  By performing first principles calculations we investigate the intrinsic
anomalous Hall conductivity (AHC) and its anisotropy in ordered L1o FePt, CoPt
and NiPt ferromagnets, and their intermediate alloys. We demonstrate that the
AHC in this family of compounds depends strongly on the direction of the
magnetization in the crystal. We predict that such pronounced orientational
dependence in combination with the general decreasing trend of the AHC when
going from FePt to NiPt leads to a sign change of the AHC upon rotating the
magnetization direction in the crystal of CoPt alloy. We also suggest that for
a range of concentration x in Co(x)Ni(1-x)Pt alloy it is possible to achieve a
complete quenching of the anomalous Hall current for a certain direction of the
magnetization in the crystal. By analyzing the spin-resolved AHC in 3dPt alloys
we endeavor to relate the overall trend of the AHC in these compounds to the
changes in their densities of d-states around the Fermi energy upon varying the
atomic number. Moreover, we show the generality of the phenomenon of
anisotropic anomalous Hall effect by demonstrating its occurrence within the
three-band tight-binding model.
