Giant anisotropic magneto-resistance in the magnetic topological insulator Cr$_x$(Bi,Sb)$_{2-x}$Te$_3$

We report the observation of a giant anisotropic magneto-resistance (GAMR) effect in the magnetic topological insulator Cr$_x$(Bi,Sb)$_{2-x}$Te$_3$ as an external field (and the magnetization $M$) is rotated from out-of-plane (azimuthal angle $\theta = 0^{\circ}$) to in-plane ($\theta = 0^{\circ}$)). While the rotation of a magnetic field in-plane produces a weak, conventional anisotropic magnetoresistance (AMR) that follows the standard angular dependence (AMR $\sim \cos^2\phi$, where $\phi$ is the angle between $M$ and the current density $J$), the GAMR is much larger in magnitude and deviates from the standard $\cos^2\theta$, dependence. We explain the observed GAMR through a quantum magnetic phase transition from an ``imperfect'' quantum anomalous Hall (QAH) insulator to a trivial ferromagnetic semiconductor as the magnetization is tilted from out-of-plane to in-plane. We expect the GAMR to become stronger in the ideal QAH regime where edge state conduction dominates over bulk conduction, thus providing a route toward proof-of-concept ferromagnetic topological insulator transistors and magnetic field sensors. Funded by DARPA.