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

Abstract: Rare-earth van der Waals magnets provide a route to combining strong spin-orbit coupling, large magnetic moments, and reduced dimensionality in bulk crystals. We report a comparative study of the dysprosium oxyhalides DyOX (X = Cl, Br, I), which realize square-bilayer networks of Dy3+ moments separated by a tunable van der Waals gap. Structural refinements show that increasing the halide ionic radius strongly expands the inter-bilayer spacing while leaving the local bilayer geometry nearly unchanged. Magnetization and heat-capacity measurements reveal two low-temperature anomalies in all three compounds: antiferromagnetic order at TN ~ 7-10 K and a broader anomaly near TQ ~ 27-30 K. Single-crystal magnetization on DyOCl and DyOBr establishes a strong hard-c-axis anisotropy, consistent with crystal-field analysis of DyOCl, which yields an XY-like ground-state g tensor. Neutron diffraction shows long-range antiferromagnetic order in DyOCl, whereas DyOBr and DyOI exhibit sharp magnetic scattering coexisting with Warren-like diffuse features, consistent with robust in-plane correlations and imperfect inter-bilayer registry. Inelastic neutron scattering on DyOCl identifies crystal-field excitations near 25-30 meV and an additional magnetic mode near 10 meV whose temperature dependence is tied to the high-temperature anomaly. Taken together, these results establish DyOX as a tunable family of quasi-two-dimensional rare-earth magnets and point to candidate multipolar physics associated with low-lying crystal-field states. Direct probes of quadrupolar order, such as resonant x-ray scattering or elastic-constant measurements, will be required to determine the order parameter at TQ.

• The paper demonstrates chemical substitution of halides (Cl, Br, I) to expand inter-bilayer spacing by 60% without changing intra-bilayer Dy$^{3+}$ geometry while shifting magnetic behavior.
• Structural differences suggest evolving magnetic order across the series from 3D antiferromagnetic in DyOCl to partially coherent bilayer stacking in DyOBr and DyOI.
• All compounds exhibit a broader, entropy-rich anomaly near 27-30 K consistent with but not confirming multipolar (quadrupolar) physics, necessitating follow-up studies to clarify.

The dysprosium oxyhalides DyO$X$ ($X=$ Cl, Br, I) form a chemically tunable family of van der Waals rare-earth magnets in which square bilayers of Dy$^{3+}$ ions are separated by a halide-terminated gap whose width can be varied systematically. This paper reports a comparative experimental study of all three members using single-crystal and powder x-ray diffraction, neutron powder diffraction, magnetization, heat capacity, and inelastic neutron scattering. The central findings are threefold: first, halide substitution expands the inter-bilayer spacing by roughly 60% while leaving the intra-bilayer Dy geometry nearly rigid; second, this structural tuning produces a qualitative change in the low-temperature magnetic state, from fully coherent three-dimensional antiferromagnetic order in DyOCl to partially coherent stacking of strongly correlated bilayers in DyOBr and DyOI; third, all three compounds share a higher-temperature thermodynamic anomaly near $T_Q \simeq 27$–30 K whose properties are consistent with, but do not establish, multipolar (quadrupolar) physics.

Structural tuning of a rigid bilayer motif

All three compounds crystallize in the tetragonal space group $P4/nmm$, confirmed by Rietveld refinement of powder neutron diffraction data collected at 40–80 K. The key structural result is the decoupling of intra-bilayer and inter-bilayer length scales across the series. The $a$ axis remains fixed near 3.9 Å, while the $c$ axis elongates from 6.608 Å (DyOCl) to 8.152 Å (DyOBr) and 9.148 Å (DyOI). Correspondingly, the nearest-neighbor Dy–Dy distance within a bilayer stays at approximately 3.56 Å for all three compounds, whereas the van der Waals gap distance $d_{\rm VdW}^X$ grows from 3.02 Å to 5.03 Å — a change of about 60%. Temperature-dependent x-ray diffraction on DyOCl between 300 K and 14 K shows smooth lattice contraction ($\Delta c/c \approx 0.22\%$) with no resolved symmetry lowering down to the lowest measured temperatures, including through the $T_Q$ anomaly.

