Correlation-enhanced spin-orbit coupling and quantum anomalous Hall insulator with large band gap and stable ferromagnetism in monolayer $\mathrm{Fe_2Br_2}$

Nontrivial band topology combined with magnetic ordering can produce quantum anomalous Hall insulator (QAHI), which may lead to advances in device concepts. Here, through first-principles calculations, stable monolayer $\mathrm{Fe_2Br_2}$ is predicted as a room-temperature large-gap high-Chern-number QAHI by using generalized gradient approximation plus $U$ (GGA+$U$) approach. The large gap is due to correlation-enhanced spin-orbit coupling (SOC) effect of Fe atoms, which equates with artificially increasing the strength of SOC without electronic correlation. Out-of-plane magnetic anisotropy is very key to produce quantum anomalous Hall (QAH) state because in-plane magneitization will destroy nontrivial band topology. In the absence of SOC, $\mathrm{Fe_2Br_2}$ is a half Dirac semimetal state protected by mirror symmetry, and the electronic correlation along with SOC effect creates QAH state with a sizable gap and two chiral edge modes. It is found that the QAH state is robust against biaxial strain ($a/a_0$: 0.96 to 1.04) in monolayer $\mathrm{Fe_2Br_2}$ with stable ferromagnetic (FM) ordering and out-of-plane magnetic anisotropy. Calculated results show that Curie temperature is sensitive to correlation strength and strain. The reduced correlation and compressive strain are in favour of high Curie temperature. These analysis and results can be readily extended to other monolayer $\mathrm{Fe_2XY}$ (X/Y=Cl, Br and I), which possesses the same Fe-dominated low-energy states with a $\mathrm{Fe_2Br_2}$ monolayer. These findings open new opportunities to design new high-temperature topological quantum devices.