Problems / 238

8 MAGNETOSTRICTION AND THE EFFECTS OF STRESS 241

8.1 Introduction / 241

8.2 Magnetostriction of Single Crystals / 243

8.2.1 Cubic Crystals / 245

8.2.2 Hexagonal Crystals / 251

8.3 Magnetostriction of Polycrystals / 254

8.4 Physical Origin of Magnetostriction / 257

8.4.1 Form Effect / 258

8.5 Effect of Stress on Magnetic Properties / 258

8.6 Effect of Stress on Magnetostriction / 266

8.7 Applications of Magnetostriction / 268

8.8 DE Effect / 270

8.9 Magnetoresistance / 271

Problems / 272

9 DOMAINS AND THE MAGNETIZATION PROCESS 275

9.1 Introduction / 275

9.2 Domain Wall Structure / 276

9.2.1 Ne´el Walls / 283

viii CONTENTS

9.3 Domain Wall Observation / 284

9.3.1 Bitter Method / 284

9.3.2 Transmission Electron Microscopy / 287

9.3.3 Optical Effects / 288

9.3.4 Scanning Probe; Magnetic Force

Microscope / 290

9.3.5 Scanning Electron Microscopy with

Polarization Analysis / 292

9.4 Magnetostatic Energy and Domain Structure / 292

9.4.1 Uniaxial Crystals / 292

9.4.2 Cubic Crystals / 295

9.5 Single-Domain Particles / 300

9.6 Micromagnetics / 301

9.7 Domain Wall Motion / 302

9.8 Hindrances to Wall Motion (Inclusions) / 305

9.8.1 Surface Roughness / 308

9.9 Residual Stress / 308

9.10 Hindrances to Wall Motion (Microstress) / 312

9.11 Hindrances to Wall Motion (General) / 312

9.12 Magnetization by Rotation / 314

9.12.1 Prolate Spheroid (Cigar) / 314

9.12.2 Planetary (Oblate) Spheroid / 320

9.12.3 Remarks / 321

9.13 Magnetization in Low Fields / 321

9.14 Magnetization in High Fields / 325

9.15 Shapes of Hysteresis Loops / 326

9.16 Effect of Plastic Deformation (Cold Work) / 329

Problems / 332

10 INDUCED MAGNETIC ANISOTROPY 335

10.1 Introduction / 335

10.2 Magnetic Annealing (Substitutional

Solid Solutions) / 336

10.3 Magnetic Annealing (Interstitial

Solid Solutions) / 345

10.4 Stress Annealing / 348

10.5 Plastic Deformation (Alloys) / 349

10.6 Plastic Deformation (Pure Metals) / 352

10.7 Magnetic Irradiation / 354

10.8 Summary of Anisotropies / 357

CONTENTS ix

11 FINE PARTICLES AND THIN FILMS 359

11.1 Introduction / 359

11.2 Single-Domain vs Multi-Domain Behavior / 360

11.3 Coercivity of Fine Particles / 360

11.4 Magnetization Reversal by Spin Rotation / 364

11.4.1 Fanning / 364

11.4.2 Curling / 368

11.5 Magnetization Reversal by Wall Motion / 373

11.6 Superparamagnetism in Fine Particles / 383

11.7 Superparamagnetism in Alloys / 390

11.8 Exchange Anisotropy / 394

11.9 Preparation and Structure of Thin Films / 397

11.10 Induced Anisotropy in Films / 399

11.11 Domain Walls in Films / 400

11.12 Domains in Films / 405

Problems / 408

12 MAGNETIZATION DYNAMICS 409

12.1 Introduction / 409

12.2 Eddy Currents / 409

12.3 Domain Wall Velocity / 412

12.3.1 Eddy-Current Damping / 415

12.4 Switching in Thin Films / 418

12.5 Time Effects / 421

12.5.1 Time Decrease of Permeability / 422

12.5.2 Magnetic After-Effect / 424

12.5.3 Thermal Fluctuation After-Effect / 426

12.6 Magnetic Damping / 428

12.6.1 General / 433

12.7 Magnetic Resonance / 433