A notable detail is that in DyOCl the inter-bilayer Dy–Cl distance approximately equals the intra-bilayer Dy–Cl ligand distance ($X=$0), so chlorine atoms across the gap act effectively as additional first-shell ligands; this ratio drops to roughly 0.75 and 0.67 for Br and I. This asymmetry provides a plausible microscopic handle on how the axial crystal field and inter-bilayer exchange pathways evolve across the series.

Thermodynamics: two anomalies with distinct field responses

Magnetization and heat capacity reveal two low-temperature anomalies in every compound. A sharp lambda-like anomaly at $X=$1 = 8.84 K (DyOCl), 6.95 K (DyOBr), and 6.85 K (DyOI) coincides with a susceptibility cusp and magnetic Bragg scattering, identifying it unambiguously as dipolar antiferromagnetic order. Curie–Weiss fits above 50 K yield negative Weiss temperatures ($X=$2, $X=$3, $X=$4 K) and effective moments close to the free-ion value of 10.62 $X=$5, giving frustration ratios $X=$6 of 2.0–2.9.

The second anomaly at $X=$7 = 26.5–29.9 K behaves qualitatively differently. It is broader, carries substantial entropy, shifts only weakly (and sometimes upward) under applied magnetic field, and produces no detectable magnetic Bragg intensity or structural distortion. These observations exclude a conventional second dipolar ordering transition as its simplest explanation. Entropy analysis, after Debye-model lattice subtraction, shows accumulation of order $X=$8 through the low-temperature transition — consistent with ordering of an isolated Kramers doublet — but a total approaching $X=$9 by 60 K, indicating participation of additional low-energy degrees of freedom beyond a single doublet. The authors emphasize that this quasi-quartet interpretation is consistent with candidate multipolar physics but is not established by thermodynamics alone; crystal-field population effects, magnetoelastic coupling, or short-range correlations remain viable alternatives.

Single-crystal heat capacity of DyOCl maps out four regimes in the field–temperature plane: antiferromagnetic, paramagnetic, field-polarized, and an intermediate regime bounded by $^{3+}$0. The rapid suppression of $^{3+}$1 versus the weak field response of $^{3+}$2 demonstrates that the two anomalies originate from different components of the low-energy manifold.

Anisotropy and metamagnetism

Single-crystal magnetization on DyOCl and DyOBr establishes strong hard-$^{3+}$3-axis anisotropy. For fields perpendicular to $^{3+}$4, the magnetization reaches the full Dy$^{3+}$5 moment of approximately 10.5 $^{3+}$6/Dy by 3.5 T at 1.8 K; for fields parallel to $^{3+}$7, it remains small and unsaturated up to 14 T. Powder samples show incomplete saturation near 7–8 $^{3+}$8/Dy at 14 T, naturally explained by orientational averaging of this anisotropy. All compounds exhibit a low-field metamagnetic jump (1.57–1.79 T in powder), followed by plateau-like behavior for in-plane fields up to roughly 2.4 T in DyOCl. The authors deliberately avoid calling the anisotropy "easy-plane," since ordered moments select specific in-plane directions; the correct description is hard-$^{3+}$9-axis anisotropy plus a secondary in-plane anisotropy relevant to the ordered state.

Magnetic diffraction: long-range order versus imperfect registry

Neutron powder diffraction at 1.5 K reveals a sharp contrast across the series. DyOCl orders with propagation vector $T_Q \simeq 27$0 in magnetic space group $T_Q \simeq 27$1: ferromagnetic monolayers coupled antiferromagnetically within each bilayer and ferromagnetically across the van der Waals gap, with moments along the crystallographic $T_Q \simeq 27$2 axis refining to 7.52 $T_Q \simeq 27$3/Dy. The refined moment is smaller than the ~10 $T_Q \simeq 27$4 previously reported; given the severe neutron absorption of natural Dy and correlations among absorption correction, scale factor, and moment amplitude in powder refinements, the authors regard the moment direction and periodicity as more robust than the absolute magnitude.

