  We carry out first-principles calculations which demonstrate the importance
of spin-flip transitions for the intrinsic anomalous Hall conductivity of
ordered FePt alloys. We show the such transitions get enhanced by large
spin-orbit coupling of Pt atoms, becoming negligible when Pt is replaced by
lighter isoelectronic Pd. We find that spin-flip transitions in FePt originate
not only from conventional band anticrossings at the Fermi level, but also from
transitions between well-separated pairs of bands with similar dispersions. We
also predict a strong anisotropy in the anomalous Hall conductivity of FePt,
which comes from spin-flip transitions entirely, and investigate the influence
of disorder on it.
