Temperature for a dynamic spin ensemble

In molecular dynamics simulations, temperature is evaluated, via the equipartition principle, by computing the mean kinetic energy of atoms. There is no similar recipe yet for evaluating temperature of a dynamic system of interacting spins. By solving semiclassical Langevin spin-dynamics equations, and applying the fluctuation-dissipation theorem, we derive an equation for the temperature of a spin ensemble, expressed in terms of dynamic spin variables. The fact that definitions for the kinetic and spin temperatures are fully consistent is illustrated using large-scale spin dynamics and spin-lattice dynamics simulations.