  Valley, as a new degree of freedom for electrons, has drawn considerable
attention due to its significant potential for encoding and storing
information. Lifting the energy degeneracy to achieve valley polarization is
necessary for realizing valleytronic devices. Here, on the basis of
first-principles calculations, we show that single-layer FeCl2 exhibits a large
spontaneous valley polarization (~101 meV) arising from the broken
time-reversal symmetry and spin-orbital coupling, which can be continuously
tuned by varying the direction of magnetic crystalline. By employing the
perturbation theory, the underlying physical mechanism is unveiled. Moreover,
the coupling between valley degree of freedom and ferromagnetic order could
generate a spin- and valley-polarized anomalous Hall current in the presence of
the in-plane electric field, facilitating its experimental exploration and
practical applications.
