Micromagnetic simulation of thermally activated switching in fine particles

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. (C) 2001 Elsevier Science B.V. All rights reserved.