New three‑dimensional magnetic structure discovered with laser light

Magnetism is often imagined as something simple, pointing in one direction or another. At very small scales, however, magnetism can behave in far more complex ways. Magnetism originates from a quantum property of electrons known as spin, which can be thought of as a tiny internal compass carried by each electron. When many spins interact inside a solid material, they can organize into stable patterns.

Observed for the first time

In this study, a Swedish-German-Luxembourg-Chinese collaboration of researchers has observed magnetic hopfions. A hopfion is a three-dimensional magnetic structure, in which electron spins exhibit all possible directions in a limited volume of the material.

Counterparts of magnetic hopfions have previously been observed in non‑magnetic systems. In magnetic materials, however, their independent existence had so far only been predicted by theory, and direct experimental observation had remained a major challenge.

“Hopfions are fascinating because of their structure. 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,” says Philipp Rybakov, Researcher at the Department of Physics and Astronomy at Uppsala University and one of the researchers behind the study.

The experiments were carried out on chiral magnetic crystals. In a chiral magnetic crystal the structure comes in two variants that are mirror images of each other, like a left hand and a right hand. Although they are made of the same atoms, the two forms cannot be perfectly aligned by rotation. This built‑in asymmetry strongly influences how magnetic spins arrange themselves inside the material.

Created using femtosecond laser pulses

The researchers studied thin films of iron germanium (FeGe) with a thickness of about 110–200 nanometres. Although magnetic hopfions had been predicted by theory for several years, observing them experimentally proved extremely difficult. Under normal conditions, the magnetic system does not easily reach these states because it must overcome energy barriers.

What made the breakthrough possible was the use of femtosecond laser pulses. A femtosecond is an extremely short moment in time, one millionth of a billionth of a second. Laser pulses can briefly disturb the spin system and push it out of equilibrium, allowing new magnetic states to form.

In the experiment, a relatively large surface was covered with FeGe and illuminated with femtosecond laser light once per second. After the laser exposure, the researchers examined the magnetic state of the material using advanced electron‑based microscopy techniques. The experiment could then be repeated under the same conditions, making it possible to carefully test and verify the results.

Experiments, teoretical calculations and simulations

At the same time as the experiments were performed, the same magnetic structures were recreated in detailed computer simulations using Excalibur, a simulation program previously developed by Rybakov and adopted by the research team. The software models how millions of interacting spins evolve and organize into complex three‑dimensional patterns. These simulations act as digital twins of the experiments.

When the measurements were compared with simulations, the observed structures were consistent with theoretical models of magnetic hopfions.

A key part of the work was the topological analysis of the magnetic states. Topology is a branch of mathematics that describes properties of shapes and more complex geometric objects that remain unchanged under continuous deformations, such as knots or linked loops. Philipp Rybakov led the theoretical and topological work that made it possible to identify hopfions as distinct and stable three‑dimensional magnetic structures.

The study is the result of a close collaboration between theory and experiment, with experimental work and theoretical modelling developed in parallel.

“Theory helped point us in the right direction, experiments made the structures visible, and simulations and topology helped us interpret what we were seeing,” says Philipp Rybakov.

Parallell experiment

The results are not limited to hopfions in a single material. In parallel work carried out at the Synergetic Extreme Condition User Facility (SECUF), the same light‑based approach was used to control magnetism in a different chiral material. In that study, researchers demonstrated so‑called bimerons, two‑dimensional magnetic structures that can be seen as counterparts of three‑dimensional hopfions. Taken together, these studies show that laser light can serve as a general tool for accessing new magnetic states in different materials and in both two and three dimensions.

New opportunities using spintronics

The discovery opens up new opportunities for future research. Because hopfions are stable, three‑dimensional magnetic structures, they are of interest for spintronics, where electron spin is used instead of electric charge to store and process information.

“Using femtosecond laser light, we now have a way to switch magnetism into these complex states. That allows us to explore magnetic phenomena in ways that were not possible before,” says Philipp Rybakov.

Camilla Thulin