Spin-valley coupling in a two-dimensional <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi mathvariant="normal">V</mml:mi><mml:msub><mml:mi>Si</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">N</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:mrow></mml:math> monolayer
Qirui Cui, Yingmei Zhu, Jinghua Liang, Ping Cui, Hongxin Yang
Abstract
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.