  Using the Kubo formalism we derived expressions and implemented the method
for calculating the anomalous Hall conductivity (AHC) in ferromagnets with
short-range Gaussian disorder directly from first-principles electronic
structure of the perfect crystal. We used this method to calculate the AHC in
bcc Fe, fcc Co, L1o-FePd, L1o-FePt as well as thin bcc Fe(001) films. Within
our approach we can transparently decompose the conductivity into intrinsic
(IC), side jump (SJ) and intrinsic skew-scattering (ISK) contributions. The
existence of ISK, which originates from asymmetric Mott scattering but is
clearly distinguishable from conventional skew-scattering in that it converges
to a finite value in clean limit, was pointed out by Sinitsyn et al. [Phys.
Rev. B 75, 045315 (2007)]. Here, we collect all contributions to the AHC in
ferromagnets which result in "scattering-independent" AHE in clean limit, and
analyze their relative magnitude from first principles calculations. By
comparing our results to existing experiments we show that the Gaussian
disorder is well suited to model various types of disorder present in real
materials, to some extent including the effect of temperature. In particular,
we show that in addition to intrinsic and side-jump AHE, the intrinsic
skew-scattering can be a major player in determining the magnitude of the AHE
in ferromagnets.
