🔬 mesoscale physics

Unveiling Three-Dimensional Skyrmion Transitions Through Vortices and Monopoles

This study presents the first experimental visualization of three-dimensional topological $Q=0$ skyrmion structures in a Co $_8$ Zn $_8$ Mn $_4$ sample using neutron scattering tomography, revealing novel metastable states and transition pathways mediated by vortex-antivortex lattices, merons, and monopoles that pave the way for advanced bulk spintronic applications.

Original authors: Melissa E. Henderson, Daichi Kurebayashi, Benjamin Heacock, Wangchun Chen, Charles W. Clark, David G. Cory, Dusan Sarenac, Shannon Watson, Jonathan S. White, Lisa DeBeer-Schmitt, Oleg A. Tretiakov, Dm

Published 2026-09-30

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CC BY 4.0

Original authors: Melissa E. Henderson, Daichi Kurebayashi, Benjamin Heacock, Wangchun Chen, Charles W. Clark, David G. Cory, Dusan Sarenac, Shannon Watson, Jonathan S. White, Lisa DeBeer-Schmitt, Oleg A. Tretiakov, Dmitry A. Pushin

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the microscopic world of magnetic materials, atoms do not always align in neat, parallel rows. Sometimes, their magnetic directions twist and curl around a central point, forming tiny, stable whirlpools known as skyrmions. These structures are not merely abstract curiosities; they are robust, particle-like knots of magnetism that scientists hope to use as the building blocks for next-generation computer memory. For decades, researchers have studied these objects as if they were flat, two-dimensional sheets, like coins lying on a table. However, the materials that host them are three-dimensional solids. When these magnetic whirlpools extend through the thickness of a material, they become strings rather than coins, and their behavior becomes far more complex. Understanding how these three-dimensional strings form, change, and interact is crucial for unlocking their potential in technology, yet the tools to see inside a solid block of magnetic material without cutting it apart have been missing.

A team of researchers has now taken the first clear look inside a bulk magnetic sample to visualize these three-dimensional skyrmion strings and the surprising ways they transform. Using a powerful technique that involves firing neutrons through a sample of a cobalt-zinc-manganese alloy, the scientists reconstructed the magnetic landscape in three dimensions. They discovered that these magnetic strings do not simply appear or disappear; they undergo a complex metamorphosis involving the creation and merging of smaller, fractional magnetic defects. The study reveals that the transition between different magnetic states is mediated by a hidden lattice of vortex and anti-vortex patterns, which act as channels for these changes. Most notably, the researchers observed the formation of a unique, doughnut-shaped magnetic structure that has a net charge of zero, a state that had been theorized but never seen in a three-dimensional bulk material before.

The experiment was conducted on a disordered sample of the alloy Co8Zn8Mn4, a material known to host these magnetic textures. By carefully adjusting the magnetic field and temperature, the team used neutron scattering tomography to map the magnetic orientation throughout the entire volume of the sample. Unlike traditional microscopes that only see the surface or a thin slice, this method allowed them to see the full depth of the magnetic structures. What they found was a dynamic world where magnetic strings could split, merge, and reconfigure. In the disordered state of the material, they identified a specific structure they call a skyrmionium. This object looks like a hollow tube or a magnetic doughnut, where the inner core and the outer ring have opposite magnetic twists that cancel each other out, resulting in a total topological charge of zero. In simpler terms, it is a stable magnetic knot that carries no net "twist" count, a feature that distinguishes it from the standard skyrmions which carry a charge of one.

The researchers traced how these skyrmioniums form and evolve. They observed that the process begins with four separate magnetic strings coming together. As these strings merge, they do not simply fuse into a single solid line. Instead, they pass through an intermediate stage where they form a pair of elongated structures that eventually settle into the concentric, doughnut-like shape of the skyrmionium. This transformation is driven by the interaction of smaller magnetic defects called merons and monopoles. Merons are like half-skyrmions, carrying a fractional charge, while monopoles are points where the magnetic field lines diverge or converge, similar to how electric charges behave. The study shows that these merons and monopoles couple together at specific points along the magnetic strings, acting as the mechanism that allows the topology of the material to change. This coupling creates a pathway for the magnetic strings to reorganize without destroying the overall stability of the system.

