Spin polarization and tunable valley degeneracy in a MoS monolayer via proximity coupling to a CrO 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 MoS monolayer via magnetic proximity coupling to an insulating antiferromagnetic CrO substrate and the gate-voltage tunability of the MoS/CrO heterojunction on the basis of first-principles calculations. Our calculations suggest that there is a large Zeeman splitting of 23.4 meV in the MoS 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 CrO 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 CrO/MoS heterojunction in nanoscale spintronics.