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An efficient method for computing thermodynamic equilibrium states at themicromagnetic length scale is introduced, using the Markov chain Monte Carlomethod. Trial moves include not only rotations of vectors, but also a change intheir magnetization length. The method is parameterized using the longitudinalsusceptibility, reproduces the same Maxwell-Boltzmann distribution as thestochastic Landau-Lifshitz-Bloch equation, and is applicable both below andabove the Curie temperature. The algorithm is fully parallel, can be executedon graphical processing units, and efficiently includes the long range dipolarinteraction. This method is generally useful for computing finite-temperaturerelaxation states both for uniform and non-uniform temperature profiles, andcan be considered as complementary to zero-temperature micromagnetic energyminimization solvers, with comparable computation time. Compared to the dynamicapproach it is shown the micromagnetic Monte Carlo method is up to almost 20times faster. Moreover, unlike quasi-zero temperature approaches which do nottake into account the magnetization length distribution and stochasticity, themethod is better suited for structures with unbroken symmetry around theapplied field axis, granular films, and at higher temperatures and fields. Inparticular, applications to finite-temperature hysteresis loop modelling,chiral magnetic thin films, granular magnetic media, and artificial spin icesare discussed.

journal of applied physics

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