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arxiv: 2509.26151 · v1 · submitted 2025-09-30 · ❄️ cond-mat.str-el

Spin-supersolidity induced quantum criticality and magnetocaloric effect in the triangular-lattice antiferromagnet Rb₂Co(SeO₃)₂

Yi Cui , Zhanlong Wu , Zhongcen Sun , Kefan Du , Jun Luo , Shuo Li , Jie Yang , Jinchen Wang
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Rui Zhou Qian Chen Yoshimitsu Kohama Atsuhiko Miyata Zhuo Yang Rong Yu Weiqiang Yu
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Pith reviewed 2026-05-18 12:29 UTC · model grok-4.3

classification ❄️ cond-mat.str-el
keywords spin supersolidquantum criticalitymagnetocaloric effecttriangular lattice antiferromagnetNMR relaxationIsing modelRb2Co(SeO3)2high magnetic field
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The pith

Rb2Co(SeO3)2 enters a spin supersolid phase with gapless excitations from 15.8 to 18.5 T before a continuous quantum phase transition at 19.5 T.

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

The study maps the high-field magnetic phases of the Ising triangular-lattice antiferromagnet Rb2Co(SeO3)2 through magnetization, magnetocaloric effect, and NMR measurements. Below 15.8 T the system occupies a gapped up-up-down ordered state marked by the one-third magnetization plateau and thermally activated spin relaxation. Between 15.8 T and 18.5 T the data indicate a spin supersolid ground state containing gapless spin excitations, while a continuous quantum phase transition appears at approximately 19.5 T with the product of exponents νz near 1. Near this critical field the enhanced spin fluctuations produce a sizable magnetocaloric effect at elevated temperatures, positioning the compound as a candidate for cryogenic cooling.

Core claim

In Rb₂Co(SeO₃)₂ the ground state evolves from a gapped UUD magnetic order below 15.8 T to a spin supersolid with gapless excitations between 15.8 T and 18.5 T, as shown by the transition from thermal activation to power-law behavior in 1/T1, the slow saturation of the NMR spectral ratio, and the susceptibility anomaly. A continuous quantum phase transition occurs at H_C ≈ 19.5 T with νz ≈ 1, detected via the Grüneisen ratio extracted from magnetocaloric data, accompanied by universal scaling and strong spin fluctuations that generate large high-temperature magnetocaloric signals.

What carries the argument

The spin supersolid phase with gapless excitations, which occupies the intermediate field window and directly precedes the quantum critical point at 19.5 T.

If this is right

  • A large high-temperature magnetocaloric effect appears near H_C driven by frustration and quantum criticality.
  • Universal quantum critical scaling with νz ≈ 1 holds in the vicinity of 19.5 T.
  • Strong spin fluctuations persist over a broad temperature range around the critical field.
  • The compound functions as a platform for studying field-tuned quantum criticality in frustrated magnets.

Where Pith is reading between the lines

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

  • Similar field-induced supersolid windows may exist in other triangular-lattice Ising materials with comparable exchange parameters.
  • Specific-heat or thermal-conductivity measurements could independently confirm the gapless nature of the supersolid excitations.
  • The observed magnetocaloric response suggests the material could be tested for cooling performance at millikelvin temperatures.

Load-bearing premise

The power-law temperature dependence of 1/T1 together with the slow saturation of the NMR spectral ratio are interpreted as signatures of a spin supersolid rather than other possible gapless or partially disordered states.

What would settle it

Direct measurement of a finite spin gap persisting through the 15.8–18.5 T window or a clear departure from νz ≈ 1 scaling in higher-resolution Grüneisen-ratio data would falsify the supersolid and continuous-transition claims.

Figures

Figures reproduced from arXiv: 2509.26151 by Atsuhiko Miyata, Jie Yang, Jinchen Wang, Jun Luo, Kefan Du, Qian Chen, Rong Yu, Rui Zhou, Shuo Li, Weiqiang Yu, Yi Cui, Yoshimitsu Kohama, Zhanlong Wu, Zhongcen Sun, Zhuo Yang.

