Reinventing atomistic magnetic simulations with spin-orbit coupling

We propose a powerful extension to combined molecular and spin dynamics that fully captures the coupling between the atomic and spin subsystems via spin-orbit interactions. Its foundation is the inclusion of the local magnetic anisotropies that arise as a consequence of the lattice symmetry breaking due to phonons or defects. We demonstrate that our extension enables the exchange of angular momentum between the atomic and spin subsystems, which is critical to the challenges arising in the study of fluctuations and nonequilibrium processes in complex, natural, and engineered magnetic materials.

Figure 1

Thermal relaxation in a conventional molecular and spin dynamics simulation, with the lattice subsystem coupled to a heat bath at the temperature $T=800$ K. The instantaneous lattice and the spin temperatures are plotted as functions of time. The inset shows the time evolution of magnetization as a fraction of the saturation magnetization.

Figure 2

Thermal relaxation in a combined molecular and spin dynamics simulation enhanced with SO coupling. The lattice subsystem is coupled to a heat bath at the temperature $T=800$ K. Anisotropy coefficients $C_1$ and $C_2$ were set to $0.2$ and $0.1$ eV, respectively.

Figure 3

Thermalization of the spin subsystem under varying anisotropy strengths: (a) varying the first-order anisotropy coefficient $C_1$ while the second-order coefficient $C_2$ is set to zero, and (b) varying $C_2$ while $C_1$ is held constant at $0.2$ eV. The lattice subsystem is coupled to a heat bath at the temperature $T=800$ K.

Figure 4

Thermalization of the spin subsystem under varying vacancy concentrations, with the lattice subsystem coupled to a heat bath at the temperature $T=800$ K. Anisotropy coefficients $C_1$ and $C_2$ were set to $0.2$ and $0.1$ eV, respectively.