We study RKKY interactions between local magnetic moments for both doped and undoped graphene. In the former case interactions for moments located on definite sublattices fall off as $1/R^2$, whereas for those placed at interstitial sites they decay as $1/R^3$. The interactions are primarily (anti)ferromagnetic for moments on (opposite) equivalent sublattices, suggesting that at low temperature dilute magnetic moments embedded in graphene can order into a state analogous to that of a dilute antiferromagnet. In the undoped case we find no net magnetic moment in the ground state, and demonstrate numerically this effect for ribbons, suggesting the possibility of an unusual spin-transfer device.

• Received 9 May 2007

DOI:https://doi.org/10.1103/PhysRevLett.99.116802