Graph Neural Network Force Fields for Spin Dynamics in Metallic Magnets

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.

Magnetic order is a fundamental property of materials, governing collective behavior and enabling a broad range of functionalities. Yet magnetic structure remains difficult to determine: experiments are costly and specialized, while first-principles methods often struggle with the noncollinear and incommensurate orders found in real materials. Here we introduce magnetic structure network (MSN), an E(3) equivariant graph neural network that predicts both collinear and non-collinear magnetic structures directly from atomic crystal structures, trained directly on experimentally determined structures from MAGNDATA. By proposing the primitive modulated structure representation (PMSR), we are able to encode commensurate and incommensurate structures in a unified way without symmetry assumptions. The model achieves strong performance across all modulation components and reconstructs experimental magnetic structures with high fidelity. Our approach provides a scalable framework for rapid magnetic structure prediction and opens a route to data-driven discovery of magnetic materials.

Computational discovery of magnetic materials remains challenging because magnetism arises from the competition between kinetic energy and Coulomb interaction that is often beyond the reach of standard electronic-structure methods. Here we tackle this challenge by directly solving the many-electron Schrödinger equation with neural-network variational Monte Carlo, which provides a highly expressive variational wavefunction for strongly correlated systems. Applying this technique to transition metal dichalcogenide moiré semicondutors, we predict itinerant ferromagnetism in WSe$_2$/WS$_2$ and an antiferromagnetic insulator in twisted $Γ$-valley homobilayer, using the same neural network without any physics input beyond the microscopic Hamiltonian. Crucially, both types of magnetic states are obtained from a single calculation within the $S_z=0$ sector, removing the need to compute and compare multiple $S_z$ sectors. This significantly reduces computational cost and paves the way for faster and more reliable magnetic material design.