🔬 materials science

Neutron study of magnetic correlations in rare-earth-free Mn-Bi magnets

This study utilizes unpolarized small-angle neutron scattering to characterize magnetic correlations in rare-earth-free Mn-Bi permanent magnets, revealing that their remanent state features long-wavelength transversal magnetization fluctuations with a radius of gyration of 220–240 nm originating from slightly shape-anisotropic structures.

Original authors: Artem Malyeyev, Ivan Titov, Philipp Bender, Mathias Bersweiler, Vitaliy Pipich, Sebastian Mühlbauer, Semih Ener, Oliver Gutfleisch, Andreas Michels

Published 2026-08-19

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CC BY 4.0

Original authors: Artem Malyeyev, Ivan Titov, Philipp Bender, Mathias Bersweiler, Vitaliy Pipich, Sebastian Mühlbauer, Semih Ener, Oliver Gutfleisch, Andreas Michels

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

Permanent magnets are the silent workhorses of modern technology, powering everything from the motors in electric cars to the speakers in our phones. For decades, the most powerful magnets have relied on rare-earth elements like neodymium, which are expensive and difficult to source. Scientists have been searching for a cheaper, more sustainable alternative that can still perform well, especially at the high temperatures found inside electric motors. One promising candidate is a mixture of manganese and bismuth. While these magnets are not yet as strong as the rare-earth champions, they offer a unique advantage: their magnetic strength actually improves as they get hotter, a trait that makes them ideal for demanding applications. However, to make these magnets better, researchers need to understand what is happening inside them on a scale too small to see with ordinary microscopes. They need to know how the magnetic forces are arranged within the material's tiny grains and how defects in the crystal structure influence the overall magnetism.

To solve this puzzle, a team of researchers turned to a technique called neutron scattering. Imagine shining a beam of neutrons, which are tiny particles found in the center of atoms, through a sample of the magnet. As these neutrons pass through, they bounce off the magnetic fields inside the material. By carefully measuring how the neutrons scatter, scientists can map out the invisible magnetic landscape within the solid metal. In this study, the team examined three different versions of manganese-bismuth magnets, each with a slightly different ratio of the two metals. They first magnetized the samples to a strong field and then reduced the field to zero, leaving the magnets in a "remanent" state, where they still hold their magnetism without an external push. By comparing the neutron scattering patterns at this remanent state against patterns taken when the magnet was fully saturated, they were able to isolate the specific signal coming from the magnetic fluctuations, filtering out the background noise from the atoms themselves.

The results revealed that the magnetic behavior in these materials is dominated by long-wavelength fluctuations, which are essentially gentle, large-scale wobbles in the direction of the magnetic alignment. These wobbles are not random; they are tied to the physical imperfections in the crystal structure, such as tiny pores or boundaries between grains. The researchers found that these magnetic disturbances extend over a surprisingly large distance, ranging from about 220 to 240 nanometers in the remanent state. To put this in perspective, these magnetic regions are distinct, measurable features that span a significant portion of the microscopic world. This size is crucial because it represents the scale over which a defect in the crystal can disrupt the magnetic order, a factor that directly determines how hard it is to demagnetize the material.

Beyond just measuring the size of these regions, the study uncovered a subtle but important difference between the alloy compositions. For two of the samples, the magnetic structures appeared to be roughly spherical or globular. However, for the sample with the highest bismuth content, the data pointed to a different shape. The analysis suggested that the magnetic scattering in this specific alloy originated from slightly elongated, rod-like structures rather than round blobs. This finding was unexpected because standard electron microscopy images of similar samples had not previously revealed such shape-anisotropic particles. The neutron data, however, provided a unique window into the magnetic arrangement itself, indicating that increasing the bismuth content might be causing the magnetic domains to stretch out.

This distinction matters because the shape of these magnetic regions influences the magnet's overall performance. If the magnetic structures are elongated, they can provide a form of shape anisotropy, which acts like a natural lock that helps the magnet resist losing its strength. The researchers suggest that by adjusting the alloy composition to encourage these elongated structures, it might be possible to create manganese-bismuth magnets that are even harder and more resistant to demagnetization. While the study did not solve every mystery—such as why the mathematical patterns of the scattering were slightly different from what is seen in other types of magnets—it provided a clear, new way to correlate the microscopic magnetic defects with the macroscopic properties of the magnet. By using neutrons to peer into the hidden magnetic architecture, the team has offered a roadmap for engineers to tune these rare-earth-free magnets, potentially bridging the gap between cheap, low-performance magnets and the expensive, high-performance ones that drive our modern world.

