What determines the sign of the spin Hall effects in Cu alloys doped with 5d elements?

We perform a systematical analysis of the spin Hall effect (SHE) in the Cu alloys doped with a series of 5d elements, by the combined approach of density functional theory and Hartree-Fock approximation. We find that not only the spin orbit interactions (SOI) in both the 5d and 6p orbitals, but also the local correlations in the 5d orbitals of the impurities, are decisive on the sign of the spin Hall angle (SHA). Including all of these three factors properly, we predict the SHA for each alloy in the series. The signs of CuIr and CuPt are sensitive to perturbation of the local correlations. This observation is favorable for controlling the sign of the transverse spin Hall voltage.