Berry-curvatures and anomalous Hall effect in Heusler compounds

Berry curvatures are computed for a set of Heusler compounds using density functional (DF) calculations and the wave functions that DF provide. The anomalous Hall conductivity is obtained from the Berry curvatures. It is compared with experimental values in the case of Co$_2$CrAl and Co$_2$MnAl. A notable trend cannot be seen but the range of values is quite enormous. The results for the anomalous Hall conductivities and their large variations can be qualitatively understood by means of the band structure and the Fermi-surface topology.