Unexpected Discovery
Within the European NIMFEIA project, physicists Johan Mentink and Lukas Körber from Radboud University study magnetic vortices: tiny whirlpools in nanoscopic magnetic disks. In these structures, magnetic moments arrange themselves like small compass needles in a swirling pattern around the vortex core. When the core is displaced and released, it begins to rotate around its equilibrium position. This motion is known as gyration.
The team investigates how magnons (magnetic waves) behave in these vortices. During numerical simulations, Körber discovered unexpected patterns in these waves. "When we set the vortex core gyrating, extra waves suddenly appeared that we had never seen before. It looked like a calculation error," says Körber. Years later, PhD student Christopher Heins from Dresden observed exactly the same patterns experimentally within the NIMFEIA project. "At that moment, we knew we had to revisit those initial results to understand what was really happening," Körber explains.
Floquet Engineering
The extra waves turned out to be a signature of Floquet theory, an old and relatively unknown theory that describes periodically driven systems. Through periodic driving, for example with laser light, materials can acquire entirely new properties. This is called Floquet engineering. Until now, this has mainly been investigated for electrons. For magnons, it is difficult to achieve because the coupling of laser light to magnons is relatively weak and dissipates quickly.
Körber explains: "In this study, we have shown that Floquet states can also emerge in a magnetic vortex. When the vortex core starts gyrating, the magnetic system is internally driven rather than externally. As a result, the magnons form new energy bands: the Floquet states."
A Self-Driving System
The gyration of the vortex core can be induced directly by stimulating the vortex core with an external magnetic field in the MHz range. But the team discovered that it can also happen indirectly: by stimulating the magnons with an external magnetic field in the GHz range. Vibrations of the magnons can set the vortex core in motion, which in turn changes their energy distribution. The vortex core then influences the magnons again, creating what is essentially a self-driving system. These kinds of self-driven Floquet systems have never been seen before and can only arise in strongly nonlinear systems like magnets.
Mentink adds: “This discovery offers a completely new perspective on Floquet engineering. The behavior of nonlinear waves is normally very difficult to understand, especially when the waves are periodically driven. We have now found that we can describe this behavior relatively easily using Floquet theory. This opens up possibilities that extend beyond magnetic systems and could be highly relevant for other areas of physics.”