Figure 1
Figure 1. Figure 1: b, the peak and the dip features are seen as connected by the dashed lines. These dip and peak temperatures track exactly the Neel temperature ´ TN, as confirmed by the NMR spectra shown below. TN extracted at each field is then plotted in the phase diagram of [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
read the original abstract

We performed high-field magnetization, magnetocaloric effect (MCE), and NMR measurements on the Ising triangular-lattice antiferromagnet Rb$_2$Co(SeO$_3$)$_2$. The observations of the 1/3-magnetization plateau, the split NMR lines, and the thermal activation behaviors of the spin-lattice relaxation rate $1/T_1$ between 2 T and 15.8 T provide unambiguous evidence of a gapped up-up-down (UUD) magnetic ordered phase. For fields between 15.8 T and 18.5 T, the anomaly in the magnetic susceptibility, the slow saturation of the NMR line spectral ratio with temperature, and the power-law temperature dependence of $1/T_1$ suggest the ground state to be a spin supersolid with gapless spin excitations. With further increasing the field, the Gr\"{u}neisen ratio, extracted from the MCE data, reveals a continuous quantum phase transition at $H_{\rm C}\approx$ 19.5 T and a universal quantum critical scaling with the exponents ${\nu}z~\approx~$1. Near $H_{\rm C}$, the large high-temperature MCE signal and the broad peaks in the NMR Knight shift and $1/T_1$, manifest the strong spin fluctuations driven by both magnetic frustration and quantum criticality. These results establish Rb$_2$Co(SeO$_3$)$_2$ as a candidate platform for cryogenic magnetocaloric cooling.

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 high-field magnetization, magnetocaloric effect (MCE), and NMR measurements on the Ising triangular-lattice antiferromagnet Rb₂Co(SeO₃)₂. It identifies a gapped up-up-down (UUD) ordered phase between 2 T and 15.8 T based on the 1/3-magnetization plateau, split NMR lines, and thermally activated 1/T₁. Between 15.8 T and 18.5 T, anomalies in susceptibility, slow saturation of the NMR spectral ratio, and power-law T dependence of 1/T₁ are interpreted as evidence for a spin supersolid with gapless excitations. A continuous quantum phase transition at H_C ≈ 19.5 T with νz ≈ 1 is inferred from the Grüneisen ratio extracted from MCE data, with additional signatures of strong spin fluctuations near H_C. The work positions the material as a platform for cryogenic magnetocaloric cooling.

Significance. If the phase assignments and quantum-critical scaling hold, the results add a new experimental realization of spin supersolidity and field-tuned quantum criticality in a frustrated Ising magnet, with the combination of MCE-derived Grüneisen ratio and NMR relaxation providing a multi-probe characterization of the critical regime. The reported large high-temperature MCE signal near H_C is a concrete strength that directly supports the suggested cooling application.

major comments (2)
  1. [NMR results, 15.8–18.5 T window] § on NMR results (field range 15.8–18.5 T): the assignment of gapless spin-supersolid excitations rests on the power-law form of 1/T₁ and the slow saturation of the spectral ratio, yet the manuscript provides no quantitative comparison or fit to theoretical predictions for alternative gapless states (e.g., incommensurate order or a spin liquid); this interpretive uniqueness is load-bearing for the central supersolid claim.
  2. [MCE and quantum-critical scaling] MCE and Grüneisen-ratio analysis near H_C ≈ 19.5 T: the reported νz ≈ 1 is stated without the explicit fitting procedure, temperature range used, or error bars on the exponent; the scaling collapse or power-law extraction therefore cannot be independently assessed from the presented data.
minor comments (2)
  1. [Figures 2–4] Figure captions and text should explicitly state whether raw magnetization and NMR spectra are shown or only processed quantities; inclusion of representative raw data would strengthen reproducibility.
  2. [Abstract and discussion] The abstract and main text use “suggest” for the supersolid assignment; a brief sentence clarifying that alternative gapless scenarios have not been quantitatively ruled out would improve precision.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thorough review and constructive feedback on our manuscript. We appreciate the recognition of the significance of our findings on spin supersolidity and quantum criticality in Rb₂Co(SeO₃)₂. We address the major comments below and will revise the manuscript accordingly where appropriate.

read point-by-point responses

  1. Referee: [NMR results, 15.8–18.5 T window] § on NMR results (field range 15.8–18.5 T): the assignment of gapless spin-supersolid excitations rests on the power-law form of 1/T₁ and the slow saturation of the spectral ratio, yet the manuscript provides no quantitative comparison or fit to theoretical predictions for alternative gapless states (e.g., incommensurate order or a spin liquid); this interpretive uniqueness is load-bearing for the central supersolid claim.

