Machine Learning Force-Field Approach for Itinerant Electron Magnets

TL;DR

This paper develops a machine learning force-field framework for simulating the dynamics of itinerant electron magnets, accurately reproducing complex spin structures and revealing new magnetic phenomena.

Contribution

It introduces a symmetry-invariant ML approach for LLG simulations, enabling efficient and accurate modeling of complex spin configurations in itinerant magnets.

Findings

Successfully reproduces non-collinear spin structures like skyrmions and tetrahedral orders.

Enables large-scale thermal quench simulations revealing glassy and stripe states.

Demonstrates the utility of ML force-fields in complex magnetic dynamical modeling.

Abstract

We review the recent development of machine-learning (ML) force-field frameworks for Landau-Lifshitz-Gilbert (LLG) dynamics simulations of itinerant electron magnets, focusing on the general theory and implementations of symmetry-invariant representations of spin configurations. The crucial properties that such magnetic descriptors must satisfy are differentiability with respect to spin rotations and invariance to both lattice point-group symmetry and internal spin rotation symmetry. We propose an efficient implementation based on the concept of reference irreducible representations, modified from the group-theoretical power-spectrum and bispectrum methods. The ML framework is demonstrated using the s-d models, which are widely applied in spintronics research. We show that LLG simulations based on local fields predicted by the trained ML models successfully reproduce representative non-collinear spin structures, including 120$^\circ$, tetrahedral, and skyrmion crystal orders of the triangular-lattice s-d models. Large-scale thermal quench simulations enabled by ML models further reveal intriguing freezing dynamics and glassy stripe states consisting of skyrmions and bi-merons. Our work highlights the utility of ML force-field approach to dynamical modeling of complex spin orders in itinerant electron magnets.