  A form of an indirect Ruderman-Kittel-Kasuya-Yosida (RKKY)-like coupling
between magnetic on-site impurities in armchair graphene nanoribbons is studied
theoretically. The calculations are based on a tight-binding model for a finite
nanoribbon system with periodic boundary conditions. A pronounced
Friedel-oscillation-like dependence of the coupling magnitude on the impurity
position within the nanoribbon resulting from quantum size effects is found and
investigated. In particular, the distance dependence of coupling is analysed.
For semiconducting nanoribbons, this dependence is exponential-like, resembling
the Bloembergen-Rowland interaction. In particular, for metallic nanoribbons,
interesting behaviour is found for finite length systems, in which zero-energy
states make an important contribution to the interaction. In such situation,
the coupling decay with the distance can be then substantially slower.

Mesoscale and Nanoscale Physics;Materials Science;Strongly Correlated Electrons