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The Fermi-surfaces and Elliott-Yafet spin-mixing parameter (EYP) of severalelemental metals are studied by \emph{ab initio} calculations. We focus firston the anisotropy of the EYP as a function of the direction of thespin-quantization axis [Phys.~Rev.~Lett.\ \textbf{109}, 236603 (2012)]. Weanalyze in detail the origin of the gigantic anisotropy in $5d$ hcp metals ascompared to $5d$ cubic metals by band-structure calculations and discuss thestability of our results against an applied magnetic field. We further presentcalculations of light (4$d$ and 3$d$) hcp crystals, where we find a hugeincrease of the EYP anisotropy, reaching colossal values as large as $6000\%$in hcp Ti. We attribute these findings to the reduced strength of spin-orbitcoupling, which promotes the anisotropic spin-flip hot loops at the Fermisurface.  In order to conduct these investigations, we developed an adaptedtetrahedron-based method for the precise calculation of Fermi surfaces ofcomplicated shape and accurate Fermi-surface integrals within thefull-potential relativistic Korringa-Kohn-Rostoker Green-function method.

Fermi surfaces, spin-mixing parameter, and colossal anisotropy of spin relaxation in transition metals from ab initio theory