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We investigate the effect of vacancy defects on the electronic and magnetic properties of zigzag graphene nanoribbons (zGNRs) by making use of the Green's function formalism in combination with the tight-binding Hamiltonian. The evolution of the indirect exchange coupling, known as Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, including single, double, and multiple 5-8-5 divacancy defects is explained. Our numerical calculations show that the changes in the electronic structure and the exchange coupling of zGNRs depend significantly on the location of the divacancy defects with respect to the ribbon edges and on the number of the divacancy defects.
Introducing vacancies into zGNR changes the spatial variation of the RKKY interaction, particularly those magnetic moments located around the vacancies.
In the case both the impurities are located on the edge, the magnitude of the exchange coupling is several orders of magnitude strengthen that result when they are placed on the interior of the nanoribbon. We show that different values of the vacancy potential in the same zigzag nanoribbon give rise to different changes in the electronic and magnetic properties of defected zGNRs. Furthermore, a periodic divacancy causes a dramatic change in the magnetic ground state of the ribbon. A strong perturbation of the regular RKKY oscillations appears in the spatial profile of the RKKY coupling when the magnetic impurities approach a divacancy. In the limit of high vacancy potential, the strength of the RKKY interaction is approximately independent of the Fermi energy
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