Anomalous valley Hall effect in monolayer chromium-based triple-Q magnets

Abstract: Using the density functional theory calculations, we predict that several monolayer chromium-based materials exhibit a triple-Q tetrahedral magnetic insulating ground state. By studying the effect of biaxial strain on monolayer CrSi$\rm{_2}$P$\rm{_4}$ under various on-site Coulomb interactions, we reveal that this magnetic insulating state, sandwiched between the itinerant $120^{\circ}$ coplanar noncollinear antiferromagnetic and ferromagnetic states, originates from the competition between antiferromagnetic exchange and double exchange interactions of Cr 3$d$ electrons which can also be applied to account for the ground states in other chromium-based materials. Remarkably, anomalous valley Hall effect with giant valley splitting is discovered in the magnetic states of these inversion-asymmetric systems without requiring spin-orbit coupling or net magnetization. Our findings open a new avenue towards exploring monolayer materials for valleytronics.