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

Electronic correlation may have an essential influence on the electronic structure in some materials with special structures and localized orbital distribution. In this work, taking a Janus monolayer FeClF as a concrete example, the correlation effects on its electronic structures are investigated by using the generalized gradient approximation plus $U$ approach. For perpendicular magnetic anisotropy (PMA), increasing electron correlation effects can induce the ferrovalley (FV) to half-valley-metal (HVM) to quantum anomalous Hall (QAH) to HVM to FV transitions. For the QAH state, there is 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 and Curie temperature strongly depend on the $U$. With PMA, taking a 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. When considering intrinsic magnetic anisotropy, the easy axis of FeClF changes from out of plane to in plane with increasing $U$, and the critical $U$ value is about 1.15 eV. With intrinsic magnetic anisotropy, a monolayer FeClF shows no special QAH and HVM states. The analysis and results can be readily extended to the other nine members of monolayer $\mathrm{Fe}XY$ ($X/Y=\text{F}$, Cl, Br, and I) due to sharing the same Fe-dominated low-energy states and electronic correlations with a FeClF monolayer. Our work emphasizes the importance of electronic correlation and magnetic anisotropy to determine the electronic state of some materials and shows that electronic correlation can induce exceptional phase transitions.

Figure 1

(a) Top view and (b) side view of the crystal structure of a Janus monolayer FeClF, and the rhombus primitive cell is marked by the black frame. (c) The Brillouin zone with high-symmetry points labeled.

Figure 2

For a Janus monolayer FeClF, the lattice constants and energy differences (rectangle supercell) between AFM and FM ordering as a function of $U$.

Figure 3

For out-of-plane magnetic anisotropy, the energy band gap of a Janus monolayer FeClF as a function of $U$ (0–3 eV). The bottom plane is the enlarged view of the top plane near the $U=1.45$ eV and the phase diagram with different $U$ is shown.

Figure 4

For out-of-plane magnetic anisotropy, the energy band structures of a Janus monolayer FeClF with $U$ being 0.00 eV, 1.00 eV, 1.40 eV, 1.45 eV, 1.50 eV, and 2.50 eV.

Figure 5

For out-of-plane magnetic anisotropy, topological edge states of a Janus monolayer FeClF calculated along the (100) direction with $U$ being 1.45 eV, including left (a) and right (b) edges.

Figure 6

For out-of-plane magnetic anisotropy, the calculated Berry curvature distribution of a Janus monolayer FeClF in the 2D Brillouin zone with $U$ being 1.00 eV, 1.45 eV, and 2.50 eV.

Figure 7

For in-plane magnetic anisotropy, the energy band gap of a Janus monolayer FeClF as a function of $U$ (0–3 eV).

Figure 8

For in-plane magnetic anisotropy, the energy band structures of a Janus monolayer FeClF with $U$ being 1.00 eV, 1.45 eV, and 2.50 eV.

Figure 9

Top: the MAE of a Janus monolayer FeClF as a function of $U$ (0–3 eV). Bottom: the phase diagram for a monolayer FeClF with different $U$ values—A region means the FV semiconductor, B and D regions mean the common FM semiconductor, and C point means the common FM semimetal.

Figure 10

For out-of-plane magnetic anisotropy with $U=2.5$ eV, the energy band structures of a Janus monolayer FeClF (a) without SOC and (b) and (c) with SOC for the magnetic moment of Fe along the positive and negative $z$ direction, respectively. In (a), the blue (red) lines represent the band structure in the spin-up (spin-down) direction.

Figure 11

(a) Schematics of anomalous valley Hall effect under electron doping. Panel (b) is the same as (a) but with opposite magnetic moment. The green arrows represent spin-down or spin-up states.

Figure 12

For a Janus monolayer FeClF, the normalized magnetic moment (S) and autocorrelation as a function of temperature with $U=1.5$ eV (left) and 2.5 eV (right).