Intrinsic spin Hall effect and orbital Hall effect in 4 d and 5 d transition metals

We study the intrinsic spin Hall conductivity (SHC) in various $5d$ transition metals (Ta, W, Re, Os, Ir, Pt, and Au) and $4d$ transition metals (Nb, Mo, Tc, Ru, Rh, Pd, and Ag) based on the Naval Research Laboratory tight-binding model, which enables us to perform quantitatively reliable analysis. In each metal, the obtained intrinsic SHC is independent of resistivity in the low resistive regime $(\ensuremath{\rho}<50\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\ensuremath{\Omega}\phantom{\rule{0.2em}{0ex}}\mathrm{cm})$ whereas it decreases in proportion to ${\ensuremath{\rho}}^{\ensuremath{-}2}$ in the high resistive regime. In the low resistive regime, the SHC takes a large positive value in Pt and Pd,…