Observation of superparamagnetism in coexistence with quantum anomalous Hall C=$\pm$1 and C=0 Chern states

TL;DR

This study reveals superparamagnetic behavior coexisting with quantum anomalous Hall states in doped topological insulators, highlighting the importance of magnetic island alignment for robust quantization and potential axion states.

Contribution

It demonstrates superparamagnetic order within quantum anomalous Hall regimes and shows how modulation doping influences magnetic island size and state robustness.

Findings

Superparamagnetic islands are present in quantum anomalous Hall regimes.

Larger islands from modulation doping enhance state robustness.

Full quantization requires at least 95% magnetic island alignment.

Abstract

Simultaneous transport and scanning nanoSQUID-on-tip magnetic imaging studies in Cr-(Bi,Sb)$_2$Te$_3$ modulation-doped films reveal the presence of superparamagnetic order within the quantum anomalous Hall regime. In contrast to the expectation that a long-range ferromagnetic order is required for establishing the quantum anomalous Hall state, superparamagnetic dynamics of weakly interacting nanoscale magnetic islands is observed both in the plateau transition regions as well as within the fully quantized C=$\pm$1 Chern plateaus. Modulation doping of the topological insulator films is found to give rise to significantly larger superparamagnetic islands as compared to uniform magnetic doping, evidently leading to enhanced robustness of the quantum anomalous Hall effect. Nonetheless, even in this more robust quantum state, attaining full quantization of transport coefficients requires magnetic alignment of at least 95% of the superparamagnetic islands. The superparamagnetic order is also found within the incipient C=0 zero Hall plateau, which may host an axion state if the top and bottom magnetic layers are magnetized in opposite directions. In this regime, however, a significantly lower level of island alignment is found in our samples, hindering the formation of the axion state. Comprehension and control of superparamagnetic dynamics is thus a key factor in apprehending the fragility of the quantum anomalous Hall state and in enhancing the endurance of the different quantized states to higher temperatures for utilization of robust topological protection in novel devices.