Microscopic theory for Gilbert damping in materials with inhomogeneous spin dynamics

We study Gilbert damping in bulk metallic ferromagnets in the presence of nonmagnetic and magnetic impurities. A microscopic expression is obtained for the Gilbert damping parameter using linear response theory with respect to the interaction between magnetization and the conduction electrons in the ferromagnets. In an inhomogeneous precession system, a space-dependent damping torque term of the form ηM × ∇ _r ² M is added to the space-independent term αM × M. We show that the magnetic impurities contribute to both α and η, but the nonmagnetic impurities to only in the absence of spin-orbit coupling.