Valley selectivity induced by magnetic adsorbates: Triplet oxygen on monolayer MoS2

The recent discovery of ferromagnetic two-dimensional material has moved the subject of 2D magnetism into the center of interest. Besides materials with intrinsic magnetic properties, nonmagnetic 2D materials in the proximity of bulk magnets or in heterostructures have been proposed as candidates. By breaking the time-reversal symmetry the energy degeneracy is lifted and allows for an independent manipulation of different valleys in the band structure. In contrast to these systems, magnetic adsorbates allow for an easy manipulation and a huge variety of molecular magnets has already been identified. In this work we study the interaction of magnetic molecules adsorbed on the transitions metal dichalcogenide monolayer ${\mathrm{MoS}}₂$ by performing first-principles $GW$ and Bethe-Salpeter equation calculations. For the (spin-polarized) triplet ${\mathrm{O}}₂$ on ${\mathrm{MoS}}₂$ we find that both the electronic band structure close to the band edges as well as the low-energy excitons localized at different valleys obtain a small splitting which should be measurable by circular polarized light. Its size ranges up to about 10 meV and can be controlled by different coverages or by the distance dependent overlap.