Graph Neural Network Potential for Magnetic Materials

Machine Learning (ML) interatomic potential has shown its great power in condensed matter physics. However, ML interatomic potential for a magnetic system including both structural degrees of freedom and magnetic moments has not been well developed yet. A spin-dependent ML interatomic potential approach based on the crystal graph neural network (GNN) has been developed for any magnetic system. It consists of the Heisenberg edge graph neural network (HEGNN) and spin-distance edge graph neural network (SEGNN). The network captures the Heisenberg coefficient variation between different structures and the fine spin-lattice coupling of high order and multi-body interaction with high accuracy. In the tests, this method perfectly fitted a high-order spin Hamiltonian and two complex spin-lattice Hamiltonian and captured the fine spin-lattice coupling in BiFeO3. In addition, a disturbed structure of BiFeO3 with strain was successfully optimized with the trained potential. Our work has expanded the powerful ML GNN potentials to magnetic systems, which paves a new way for large-scale dynamic simulations on spin-lattice coupled systems.