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Valley, as a new degree of freedom for electrons, has drawn considerableattention due to its significant potential for encoding and storinginformation. Lifting the energy degeneracy to achieve valley polarization isnecessary for realizing valleytronic devices. Here, on the basis offirst-principles calculations, we show that single-layer FeCl2 exhibits a largespontaneous valley polarization (~101 meV) arising from the brokentime-reversal symmetry and spin-orbital coupling, which can be continuouslytuned by varying the direction of magnetic crystalline. By employing theperturbation theory, the underlying physical mechanism is unveiled. Moreover,the coupling between valley degree of freedom and ferromagnetic order couldgenerate a spin- and valley-polarized anomalous Hall current in the presence ofthe in-plane electric field, facilitating its experimental exploration andpractical applications.

Intrinsic Valley Polarization and Anomalous Valley Hall Effect in Single-Layer 2H-FeCl2