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

TL;DR

This study uses first-principles calculations to analyze how correlations and finite temperatures influence the anomalous Hall conductivity in 3d transition metals, highlighting the importance of these factors for accurate modeling.

Contribution

It presents a comprehensive first-principles approach incorporating temperature effects and correlations to accurately predict the anomalous Hall conductivity in transition metals.

Findings

Correlations and thermal vibrations significantly affect AHC predictions.

Impurity scattering contributes to the AHC in transition metals.

Material-specific AHC requires considering both correlations and temperature effects.

Abstract

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.