Spin relaxation and the Elliott-Yafet parameter in W(001) ultrathin films: surface states, anisotropy and oscillation effects

Using first-principles methods based on density-functional theory we investigate the spin relaxation in W(001) ultrathin films. Within the framework of the Elliott-Yafet theory we calculate the spin mixing of the Bloch states and we explicitly consider spin-flip scattering off self-adatoms. We find an oscillatory behavior of the spin-mixing parameter and relaxation rate as a function of the film thickness, which we trace back tosurface-state properties. We also analyze the Rashba effect experienced by the surface states and discuss its influence on the spin relaxation. Finally we calculate the anisotropy of the spin-relaxation rate with respect to the polarization direction of the excited spin population relative to the crystallographic axes of thefilm. We find that the spin-relaxation rate can increase by as much as 47% when the spin polarization is directed out of plane, compared to the case when it is in plane. Our calculations are based on the multiple-scattering formalism of the Korringa-Kohn-Rostoker Green-function method.