  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.
