Anisotropy of spin relaxation in metals and ultrathin metallic films*

We predict a hitherto overlooked anisotropy of the spin relaxation time $T_1$ in non-magnetic metallic systems with respect to the orientation of the spin porlarization $\hat{s}$ of the injected electrons relative to the crystallographic directions. In the Elliott-Yafet mechanism, the spin relaxation time is related to the Elliott-Yafet parameter $b^2$ that quantifies the degree of spin-mixing of Bloch states due to spin-orbit interaction. It can be demonstrated that $b^2$ depends on $\hat{s}$ due to the directional dependence of the spin-orbit matrix-elements between Bloch states comprising directional orbitals. The directional dependence becomes very pronounced in the case of degeneracies or near-degeneracies leading to {\it spin-flip hot spots} or even extended {\it hot areas} on the Fermi surface. The calculated anisotropy can reach values as large as 830\% for hcp Hf or 87\% in W(110) 10-layer-films, as we find from first-principles calculations employing the Kohn-Korringa-Rostoker Green function method. The anisotropy offers interesting new functionalities in spintronics applications such as GMR, spin Hall effect as well as spin dynamics. [1] B. Zimmermann, P. Mavropoulos, S. Heers, N. H. Long, S. Blugel, and Y. Mokrousov, Phys. Rev. Lett., in press (arXiv:1210.1801).