  The indirect exchange interaction is one of the key factors in determining
the overall alignment of magnetic impurities embedded in metallic host
materials. In this work we examine the range of this interaction in
magnetically-doped graphene systems in the presence of armchair edges using a
combination of analytical and numerical Green function (GF) approaches. We
consider both a semi-infinite sheet of graphene with a single armchair edge,
and also quasi-one-dimensional armchair edged graphene nanoribbons (GNRs).
While we find signals of the bulk decay rate in semi-infinite graphene and
signals of the expected one-dimensional decay rate in GNRs, we also find an
unusually rapid decay for certain instances in both, which manifests itself
whenever the impurities are located at sites which are a multiple of three
atoms from the edge. This decay behavior emerges from both the analytic and
numerical calculations, and the result for semi-infinite graphene can be
interpreted as an intermediate case between ribbon and bulk systems.

Mesoscale and Nanoscale Physics