Magnetic HIP-NN for spin dynamics in disordered itinerant magnets

2026-06-08

AI Summary

This work addresses the challenge of efficiently simulating electron-mediated spin dynamics in disordered itinerant magnets at scale by introducing the magnetic HIP-NN model. It uniquely integrates spin rotational symmetry into a hierarchical message-passing neural network to construct a symmetry-aware geometric-spin coupled representation, enabling accurate learning of the magnetic energy landscape and effective local fields. By leveraging rotationally invariant spin correlation features and a differentiable energy functional, the method achieves end-to-end modeling of joint spin-atomic potentials and supports efficient, scalable nonequilibrium dynamics simulations through integration with the Landau–Lifshitz–Gilbert equation. Experiments demonstrate that the model accurately reproduces local spin torques and faithfully captures the evolution of spatial spin correlations following thermal quenches, confirming its effectiveness and scalability in complex itinerant magnetic systems.

Abstract

We present a magnetic extension of the Hierarchically Interacting Particle Neural Network (HIP-NN) that enables large-scale simulations of electron-mediated spin dynamics in disordered itinerant magnets. The resulting magnetic HIP-NN (mHIP-NN) incorporates rotationally invariant spin correlations directly into hierarchical message-passing layers, enabling the network to learn emergent magnetic energy landscapes and effective local fields from coupled geometric-spin environments while preserving spin-rotation symmetry. As a benchmark application, we consider structurally disordered itinerant $s$-$d$ exchange models in which the effective magnetic forces arise dynamically from the instantaneous electronic structure and are computationally prohibitive to evaluate using conventional exact-diagonalization-based approaches. We show that mHIP-NN accurately reproduces the local torques governing Landau-Lifshitz-Gilbert dynamics and faithfully captures the nonequilibrium evolution of spatial spin correlations following thermal quenches. Our results establish symmetry-aware hierarchical message-passing networks as an efficient and scalable framework for large-scale simulations of frustrated itinerant spin systems and nonequilibrium magnetic dynamics. More broadly, because the learned energy functional remains fully differentiable with respect to both atomic coordinates and spin variables, the framework also provides a natural foundation for spin-dependent interatomic potentials and coupled atom-spin dynamics.

Problem

• spin dynamics
• disordered itinerant magnets
• magnetic simulation
• nonequilibrium dynamics
• effective magnetic forces

Innovation

• magnetic HIP-NN
• rotationally invariant spin correlations
• hierarchical message-passing
• itinerant magnets
• differentiable energy functional