Magnetically doped topological insulators have been shown to host a quantum anomalous Hall state at low temperatures. In the theoretical literature, the magnetic structure that underlies this topological state has been assumed to consist of long range magnetic order, with the polarization transition mediated by domain walls hosting topological edge states. Transport and global magnetometry measurements seem consistent with this idea, suggesting that the quantized resistance emerges from the breaking of time reversal symmetry in the form of large ferromagnetic domains. In contrast to this expectation, simultaneous transport and scanning nanoSQUID-on-tip magnetic imaging studies in uniform and modulation-doped Cr-(Bi,Sb)2Te3 films reveal that the magnetic structure is in fact superparamagnetic.
The superparamagnetic state is formed by weakly interacting nanoscale magnetic domains, with a characteristic size of a few tens of nanometers. These domains undergo random reversals, which drive the electronic state from one Hall plateau to the other. The superparamagnetic state is metastable, with very small energy barriers to relaxation. We observe magnetic relaxation on laboratory time scales even at 300 mK, evident also in transport measurements. Unexpectedly, magnetic relaxation can also be induced by varying the back gate voltage, and we propose a mechanism for the influence of the electronic phase on the magnetic relaxation. We speculate that the dynamic nature of magnetic disorder in quantum anomalous Hall systems may be at least partially responsible for the observed fragility of the quantum anomalous hall state at elevated temperatures.