Table Of ContentFerromagnetodynamics
By the same author
MAGNETIC BUBBLES
Ferromagnetodynamics
The dynamics of magnetic bubbles,
domains and domain walls
T. H. O'Dell
Reader in Electronics,
Department of Electrical Engineering,
Imperial College of Science and Technology,
University of London
M
©T. H. O'Dell 1981
Softcover reprint of the hardcover 1st edition 1981 978-0-333-26413-3
All rights reserved. No part of this publication may be reproduced or
transmitted, in any form or by any means, without permission.
First published 1981 by
THE MACMILLAN PRESS LTD
London and Basingstoke
Companies and representatives
throughout the world
Typeset in 10/12 Times by
MULTIPLEX techniques ltd
ISBN 978-1-349-81417-6 ISBN 978-1-349-81415-2 (eBook)
DOI 10.1007/978-1-349-81415-2
Contents
Preface ix
1. The History and Experimental Techniques of Ferro-
magnetodynarnics 1
1.1 Introduction 1
1.2 Early Experimental Work 2
1.3 The Experiments of Sixtus and Tonks 3
1.4 The First Dynamic Experiments with Single Crystals 4
1.5 The Use of Optical Techniques 12
1.6 The First Use of High-speed Photography in Ferromagneto-
dynamics 15
1.7 Magnetic Bubble Domain Materials 16
1.8 The Bubble Collapse Experiment 18
1.9 The Bubble Translation Experiment 20
1.10 The Application of High-speed Photography to Bubble
Domain Dynamics 24
2. The Landau-Lifshitz Equation 27
2.1 Introduction 27
2.2 The Problem of Magnetostatic Stability 27
2.3 The Anisotropy Field 29
2.4 The Exchange Field 30
2.5 The Magnetostatic Field 33
2.6 The Structure of the Landau-Lifshitz Wall 34
2.7 Other Kinds of One-dimensional Wall Structure 37
2.8 Experimental Evidence for the Landau-Lifshitz
Structure 38
2.9 The Formulation of the Landau-Lifshitz Equation 40
2.10 The Application of the Landau-Lifshitz Equation to
Domain Wall Motion 42
2.11 The Walker Limiting Velocity 46
2.12 The Relationship to Ferromagnetic Resonance 47
2.13 Experimental Work; the Magnitude of A and its
Implications 51
2.14 Wall Acceleration; the Doring Mass 53
2.15 A Field Interpretation of the Effective Wall Mass 55
vi Fe"omagnetodynamics
2.16 Experimental Work on Wall Inertia 57
2.17 Including the Exchange and Anisotropy Fields 57
2.18 Conclusions 64
3. Straight Wall Motion in Magnetic Bubble Films 69
3.1 Introduction 69
3.2 Magnetic Bubble Domain Materials 69
3.3 The Domain Wall Structure in a Magnetic Bubble Film 70
3.4 The Stability of Straight Walls in Magnetic Bubble Films 72
3.5 Producing a Landau-Lifshitz Wall Structure in a
Magnetic Bubble Film 74
3.6 Motion of a Landau-Lifshitz Wall when a Magnetic
Field is Applied Perpendicular to the Wall Plane 75
3.7 Experimental Work on Wall Motion when a Field is
Applied Perpendicular to the Wall Plane 81
3.8 The Importance of the Wall Screw·sense 85
3.9 The Saturation Velocity 86
3.10 Inertial Effects when a Field is Applied Perpendicular
to the Wall Plane 89
3.11 Wall Motion when an In·plane Field is Applied Parallel
to the Wall 91
3.12 Conclusions 95
4. Magnetic Bubble Domain Dynamics 98
4.1 Introduction 98
4.2 Historical Development 98
4.3 The Statics of Normal Magnetic Bubbles 100
4.4 Hard Bubble Statics 103
4.5 Hard Bubble Wall Mobility 109
4.6 The Hard Bubble in Translation 111
4.7 The Generation of Hard Bubbles 114
4.8 The Suppression of Hard Bubbles 117
4.9 The Statics of Bubble Domains with Low S-numbers 119
4.10 The Dynamics of Bubble Domains with Low
S-numbers in Small Applied Fields 124
4.10.1 Experimental Problems 125
4.10.2 The Bubble Deflection Angle 127
=
4.10.3 The Physical Origin of the S +1 Bubble
Deflection 132
4.10.4 Experimental Work on the Translation of
S = + 1 Bubbles 134
4.10.5 Translation of Bubbles with Low S-numbers 139
4.10.6 Theoretical Problems 144
Contents vii
4.11 Bubble Dynamics in Ion-implanted and Multilayer
Garnet Films 146
4.12 Automation 151
4.13 Bubble Translation under High Drive Fields 156
5. Ferromagnetodynamics of Conducting Media 165
5.1 Introduction 165
5.2 Simple Domain Wall Motion in a Thin Sheet 165
5.3 The Equation of Motion for Conducting Media 170
5.4 The Low Drive Mobility in Thin Permalloy Films 173
5.5 Domain Wall Motion in a Thin Sheet under Conditions
of High Drive 180
5.6 Domain Wall Inertia in Conducting Media 187
5.7 Magnetic Reversal in Thin Permalloy Films 189
5.8 Wall Motion in Conducting Bubble Domain Films 199
5.9 The Interaction Between Domain Walls and Electric
Currents 200
5.10 Conclusions 205
References and Author Index 207
Subject Index 229
Preface
This book was started during a most interesting visit to the Central Research
Institute for Physics, Hungarian Academy of Sciences, Budapest, early in 1977.
