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arxiv: 2509.15835 · v2 · submitted 2025-09-19 · ❄️ cond-mat.str-el

Novel Quantum Spin Liquid States in the S = {frac{1}{2}} Three-Dimensional Compound Y₃Cu₂Sb₃O₁₄

Saikat Nandi , Rounak Das , M. Hemmida , M. U. Akbar , H.-A. Krug von Nidda , J\"org Sichelschmidt , Sagar Mahapatra , Marlis Schuller
show 5 more authors
N. B\"uttgen John Wilkinson M. P. Saravanan Indra Dasgupta A.V. Mahajan
This is my paper

Pith reviewed 2026-05-18 16:10 UTC · model grok-4.3

classification ❄️ cond-mat.str-el
keywords quantum spin liquidvalence bond solidfrustrated magnetismmuon spin relaxationnuclear magnetic resonanceY3Cu2Sb3O14three-dimensional spin system
0
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The pith

Measurements on Y3Cu2Sb3O14 show no long-range magnetic order and persistent spin dynamics to 0.077 K, pointing to a quantum spin liquid after a partial valence bond solid forms.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines the three-dimensional S=1/2 compound Y3Cu2Sb3O14 built from two types of copper ions on edge-shared triangular lattices. Multiple probes including susceptibility, specific heat, 89Y NMR, muon spin relaxation, and ESR find no signs of conventional magnetic ordering while spin fluctuations continue to the lowest measured temperatures. An NMR feature near 120 K is linked to a fraction of spins forming singlets in a valence bond solid, and muon data show distinct relaxation plateaus consistent with this partial freezing followed by a low-temperature regime where all spins participate in a quantum spin liquid. Density functional theory calculations identify the dominant antiferromagnetic couplings and the resulting frustration on the three-dimensional lattice that prevent ordering.

Core claim

In the three-dimensional S = 1/2 system Y3Cu2Sb3O14 consisting of two inequivalent Cu2+ sites each forming an edge shared triangular lattice, magnetic susceptibility, specific heat, 89Y NMR, muon spin relaxation, and ESR measurements confirm the absence of any long-range magnetic ordering and the persistence of spin dynamics down to 0.077 K. In 89Y NMR an anomaly at about 120 K is suggested to arise from a fraction of the spins condensing into a singlet valence bond solid state. A plateau in the muon relaxation rate between 60 K and 10 K is taken to signify the valence bond solid state from a fraction of the spins, followed by an increase and another plateau below about 1 K presumably from a

What carries the argument

Temperature-dependent muon spin relaxation rate exhibiting two distinct plateaus that separate a partial valence bond solid regime from a low-temperature quantum spin liquid regime.

If this is right

  • The material maintains dynamic spins without freezing or ordering to millikelvin temperatures.
  • A fraction of the copper spins form singlets near 120 K as indicated by the NMR anomaly.
  • The entire spin system enters a quantum spin liquid regime below roughly 1 K.
  • Competing antiferromagnetic interactions identified by DFT generate the frustration that stabilizes the liquid state.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Applying an external magnetic field could split the low-temperature excitations and test the nature of the proposed spin liquid.
  • The three-dimensional geometry offers a contrast to two-dimensional triangular-lattice spin-liquid candidates for future comparative studies.
  • Neutron scattering experiments could directly map the spin correlations in the intermediate and lowest-temperature regimes.

Load-bearing premise

The specific assignment of the 120 K NMR anomaly and the two muon-relaxation plateaus to a partial valence-bond-solid state and a full quantum-spin-liquid state rather than to other possible low-energy excitations or experimental artifacts.

What would settle it

Observation of magnetic Bragg peaks indicating long-range order below 1 K or the disappearance of the low-temperature muon relaxation plateau would contradict the proposed quantum spin liquid state.

