Impact of correlations and finite temperatures on the anomalous Hall conductivity of 3d-transition-metals

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 based on density-functional theory (DFT) of the anomalous Hall conductivity (AHC) of the 3$d$-transition-metals Fe, Co and Ni is presented. To account for the temperature dependence of the AHC an alloy-analogy for a set of thermal lattice displacements acting as a scattering mechanism is used which is subsequently solved using the coherent potential approximation. Further, impurity scattering has been considered to elucidate the importance of an additional possible contribution to the AHC that might be present in experiment. The impact of correlations beyond the local spin-density approximation to the exchange-correlation functional in DFT is studied within the LSDA+$U$ approach. It is shown that both, the inclusion of correlations and thermal lattice vibrations, is needed to give a material-specific description of the AHC in transition-metals.