Two-dimensional Janus 1T-CrXY (X=S, Se, Te, Y=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 $(\ensuremath{-}5.78\ensuremath{-}3.54\phantom{\rule{0.16em}{0ex}}\mathrm{pm}/\mathrm{V})$ and outside plane piezoelectric polarization ($\ensuremath{-}5.03\ensuremath{-}2.53\phantom{\rule{0.16em}{0ex}}\mathrm{pm}/\mathrm{V}$) 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.