Using 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 $\mathrm{CrSi}{}_2\mathrm{P}{}_4$ 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 $3d$ electrons which can also be applied to account for the ground states in other chromium-based materials. Remarkably, an 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 another avenue towards exploring monolayer materials for valleytronics.

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• Hall effect
• Magnetic order
• Phase diagrams
• Valleytronics
• 2-dimensional systems
• Noncollinear magnets
• First-principles calculations