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We investigate the twist-angle and gate dependence of the proximity exchangecoupling in twisted graphene on monolayer Cr$_2$Ge$_2$Te$_6$ from firstprinciples. The proximitized Dirac band dispersions of graphene are fitted to amodel Hamiltonian, yielding effective sublattice-resolved proximity-inducedexchange parameters ($\lambda_{\textrm{ex}}^\textrm{A}$ and$\lambda_{\textrm{ex}}^\textrm{B}$) for a series of twist angles between0$^{\circ}$ and 30$^{\circ}$. For aligned layers (0$^{\circ}$ twist angle), theexchange coupling of graphene is the same on both sublattices,$\lambda_{\textrm{ex}}^\textrm{A} \approx \lambda_{\textrm{ex}}^\textrm{B}\approx 4$ meV, while the coupling is reversed at 30$^{\circ}$ (with$\lambda_{\textrm{ex}}^\textrm{A} \approx \lambda_{\textrm{ex}}^\textrm{B}\approx -4$ meV). Remarkably, at 19.1$^{\circ}$ the induced exchange couplingbecomes antiferromagnetic: $\lambda_{\textrm{ex}}^\textrm{A} < 0,\lambda_{\textrm{ex}}^\textrm{B} > 0$. Further tuning is provided by atransverse electric field and the interlayer distance. The predicted proximitymagnetization reversal and emergence of an antiferromagnetic Dirac dispersionmake twisted graphene/Cr$_2$Ge$_2$Te$_6$ bilayers a versatile platform forrealizing topological phases and for spintronics applications.

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