This chapter combines brief summaries of computational as well as experimental procedures that have been instrumental for the study of nanostructure magnetism. All of the methods sketched here have been successfully applied to magnetic carbon nanostructures. None of them, however, is specific to this type of materials. The models and techniques included in this chapter are pertinent to condensed matter systems or have, in some cases, an even wider scope of usage, including matter at the molecular scale. They thus have the status of standard methods. Procedures more specifically adjusted to exploring magnetism in carbon-based materials, such non-local measurement of spin signals in carbon transmission elements, will be introduced later in their distinct theoretical or experimental contexts.

Computational Methods

In the first part of this chapter we survey a variety of methods that have proved to be efficient in modeling carbon nanostructure magnetism. Procedures based on the tight-binding and the Hubbard model, as sketched in Section 3.1, have played important roles in clarifying the electronic architecture of graphene and its derivatives. Tight-binding schemes have successfully addressed salient phenomena pertaining to these materials, among them the nature of electronic states at the Fermi level of graphene as massless Dirac Fermions. Lifting the methodological constraints typical for these methods, such as the restriction of interatomic coupling to next-neighbor sites, or the representation of a given lattice site by a single electron, leads to more general theories of electronic structure. These are the topic of Section 3.2, which deals with ab initio and density functional theory (DFT) methods. In all cases covered in this survey, emphasis is placed on the capacity of a given computational approach to describe magnetic states and to represent magnetic properties.

The Tight-Binding and the Hubbard Model

The theory of one- or two-dimensional carbon nanostructures, represented respectively by the nanotube and the graphene paradigms, has been largely developed by use of the tight-binding or the Hubbard model. In this section we will introduce some general traits of these approaches, insofar as they are of relevance to this text. Both models rest on the tight-binding premise. According to this condition, the system in its ground state may be described as a lattice populated with atoms in a hydrogen-like configuration.