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1. Introduction
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Thermally Activated Switching
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Kurzfassung
Contents
Abstract
Kurzfassung
Contents
1. Introduction
2. Micromagnetics
2.1 Thermodynamic relations
2.1.1 Exchange energy
2.1.2 Magnetocrystalline anisotropy energy
2.1.3 Magnetostatic energy
2.1.4 Zeeman energy
2.2 Energy minimization
2.3 The dynamic equation
3. The finite difference method
3.1 Discretization of the exchange energy
3.2 Discretization of the demagnetizing field
3.3 Evaluation of the method
4. The finite element method
4.1 Finite element micromagnetics
4.2 The open boundary problem
Dirichlet boundary conditions
Neumann boundary conditions
Robin boundary conditions
Asymptotic boundary conditions
Hybrid FE/Boundary element method
5. Thermal activation
5.1 Stochastic processes
5.2 The stochastic Landau-Lifshitz equation
6. Stochastic calculus
6.1 Gaussian white noise
6.2 Stochastic differential equations
6.3 Interpretation of stochastic integrals
6.4 Taylor expansions
6.4.1 Itô-Taylor expansion
6.4.2 Stratonovich-Taylor expansion
6.5 The Fokker-Planck equation
7. Numerical time integration methods
7.1 Deterministic integration schemes
7.1.1 Fixpoint iteration
7.2 Stochastic integration schemes
7.2.1 Euler scheme
7.2.2 Milshtein scheme
7.2.3 Heun scheme
7.2.4 Higher order integration schemes
7.3 Pseudo-random number generators
7.3.1 Uniform distribution
7.3.2 Gaussian distribution
8. Implementation
8.1 Finite difference model
External field
Anisotropy field
Exchange field
Dipole field
Thermal field
8.1.1
mag standard problem #3
8.2 Finite element model
8.3 Numerical integration
8.3.1 Milshtein scheme
8.3.2 Heun scheme
9. Rigid magnetic moment
9.1 Deterministic behaviour -
The Stoner-Wohlfarth model
9.2 Stochastic perturbation
9.3 Time step dependence
10. Simulation of fine particles
10.1 Cubic particles
10.2 Spherical particles
10.3 Interacting particles
10.4 Experimental results
Conclusions and outlook
Appendix
The finite difference program
Dimensionless equations
Anisotropy field
Exchange field
Dipole field
Thermal field
Program structure
main program
init_par.F
calc_bloc.F
timestep.F
The finite element program
Program structure
vecmesh
vecuws
Stochastic time integration
Bibliography
List of Figures
List of Tables
Acknowledgment
Curriculum vitæ
About this document ...
Werner Scholz 2000-05-16