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 MxyT 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 LiFe4O6. Additionally, the anomalous dual valley Hall effect in monolayer LiFe4O6 can be modulated by reversing the magnetization orientation. Our findings enrich the research on valley-correlated AHE in 2D materials.