Effects of the interplay between electron-electron interaction and intrinsic spin-orbit interaction on the indirect RKKY coupling in graphene nanoflakes

The effects of electron-electron (e-e) interaction and intrinsic spin-orbit interaction (ISOI) on the maximum of the magnetization and the indirect RKKY (Ruderman-Kittel-Kasuya-Yosida) coupling between the magnetic impurities embedded in zig-zag graphene nanoflakes are investigated using the tight-binding Hamiltonian and the mean-field Hubbard model. The RKKY coupling energy values as a function of the e-e interaction strengths are plotted for different values of ISOI strength. The appearance of the e-e interaction and ISOI changes drastically the magnitude of the indirect coupling so that increasing or decreasing of the indirect coupling depends on strength of the e-e interaction and ISOI and the size of the nanoflake. The dependence of the RKKY coupling and the maximum of the magnetization on the positions of the magnetic impurities and the size of the system are studied. We find that the e-e interaction and the ISOI are responsible for changes of the magnetization along the zig-zag edges of the nanoflake.