# Magnetization Oscillations and Waves A.G. Gurevich, Ph.D., D.Sci. Chief Researcher and Professor Magnetic Laboratory Ioffe Physico-Technical Institute St. Petersburg, Russia G.A. Melkov, Ph.D., D.Sci. Professor Dean of Department, Radiophysical Shevchenko Kiev National University Kiev, Ukraine CRC Press Boca Raton New York London ## Library of Congress Cataloging-in-Publication Data Catalog record is available from the Library of Congress. This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage or retrieval system, without prior permission in writing from the publisher. CRC Press consent does not extend to copying for general distribution, for promotion, for creating new works, or for resale. Specific permission must be obtained in writing from CRC Press for such copying. Direct all inquiries to CRC Press 2000 Corporate Blvd., N.W., Boca Raton, Florida 33431. ## © 1996 by CRC Press No claim to original U.S. Government works International Standard Book Number 0-8493-9460-0 Printed in the United States of America 2 3 4 5 6 7 8 9 0 Printed on acid-free paper ## Contents Preface ix 1 Isotropic ferromagnet magnetized to saturation 1 1.1 Ferromagnetism 1 1.1.1 Elementary magnetic moments 2 1.1.2 Paramagnetism 4 1.1.3 Weiss theory 6 1.1.4 Exchange interaction 7 1.2 Equation of motion of magnetization 8 1.3 High-frequency magnetic susceptibility 10 1.3.1 Solution of the linearized equation of motion 11 1.3.2 Peculiarities of the susceptibility tensor 12 1.3.3 High-frequency permeability 14 1.4 Allowance for magnetic losses 17 1.4.1 Dissipative terms and dissipation parameters 17 1.4.2 Susceptibility tensor components 19 1.5 Uniform oscillations in a small ellipsoid 22 1.5.1 Internal and external magnetic fields 23 1.# Magnetization Oscillations and Waves A.G. Gurevich, Ph.D., D.Sci. Chief Researcher and Professor Magnetic Laboratory Ioffe Physico-Technical Institute St. Petersburg, Russia G.A. Melkov, Ph.D., D.Sci. Professor Dean of Department, Radiophysical Shevchenko Kiev National University Kiev, Ukraine CRC Press Boca Raton New York London ## Library of Congress Cataloging-in-Publication Data Catalog record is available from the Library of Congress. This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage or retrieval system, without prior permission in writing from the publisher. CRC Press consent does not extend to copying for general distribution, for promotion, for creating new works, or for resale. Specific permission must be obtained in writing from CRC Press for such copying. Direct all inquiries to CRC Press 2000 Corporate Blvd., N.W., Boca Raton, Florida 33431. ## © 1996 by CRC Press No claim to original U.S. Government works International Standard Book Number 0-8493-9460-0 Printed in the United States of America 2 3 4 5 6 7 8 9 0 Printed on acid-free paper ## Contents Preface ix 1 Isotropic ferromagnet magnetized to saturation 1 1.1 Ferromagnetism 1 1.1.1 Elementary magnetic moments 2 1.1.2 Paramagnetism 4 1.1.3 Weiss theory 6 1.1.4 Exchange interaction 7 1.2 Equation of motion of magnetization 8 1.3 High-frequency magnetic susceptibility 10 1.3.1 Solution of the linearized equation of motion 11 1.3.2 Peculiarities of the susceptibility tensor 12 1.3.3 High-frequency permeability 14 1.4 Allowance for magnetic losses 17 1.4.1 Dissipative terms and dissipation parameters 17 1.4.2 Susceptibility tensor components 19 1.5 Uniform oscillations in a small ellipsoid 22 1.5.1 Internal and external magnetic fields 23 1.