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

TL;DR

This paper introduces a parallel micromagnetic Monte Carlo method based on the Landau-Lifshitz-Bloch equation, capable of efficiently computing thermodynamic equilibrium states at finite temperatures, including near and above the Curie point.

Contribution

The paper presents a novel Monte Carlo algorithm that incorporates variable magnetization length, reproduces the Maxwell-Boltzmann distribution, and is optimized for large-scale, high-temperature micromagnetic simulations.

Findings

Method is up to 20 times faster than dynamic approaches.

Reproduces Maxwell-Boltzmann distribution across temperature ranges.

Applicable to various magnetic structures and temperature profiles.

Abstract

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