Anomalous dual valley Hall effect in the two-dimensional ferromagnetic honeycomb lattice

The long-sought valley-correlated anomalous Hall effect (AHE) that is manifested in two-dimensional (2D) magnets is typically considered to occur in ferromagnetic triangular and antiferromagnetic honeycomb lattices. Here, we theoretically predict the realizability of valley-correlated AHE in 2D ferromagnetic honeycomb lattice, in which the magnetic triangular sublattices are connected by ${M}_{xy}T$ symmetry, developing the concept of anomalous dual valley Hall effect. Our model analysis provides a comprehensive understanding of this phenomenon, unveiling that the antiparallel arrangement of the two trigons formed by magnetic atoms is required. Through performing first-principles calculations, such mechanism for realizing anomalous dual valley Hall effect is further demonstrated in monolayer $\mathrm{Li}{\mathrm{Fe}}_{4}{\mathrm{O}}_{6}$. Additionally, the anomalous dual valley Hall effect in monolayer $\mathrm{Li}{\mathrm{Fe}}_{4}{\mathrm{O}}_{6}$ can be modulated by reversing the magnetization orientation. Our findings enrich the research on valley-correlated AHE in 2D materials.