Spin-dependent graph neural network potential for magnetic materials

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 multibody 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 $\mathrm{BiFe}{\mathrm{O}}_{3}$ and performs large-scale spin-lattice dynamics simulations, predicting its antiferromagnetic ground state, magnetic phase transition, and domain-wall energy landscape with high accuracy. Finally, we perform spin-lattice simulations over one million atoms across GPUs in parallel. 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 in first-principle accuracy on such systems.