Origin Of Magnetism in Graphene Nanostructures*

The magnetic orderings of traditional magnetic materials originate from their partially filled $d$- or $f$-electron bands. Surprisingly, theoretical and experimental studies show that graphene nanostructures which contain only $s$ and $p$ electrons can also exhibit magnetic ground states. On the basis of the bonding properties of $pi$-electrons, we propose a theoretical model to explain the origin of magnetism in graphene nanostructures. Our theory is justified via examples ranging from nanoflakes to nanoribbons. Our theory also provides a simple physical insight into Lieb's theorem about the ground state magnetic momentum of a bipartite system.