Graphene has attracted a great interest in material science due to its novel electronic structrues. Recently, magnetism discovered in graphene based systems opens the possibility of their spintronics application. This paper provides a comprehensive review on the magnetic behaviors and electronic structures of graphene systems, including 2-dimensional graphene, 1-dimensional graphene nanoribbons, and 0-dimensional graphene nanoclusters. Theoretical research suggests that such metal-free magnetism mainly comes from the localized states or edges states. By applying external electric field, or by chemical modification, we can turn the zigzag nanoribbon systems to half metal, thus obtain a perfect spin filter.
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