Graphene-based devices have opened up a new area of research in nanoelectronics. Graphene is a truly 2D zero-gap semiconductor with peculiar transport and magnetotransport properties that make it very different from conventional semiconductors and metals. For example, electrons in graphene need to be treated as relativistic particles called massless Dirac fermions, unlike electrons in most conductors that can be described by non-relativistic quantum mechanics.

Researchers expect the electronic structure of graphene to be very different from bulk graphene thanks to surface or edge effects. While bulk graphene is a diamagnetic semimetal, 1D graphene ribbons with zigzag edges should be semiconducting because magnetic interactions open up an energy gap. "We have found spontaneous spin polarization associated with the shape and size of a nanostructure in a material without atomic magnetism," Joaquin Fernandez Rossier of Alicante University told

Surprising result

The result is surprising: standard magnetic order in solids occurs in a material whose atoms are already magnetic. Examples include manganese, iron, nickel and cobalt. Magnetism in these atoms happens when degenerate atomic shells are not completely filled. The Coulomb repulsion is minimized when the spins in the atomic shell are aligned – something known as Hund's rule.

In contrast, magnetism in graphene islands occurs because clusters with certain shapes, such as triangles and hexagons, have partially filled degenerate states that extend over edge atoms, explains Fernandez Rossier. "This is unique to the atomic structure of graphene. Very much like in the case of Hund's rule for atoms, maximizing the spin reduces the Coulomb repulsion in these shapes at a superatomic scale."

The researchers studied the electronic structure of graphene triangles or hexagons using several methods. In the simplest, they used a non-interacting Huckel or tight-binding approximation to compute the energy levels of graphene nanoislands while neglecting Coulomb interactions between electrons. "This method correctly describes graphene as a zero-gap semiconductor with linear bands close to the Fermi energy," said Fernandez Rossier.

Island shape

The technique also allowed the scientists to establish the relationship between the shape of the island and the degeneracy of the cluster's particle spectrum. "We find that triangular islands always have a set of 2N degenerate energy states occupied by N electrons, where N is proportional to the number of edge atoms," he explained. "These states are localized on the edges of the island."

As well as confirming the magnetism seen in triangular nanoislands, the results also predict ferrimagnetic order in hexagonal ones.

"Our work implies a new type of magnetism that arises from degeneracies of the cluster’s spectrum, in contrast to degeneracies at the atomic level," said Fernandez Rossier. "This means that clusters of other non-magnetic materials could be magnetic as well, opening up a new venue for research and applications in nanomagnetism."

The researchers reported their work in Physical Review Letters.