Ferromagnetic Anomalous Hall Effect in Cr-Doped Bi₂Se₃ Thin Films via Surface-State Engineering

The anomalous Hall effect (AHE) is a nonlinear Hall effect appearing in magnetic conductors, boosted by internal magnetism beyond what is expected from the ordinary Hall effect. With the recent discovery of the quantized version of the AHE, the quantum anomalous Hall effect (QAHE), in Cr- or V-doped topological insulator (TI) (Sb,Bi)₂Te₃ thin films, the 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 AHE, Cr-doped Bi₂Se₃ has failed to exhibit even ferromagnetic AHE, the expected predecessor to the QAHE, though it is the first material predicted to exhibit the QAHE. Here, we have successfully implemented ferromagnetic AHE in Cr-doped Bi₂Se₃ thin films by utilizing a surface state engineering scheme. Surprisingly, the observed ferromagnetic AHE in the Cr-doped Bi₂Se₃ thin films exhibited only a positive slope regardless of the carrier type. We show that this sign problem can be explained by the intrinsic Berry curvature of the system as calculated from a tight-binding model combined with a first-principles method.