12.7.1 Electron Paramagnetic Resonance / 433

12.7.2 Ferromagnetic Resonance / 435

12.7.3 Nuclear Magnetic Resonance / 436

Problems / 438

13 Soft Magnetic Materials 439

13.1 Introduction / 439

13.2 Eddy Currents / 440

13.3 Losses in Electrical Machines / 445

13.3.1 Transformers / 445

13.3.2 Motors and Generators / 450

x CONTENTS

13.4 Electrical Steel / 452

13.4.1 Low-Carbon Steel / 453

13.4.2 Nonoriented Silicon Steel / 454

13.4.3 Grain-Oriented Silicon Steel / 456

13.4.4 Six Percent Silicon Steel / 460

13.4.5 General / 461

13.5 Special Alloys / 463

13.5.1 Iron–Cobalt Alloys / 466

13.5.2 Amorphous and Nanocrystalline

Alloys / 466

13.5.3 Temperature Compensation Alloys / 467

13.5.4 Uses of Soft Magnetic Materials / 467

13.6 Soft Ferrites / 471

Problems / 476

14 HARD MAGNETIC MATERIALS 477

14.1 Introduction / 477

14.2 Operation of Permanent Magnets / 478

14.3 Magnet Steels / 484

14.4 Alnico / 485

14.5 Barium and Strontium Ferrite / 487

14.6 Rare Earth Magnets / 489

14.6.1 SmCo5 / 489

14.6.2 Sm2Co17 / 490

14.6.3 FeNdB / 491

14.7 Exchange-Spring Magnets / 492

14.8 Nitride Magnets / 492

14.9 Ductile Permanent Magnets / 492

14.9.1 Cobalt Platinum / 493

14.10 Artificial Single Domain Particle

Magnets (Lodex) / 493

14.11 Bonded Magnets / 494

14.12 Magnet Stability / 495

14.12.1 External Fields / 495

14.12.2 Temperature Changes / 496

14.13 Summary of Magnetically Hard Materials / 497

14.14 Applications / 498

14.14.1 Electrical-to-Mechanical / 498

14.14.2 Mechanical-to-Electrical / 501

14.14.3 Microwave Equipment / 501

14.14.4 Wigglers and Undulators / 501

CONTENTS xi

14.14.5 Force Applications / 501

14.14.6 Magnetic Levitation / 503

Problems / 504

15 MAGNETIC MATERIALS FOR RECORDING

AND COMPUTERS 505

15.1 Introduction / 505

15.2 Magnetic Recording / 505

15.2.1 Analog Audio and Video Recording / 505

15.3 Principles of Magnetic Recording / 506

15.3.1 Materials Considerations / 507

15.3.2 AC Bias / 507

15.3.3 Video Recording / 508

15.4 Magnetic Digital Recording / 509

15.4.1 Magnetoresistive Read Heads / 509

15.4.2 Colossal Magnetoresistance / 511

15.4.3 Digital Recording Media / 511

15.5 Perpendicular Recording / 512

15.6 Possible Future Developments / 513

15.7 Magneto-Optic Recording / 513

15.8 Magnetic Memory / 514

15.8.1 Brief History / 514

15.8.2 Magnetic Random Access Memory / 515

15.8.3 Future Possibilities / 515

16 MAGNETIC PROPERTIES OF SUPERCONDUCTORS 517

16.1 Introduction / 517

16.2 Type I Superconductors / 519

16.3 Type II Superconductors / 520

16.4 Susceptibility Measurements / 523

16.5 Demagnetizing Effects / 525

APPENDIX 1: DIPOLE FIELDS AND ENERGIES 527

APPENDIX 2: DATA ON FERROMAGNETIC ELEMENTS 531

APPENDIX 3: CONVERSION OF UNITS 533

APPENDIX 4: PHYSICAL CONSTANTS 535

INDEX 537

xii CONTENTS

PREFACE TO THE FIRST EDITION

Take a pocket compass, place it on a table, and watch the needle. It will jiggle around,

oscillate, and finally come to rest, pointing more or less north. Therein lie two mysteries.

