Anisotropic RKKY interaction in spin-polarized graphene

Abstract

We study the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in the presence of spin polarized two-dimensional Dirac fermions. We show that an externally applied spin polarization along the $z$ axis mediates an anisotropic interaction which corresponds to an $XXZ$ model interaction between two magnetic moments. For undoped graphene, while the $x$ part of interaction keeps its constant ferromagnetic sign, its $z$ part oscillates with the distance $R$ of magnetic impurities. A finite doping causes both parts of the interaction to oscillate with $R$. We explore a beating pattern of oscillations of the RKKY interaction along armchair and zigzag lattice directions, which occurs for some certain values of the chemical potential. The two characteristic periods of the beating are determined by inverse of the difference and the sum of the chemical potential and the spin polarization.