Angular momentum conservation in spin-lattice dynamics simulations

Abstract

Kuzkin's angular momentum balance method is implemented in the LAMMPS SPIN package for atomistic spin-lattice dynamics, along with shifted-force exchange and N\'eel Hamiltonians parameterized to minimize energy drifts in the simulations. Angular momentum contributions arising from two mechanisms are quantified using this method: particle transport across the boundaries of a periodic simulation domain and external torques applied to the domain by periodic image atoms. When these mechanisms are accounted for, lattice angular momentum is exactly conserved in lattice systems and in spin-lattice systems with isotropic exchange interactions. The calculations show that spin-lattice angular momentum exchange only occurs when the N\'eel anisotropy energy is added to the exchange energy, and that with this addition, total angular momentum is approximately conserved in the magnetization direction but not in other directions. Inclusion of the N\'eel anisotropy increases the energy drifts observed in simulations of iron nanoparticles. These drifts are linearly proportional to the magnitude of the anisotropy energy and the simulation time step.