Massively parallel symplectic algorithm for coupled magnetic spin dynamics and molecular dynamics

TL;DR

This paper introduces a parallel symplectic algorithm for coupled magnetic spin and molecular dynamics, enabling efficient large-scale simulations with high accuracy in the LAMMPS package.

Contribution

It presents a novel parallel symplectic integration method for coupled spin-lattice dynamics that maintains geometric properties and scales efficiently on large systems.

Findings

The serial implementation conserves energy and magnetization up to second order.

The parallel algorithm is both accurate and scalable for large systems.

Validation confirms the method's correctness and efficiency.

Abstract

A parallel implementation of coupled spin-lattice dynamics in the LAMMPS molecular dynamics package is presented. The equations of motion for both spin only and coupled spin-lattice dynamics are first reviewed, including a detailed account of how magneto-mechanical potentials can be used to perform a proper coupling between spin and lattice degrees of freedom. A symplectic numerical integration algorithm is then presented which combines the Suzuki-Trotter decomposition for non-commuting variables and conserves the geometric properties of the equations of motion. The numerical accuracy of the serial implementation was assessed by verifying that it conserves the total energy and the norm of the total magnetization up to second order in the timestep size. Finally, a very general parallel algorithm is proposed that allows large spin-lattice systems to be efficiently simulated on large numbers of processors without degrading its mathematical accuracy. Its correctness as well as scaling efficiency were tested for realistic coupled spin-lattice systems, confirming that the new parallel algorithm is both accurate and efficient.