``It is difficult to make predictions, especially about the future''

Yogi Berra, baseball coach

In this chapter we present numerical methods for magnetic material modeling. Some of these methods can be considered in our days as standard for micromagnetic modeling. Special attention is paid to the methods which were developed by the author of the thesis (Sections 2.2.4, 2.3.6 and 2.3.7). Several of them were taken from the modeling in other branches of physics and firstly applied to magnetic properties, as for example, the A.Voter method for dynamics acceleration. Other methods, as for example, the Lagrangian multiplier technique was previously applied in magnetism to small nanoparticles only. The development of methods has been done in collaboration with Seagate Technology with the aim to find ways to predict correctly long-time thermal stability.

- 2.1 Multiscale character of magnetism
- 2.2 Linking different spatial scales
- 2.2.1 Ab-initio calculation of magnetic properties.
- 2.2.2 Atomistic models in magnetism
- 2.2.3 Micromagnetics: classical approach to model magnetization distribution
- 2.2.4 Passing atomistic information to micromagnetics: a multiscale model

- 2.3 Linking different timescales
- 2.3.1 The magnetization dynamics and the Landau-Lifshitz-Gilbert equation
- 2.3.2 Non-thermal adiabatic approximation
- 2.3.3 Short-time thermal description: stochastic LLG equations
- 2.3.4 Long-time behavior: Arrhenius-Néel law
- 2.3.5 Monte Carlo methods
- 2.3.6 Energy barriers calculations
- 2.3.7 Acceleration methods: Victora and Voter methods
- 2.3.8 Victora method
- 2.3.9 Voter method

2008-04-04