Emergence of magnetism in graphene materials and nanostructures

Magnetic materials and nanostructures based on carbon offer unique opportunities for future technological applications such as spintronics. This article reviews graphene-derived systems in which magnetic correlations emerge as a result of reduced dimensions, disorder and other possible scenarios. In particular, zero-dimensional graphene nanofragments, one-dimensional graphene nanoribbons, and defect-induced magnetism in graphene and graphite are covered. Possible physical mechanisms of the emergence of magnetism in these systems are illustrated with the help of computational examples based on simple model Hamiltonians. In addition, this review covers spin transport properties, proposed designs of graphene-based spintronic devices, magnetic ordering at finite temperatures as well as the most recent experimental achievements.