Theory of ac anomalous Hall conductivity in d-electron systems

To elucidate the intrinsic nature of anomalous Hall effect in d-electron systems, we study the ac anomalous Hall conductivity (AHC) in a tight-binding model with (d(xz),d(yz),) orbitals. We drive an analytical expression for the ac AHC sigma(xy)(omega), which is valid for finite quasiparticle damping rate gamma=h/2 tau, and find that the ac AHC is strongly dependent on gamma. When gamma= +0, the ac AHC shows a spiky peak at finite energy A that originates from the interband particle-hole excitation, where Delta represents the minimum band splitting measured from the Fermi level. In contrast, we find that this spiky peak is quickly suppressed when gamma is finite. By using a realistic value of gamma(omega) at omega=Delta/2 in d-electron systems, the spiky peak is considerably suppressed. In the present model, the obtained results also represent the ac spin Hall conductivity in a paramagnetic state.