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We address the electronic structure and magnetic properties of vacancies andvoids both in graphene and graphene ribbons. Using a mean field Hubbard model,we study the appearance of magnetic textures associated to removing a singleatom (vacancy) and multiple adjacent atoms (voids) as well as the magneticinteractions between them. A simple set of rules, based upon Lieb theorem, linkthe atomic structure and the spatial arrangement of the defects to the emergingmagnetic order. The total spin $S$ of a given defect depends on its sublatticeimbalance, but some defects with S=0 can still have local magnetic moments. Thesublattice imbalance also determines whether the defects interactferromagnetically or antiferromagnetically with one another and the range ofthese magnetic interactions is studied in some simple cases. We find that insemiconducting armchair ribbons and two-dimensional graphene without globalsublattice imbalance there is maximum defect density above which localmagnetization disappears. Interestingly, the electronic properties ofsemiconducting graphene ribbons with uncoupled local moments are very similarto those of diluted magnetic semiconductors, presenting giant Zeeman splitting.

Vacancy induced magnetism in graphene and graphene ribbons