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MAGNETIC HYSTERESIS

IEEE Press445 Hoes Lane, P.O. Box 1331

Piscataway, NJ 08855-1331

IEEE Press Editorial BoardRobert J. Herrick, Editor in Chief

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Cover design: William T. Donnelly, WT Design

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MAGNETIC HYSTERESIS

Edward Della TorreThe George Washington University

IEEE~PRESS

IEEE MAGNETICS SOCIETY, SPONSOR

The Institute of Electrical and Electronics Engineers, Inc., New York

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1999 by the Institute of Electrical and Electronics Engineers, Inc.3 Park Avenue, 17th floor, New York, NY 10016-5997

All rights reserved. No part ofthis book may be reproduced in any form,nor may it be stored in a retrieval system or transmitted in any form,without written permission from the publisher.

10 9 8 7 6 5 4 3 2

ISBN 0-7803-6041-9IEEE Order Number: PP5766

The Library of Congress has catalogued the hard coveredition of this title as follows:

DellaTorre, Edward 1934-MagneticHysteresis I Edward Della Torre.

p. em.Includes bibliographical references and index.ISBN0-7803-4719-61. Hysteresis. I. Title

QC754.2H9T67 1999538'.3- -dc21 98-46940

CIP

To the memory ofCharles V. Longo

CONTENTSPreface xi

Acknowledgments xiii

Chapter 1 Physics of Magnetism 11.1 Introduction 11.2 Diamagnetism and Paramagnetism 21.3 Ferro-, Antiferro-, and Ferrimagnetic

Materials 51.4 Micromagnetism 81.5 Domains and Domain Walls 12

1.5.1 Bloch Walls 131.5.2 Neel Walls 151.5.3 Coercivity of a Domain Wall 16

1.6 The Stoner-Wohlfarth Model 171.7 Magnetization Dynamics 26

1.7.1 Gyromagnetic Effects 261.7.2 Eddy Currents 281.7.3 Wall Mobility 28

1.8 Conclusions 29References 30

Chapter 2 The Preisach Model 312.1 Introduction 312.2 Magnetizing Processes 312.3 Preisach Modeling 332.4 The Preisach Differential Equation 40

2.4.1 Gaussian Preisach Function 412.4.2 Increasing Applied Field 43

vii

viii CONTENTS

2.4.3 Decreasing Applied Field 442.5 Model Identification: Interpolation 462.6 Model Identification: Curve Fitting 472.7 The Congruency and the Deletion Properties

492.8 Conclusions 51References 51

Chapter 3 Irreversible and Locally ReversibleMagnetization 533.1 Introduction 533.2 State-Independent Reversible Magnetization

533.3 Magnetization-Dependent Reversible Model

553.4 State-Dependent Reversible Model 583.5 Energy Considerations 62

3.5.1 Hysteron Assemblies 643.6 Identification of Model Parameters 663.7 Apparent Reversible Magnetization 673.8 Crossover Condition 713.9 Conclusions 73References 73

Chapter 4 The Moving Model and the Product Model 754.1 Introduction 754.2 Hard Materials 754.3 Identification of the Moving Model 80

4.3.1 The Symmetry Method 804.3.2 The Method of Tails 84

4.4 The Variable-Variance Model 864.5 Soft Materials 924.6 Henkel Plots 934.7 Congruency Property 95

4.7.1 The Classical Preisach Model 974.7.2 Output-Dependent Models 97

4.8 Deletion Property 1004.8.1 Hysteresis in Intrinsically

Nonhysteretic Materials 1024.8.2 Proof of the Deletion Property 104

4.9 Conclusions 107References 108

CONTENTS ix

Chapter 5 Aftereffect and Accommodation 1115.1 Introduction 1115.2 Aftereffect 1125.3 Preisach Interpretation of Aftereffect 1205.4 Aftereffect Dependence on Magnetization

History 1235.5 Accommodation 1255.6 Identification of Accommodation Parameters

1345.7 Properties of Accommodation Models 137

5.7.1 Types of Accommodation Processes139

5.8 Deletion Property 1435.9 Conclusions 144References 144

Chapter 6 Vector Models 1476.1 Introduction 1476.2 General Properties of Vector Models 1486.3 The Mayergoyz Vector Model 1516.4 Pseudoparticle Models 1526.5 Coupled-Hysteron Models 154

