Spin-orbit induced relaxation in combined molecular and spin dynamics simulations of BCC iron

The combined molecular and spin dynamics (MD-SD) method has emerged as a powerful tool for integrating the effect of magnetism into the atomistic simulations of transition metals. The coupling between the atomic and spin degrees of freedom is established via a coordinate-dependent exchange interaction, which allows the dynamic exchange of energy between the lattice and spin subsystems; however such exchange-based coupling alone cannot facilitate the transfer of angular momentum between the two subsystems. This results in an unrealistic depiction of the spin-lattice relaxation process. To circumvent this drawback, we extend the conventional MD-SD approach by incorporating additional interaction terms that characterize spin-orbit coupling. These interactions are modeled in terms of the local magnetic anisotropies that arise as a consequence of the symmetry breaking due to lattice vibrations. Using MD-SD simulations, we investigate the effect of these terms on the spin-lattice relaxation in BCC iron. By coupling a conventional thermostat to the lattice subsystem, we show that this novel extension enables the exchange of angular momentum and leads to the mutual thermalization of both lattice and spin subsystems.