Engineers at the University of Illinois Urbana-Champaign have found that magnetic waves in specially designed materials follow the same mathematical rules as electrons in graphene — a connection that was not expected and, according to the researchers, is not yet fully explained.
The study, published in Physical Review X, focused on a thin magnetic film etched with tiny holes arranged in a hexagonal pattern — mirroring graphene’s atomic structure. Inside that film, microscopic magnetic moments called “spins” interact and produce traveling disturbances known as spin waves.
When the team calculated the energies of those spin waves, the math matched graphene’s electron behavior closely.
Deeper Than Expected
The analogy turned out to be more complex than a simple one-to-one match. The researchers identified nine distinct energy bands within the system. Those bands allow multiple behaviors to coexist simultaneously — including massless spin waves, low-dispersion bands linked to localized states, and topological effects that span several bands at once.
“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 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.”
The idea grew from Kaman’s earlier work with metamaterials — engineered structures whose large-scale geometry produces behaviors absent from the material’s natural atomic arrangement. Kaman, a graduate student in professor Axel Hoffmann‘s research group, noticed that both graphene electrons and magnetic excitations in magnonic materials behave as waves. That shared characteristic prompted the question of whether reshaping a magnetic system geometrically could make it act like graphene.
“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 said.
Why It Matters for Magnonic Research
Magnonic crystals — the class of materials this work falls into — are known for producing a wide variety of structure-dependent phenomena that researchers have largely cataloged without understanding. The graphene analogy offers a framework to interpret those behaviors more systematically.
“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.
According to the announcement, the mathematical connection could also influence the design of radiofrequency devices, in addition to giving researchers a new analytical tool for engineering two-dimensional magnetic materials.
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