Magnetic Hopfion Rings in New Era for Topology

The figure illustrates the directions of magnetic spins in a hopfion ring.

Exotic Structure: Physicists have, for the first time, generated so-called Hopfion rings in a crystalline material—ring-shaped magnetic structures formed by directed electron spins. The existence of such twisted spin rings was predicted in 1975, and now researchers have experimentally produced and demonstrated them for the first time in a metal alloy. The intriguing aspect of Hopfion rings lies in their three-dimensional mobility, potentially enabling new spintronic applications, as reported in Nature.

Under the influence of magnetic fields, some metals become ferromagnetic; the spins of their atoms align uniformly like tiny compass needles. However, under certain conditions, spins can also form more complex patterns. An example is the vortex-shaped Skyrmions, a kind of magnetic mini-tornado. Such magnetic structures can behave like quasi-particles and are considered potential candidates for magnetic data storage or qubits in quantum computers.

Hopfions: Rings of Twisted Spins

As originally proposed in 1975, a team from the Jülich Research Center under the direction of Fengshan Zheng has now succeeded in producing a variation of such skyrmions in regular material. These are known as hopfion rings—skyrmion threads that are twisted within themselves and closed into a ring. Despite extensive research on magnetic skyrmions, the direct observation of such hopfion rings has been challenging and has only been achieved once before in a synthetic material, as explained by the team. Physicists have, for the first time, generated a photonic version of hopfion rings in early 2023.

For their experiment, the physicists utilized a 180-nanometer-thick disc made of an iron-germanium alloy (FeGe), which they cooled down to minus 70 to 90 degrees Celsius. Subsequently, they applied an external magnetic field perpendicular to the disc and observed, using Lorentz transmission electron microscopy, the spin structures that emerged.

First Edge Deformations, Then A Ring

Initially, only three intertwined skyrmion threads formed in the center of the disk, pointing in the direction of the field lines. However, when the team reversed the polarization of the magnetic field, magnetic swirls began to form in the outer region of the metal disk. After another reversal and an increase in magnetic intensity, a completely new structure emerged there: “On further increasing the field in the positive direction, the edge modulations contract towards the centre of the sample, forming a hopfion ring around three skyrmion strings,” report the physicists.

This marks the team’s first successful demonstration of exotic Hopfion rings in a crystalline material. “We present direct observational evidence of Hopfions in crystals,” say Zheng and his colleagues. “The results are highly reproducible and in full agreement with micromagnetic simulations.”

Triangles, Pentagons and Rings

The findings from additional experiments reveal that the size and shape of the Hopfion ring are primarily dependent on the strength of the magnetic field. As the magnetic field intensifies, the Hopfion ring transitions from a triangular to a pentagonal and ultimately to a circular form, as described by Zheng and colleagues. Increasing the magnetic field strength further results in a reduction in the distance between the Hopfion ring and the central Skyrmion threads. The bright points of the Skyrmion threads eventually come into close proximity to the Hopfion ring before its collapse, according to the physicists. The number of central Skyrmion threads is also subject to variation.

Temperature plays a crucial role, with the temperature range of 180 to 200 Kelvin (minus 73 to 93 degrees Celsius) identified as the optimal range for their generation protocol. Below this range, more reversal cycles of the external magnetic field are required before the rings form. If the temperature is higher, an energy barrier arises, impeding the contraction of the edge turbulence into the Hopfion ring.

Potentially Relevant for Spintronic Applications

According to Zheng and his team, this discovery not only provides new insights into the world of magnetic nanostructures but also holds potential practical relevance. Co-author Filipp Rybakov from the University of Uppsala in Sweden states, “While this phenomenon is new and many of its potentially interesting properties are yet to be discovered, our results are significant both in terms of fundamental understanding and from an applied perspective.

Similar to skyrmions, hopfion rings could expand the spectrum of future spintronic applications, particularly because they exist in three dimensions, unlike the solely two-dimensional skyrmions. The physicists suggest that hopfion rings may move and interact in three dimensions in thicker samples, such as along the skyrmion threads.

This could prove useful for magnetic storage systems, neuromorphic computers, and also for qubits in quantum computers. Zheng’s team aims to further investigate the characteristics of hopfion rings and explore additional crystalline materials capable of generating this magnetic phenomenon.