  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. 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. Furthermore, a periodic divacancy causes a
dramatic change in the magnetic ground state of the ribbon. In the limit of
high vacancy potential, the strength of the RKKY interaction is approximately
independent of the Fermi energy.
