Impact of finite temperatures and correlations on the anomalous Hall conductivity from ab initio theory

Finite-temperature effects in the first-principles calculations of electronic transport up to now include almost exclusively only electronic temperatures by means of the Fermi-distribution function neglecting the influence of lattice vibrations. Here, employing the linear response Kubo formalism as implemented in a fully relativistic multiple-scattering Korringa-Kohn-Rostoker Green function method a systematic first-principles study of the anomalous Hall conductivity (AHC) of the 3d-transition metals Fe, Co and Ni is presented. It is shown that the inclusion of both correlations and thermal lattice vibrations is needed to give a material-specific description of the AHC in transition metals. The employed general framework will allow a first-principles description of other transverse transport phenomena treating correlations, finite temperatures and disorder on the same footing, giving valuable insights for experiments.