Theory of Magnetism in Graphitic Materials

Abstract

This chapter provides a pedagogical introduction into the theoretical models of magnetism in graphene nanostructures and graphite. The onset of magnetism in the considered systems is mostly discussed at the level of very simple models, namely, the tight-binding model and the Hubbard model in the mean-field approximation. The simplicity of these models further allows to introduce two counting-rule theorems that establish basic intuition behind the emergence of ferromagnetic and antiferromagnetic correlations in graphene systems. The chapter covers different models of magnetic graphene systems categorized according to their dimensionality. First, several examples of magnetic graphene molecules are discussed for the purpose of illustrating the application of counting-rule theorems. Next, the physical mechanism behind the magnetic ordering at one-dimensional edges of graphene is extensively covered. It will be shown how the presence of localized edge states results in the onset of magnetism in zigzag and chiral graphene nanoribbons. Finally, we will discuss common defects in graphene and graphite created as a result of irradiation by high-energy particles and the physical mechanism of defect-induced magnetism in these materials. The theoretical developments of this chapter are presented along with the latest achievements in studying the electronic structure and magnetic properties of graphene-based systems using experimental methods, notable a range of scanning probe microscopy techniques.