The magnetic proximity effect at the MoS₂/CrI₃interface

The vicinity to a two-dimensional magnetic material provides a simple and effective way to break the valley degeneracy of transition-metal dichalcogenides because of the magnetic proximity effect. Based on first-principles calculations, we study the band structure of a MoS₂/CrI₃van der Waals heterostructure and its manipulation by vertical electric fields. A huge valley splitting of about 19.60 meV, equivalent to an external magnetic fields of about 89.0 T can be generated by an electric field of 0.115 V Å^-1. The electric field causes discontinuous changes in the valley splitting. The electric field drives the bands of MoS₂across those of CrI₃. At the critical electric fields, the interlayer orbital hybridization leads to the energy level repulsion and an abrupt exchange of the band index. We also study the effect of interlayer distance on the valley splitting and observe a more significant electric field modulation. This work deepens our understanding on the interfacial magnetic proximity effect as a result of the orbital hybridization across the van der Waals gap.