University of Illinois Engineers Discover That Magnetic Materials Can Follow Graphene's Exotic Quantum Equations

Engineers at the University of Illinois Grainger College of Engineering have discovered an unexpected and deep mathematical link between two previously unrelated realms of physics: the quantum behavior of electrons racing through graphene, the Nobel Prize-winning single-atom-thick carbon sheet, and the behavior of magnetic spin waves — called magnons — propagating through specially engineered magnetic films. The finding, published in the journal Physical Review X in March 2026, opens a new field of research the team calls "magnonic graphene" and could lead to dramatically miniaturized microwave devices used in wireless communications and radar systems.

Graphene has fascinated physicists and engineers since its isolation in 2004 because its electrons behave in a profoundly unusual way. Rather than slowing down as they interact with the carbon lattice, they race through it as if they have no mass at all — mimicking the behavior of photons of light. This "massless fermion" behavior gives graphene its extraordinary electrical conductivity and is governed by a precise mathematical framework derived from relativistic quantum mechanics. For more than 20 years, researchers have tried to find other materials or systems that naturally replicate those equations, because wherever graphene's mathematics appears, exotic and useful physical phenomena tend to follow.

The University of Illinois team, led by professor Axel Hoffmann and doctoral student Bobby Kaman, took a counterintuitive approach. Instead of looking for another electronic material, they asked whether a magnetic material could be deliberately designed to produce spin waves — collective oscillations in the alignment of electron spins — that follow the same mathematical rules as graphene's massless electrons. To test the idea, they fabricated a thin magnetic film — specifically a permalloy nickel-iron alloy — and etched a precise hexagonal pattern of tiny holes into it, mimicking the honeycomb atomic structure that gives graphene its unusual properties.

Using a microwave technique called Brillouin light scattering spectroscopy, the team measured how spin waves propagated through the patterned film and mapped their energy across different frequencies and directions. What they found was striking: the spin waves displayed the same mathematical behaviors as electrons in graphene. They identified nine distinct energy bands in the magnetic system, including modes that behave as massless quasi-particles — the magnetic equivalent of graphene's celebrated electrons — as well as flat bands associated with localized states and topological effects spanning multiple bands simultaneously. "It's not at all obvious that there is an analogy between 2D electronics and 2D magnetic behaviors," Kaman said. "But we found the connection runs surprisingly deep."

The practical payoff lies in microwave circulators — devices that direct microwave radio signals to flow in only one direction. They are essential components in smartphones, satellites, radar systems, and any wireless device that must transmit and receive on the same antenna without self-interference. Today's microwave circulators typically rely on bulky, permanent magnets and measure several centimeters across. The magnonic graphene approach, Hoffmann explained, could shrink them to the micrometer scale — orders of magnitude smaller — because the directional behavior emerges from the geometry of the magnetic pattern rather than from an external magnet. The team has filed a patent application on the microwave device concept.

The broader significance of the work is that it provides a new toolkit for understanding complex magnetic materials. Physicists study many classes of magnets whose mathematical structure they suspect is related to graphene's equations, but until now they lacked a clear experimental system to test and probe those relationships. Magnonic graphene offers an accessible, tunable platform where the critical parameters — hole size, spacing, film thickness, applied magnetic field — can be adjusted at will to explore phenomena that are difficult or impossible to isolate in purely electronic systems. The University of Illinois team is now working to realize specific topological states predicted by the theory that could enable robust, error-resistant signal processing analogous to topological quantum computing but operating at room temperature.