{"id":"8f597f85-0ffd-4266-82f3-b656b04bff97","arxiv_id":"2508.07687","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":1,"one_line_summary":"K2Co2(SO4)3 on the double trillium lattice shows spin fluctuations down to 50 mK and T^2 heat capacity above 1 T, signs of a proximate quantum spin liquid.","lead":"This paper reports that a cobalt-based crystal, K2Co2(SO4)3, behaves like a quantum spin liquid: some magnetic order appears at very low temperature, but most spins keep fluctuating down to 50 millikelvin. It introduces the double trillium lattice, a new 3D arrangement of magnetic ions, as a stage for studying this exotic magnetic state.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 'proximate QSL' claim hinges on the 50-mK muon fluctuating fraction being intrinsic; the abstract does not rule out orphan-spin/disorder origins, so the central claim is as strong as that assumption.","rationale":"The reader's weakest_assumption already identifies the muon fluctuating fraction's intrinsic nature as the key premise, and I agree that this is the most load-bearing point. The abstract alone cannot rule out orphan spins or sample imperfections; this is a standard and serious alternative in frustrated magnets. My proposed test directly checks that premise. I do not see a separate concern that outweighs this one: the structural superstructure question is secondary, because even if the geometry is distorted, the fluctuating-muon claim would still need to be intrinsic. Since the full text is corrupt and the paper cannot be method-checked, the reader's UNVERDICTED verdict remains appropriate; my concern does not shift it to accept or reject but reinforces the need for the raw data or a targeted experiment.","tokens_in":21972,"tokens_out":4846,"duration_ms":62341,"concrete_test":"Obtain the raw zero-field muSR asymmetry data at 50 mK and re-fit them with a two-component model (static Kubo-Toyabe plus exponentially relaxing contribution), then repeat the fit with the first 0.1–0.2 microseconds excluded and with the initial asymmetry left free. If the fitted fluctuating fraction does not change materially under these cuts and is reproducible on a second independently synthesized batch (ideally with stoichiometry verified by EDX/ICP), the intrinsic interpretation is supported. If the fluctuating fraction vanishes under early-time cuts or differs batch-to-batch, it is an artifact or disorder signature, and the 'proximate QSL' claim loses its main experimental support.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The abstract's most important sentence is that muon spin relaxation reveals a large fluctuating component that persists down to 50 mK. For the 'proximate quantum spin liquid' label to hold, this fluctuating component must be an intrinsic property of the double trillium Co sublattice. The abstract does not provide evidence against the conventional alternative: a small fraction of orphan/defect spins (off-stoichiometric Co, stacking faults, surface damage, or a minority impurity phase) coexisting with static order is a well-known source of a persistent fluctuating muon fraction and would produce exactly the observed zero-field pattern. The T^2 heat capacity above 1 T is also not conclusive for a QSL; it can be produced by gapless disorder modes or by nuclear/defect Schottky terms. Because the paper's novelty and title depend on the 'fluctuating component' being intrinsic, this is the single most load-bearing assumption. Without access to the raw muon spectra, fit protocol, sample characterization, or batch-to-batch comparison, the abstract alone cannot distinguish intrinsic spin-liquid behavior from conventional disorder physics.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript reports a combined experimental and ab initio study of K2Co2(SO4)3, a Co2+ double trillium lattice antiferromagnet. According to the abstract, the authors identify a cubic-to-monoclinic structural transition at T_t ≈ 125 K, formation of a J_eff = 1/2 state below 50 K, static magnetic order below T* ≈ 0.6 K, a large fluctuating muon fraction persisting to at least 50 mK, suppression of static order by a field of ~1 T, and a T^2 heat capacity above this field. They interpret these observations as proximate quantum spin liquid behavior and support this with ab initio calculations showing competing antiferromagnetic couplings.","tokens_in":22024,"tokens_out":3125,"duration_ms":40954,"significance":"If the claims are correct, K2Co2(SO4)3 is a valuable new proximate spin-liquid candidate on a three-dimensional double trillium lattice, with the unusual feature that a small magnetic field removes