Recent progress on the planar Hall effect in quantum materials

The planar Hall effect (PHE), which originates from anisotropic magnetoresistance, presents a qualitative and simple approach to characterize electronic structures of quantum materials by applying an in-plane rotating magnetic field to induce identical oscillations in both longitudinal and transverse resistances. In this review, we focus on the recent research on the PHE in various quantum materials, including ferromagnetic materials, topological insulators, Weyl semimetals, and orbital anisotropic matters. Firstly, we briefly introduce the family of Hall effect and give a basic deduction of PHE formula with the second-order resistance tensor, showing the mechanism of the characteristic π-period oscillation in trigonometric function form with a π/4 phase delay between the longitudinal and transverse resistances. Then, we will introduce the four main mechanisms to realize PHE in quantum materials. After that, the origin of the anomalous planar Hall effect (APHE) results, of which the curve shapes deviate from that of PHE, will be reviewed and discussed. Finally, the challenges and prospects for this field of study are discussed.