Machine-learning modeling of magnetization dynamics in quasi-equilibrium and driven metallic spin systems

TL;DR

This paper reviews machine-learning force-field methods for large-scale Landau-Lifshitz-Gilbert simulations of metallic spin systems, introducing symmetry-aware descriptors and extending models to nonequilibrium conditions.

Contribution

It generalizes the Behler-Parrinello ML architecture for spin systems, enabling scalable, transferable models that capture complex magnetic behaviors and nonequilibrium spin dynamics.

Findings

Successfully reproduces non-collinear magnetic orders in simulations.

Captures complex spin textures in mixed-phase states.

Predicts voltage-driven domain-wall motion accurately.

Abstract

We review recent advances in machine-learning (ML) force-field methods for large-scale Landau-Lifshitz-Gilbert (LLG) simulations of metallic spin systems. We generalize the Behler-Parrinello (BP) ML architecture -- originally developed for quantum molecular dynamics -- to construct scalable and transferable ML models capable of capturing the intricate dependence of electron-mediated exchange fields on the local magnetic environment characteristic of itinerant magnets. A central ingredient of this framework is the implementation of symmetry-aware magnetic descriptors based on group-theoretical bispectrum formalisms. Leveraging these ML force fields, LLG simulations faithfully reproduce hallmark non-collinear magnetic orders -- such as the $120^\circ$ and tetrahedral states -- on the triangular lattice, and successfully capture the complex spin textures emerging in the mixed-phase states of a square-lattice double-exchange model under thermal quench. We further discuss a generalized potential theory that extends the BP formalism to incorporate both conservative and nonconservative electronic torques, thereby enabling ML models to learn nonequilibrium exchange fields from computationally demanding microscopic approaches such as nonequilibrium Green's-function techniques. This extension yields quantitatively accurate predictions of voltage-driven domain-wall motion and establishes a foundation for quantum-accurate, multiscale modeling of nonequilibrium spin dynamics and spintronic functionalities.