Universal classes of disorder scattering for the in-plane anomalous Hall effect

The in-plane anomalous Hall effect (IPAHE) with planar Hall current and magnetization/magnetic fields in various quantum materials has received increasing attention. Most of the current efforts are devoted to the intrinsic part due to the Berry curvature of electronic bands, however, how disorder scattering affects the extrinsic part (the skew scattering and side jump) remains largely elusive. Here we theoretically investigate the three universal classes of disorder scattering (scalar, spin-conserving, and spin-flipping) for the IPAHE, based on the prototypical two-dimensional massive Dirac fermion model with warping term under generic Zeeman fields. We find that the different disorder scattering results in a distinct dependence of the anomalous Hall conductivity on disorder strength, and we recover previously known results within some limits. Remarkably, the spin-flipping scattering could give rise to nontrivial contributions featuring sinusoidal oscillations with periods of \textgreek{π} and 2\textgreek{π} to the extrinsic part, in contrast to the standard two-dimensional massive Dirac fermions. Our work unveils the rich features of anomalous transport in planar Hall geometry in the presence of disorder scattering and provides some useful insights into the magnetotransport phenomena.