Fokker--Planck framework for stochastic octupole moment dynamics in chiral antiferromagnet Mn3Sn

TL;DR

This paper introduces a reduced stochastic Fokker-Planck framework for modeling thermally assisted octupole moment dynamics in Mn3Sn, validated against full models and Monte Carlo simulations, enabling efficient ultra-low error probability analysis.

Contribution

The authors develop a simplified Fokker-Planck approach combined with CUDA acceleration to accurately and efficiently simulate octupole dynamics in Mn3Sn, surpassing traditional Monte Carlo methods.

Findings

The reduced model accurately captures switching behavior.

The CUDA solver efficiently computes ultra-low error probabilities.

Dynamics are highly sensitive to out-of-plane grid resolution.

Abstract

We develop a reduced stochastic framework for thermally assisted octupole moment dynamics in Mn3Sn by combining the reduced Landau--Lifshitz--Gilbert (LLG) equation with the Fokker--Planck formalism. The reduced model is benchmarked against the complete three-sublattice octupole dynamics and is shown to capture the essential switching behavior with good accuracy. We then derive the corresponding Fokker--Planck equation, which is implemented and solved via a CUDA-accelerated solver. The analysis shows that the octupole dynamics are highly sensitive to the out-of-plane grid resolution because ultrafast rotation of the octupole is controlled by its very small deviations from the basal plane. The solver is validated against Monte Carlo simulations through equilibrium distributions, relaxation trajectories, and switching times. Finally, we apply the method to thermally assisted field-driven switching and demonstrate efficient access to ultra-low error probabilities beyond the practical reach of direct Monte Carlo simulations.