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 W