  Using first principles methods we explore the anisotropy of the spin
relaxation and transverse transport properties in bulk metals with respect to
the direction of the spin quantization axis in paramagnets or of the
spontaneous magnetization in ferromagnets. Owing to the presence of the
spin-orbit interaction the orbital and spin character of the Bloch states
depends sensitively on the orientation of the spins relative to the crystal
axes. This leads to drastic changes in quantities which rely on interband
mixing induced by the spin-orbit interaction. The anisotropy is particularly
striking for quantities which exhibit spiky and irregular distribution in the
Brillouin zone, such as the spin-mixing parameter or the Berry curvature of the
electronic states. We demonstrate this for three cases: (i) the Elliott-Yafet
spin-relaxation mechanism in paramagnets with structural inversion symmetry;
(ii) the intrinsic anomalous Hall effect in ferromagnets; and (iii) the spin
Hall effect in paramagnets. We discuss the consequences of the pronounced
anisotropic behavior displayed by these properties for spin-polarized transport
applications.
