Micromagnetic Monte Carlo method with variable magnetization length based on the Landau–Lifshitz–Bloch equation for computation of large-scale thermodynamic equilibrium states

An efficient method for computing thermodynamic equilibrium states at the micromagnetic length scale is introduced, using Markov chain Monte Carlo method. Trial moves include not only rotations of vectors, but also a change in their magnetization length. The parameterized longitudinal susceptibility, reproduces same Maxwell-Boltzmann distribution as stochastic Landau-Lifshitz-Bloch equation, and applicable both below above Curie temperature. algorithm fully parallel, can be executed on graphical processing units, efficiently includes long range dipolar interaction. This generally useful finite-temperature relaxation uniform non-uniform temperature profiles, considered complementary to zero-temperature energy minimization solvers, with comparable computation time. Compared dynamic approach it shown up almost 20 times faster. Moreover, unlike quasi-zero approaches which do take into account stochasticity, better suited structures unbroken symmetry around applied field axis, granular films, higher temperatures fields. In particular, applications hysteresis loop modelling, chiral magnetic thin media, artificial spin ices are discussed.