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Abstract
Simultaneous transport and scanning nanoSQUID-on-tip magnetic imaging studies in Cr-(Bi,Sb)2Te3 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 = ±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.
Quantum anomalous Hall state: formed without long-range ferromagnetic order
In contrast to the expectation that the quantum anomalous Hall state (QAH) should be formed by a long-range ferromagnetic order, such a state is established by a superparamagnetic order. An international team led by Eli Zeldov from the Weizmann Institute of Science perform magnetic imaging of modulation-doped (Bi,Sb)2Te3 films concurrently with electron transport measurements. They observe superparamagnetic dynamics in contrast to the common expectation that QAH states can only be stabilized by a long-range ferromagnetic order. Although Cr modulation doping gives rise to significantly larger superparamagnetic islands and enhanced robustness of the QAH as compared to uniform doping, attaining full quantization of transport coefficients requires magnetic alignment of a large majority of the superparamagnetic islands. The results suggest that understanding and control of superparamagnetic dynamics is a key factor to apprehend the fragility of QAH states in topological materials-based devices.
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Details

1 Weizmann Institute of Science, Department of Condensed Matter Physics, Rehovot, Israel (GRID:grid.13992.30) (ISNI:0000 0004 0604 7563)
2 University of Tokyo, Department of Applied Physics and Quantum Phase Electronics Center (QPEC), Tokyo, Japan (GRID:grid.26999.3d) (ISNI:0000 0001 2151 536X)
3 Weizmann Institute of Science, Department of Condensed Matter Physics, Rehovot, Israel (GRID:grid.13992.30) (ISNI:0000 0004 0604 7563); The Hebrew University, Racah Institute of Physics, Jerusalem, Israel (GRID:grid.9619.7) (ISNI:0000 0004 1937 0538)
4 University of Colorado Denver, Department of Physics, Denver, USA (GRID:grid.241116.1) (ISNI:0000000107903411)
5 Tohoku University, Institute for Materials Research, Sendai, Japan (GRID:grid.69566.3a) (ISNI:0000 0001 2248 6943)
6 University of Tokyo, Department of Applied Physics and Quantum Phase Electronics Center (QPEC), Tokyo, Japan (GRID:grid.26999.3d) (ISNI:0000 0001 2151 536X); RIKEN Center for Emergent Matter Science (CEMS), Wako, Japan (GRID:grid.474689.0)