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 $\hat{I}\pm$ 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 $\hat{I}\pm$ 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${}_{1-x}$Co${}_x$, fcc Ni${}_{1-x}$Fe${}_x$, fcc Ni${}_{1-x}$Co${}_x$ and bcc Fe${}_{1-x}$V${}_x$, and for 5d impurities in transition-metal alloys. All results are in satisfying agreement with experiment.