Prediction of the two-dimensional Janus ferrovalley material LaBrI

Two-dimensional (2D) ferrovalley materials, displaying coexistence of spontaneous spin and valley polarizations, have recently attracted significant attention due to their potential for applications in the fields of spintronics and valleytronics. However, unfortunately, to date only a few 2D ferrovalley materials exist. Here, first-principles calculations predict a 2D Janus ferrovalley material lanthanum bromiodide (LaBrI). It is found that LaBrI is a stable ferromagnetic electride, whose magnetic moment originates mainly from the interstitial anionic electrons. The magnetic transition temperature of LaBrI monolayers is estimated to be far beyond room temperature, and a sizable magnetic anisotropy with easy in-plane magnetization is also present. Most importantly, LaBrI monolayers exhibit a large valley polarization due to the concurrent broken space- and time-reversal symmetries, with the calculated valley polarization reaching up to 59 meV. This value is comparable to that of the ferrovalley materials reported to date. Intriguingly, the inequivalent Berry curvature at the two valleys takes opposite values, giving rise to an anomalous valley Hall effect, where a valley current with an accompanying net charge Hall current may be induced.

Figure 1

(a) Top and (b) side views of the 2D Janus LaBrI monolayer. (c) The Brillouin zone of a generic 2D hexagonal system. (d) Top and (e) side views of the 3D spatial ELF of the LaBrI monolayer with the isovalue taken to 0.7. (f) The phonon dispersion of the LaBrI monolayer. (g) Variation of the total energy (eV/f.u.) with the simulation time in a AIMD run at 500 K. The inset shows a snapshot of the structure after 10 ps.

Figure 2

(a) Top and side views of 3D spin density of the LaBrI monolayer with the isosurface value set as 0.008 $e$/${\mathrm{bohr}}^3$. (b) The orbital-projected band structure and DOS of the LaBrI monolayer in the NM state. The inset shows the partial charge density of the metallic band near the Fermi level with the isosurface value set as 0.008 $e$/${\mathrm{bohr}}^3$. The (c) nonprojected and (d) projected spin-polarized band structure of the LaBrI monolayer in the FM ground state.

Figure 3

The band structures of 2D Janus LaBrI monolayer computed by including SOC: the magnetization direction is along (a) $+z$ axis and (b) $-z$ axis. The out-of-plane spin component $S_z$ is denoted by color.

Figure 4

The Berry curvature ${\mathrm{\Omega }}_z$ of the LaBrI monolayer computed: (a) along the high symmetry lines, and (b) over the 2D Brillouin zone. (c) Schematic diagrams of the AVHE for the $K$ and $-K$ carriers in the hole-doped LaBrI monolayer when the direction of the magnetic moment is along $+z$ axis. (d) Schematic diagrams of the Hall voltages for hole-doped LaBrI monolayer when the magnetic moment is along $+z$ (left plot) and $-z$ (right plot) direction, respectively. The red and blue spheres in (c) and (d) denote the spin-up and spin-down components, respectively.