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Gilbert Damping in Conducting Ferromagnets I: Kohn-Sham Theory and Atomic-Scale Inhomogeneity

We derive an approximate expression for the Gilbert damping coefficient α_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 α_G is closely related to the previously proposed spin-torque correlation-function expression.