Researchers in Uppsala have achieved something physicists thought impossible: they've watched three-dimensional magnetic structures called hopfions spring into existence, using pulses of laser light so brief they last mere trillionths of a second. The discovery, published in Nature Physics, represents the first direct experimental observation of these exotic magnetic arrangements in real materials—a breakthrough that confirms decades of theoretical predictions and opens new possibilities for understanding magnetism at the nanoscale.
Magnetism is rarely as simple as the image of a compass needle pointing north. Inside materials at tiny scales, the quantum world takes over. Each electron carries a property called spin, which behaves like an infinitesimal compass inside an atom. When countless spins interact within a solid, they don't point randomly but organize into elaborate stable patterns—sometimes into structures so complex that they've never been directly seen before. A hopfion is one such pattern: a three-dimensional magnetic object in which electron spins point in every possible direction within a confined space, forming closed loops that link together like topological knots.
"Hopfions are fascinating because of their structure," explains Philipp Rybakov, a researcher at Uppsala University's Department of Physics and Astronomy and a lead author of the study. "They are three-dimensional objects made of spins that form closed and linked loops. Once they appear, they keep their form and are largely unaffected by their surroundings." Theoretical physicists had predicted hopfions should exist in magnetic materials, but the gap between prediction and proof had resisted experimental verification. Under normal conditions, magnetic systems lack the energy to reach these exotic states—they get stuck in more conventional arrangements, unable to cross the barriers that separate them from hopfion configurations.
The breakthrough came through an elegant experimental technique. The team worked with thin films of iron germanium (FeGe), just 110 to 200 nanometers thick, cooled and illuminated with femtosecond laser pulses—pulses so brief they last for one millionth of a billionth of a second. Each pulse briefly disturbed the spin system, jostling it out of its usual equilibrium and allowing it to explore new magnetic states. After each laser flash, the researchers examined the material's magnetic structure using advanced electron microscopy, then repeated the experiment with precise consistency.
Parallel to the experiments, the same team ran detailed computer simulations that recreated the observed structures using software called Excalibur, previously developed by Rybakov. These digital twins modeled how millions of interacting spins evolved and organized themselves into three-dimensional patterns. When the experimental observations were compared with the simulations and theoretical models, the results aligned perfectly: the researchers had indeed created and detected magnetic hopfions.
The work succeeded because theory, experiment, and simulation advanced together. Topological mathematics—a branch that describes properties of shapes and knots that remain unchanged through continuous deformation—provided the framework for identifying the hopfions as distinct and stable structures. As Rybakov notes, "Theory helped point us in the right direction, experiments made the structures visible, and simulations and topology helped us interpret what we were seeing." This Swedish-German-Luxembourg-Chinese collaboration demonstrates how fundamental discoveries emerge when different approaches reinforce one another, each providing what the others cannot alone achieve.