Ambi-chiral anomalous Hall effect in magnetically doped topological insulators

The chirality associated with broken time reversal symmetry in magnetically doped topological insulators has important implications to the quantum transport phenomena. Here we report anomalous Hall effect studies Mn- and Cr-doped Bi$_2$Te$_3$ varied thickness doping content. By tracing of loops, find that Mn-type clockwise is strengthened by reduction film thickness, which opposite Cr-type counterclockwise chirality. We provide a phenomenological model explain evolution magnetic order insulators.