Graphene's extraordinary electronic properties arise from its geometry. Carbon atoms arranged in a honeycomb lattice produce a band structure with Dirac cones — points where the energy-momentum relationship is linear rather than parabolic. Electrons near these points behave as if they have no mass, moving at a constant speed regardless of their energy. The massless behavior is not a property of carbon. It is a property of the honeycomb.
Kaman, Hoffmann, and colleagues at the University of Illinois (Physical Review X, 2026) demonstrate that spin waves in a magnetic film with hexagonal holes reproduce graphene's band structure — Dirac cones, massless dispersion, and all.
The film is a thin magnetic layer with a periodic array of circular holes punched in a honeycomb arrangement. Spin waves — collective oscillations of magnetic moments, also called magnons — propagate through the film. The holes act as scatterers. The hexagonal pattern of scatterers imposes the same symmetry constraints on magnons that carbon's honeycomb imposes on electrons. The result: nine energy bands, including pairs that meet at Dirac points with linear dispersion. Near these points, spin waves propagate as if massless.
The system is richer than graphene in one respect. Graphene has two atoms per unit cell and produces two bands meeting at each Dirac point. The magnonic crystal has more structure — the nine bands include not only Dirac cones but also flat bands, where the group velocity drops to near zero and waves become localized. Flat bands in electronic systems produce exotic phenomena: superconductivity, ferromagnetism, fractional quantum Hall states. Flat bands in magnonic systems are unexplored territory.
The mathematical mapping is exact. The Hamiltonian governing spin waves in the patterned magnetic film is formally equivalent to the tight-binding Hamiltonian governing electrons in graphene, with hopping parameters set by the geometry of the holes. The physical substrate — electronic charge versus magnetic moment — is irrelevant to the band structure. What matters is the lattice. Geometry is the mechanism.
Kaman, Hoffmann et al., "Magnonic crystal with graphene band structure," Physical Review X (2026).