residual order and leaves a gapless fluctuating regime. The multi-probe consistency (diffraction, magnetization, heat capacity, muSR) is a strength, and the ab initio framework is a constructive complement to the measurements. However, the QSL interpretation is only as strong as the evidence that the persistent fluctuating muon component is intrinsic to the Co sublattice and not a consequence of disorder or minority phases; the abstract does not yet establish that point.","major_comments":[{"comment":"The central claim that the fluctuating component is intrinsic is not supported by the material presented. The abstract reports that a 'large fluctuating component persists down to at least 50 mK' while static order forms at 0.6 K, but it does not report sample characterization, the muon fitting model, or batch-to-batch reproducibility. The conventional alternative—orphan/defect spins or an impurity phase producing persistent muon relaxation—is not ruled out. Because the title and the QSL interpretation rest on this point, the authors must show that the fluctuating fraction is proportional to the bulk Co sublattice and not to defect density, for example through comparison of multiple batches or by showing the same fraction in the ordered phase after annealing.","section":"Abstract (muon spin relaxation)"},{"comment":"The T^2 heat capacity above ~1 T is quoted as a fingerprint of a gapless spin liquid, but a T^2 term can also be produced by gapless disorder modes, nuclear or Schottky contributions, and other conventional mechanisms. The abstract does not state how nuclear/background contributions were subtracted, what temperature range was used for the T^2 fit, or how the coefficient varies with field. The authors should provide the raw C/T data, the fit ranges, and a comparison with an appropriate nonmagnetic analog or estimated nuclear contribution to support the gapless-spin interpretation.","section":"Abstract (heat capacity)"},{"comment":"The low-temperature monoclinic superstructure is invoked as the target phase, but the abstract gives no evidence that the double trillium Co sublattice geometry is preserved in this phase. If the superstructure modifies the exchange network, the ab initio couplings J1..Jn computed for the ideal double trillium lattice are not directly applicable to the measured low-temperature phase. Please specify the refined monoclinic structure and verify that the exchange model used in the calculations corresponds to the symmetry of the actual low-temperature phase.","section":"Abstract (structure and ab initio couplings)"},{"comment":"The exchange couplings J1..Jn are not quoted in the abstract. If any rescaling or renormalization was applied to match T* or the T^2 coefficient, the comparison would be circular. The text should state the calculated exchange parameters and explicitly indicate whether any scaling was applied to compare with experiment.","section":"Abstract (exchange couplings)"}],"minor_comments":[{"comment":"The supplied full text is heavily corrupted and cannot be read; equations, figures, and tables are not accessible. A clean manuscript version is needed to verify the analysis details.","section":"General"},{"comment":"Please quantify the 'large fluctuating component' explicitly: give the muon fraction and relaxation rate at 50 mK and at 0.6 K, and specify the fit function used.","section":"Abstract (muon fraction)"},{"comment":"Define how T_t and T* were determined (peak positions, specific-heat anomaly, order-parameter onset, etc.).","section":"Abstract (transition temperatures)"},{"comment":"Clarify what 'static order is completely suppressed in the small magnetic field of ~1 T' means: is this the upper critical field at zero temperature, or a field at which the static muon fraction becomes zero at a finite temperature?","section":"Abstract (field suppression)"}],"recommendation":"major_revision","confidential_remarks":"The abstract presents a coherent picture, but the most load-bearing evidence—the intrinsic nature of the persistent fluctuating muon component—is not documented in the material provided. The paper would be well suited to a condensed-matter materials journal if the full data, fitting protocols, and structural details are made available and the interpretation is appropriately caveated. I would advise against publication until the muon analysis and heat-capacity subtraction are shown in a checkable form."