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Numerical integration of the stochastic Landau-Lifshitz-Gilbert equation in generic time-discretization schemes
Federico Romá1, Leticia F Cugliandolo2, Gustavo S Lozano3
1Departamento de Física, Universidad Nacional de San Luis & INFAP CONICET, Chacabuco 917, D5700BWS San Luis, Argentina.
Abstract:
We introduce a numerical method to integrate the stochastic Landau-Lifshitz-Gilbert equation in spherical coordinates for generic discretization schemes. This method conserves the magnetization modulus and ensures the approach to equilibrium under the expected conditions. We test the algorithm on a benchmark problem: the dynamics of a uniformly magnetized ellipsoid. We investigate the influence of various parameters, and in particular, we analyze the efficiency of the numerical integration, in terms of the number of steps needed to reach a chosen long time with a given accuracy.
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