First-principles calculation of the Gilbert damping parameter via the linear response formalism with application to magnetic transition metals and alloys

Abstract

A method for the calculations of the Gilbert damping parameter $\ensuremath{\alpha}$ is presented, which, based on the linear response formalism, has been implemented within the fully relativistic Korringa-Kohn-Rostoker band structure method in combination with the coherent potential approximation alloy theory. To account for thermal displacements of atoms as a scattering mechanism, an alloy-analogy model is introduced. This allows the determination of $\ensuremath{\alpha}$ for various types of materials, such as elemental magnetic systems and ordered magnetic compounds at finite temperature, as well as for disordered magnetic alloys at $T=0$ K and above. The effects of spin-orbit coupling, chemical- and temperature-induced structural disorder, are analyzed. Calculations have been performed for the 3$d$ transition metals bcc Fe, hcp Co, and fcc Ni; their binary alloys bcc Fe${}_{1\ensuremath{-}x}$Co${}_{x}$, fcc Ni${}_{1\ensuremath{-}x}$Fe${}_{x}$, fcc Ni${}_{1\ensuremath{-}x}$Co${}_{x}$ and bcc Fe${}_{1\ensuremath{-}x}$V${}_{x}$; and for $5d$ impurities in transition-metal alloys. All results are in satisfying agreement with experiment.