🔬 mesoscale physics

Helical Magnetic Nature of $\beta$ -Mn Structured CoZn Thin-Films Determined by a Bayesian Approach to Modeling Polarized Neutron Reflectivity Data

Using a novel Bayesian model selection approach to analyze polarized neutron reflectivity data, researchers demonstrated that the helimagnetic ground state of bulk $\beta$ -Mn structured CoZn persists in 100 nm thin films with a Curie temperature of approximately 130°C, thereby mapping the material's field-temperature phase diagram for potential room-temperature spintronic applications.

Original authors: M. Dearg, A. J. Caruana, C. J. Kinane, N. Satchell, G. Burnell, S. Langridge, C. H. Marrows

Published 2026-11-03

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CC BY 4.0

Original authors: M. Dearg, A. J. Caruana, C. J. Kinane, N. Satchell, G. Burnell, S. Langridge, C. H. Marrows

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

Imagine a world where information is stored not by flipping tiny switches, but by twisting magnetic fields into intricate, three-dimensional spirals. This is the promise of chiral magnetic materials, a class of substances where the atoms' magnetic spins do not simply line up in a straight row, but instead twist around one another like a corkscrew. This twisting creates a special kind of magnetic texture that can host tiny, stable whirlpools of magnetism called skyrmions. These skyrmions are highly prized by scientists because they could one day power ultra-efficient, low-energy computers and storage devices. However, for these materials to be useful in real-world technology, they must work at room temperature and be thin enough to fit inside the microchips of modern electronics. While some materials exhibit these twisting properties, they often only do so at extremely cold temperatures or in thick blocks that are too bulky for practical use. The challenge has been finding a material that combines the right magnetic structure with the stability and thinness required for everyday devices.

Researchers have turned their attention to a specific alloy made of cobalt and zinc, which naturally forms a crystal structure known as the beta-manganese phase. This structure is inherently chiral, meaning it has a specific handedness that forces the magnetic spins to twist. In large, bulk samples of this material, scientists have already confirmed that it hosts skyrmions at room temperature. But to use it in a computer chip, the material must be grown as a very thin film, just a few hundred atoms thick. The question remained: does this delicate twisting magnetic order survive when the material is squeezed into such a thin layer, or does the confinement force the spins to line up in a simple, straight row? To answer this, a team of scientists at the University of Leeds and the ISIS Neutron and Muon Source in the United Kingdom grew a thin film of this cobalt-zinc alloy and subjected it to a rigorous test using a technique called polarized neutron reflectometry.

The experiment involved shooting a beam of neutrons at the thin film while varying the temperature and applying different strengths of magnetic fields. Neutrons are subatomic particles that act like tiny magnets; when they bounce off the film, their behavior changes depending on how the magnetic spins inside the material are arranged. The goal was to distinguish between two possible states: a uniform state where the spins are all pointing in the same direction, and a helical state where they twist as they move through the depth of the film. This distinction is notoriously difficult to make because the film is only about 100 nanometers thick, which is roughly half the length of one full twist of the magnetic spiral. In such a thin space, the signal from a twisting spiral looks almost identical to the signal from a uniform magnet that is slightly weaker near the edges. It is like trying to tell if a very short piece of rope is twisted or straight just by looking at its ends; the difference is subtle and easily missed.

To solve this puzzle, the researchers employed a sophisticated statistical method known as Bayesian model selection. Instead of simply guessing which picture fits the data better, this approach calculates the probability that the observed data came from a twisting spiral versus a uniform magnet. It weighs the evidence carefully, accounting for the fact that the twisting model is more complex and flexible than the simple uniform one. The analysis revealed that for temperatures below a certain point, known as the Curie temperature, and for magnetic fields below a specific saturation level, the data overwhelmingly favors the existence of the helical state. The team found that the magnetic spins in the thin film do indeed twist, forming a structure that extends through the thickness of the material. They determined that the length of one full twist, or the helix pitch, is approximately 1724 angstroms, a value very close to what is seen in the thicker, bulk versions of the material.

The study also mapped out exactly when this twisting behavior stops. As the researchers increased the strength of the applied magnetic field, the material eventually transitioned from the twisting state to a uniform state where all spins align with the field. This transition happened at lower field strengths as the temperature got closer to the point where the material loses its magnetism entirely. The results confirm that the beta-manganese structured cobalt-zinc film retains its chiral magnetic nature even when thinned down to just a fraction of the size of a single twist. This is a significant finding because it proves that the fundamental physics allowing for skyrmions can exist in a format suitable for thin-film devices. The researchers noted that while the material works well, the transition from a twist to a straight alignment happens gradually, with the spiral slowly unwinding into a uniform state as the magnetic field pulls the spins into alignment.

By successfully identifying this helical order in a thin film, the work provides a crucial stepping stone toward the development of room-temperature spintronic devices. The team demonstrated that even with the limitations of a thin film, the material's natural tendency to twist remains robust. This discovery opens the door for future experiments to directly image these magnetic textures, such as skyrmions, within the film using advanced microscopy. If these swirling magnetic patterns can be controlled and manipulated in thin layers, they could form the basis of a new generation of computing technology that is faster and consumes far less power than current electronics. The study stands as a clear demonstration that the complex magnetic behaviors needed for next-generation storage are not just theoretical possibilities, but physical realities that can be engineered into the thin films of tomorrow.

