Direct evidence of ferromagnetism in a quantum anomalous Hall system

Abstract

Quantum anomalous Hall (QAH) systems are of great fundamental interest and potential application because of their dissipationless conduction without the need for external magnetic field. The QAH effect has been realized in magnetically doped topological insulator thin films. However, full quantization requires extremely low temperature ($T< 50\,$mK) in the initial works, though it has been significantly improved with modulation doping or co-doping of magnetic elements. Improved ferromagnetism has been shown in these thin films, yet direct evidence of long-range ferromagnetic order is lacking. Herein, we present direct visualization of long-range ferromagnetic order in thin films of Cr and V co-doped (Bi,Sb)$_2$Te$_3$ using low-temperature magnetic force microscopy with $\textit{in-situ}$ transport. The magnetization reversal process reveals typical ferromagnetic domain behavior, i.e., domain nucleation and possibly domain wall propagation, in contrast to much weaker magnetic signals observed in the end members, possibly due to superparamagnetic behavior. The observed long-range ferromagnetic order resolves one of the major challenges in QAH systems, and paves the way to high-temperature dissipationless conduction by exploring magnetic topological insulators.