The problem of the nature of anomalous Hall effect was debated since its discovery. In magnetic topological insulators, the quantum anomalous Hall effect has been predicted and experimentally confirmed. However, in other materials with strong spin-orbit coupling, such as semiconductors with Rashba splitting, the transverse conductivity phenomenon is poorly studied.

In this letter, we theoretically investigate how electron scattering on domain walls modifies the intrinsic anomalous Hall response on the surface of a magnetic semiconductor with strong Rashba effect. The band structure of such a semiconductor, characterized by a nontrivial Berry curvature, determines the appearance of a one-dimensional resonant state on the magnetic domain wall in a local exchange gap. Under relatively weak exchange splitting, the resonant state has linear dispersion with small spectral broadening (see the figure). Moreover, it is chiral and localized near the domain wall. It is shown that the presence of a pair of parallel domain walls on the surface can have a measurable physical consequence: an additional almost half-quantized contribution to the anomalous Hall effect. The surface of the BiTeI polar semiconductor doped with transition metal atoms is a suitable material platform for experimental detection of such a contribution.

Spectral behavior, (a) and (b), and spatial profile (c) of electronic resonant states on the surface of the magnetic semiconductor with two parallel domain walls under varying magnetization magnitude in domains.

V. N. Men’shov, I. P. Rusinov, E. V. Chulkov
JETP Letters 121, issue 5 (2025)