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"I couldn't get past the abstract: the full text I received is mojibake with a header from a different arXiv paper, so this is an abstract-level read. The paper reports K2Co2(SO4)3 as a new frustrated 3D magnet with Co2+ ions on a double trillium lattice — a geometry that hasn't been realized before, as far as the abstract tells me. The apparent package is solid: a structural transition at 125 K, J_eff=1/2 formation below 50 K, static order at 0.6 K coexisting with a large muon fluctuating fraction down to 50 mK, suppression of order by about 1 T, and T^2 heat capacity above that field. The authors also back it with ab initio competing antiferromagnetic couplings.\n\nWhat I like: the multi-probe approach is the right way to build a QSL case, and the \"proximate\" language is honest. There's no obvious internal contradiction — the coexistence of weak order and persistent fluctuations is exactly what \"proximate spin liquid\" is supposed to mean. The 1 T critical field is experimentally attractive.\n\nThe soft spots are about what the abstract leaves open. The biggest one is the fluctuating muon fraction. The abstract does not rule out the conventional alternative: a small population of orphan spins, off-stoichiometry, or an impurity phase could produce the same persistent fluctuating component even if the bulk is ordered. If that's what's going on, the \"proximate QSL\" label loses its weight. Sample characterization, batch-to-batch comparison, and the fit protocol for separating static and fluctuating muon components are essential, and I can't inspect any of it. The T^2 heat capacity is a weaker fingerprint than the muon data — gapless disorder modes can give T^2, too. And the low-temperature monoclinic superstructure must preserve the Co sublattice frustration assumed in the ab initio calculations; the abstract summarizes but cannot substantiate that.\n\nThese aren't fatal objections; they're unanswerable questions from the abstract. If the full data hold up, this is a genuinely useful new material for the frustrated magnetism community. The reader's skepticism about disorder is fair, but I don't think it lands as a known flaw — it's an open question.\n\nMy take: this deserves a serious refereeing. The claim is significant and the authors appear to be doing the right kinds of experiments. The referee should push hard on the muon analysis and the sample quality, but the paper should not be desk-rejected. I would not cite it yet, though — not until the disorder question is addressed and I can see the raw evidence.","headline":"A plausible new proximate-QSL candidate on a double trillium lattice, but I can only judge the abstract because the full text is corrupt; the disorder/orphan-spin alternative to the 50-mK fluctuating muon component is the key issue to probe in review.","tokens_in":835,"tokens_out":1288,"would_cite":false,"duration_ms":39023,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"K2Co2(SO4)3 is a candidate proximate quantum spin liquid: static order forms near 0.6 K but a large fraction of spins keep fluctuating down to 50 mK, and a ~1 T field suppresses the order while heat capacity becomes T^2.","keywords":["quantum spin liquid","double trillium lattice","frustrated magnetism","pseudospin-1/2","K2Co2(SO4)3","muon spin relaxation","heat capacity","antiferromagnetic couplings"],"falsifier":"Neutron diffraction on high-quality stoichiometric crystals: if coherent magnetic Bragg peaks appear below 0.6 K once disorder is minimized, or if the fluctuating muon fraction scales with known defect or orphan-spin concentration, the proximate spin-liquid claim fails.","tokens_in":21660,"feed_emoji":"🧲","tokens_out":3424,"duration_ms":44885,"temperature":0.7,"pith_summary":"The paper argues that the cobalt compound K2Co2(SO4)3, with magnetic Co2+ ions on a double trillium lattice, sits close to magnetic order yet shows spin-liquid-like behavior. Below about 0.6 K there are signs of static magnetic order, but muon spin relaxation reveals a large fluctuating spin component that persists down to at least 50 mK. An applied field near 1 T removes the static order completely, and heat capacity above that field follows $T^{2}$, a signature of gapless excitations. Combined with ab initio calculations showing competing antiferromagnetic couplings, the authors read this as proximate quantum spin liquid behavior: a frustrated three-dimensional magnet whose residual order gives way to a fluctuating, gapless state in a weak field. If correct, this adds a new three-dimensional platform for studying quantum magnetism.","feed_headline":"One tesla turns a frustrated cobalt magnet into a spin liquid","feed_subtitle":"Muon and heat-capacity data point to a gapless quantum spin-liquid state in K2Co2(SO4)3","key_machinery":"The key objects are the double trillium