Retardation effects in the Landau-Lifshitz-Gilbert equation

We analyze the Landau-Lifshitz-Gilbert equation under the inclusion of retardation effects by introducing a memory kernel comprised of an instantaneous and a time-dependent part. Due to the delay term the spin waves become decoherent, leading to an additional damping process. Based on a linear spin-wave analysis, we find that the total damping process is a superposition of the intrinsic Gilbert damping and the retardation-induced attenuation. By means of the mutual influence of both damping sources a quite complex behavior results: the appearance of long-living spin-wave excitations with small damping or an overdamped behavior where spin-wave excitations are totally suppressed. The parameters of the model are estimated, and the effects should be accessible experimentally.