| Summary: | Magnetically-doped graphene systems are potential candidates for application in future spintronic devices. A key step is to understand the pairwise interactions between magnetic impurities embedded in graphene that are mediated by the graphene conduction electrons. A large number of studies have been undertaken to investigate the indirect exchange, or RKKY (Ruderman-Kittel-Kasuya-Yosida), interactions in graphene. Many of these studies report a decay rate faster than expected for a two-dimensional material and the absence of the usual distance dependent oscillations. In this review we summarize the techniques used to calculate the interaction and present the key results obtained to date. The effects of more detailed parameterisations of the magnetic impurities and graphene host are considered, as are results obtained from ab initio calculations. Since the fast decay of the interaction presents an obstacle to spintronic applications, we focus in particular on the possibility of augmenting the interaction range by a number of methods including doping, spin precession and the application of strain.
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