W. Scholz, T. Schrefl and J. Fidler

J.M.M.M. 233 (2001) 296-304.

Effects of thermal activation are included in micromagnetic simulations by adding a random thermal field to the effective magnetic field. As a result, the Landau-Lifshitz equation is converted into a stochastic differential equation of Langevin type with multiplicative noise. The Stratonovich interpretation of the stochastic Landau-Lifshitz equation leads to the correct thermal equilibrium properties. The proper generalization of Taylor expansions to stochastic calculus gives suitable time integration schemes. 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. Small cubic and spherical ferromagnetic particles are studied.

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Feb. 13, 2001