Control of spin and valley Hall effects in monolayer transition metal dichalcogenides by magnetic proximity effect

Monolayer transition metal dichalcogenides have strong spin-orbit coupling and broken space inversion symmetry, which enable them to be the key building blocks in realizing spin and valley-related effects. Here, we report the spin and valley Hall conductivities of monolayer transition metal dichalcogenides in the presence of the magnetic proximity effect, which is introduced by a ferromagnetic substrate. It is found that the profile and magnitude of the spin and valley Hall conductivities in monolayer transition metal dichalcogenides are different with and without magnetic exchange interactions. This difference can be attributed to the asymmetrical band structure of monolayer transition metal dichalcogenides and chemical potential-dependent interband transitions. The former comes from the fact that the magnetic proximity effect can effectively break the time reversal symmetry and thus lead to the asymmetry of the band structures between K+ and K- valleys, which causes the final changes in the spin and valley Hall conductivities. Our findings demonstrate that the magnetic proximity effect can affect the spin as well as valley Hall behaviors in monolayer transition metal dichalcogenides, and this strategy is applicable for other two-dimensional layered materials, which is promising for spintronic and valleytronic devices.