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Tunable inter-bilayer magnetic correlations and candidate multipolar physics in the van der Waals oxyhalides DyOCl, DyOBr, and DyOI

This study establishes the van der Waals oxyhalides DyOCl, DyOBr, and DyOI as a tunable family of quasi-two-dimensional rare-earth magnets featuring strong hard-axis anisotropy and candidate multipolar physics associated with a high-temperature anomaly near 27–30 K.

Original authors: F. C. Brooks, X. Bai, J. Bacsa, V. O. Garlea, S. Calder, N. Butch, M. B. Stone, M. Mourigal

Published 2026-08-21

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CC BY 4.0

Original authors: F. C. Brooks, X. Bai, J. Bacsa, V. O. Garlea, S. Calder, N. Butch, M. B. Stone, M. Mourigal

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

Magnetism is usually thought of as a property of the whole, a collective behavior where countless tiny atomic magnets align to create a force we can feel. But in the world of quantum materials, the story often begins with the individual. Scientists have long been fascinated by rare-earth elements, a group of metals known for carrying enormous magnetic moments and for how their electrons interact with the atom's internal structure. When these elements are arranged in thin, layered sheets, a unique opportunity arises: the layers can be separated by a tiny gap, allowing researchers to tune how strongly the layers talk to one another. This tuning is possible because the layers are held together not by strong chemical bonds, but by a much weaker force, similar to how two sheets of paper might stick together just from the slight stickiness of their surfaces. By changing the size of the atoms that sit in this gap, scientists can stretch or shrink the distance between the magnetic layers, effectively turning a dial to see how the collective behavior changes. This approach offers a rare chance to study how magnetic order emerges from the bottom up, revealing whether the behavior of a material is dictated by the local environment of a single atom or by the complex dance of neighbors across a vast distance.

A team of researchers has now applied this tuning strategy to a family of crystals made from dysprosium, oxygen, and a halogen element. They synthesized three distinct versions of this material: one with chlorine, one with bromine, and one with iodine. While the basic building block of the crystal—a square layer of dysprosium atoms sandwiched between oxygen and halogen atoms—remained nearly identical in all three, the size of the halogen atom acted as a wedge, pushing the layers further apart. The gap between the layers in the iodine version was nearly sixty percent larger than in the chlorine version. The researchers then subjected these crystals to a battery of tests, including measuring how they responded to magnetic fields, how they absorbed heat, and how they scattered neutrons, a technique that acts like a high-speed camera to reveal the arrangement of atoms and their magnetic spins.

The results revealed a fascinating split between what the materials do as a whole and how their internal structures behave. All three compounds showed the same broad thermodynamic behavior: they became magnetically ordered at low temperatures, around 7 to 10 degrees above absolute zero, and displayed a second, broader anomaly at a higher temperature near 27 to 30 degrees. This second anomaly was particularly intriguing because it did not look like a standard magnetic transition. In the chlorine version, the magnetic layers stacked up in a perfect, repeating pattern, creating a three-dimensional magnetic order. However, as the researchers moved to the bromine and iodine versions, this perfect stacking began to break down. While the magnetic layers remained strongly ordered within themselves, the alignment between one layer and the next became imperfect, like a stack of cards that is perfectly ordered in the middle but slightly shifted at the edges. This loss of long-range stacking order occurred even though the overall heat and magnetic properties of the three materials remained surprisingly similar.

The study also uncovered a strong preference in how the magnetic atoms orient themselves. In all three materials, the magnetic moments were locked tightly into the flat plane of the layers, resisting any attempt to point them up or down. This "hard-axis" behavior was consistent with theoretical models of the atoms' internal energy levels. Furthermore, the researchers identified a specific magnetic vibration, or excitation, in the chlorine crystal that appeared at an energy level of about 10 millielectronvolts. This vibration was distinct from the higher-energy excitations caused by the atoms' internal structure. Crucially, the intensity and sharpness of this 10 millielectronvolt vibration changed in direct correlation with the mysterious high-temperature anomaly. As the material warmed toward that anomaly, the vibration became broader and less distinct, suggesting that the two phenomena are deeply linked.

Despite these clear connections, the researchers could not definitively identify the nature of the high-temperature anomaly. The data ruled out a simple explanation involving a second type of standard magnetic order. Instead, the evidence points toward a more exotic possibility involving "multipolar" physics, a state where the atoms organize not just by their magnetic poles, but by more complex shapes of their electron clouds. The entropy, or disorder, released as the material cooled suggested that more than just a simple pair of energy states were involved in this process. However, without a direct probe capable of seeing these complex shapes, the exact order parameter remains a candidate rather than a confirmed fact. The work establishes this family of crystals as a powerful, tunable platform for exploring these complex states. By simply swapping one halogen for another, scientists can stretch the gap between magnetic layers and watch how the delicate balance between local atomic physics and long-range collective order shifts, offering a clear window into the hidden rules that govern magnetism in reduced dimensions.

Technical Summary: Tunable Inter-bilayer Magnetic Correlations and Candidate Multipolar Physics in DyOCl, DyOBr, and DyOI

Problem and Motivation
Rare-earth van der Waals (VdW) magnets offer a unique platform to combine strong spin-orbit coupling, large magnetic moments, and reduced dimensionality. While transition-metal VdW magnets have been extensively studied, rare-earth oxyhalides ( $LnOX$ ) remain less explored despite their potential for tunable anisotropy and low-dimensional behavior. The dysprosium oxyhalide series ( $DyOX$ , where $X = \text{Cl, Br, I}$ ) presents a specific opportunity to decouple robust intra-bilayer physics from inter-bilayer magnetic coupling. In this series, the local square-bilayer geometry of $Dy^{3+}$ ions remains largely rigid, while the inter-bilayer VdW gap expands significantly (by ~60%) as the halide ionic radius increases. Furthermore, previous studies on related compounds (e.g., $DyOCl$ , $DyOBr$ ) have reported anomalies near 30 K that cannot be explained by conventional dipolar antiferromagnetic order, suggesting the potential for multipolar physics (e.g., quadrupolar order) associated with low-lying crystal-field states. The central problem addressed is the comparative characterization of how chemical tuning of the VdW gap affects magnetic dimensionality, order, and the nature of these high-temperature anomalies.

