Magnets arranged like graphene obey the same physics, with nine times the complexity

Graphene's unusual electronic properties stem from its honeycomb lattice structure, which forces electrons to behave as if they have no mass. This makes them extraordinarily fast and efficient carriers of electrical signals. For two decades, researchers have explored this physics intensively. What they had not considered seriously was whether the same mathematical framework could describe something entirely different: magnetic waves.

Bobby Kaman, a graduate student in materials science and engineering at the University of Illinois Urbana-Champaign, wondered exactly that. If you arranged magnetic elements in a honeycomb pattern, would their collective vibrations -- called spin waves -- obey the same equations as graphene's electrons? He built the theoretical model to find out.

The answer, published in Physical Review X, was more than a yes. It was a yes with nine energy bands instead of graphene's two.

Punching holes in a magnet

The system Kaman studied is conceptually simple: a thin magnetic film with holes distributed in a hexagonal pattern across its surface. This creates what physicists call a magnonic crystal -- a material whose periodic structure affects spin waves the way a crystal lattice affects electrons.

By calculating the energies of spin waves propagating through this structure, Kaman and his collaborators found that the waves display the same mathematical behaviors as electrons in graphene. The analogy was not approximate or qualitative. The spin waves obey the same fundamental equations.

"It's not at all obvious that there is an analogy between 2D electronics and 2D magnetic behaviors, and we're still amazed at how well this analogy works," Kaman said.

Nine bands, not two

But the magnonic system turned out to be far richer than a simple magnetic analogue of graphene. Where graphene's electronic structure produces two energy bands that touch at a point (the famous Dirac cone), the magnonic honeycomb produces nine distinct energy bands. These allow multiple phenomena to coexist simultaneously: massless spin waves analogous to graphene electron waves, low-dispersion bands corresponding to localized states (where energy is trapped in place rather than propagating), and topological effects that span multiple bands.

"What makes Bobby's work remarkable is that it makes a direct connection between an engineered spin system and a fundamental physics model," said Axel Hoffmann, a Founder Professor at Illinois and the study's senior author. "Magnonic crystals are notorious for producing an overwhelming variety of structure- and geometry-dependent phenomena, most of which are cataloged without really being understood. The graphene analogy in this system provides a clear explanation for the observed behaviors."

Shrinking microwave devices

The practical application the team has in mind is radiofrequency technology. One specific device is a microwave circulator, which allows microwave radio signals to propagate in only one direction. Circulators are essential components in wireless and cellular networks, but current designs are bulky. The magnonic system studied here could, in principle, allow these devices to be miniaturized to the micrometer scale.

Hoffmann's research group has applied for a patent on the microwave device concepts.

Theory, not yet hardware

This is a theoretical and computational study. The nine-band structure and the graphene analogy have been demonstrated mathematically, but the magnonic crystals described here have not yet been fabricated and experimentally tested. Whether the predicted behaviors survive the imperfections and losses present in real materials remains to be verified. The topological effects, in particular, can be sensitive to disorder.

The study was supported by the Illinois Materials Research Science and Engineering Center through the National Science Foundation. Additional contributors include Jinho Lim and Yingkai Liu.