Engineering Proximity Exchange by Twisting: Reversal of Ferromagnetic and Emergence of Antiferromagnetic Dirac Bands in Graphene/Cr${}_2$Ge${}_2$Te${}_6$

Abstract

We investigate the twist-angle and gate dependence of the proximity exchange coupling in twisted graphene on monolayer Cr${}_2$Ge${}_2$Te${}_6$ from first principles. The proximitized Dirac band dispersions of graphene are fitted to a model Hamiltonian, yielding effective sublattice-resolved proximity-induced exchange parameters (${\lambda }_{\text{ex}}^{\text{A}}$ and ${\lambda }_{\text{ex}}^{\text{B}}$) for a series of twist angles between 0${}^{\circ }$ and 30${}^{\circ }$. For aligned layers (0${}^{\circ }$ twist angle), the exchange coupling of graphene is the same on both sublattices, ${\lambda }_{\text{ex}}^{\text{A}}\approx {\lambda }_{\text{ex}}^{\text{B}}\approx 4$ meV, while the coupling is reversed at 30${}^{\circ }$ (with ${\lambda }_{\text{ex}}^{\text{A}}\approx {\lambda }_{\text{ex}}^{\text{B}}\approx -4$ meV). Remarkably, at 19.1${}^{\circ }$ the induced exchange coupling becomes antiferromagnetic: ${\lambda }_{\text{ex}}^{\text{A}}<0,{\lambda }_{\text{ex}}^{\text{B}}>0$. Further tuning is provided by a transverse electric field and the interlayer distance. The predicted proximity magnetization reversal and emergence of an antiferromagnetic Dirac dispersion make twisted graphene/Cr${}_2$Ge${}_2$Te${}_6$ bilayers a versatile platform for realizing topological phases and for spintronics applications.

9 pages, 5 figures + Supplemental Material

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