Engineers have discovered an unexpected link between two very different realms of physics: the behaviour of electrons in graphene and magnetic waves in specially engineered materials.

By designing a thin magnetic film with a hexagonal pattern of holes – similar to graphene’s structure – the researchers showed that magnetic 'spin waves' can follow the same mathematical rules as graphene’s famously unusual electrons. The surprising overlap reveals a deeper connection between electronic and magnetic systems and gives scientists a powerful new way to study complex magnetic materials. 

Two dimensional materials have drawn intense interest because their electronic and magnetic properties could power future technologies. Scientists have traditionally treated these two behaviours as separate. Engineers at Illinois Grainger Engineering have now shown that they are connected by the same underlying mathematics. 

Spin waves on a thin film with holes arranged in a hexagonal pattern. Researchers have demonstrated that this system shows the same mathematical behaviours as electrons in graphene. Image: Bobby Kaman.

In a study published in Physical Review X, researchers from the Grainger College of Engineering at the University of Illinois Urbana Champaign demonstrated how specially designed two dimensional magnetic systems can follow the same equations that describe mobile electrons in graphene. This mathematical connection could influence the design of radiofrequency devices and also provide researchers with a powerful new way to analyse and engineer these materials. 

"It's not at all obvious that there is an analogy between 2D electronics and 2D magnetic behaviours, and we're still amazed at how well this analogy works," said Bobby Kaman, the study's lead author. "2D electronics are very well studied thanks to the discovery of graphene, and now we've shown that a not-so-well-studied class of materials obeys the same fundamental physics."

Inspiration from metamaterials and graphene

The concept grew out of Kaman's work with metamaterials. These materials are engineered so that their larger scale structure produces behaviours that would not normally occur in the material's natural atomic arrangement.

Kaman, a materials science and engineering graduate student working in the research group of professor Axel Hoffmann, realised that both graphene electrons and microscopic magnetic excitations in so called magnonic materials behave like waves. This similarity raised an intriguing possibility. Perhaps a magnetic system could be designed so that it behaves mathematically like graphene.

"Graphene is unique because its conduction electrons organise into massless waves, so I was curious if altering the physical geometry of a magnonic material to look like graphene would make it act like graphene," said Kaman. "I thought it would maybe have a handful of similar properties to graphene, but the analogy was much deeper and richer than I expected."

Designing a magnetic system that mimics graphene

To explore the idea, the researchers modelled a thin magnetic film containing tiny holes arranged in a hexagonal pattern. Within this structure, microscopic magnetic moments, known as 'spins', interact and produce travelling disturbances called spin waves.

When the team calculated the energies of these spin waves, they discovered that their mathematical behaviour closely matched that of electrons moving through graphene. 

The system turned out to be even more complex than expected. Instead of a simple oneto one analogy, the researchers identified nine distinct energy bands. These bands allow several types of behaviours to appear at the same time. Among them are massless spin waves similar to graphene's electron waves, as well as low dispersion bands associated with localised states and even 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 Hoffmann. "Magnonic crystals are notorious for producing an overwhelming variety of structure- and geometry-dependent phenomena, most of which are catalogued without really being understood. The graphene analogy in this system provides a clear explanation for the observed behaviours."

Potential for smaller microwave devices

Beyond its importance for basic physics, the research could have practical applications. The team believes the system may be useful in microwave technology used in wireless and cellular communication.

"One such device is a 'microwave circulator' that only allows microwave radio signals to propagate in one direction," said Hoffmann. "They are usually bulky, but the magnonic system we studied could allow microwave devices to be miniaturised to the micrometer scale."