Staggered potential and spin polarization effects on RKKY interaction in armchair graphene nanoribbon

Indirect exchange interaction between two magnetic external atoms, named by Ruderman-Kittle-Kasuya-Yosida (RKKY) interaction, has been presented in the staggered armchair graphene nanoribbon. We have studied RKKY interaction as a function of distance between localized moments. 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. The static spin susceptibility components of armchair graphene nanoribbon have been calculated to find exchange interaction between arbitrary components of magnetic moments. We have exploited Green's function approach in order to calculate spin susceptibility components of electronic gas in nanoribbon structure in the context of tight binding model Hamiltonian. The effects of parameter and ribbon width on the dependence of exchange interaction on distance between moments are investigated. Our results show the spin polarization along perpendicular to the plane leads to anisotropic behavior for exchange interaction between the two magnetic moments. In other words the spatial behavior of RKKY interaction between longitudinal components of magnetic moments is different from that of transverse components.