Imaging short- and long-range magnetic order in a quantum anomalous Hall insulator

Abstract

The quantum anomalous Hall effect has been observed in several magnetically doped topological insulators, where its robustness and macroscopic magnetization properties have been taken to suggest the presence of long-range ferromagnetic order. However, experiments in such systems have found evidence for both long- and short-range order, leaving the precise nature of the magnetism in these systems unclear. Here, we use scanning superconducting quantum interference device microscopy to study magnetic domains in V-doped (Bi,Sb)$_2$Te$_3$ exhibiting a quantum anomalous Hall effect with precise quantization. By imaging stray magnetic fields as a function of applied field, we map the formation and evolution of domains through magnetic reversal. We reconstruct the magnetization configuration underlying the measured stray field and find that magnetic domains and crystallographic grains are of similar size. Moreover, magnetic reversal is found to occur through domain expansion, typical of ferromagnets, rather than through nucleation at random sites. Our measurements thus reveal a coexistence of both local magnetic interactions within crystallographic grains and long-range ferromagnetic coupling between grains. This behavior in V-doped (Bi,Sb)$_2$Te$_3$ is markedly distinct from that previously reported for Cr-doped (Bi,Sb)$_2$Te$_3$.