RKKY interaction in spin polarized armchair graphene nanoribbon

We present the Ruderman-Kittle-Kasuya-Yosida (RKKY) interaction in the presence of magnetic long range ordered armchair graphene nanoribbon. RKKY interaction as a function of distance between localized moments has been analyzed. It has been shown that a magnetic ordering along the z-axis mediates an anisotropic interaction which corresponds to a XXZ model interaction between two magnetic moments. In order to calculate the exchange interaction along arbitrary direction between two magnetic moments, we should obtain the static spin susceptibilities of armchair graphene nanoribbon. The spin susceptibility components are calculated using Green's function approach for tight binding model Hamiltonian. The effects of spin polarization on the dependence of exchange interaction on distance between moments are investigated via calculating correlation function of spin density operators. Our results show that the chemical potential impacts the spatial behavior of RKKY interaction.