Absence of strong skew scattering in crystals with multi-sheeted Fermi surfaces

We consider an extrinsic contribution to the anomalous and spin Hall effect in dilute alloys
based on Fe, Co, Ni, and Pt hosts with different substitutional impurities. It is shown that
a strong skew-scattering mechanism is absent in such crystals with multi-sheeted Fermi
surfaces. Based on this finding, we conclude on the mutual exclusion of strong intrinsic and
skew-scattering contributions to the considered transport phenomena. It also allows us to draw
general conclusions in which materials with a giant anomalous Hall effect caused by the skew
scattering can be achieved.