Valley polarization transition driven by biaxial strain in Janus GdClF monolayer

The valley degree of freedom of carriers in crystals is useful to process information and perform logic operations, and it is a key factor for valley application to realize valley polarization. Here, we propose a model that the valley polarization transition at different valley points (-K and K points) is produced by biaxial strain. Using first-principles calculations, we illustrate our idea with a concrete example of a Janus GdClF monolayer. The predicted GdClF monolayer is dynamically, mechanically and thermally stable, and is a ferromagnetic (FM) semiconductor with perpendicular magnetic anisotropy (PMA), valence band maximum (VBM) at valley points and a high Curie temperature (T_C). Due to its intrinsic ferromagnetism and spin-orbit coupling (SOC), a spontaneous valley polarization will be induced, but the valley splitting is only -3.1 meV, which provides an opportunity to achieve valley polarization transition at different valley points by strain. In the considered strain range (a/a₀: 0.94-1.06), the strained GdClF monolayer always has an energy bandgap, strong FM coupling and PMA. The compressive strain is in favour of -K valley polarization, while the tensile strain is favorable for K valley polarization. The corresponding valley splittings at 0.96 and 1.04 strains are -44.5 meV and 29.4 meV, respectively, which are higher than the thermal energy at room temperature (25 meV). Due to its special Janus structure, both in-plane and out-of-plane piezoelectric polarizations can be observed. It is found that the direction of in-plane piezoelectric polarization can be overturned by strain, and the d₁₁ values at 0.96 and 1.04 strains are -1.37 pm V^-1 and 2.05 pm V^-1, respectively. Our work paves the way to design ferrovalley materials for application in multifunctional valleytronic and piezoelectric devices by strain.