Study of intrinsic spin and orbital hall effects in pt based on a (6s, 6p, 5d) tight-binding model

We study the origin of the intrinsic spin Hall conductivity (SHC) and the d-orbital Hall conductivity (OHC) in Pt based on a multiorbital tight-binding model with spin-orbit interaction. We find that the SHC exceeds 1000he(-1) .Omega(-1) cm(-1) when the resistivity p is smaller than similar to 10 mu Omega cm, whereas it decreases to 300 he(-1) .Omega(-1) cm(-1) when rho similar to 100 mu Omega cm. In addition, the OHC is still larger than the SHC. The origin of the huge spin Hall effect (SHE) and d-orbital Hall effect (OHE) in Pt is the effective Aharonov-Bohm phase that is induced by the interorbital transition between d(xy)- and d(x2-y2)-orbitals with the aid of the strong spin-orbit interaction.