Indirect exchange interaction between magnetic impurities in a gapped graphene structure

We study exchange interaction between two magnetic impurities in doped gapped graphene (the Ruderman-Kittel-Kasuya-Yosida [RKKY]) interaction by directly computing Green’s function beyond Dirac approximation. 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 magnetic ordering along the z-axis mediates two different interactions for spin directions which corresponds to a XXZ model interaction between two magnetic moments. 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 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 gap parameter effects on RKKY interaction have been investigated in details.