Engineering Proximity Exchange by Twisting: Reversal of Ferromagnetic and Emergence of Antiferromagnetic Dirac Bands in Graphene/Cr_{2}Ge_{2}Te_{6}.

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 (λ_{ex}^{A} and λ_{ex}^{B}) for a series of twist angles between 0° and 30°. For aligned layers (0° twist angle), the exchange coupling of graphene is the same on both sublattices, λ_{ex}^{A}≈λ_{ex}^{B}≈4  meV, while the coupling is reversed at 30° (with λ_{ex}^{A}≈λ_{ex}^{B}≈-4  meV). Remarkably, at 19.1° the induced exchange coupling becomes antiferromagnetic: λ_{ex}^{A}<0, λ_{ex}^{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.