Metamagnetic multiband Hall effect in Ising antiferromagnet ErGa$_2$

Abstract: Frustrated rare-earth-based intermetallics provide a promising platform for emergent magnetotransport properties through exchange coupling between conduction electrons and localized rare-earth magnetic moments. Metamagnetism, the abrupt change of magnetization under an external magnetic field, is a signature of first-order magnetic phase transitions; recently, metamagnetic transitions in frustrated rare earths intermetallics have attracted interest for their accompanying nontrivial spin structures (e.g. skyrmions) and associated non-linear and topological Hall effects. Here, we present metamagnetism-induced Hall anomalies in single-crystalline ErGa$_2$, which recalls features arising from the topological Hall effect but wherein the strong Ising type anisotropy of Er moments prohibit noncoplanar spin structures. We show that the observed anomalies are neither due to anomalous Hall effect nor topological Hall effect, instead, can be accounted for via 4f-5d interactions which produce a band-dependent mobility modulation. This leads to a pronounced multiband Hall response across the magnetization process -- a metamagnetic multiband Hall effect that resembles a topological-Hall-like response but without nontrivial origins. The present findings may be of general relevance in itinerant metamagnetic systems regardless of coplanar/non-coplanar nature of spins and are important for the accurate identification of Hall signals due to emergent magnetic fields.