Methodology
The authors employed a comprehensive suite of experimental techniques on polycrystalline and single-crystal samples of $DyOCl$ , $DyOBr$ , and $DyOI$ :

Synthesis: Solid-state reactions for powders and flux growth for single crystals ( $DyOCl$ , $DyOBr$ ).
Structural Characterization: Powder X-ray diffraction (PXRD) and neutron powder diffraction (NPD) were used to refine lattice parameters and atomic positions. NPD data were analyzed using Rietveld refinement and, for $DyOBr$ and $DyOI$ , reverse Monte Carlo (RMC) simulations (using SPINVERT) to model magnetic diffuse scattering and inter-bilayer correlations.
Thermodynamic Measurements: Magnetization ( $M(T, H)$ ) and heat capacity ( $C_p(T, H)$ ) were measured on powders and oriented single crystals to identify phase transitions and anisotropy.
Inelastic Neutron Scattering (INS): Measurements were performed on $DyOCl$ using time-of-flight spectrometers (SEQUOIA, HYSPEC, DCS) to probe crystal-field (CF) excitations and low-energy magnetic modes.

Key Results

Structural Tuning: Structural refinements confirm that increasing the halide radius from Cl to I expands the inter-bilayer spacing ( $c$ -axis) from ~6.6 Å to ~9.1 Å, while the intra-bilayer $Dy-Dy$ distances and local ligand environment remain nearly rigid. The $Dy^{3+}$ site exhibits an asymmetric, Janus-like coordination (oxygen on one side, halide on the other).
Thermodynamics and Anisotropy: All three compounds exhibit two low-temperature anomalies:
- A sharp transition at $T_N \approx 7\text{--}10$ K, identified as antiferromagnetic (AFM) dipolar ordering.
- A broader anomaly at $T_Q \approx 27\text{--}30$ K.
  Single-crystal magnetization reveals strong hard- $c$ -axis anisotropy, with moments confined to the basal plane. The effective moments derived from Curie-Weiss fits are close to the free-ion value ( $\sim 10.6 \mu_B$ ), though $DyOI$ shows a slight reduction. The ratio $|\theta_W|/T_N$ suggests magnetic frustration in all compounds.
Magnetic Order and Dimensionality:
- $DyOCl$ : Neutron diffraction reveals long-range 3D AFM order with propagation vector $k_m = (0, 0, 1/2)$ . Moments are aligned along the $a$ -axis within bilayers, with ferromagnetic alignment across the VdW gap, doubling the unit cell along $c$ .
- $DyOBr$ and $DyOI$ : These compounds show a coexistence of sharp magnetic reflections (indexed with $k_m = (0, 0, 0)$ ) and broad, Warren-like diffuse scattering. RMC analysis indicates that while strong in-plane and intra-bilayer correlations persist, the inter-bilayer registry is imperfect (finite coherence). This suggests a transition from 3D order in $DyOCl$ to quasi-2D correlated states in the bromide and iodide.
Excitations and Multipolar Candidates:
- Crystal Field: INS on $DyOCl$ identifies CF excitations at 24 and 29 meV. A point-charge model fits these and predicts a ground-state $g$ -tensor consistent with the observed hard- $c$ -axis anisotropy ( $g_{\perp} \approx 21$ , $g_{\parallel} \approx 1$ ). However, the model also predicts a low-energy excited doublet near 0.73 meV, which was not observed in high-resolution measurements.
- 10 meV Mode: A distinct magnetic mode near 10 meV was observed. Its intensity and energy evolve with temperature, broadening and softening as $T$ approaches $T_Q$ . This behavior links the mode to the high-temperature anomaly rather than the dipolar ordering at $T_N$ .
- Entropy: Heat capacity integration shows entropy release approaching $R \ln 4$ by 60 K, suggesting a low-lying quasi-quartet manifold involving degrees of freedom beyond a single Kramers doublet.

Significance and Claims
The paper establishes the $DyOX$ series as a tunable family of quasi-two-dimensional rare-earth magnets where the inter-bilayer coupling can be chemically controlled without altering the local magnetic building block. The authors claim that:

The series demonstrates a clear evolution from 3D long-range order to imperfect inter-bilayer coherence as the VdW gap increases.
The anomaly at $T_Q$ is thermodynamic and distinct from conventional dipolar ordering, exhibiting weak field dependence and significant entropy release consistent with "candidate multipolar physics."
While the data (entropy, weak field dependence, absence of structural distortion) are consistent with quadrupolar order or other multipolar phenomena, the paper does not definitively identify the order parameter at $T_Q$ .
The 10 meV excitation in $DyOCl$ is directly tied to the $T_Q$ anomaly, but its origin (renormalized CF, collective multipolar, or magnetoelastic) remains unresolved by the current data.

The authors conclude that direct probes such as resonant x-ray scattering, elastic-constant measurements, or single-crystal diffuse neutron scattering are required to determine the specific order parameter at $T_Q$ and fully elucidate the nature of the multipolar physics in this system.

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