Landau-Lifshitz Equation of Ferromagnetism: Exact Treatment of the Gilbert Damping

Abstract
In the Landau-Lifshitz equation which describes the evolution of spin fields in nonequilibrium continuum ferromagnets, by stereographic projection of the unit sphere of spin onto a complex plane, it is shown that the effect of the Landau-Lifshitz-Gilbert damping term is a mere rescaling of time by a complex constant. Consequently, for any given undamped motion of spatially regular and/or irregular spin structures, the nature of the damping can be analyzed exactly in a simplified manner.