  We present a first principles investigation of the electronic properties of
monolayer WS$_2$ coated with an overlayer of Fe. Our ab initio calculations
reveal that the system is a half-metallic ferromagnet with a gap of $\sim 1$ eV
for the majority spin channel. Furthermore, the combined effect of
time-reversal symmetry breaking due to the magnetic Fe overlayer and the large
spin-orbit coupling induced by W gives rise to non-degenerate K and K$'$
valleys. This has a tremendous impact on the excited state properties induced
by externally applied circularly polarized light. Our analysis demonstrates
that the latter induces a singular hot spot structure of the transition
probability around the K and K$'$ valleys for right and left circular
polarization, respectively. We trace back the emergence of this remarkable
effect to the strong momentum dependent spin-noncollinearity of the valence
band involved. As a main consequence, a strong valley-selective magnetic
circular dichroism is obtained, making this system a prime candidate for
spintronics and photonics applications.
