thin films via surface-state engineering and carrier-selective anomalous Hall effect*

Anomalous Hall effect (AHE) is a non-linear Hall effect appearing on magnetic conductors, boosted by internal magnetism beyond what is expected from ordinary Hall effect. With the recent discovery of quantized version of the AHE, the quantum anomalous Hall effect (QAHE), in Cr- or V-doped topological insulator (TI) (Sb,Bi)₂Te₃ thin films, AHE in magnetic TIs has been attracting significant interest. However, one of the puzzles in this system has been that while Cr- or V-doped (Sb,Bi)₂Te₃ and V-doped Bi₂Se₃ exhibit ferromagnetic (hysteretic) AHE, Cr-doped Bi₂Se₃ has failed to exhibit even ferromagnetic AHE, the necessary predecessor to QAHE, though it is the first material predicted to exhibit QAHE. Here, we have successfully implemented ferromagnetic AHE in Cr-doped Bi₂Se₃ thin films by utilizing a surface state engineering scheme. Surprisingly, all the observed ferromagnetic AHE, as in other Cr- or V-doped TIs, are always p-type even if the majority carrier type remains n-type. This can be well explained by a carrier-selective anomalous-Hall-effect model in which the local magnetic moments interact only through p-type carriers.