  Lifting the valley degeneracy of monolayer transition metal dichalcogenides
(TMD) would allow versatile control of the valley degree of freedom. We report
a giant valley exciton splitting of 18 meV/T for monolayer WS2, using the
proximity effect from a ferromagnetic EuS substrate, which is enhanced by
nearly two orders of magnitude from the 0.2 meV/T obtained by an external
magnetic field. More interestingly, a sign reversal of the valley exciton
splitting is observed as compared to that of WSe2 on EuS. Using first
principles calculations, we investigate the complex behavior of exchange
interactions between TMDs and EuS, that is qualitatively different from the
Zeeman effect. The sign reversal is attributed to competing ferromagnetic (FM)
and antiferromagnetic (AFM) exchange interactions for Eu- and S- terminated EuS
surface sites. They act differently on the conduction and valence bands of WS2
compared to WSe2. Tuning the sign and magnitude of the valley exciton splitting
offers opportunities for versatile control of valley pseudospin for quantum
information processing.
