For the first time, physicists have tracked in real time how an ordered lattice of magnetic vortices gradually turns into a disordered structure. The experiment allowed them to directly observe defects that emerge and change during this transition, and to establish that these defects move up to a hundred times faster than the magnetic vortices themselves. The findings help improve our understanding of the fundamental mechanisms of phase transitions in two-dimensional systems and could open up new opportunities for developing energy-efficient information storage and processing technologies.

The study was published in the journal Nature Nanotechnology in 2025. An international team of researchers used a specially designed magnetic thin-film structure and Kerr microscopy to observe changes in the magnetic lattice with high spatial and temporal resolution.

What skyrmions are and why scientists are interested in them

The experiment centered on skyrmions—stable magnetic structures that behave like individual particles. They arise in certain magnetic materials and consist of a particular configuration of spins—the intrinsic magnetic moments of particles. Skyrmions are notable for their topological nature: their internal magnetic structure has certain properties that cannot be changed through a simple continuous transformation. This allows these structures to remain stable and move within a material, interacting with one another.

In thin magnetic films, skyrmions can form ordered two-dimensional lattices. This makes them interesting not only for fundamental physics but also for developing low-power information storage and processing technologies. However, these systems are particularly valuable because they allow researchers to study fundamental processes occurring in two-dimensional matter. One such process is melting, or the transition from an ordered state to a disordered one.

In an ordinary three-dimensional material, this transition is often accompanied by a fairly abrupt breakdown of the crystal structure. In two-dimensional systems, the process can unfold differently: an intermediate state emerges between the ordered state and the liquid-like phase, in which the arrangement of particles no longer retains its previous order, but their relative orientations remain aligned. This is the process the physicists sought to track in detail for the first time directly during an experiment.

The transition from order to chaos occurs in two stages

According to Kosterlitz–Thouless–Halperin–Nelson–Young (KTHNY) theory, melting in two-dimensional systems can proceed through two successive phase transitions. First, long-range translational order—the regularity of particle positions relative to one another—breaks down. Orientational order is preserved, however: the particles remain predominantly oriented in accordance with the overall geometry of the structure. This produces what is known as the hexatic phase. The name refers to the sixfold symmetry characteristic of the system under consideration: neighboring particles retain a preferred orientation, even though their positions no longer form a fully ordered lattice.

At the next stage, orientational order also breaks down. The system enters a liquid-like state in which order has almost entirely disappeared. Topological defects—disruptions in the ideal lattice structure—play a key role in these transitions. In particular, these include dislocations, associated with disruptions in the relative positions of neighboring particles, and disclinations, which reflect disruptions in their orientational order.

The theory predicts that the emergence and evolution of these defects determine the mechanism of two-dimensional melting. Until now, however, experimental methods had not allowed researchers to track the full sequence of events directly in space and time with sufficient precision. The researchers overcame this limitation by observing the movement of individual skyrmions and changes in the structure of their lattice.

How physicists observed melting

For the experiment, the scientists created a multilayer magnetic film made of tantalum, cobalt, iron, boron, and magnesium oxide. Within it, skyrmions formed a two-dimensional structure that the researchers were able to stabilize inside a hexagonal region.

Kerr microscopy allowed the team to image magnetic structures with a spatial resolution of about 300 nanometers and a temporal resolution of 62.5 milliseconds. This made it possible to track the positions of individual skyrmions and observe how their arrangement relative to one another changed.

The scientists used two methods to induce the transition from an ordered lattice to a disordered state.

In the first, they gradually increased an external magnetic field directed perpendicular to the sample surface. Under its influence, the skyrmions shrank, reducing their packing density. The particles gained more room to move, the number of available configurations increased, and the system gradually lost its original order.

In the second, the researchers applied magnetic field oscillations that increased skyrmion mobility. This enhanced their diffusion and provided another way to induce the transition to a disordered state.

Both approaches produced consistent results: the scientists observed a transition from an ordered lattice through a hexatic phase to a liquid-like state.

The researchers did not limit themselves to comparing images taken at different times. They analyzed correlations between particle positions and orientations to determine the stage at which the system lost each type of order.

In this way, they were able to experimentally track the sequence of phase transitions predicted by KTHNY theory.

Why the discovery matters for future technologies

The study is primarily of fundamental importance: it enabled direct observation of the mechanism of two-dimensional melting, which had previously been described mainly in theoretical terms and studied using limited experimental capabilities.

However, the findings may also be relevant to the development of new technologies. Skyrmions are considered promising building blocks for information storage and processing devices. Their magnetic properties could potentially be used to create compact systems in which moving and reconfiguring information-bearing elements requires relatively little energy.

In this context, understanding the behavior of defects takes on practical significance. If their formation, movement, and interaction can be controlled, this could help in developing devices capable of rapidly changing the state of a magnetic structure. The researchers note that carefully tuning a material's energy landscape could potentially make certain defect rearrangements controllable. In the longer term, this could allow their movement to be used for low-power information transmission.

Nevertheless, practical implementation of such devices remains a long way off. The authors point out that further research requires materials with fewer skyrmion pinning sites, which hinder their free movement. This would allow more precise studies of defect interactions, the effects of mechanical deformation, and other features of two-dimensional magnetic systems.