  By using the first-principles calculations and model analyses, we found that
the combination of defected tungsten disulfide monolayer and sparse manganese
adsorption may give a KK` valley spin splitting up to 210 meV. This system also
has a tunable magnetic anisotropy energy, a clean band gap, and an appropriate
band alignment, with the Fermi level sitting right above the top of valence
bands at the K-valleys. Therefore, it can be used for the realization of the
valley-polarized anomalous Hall effect and for the exploration of other valley
related physics without using optical methods. A protective environment can be
formed by covering it with a hexagonal BN layer, without much disturbance to
the benign properties of Mn/WS2.
