Orbital magnetization and anomalous Hall effect in interacting Weyl semimetals

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.