# Spin-Dependent Graph Neural Network Potential for Magnetic Materials

arXiv: https://arxiv.org/abs/2203.02853 · HTML: https://mlsanity.com/paper/2203.02853/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 87 references that are in the map.
- First posted on arXiv 6 Mar 2022.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [GemNet: Universal Directional Graph Neural Networks for Molecules](https://mlsanity.com/paper/2106.08903/) (2021)
- [Crystal Diffusion Variational Autoencoder for Periodic Material Generation](https://mlsanity.com/paper/2110.06197/) (2021)
- [Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Molecules](https://mlsanity.com/paper/2011.14115/) (2020)
- [Geometric and Physical Quantities Improve E(3) Equivariant Message Passing](https://mlsanity.com/paper/2110.02905/) (2021)
- [Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanics](https://mlsanity.com/paper/1707.09571/) (2017)
- [TorchMD-NET: Equivariant Transformers for Neural Network based Molecular Potentials](https://mlsanity.com/paper/2202.02541/) (2022)
- [Complex Spin Hamiltonian Represented by Artificial Neural Network](https://mlsanity.com/paper/2110.00724/) (2021)

## Built on by (most cited first, 9 of 9)

- [A practical guide to machine learning interatomic potentials -- Status and future](https://mlsanity.com/paper/2503.09814/) (2025)
- [AQCat25: Unlocking spin-aware, high-fidelity machine learning potentials for heterogeneous catalysis](https://mlsanity.com/paper/2510.22938/) (2025)
- [Accelerating the Training and Improving the Reliability of Machine-Learned Interatomic Potentials for Strongly Anharmonic Materials through Active Learning](https://mlsanity.com/paper/2409.11808/) (2024)
- [Do Graph Neural Networks Work for High Entropy Alloys?](https://mlsanity.com/paper/2408.16337/) (2024)
- [SpinMultiNet: Neural Network Potential Incorporating Spin Degrees of Freedom with Multi-Task Learning](https://mlsanity.com/paper/2409.03253/) (2024)
- [Renormalization-Inspired Effective Field Neural Networks for Scalable Modeling of Classical and Quantum Many-Body Systems](https://mlsanity.com/paper/2502.17665/) (2025)
- [Learning Magnetic Order Classification from Large-Scale Materials Databases](https://mlsanity.com/paper/2509.05909/) (2025)
- [Magnetic HIP-NN for spin dynamics in disordered itinerant magnets](https://mlsanity.com/paper/2606.10349/) (2026)
- [Graph Neural Network Force Fields for Spin Dynamics in Metallic Magnets](https://mlsanity.com/paper/2607.28537/) (2026)

## Abstract (arXiv)

The development of machine learning interatomic potentials has immensely contributed to the accuracy of simulations of molecules and crystals. However, creating interatomic potentials for magnetic systems that account for both magnetic moments and structural degrees of freedom remains a challenge. This work introduces SpinGNN, a spin-dependent interatomic potential approach that employs the graph neural network (GNN) to describe magnetic systems. SpinGNN consists of two types of edge GNNs: Heisenberg edge GNN (HEGNN) and spin-distance edge GNN (SEGNN). HEGNN is tailored to capture Heisenberg-type spin-lattice interactions, while SEGNN accurately models multi-body and high-order spin-lattice coupling. The effectiveness of SpinGNN is demonstrated by its exceptional precision in fitting a high-order spin Hamiltonian and two complex spin-lattice Hamiltonians with great precision. Furthermore, it successfully models the subtle spin-lattice coupling in BiFeO3 and performs large-scale spin-lattice dynamics simulations, predicting its antiferromagnetic ground state, magnetic phase transition, and domain wall energy landscape with high accuracy. Our study broadens the scope of graph neural network potentials to magnetic systems, serving as a foundation for carrying out large-scale spin-lattice dynamic simulations of such systems.