Spin polarization and tunable valley degeneracy in a MoS ₂ monolayer via proximity coupling to a Cr ₂ O ₃ substrate

Introducing magnetism in two-dimensional materials is of particular importance for both fundamental research and practical applications in nanoscale spintronics. Herein, we report the lifting of valley degeneracy in a MoS₂ monolayer via magnetic proximity coupling to an insulating antiferromagnetic Cr₂O₃ substrate and the gate-voltage tunability of the MoS₂/Cr₂O₃ heterojunction on the basis of first-principles calculations. Our calculations suggest that there is a large Zeeman splitting of 23.4 meV in the MoS₂ monolayer due to strong spin-orbit coupling, corresponding to a magnetic exchange field of 100 T. Both spin and valley indices flip when the magnetic ordering of Cr₂O₃ is reversed. More interestingly, the charge transfer, magnetic moment, band gap and Schottky barrier of the heterojunction can be tuned continually by applying an external out-of-plane gate voltage, resulting in variable valley Zeeman splitting ranging from 11.3 to 34.5 meV. These findings demonstrate great potential applications of the Cr₂O₃/MoS₂ heterojunction in nanoscale spintronics.