Spin-dependent Dirac electrons and valley polarization in the ferromagnetic stanene/CrI3 van der Waals heterostructure

Realization and regulation of valley polarization is a core issue in the valleytronics fields. Here, through first-principles calculations, we find that the valley polarization (up to 39.6 meV) can be realized in stanene, by stacking it on a monolayer ferromagnetic insulator $\mathrm{Cr}{\mathrm{I}}_{3}$, forming the ferromagnetic stanene/$\mathrm{Cr}{\mathrm{I}}_{3}$ van der Waals heterostructure. The heterostructure possesses a magneto band-structure effect, whereby the spin orientation of Cr atoms can significantly influence valley polarization. When the spin orientation of Cr atoms is parallel (perpendicular) to the $c$ axis, the largest (smallest) valley polarization is achieved with the value of 71.7 meV (1.7 meV). Additionally, the spin-polarized Dirac electrons and hole doping are induced in stanene due to the magnetic proximity effect, and the Dirac cone of stanene is opened with the value of 187.6 meV. These results indicate that the stanene/$\mathrm{Cr}{\mathrm{I}}_{3}$ heterostructure is very promising to be applied in future spintronics and valleytronics.