  The anomalous Hall conductivity has an important extrinsic contribution known
as side jump contribution, which is independent of both scattering strength and
disorder density. Nevertheless, we discover that side jump has strong
dependence on the spin structure of the scattering potential. We propose three
universality classes of scattering for the side jump contribution, having the
characters of being spin-independent, spin-conserving and spin-flip
respectively. For each individual class, the side jump contribution takes a
different unique value. When two or more classes of scattering are present, the
value of side jump is no longer fixed but varies as a function of their
relative disorder strength. As system control parameter such as temperature
changes, due to the competition between different classes of disorder
scattering, the side jump Hall conductivity could flow from one class dominated
limit to another class dominated limit. Our result indicates that magnon
scattering plays a role distinct from normal impurity scattering and phonon
scattering in the anomalous Hall effect because they belong to different
scattering classes.