DyOBr and DyOI behave differently. Their sharp magnetic reflections index with $T_Q \simeq 27$5 in $T_Q \simeq 27$6, but the resulting refinements place moments along $T_Q \simeq 27$7 (3.54 and 2.57 $T_Q \simeq 27$8/Dy) — directly contradicting the independently established hard-$T_Q \simeq 27$9-axis anisotropy. The authors resolve this contradiction by showing that broad, asymmetric Warren-like diffuse scattering coexists with the sharp peaks, characteristic of correlations extended in-plane but finite along the stacking direction. Reverse Monte Carlo (SPINVERT) refinements constrained to in-plane moments reproduce both components simultaneously: strong antiferromagnetic correlations exist within each bilayer and persist across the nearest van der Waals gap, then decay with layer separation. The apparent absence of sharp $P4/nmm$0 and $P4/nmm$1 reflections is explained by their broadening due to finite inter-bilayer coherence rather than absence of in-plane moments. The correlation profiles are explicitly not unique microscopic structures; distinguishing stacking faults from finite correlation lengths or competing domains requires single-crystal diffuse scattering.

Crystal-field spectroscopy and the unresolved 10 meV mode

Inelastic neutron scattering on DyOCl resolves two magnetic excitations near 24 and 29 meV (FWHM 3.8 and 4.0 meV) whose intensity decreases with $P4/nmm$2. A point-charge crystal-field model built from the neutron-refined ligand coordinates, with uniformly renormalized charges (factor 1.196), reproduces these transitions and yields Stevens parameters consistent with a ground-state doublet having $P4/nmm$3 and $P4/nmm$4 — matching the hard-$P4/nmm$5-axis magnetization quantitatively. However, the model predicts a neutron-active transition at 0.73 meV that neither HYSPEC nor high-resolution DCS measurements observe. The authors state plainly that either the high-energy spectrum does not constrain the low-energy level scheme uniquely, or interactions neglected by the single-ion model substantially renormalize the low-energy states.

A separate, weakly dispersive mode near 10 meV exhibits magnetic $P4/nmm$6 dependence and a striking temperature evolution: it broadens from 0.62 meV FWHM at 1.5 K to 1.5 meV at 15 K, softens, and disappears as a resolved feature by 30 K — tracking $P4/nmm$7 rather than $P4/nmm$8. Its energy cannot be reconciled with the predicted sub-meV transition: a magnetostatic estimate gives local fields of only order 0.6 T, far too small to shift the level by 10 meV. Phenomenological mean-field tests adding rank-two quadrupolar operators ($P4/nmm$9, $a$0, $a$1) show that such fields can generate a neutron-active level near 10 meV, but none reproduces it simultaneously with the 25–30 meV excitations without introducing unobserved transitions. This negative result excludes static single-ion mean-field descriptions within the point-charge Hamiltonian, while leaving open collective multipolar excitations acquiring dipolar intensity through mixing, or magnetoelastic hybridization.

Limitations and open questions

Several limitations bear directly on the conclusions. The DyOBr single-crystal magnetization was normalized assuming a saturated moment rather than measured mass, introducing systematic uncertainty in absolute scale. The entropy analysis relies on phenomenological Debye lattice subtractions (two scales required for DyOBr and DyOI) and integration from finite temperature. The reverse Monte Carlo correlation profiles are non-unique, and the in-plane easy-axis choice shown connects continuously to DyOCl but is not independently determined. Most fundamentally, the order parameter at $a$2 remains undetermined: no direct quadrupolar-sensitive measurement has been performed. The paper identifies resonant x-ray scattering, elastic-constant or ultrasound measurements, Raman spectroscopy across $a$3, polarized inelastic neutron scattering on single crystals to characterize the 10 meV mode's dispersion and character, and single-crystal diffuse neutron scattering to determine the inter-bilayer correlation function as the decisive experiments.

Conclusion

This work establishes DyO$a$4 as a rare-earth van der Waals platform in which chemical substitution tunes inter-bilayer coupling over a wide range while preserving the local magnetic building block. The progression from coherent three-dimensional $a$5-type order in DyOCl to correlated-but-incoherently-stacked bilayers in DyOBr and DyOI demonstrates that halide substitution changes the nature, not merely the strength, of interlayer coupling. The shared anomaly at $a$6, its substantial entropy, weak field dependence, absence of dipolar Bragg order, and association with a softening 10 meV excitation collectively motivate — without proving — a multipolar interpretation. Resolving whether $a$7 marks quadrupolar order, magnetoelastic coupling, or another instability of the quasi-quartet manifold is the central open question this study leaves for future work.