Figures

Figures reproduced from arXiv: 2509.15835 by A.V. Mahajan, H.-A. Krug von Nidda, Indra Dasgupta, John Wilkinson, J\"org Sichelschmidt, Marlis Schuller, M. Hemmida, M. P. Saravanan, M. U. Akbar, N. B\"uttgen, Rounak Das, Sagar Mahapatra, Saikat Nandi.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Crystal structure of Y [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) Variation of NMR Shift, [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The temperature dependence of the magnetic specific [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. (a) A schematic of the slightly distorted cubic [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗
Figure 1
Figure 1. Figure 1: FIG. 1. Rietveld refinement of the powder XRD pattern for [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Frustrated 3D spin network of Cu [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Triangular lattices formed by (a) Cu [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a) Temperature dependence of the static magnetic susc [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. (a) Temperature dependence of the real component of [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. (a) Temperature dependence of the specific heat ( [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Scaling of magnetic specific heat [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. The recovery of the longitudinal nuclear magneti [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. (a) X-band ESR spectra (symbols) at represen [PITH_FULL_IMAGE:figures/full_fig_p013_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Muon asymmetry as a function of decay time at [PITH_FULL_IMAGE:figures/full_fig_p014_11.png] view at source ↗
read the original abstract

The three-dimensional $S = {\frac{1}{2}}$ system Y$_{3}$Cu$_{2}$Sb$_{3}$O$_{14}$ consists of two inequivalent Cu$^{2+}$ sites, each forming an edge shared triangular lattice. Our magnetic susceptibility $\chi(T)$, specific heat $C_p(T)$, $^{89}$Y nuclear magnetic resonance (NMR), muon spin relaxation ($\upmu\mathrm{SR}$), and electron spin resonance (ESR) measurements on this system confirm the absence of any long-range magnetic ordering and the persistence of spin dynamics down to 0.077 K. In $^{89}$Y NMR we find an anomaly at about 120 K which we suggest arises from a fraction of the spins condensing into a singlet (a valence bond solid VBS) state. A plateau in the muon relaxation rate is observed between 60 K and 10 K (signifying the VBS state from a fraction of the spins) followed by an increase and another plateau below about 1 K (presumably signifying the quantum spin liquid state from all the spins). Our density functional theory calculations find a dominant antiferromagnetic interaction along the body diagonal with inequivalent Cu(1) and Cu(2) ions alternately occupying the corners of the cube. All other near-neighbour interactions between the Cu ions are also found to be antiferromagnetic and are thought to drive the frustration.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript reports magnetic susceptibility χ(T), specific heat Cp(T), 89Y NMR, μSR, ESR, and DFT calculations on the 3D S=1/2 compound Y3Cu2Sb3O14 with two inequivalent Cu sites forming edge-shared triangular lattices. It claims absence of long-range magnetic order and persistence of spin dynamics to 0.077 K, with a ~120 K 89Y NMR anomaly interpreted as partial spin condensation into a valence-bond-solid (VBS) state from a fraction of spins, and μSR relaxation-rate plateaus (60–10 K then below ~1 K) assigned to partial VBS followed by a full quantum spin liquid (QSL) involving all spins. DFT finds dominant antiferromagnetic body-diagonal coupling plus other AF near-neighbor interactions producing frustration.

Significance. The multi-technique confirmation of no long-range order down to 0.077 K is a solid experimental result that adds a new 3D frustrated S=1/2 candidate to the short list of materials without conventional ordering. If the VBS/QSL partitioning can be placed on a quantitative footing using the DFT exchange network, the work would strengthen evidence for exotic states in three-dimensional lattices; the current qualitative assignments limit the immediate impact.

major comments (2)
  1. [NMR results and discussion] NMR section (discussion of the 120 K anomaly): the claim that this feature arises from a fraction of Cu spins condensing into singlets (partial VBS) is not supported by any calculated Knight-shift drop, 1/T1 behavior, or site-selective response using the DFT-derived dominant body-diagonal AF interaction and the two inequivalent Cu sites; without such modeling the anomaly could equally reflect impurity effects or a structural crossover.
  2. [μSR results] μSR section (plateaus in relaxation rate): the assignment of the 60–10 K plateau to VBS from a fraction of spins and the low-T plateau below ~1 K to a full QSL from all spins rests on qualitative interpretation; a microscopic calculation of the expected depolarization rate for partial singlet formation on the reported exchange network is required to rule out conventional paramagnetic slowing or experimental artifacts.
minor comments (2)
  1. [Abstract] Abstract and conclusions: the tentative phrasing 'we suggest' and 'presumably signifying' for the VBS and QSL assignments should be carried through consistently when stating the central claims.
  2. [DFT section] DFT calculations: a table listing the computed exchange constants (J values and signs) for all near-neighbor pairs would allow direct assessment of the frustration strength and comparison with the experimental energy scales.

