Disorder tuned anomalous Hall effect in thin films of Cr doped topological insulators

The anomalous Hall effect (AHE) -- an appearance of a voltage transverse to the electric current in the absence of an external magnetic field -- is a process that arises from the spin-orbit coupling between current and magnetic moments that has been fundamentally linked to the topological nature of the Hall current. Recent first-principle calculations predict that when topological insulators (TIs) are doped with transition metal ions, such as Cr or Fe, a novel \emph{magnetically ordered} insulating state will form -- a state that in thin samples may support a \textit{quantized} anomalous Hall conductance. Here we report an observation of AHE in \textit{rf} sputtered thin Cr doped films of Bi$_2$Te$_3$. The anomalous Hall resistivity $\rho_{xy}$ scales with the longitudinal resistivity squared, $\rho_{xx}^2$, and a distinct ferromagnetic hysteretic response (loops) at temperatures below 10 K with coercive fields of the order of 0.5 T is observed. In as-deposited films the resistivity is below the resistivity quantum $h/e^2$. Using 2.5 MeV electron beam irradiation with varying fluence we can tune the resistivity upward by orders of magnitude. A large effect of controlled quenched point disorder on the quantization of AHE in Bi$_2$Te$_3$ will be discussed.