Spin and valley splittings in Janus monolayer WSSe on a MnO(111) surface: Large effective Zeeman field and opening of a helical gap

Abstract

In this research, we demonstrate the large spin and valley splittings in Janus monolayer WSSe brought by the interaction with a magnetic substrate. The MnO(111) substrate plays the role of ferromagnet since the importance lies in the magnetism of the surface Mn atoms. The responses of both in-plane and out-of-plane spin splittings with the magnetic direction of the substrate are investigated. It is indicated that a large valley splitting of about 410 meV at the $K$ and ${K}^{\ensuremath{'}}$ points can be produced by the magnetic substrate, which is positively correlated with the vertical magnetic moments of the surface Mn atoms. In addition, a helical gap is opened and the Rashba spin-orbit coupling induced dispersion relation is also significantly modified under the action of proximity coupling with the substrate. Through the effective Hamiltonian method, the derived effective Zeeman fields from the $K/{K}^{\ensuremath{'}}$ point and the $\mathrm{\ensuremath{\Gamma}}$ point are greatly different, due to the combination with other factors, such as the difference of the $g$ factor, the existence of charge transfer, or electrostatic interaction with the substrate. The greatly manipulated asymmetric electronic structure and spin/valley splittings can be realized in the spin- and valley-polarized transmission, which are of some significance for the realization of spintronic and valleytronic devices using magnetic substrates and Janus two-dimensional materials.