  The spin-orbit coupling (SOC) effect has been known to be profound in
monolayer pristine transition metal dichalcogenides (TMDs). Here we show that
point defects, which are omnipresent in the TMD membranes, exhibit even
stronger SOC effects and change the physics of the host materials drastically.
In this Article we chose the representative monolayer WS\sub{2} slabs from the
TMD family together with seven typical types of point defects including
monovacancies, interstitials, and antisites. We calculated the formation
energies of these defects, and studied the effect of spin-orbit coupling (SOC)
on the corresponding defect states. We found that the S monovacancy (V\sub{S} )
and S interstitial (adatom) have the lowest formation energies. In the case of
V\sub{S} and both of the W\sub{S and W\sub{S2} antisites, the defect states
exhibit giant splitting up to 296 meV when SOC is considered. Depending on the
relative position of the defect state with respect to the conduction band
minimum (CBM), the hybrid functional HSE will either increase the splitting by
up to 60 meV (far from CBM), or decrease the splitting by up to 57 meV (close
to CBM). Furthermore, we found that both the W\sub{S} and W\sub{S2} antisites
possess a magnetic moment of 2 $\mu_{B}$ localized at the antisite W atom and
the neighboring W atoms. All these findings provide new insights in the defect
behavior under SOC point to new possibilities for spintronics applications for
TMDs.
