Engineering Proximity Exchange by Twisting: Reversal of Ferromagnetic and Emergence of Antiferromagnetic Dirac Bands in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mtext>Graphene/</mml:mtext><mml:msub><mml:mrow><mml:mi>Cr</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:msub><mml:mrow><mml:mi>Ge</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>Te</mml:mi></mml:mrow><mml:mrow><mml:mn>6</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:mrow></mml:math>
Klaus Zollner, Jaroslav Fabian
Abstract
We investigate the twist-angle and gate dependence of the proximity exchange coupling in twisted graphene on monolayer ${\mathrm{Cr}}_{2}{\mathrm{Ge}}_{2}{\mathrm{Te}}_{6}$ from first principles. The proximitized Dirac band dispersions of graphene are fitted to a model Hamiltonian, yielding effective sublattice-resolved proximity-induced exchange parameters (${\ensuremath{\lambda}}_{\mathrm{ex}}^{A}$ and ${\ensuremath{\lambda}}_{\mathrm{ex}}^{B}$) for a series of twist angles between 0\ifmmode^\circ\else\textdegree\fi{} and 30\ifmmode^\circ\else\textdegree\fi{}. For aligned layers (0\ifmmode^\circ\else\textdegree\fi{} twist angle), the exchange coupling of graphene is the same on both sublattices, ${\ensuremath{\lambda}}_{\mathrm{ex}}^{A}\ensuremath{\approx}{\ensuremath{\lambda}}_{\mathrm{ex}}^{B}\ensuremath{\approx}4\text{ }\text{ }\mathrm{meV}$, while the coupling is reversed at 30\ifmmode^\circ\else\textdegree\fi{} (with ${\ensuremath{\lambda}}_{\mathrm{ex}}^{A}\ensuremath{\approx}{\ensuremath{\lambda}}_{\mathrm{ex}}^{B}\ensuremath{\approx}\ensuremath{-}4\text{ }\text{ }\mathrm{meV}$). Remarkably, at 19.1\ifmmode^\circ\else\textdegree\fi{} the induced exchange coupling becomes antiferromagnetic: ${\ensuremath{\lambda}}_{\mathrm{ex}}^{A}<0$, ${\ensuremath{\lambda}}_{\mathrm{ex}}^{B}>0$. 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 $\text{graphene}/{\mathrm{Cr}}_{2}{\mathrm{Ge}}_{2}{\mathrm{Te}}_{6}$ bilayers a versatile platform for realizing topological phases and for spintronics applications.