An implicit spin lattice dynamics integrator in LAMMPS

Abstract

An iterative implicit solver is implemented in LAMMPS for spin lattice dynamics simulations. An approach to treat multibody interactions, specifically in metallic materials described by the embedded atom method, is presented for the first time in an implicit solver. Magnetization is extremely well preserved in this integrator, with fluctuations eight orders of magnitude smaller than those observed using a timestep of 0.1 fs in the explicit solver currently in LAMMPS. This is true even when larger timesteps than 0.1 fs are used in the implicit integrator, enabling the implicit integrator in some cases to have smaller magnetization error and shorter runtime than the explicit solver for the same overall simulation time. The integrator also conserves energy well. Energy error comparable to or lower than that of the explicit solver is achieved for implicit timesteps up to five times larger than the explicit timestep, with minimal increase in runtime. Errors in energy grow as timestep cubed, while errors in magnetization remain unchanged as timestep increases.