Researchers from Beijing University of Technology, South China University of Technology, Forschungszentrum Jülich and Uppsala University have reported the first experimental evidence of hopfions, which are magnetic spin structures predicted decades ago that have become a fascinating research topic in recent years.
The team used transmission electron microscopy to observe hopfions forming coupled states with skyrmion strings in B20-type FeGe plates. They provided a protocol for nucleating such hopfion rings, which they verified using Lorentz imaging and electron holography. The scientists' results are said to be highly reproducible and in full agreement with micromagnetic simulations.
"Our results are important from both a fundamental and applied point of view, as a new bridge has emerged between experimental physics and abstract mathematical theory, potentially leading to hopfions finding an application in spintronics," says Philipp Rybakov, researcher at the Department of Physics and Astronomy at Uppsala University, Sweden.
Magnetic skyrmions and hopfions are topological structures—well-localized field configurations that have been a hot research topic over the past decade owing to their unique particle-like properties, which make them promising objects for spintronic applications.
Skyrmions are two-dimensional, resembling vortex-like strings, while hopfions are three-dimensional structures within a magnetic sample volume resembling closed, twisted skyrmion strings in the shape of a donut-shaped ring in the simplest case.
Despite extensive research in recent years, direct observation of magnetic hopfions has only been reported in synthetic materials. This current work is the first experimental evidence of such states stabilized in a crystal of B20-type FeGe plates using transmission electron microscopy and holography.
The researchers provided a unified skyrmion–hopfion homotopy classification and offer insight into the diversity of topological solitons in three-dimensional chiral magnets.
The findings open up new fields in experimental physics: identifying other crystals in which hopfions are stable, studying how hopfions interact with electric and spin currents, hopfion dynamics, and more.
"Since the object is new and many of its interesting properties remain to be discovered, it is difficult to make predictions about specific spintronic applications. However, we can speculate that hopfions may be of greatest interest when upgrading to the third dimension of almost any technology being developed with magnetic skyrmions: racetrack memory, neuromorphic computing, and qubits," explains Rybakov.
"Compared to skyrmions, hopfions have an additional degree of freedom due to three-dimensionality and thus can move in three rather than two dimensions."