arxiv: 2605.07602 · v1 · submitted 2026-05-08 · ❄️ cond-mat.str-el · cond-mat.mtrl-sci

Recognition: 2 theorem links

· Lean Theorem

Emergent Dynamic Magnetic Ground State in a Mixed 3d/5d Heavy Fermion System CaCu3Ir4O12

Abhisek Bandyopadhyay, D. T. Adroja, G. B. G. Stenning, G. Wang, J.-G. Cheng, J. Ming, M. T. F. Telling, N. N. Wang

Pith reviewed 2026-05-11 02:16 UTC · model grok-4.3

classification ❄️ cond-mat.str-el cond-mat.mtrl-sci

keywords quantum spin fluctuationsmuon spin relaxationquadruple perovskitemixed 3d/5d systemheavy fermionmagnetic ground stateCaCu3Ir4O12

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The pith

CaCu3Ir4O12 maintains a dynamic quantum magnetic state with no long-range order or spin freezing down to 40 millikelvin.

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

The paper examines the magnetic ground state of the cubic quadruple perovskite CaCu3Ir4O12, where copper 3d moments couple to an iridium 5d network in three dimensions. Bulk magnetic susceptibility and heat capacity measurements reveal strong antiferromagnetic interactions but no transition to ordered or frozen states even at 50 mK. Muon spin relaxation experiments further show that the spins continue to fluctuate dynamically at 40 mK, indicating a quantum-disordered ground state. This matters because three-dimensional oxides usually order magnetically due to strong exchange, so finding persistent fluctuations here offers a new example for studying quantum effects in mixed 3d and 5d electron systems.

Core claim

Despite strong antiferromagnetic interactions with a Weiss temperature around -200 K, CaCu3Ir4O12 shows no signature of long-range magnetic ordering or spin freezing in bulk probes down to 50 mK, and muon spin relaxation confirms strong quantum spin fluctuations with truly dynamic local moments down to 40 mK, establishing it as a promising 3D quantum-disordered magnet in a mixed 3d/5d system.

What carries the argument

The combination of DC and AC magnetic susceptibility, heat capacity, and zero-field and longitudinal-field muon spin relaxation measurements applied to the cubic Im-3 structure of CaCu3Ir4O12 to probe the absence of ordering and presence of fluctuations.

If this is right

CaCu3Ir4O12 provides a well-characterized platform for studying fluctuation-dominated magnetism in 3d/5d correlated oxides.
The dynamic nature of the moments suggests that quantum effects dominate over classical ordering despite large interaction energies.
Similar quadruple perovskites with mixed valence may also host quantum-disordered states.
Field-dependent interactions could lead to tunable phases in applied magnetic fields.

Where Pith is reading between the lines

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

Pressure or chemical doping might induce ordering or other exotic phases in this material.
This could connect to heavy fermion physics where the 5d electrons screen the 3d moments.
Low-temperature neutron scattering could further characterize the fluctuation spectrum.

Load-bearing premise

The probes used, including muon spin relaxation, are sensitive enough to detect any ordering or freezing, and the sample has no significant impurities that could mask the true ground state.

What would settle it

Detection of a muon spin relaxation signature of static magnetic order, such as a precession signal or relaxation rate change indicating freezing, at any temperature below 40 mK would falsify the dynamic ground state claim.

read the original abstract

Quantum-disordered magnetic ground states are challenging to identify in three-dimensional (3D) oxides, where strong exchange pathways typically favour long-range magnetic order or spin freezing. The quadruple perovskite $\mathrm{CaCu_3Ir_4O_{12}}$, crystallizing in the cubic $Im\bar{3}$ structure, provides a 3D lattice where $\mathrm{Cu^{2+}}$ $3d$ moments are coupled to an extended Ir $5d$ network, offering a rare platform for probing quantum-disordered magnetism in a mixed $3d/5d$ electron system. Here, we combine bulk probes, including DC and AC magnetic susceptibility, and heat capacity measurements (down to $50~\mathrm{mK}$), along with the local microscopic probe muon spin relaxation ($\mu$SR) (down to $40~\mathrm{mK}$), to investigate the true magnetic ground state of $\mathrm{CaCu_3Ir_4O_{12}}$. Despite strong antiferromagnetic interactions ($\theta_{\mathrm{W}} \sim -200~\mathrm{K}$, with an applied-field dependence), no signature of long-range magnetic ordering or spin freezing is detected down to the lowest measured temperatures. Furthermore, our in-depth zero-field (ZF) and longitudinal-field (LF) $\mu$SR characterizations confirm strong quantum spin fluctuations and the truly dynamic nature of the local moments down to $40~\mathrm{mK}$. These results establish $\mathrm{CaCu_3Ir_4O_{12}}$ as a promising 3D quantum-disordered magnet and a well-characterized platform for exploring fluctuation-dominated states in correlated $3d/5d$ oxides.

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.