There, the author was introduced to the powerful experimental technique of high
speed microphotography, which has played such an important part in the de
velopment of magnetic bubble domain dynamics, by Dr G. J. Zimmer and his
colleagues, Dr L. Gal and Dr G. Kadar. The fmancial support of the Institute and
Imperial College during this visit is gratefully acknowledged.
In completing this book, the author has drawn on discussions and corre
spondence with many people and this should be reflected in the bibliography
which, it is hoped, is as complete as possible. Particular thanks are due to Professor
E. P. Wohlfarth, who has always been a source of good advice and encourage
ment, and to Dr K. D. Leaver, who was very helpful on the ripple problem.
For line drawings which have a citation in the caption, permission to reproduce
or adapt has kindly been given by the authors cited and by the copyright holders:
The American Institute of Physics, The Bell System Technical Journal, The
Institute of Electronic and Electrical Engineers, The Institute of Physics, North
Holland Publishing Co., Amsterdam, and Springer-Verlag, Heidelberg.
Finally, sincere thanks to Mrs Joan Jeffery for her skilful preparation of the
typescript.
T.H.O'DELL
1 The History and Experimental Techniques of
Ferromagnetodynamics
1.1 Introduction
Ferromagnetodynamics is the study of the way in which the magnetisation of a
ferromagnet can be changed in both space and time. Experimentally, the subject
really began just after 1930, when the idea of ferromagnetic domains was very
new and very little was known about the way in which the magnetisation could
change with time. Mter the Second World War, our knowledge of magnetism
had advanced very considerably and experimental work became far more exact
when single crystals of magnetic materials, both metals and insulators, became
available. It was then possible to make very defmite assumptions about the
spatial distribution of the magnetisation and concentrate on a measurement of
its time dependence under the action of a time dependent applied field.
Around 1950, it became possible to discuss the experimental work from the
point of view of existing theory. At the same time, the closely related fields of
magnetic resonance and spin waves were undergoing rapid development. Magnetic
resonance and spin waves involve changes in the magnetisation which are rela
tively small compared to the magnetisation itself and the time scales involved are
usually shorter than 10-9 s. Ferromagnetodynamics, on the other hand, is
concerned with very large changes in the magnetisation, a complete reversal for
example, occurring over distances which may be well under 10-6 m but the time
scales involved are usually longer than 10-9 s.
In this chapter we shall review the early experimental work briefly and then
outline the development of the subject from the experimentalists' point of view.
This will help to fix the order of magnitude of the scales we are involved with,
in both space and time, and the kind of experimental facts which need expla
nation. It will be seen that the subject of ferromagnetodynamics has always been
under pressure from technology. The application of magnetic materials in elec
tronics, for microwave devices, for computer memories and, for a very long
time, in the realisation of high frequency inductors, has always kept magnetism
an active and developing field. In heavy electrical engineering we find the same
importance attached to magnetic materials and this has had a great influence on
the development of new alloys.
In the following chapters, we shall try to describe and develop the theory of
ferromagnetodynamics and apply it to the experimental work. The theory itself
has only recently become advanced enough for us to understand some of the
most simple experimental results and the reason for this advance is certainly the
