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Employing the linear response Kubo formalism as implemented in a fullyrelativistic multiple-scattering Korringa-Kohn-Rostoker Green function method asystematic first-principles study based on density-functional theory (DFT) ofthe anomalous Hall conductivity (AHC) of the 3$d$-transition-metals Fe, Co andNi is presented. To account for the temperature dependence of the AHC analloy-analogy for a set of thermal lattice displacements acting as a scatteringmechanism is used which is subsequently solved using the coherent potentialapproximation. Further, impurity scattering has been considered to elucidatethe importance of an additional possible contribution to the AHC that might bepresent in experiment. The impact of correlations beyond the local spin-densityapproximation to the exchange-correlation functional in DFT is studied withinthe LSDA+$U$ approach. It is shown that both, the inclusion of correlations andthermal lattice vibrations, is needed to give a material-specific descriptionof the AHC in transition-metals.

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