Micromagnetic simulations of permanent magnetic materials reveal the details of the magnetization distribution and dynamic magnetization reversal processes. The knowledge of the dynamic behaviour is of great importance for the design of future magnetic recording media. When the desired magnetization switching frequencies reach an order of magnitude, which is comparable to the intrinsic relaxation time of the media, the switching dynamics have to be investigated in more detail.
Especially effects of thermal activation have to be included in the simulations, which is achieved by adding a random thermal field to the effective magnetic field. As a result, the Landau-Lifshitz equation, which is the equation of motion for the magnetization, is converted into a stochastic differential equation of Langevin type with multiplicative noise. The solution of this stochastic differential equation has to be found by applying the rules of stochastic calculus. The correct interpretation in the context of our physical system is the Stratonovich interpretation of the stochastic Landau-Lifshitz equation, since it leads to the correct thermal equilibrium properties.
The proper generalization of Taylor expansions to stochastic calculus gives suitable time integration schemes. These are tested with a micromagnetic simulation program using the finite difference method. For a single rigid magnetic moment the thermal equilibrium properties are investigated. It is found, that the Heun scheme is a good compromise between numerical stability and computational complexity.
The results of simulations of fine cubic particles whose magnetization reverses coherently show a switching behaviour in agreement with the Arrhenius-Néel law. The implementation of the time integration scheme in a finite element package is verified by comparing its results with those of the finite difference package.
Small spherical magnetic particles exhibit complex magnetization reversal mechanisms for different material parameters and external fields. Depending on the strength of the external field three different magnetization reversal regimes have been identified. For particles with small magnetocrystalline anisotropy coherent reversal modes are found at fields, which are smaller than the anisotropy field. High anisotropy leads to the nucleation of a small volume of reversed magnetization, which expands through the whole particle. For external fields which are comparable to the anisotropy field single droplet nucleation occurs and for higher fields multi-droplet nucleation is the driving reversal process.
The interaction of fine magnetic particles is caused by the magnetic stray field. Depending on distance and alignment the metastable lifetime of a pair of particles changes. Particles aligned along their easy axes stabilize each other, whereas two particles aligned perpendicular to their easy axes exhibit a reduced metastable lifetime.