As data transfer rates increase within the magnetic recording industry, improvements in device performance and reliability crucially depend on the thorough understanding of nonlinear magnetization dynamics at a sub-nanoscale level.

This book offers a modern, stimulating approach to the subject of nonlinear magnetization dynamics by discussing important aspects such as the Landau-Lifshitz-Gilbert (LLG) equation, analytical solutions, and the connection between the general topological and structural aspects of dynamics.

An advanced reference for the study and understanding of nonlinear magnetization dynamics, it addresses situations such as the understanding of spin dynamics in short time scales and device performance and reliability in magnetic recording. Topics covered include nonlinear magnetization dynamics and the Landau-Lifshitz-Gilbert equation, nonlinear dynamical systems, spin waves, ferromagnetic resonance and pulsed magnetization switching.

The book explains how to derive exact analytical solutions for the complete nonlinear problem and emphasises the connection between the general topological and structural aspects of nonlinear magnetization dynamics and the discretization schemes better suited to its numerical study. It is an exceptional research tool providing an advanced understanding of the study of magnetization dynamics in situations of fundamental and technological interest.


Graduate students, applied engineers and researchers in electromagnetism, magnetic materials, magnetic recording and microwave materials

Table of Contents

1. Introduction 2. Basic equations for magnetization dynamics 2.1 Landau-Lifshitz equation 2.2 Landau-Lifshitz-Gilbert equation 2.3 Other equations for the description of magnetization dynamics 2.4 Landau-Lifshitz-Gilbert equation in normalized form 3. Spatially uniform magnetization dynamics 3.1 Spatially uniform solutions of LLG-Maxwell equations 3.2 Structural aspects of spatially uniform magnetization dynamics 3.3 Generalized magnetization dynamics 3.4 Analysis of equilibrium points of magnetization dynamics 4. Precessional magnetization dynamics 4.1 Geometric aspects of precessional dynamics 4.2 Analytical study of precessional dynamics 4.3 Precessional dynamics under transverse magnetic field 4.4 Precessional dynamics under longitudinal magnetic field 4.5 Hamiltonian structure of precessional dynamics 5. Dissipative magnetization dynamics 5.1 Damping switching in uniaxial media 5.2 Two-time-scale formulation of LLG dynamics and averaging technique 5.3 Magnetization relaxation under zero applied magnetic field 5.4 Magnetization relaxation under applied magnetic fields 5.5 Self-oscillations and Poincaré-Melnikov theory 6. Magnetization switching 6.1 Physical mechanisms of precessional switching 6.2 Critical fields for precessional switching 6.3 Field-pulse duration for precessional switching 6.4 Switching under non-rectangular field pulses (inverse-problem approach) 7. Magnetization dynamics under time-harmonic excitation 7.1 LLG dynamics in the presence of rotational invariance


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© 2009
Elsevier Science
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About the authors

Isaak Mayergoyz

Prof. Mayergoyz received his Master and Ph.D. degrees in the former Soviet Union where he worked as a senior research scientist in the Institute of Cybernetics of Ukranian Academy of Sciences before his emigration to the United States. On his arrival to the United States in 1980, he became a full professor of Electrical and Computer Engineering Department of University of Maryland, College Park. He served as a consultant for many years for the Research and Development Center of General Electric Company and has been selected as a visiting research fellow of this center. He has published more than 300 scientific papers and patents as well as eight scientific books. He has been recognized by many awards at the University of Maryland and at the Magnetics Society of IEEE. He is a recognized authority in magnetics which is the area of this book.

Giorgio Bertotti

Giorgio Bertotti is a senior scientist at INRIM, Istituto Nazionale di Ricerca Metrologica (previously known as IEN Galileo Ferraris), in Torino, Italy, where he has been a researcher since 1979. His research interests are in the field of magnetism and magnetic materials, hysteresis modeling, thermodynamics, noise phenomena. He is author of more than 200 scientific articles and of the book "Hysteresis in Magnetism".