Two-dimensional Janus 1T-$\mathrm{Cr}\mathit{XY}$ ($X=\mathrm{S}$, Se, Te, $Y=\mathrm{F}$, Cl, Br, I): Multifunctional ferromagnetic semiconductor with large valley and piezoelectric polarizations

Ferrovalley, spin, and piezoelectric polarizations are novel characteristics for electronic materials, and so far, there are few reports that these properties coexist in a single system. By first-principles calculations, we predict a series of highly stable intrinsic ferrovalley materials, i.e., single layer $\mathrm{Cr}\mathit{XY}$ ($X=\mathrm{S}$, Se, Te, $Y=\mathrm{F}$, Cl, Br, I) with large valley polarization up 76.1 meV and appropriate Curie temperature higher than room temperature. For CrSF, the large bandgap of spin-up (spin-down) is as high as 1.96 eV (3.11 eV), which is beneficial for generating 100% spin polarized carriers by optical excitation or electrical gating. The quasianomalous valley Hall effect with valley contrast properties can be induced by compressive strain in CrSI and CrTeX ($X=\mathrm{Cl}$, Br, I). Meanwhile, the large in-plane $(-5.78-3.54\mathrm{pm}/\mathrm{V})$ and outside plane piezoelectric polarization ($-5.03-2.53\mathrm{pm}/\mathrm{V}$) of $\mathrm{Cr}\mathit{XY}$ are higher than most reported two-dimensional materials. Our work provides a pathway for a wide variety of applications in nanoelectronics, spintronics, valleytronics, piezoelectrics, and other demanding areas.

Figure 1

(a) Top and (b) side views of the SL $\mathrm{Cr}\mathit{XY}$. The unit cell is marked by the red dashed lines. (c) The differential charge densities of SL CrSBr, and the red number represents the result of transferred charges. (d) The schematic diagram of the first Brillouin zone (BZ). (e) AFM1, (f) AFM2, and (g) AFM3 states of crystal structures, and the orange (red) arrow shows the direction of spin-up (spin-down). (h) Planar average electrostatic potential energy, and the slope of the red dashed line corresponds to the intrinsic electric field $\left(\mathrm{eV}/\AA \right)$ of SL CrSBr. (i) The phonon dispersion of SL CrSBr. (j) The fluctuation of total energy and snapshots of geometric structures for SL CrSBr at 300 K.

Figure 2

(a) Dependence of MAE on the polar angle ($\theta$) for the SL CrSBr with the direction of magnetization lying on $xy, xz,$ and $yz$ planes as well as (b) the whole space. (c) The temperature-dependent magnetic moments and magnetic susceptibility of SL CrSBr. (d) Dependence of MAE on the polar angle ($\theta$) for the SL CrSeCl with the direction of magnetization lying on $xy, xz,$ and $yz$ planes as well as (e) the whole space. (f) The temperature-dependent magnetic moments and magnetic susceptibility of SL CrSeCl.

Figure 3

The electronic band structures of SL CrSCl without SOC (a), (b) and (c) with SOC for the magnetic moment of Cr atom along $+z$ and $-z$. The electronic band structures of SL CrTeCl without SOC (d), (e), and (f) with SOC for the magnetic moment of Cr atom along $+z$ and $-z$. The red and purple lines represent the spin-up and spin-down states, respectively. The Fermi level is set to zero.

Figure 4

The projected PBE electronic band structures for the (a) CrSF, (b) CrSI, (c) CrSeCl, and (d) CrTeF with considering SOC.

Figure 5

(a) Contour map of Berry curvatures in the $k$ space for SL CrSI. Diagrams of regulating Fermi energy levels in the +z (b) and −z (c) directions of magnetization under electron doping. (d) The Berry curvatures $\mathrm{\Omega }\left(k\right)$ of SL CrSI as the curve along the high-symmetry path with the unit of $\mathrm{Boh}{\mathrm{r}}^2$. Diagram of the AVHE in SL CrSI when electrons are doped and in-plane electric field are applied in the −z (e) and +z (f) directions of magnetization. The purple and red balls with an arrow are spin-down and spin-up electrons, respectively.

Figure 6

(a) The illustration of band structure of quasiHVM with Fermi energy levels penetrating the K valley. (b) The band structure of SL CrTeBr under −5% strain. (c) Schematic illustration of quasiAVHE for SL CrTeBr. (d) The illustration of of band structure of quasiHVM with Fermi energy levels penetrating the K' Valley. (e) The band structure of SL CrSI under −6% strain. (f) Schematic illustration of quasiAVHE for SL CrSI.

Figure 7

The piezoelectric strain coefficients $d_{31}$ of SL $\mathrm{Cr}\mathit{XY}$ ($X=\mathrm{S}$, Se, Te, and $Y=\mathrm{Cl}$, Br, I) and the ED between the X and Y atoms. The value of ED is given in the chart. in the bar chart.