Technical Summary: Neutron Study of Magnetic Correlations in Rare-Earth-Free Mn–Bi Magnets

Problem Statement
Permanent magnets are critical components in electronics and motors, yet the market is currently dominated by high-performance Nd-Fe-B magnets and low-performance ferrites. There is a specific technological gap for medium-performance, cost-effective materials capable of operating at temperatures up to 500 K, where Nd-Fe-B performance degrades significantly. Rare-earth-free Mn-based permanent magnets, particularly the low-temperature phase of the Mn–Bi binary alloy, are prime candidates to fill this gap due to their positive temperature coefficient of magnetic anisotropy. However, while most existing research focuses on integral measurement techniques and engineering aspects, the macroscopic magnetic properties of these materials arise from spatial variations in the magnetization vector field on a mesoscopic length scale (nanometers to microns). A deeper understanding of magnetic correlations and long-wavelength magnetization fluctuations is required to optimize material properties from both a basic science and materials science perspective.

Methodology
The authors investigated cold-compacted, isotropic Mn–Bi magnets with three different alloy compositions: Mn $_{55}$ Bi $_{45}$ , Mn $_{50}$ Bi $_{50}$ , and Mn $_{45}$ Bi $_{55}$ . The samples were synthesized via arc melting, annealing, and ball milling, then cold-compacted into pellets.

The primary experimental technique employed was unpolarized very small-angle neutron scattering (VSANS) conducted at room temperature using the KWS-3 instrument at the Heinz Maier-Leibnitz Zentrum (MLZ).

Geometry: An external magnetic field ( $H_0$ ) was applied perpendicular to the incident neutron beam ( $H_0 \perp k_0$ ).
Data Acquisition: Measurements were taken at a saturation field of 2.2 T and subsequently at lower fields, including the remanent state (0 T).
Data Processing: To isolate the magnetic signal, the total scattering cross-section at 2.2 T (where the magnetization is saturated and nuclear scattering dominates) was subtracted from the data at lower fields. This procedure eliminates the nuclear contribution and yields the purely magnetic SANS cross-section ( $d\Sigma_M/d\Omega$ ).
Analysis: The resulting magnetic scattering data were analyzed using two complementary approaches:
1. Generalized Guinier-Porod (GP) Model: An empirical model used to decompose the scattering curve into Guinier and Porod regions, providing parameters such as the Guinier radius ( $R_G$ ), a dimensionality factor ( $s$ ), and a Porod power-law exponent ( $n$ ).
2. Distance Distribution Function ( $p(r)$ ): A model-independent calculation derived from the scattering data to characterize the size and shape of the scattering objects and interparticle correlations.

Key Results

Magnetic Correlation Length: The magnetic SANS cross-section was dominated by long-wavelength transversal magnetization fluctuations. The analysis yielded Guinier radii ( $R_G$ ) in the remanent state ranging between approximately 220 nm and 240 nm for all three compositions. This length scale represents the size of inhomogeneously magnetized regions around microstructural defects (such as dislocations or interfaces) where spin-misalignment occurs.
Field Dependence: The behavior of $R_G$ under varying magnetic fields varied by composition. The Mn $_{45}$ Bi $_{55}$ sample showed a decrease in $R_G$ from ~220 nm at remanence to ~100 nm at 1.5 T, consistent with the suppression of spin-misalignment fluctuations by the applied field. The Mn $_{50}$ Bi $_{50}$ sample showed a potential increase in $R_G$ with field, though uncertainties were large. The Mn $_{55}$ Bi $_{45}$ sample showed field-independent $R_G$ within error bars.
Structural Anisotropy:
- The Porod exponent ( $n$ ) was found to be systematically lower than the sharp-interface value of 4 (ranging from 3.38 to 3.58), suggesting smoothed surfaces or continuous magnetization density variations.
- The dimensionality parameter ( $s$ ) and the distance distribution function ( $p(r)$ ) revealed differences in the shape of the magnetic structures.
  - Mn $_{55}$ Bi $_{45}$ and Mn $_{50}$ Bi $_{50}$ samples exhibited $s$ values close to 0 and $p(r)$ profiles typical of globular (spherical) scatterers.
  - The Mn $_{45}$ Bi $_{55}$ sample exhibited an $s$ value of 1.07 and a $p(r)$ profile with a broad maximum at ~470 nm and a long tail. This indicates that the magnetic scattering in this composition originates from slightly shape-anisotropic, elongated structures, despite electron microscopy on similar samples not revealing such particles on that specific length scale.

Significance and Claims
The paper claims that the presented neutron methodology—specifically the combination of difference data analysis, the generalized Guinier-Porod model, and the distance distribution function—provides a unique means to systematically correlate the spin-misalignment length (a property of defects) with macroscopic permanent magnet parameters like coercivity and maximum energy product.

The study suggests that increasing the Bi content in Mn–Bi alloys may lead to increasingly elongated magnetic structures. The authors posit that this shape anisotropy could be a valid approach to enhance the magnetic hardness of the compound, offering a potential route to improve coercivity without relying on rare-earth elements. Furthermore, the work highlights that magnetic SANS can determine relevant figures of merit ( $R_G$ , $s$ , $n$ ) that are not accessible through integral measurement techniques, thereby bridging the gap between mesoscopic magnetic microstructure and macroscopic performance.

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