Ab initio calculation of intrinsic anomalous and spin Hall conductivity using localized pseudoatomic orbitals

For first-principles calculation of intrinsic anomalous Hall conductivity (AHC) and spin Hall conductivity (SHC), we implemented AHC and SHC formulas into the SIESTA code, which uses localized pseudoatomic orbitals to expand electronic wavefunctions. We calculate AHC from the Brillouin zone integration of the Berry curvature, and SHC by replacing a velocity operator in the AHC formula with a symmetrized product of spin and velocity operators. For AHC and SHC calculations, it is crucial to perform noncollinear-spin calculations including the spin-orbit coupling. We conduct AHC calculations of Fe, Co and SHC calculations of Pd, Pt and Ta. We compare our calculations with experimental results. We also investigate Berry curvature along high symmetry k points and the energy dependence of AHC and SHC.