A key finding of the research is the role of disorder in this process. The sample used was not a perfect crystal but contained a mix of different atoms that created a disordered environment. The researchers found that this disorder, combined with the applied magnetic field, helped stabilize these exotic structures. In the disordered state, the material was filled with a complex web of vortex and anti-vortex lattices. These lattices are not just background noise; they actively facilitate the movement and transformation of the magnetic strings. The study suggests that these vortex patterns provide the necessary energy conditions for the magnetic strings to nucleate and change their shape. When the researchers applied a specific ordering procedure to the sample, forcing the magnetic strings into a more regular, triangular arrangement, the exotic skyrmionium structures disappeared, decaying back into standard skyrmions and vortices. This indicates that the skyrmioniums are metastable, meaning they are stable only under certain conditions and can be easily disrupted.

The implications of these findings extend beyond just seeing something new. The ability to create and control these three-dimensional magnetic structures opens up new possibilities for information storage. Because these objects can exist in different states with varying topological charges, they could potentially be used to encode more than just a simple zero or one. The researchers propose that the unique properties of skyrmioniums and the way they move through the material could allow for multi-bit encoding schemes, where a single magnetic string carries multiple pieces of information. Furthermore, the discovery of how merons and monopoles mediate these transitions suggests new ways to control the movement of magnetic data. The study highlights that by tuning the disorder in the material and the strength of the magnetic field, it might be possible to switch between different magnetic states, creating a new class of spintronic devices that operate in three dimensions rather than being limited to flat surfaces.

The visualization of these processes was made possible by a specific technique called small-angle neutron scattering tomography. Neutrons are ideal for this task because they can penetrate deep into the bulk of a material without being absorbed, unlike X-rays which are often limited to surface layers. By rotating the sample and the magnetic field and collecting data from many different angles, the team was able to reconstruct a three-dimensional map of the magnetic orientation. This map revealed the intricate details of the skyrmionium structure, showing the hollow core and the surrounding ring of opposite magnetization. The researchers also used computer simulations to model the behavior of these structures, and the simulations confirmed that the observed transitions were consistent with the physics of meron and monopole coupling. The agreement between the experimental data and the simulations strengthens the conclusion that these are real, physical phenomena occurring within the material.

This work represents a significant step forward in the field of magnetic materials. For years, the study of skyrmions has been dominated by two-dimensional models and thin films. This research demonstrates that the full complexity of these magnetic objects can only be understood when viewed in three dimensions. The discovery of the skyrmionium and the detailed mapping of its formation pathway provide a new framework for understanding how magnetic textures behave in bulk materials. It shows that the interplay between disorder, dimensionality, and topology creates a rich landscape of magnetic states that were previously hidden from view. As scientists continue to explore these three-dimensional magnetic worlds, the insights gained from this study will likely guide the development of more efficient and powerful technologies for data storage and processing. The ability to see and manipulate these structures in their natural, three-dimensional environment marks a transition from theoretical possibility to experimental reality.

Technical Summary: Unveiling Three-Dimensional Skyrmion Transitions Through Vortices and Monopoles

Problem Statement
Magnetic skyrmions are typically treated as two-dimensional objects with integer topological charge ( $Q$ ), yet their extension into three dimensions realizes composite structures with unique functionalities that transcend planar frameworks. Despite the theoretical prediction of 3D topological structures—such as skyrmion strings interrupted by Bloch points and coupled to emergent monopoles (MPs) and antimonopoles (AMPs)—experimental observation has been hindered by a lack of bulk probes. Traditional imaging techniques (e.g., thin-film microscopy) suffer from 2D projection ambiguities, while X-ray and electron tomography are often limited to geometry-constrained samples dominated by surface effects. Consequently, the transition pathways of 3D topological structures, particularly those involving fractional charges and bulk quasiparticles, have remained largely elusive.

