Gilbert damping in conducting ferromagnets. I. Kohn-Sham theory and atomic-scale inhomogeneity

We derive an approximate expression for the Gilbert damping coefficient ${\alpha }_G$ of itinerant electron ferromagnets which is based on their description in terms of spin-density-functional theory (SDFT) and Kohn-Sham quasiparticle orbitals. We argue for an expression in which the coupling of magnetization fluctuations to particle-hole transitions is weighted by the spin-dependent part of the theory’s exchange-correlation potential, a quantity which has large spatial variations on an atomic length scale. Our SDFT result for ${\alpha }_G$ is closely related to the previously proposed spin-torque correlation-function expression.