# General time-reversal equivariant neural network potential for magnetic materials

arXiv: https://arxiv.org/abs/2211.11403 · HTML: https://mlsanity.com/paper/2211.11403/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 39 references that are in the map.
- First posted on arXiv 21 Nov 2022.

## Builds on (most cited first, 4 of 4)

- [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)
- [Learning Local Equivariant Representations for Large-Scale Atomistic Dynamics](https://mlsanity.com/paper/2204.05249/) (2022)
- [Transferable E(3) equivariant parameterization for Hamiltonian of molecules and solids](https://mlsanity.com/paper/2210.16190/) (2022)

## Built on by (most cited first, 2 of 2)

- [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)

This study introduces time-reversal E(3)-equivariant neural network and SpinGNN++ framework for constructing a comprehensive interatomic potential for magnetic systems, encompassing spin-orbit coupling and noncollinear magnetic moments. SpinGNN++ integrates multitask spin equivariant neural network with explicit spin-lattice terms, including Heisenberg, Dzyaloshinskii-Moriya, Kitaev, single-ion anisotropy, and biquadratic interactions, and employs time-reversal equivariant neural network to learn high-order spin-lattice interactions using time-reversal E(3)-equivariant convolutions. To validate SpinGNN++, a complex magnetic model dataset is introduced as a benchmark and employed to demonstrate its capabilities. SpinGNN++ provides accurate descriptions of the complex spin-lattice coupling in monolayer CrI3 and CrTe2, achieving sub-meV errors. Importantly, it facilitates large-scale parallel spin-lattice dynamics, thereby enabling the exploration of associated properties, including the magnetic ground state and phase transition. Remarkably, SpinGNN++ identifies a new ferrimagnetic state as the ground magnetic state for monolayer CrTe2, thereby enriching its phase diagram and providing deeper insights into the distinct magnetic signals observed in various experiments.