Anisotropic RKKY interaction in doped magnetic ordered bilayer graphene

We study exchange interaction between two magnetic impurities, i.e. (the Ruderman-Kittel-Kasuya-Yosida [RKKY]), in doped biased bilayer graphene by directly computing Green's function within full band method. Tight binding model Hamiltonian in the presence of magnetic long range ordering has been applied to describe electron dynamics. RKKY interaction as a function of distance between localized moments has been analyzed. It has been shown that a field induced ferromagnetic ordering along the z-axis mediates an anisotropic interaction which corresponds to a XXZ model interaction between two magnetic moments. Such field induced ferromagnetic ordering is due to external magnetic field. The exchange interaction along arbitrary direction between two magnetic moments, has been obtained using the static spin susceptibilities of gapped graphene structure. 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 the chemical potential impacts the spatial behavior of RKKY interaction. Moreover bias voltage effects on RKKY interaction have been investigated for both stacking types of bilayer graphene.