Nonlinear Magnetization Dynamics in Nanosystems


  • Isaak Mayergoyz, University of Maryland, ECE Department, College Park, USA
  • Giorgio Bertotti, INRIM - Istituto Nazionale di Ricerca Metrologica, Italy
  • Claudio Serpico, Electrical Engineering, University of Naples 'Federico II', Italy

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


Book information

  • Published: December 2008
  • Imprint: ELSEVIER
  • ISBN: 978-0-08-044316-4

Table of Contents

1. Introduction2. Basic equations for magnetization dynamics2.1 Landau-Lifshitz equation 2.2 Landau-Lifshitz-Gilbert equation2.3 Other equations for the description of magnetization dynamics2.4 Landau-Lifshitz-Gilbert equation in normalized form 3. Spatially uniform magnetization dynamics3.1 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 dynamics4. Precessional magnetization dynamics4.1 Geometric aspects of precessional dynamics4.2 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 switching6.4 Switching under non-rectangular field pulses (inverse-problem approach) 7. Magnetization dynamics under time-harmonic excitation7.1 LLG dynamics in the presence of rotational invariance7.2 Periodic magnetization modes 7.3 Quasi-periodic magnetization modes 7.4 Bifurcation diagrams 7.5 Nonlinear ferromagnetic resonance, foldover, and switching phenomena 7.6 Magnetization dynamics under deviations from rotational symmetry 8. Spin-waves and parametric instabilities8.1 Linearized LLG equation 8.2 Spin-wave perturbations 8.3 Stability analysis 8.4 Spin-wave instabilities and instability diagrams8.5 Spin-wave perturbations for ultra-thin films 9. Spin-transfer-driven magnetization dynamics9.1 Spin-transfer modification of LLG equation 9.2 Stationary states 9.3 Self-oscillations 9.4 Phase portraits and bifurcations 9.5 Stability diagrams 9.6 Systems with uniaxial symmetry10. Stochastic magnetization dynamics 10.1 Stochastic Landau-Lifshitz and Landau-Lifshitz-Gilbert equations 10.2 Fokker-Planck equation for stochastic magnetization dynamics10.3 Analysis of magnetization dynamics by using stochastic processes on graphs 10.4 Stationary distributions and thermal transitions 10.5 Stochastic magnetization dynamics in uniaxial systems 10.6 Autocorrelation function and power spectral density 10.7 Stochastic magnetization dynamics in nonuniformly magnetized ferromagnets 11. Numerical techniques for magnetization dynamics analysis11.1 Mid-point finite-difference schemes 11.2 Mid-point finite-difference schemes for stochastic magnetization dynamics 11.3 Numerical techniques for nonuniformly magnetized particles 11.4 Micromagnetic simulations of magnetization reversal and spin-wave excitation11.5 Micromagnetic simulations of chaotic dynamics