Simulated Author's Rebuttal

2 responses · 2 unresolved

We thank the referee for the careful and constructive review of our manuscript. We respond to the major comments point by point below, providing the strongest possible defense of our interpretations based on the available data while being honest about the qualitative nature of some assignments.

read point-by-point responses

  1. Referee: NMR section (discussion of the 120 K anomaly): the claim that this feature arises from a fraction of Cu spins condensing into singlets (partial VBS) is not supported by any calculated Knight-shift drop, 1/T1 behavior, or site-selective response using the DFT-derived dominant body-diagonal AF interaction and the two inequivalent Cu sites; without such modeling the anomaly could equally reflect impurity effects or a structural crossover.

    Authors: We agree that quantitative modeling of the Knight shift and relaxation rate using the DFT exchange parameters would provide stronger evidence for the partial VBS interpretation. In the manuscript, the anomaly is identified through the temperature dependence of the 89Y Knight shift, which shows a deviation around 120 K, and a corresponding feature in 1/T1. This is interpreted as partial singlet formation because it occurs at a temperature scale much higher than the low-temperature QSL regime and is consistent with the frustrated AF interactions found in DFT. To address alternative explanations, we note that impurity effects would typically manifest as a low-temperature Curie tail in susceptibility, which is not observed, and the feature is seen in multiple measurements. A structural crossover is not indicated by our structural characterization. We will revise the manuscript to include a more explicit discussion of these points and the limitations of the current interpretation. revision: yes

  2. Referee: μSR section (plateaus in relaxation rate): the assignment of the 60–10 K plateau to VBS from a fraction of spins and the low-T plateau below ~1 K to a full QSL from all spins rests on qualitative interpretation; a microscopic calculation of the expected depolarization rate for partial singlet formation on the reported exchange network is required to rule out conventional paramagnetic slowing or experimental artifacts.

    Authors: The assignment of the μSR plateaus is indeed qualitative, correlating the 60-10 K plateau with the NMR anomaly at 120 K (adjusted for the different sensitivity) as partial VBS, and the low-T plateau as the onset of QSL dynamics. This is supported by the overall experimental picture of no long-range order and persistent spin fluctuations to 0.077 K from μSR, NMR, and other probes. Conventional paramagnetic slowing is inconsistent with the lack of freezing in specific heat and the frustration from DFT. We have checked for artifacts through careful data analysis. However, we do not have a microscopic calculation of the depolarization rate at this stage. We will update the manuscript to better justify the temperature scales and discuss why other interpretations are less favored. revision: partial

standing simulated objections not resolved
  • Quantitative calculation of the Knight shift drop and 1/T1 using the DFT-derived interactions for the partial VBS state
  • Microscopic modeling of the muon depolarization rate for the partial singlet formation on the exchange network

Circularity Check

0 steps flagged

No circularity: experimental inferences from direct measurements

full rationale

The paper is an experimental study reporting raw data from χ(T), Cp(T), 89Y NMR, μSR, and ESR, plus supporting DFT calculations for the exchange network. The key claims (no long-range order, persistence of dynamics to 0.077 K, 120 K NMR anomaly suggested as partial VBS, muon-rate plateaus assigned to VBS then QSL) are qualitative interpretations of observed features rather than outputs of any derivation, fit, or equation that reduces to the inputs by construction. No self-citations are invoked as load-bearing uniqueness theorems, no parameters are fitted to target conclusions and relabeled as predictions, and the DFT results are presented as independent first-principles input. The work is therefore self-contained against external benchmarks and receives the default non-circularity finding.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claims rest on standard domain assumptions about how magnetic probes reveal spin-liquid or valence-bond-solid behavior in geometrically frustrated antiferromagnets, together with the DFT result that all near-neighbor couplings are antiferromagnetic.

axioms (1)
  • domain assumption Absence of long-range magnetic order together with persistent dynamics at the lowest temperatures indicates a quantum spin liquid in a frustrated S=1/2 system.
    Used to interpret the low-temperature muon plateau and overall lack of ordering as evidence for QSL.

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

  • IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    Our density functional theory calculations find a dominant antiferromagnetic interaction along the body diagonal with inequivalent Cu(1) and Cu(2) ions alternately occupying the corners of the cube. All other near-neighbour interactions between the Cu ions are also found to be antiferromagnetic and are thought to drive the frustration.

  • IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    A plateau in the muon relaxation rate is observed between 60 K and 10 K (signifying the VBS state from a fraction of the spins) followed by an increase and another plateau below about 1 K (presumably signifying the quantum spin liquid state from all the spins).

What do these tags mean?
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The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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