3/2/2026 Michael O'Boyle
Materials graduate student Robert Kaman and Founder Professor Axel Hoffmann have demonstrated that spin waves in engineered two-dimensional magnonic crystals obey the same mathematical equations as electrons in graphene, revealing a surprisingly deep analogy between two previously distinct areas of physics. Beyond advancing fundamental understanding of magnonic systems, this work has practical implications for wireless technology, as the magnonic platform could enable microwave circulators to be miniaturized to the micrometer scale — a major reduction from current bulky designs.
Written by Michael O'Boyle
Illinois Grainger engineers have discovered a surprising connection between the electrons in graphene and magnetic spin waves in certain magnonic crystals. The analogy has important implications for radiofrequency technology, and it provides a new lens through which to study both systems.
The electronic and magnetic properties of two-dimensional materials both have strong potential for technological applications. Researchers have long assumed that they are distinct phenomena, but Illinois Grainger engineers have demonstrated that they share a mathematical language.
In an article recently published in Physical Review X, a team in The Grainger College of Engineering at the University of Illinois Urbana-Champaign showed how to engineer two-dimensional magnetic systems to obey the same equations as mobile electrons in the two-dimensional material graphene. The mathematical mapping not only has implications for radiofrequency technology, but it also opens the door to a new method for studying and engineering these kinds of systems.
“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,” said Robert 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.”
The idea came to Kaman — a materials science and engineering graduate student in the research group of professor Axel Hoffmann — from studying metamaterials, or materials whose mesoscopic structure is engineered to produce new behaviors not possible with the original substance’s atomic-scale structure. Since the electrons in graphene and microscopic magnetizations in so-called magnonic materials can both display wavelike behaviors, he wondered if the latter could be designed to behave like the former.
“Graphene is unique because its conduction electrons organize 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,” Kaman said. “I thought it would maybe have a handful of similar properties to graphene, but the analogy was much deeper and richer than I expected.”
Kaman and his collaborators considered a system in which microscopic magnetic moments, or “spins,” are arranged in a thin film with holes in the surface distributed in a hexagonal pattern. By calculating the energies of propagating disturbances, or spin waves, the researchers found that they display the same mathematical behaviors as electrons in graphene.
However, the system proved to be far more complex than the simple analogy that the researchers were pursuing. They found nine distinct energy bands, allowing for more behaviors to simultaneously exist. Massless spin waves analogous to graphene electron waves are one, but the system also allows for low-dispersion bands corresponding to localized states and even topological effects across bands.
“What makes Bobby’s work remarkable is that it makes a direct connection between an engineered spin system and a fundamental physics model,” Hoffmann said. “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.”
The researchers noted that the system they studied would have important technological implications beyond fundamental research. Specifically, they have in mind an application to microwave technology used in wireless and cellular networks.
“One such device is a ‘microwave circulator’ that only allows microwave radio signals to propagate in one direction,” Hoffmann explained. “They are usually bulky, but the magnonic system we studied could allow microwave devices to be miniaturized to the micrometer scale.”
Hoffmann’s research group has applied for a patent for their microwave device concepts.
Jinho Lim and Yingkai Liu also contributed to this work.
The study, “Emulating 2D Materials with Magnons,” is available online. DOI: 10.1103/t7tm-nxyl
Support was provided by Illinois Materials Research Science and Engineering Center through the National Science Foundation.
Illinois Grainger Engineering Affiliations
Axel Hoffmann is an Illinois Grainger Engineering professor of materials science and engineering in the Department of Materials Science and Engineering. He is also affiliated with the Materials Research Laboratory. He holds a Founder Professor appointment.