▎ 摘　　要

We study the indirect exchange interaction, named Ruderman-Kittel-Kasuya-Yosida (RKKY) coupling, between localized magnetic impurities in graphene nanoflakes with zig-zag edges in the presence of the Rashba spin-orbit interaction (RSOI). We calculate the isotropic and anisotropic RKKY amplitudes by utilizing the tight-binding (TB) model. The RSOI, as a gate tunable variable, is responsible for changes of the RKKY amplitude. We conclude that there is not any switching of the magnetic order (from ferroto antiferro-magnetic and vice versa) in such a system through the RSOI. The dependence of the RKKY amplitude on the positions of the magnetic impurities and the size of the system is studied. The symmetry breaking, which can occur due to the Rashba interaction, leads to spatial anisotropy in the RKKY amplitude and manifests as collinear and noncollinear terms. Our results show the possibility of control and manipulation of spin correlations in carbon spin-based nanodevices.