A Kubo-Greenwood-like equation for the Gilbert damping parameter α is presented. Its implementation within the fully relativistic Korringa-Kohn-Rostoker (KKR) band structure method in combination with Coherent Potential Approximation (CPA) alloy theory gives an access to a broad variety of systems and situations. This is demonstrated with results obtained for the binary alloys of 3d-metals as well as for a series of alloys of permalloy with 5d transition metals. To account for the thermal displacements of atoms as a scattering mechanism, an alloy-analogy model is introduced. The corresponding calculations for Ni correctly describe the rapid change of α when small amounts of substitutional Cu are introduced. |