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

Highlights: • A coupled magnetic spin and molecular dynamics implementation in the large scale molecular dynamics code LAMMPS is presented. • The integration of the equations of motion is performed with an algorithm based on the Suzuki–Trotter decomposition. • Excellent results in terms of energy and magnetization norm preservation are recovered. • A sectoring algorithm for parallel calculations was developed and implemented. • It allows parallel spin–lattice calculations while perfectly preserving the properties of the integration algorithm. • The scaling efficiency of this parallel algorithm is probed and compared to usual LAMMPS calculations. • Efficient massively parallelized simulations of systems containing millions of magnetic atoms are now enabled. A parallel implementation of coupled spin–lattice dynamics in the LAMMPS molecular dynamics package is presented. The approach is very general, and can be applied to simple ferromagnets, magnetic alloys, or amorphous magnetic materials. 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.