Technical Summary: Helical Magnetic Nature of β-Mn Structured CoZn Thin-Films Determined by a Bayesian Approach to Modeling Polarized Neutron Reflectivity Data

Problem Statement
Chiral magnetic materials with the B20 or β-Mn crystal structure are of significant interest for spintronic applications, particularly low-power storage, due to their ability to host skyrmions. While bulk materials like MnSi and FeGe exhibit well-characterized helimagnetic ground states, realizing these phenomena in thin-film formats at room temperature remains a challenge. The specific material under investigation, CoZn with a β-Mn structure, possesses a Curie temperature ( $T_C \approx 130^\circ\text{C}$ ) above room temperature and hosts skyrmions in bulk. However, confirming the existence of a helimagnetic ground state in thin films is experimentally difficult. The film thickness studied (~~100 nm) is approximately half the bulk helical wavelength (~~1850–2100 Å), meaning a full spin rotation cannot fit within the film. Consequently, distinguishing a true helical state from a uniform state with reduced interfacial magnetism is subtle, as both can produce similar magnetic depth profiles when measured along the field direction. Standard model selection based on goodness-of-fit ( $\chi^2$ ) is insufficient due to the inverse phase problem in reflectometry, which allows multiple parameter sets to yield similar fits.

Methodology
The authors investigated sputtered, polycrystalline CoZn thin films (~1000 Å thick) grown on Si/SiO $_2$ substrates and capped with ZnO. The samples were annealed to promote the β-Mn crystal structure. Characterization was performed using:

X-Ray Reflectometry (XRR) and Diffraction (XRD): To confirm film thickness, roughness, and crystallographic texture (predominantly $\langle 221 \rangle$ $\beta$ -Mn).
SQUID-VSM Magnetometry: To determine the Curie temperature and saturation fields at various temperatures (25°C to 156°C).
Polarized Neutron Reflectometry (PNR): Conducted at the ISIS Neutron and Muon Source to measure depth-dependent in-plane magnetization profiles under varying magnetic fields and temperatures.

The core methodological innovation lies in the data analysis. The authors developed a Bayesian approach to model selection. They compared two competing physical models against the PNR data:

Uniform Model: Magnetization is reduced near interfaces but lacks transverse moments (no helix).
Helical Model: Magnetization forms a "helicoid" (a distorted helix constrained by shape anisotropy), described by a depth-dependent profile $M(z)$ involving sinusoidal and elliptical distortion components.

Instead of relying solely on $\chi^2$ , the authors calculated the Bayesian model evidence (marginal likelihood) for both models using nested sampling (UltraNest). This approach integrates over the entire parameter space, naturally penalizing model complexity (Occam's factor). The ratio of these evidences (the Bayes factor) was used to determine the probability of the helical state versus the uniform state for each field-temperature condition.

Key Results

Structural Confirmation: XRR and XRD confirmed the growth of a smooth, ~976 Å thick CoZn film with the intended $\beta$ -Mn texture and a ZnO capping layer.
Magnetic Characterization: SQUID measurements confirmed a Curie temperature of $128.6^\circ\text{C}$ , consistent with bulk behavior, and identified saturation fields (~700 mT).
Phase Diagram Mapping: The Bayesian analysis successfully mapped the field-temperature phase diagram.
- At 25°C, the helical model is overwhelmingly probable for fields up to ~47 mT. Above this, the uniform model becomes more probable.
- At 106°C, the transition to the uniform state occurs at a lower field (~10 mT).
- At 156°C (above $T_C$ ), the film is paramagnetic, and no helimagnetism is detected.
Helix Pitch Determination: In the field range where the helical model was most probable (specifically 5–47 mT at 25°C), the helix pitch ( $\lambda_h$ ) was determined to be $1724^{+68}_{-54}$ Å. This value is invariant with respect to temperature and field within the measurement uncertainty and is slightly shorter than the reported bulk value (~1850–2100 Å).
Helicoid Distortion: Analysis of the amplitude ratio ( $A_1/A_2$ ) in the helical model suggests that as the applied field increases, the distortion component ( $A_2$ ) grows, indicating a transition from a pure helix to a helicoid where moments cant toward the field direction, eventually unwinding to a uniform state.

Significance and Claims
The paper claims that the primary contribution is the detection of helimagnetic ordering in a CoZn thin film despite the film thickness being only half a helical period. This was achieved by overcoming the ambiguity of distinguishing helical states from uniform states with interfacial defects.

The authors emphasize the utility of Bayesian model selection in polarized neutron reflectometry. They demonstrate that this statistical approach provides a robust metric to reject the uniform magnetization model in favor of the helical model with high confidence (Bayes factors $> 5.0\sigma$ in many cases), a distinction that would be difficult to make using standard fitting metrics alone.

The work establishes that sputtered $\beta$ -phase CoZn thin films retain the chiral magnetic order necessary for hosting skyrmions. The authors state that this finding serves as a "stepping stone" for future real-space imaging of chiral spin textures (e.g., via Lorentz microscopy) and the development of room-temperature planar spintronic devices based on skyrmions in this material system. The paper does not claim to have observed skyrmions directly, but rather establishes the prerequisite helimagnetic ground state in the thin-film geometry.

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