Sign Competing Sources of Berry Curvature and Anomalous Hall Conductance Humps in Topological Ferromagnets

The use of Berry-phase concepts has established a strong link between the anomalous Hall effect (AHE) and the topological character of the Hall currents. However, the occurrence of sign competition in the Berry curvature often hinders the topological origin of the observed anomalous Hall effects. Here, a 2D topological ferromagnet is studied with coupled spin and orbital degrees of freedom to assess the anomalous Hall effects in the presence of sign-competing sources of Berry curvature. It is shown that itinerant topological ferromagnets can generally lead to topological metallic bands marked by a non-zero Chern number. It is found that the resulting Berry curvature exhibits a characteristic anisotropic profile with a non-monotonous angular dependence. The sign change of the intrinsic contribution to the anomalous Hall conductance can occur together with topological transitions or be driven by the population imbalance of the topological bands. The breaking of the inversion symmetry introduces the orbital Rashba coupling in the system. The interplay between the orbital Rashba and sign competing sources of Berry curvature leads to anomalies in the anomalous Hall conductance at values of magnetic fields for which the magnetization switches its orientation. The humps in topological ferromagnets arise when the anomalous Hall conductivity is small in absolute value and they can be detected only far from half-filling. This study can be relevant for the family of the topological 2D ferromagnets as well as Weyl ferromagnets, and can particularly account for the variety of unconventional behaviors observed in ultrathin films of SrRuO₃.