Strong manipulation of the valley splitting upon twisting and gating in MoSe${}_2$/CrI${}_3$ and WSe${}_2$/CrI${}_3$ van der Waals heterostructures

Abstract

We investigate the twist-angle and gate dependence of the proximity-induced exchange coupling in the monolayer transition-metal dichalcogenides (TMDCs) MoSe${}_2$ and WSe${}_2$ due to the vdW coupling to the ferromagnetic semiconductor CrI${}_3$, from first-principles calculations. A model Hamiltonian, that captures the relevant band edges at the $K/K^{\prime }$ valleys of the proximitized TMDCs, is employed to quantify the proximity-induced exchange. Upon twisting from 0° to 30°, we find a transition of the TMDC valence band (VB) edge exchange splitting from about $-2$ to $2$ meV, while the conduction band (CB) edge exchange splitting remains nearly unchanged at around $-3$ meV. For the VB of WSe${}_2$ (MoSe${}_2$) on CrI${}_3$, the exchange coupling changes sign at around 8° (16°). We find that even at the angles with almost zero spin splittings of the VB, the real-space spin polarization profile of holes at the band edge is highly non-uniform, with alternating spin up and spin down orbitals. Furthermore, a giant tunability of the proximity-induced exchange coupling is provided by a transverse electric field of a few V/nm. We complement our \textit{ab initio} results by calculating the excitonic valley splitting to provide experimentally verifiable optical signatures of the proximity exchange. Specifically, we predict that the valley splitting increases almost linearly as a function of the twist angle. Furthermore, the proximity exchange is highly tunable by gating, allowing to tailor the valley splitting in the range of 0 to 12 meV in WSe${}_2$/CrI${}_3$, which is equivalent to external magnetic fields of up to about 60 Tesla. Our results highlight the important impact of the twist angle and gating when employing magnetic vdW heterostructures in experimental geometries.

16 pages, 7 figures, 2 tables + Supplemental Material

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• Magnetic Anisotropy in Two-dimensional van der Waals Magnetic Materials and Their Heterostructures: Importance, Mechanisms, and Opportunities
• Signatures of electric field and layer separation effects on the spin-valley physics of MoSe${}_2$/WSe${}_2$ heterobilayers: from energy bands to dipolar excitons
• Ultralong 100 ns Spin Relaxation Time in Graphite at Room Temperature
• Proximity-enhanced valley Zeeman splitting at the WS${}_2$/graphene interface
• Multidimensional sensing of proximity magnetic fields via intrinsic activation of dark excitons in WSe${}_2$/CrCl${}_3$ heterostructure
• Transport Signatures of Radial Rashba Spin-Orbit Coupling at Ferromagnet/Superconductor Interfaces
• Raman tensor for two-dimensional massive Dirac fermions
• Current-induced spin-orbit torque on the surface of a transition metal dichalcogenide connected to a two-dimensional ferromagnet CrI${}_3$: Effects of twisting and gating