Tunable valley splitting in two-dimensional CrI3/MSi2P4(M=Mo, W) heterostructures: Interlayer coupling effects

Valleytronics has become an emerging field for both theoretical and experimental research. Based on first-principles calculations, we demonstrate that the spin valley coupling and valley splitting properties of the $\mathrm{Mo}/{\mathrm{WSi}}_{2}{\mathrm{P}}_{4}$ monolayers can be modulated by using the two-dimensional ferromagnetic ${\mathrm{CrI}}_{3}$ semiconductor via the magnetic proximity effect. We show that the ${\mathrm{CrI}}_{3}/{\mathrm{MoSi}}_{2}{\mathrm{P}}_{4}\phantom{\rule{4pt}{0ex}}({\mathrm{CrI}}_{3}/{\mathrm{WSi}}_{2}{\mathrm{P}}_{4})$ heterostructures are thermally stable and exhibit type-II band alignment at room temperature, leading to their possible applications for optoelectronic devices at ambient conditions. Moreover, we estimate the Curie temperature of the ${\mathrm{CrI}}_{3}/{\mathrm{MoSi}}_{2}{\mathrm{P}}_{4}\phantom{\rule{4pt}{0ex}}({\mathrm{CrI}}_{3}/{\mathrm{WSi}}_{2}{\mathrm{P}}_{4})$ heterostructures and find that both valley splitting and valley-contrasting transport properties are expected to be enhanced below Curie temperature. Meanwhile, the valley polarization can be tuned by changing the magnetization direction and layer spacing. Most importantly, due to the influence of the Si-P sublayer, the valley-related properties of the ${\mathrm{CrI}}_{3}/{\mathrm{MoSi}}_{2}{\mathrm{P}}_{4}\phantom{\rule{4pt}{0ex}}({\mathrm{CrI}}_{3}/{\mathrm{WSi}}_{2}{\mathrm{P}}_{4})$ heterostructures are predicted to be quite robust. The calculated Berry curvature and circular polarization indicate that the ${\mathrm{CrI}}_{3}/{\mathrm{MoSi}}_{2}{\mathrm{P}}_{4}\phantom{\rule{4pt}{0ex}}({\mathrm{CrI}}_{3}/{\mathrm{WSi}}_{2}{\mathrm{P}}_{4})$ heterostructures can achieve the valley/spin Hall effect. Our research provides a comprehensive understanding of valley splitting in ${MA}_{2}{Z}_{4}$-based heterostructures.