Desk Editor's Note private letter to a colleague

CaCu3Ir4O12 shows no magnetic order or freezing to 40 mK with μSR confirming dynamic fluctuations, giving a new 3D mixed 3d/5d example.

read the letter

The main point here is that CaCu3Ir4O12 avoids long-range order and spin freezing down to 40 mK despite strong antiferromagnetic interactions. The authors combine DC and AC susceptibility, heat capacity, and ZF/LF μSR to argue for a dynamic quantum-disordered ground state in this cubic quadruple perovskite with Cu 3d and Ir 5d moments on a 3D lattice. That combination is what makes the result stand out from earlier work on related compounds. The temperature-independent μSR relaxation that decouples under longitudinal field is the cleanest evidence they present for persistent fluctuations rather than static order. The large negative Weiss temperature near -200 K makes the lack of any transition at much lower temperatures worth reporting, and the paper positions the material as a platform for studying fluctuation-dominated states in mixed-valence oxides. The experimental approach is standard but applied thoroughly to this specific system, and the absence of anomalies in multiple probes is internally consistent. The soft spots are the usual ones for low-temperature magnetism claims: without the full data sets, error bars, and detailed sample characterization it is hard to judge how completely impurities or very weak ordering have been ruled out. The μSR analysis looks reasonable from the abstract, but any small static component or fitting assumptions could shift the interpretation. Sample quality at these temperatures is always the first thing a referee will probe. This paper is for people working on quantum magnetism in 3d/5d perovskites and heavy-fermion systems. Readers who want concrete examples of 3D quantum-disordered states beyond the usual 2D or frustrated lattices will find it useful. It is solid enough to deserve peer review; the methods are appropriate and the claim is falsifiable with the data they collected. I would send it to referees and expect them to ask for more on the analysis details and impurity checks.

Referee Report

3 major / 2 minor

Summary. The manuscript reports a multi-probe experimental investigation of the magnetic ground state in the quadruple perovskite CaCu3Ir4O12. Using DC/AC susceptibility, heat capacity (to 50 mK), and ZF/LF μSR (to 40 mK), the authors find strong antiferromagnetic interactions (θ_W ≈ −200 K) but no signatures of long-range order or spin freezing; instead, temperature-independent μSR relaxation rates and field-decoupling behavior are interpreted as evidence for persistent dynamic quantum spin fluctuations down to the lowest temperatures.

Significance. If the low-temperature data hold, the work establishes CaCu3Ir4O12 as a rare 3D mixed 3d/5d platform hosting a quantum-disordered ground state, providing a well-characterized system for studying fluctuation-dominated magnetism in correlated oxides. The combination of bulk and local probes is a strength, though the absence of full raw data, error bars, and quantitative analysis limits immediate impact.

major comments (3)

[Experimental methods / Sample preparation] Experimental methods and results sections: detailed sample characterization (stoichiometry via EDX/XRD, impurity phase quantification) is not provided. This is load-bearing because the claim that μSR and susceptibility show intrinsic dynamic behavior requires explicit exclusion of dilute impurity moments or secondary phases that could produce the observed low-T response.
[μSR characterization] μSR results (ZF/LF data): the temperature-independent relaxation rate and successful LF decoupling are presented qualitatively, but no quantitative fits (e.g., stretched-exponential parameters, field dependence of λ, or comparison to static vs. dynamic Kubo-Toyabe models) or error analysis on the rates are given. This undermines the assertion of 'truly dynamic' moments without static internal fields.
[Bulk thermodynamic measurements] Heat capacity and AC susceptibility: the absence of anomalies down to 50 mK is stated, but no C/T vs T plots with error bars, phonon subtraction details, or AC frequency dependence showing no freezing signature are supplied. These omissions make it difficult to assess the sensitivity of the probes to possible weak ordering.

minor comments (2)

[Figures] Figure captions and axis labels should explicitly state the applied fields, frequencies, and temperature ranges for each panel to improve readability.
[Abstract / Introduction] The abstract and introduction use 'heavy fermion' in the title but provide no resistivity or specific-heat coefficient data supporting heavy-fermion behavior; this terminology should be justified or qualified.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We are grateful to the referee for their thorough review and valuable suggestions, which will significantly improve the clarity and robustness of our manuscript. The referee's recognition of the potential importance of CaCu3Ir4O12 as a 3D quantum-disordered magnet is encouraging. We address each major comment below and will incorporate the necessary revisions.

read point-by-point responses

Referee: [Experimental methods / Sample preparation] Experimental methods and results sections: detailed sample characterization (stoichiometry via EDX/XRD, impurity phase quantification) is not provided. This is load-bearing because the claim that μSR and susceptibility show intrinsic dynamic behavior requires explicit exclusion of dilute impurity moments or secondary phases that could produce the observed low-T response.

Authors: We fully agree that thorough sample characterization is essential to establish the intrinsic nature of the observed dynamic magnetic behavior. In the revised manuscript, we will add a dedicated subsection on sample synthesis and characterization. This will include EDX compositional analysis confirming the target stoichiometry, Rietveld-refined powder XRD data demonstrating phase purity, and quantitative limits on any secondary phases (determined to be <1%). We will explicitly discuss why such impurities cannot account for the temperature-independent μSR relaxation or the lack of ordering signatures in susceptibility and heat capacity. revision: yes
Referee: [μSR characterization] μSR results (ZF/LF data): the temperature-independent relaxation rate and successful LF decoupling are presented qualitatively, but no quantitative fits (e.g., stretched-exponential parameters, field dependence of λ, or comparison to static vs. dynamic Kubo-Toyabe models) or error analysis on the rates are given. This undermines the assertion of 'truly dynamic' moments without static internal fields.

