  Ferromagnetic Weyl semi-metals exhibit an anomalous Hall effect, a
consequence of their topological properties. In the non-interacting case, the
derivative of the orbital magnetization with respect to chemical potential is
proportional to this anomalous Hall effect, the Str$\check{\text{e}}$da
formula. Motivated by compounds such as $\text{Mn}_3\text{Sn}$, here we
investigate how interactions modeled by a Hubbard $U$ impact on both quantities
when the Fermi energy is either aligned with the Weyl nodes or away from them.
Within Dynamical Mean-Field Theory, we find, in the Weyl semimetal regime, away
from interaction-induced Mott or band-insulating phases, that interactions lead
not only to spectral weight redistribution between coherent bands and Hubbard
bands, but also to an increase in the imbalance between the densities of spin
species. This increased imbalance leads to a larger anomalous Hall effect in
ferromagnetic Weyl semimetals. But this interaction-induced spin imbalance also
compensates the reduction in orbital magnetization of each spin species that
comes from smaller quasiparticle weight. The combined effects lead to an
orbital magnetization that depends weakly on interaction strength and changes
linearly upon doping at small doping. The Str$\check{\text{e}}$da formula is
no-longer satisfied. Away from the insulating phases, the quasiparticle picture
and low-order perturbation theory go a long way to explain these results.
