Monolayer <i>h</i>-TiX: Intrinsic ferrovalley materials in a honeycomb lattice

Two-dimensional robust ferromagnetic semiconductors with intrinsic valley polarization have tremendous potential for applications in next-generation nano-information storage devices. Based on first-principles calculations, we predict that a novel honeycomb family of monolayer h-TiX (X = N, P, As, Sb, and Bi ) is intrinsic ferrovalley materials. The ferromagnetism of monolayer h-TiX is attributed to the dz2 orbitals of Ti atoms, exhibiting a magnetic direction tilted out of the plane. Strain engineering can adjust magnetic properties, including variations in Curie temperature, which primarily respond sensitively to the strain-induced changes in exchange coupling coefficient J to strain. Because of the absence of time-reversal symmetry and inversion symmetry, spontaneous valley polarization phenomenon can be observed in monolayer h-TiN, which can be explained using perturbation theory of spin–orbit coupling. Both the ferromagnetic semiconductors and spontaneous valley polarization can be achieved in h-TiN, which offer a promising candidate material and foundational research value for spintronic devices and valleytronic devices.