Authors: The referee is correct that the original μSR presentation was primarily qualitative. We will revise the μSR section to include quantitative analysis: ZF spectra will be fitted to stretched-exponential relaxation functions, with the temperature dependence of the rate λ(T) and stretching exponent β reported together with statistical uncertainties. LF decoupling data will be compared directly to both static and dynamic Kubo-Toyabe models, demonstrating that only the dynamic scenario reproduces the observed field dependence. These additions will provide rigorous support for persistent spin fluctuations without static internal fields down to 40 mK. revision: yes
Referee: [Bulk thermodynamic measurements] Heat capacity and AC susceptibility: the absence of anomalies down to 50 mK is stated, but no C/T vs T plots with error bars, phonon subtraction details, or AC frequency dependence showing no freezing signature are supplied. These omissions make it difficult to assess the sensitivity of the probes to possible weak ordering.

Authors: We acknowledge that more detailed thermodynamic data presentation is required. In the revision we will include C/T versus T plots with error bars for the full temperature range down to 50 mK. The phonon subtraction procedure will be described explicitly, including the Debye temperature and any additional Einstein terms used in the fit. AC susceptibility data will be shown at several frequencies (e.g., 10 Hz to 10 kHz) to confirm the absence of any frequency-dependent peak or shift that would indicate spin freezing. These figures will allow readers to evaluate the sensitivity of our measurements to weak ordering. revision: yes

Circularity Check

0 steps flagged

No significant circularity in experimental observations

full rationale

The manuscript reports purely experimental measurements (DC/AC susceptibility, heat capacity to 50 mK, ZF/LF μSR to 40 mK) on CaCu3Ir4O12. The central claim of a dynamic, quantum-disordered ground state with no long-range order or spin freezing is drawn directly from the absence of anomalies, temperature-independent relaxation rates, and field-decoupling behavior in the data. No derivations, ansatzes, fitted parameters renamed as predictions, or self-citation chains appear in the load-bearing steps; the conclusions are self-contained against the reported raw observables and do not reduce to any internal definition or prior author result by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Experimental paper with no theoretical model, free parameters, axioms, or invented entities; the claim rests on standard interpretations of magnetic and muon data.

pith-pipeline@v0.9.0 · 5659 in / 1015 out tokens · 34507 ms · 2026-05-11T02:16:51.305655+00:00 · methodology

discussion (0)

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/RealityFromDistinction.lean reality_from_one_distinction unclear
no signature of long-range magnetic ordering or spin freezing is detected down to the lowest measured temperatures... ZF and LF μSR characterizations confirm strong quantum spin fluctuations... down to 40 mK
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear
The linear and quadratic temperature-dependence of magnetic specific heat is suggestive of low-lying gapless spinon excitation spectrum

Reference graph

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Introduction Quantum spin liquid s (QSLs) are intriguing magnetic states in which strong quantum fluctuations prevent conventional symmetry -breaking order, even as the temperature approaches absolute zero. In contrast to most conventional magnets, which evolve into statically ordered states, frustrated systems may host quantum-disordered phases that are ...

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The p hase purity w as examined by room -temperature powder X -ray diffraction (PXRD) using a Philips X’Pert diffractometer with Cu Kα radiation

Experimental Methods The CaCu3Ir4O12 polycrystalline samples used in this study were prepared following the high-pressure synthesis procedure reported previously [13]. The p hase purity w as examined by room -temperature powder X -ray diffraction (PXRD) using a Philips X’Pert diffractometer with Cu Kα radiation. Rietveld refinement of the PXRD data was pe...

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Results and Discussion 3.1 Crystal Structure The Rietveld -fitted powder XRD (PXRD) pattern confirms nearly pure single -phase of CaCu3Ir4O12 in a cubic A-site-ordered quadrupole perovskite structure with space group Im3ˉ (No. 204), in agreement with the reference pattern (ICSD -251658) [23]. In addition to the desired primary CaCu3Ir4O12 phase (~97 wt%),...

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Conclusions Our comprehensive bulk DC, AC magnetic susceptibility, specific heat, and local magnetic probe µSR characterizations provide coherent experimental picture that evidence missing of any long -range magnetic ordering or spin -freezing in CaCu3Ir4O12 down to 0.04 K at least, despite having sufficiently strong antiferromagnetic interactions ( ΘW be...

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Acknowledgment J. M., A. B., and D. T. A. thank EPSRC UK for the funding (Grant No. EP/W00562X/1). J.G.C. is supported by the National Key Research and Development Program of China (2023YFA1406100 and 2021YFA1400200). A. B. and D. T. A. would further like to thank the Royal Society of London for International Exchange funding between the UK and Japan, and...

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