Contents

• Introduction
• 1. The Micromagnetic Model and The Dynamic Equation
  • 1.1 Micromagnetic Free Energy
    • 1.1.1 Continuum Hypothesis
    • 1.1.2 Basic Thermodynamics for magnetized media. Thermodynamic potentials
    • 1.1.3 Exchange interaction and energy
    • 1.1.4 Anisotropy
    • 1.1.5 Magnetostatic interactions
    • 1.1.6 The External Field. Zeeman Energy
    • 1.1.7 Magnetoelastic interactions
    • 1.1.8 The Free Energy Functional
  • 1.2 Micromagnetic Equilibrium
    • 1.2.1 First-order Variation of the Free Energy
    • 1.2.2 Effective Field and Brown's Equations
  • 1.3 The Dynamic Equation
    • 1.3.1 Gyromagnetic precession
    • 1.3.2 The Landau-Lifshitz equation
    • 1.3.3 Landau-Lifshitz-Gilbert equation
    • 1.3.4 Normalized equations
    • 1.3.5 Properties of magnetization dynamics
  
  
• 2. Uniformly magnetized particles
  • 2.1 The uniform mode approximation
  • 2.2 The static model. Stoner-Wohlfarth theory
  • 2.3 Uniform mode magnetization dynamics
  • 2.4 Magnetization switching process
    • 2.4.1 Critical parameters for magnetization switching
    • 2.4.2 Damping switching
    • 2.4.3 Precessional switching
  • 2.5 LLG dynamics under circularly polarized field
    • 2.5.1 Equation of motion
    • 2.5.2 Quasiperiodic solutions of LLG dynamics under circularly polarized field
  • 2.6 Spin-transfer Effect and Current-induced Magnetization Switching
    • 2.6.1 Landau-Lifshitz-Gilbert equation with Slonczewski spin-transfer torque term
    • 2.6.2 Discussion about units and typical values of parameters
    • 2.6.3 Analytical investigation of self-oscillating behavior and current-induced switching
  
  
• 3. Non-uniform Magnetization Dynamics in thin-films reversal processes
  • 3.1 Magnetostatic field computation
    • 3.1.1 FFT Discrete convolution method
    • 3.1.2 Hybrid Finite elements-Boundary elements method
  • 3.2 Comparison between Damping and Precessional switching in magnetic thin-films
    • 3.2.1 Reversal speed in the switching process
    • 3.2.2 Spatial Magnetization uniformity
    • 3.2.3 Uniform mode approximation
    • 3.2.4 Numerical results
    • 3.2.5 Precessional switching: dependance on the anisotropy and switching time tolerance window
  • 3.3 Fast switching of Tilted Media
    • Introduction
    • 3.3.2 Uniform mode approximation
    • 3.3.3 Micromagnetic simulations of Fast switching process
  
  
• 4. Geometric integration of Landau-Lifshitz-Gilbert equation
  • 4.1 Introduction
  • 4.2 The mathematical model
    • 4.2.1 General properties of the effective field
    • 4.2.2 Constraints for magnetization dynamics and hamiltonian structure of conservative dynamics
  • 4.3 Spatially semi-discretized LLG equation
    • 4.3.1 Discretized free energy and effective field
    • 4.3.2 Semi-discretized LLG equation properties
  • 4.4 Mid-point LLG discrete dynamics
    • 4.4.1 Properties of mid-point rule induced dynamics
  • 4.5 Solution of the time-stepping equation
  • 4.6 Accuracy tests for LLG discrete dynamics
  • 4.7 Finite differences spatial discretization of LLG equation
  • 4.8 Numerical Simulations of -mag standard problem n. 4
    • 4.8.1 Definition of the problem
    • 4.8.2 Numerical results
    • 4.8.3 Discussion about computational cost
  
  
• Conclusions and Outlook
• A. Appendix A
  • A.1 Main Properties of Ferromagnetic Materials
  
  
• B. Appendix B
  • B.1 Elliptic Functions
  • B.2 Perturbative analysis of limit cycles in 2D dynamical systems
  
  
• C. Appendix C
  • C.1 Brief remarks on the mid-point rule numerical technique
  
  
• Bibliography
• About this document ...