Giant anisotropic magneto-resistance in the magnetic topological insulator Cr$_y$(Bi$_{1-x}$Sb$_x$)$_{2-y}$Te$_3$

We demonstrate magnetization control of edge state transport and report the observation of a gate-tunable giant anisotropic magneto-resistance (GAMR) effect in the magnetic topological insulator Cr$_y$(Bi$_{1-x}$Sb$_x$)$_{2-y}$Te$_3$ as an external field (and the magnetization $M$) is rotated from out-of-plane (polar angle $\theta = 0^{\circ}$) to in-plane ($\theta = 90^{\circ}$). The angular dependence of the GAMR deviates from the standard $\cos^2\phi$ form (where $\phi$ is the angle between $M$ and the current density $J$), and is instead explained by a Landauer-Buttiker formalism that accounts for bulk-edge mixing. However, the rotation of the magnetization in-plane produces a weak, conventional AMR. These results serve as evidence for a field tilt-tuned crossover between an ``imperfect'' quantum anomalous Hall insulator (QAH) and a gapless, ferromagnetic topological insulator. 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.