Magnetotransport induced by anomalous Hall effect

In a magnetic metal, the Hall resistance is generally taken to be the sum of the ordinary Hall resistance and the anomalous Hall resistance. Here it is shown that this empirical relation is no longer valid when either the ordinary Hall angle or the anomalous Hall angle is not small. Using the proper conductivity relation, we reveal an unexpected magnetoresistance (MR) induced by the anomalous Hall effect (AHE). A $B$-linear MR arises and the sign of the slope depends on the sign of the anomalous Hall angle, giving rise to a characteristic bowtie shape. The Hall resistance in a single-band system can exhibit a nonlinearity which is usually considered as a characteristic of a two-band system. A $B$-symmetric component appears in the Hall. These effects reflect the fundamental difference between the ordinary Hall effect and the AHE. Furthermore, we experimentally reproduce the unusual MR and Hall reported before in Co$_3$Sn$_2$S$_2$ and show that these observations can be well explained by the proposed mechanism. MR often observed in quantum anomalous Hall insulators provides further confirmation of the picture. The effect may also account for the large MR observed in non-magnetic three-dimensional topological Dirac semimetals.