Machine learning nonequilibrium electron forces for adiabatic spin dynamics

TL;DR

This paper introduces a machine learning approach to accurately model nonequilibrium spin torques in magnetic systems, enabling efficient simulations of voltage-driven domain-wall dynamics in spintronics.

Contribution

It develops a deep learning neural network to predict nonequilibrium forces in spin systems, integrating potential theory with machine learning for adiabatic spin dynamics.

Findings

Neural network accurately learns forces from nonequilibrium Green's function data.

Simulations with the model reproduce voltage-driven domain-wall propagation.

The approach enables multi-scale modeling of nonequilibrium magnetic phenomena.

Abstract

We present a generalized potential theory of nonequilibrium torques for the Landau-Lifshitz equation. The general formulation of exchange forces in terms of two potential energies allows for the implementation of accurate machine learning models for adiabatic spin dynamics of out-of-equilibrium itinerant magnetic systems. To demonstrate our approach, we develop a deep-learning neural network that successfully learns the forces in a driven s-d model computed from the nonequilibrium Green's function method. We show that the Landau-Lifshitz dynamics simulations with forces predicted from the neural-net model accurately reproduce the voltage-driven domain-wall propagation. Our work opens a new avenue for multi-scale modeling of nonequilibrium dynamical phenomena in itinerant magnets and spintronics based on machine-learning models.