Importance of electron-electron interactions in the RKKY coupling in graphene

We show that the carrier-mediated exchange interaction, the so-called Ruderman-Kittel-Kasuya-Yoshida (RKKY) coupling, between two magnetic impurity moments in graphene is significantly modified in the presence of electron-electron (el-el) interactions. Within the mean-field approximation of the Hubbard-U model we show that for increasing el-el interactions the oscillations disappear and the power-law decay becomes more long ranged. In zigzag graphene nanoribbons the effects are even more striking with any finite U rendering the RKKY coupling distance independent. Since the RKKY coupling is directly proportional to the magnetic susceptibility, these results are important for any physical property of graphene related to magnetism. Comparing our mean-field results with first-principles results we also extract a surprisingly large value of U indicating that graphene is very close to an antiferromagnetic instability.