Spontaneous valley polarization in two-dimensional organometallic lattices

Two-dimensional (2D) ferrovalley materials that exhibit spontaneous valley polarization are both fundamentally intriguing and practically appealing to be used in valleytronic devices. Usually, the research on 2D is mainly focused inorganic systems, severely suffering from in-plane magnetization. Here, we alternatively show by k\ifmmode\cdot\else\textperiodcentered\fi{}p model analysis high-throughput first-principles calculations ideal present organometallic lattice. We explore design principle for organic composed of (quasi-)planer molecules transition-metal atoms hexagonal lattice, identify 12 promising candidates. These systems have a ferromagnetic or antiferromagnetic semiconducting state, importantly they robust out-of-plane The interplay between spin valley, together with strong spin-orbit coupling atoms, guarantee these facilitating anomalous Hall effect. Our findings significantly broaden scientific technological impact physics.