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 reaches 1000 \hbar/e\Omega cm when the resistivity \rho is smaller than ~10 \mu\Omega cm, whereas it decreases to 300 \hbar/e\Omega cm when \rho ~ 100 \mu\Omega cm. In addition, the OHC is still larger than the SHC. The origin of huge SHE and OHE in Pt is the large ``effective magnetic flux'' that is induced by the interorbital transition between d_{xy}- and d_{x2-y2}-orbitals with the aid of the strong spin-orbit interaction.