Methodology
The authors employed small-angle neutron scattering (SANS) tomography to achieve true, uninhibited three-dimensional access to bulk skyrmion systems.

Sample: A disordered bulk sample of $Co_8Zn_8Mn_4$ , a cubic chiral magnet.
Instrumentation: Measurements were conducted at the GP-SANS beamline at the High Flux Isotope Reactor (Oak Ridge National Laboratory) with a neutron wavelength of 8 Å.
Experimental Conditions: Data was collected at a constant temperature of 310 K. The study covered both disordered skyrmion states (nucleation trajectories at 0.015 T and 0.025 T) and ordered states (annihilation trajectories at 0.025 T and 0.035 T). Ordered states were achieved via a field-rotating procedure to precipitate rotationally oriented lattices.
Reconstruction: Tomographic reconstruction was performed over two axes (rotation and tilt) with the sample and magnetic field rotated together. Monte Carlo simulations were utilized to support disordered state reconstructions, incorporating random exchange fields to mimic site disorder alongside bulk-type Dzyaloshinskii-Moriya interaction (DMI), cubic anisotropy, and Zeeman terms.

Key Results
The study reports the first experimental visualization of three-dimensional topological structures with $Q=0$ in a bulk system, revealing a "zoology" of metastable states and novel transition dynamics.

3D Skyrmioniums ( $Q=0$ ): The researchers identified $Q=0$ skyrmionium structures, described as composite pairs formed by enclosing $Q=1$ and $Q=-1$ skyrmions of opposite polarity. In 3D reconstructions, these manifest as double-core cylindrical contours ( $m_z = -0.5$ ) with a diameter approximately twice that of a regular skyrmion (~140 nm). Unlike 2D projections which can be ambiguous, the 3D data clearly distinguishes these from hopfions.
Transition Pathways via Merons and Monopoles: The formation and evolution of skyrmioniums were observed to occur through the merging of four separate skyrmions. This process is mediated by the coupling of merons (half-skyrmions) and monopoles/antimonopoles.
- Bimerons: The merging and separation points of skyrmions involve the transformation of antivortex structures into "bimerons" (bound meron-antimeron pairs).
- Coupling: These bimeron locations correspond to coupled MP-AMP pairs in the emergent magnetic field, acting as branching (B) and segmenting (S) spin defects.
Vortex-Antivortex Lattices: Interwoven vortex-antivortex lattices were found embedded throughout the skyrmion phase.
- In disordered states (lower topological charge saturation), vortices often possess fractional topological charges.
- In ordered states (higher saturation), these structures tend to manifest with vanishing topological charge.
- The authors posit that these vortices act as geometric precursors and channels that lower nucleation energy barriers for singular 3D defects (Bloch points, MPs, merons), actively facilitating topological exchange.
Metastability: The observed $Q=0$ skyrmion bundles and skyrmioniums are identified as metastable. They are stabilized by internal disorder and nucleation processes but are susceptible to annihilation upon perturbations in field direction or magnitude (e.g., during the ordering sequence), decaying into $Q=1$ skyrmions and vortices.

Significance and Claims
The paper claims to provide the first experimental evidence of bulk $Q=0$ quasiparticles and meron-mediated dynamics in a free geometry. By visualizing the coupling of merons and monopoles, the study unveils a new topological transition pathway that transcends planar frameworks.

The authors assert that these findings pave the way for higher-dimensional spintronic frameworks. Specifically, the realization of these 3D structures suggests potential for:

Multi-bit encoding architectures utilizing sequences of topological bits (spanning $Q=0$ , $Q=\pm 1/2$ , and $Q=\pm 1$ ).
Unidirectional transport schemes via skyrmionium motion or meron propagation in confined channels.
Monopole-mediated controls for device functionality.

The work emphasizes that disorder is not merely a perturbation but a tunable control parameter that stabilizes diverse topological structures and drives these 3D dynamics, offering a new generation of spintronic devices free from the constraints of existing 2D architectures.

Technical Summary: Unveiling Three-Dimensional Skyrmion Transitions Through Vortices and Monopoles

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