🔬 materials science

Ferromagnetic resonance and magnetic anisotropy in YbMn $_\text{6}$ Sn $_\text{6}$

This study investigates the magnetic anisotropy and dynamic magnetization of ferromagnetic YbMn $_\text{6}$ Sn $_\text{6}$ using ferromagnetic resonance and DC magnetization, revealing an expected uniaxial anisotropy along the c-axis and a growth-induced twofold anisotropy within the ab-plane that breaks the material's inherent sixfold rotational symmetry.

Original authors: Philipp Schwenke, Kyle W. Fruhling, David Weffling, Vitaliy I. Vasyuchka, Fazel Tafti, Mathias Weiler

Published 2026-09-24

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Philipp Schwenke, Kyle W. Fruhling, David Weffling, Vitaliy I. Vasyuchka, Fazel Tafti, Mathias Weiler

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

Deep within the world of materials science, there exists a fascinating family of crystals known as kagome magnets. The name comes from a traditional Japanese woven pattern, a lattice of triangles that creates a unique geometric frustration for the atoms inside. In these materials, layers of manganese atoms form a specific web-like structure, separated by layers containing rare-earth elements. This arrangement is special because it forces the electrons to interact in complex ways, often leading to unusual magnetic behaviors and electronic properties that defy simple explanation. Scientists are particularly interested in these materials because they might hold the key to new types of technology, from faster computers to more efficient energy storage. However, while researchers have spent years mapping out the static magnetic properties of these crystals—essentially taking a snapshot of how they behave when sitting still—the story of how they move and respond to changing forces has remained largely untold. Understanding this dynamic behavior is crucial, as it reveals how the material's internal magnetic landscape guides the flow of information and energy.

In a recent study, a team of physicists turned their attention to a specific member of this family called YbMn6Sn6, a compound that behaves as a magnet at temperatures below 300 Kelvin. They wanted to understand the rules that govern how the magnetism in this crystal points and turns. To do this, they used a technique called ferromagnetic resonance, which is essentially a way of listening to the natural frequency at which the magnetic moments inside the material vibrate when nudged by a magnetic field. By rotating the magnetic field and observing how this vibration frequency changed, the researchers could map out the invisible energy hills and valleys that the magnetism prefers to sit in. They also performed standard measurements of how the material responds to magnetic fields in different directions to confirm their findings.

The results confirmed what scientists had long suspected about the overall shape of this magnetic landscape. The crystal has a clear "hard" direction, running vertically through its layers, where it is very difficult to force the magnetism to point. Conversely, the magnetism prefers to lie flat within the horizontal layers, which act as an "easy" plane. This vertical preference is a known feature of these materials, driven by the crystal's layered structure. However, the researchers discovered something unexpected within that flat, easy plane. If the crystal were a perfect hexagon, as its atomic structure suggests, the magnetic properties should look the same no matter which horizontal direction you choose; it should have a six-fold symmetry, like a snowflake. Instead, the measurements revealed a distinct two-fold pattern. The magnetism found one specific horizontal direction to be easier to align with than the direction perpendicular to it. It was as if the flat plane, which should have been perfectly uniform, actually had a preferred axis running through it.

This discovery of a hidden two-fold preference within the horizontal plane was a significant finding because it contradicts the simple expectation based on the crystal's geometry. The researchers determined that this extra preference is not a fundamental property of the perfect atomic lattice but is likely caused by the way the crystal grew. Small strains or imperfections introduced during the manufacturing process appear to have broken the perfect symmetry, creating a subtle but measurable bias in how the magnetism behaves. To be sure of this, the team measured the material in three different orientations: along the easy horizontal direction, along the hard vertical direction, and along the intermediate horizontal direction. In every case, the data showed that a simple model of the crystal's shape was not enough to explain the results. They needed to include this extra, growth-induced anisotropy to accurately predict how the material would respond.

The study also provided precise numbers for how strong these magnetic preferences are. The resistance to magnetizing the crystal vertically is quite high, while the difference between the two horizontal directions, though smaller, is significant enough to be clearly measured. By comparing the resonance data with standard magnetization measurements on different crystals from the same batch, the team confirmed that this two-fold effect is a real and reproducible feature, not just a fluke of a single sample. While the exact microscopic origin of this growth-induced strain remains a topic for further investigation, the work successfully demonstrates that the magnetic response of YbMn6Sn6 is more complex than previously thought. It is not just a simple magnet with a vertical hard axis; it is a material whose internal magnetic rules are subtly shaped by the history of its creation, revealing a layer of detail that only careful, dynamic probing could uncover.