6.5.1 Selection Rules 1546.5.2 The m2 Model 1586.5.3 The Simplified Vector Model or SVM

Model 1596.6 Loss Properties 1646.7 Conclusions 165References 165

Chapter 7 Preisach Applications 1677.1 Introduction 1677.2 Dynamic Effects 1677.3 Eddy Currents 1687.4 Frequency Response of the Recording

Process 1707.5 Pulsed Behavior 172

7.5.1 Dynamic Accommodation Model173

7.5.2 Single-Pulse Simulation 1787.5.3 Double-Pulse Simulation 181

7.6 Noise 1817.6.1 The Magnetization Model 183

x CONTENTS

7.6.1 The Magnetization Model 1837.6.2 The Effectof the Moving Model

1847.6.3 The Effect of the Accommodation

Model 1867.7 Magnetostriction 1887.8 The Inverse Problem 1947.9 Conclusions 195References 195

Appendix A

Appendix B

Appendix C

Index 211

The Playand StopModels 199

The Log-Normal Distribution 203

Definitions 207

About the Author 215

PREFACE

The modeling of magnetic materials can be performed at various levels ofresolution. The highest level of resolution is the atomic level. At this level, one canuse quantum mechanics to understand the basic processes involved. The next stepdown in resolution is the micromagnetic level, where the magnetization is acontinuous function of position. At a still lower level of resolution, one uses thedomain level of modeling, where the material is divided into uniformly magnetizeddomains separated by domain walls of zero thickness. Finally at the lowestresolution, the nonlinear medium level, the magnetization is the average of manydomains, and the physical nature of their formation is ignored. In this last level, themedium is characterized by an input/output relationship.

Preisach modeling is a mathematical tool that has been used principally at thenonlinear medium level, but it can also give some insight at all the levels. Itseffectiveness in describing magnetic materials is due to its ability to have abehavior when the applied field is increasing which is different from its behaviorwhen the applied field is decreasing. It is thus able to describe minor loops andother complex magnetizing processes. The classical Preisach model is limited bythe congruency property and the deletion property, neither of which is possessedby magnetic materials. Although these limitations could be removed using aphenomenological approach, this book relies on physical reasoning as much aspossible to make necessary modifications. This practice usually results in simplermodels that give physical insight into the processes of interest. Although thesemodifications have been shown to be robust, the book uses physical reasoningrather than mathematical rigor to justify its derivations.

In Chapter 1, the physics of magnetization processes is briefly summarized.Chapter 2 summarizes the classical Preisach model, which is the basis for thestatistical analysis used in modeling hysteresis. However, since it cannot describe

xi

xii PREFACE

many of the subtleties in the behavior of magnetic materials, modifications basedupon physical reasoning are presented in the subsequent chapters. In particular, theconcept of reversible magnetization is discussed in Chapter 3. Accurate behaviorof the susceptibility is obtained by a magnetization-dependent reversiblecomponent, called the DOK model. This is further improved by adding a morecomplex state-dependent reversible component, called the CMH model. As shownin Chapter 4, the congruency limitation can be removed by means of an output-dependent model, such as the moving model or the product model. Including eitheraccommodation, aftereffect, or both in the model, as shown in Chapter 5, removesthe deletion property. Even with all these modifications, the resulting model is stilla scalar model, so in Chapter 6, we discuss methods of generalizing it to a vectormodel.

Some applications are discussed in Chapter 7. First, since the model isessentially a magnetostatic model, this chapter presents two brief extensions todynamics. These extensions include the effect of eddy currents on themagnetization, the effect of the accommodation model on the pulsed behavior, andthe effect of the moving model and the accommodation model on noise. Anotherextension is the development ofa magnetostriction model. Finally, the developmentof an inverse model, which would be useful in control applications, is discussed.

I hope that this book is useful in showing how the Preisach model can beextended to describe accurately a wide range of magnetic phenomena. Although thediscussion is limited to magnetic phenomena, it can give deep insight into theanalysis of hysteretic many-body problems. The techniques presented here aregeneral and can be applied to hysteresis problems in disciplines other thanmagnetism.

Edward Dell