Ferro-Valleytricity with In-Plane Spin Magnetization

Ferro-valleytricity that manifests spin-orbit coupling (SOC)-induced spontaneous valley polarization is generally considered to occur in two-dimensional (2D) materials with out-of-plane spin magnetization. Here, we propose a mechanism to realize SOC-induced valley polarization and ferro-valleytricity in 2D materials with in-plane spin magnetization, wherein the physics correlates to non-collinear magnetism in triangular lattice. Our model analysis provides comprehensive ingredients that allow for ferro-valleytricity with in-plane spin magnetization, revealing that mirror symmetry favors remarkable valley polarization and time-reversal-mirror joint symmetry should be excluded. Through modulating the in-plane spin magnetization offset, the SOC-induced valley polarization could be reversed. Followed by first-principles, such a mechanism is demonstrated in a multiferroic triangular lattice of single-layer W₃Cl₈. We further show that the reversal of valley polarization could also be driven by applying an electric field that modulates ferroelectricity. Our findings greatly enrich valley physics research and significantly extend the scope for material classes of ferro-valleytricity.