Nonlinear Planar Hall Effect
An intriguing property of a three-dimensional (3D) topological insulator (TI) is the existence of surface states with spin-momentum locking, which offers a new frontier of exploration in spintronics. In this work, we report the observation of a new type of Hall effect in a 3D TI $\mathrm{Bi_2Se_3}$ film. The Hall resistance scales linearly with both the applied electric and magnetic fields and exhibits a $\pi/2$ angle offset with respect to its longitudinal counterpart, in contrast to the usual angle offset of $\pi/4$ between the linear planar Hall effect and the anisotropic magnetoresistance. This novel nonlinear planar Hall effect originates from the conversion of a nonlinear transverse spin current to a charge current due to the concerted actions of spin-momentum locking and time-reversal symmetry breaking, which also exists in a wide class of noncentrosymmetric materials with a large span of magnitude. Finally, it provides a new way to characterize and utilize the nonlinear spin-to-charge conversion in a variety of topological quantum materials.