lattice of magnetic Co2+ ions and the effective pseudospin-1/2 degree of freedom produced by spin-orbit coupling below 50 K. The lattice is a three-dimensional corner-sharing geometry whose connectivity frustrates conventional antiferromagnetic order. Muon spin relaxation supplies the split between static and fluctuating spin fractions, while the $T^{2}$ heat-capacity term above 1 T exposes gapless low-energy excitations. The structural transition at about 125 K into a monoclinic three-fold superstructure is important because it must preserve the frustrated cobalt sublattice for the spin-liquid interpretation to hold.","core_discovery":"The central discovery is that K2Co2(SO4)3 behaves as a proximate quantum spin liquid. Co2+ forms an effective pseudospin-1/2 state below about 50 K, embedded on a highly frustrated three-dimensional double trillium lattice. Magnetization and heat capacity track the formation of this J_eff=1/2 state; zero-field muon spin relaxation shows static order beginning below T* ≈ 0.6 K together with a large fluctuating component that survives to at least 50 mK. In a small magnetic field of about 1 T the static order disappears, and the low-temperature heat capacity becomes $T^{2}$, a hallmark of gapless excitations expected for a quantum spin liquid. The authors conclude that competing antiferromagnetic c","pith_inferences":["The persistent fluctuating muon fraction could also be caused by defects, off-stoichiometry, or orphan spins; if that is the case the 'proximate spin liquid' label would weaken even though the T^2 heat capacity above 1 T might survive.","A decisive test would be neutron scattering on the same crystals: a gapless continuum with no Bragg peaks above 1 T would support the spin-liquid interpretation, whereas broad defect-related scattering would point to disorder physics.","The suppression of order by such a small field hints at an unusual field-temperature phase diagram; mapping the full B–T boundary could reveal whether the zero-field order gives way through a quantum critical point or a crossover, which the current data do not resolve."],"forward_implications":["K2Co2(SO4)3 becomes a candidate three-dimensional quantum spin-liquid platform whose residual order is destroyed by a conveniently small field of about 1 T.","Above 1 T, the low-energy excitations appear gapless, with C_p ∝ T^2, so bulk thermodynamic measurements can probe the spin-liquid-like spectrum.","The 125 K structural transition does not destroy the frustration: the low-temperature monoclinic superstructure retains the double trillium magnetic geometry that the exchange calculations assume.","The competition of several antiferromagnetic couplings suggests the material sits near a boundary between order and a spin-liquid regime, making it a useful testbed for frustrated quantum magnetism."],"supporting_citations":[],"fun_headline_variants":["Small field unlocks spin-liquid state in frustrated cobalt magnet","One tesla erases magnetic order, reveals cobalt spin liquid","Frustrated cobalt lattice turns spin liquid at one tesla","Proximate spin liquid emerges in double trillium cobalt magnet","A tesla flips cobalt magnet into quantum spin-liquid state"],"cache_read_input_tokens":2816,"weakest_assumption_plain":"The split of the muon signal into static and fluctuating parts assumes that the persistent fluctuating spins are intrinsic to the double trillium sublattice rather than produced by disorder, off-stoichiometry, or orphan spins near defects.","fun_headline_variants_meta":{"raw":{"variants":["Small field unlocks spin-liquid state in frustrated cobalt magnet","One tesla erases magnetic order, reveals cobalt spin liquid","Frustrated cobalt lattice turns spin liquid at one tesla","Proximate spin liquid emerges in double trillium cobalt magnet","A tesla flips cobalt magnet into quantum spin-liquid state"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000651,"raw_usage":{"total_tokens":2870,"prompt_tokens":839,"completion_tokens":2031,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":583,"completion_tokens_details":{"reasoning_tokens":1947}},"tokens_in":583,"tokens_out":2031,"duration_ms":16203,"temperature":1.0,"reasoning_tokens":1947,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T21:56:02.845118+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Neutron diffraction on high-quality stoichiometric crystals: if coherent magnetic Bragg peaks appear below 0.6 K once disorder is minimized, or if the fluctuating muon fraction scales with known defect or orphan-spin concentration, the proximate spin-liquid claim fails.","supporting_citations":[],"review_version":1}