Symplectic Spin-Lattice Dynamics with Machine-Learning Potentials

Abstract

Atomic-scale modeling of magnetic materials requires precise treatment of coupled spin-lattice degrees of freedom (DOFs). Traditional spin-lattice dynamics (SLD), employing Newtonian equation for lattice evolution and the Landau-Lifshitz-Gilbert (LLG) equation for spin, encounters severe limitations with machine-learning potentials (MLPs), including poor energy conservation and excessive computational costs due to non-symplectic integration. In this work, we propose TSPIN, a unified Nos\'e-Hoover chain (NHC) framework that augments the spin-lattice Lagrangian with spin kinetic terms and thermostat/barostat variables, yielding a symplectic Hamiltonian formulation for NVE, NVT, and NPT ensembles. The method integrates spin and lattice dynamics simultaneously, ensuring energy conservation and reducing computational cost. Benchmarks on harmonic models confirm its accuracy, while Fe simulations with the DeepSPIN potential demonstrate superior stability, efficiency, and the ability to capture magnetic phase transition. TSPIN thus provides a general and efficient framework for large-scale simulations of spin-lattice phenomena and multiple-DOF systems.