  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 ferrovalley materials is
mainly focused on inorganic systems, severely suffering from in-plane
magnetization. Here, we alternatively show by kp model analysis and
high-throughput first-principles calculations that ideal spontaneous valley
polarization is present in 2D organometallic lattice. We explore the design
principle for organic 2D ferrovalley materials composed of (quasi-)planer
molecules and transition-metal atoms in hexagonal lattice, and identify twelve
promising candidates. These systems have a ferromagnetic or antiferromagnetic
semiconducting state, and importantly they exhibit robust out-of-plane
magnetization. The interplay between spin and valley, together with strong
spin-orbit coupling of transition-metal atoms, guarantee the spontaneous valley
polarization in these systems, facilitating the anomalous valley Hall effect.
Our findings significantly broaden the scientific and technological impact of
ferrovalley physics.
