Nonlinear magnetization dynamics in nanosystems / Giorgio Bertotti, Isaak D. Mayergoyz, Claudio Serpico.

Format:

Book

Author/Creator:

Bertotti, Giorgio.

Contributor:

Mayergoyz, I. D.

Serpico, Claudio.

Series:

Elsevier series in electromagnetism

Language:

English

Subjects (All):

Magnetization.

Nanoelectromechanical systems.

Nonlinear systems.

Physical Description:

ix, 466 pages : illustrations ; 24 cm.

Place of Publication:

Amsterdam ; Boston : Elsevier, 2009.

Summary:

This book deals with the analytical study of nonlinear magnetization dynamics in nanomagnetic devices and structures. This dynamics is governed by the Landau-Lifshitz equation and its generalizations to the case of spin-polarized current injection. The book is concerned with large magnetization motions when the nonlinear nature of the Landau-Lifshitz equation is strongly pronounced. For this reason, the book is distinctly unique as far as its emphasis, style of exposition, scope and conceptual depth are concerned. The topics discussed in the book are of interest to the broad audience of electrical engineers, material scientists, physicists, applied mathematicians and numerical analysts involved in the development of novel magnetic storage technology and novel nanomagnetic devices.

Contents:

2 Basic Equations for Magnetizaiton Dynamics 21

2.1 Landau-Lifshitz equation 21

2.2 Landau-Lifshitz-Gilbert equation 27

2.3 Other equations for the description of magnetization dynamics 29

2.4 Landau-Lifshitz-Gilbert equation in normalized form 31

3 Spatially Uniform Magnetization Dynamics 35

3.1 Spatially Uniform Solutions of LLG-Maxwell Equations 35

3.2 Structural Aspects of Spatially Uniform Magnetization Dynamics 41

3.3 Generalized Magnetization Dynamics 44

3.4 Analysis of Equilibrium Points of Magnetization Dynamics 51

4 Precessional Magnetization Dynamics 57

4.1 Geometric Aspects of Precessional Dynamics 57

4.2 Analytical Study of Precessional Dynamics 63

4.3 Precessional Dynamics under Transverse Magnetic Field 71

4.4 Precessional Dynamics under Longitudinal Magnetic Field 78

4.5 Hamiltonian Structure of Precessional Dynamics 85

5 Dissipative Magnetization Dynamics 91

5.1 Damping Switching in Uniaxial Media 91

5.2 Two-Time-Scale Formulation of LLG Dynamics and Averaging Technique 100

5.3 Magnetization Relaxation under Zero Applied Magnetic Field 105

5.4 Magnetization Relaxation under Applied Magnetic Fields 108

5.5 Self-Oscillations and Poincare-Melnikov Theory 115

6 Magnetization Switching 127

6.1 Physical Mechanisms of Precessional Switching 127

6.2 Critical Fields for Precessional Switching 131

6.3 Field-Pulse Duration for Precessional Switching 138

6.4 Switching under Nonrectangular Field Pulses (Inverse-Problem Approach) 144

7 Magnetization Dynamics under Time-Harmonic Excitation 153

7.1 LLG Dynamics in the Presence of Rotational Invariance 153

7.2 Periodic Magnetization Modes 157

7.3 Quasi-Periodic Magnetization Modes 167

7.4 Bifurcation Diagrams 171

7.5 Nonlinear Ferromagnetic Resonance, Foldover, and Switching Phenomena 179

7.6 Magnetization Dynamics under Deviations from Rotational Symmetry 186

8 Spin-Waves and Parametric Instabilities 193

8.1 Linearized LLG Equation 193

8.2 Spin-Wave Perturbations 202

8.3 Stability Analysis 210

8.4 Spin-Wave Instabilities and Instability Diagrams 217

8.5 Spin-Wave Perturbations for Ultra-Thin Films 226

9 Spin-Transfer-Driven Magnetization Dynamics 233

9.1 Spin-Transfer Modification of the LLG Equation 233

9.2 Stationary States 239

9.3 Self-Oscillations 242

9.4 Phase Portraits and Bifurcations 246

9.5 Stability Diagrams 254

9.6 Systems with Uniaxial Symmetry 261

10 Stochastic Magnetization Dynamics 271

10.1 Stochastic Landau-Lifshitz and Landau-Lifshitz-Gilbert Equations 271

10.2 Fokker-Planck Equation for Stochastic Magnetization Dynamics 283

10.3 Analysis of Magnetization Dynamics by using Stochastic Processes on Graphs 300

10.4 Stationary Distributions and Thermal Transitions 313

10.5 Stochastic Magnetization Dynamics in Uniaxial Systems 327

10.6 Autocorrelation Function and Power Spectral Density 334

10.7 Stochastic Magnetization Dynamics in Nonuniformly Magnetized Ferromagnets 345

11 Numerical Techniques for Magnetization Dynamics Analysis 359

11.1 Mid-Point Finite-Difference Schemes 359

11.2 Mid-Point Finite-Difference Schemes for Stochastic Magnetization Dynamics 367

11.3 Numerical Techniques for Nonuniformly Magnetized Particles 373

11.4 Micromagnetic Simulations of Magnetization Reversal and Spin-Wave Excitation 385

11.5 Micromagnetic Simulations of Chaotic Dynamics 396.

Notes:

Includes bibliographical references (pages 401-445) and index.

ISBN:

0080443168

9780080443164

OCLC:

229019265