Graph Neural Network Force-Field Model for Itinerant Spin Dynamics

In itinerant magnets, the coupling between conduction electrons and localized moments gives rise to a landscape of complex spin textures, from skyrmions to chiral magnetic orders, that underpin many of the most promising spintronic phenomena. These emergent structures stem from long-range, frustrated interactions mediated by itinerant electrons. Yet, capturing their real-time dynamics poses a major computational challenge, as each step of the simulation requires resolving the electronic structure self-consistently. Here we present a scalable machine-learning (ML) force-field framework based on graph neural networks (GNNs) to accurately and efficiently predict the electron-induced magnetic torques acting on local spins. The model employs a message-passing architecture that aggregates spin information in a rotationally covariant manner, while the inherent graph permutation symmetry guarantees preservation of the lattice point-group symmetry. We demonstrate the performance of this ML framework on the prototypical s–d exchange model, a cornerstone of spintronics theory. Landau–Lifshitz–Gilbert simulations driven by the GNN-predicted effective fields faithfully reproduce representative noncollinear spin textures, establishing the framework as a powerful tool for large-scale dynamical simulations of itinerant magnets.