Magnetic field induced Valley-Polarized Quantum Anomalous Hall Effects in Ferromagnetic van der Waals Heterostructures

The valley-polarized quantum anomalous Hall effect (VQAHE) attracts intensive interest since it uniquely combines valleytronics and spintronics with nontrivial band topology. Here, based on first-principles calculations and Wannier-function-based tight-binding (WFTB) model, we reveal that valley-based Hall effects and especially the VQAHE induced by the Zeeman exchange energy of magnetic fields can occur in two-dimensional (2D) ferromagnetic van der Waals heterostructures (vdWHs). The results show that considerable valley-splitting induced by the Zeeman exchange energy can drive these vdWHs generating the valley anomalous Hall effect and then the VQAHE. The chiral edge states and quantized Hall conductance are utilized to confirm the presence of VQAHE. Besides, it is also found that external electric fields (or tuning interlayer distances) can facilitate the realization of VQAHE, and thus we present a phase diagram in a broad parameter regime of magnetic fields and electric fields (or interlayer distances). Our work not only offers a class of ferromagnetic vdWHs to realize various valley-based Hall phases, but also can guide advancements for designing topological devices with spin-valley filtering effects based on the VQAHE.