Spin Hall effect (SHE) is studied with first-principles relativistic band calculations for platinum, which is one of the most important materials for metallic SHE and spintronics. We find that intrinsic spin Hall conductivity (SHC) is as large as $\sim 2000(\hslash /e)(\Omega \mathrm{cm}{)}^{-1}$ at low temperature and decreases down to $\sim 200(\hslash /e)(\Omega \mathrm{cm}{)}^{-1}$ at room temperature. It is due to the resonant contribution from the spin-orbit splitting of the doubly degenerated $d$ bands at high-symmetry $L$ and $X$ points near the Fermi level. By modeling these near degeneracies by an effective Hamiltonian, we show that SHC has a peak near the Fermi energy and that the vertex correction due to impurity scattering vanishes. We therefore argue that the large SHE observed experimentally in platinum is of intrinsic nature.

• Received 19 April 2007

DOI:https://doi.org/10.1103/PhysRevLett.100.096401