    Authors: We agree that providing quantitative comparisons to theoretical predictions for alternative gapless states would strengthen our interpretation. In the revised manuscript, we will add a discussion section comparing the observed temperature dependence of 1/T₁ (power-law exponent) and the NMR spectral ratio behavior to expectations from spin supersolid theory as well as alternative scenarios such as incommensurate order or a gapless spin liquid. While the overall set of observations—including the susceptibility anomaly and consistency with the triangular lattice Ising model predictions—favor the spin supersolid phase, we acknowledge the value of explicit comparisons to rule out alternatives more rigorously. revision: yes

  2. Referee: [MCE and quantum-critical scaling] MCE and Grüneisen-ratio analysis near H_C ≈ 19.5 T: the reported νz ≈ 1 is stated without the explicit fitting procedure, temperature range used, or error bars on the exponent; the scaling collapse or power-law extraction therefore cannot be independently assessed from the presented data.

    Authors: We thank the referee for pointing out this omission. In the revised manuscript, we will include a detailed description of the Grüneisen ratio analysis, specifying the temperature range over which the power-law fit was performed, the fitting procedure used to extract νz ≈ 1, and the associated error bars. We will also provide additional details or a figure showing the scaling behavior to allow for independent verification of the quantum critical scaling. revision: yes

Circularity Check

0 steps flagged

No circularity: purely experimental data interpretation

full rationale

The paper reports direct experimental measurements (magnetization, MCE, NMR 1/T1 and spectral ratios) on Rb2Co(SeO3)2. Phase assignments (UUD plateau, spin supersolid window, QCP at 19.5 T) are based on observed anomalies and standard temperature/field dependencies without any theoretical derivation, model fitting, or equation chain that reduces outputs to inputs by construction. No self-citations, ansatzes, or uniqueness theorems are invoked to force the central claims; the work is self-contained against external benchmarks such as known NMR signatures of gapped vs. gapless states.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 1 invented entities

The central claims rest on experimental data interpretation rather than derivation; critical field values and the exponent product are extracted from measurements, and the supersolid assignment is an interpretive label without independent theoretical prediction supplied in the abstract.

free parameters (2)
  • H_C = 19.5 T
    Location of the quantum critical point extracted from the peak in the Grüneisen ratio derived from MCE data.
  • νz = 1
    Product of correlation-length and dynamic exponents obtained from quantum critical scaling collapse of thermodynamic quantities.
axioms (1)
  • domain assumption Rb2Co(SeO3)2 realizes an Ising triangular-lattice antiferromagnet with dominant nearest-neighbor interactions.
    Invoked at the outset to frame the expected frustration and phase sequence.
invented entities (1)
  • spin supersolid phase no independent evidence
    purpose: Label for the intermediate-field ground state exhibiting both ordered and gapless fluid-like spin excitations.
    Introduced to unify the observed susceptibility anomaly, slow NMR saturation, and power-law 1/T1 between 15.8 T and 18.5 T.

pith-pipeline@v0.9.0 · 5870 in / 1724 out tokens · 71887 ms · 2026-05-18T12:29:45.047722+00:00 · methodology

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Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. NMR evidence of spin supersolid and Pomeranchuk effect behaviors in the triangular-lattice antiferromagnet Rb$_2$Ni$_2$(SeO$_3$)$_3$

    cond-mat.str-el 2026-03 unverdicted novelty 5.0

    NMR data identifies spin supersolid phases and a Pomeranchuk-like effect in Rb2Ni2(SeO3)3.

  2. Emergent Spin Supersolids in Frustrated Quantum Materials

    cond-mat.str-el 2026-01 unverdicted novelty 2.0

    Spin supersolids featuring coexisting longitudinal spin order breaking lattice symmetry and transverse order breaking spin U(1) symmetry have been established in frustrated quantum magnets through consistent experimen...

Reference graph

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