  Motivated by recent studies reporting the formation of localized magnetic
moments in doped graphene, we investigate the energetic cost for spin
polarizing isolated impurities embedded in this material. When a well-known
criterion for the formation of local magnetic moments in metals is applied to
graphene we are able to predict the existence of magnetic moments in cases that
are in clear contrast to previously reported Density Functional Theory (DFT)
results. When generalized to periodically repeated impurities, a geometry so
commonly used in most DFT-calculations, this criterion shows that the energy
balance involved in such calculations contains unavoidable contributions from
the long-ranged pairwise magnetic interactions between all impurities. This
proves the fundamental inadequacy of the DFT-assumption of independent unit
cells in the case of magnetically doped low-dimensional graphene-based
materials. We show that this can be circumvented if more than one impurity per
unit cell is considered, in which case the DFT results agree perfectly well
with the criterion-based predictions for the onset of localized magnetic
moments in graphene. Furthermore, the existence of such a criterion determining
whether or not a magnetic moment is likely to arise within graphene will be
instrumental for predicting the ideal materials for future carbon-based
spintronic applications.
