Numerical integration of the stochastic Landau-Lifshitz-Gilbert equation in generic time-discretization schemes

F. ROMÁ; L. F. CUGLIANDOLO; G. S. LOZANO

PHYSICAL REVIEW E

AMER PHYSICAL SOC

Lugar: New York; Año: 2014 vol. E p. 23203 - 23210

1539-3755

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.