# Graph Neural Network Force Fields for Spin Dynamics in Metallic Magnets

arXiv: https://arxiv.org/abs/2607.28537 · HTML: https://mlsanity.com/paper/2607.28537/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 79 references that are in the map.
- First posted on arXiv 30 Jul 2026.

## Builds on (most cited first, 29 of 29)

- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data](https://mlsanity.com/paper/1807.02547/) (2018)
- [Invariant and Equivariant Graph Networks](https://mlsanity.com/paper/1812.09902/) (2018)
- [Learning Local Equivariant Representations for Large-Scale Atomistic Dynamics](https://mlsanity.com/paper/2204.05249/) (2022)
- [A General Theory of Equivariant CNNs on Homogeneous Spaces](https://mlsanity.com/paper/1811.02017/) (2018)
- [Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanics](https://mlsanity.com/paper/1707.09571/) (2017)
- [Graph neural networks for materials science and chemistry](https://mlsanity.com/paper/2208.09481/) (2022)
- [The Design Space of E(3)-Equivariant Atom-Centered Interatomic Potentials](https://mlsanity.com/paper/2205.06643/) (2022)
- [DScribe: Library of Descriptors for Machine Learning in Materials Science](https://mlsanity.com/paper/1904.08875/) (2019)
- [Hierarchical modeling of molecular energies using a deep neural network](https://mlsanity.com/paper/1710.00017/) (2017)
- [Equivariant Networks for Crystal Structures](https://mlsanity.com/paper/2211.15420/) (2022)
- [Anomalous phase separation dynamics in a correlated electron system: machine-learning enabled large-scale kinetic Monte Carlo simulations](https://mlsanity.com/paper/2105.13304/) (2021)
- [Machine learning electron correlation in a disordered medium](https://mlsanity.com/paper/1810.02323/) (2018)
- [Machine learning nonequilibrium electron forces for adiabatic spin dynamics](https://mlsanity.com/paper/2112.12124/) (2021)
- [Descriptors for Machine Learning Model of Generalized Force Field in Condensed Matter Systems](https://mlsanity.com/paper/2201.00798/) (2022)
- [Machine learning for phase ordering dynamics of charge density waves](https://mlsanity.com/paper/2303.03493/) (2023)
- [Machine learning predictions for local electronic properties of disordered correlated electron systems](https://mlsanity.com/paper/2204.05967/) (2022)
- [Coarsening of chiral domains in itinerant electron magnets: A machine learning force field approach](https://mlsanity.com/paper/2403.11705/) (2024)
- [Spin-Dependent Graph Neural Network Potential for Magnetic Materials](https://mlsanity.com/paper/2203.02853/) (2022)
- [Kinetics of orbital ordering in cooperative Jahn-Teller models: Machine-learning enabled large-scale simulations](https://mlsanity.com/paper/2405.14776/) (2024)
- [Machine learning force-field model for kinetic Monte Carlo simulations of itinerant Ising magnets](https://mlsanity.com/paper/2411.19780/) (2024)
- [Machine-learning force-field models for dynamical simulations of metallic magnets](https://mlsanity.com/paper/2602.18213/) (2026)
- [General time-reversal equivariant neural network potential for magnetic materials](https://mlsanity.com/paper/2211.11403/) (2022)
- [Equivariant Neural Networks for Force-Field Models of Lattice Systems](https://mlsanity.com/paper/2601.04104/) (2026)

## Abstract (arXiv)

Metallic magnets exhibit complex spin dynamics governed by electronically generated interactions. Predictive simulations of such dynamics typically require repeated solutions of an underlying electronic problem throughout the time evolution, creating a major computational bottleneck. Here we introduce a graph neural network (GNN) magnetic force-field framework that learns the effective magnetic energy functional governing itinerant spin dynamics directly from electronic calculations. Conceptually analogous to machine-learned interatomic potentials, the proposed framework enables efficient evaluation of spin torques while capturing the nonlinear and spatially extended interactions generated by itinerant electrons. We benchmark the method on representative metallic magnetic systems exhibiting collinear, noncollinear, and noncoplanar magnetic order. The learned force fields accurately reproduce electronically generated spin torques and yield nonequilibrium spin dynamics in excellent agreement with direct electronic simulations. Our results establish graph neural networks as a powerful framework for machine-learned magnetic force fields, providing a pathway toward predictive large-scale simulations of nonequilibrium magnetism across multiple length and time scales.