Symplectic Spin-Lattice Dynamics with Machine-Learning Potentials

TL;DR

This paper introduces TSPIN, a symplectic Hamiltonian framework for coupled spin-lattice dynamics that improves energy conservation and computational efficiency in magnetic material simulations using machine-learning potentials.

Contribution

The authors develop TSPIN, a novel symplectic NHC-based method that unifies spin and lattice dynamics, enabling stable, accurate, and efficient large-scale simulations.

Findings

TSPIN achieves better energy conservation than traditional methods.

The method demonstrates superior stability and efficiency in Fe simulations.

TSPIN accurately captures magnetic phase transitions.

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.