Problem Statement
The RMn $_6$ Sn $_6$ family of kagome magnets (where R is a rare earth element) is known for exhibiting a rich variety of magnetic states and unconventional electronic properties arising from the interplay of geometric frustration, electronic correlations, and nontrivial band topology. While the static magnetic properties of these materials, including the ferromagnetic order of YbMn $_6$ Sn $_6$ below a Curie temperature ( $T_C$ ) of approximately 300 K, have been extensively investigated, their magnetization dynamics remain less explored. Specifically, previous studies established a pronounced uniaxial anisotropy between the crystallographic $c$ -axis (the magnetic hard axis) and the $ab$-plane (the easy plane). However, the nature of magnetic anisotropy within the $ab$-plane has received considerably less attention. Given the hexagonal crystal structure, a sixfold rotational symmetry is expected in the magnetic response; yet, deviations from this symmetry in the dynamic response had not been fully characterized in YbMn $_6$ Sn $_6$ .

Methodology
To address these gaps, the authors employed angle-dependent ferromagnetic resonance (FMR) spectroscopy and DC magnetization measurements on YbMn $_6$ Sn $_6$ crystals.

FMR Measurements: Angle-dependent FMR (AdFMR) was conducted at $T = 250$ K with a fixed external magnetic field of $\mu_0H = 0.8$ T. The magnetic field was rotated in various planes: within the $ab$-plane, within the plane spanned by the $c$ -axis and the $ab$-plane hard axis, and within the plane spanned by the $c$ -axis and the $ab$-plane easy axis. Additionally, field-dependent FMR spectra were recorded with the field aligned along the easy axis, hard axis, and $c$ -axis.
DC Magnetization: To validate the anisotropy constants derived from FMR, angle-dependent DC magnetization measurements were performed on a second crystal from the same growth batch and a third crystal from a different batch.
Theoretical Modeling: The resonance frequencies were calculated using the Kittel equation derived from the magnetic free energy ( $F = F_{Zee} + F_{demag} + F_{ani}$ ). The model included Zeeman energy, demagnetization (shape anisotropy) energy, and magnetocrystalline anisotropy energy. Parameters such as saturation magnetization ( $M_s$ ), the Landé g-factor ( $g$ ), uniaxial anisotropy constants ( $K_u$ , $K_{u2}$ ), and demagnetization factors ( $N_{xx}, N_{yy}, N_{zz}$ ) were extracted or manually varied to achieve agreement between calculated and experimental resonance frequencies.

Key Contributions and Results

Confirmation of Uniaxial Anisotropy: The AdFMR data confirmed the expected uniaxial anisotropy distinguishing the crystallographic $c$ -axis as the global magnetic hard axis from the $ab$-plane as the easy plane. The resonance frequency exhibited a 180 $^\circ$ periodicity with minima when the field was parallel to the $c$ -axis.
Discovery of In-Plane Twofold Anisotropy: A significant finding is the identification of a pronounced twofold anisotropy within the $ab$-plane. This was evidenced by:
- FMR: The angular dependence of the resonance frequency in the $ab$-plane showed a 180 $^\circ$ periodicity rather than the sixfold symmetry expected from the hexagonal lattice. This required the inclusion of a second-order anisotropy constant ( $K_{u2} \approx 15$ kJ m $^{-3}$ ) in the free energy model to accurately reproduce the experimental data.
- DC Magnetization: Angle-dependent DC magnetization measurements on a separate crystal independently confirmed this twofold symmetry. At low magnetic fields, the magnetization exhibited a 180 $^\circ$ periodicity, inconsistent with the crystal's sixfold rotational symmetry. The extracted anisotropy constant for this effect was $K_{u,2} = 7.2$ kJ m $^{-3}$ .
Quantitative Anisotropy Constants: The study successfully extracted consistent anisotropy constants across different measurement techniques and crystals.
- The effective uniaxial anisotropy constant along the $c$ -axis was determined to be $K_{u,1} \approx 161.5$ kJ m $^{-3}$ (after correcting for shape anisotropy), which aligns with values reported for MgMn $_6$ Sn $_6$ .
- The Gilbert damping parameter was extracted as $\alpha = (0.113 \pm 0.002)$ .
Origin of Anisotropy: The authors note that while shape anisotropy contributes significantly, it cannot fully explain the observed twofold in-plane anisotropy, as the demagnetization factors for the samples suggest the $ab$-plane should be isotropic. The observed symmetry breaking is attributed to growth-induced anisotropy or strain within the crystal, though the precise microscopic origin requires further investigation.

Significance
The paper demonstrates that the magnetic response of YbMn $_6$ Sn $_6$ is not fully captured by a simple model of $c$ -axis uniaxial anisotropy and shape anisotropy. The identification of a pronounced twofold anisotropy within the $ab$-plane reveals a breaking of the expected sixfold rotational symmetry in the magnetic response. This finding highlights the sensitivity of FMR spectroscopy to subtle anisotropy effects that may be overlooked in static measurements. The work establishes that growth-induced effects or strain can significantly alter the magnetic free-energy landscape in kagome magnets, providing a more complete understanding of the dynamic magnetization properties in the RMn $_6$ Sn $_6$ family.

More like this