Giant magneto-cubic in-plane Hall effect in a nonmagnetic material

In-plane Hall effect triggered by an external magnetic field applied in the transport plane has attracted significant experimental attentions in recent few years. However, most experiments focus on magnetic materials, where the existence of magnetic ordering may complicate understanding the physics behind, and the relatively small signal magnitudes limit the application of the effect. Here, we report a giant in-plane Hall effect in a nonmagnetic half-Heusler compound LuAuSn, with a magnitude exceeding all the previously reported values. A $2\pi /3$ -period of in-plane Hall effect and the consistent cubic dependence on the magnetic field are observed, realizing the long-sought theoretical prediction of magneto-cubic in-plane Hall effect under threefold rotational symmetry in an unexpected material. The scaling law analysis and first-principles calculations indicate that extrinsic side jump and skew scattering processes from both impurity and phonon scatterings dominate the observed effect. These findings unravel a new type of magneto-nonlinear in-plane Hall effect, and its large magnitude and wide-temperature operation may open the door to practical applications of in-plane Hall effect.