Monolayer ${\mathrm{CeI}}_2$: An intrinsic room-temperature ferrovalley semiconductor

Two-dimensional ferrovalley semiconductors with robust room-temperature ferromagnetism and sizable valley polarization hold great prospects for future miniature information storage devices. As a new member of the ferroic family, however, such ferrovalley materials have rarely been reported. By first-principles calculations, we identify that monolayer $\mathrm{Ce}{\mathrm{I}}_{\text{2}}$ is an intrinsic ferromagnetic semiconductor and exhibits excellent ambient stability, strong easy in-plane magnetocrystalline anisotropy, and a high magnetic transition temperature up to 374 K. The ferromagnetism is found to arise from the hybridization of Ce-$4f/5d$ and I-$5p$ orbitals. When monolayer $\mathrm{Ce}{\mathrm{I}}_{\text{2}}$ is magnetized toward the off-plane $z$ direction, a spontaneous valley polarization as large as 208 meV in the top valence band can be achieved due to the simultaneous breaking of both inversion symmetry and time-reversal symmetry, which is further verified by the perturbation theory of spin-orbital coupling. Also, the anomalous valley Hall effect can be observed under an in-plane electrical field due to the robust valley-contrasting Berry curvature. Overall, the combination of intrinsic semiconducting ferromagnetism and spontaneous valley polarization renders monolayer $\mathrm{Ce}{\mathrm{I}}_{\text{2}}$ a compelling room-temperature ferrovalley semiconductor for potential applications in nanoscale spintronics and valleytronics.

Figure 1

(a) Side and top views of 2D $\mathrm{Ce}{\mathrm{I}}_{\text{2}}$ crystal. The red shaded region denotes the unit cell. (b) Maps of the ELF over the (001) and (110) planes renormalized to values between 0.0, referring to charge depletion and 1.0 to charge accumulation. (c) Phonon dispersion spectrum of 2D $\mathrm{Ce}{\mathrm{I}}_{\text{2}}$ crystal. (d) Evolution of the total energy from the 5 ps AIMD simulation at 300 K. The insets show the initial and final configurations of 2D $\mathrm{Ce}{\mathrm{I}}_{\text{2}}$ crystal

Figure 2

(a) Orbital-resolved DOS and (b) spin-resolved band structure at the $\mathrm{P}\mathrm{B}\mathrm{E}+U$ level without the involvement of the SOC effect for 2D $\mathrm{Ce}{\mathrm{I}}_{\text{2}}$ crystal in the FM ground state. The Fermi level is set as energy zero. (c) Schematic diagram of the 2D first Brillouin zone with high-symmetry points. (d) Magnetic anisotropy of 2D $\mathrm{Ce}{\mathrm{I}}_{\text{2}}$ crystal. The MAE is set to zero in the $\mathit{xy}$ plane.

Figure 3

The SOC band structure at the $\mathrm{P}\mathrm{B}\mathrm{E}+U$ level with the (a) positive and (b) negative magnetic moments for 2D $\mathrm{Ce}{\mathrm{I}}_{\text{2}}$ crystal in the FM ground state. The red and blue lines near the Fermi level set as zero energy refer to the spin-up and spin-down states, respectively.

Figure 4

Berry curvature of 2D $\mathrm{Ce}{\mathrm{I}}_{\text{2}}$ crystal (a) over the 2D Brillouin zone and (b) along the high-symmetry lines. (c) Anomalous Hall conductivity as a function of the eigenvalue $E_n\mathbf{k}$. Two vertical dashed lines denote the two valley extrema in the top valence band. (d) Schematic AVHEs for the hole-doped $\mathrm{Ce}{\mathrm{I}}_{\text{2}}$ monolayer at the ${\mathrm{K}}_{+}$ and ${\mathrm{K}}_{-}$ valleys under the action of an in-plane electric field. The red and blue arrows stand for the spin-up and spin-down states, respectively.