The first is the origin of the earth’s magnetic field, which directs the needle. The second

is the origin of the magnetism of the needle, which allows it to be directed. This book

is about the second mystery, and a mystery indeed it is, for although a great deal is

known about magnetism in general, and about the magnetism of iron in particular, it

is still impossible to predict from first principles that iron is strongly magnetic.

This book is for the beginner. By that I mean a senior or first-year graduate student in

engineering, who has had only the usual undergraduate courses in physics and materials

science taken by all engineers, or anyone else with a similar background. No knowledge

of magnetism itself is assumed.

People who become interested in magnetism usually bring quite different backgrounds to

their study of the subject. They are metallurgists and physicists, electrical engineers and

chemists, geologists and ceramists. Each one has a different amount of knowledge of

such fundamentals as atomic theory, crystallography, electric circuits, and crystal chemistry.

I have tried to write understandably for all groups. Thus some portions of the book will be

extremely elementary for most readers, but not the same portions for all readers.

Despite the popularity of the mks system of units in electricity, the overwhelming

majority of magneticians still speak the language of the cgs system, both in the laboratory

and in the plant. The student must learn that language sooner or later. This book is therefore

written in the cgs system.

The beginner in magnetism is bewildered by a host of strange units and even stranger

measurements. The subject is often presented on too theoretical a level, with the result

that the student has no real physical understanding of the various quantities involved,

simply because he has no clear idea of how these quantities are measured. For this

reason methods of measurement are stressed throughout the book. All of the second

chapter is devoted to the most common methods, while more specialized techniques are

described in appropriate later chapters.

xiii

The book is divided into four parts:

1. Units and measurements.

2. Kinds of magnetism, or the difference, for example, between a ferromagnetic and a

paramagnetic.

3. Phenomena in strongly magnetic substances, such as anisotropy and magnetostriction.

4. Commercial magnetic materials and their applications.

The references, selected from the enormous literature of magnetism, are mainly of two

kinds, review papers and classic papers, together with other references required to buttress

particular statements in the text. In addition, a list of books is given, together with brief indi￾cations of the kind of material that each contains.

Magnetism has its roots in antiquity. No one knows when the first lodestone, a natural

oxide of iron magnetized by a bolt of lightning, was picked up and found to attract bits of

other lodestones or pieces of iron. It was a subject bound to attract the superstitious, and it

did. In the sixteenth century Gilbert began to formulate some clear principles.

In the late nineteenth and early twentieth centuries came the really great contributions of

Curie, Langevin, and Weiss, made over a span of scarcely more than ten years. For the next

forty years the study of magnetism can be said to have languished, except for the work of a

few devotees who found in the subject that fascinations so eloquently described by the late

Professor E. C. Stoner:

The rich diversity of ferromagnetic phenomena, the perennial

challenge to skill in experiment and to physical insight in

coordinating the results, the vast range of actual and

possible applications of ferromagnetic materials, and the

fundamental character of the essential theoretical problems

raised have all combined to give ferromagnetism a width of

interest which contrasts strongly with the apparent narrowness

of its subject matter, namely, certain particular properties

of a very limited number of substances.

Then, with the end of World War II, came a great revival of interest, and the study of

magnetism has never been livelier than it is today. This renewed interest came mainly

from three developments:

1. A new material. An entirely new class of magnetic materials, the ferrites, was devel￾oped, explained, and put to use.

2. A new tool. Neutron diffraction, which enables us to “see” the magnetic moments of

individual atoms, has given new depth to the field of magnetochemistry.

3. A new application. The rise of computers, in which magnetic devices play an essen￾tial role, has spurred research on both old and new magnetic materials.

And all this was aided by a better understanding, gained about the same time, of magnetic

domains and how they behave.

In writing this book, two thoughts have occurred to me again and again. The first is that

magnetism is peculiarly a hidden subject, in the sense that it is all around us, part of our

xiv PREFACE TO THE FIRST EDITION