Spin-valley coupling in a two-dimensional VSi2N4 monolayer

Materials that integrate magnetism, miniaturization, and valley properties hold potential for spintronic and valleytronic nanodevices. Recently, ferromagnetism was reported to be able to exist in the $\mathrm{V}{\mathrm{Si}}_{2}{\mathrm{N}}_{4}$ monolayer which is half-metallic and belongs to a new kind of two-dimensional material [Hong et al., Science 369, 670 (2020)]. Using first-principles calculations and model analysis, we find that $\mathrm{V}{\mathrm{Si}}_{2}{\mathrm{N}}_{4}$ is a ferromagnetic semiconductor harboring valley-contrasting physics and a magnetic critical temperature over room temperature. By tuning magnetization orientation from in plane to out of plane, valley polarization can be generated, resulting in the anomalous valley Hall effect in $\mathrm{V}{\mathrm{Si}}_{2}{\mathrm{N}}_{4}$. Furthermore, we obtain the formula for energy splitting of valleys and adopt a tight-binding model for $\mathrm{V}{\mathrm{Si}}_{2}{\mathrm{N}}_{4}$, which elucidates the physical mechanism of spin-valley coupling. More interestingly, under 4% tensile strain, the intrinsic magnetic anisotropy of $\mathrm{V}{\mathrm{Si}}_{2}{\mathrm{N}}_{4}$ becomes out of plane, and spontaneous valley polarization is achieved. Our results highlight that $\mathrm{V}{\mathrm{Si}}_{2}{\mathrm{N}}_{4}$ is a good candidate for spintronic and valleytronic applications.