Substantial electronic correlation effects on the electronic properties in a Janus FeClF monolayer

The electronic correlation may have essential influence on electronic structures in some materials with special structure and localized orbital distribution. In this work, taking Janus monolayer FeClF as a concrete example, the correlation effects on its electronic structures are investigated by using generalized gradient approximation plus $U$ (GGA+$U$) approach. For perpendicular magnetic anisotropy (PMA), the increasing electron correlation effect can induce the ferrovalley (FV) to half-valley-metal (HVM) to quantum anomalous Hall (QAH) to HVM to FV transitions. For QAH state, there are a unit Chern number and a chiral edge state connecting the conduction and valence bands. The HVM state is at the boundary of the QAH phase, whose carriers are intrinsically 100\% valley polarized. With the in-plane magnetic anisotropy, no special QAH states and prominent valley polarization are observed. However, for both out-of-plane and in-plane magnetic anisotropy, sign-reversible Berry curvature can be observed with increasing $U$. It is found that these phenomenons are related with the change of $d_{xy}$/$d_{x^2-y^2}$ and $d_{z^2}$ orbital distributions and different magnetocrystalline directions. It is also found that the magnetic anisotropy energy (MAE) and Curie temperature strongly depend on the $U$. With PMA, taking typical $U=$2.5 eV, the electron valley polarization can be observed with valley splitting of 109 meV, which can be switched by reversing the magnetization direction. The analysis and results can be readily extended to other nine members of monolayer FeXY (X/Y=F, Cl, Br and I) due to sharing the same Fe-dominated low-energy states and electronic correlations with FeClF monolayer.