The previous three chapters presented a survey of typical carbon nanosystems in two, one and zero dimensions, namely graphene, carbon nanotubes and fullerenes, respectively. None of these systems is intrinsically magnetic.Magnetism, however, can arise through dimensional reduction of structures with one or more dimensions. Thus, as one truncates the infinite graphene sheet, one may generate graphene nanoribbons of the zigzag type (zGNRs), as introduced in Section 4.5.1. In the first section of this chapter, we will show that localized states at the zGNR edges give rise to antiferromagnetic ground states in these systems, and review experimental confirmation for this assertion. The analysis of zigzag edges will be extended to vacancies in graphene-based structures that lack magnetic edge states, such as aGNRs. In this context, we will emphasize the importance of Lieb's theorem as a principle underlying many magnetic phenomena in carbon nanostructures, albeit not all. Further, we will describe specific one-dimensional substructures in graphene-based systems, namely zGNR edge excitations (7.2.3), and topological line defects (7.3).

Intrinsic magnetism in truncated carbon nanotubes of the zigzag type (zSWCNTs) will be discussed in analogy to zGNR magnetism. Section 7.4.1 deals with aggregates of several zSWCNTs. The magnetic effects in these complexes turn out to be rooted in the electronic features of carbon surfaces with negative Gaussian curvature. We conclude with some remarks on the controversial topic of intrinsic magnetism in pure fullerene systems.

Systems Derived from Graphene

In what follows, we review magnetic effects associated with the rupture of the pristine graphene network, as it arises from the formation of edges, or vacancies, or voids as aggregations of vacancies. The focus is here on zigzag edge structures as the preferred loci of unpaired electrons, and thus the substructures of the graphene lattice from which spin interactions originate.

Magnetism in Zigzag Graphene Nanoribbons

Zigzag graphene nanoribbons (see Section 4.5.1) exhibit magnetism in their electronic ground states. In the following we will consider the physical origin of this phenomenon. Once more, we associate the x (y) coordinate with the periodic (finite) direction. Inspecting the zGNR ground state solutions (see Eqs. (4.71)– (4.77)), we found that the graphene wave function must be modified to allow for edge-localized states.