{"id":"19025f39-1e1d-4e1c-b428-f318b8ab2d43","arxiv_id":"2607.13635","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"In the near-Ising triangular antiferromagnet K2Co(SeO3)2, the supersolid transverse ordered moment is ~11% of the longitudinal one and low-energy fluctuations are mostly longitudinal.","lead":"Neutron scattering on the triangular-lattice magnet K2Co(SeO3)2 shows that its 'supersolid' magnetic order has a small transverse component that appears only below 0.35 K, alongside predominantly longitudinal low-energy fluctuations. The result gives direct evidence that supersolidity survives in the near-Ising limit and constrains theories of frustrated quantum magnets.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Interlayer correlations are assumed common to S_zz and S_perp (and absent for INS), yet the paper's own data show they change at T_BKT,3; this untested assumption underpins both the 11% moment ratio and the longitudinal-fluctuations conclusion.","rationale":"The reader's weakest assumption correctly identifies the unverified interlayer-correlation assumption in the INS l-dependence. I extend this to the polarized-diffraction extraction of the transverse ordered moment, where the same assumption is equally load-bearing: the reported S_perp/S_zz=0.017 and m_perp/m_z≈11% rely on a common G(l) for both spin components, and the paper's own observation that interlayer correlations change at T_BKT,3 makes component-dependent stacking a live possibility. The existence of some transverse order below T_BKT,3 is robust (the flipping ratio drop cannot be explained by a common G), so the verdict should remain CONDITIONAL, not reject. The concern is concrete and addressable by re-analyzing data at additional l points or by polarized INS at l=3.5; hence no change to the reader's conditional verdict. I mark agreement as partial because the reader focused on the longitudinal-fluctuations claim, while I regard the same factorization assumption as also affecting the quantitative transverse-moment ratio, which is the central claim.","tokens_in":13936,"tokens_out":15384,"duration_ms":145671,"concrete_test":"Re-analyze the existing AMATERAS inelastic data at Q=(1/6,1/6,l) for l=0, 1.5, 3, 3.5 and 4.5, fitting the full cross section with separate interlayer correlation functions G_zz(l) and G_perp(l) (allowing A_nm to differ by channel) instead of assuming a common/largely-uncorrelated G. If the best fit returns G_zz ≠ G_perp and/or S_perp,2D/S_zz,2D inconsistent with the quoted 0.017, the longitudinal-fluctuations and moment-ratio conclusions are not uniquely determined; a l=3.5 polarized SF/NSF measurement would provide a decisive cross-check.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The decisive hidden assumption is that one interlayer correlation function G(l) multiplies both S_zz and S_perp in the polarized-diffraction analysis, and that inelastic excitations are 'largely uncorrelated between triangular-lattice layers' (imported from Ref. [26]). This is not verified in the present data, and the paper's own elastic fits show significant, temperature-dependent interlayer correlations (A_03=-0.029(4) at 0.5 K; A_02=0.022(4) at 0.06 K). For the transverse moment ratio, S_perp/S_zz at Q=(1/3,1/3,0) is converted to m_perp/m_z≈11% using structure-factor formulas that require a common G(l); if the BEC transverse component orders with a different stacking sequence (as is plausible for a U(1) order parameter), the extracted ratio is not the ordered-moment ratio. For the INS analysis, the comparison of l=0 and l=3.5 attributes the extra suppression solely to the polarization factor (1-Q_z^2/Q^2) acting on longitudinal fluctuations; but l-dependent interlayer interference from A_nm terms can suppress intensity at l=3.5 regardless of spin component. Since both headline conclusions depend on this single untested factorization, this is the most load-bearing concern.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper presents a neutron-scattering study of the near-Ising triangular-lattice antiferromagnet K2Co(SeO3)2, with the goal of detecting a transverse ordered moment and characterizing the polarization of low-energy spin fluctuations in the purported spin-supersolid phase. Polarized neutron diffraction at Q=(1/3,1/3,0) shows a drop in the flipping ratio at T≈0.35 K, which the authors interpret as the onset of a transverse (BEC-like) ordered component. Using an alpha-calibration from 0.5–2 K, they extract S_zz and S_perp, obtaining S_perp/S_zz ≈ 0.017(2) at 0.035 K, which they convert to m_perp/m_z ≈ 11(1)% and, after g-factor correction, ⟨S_perp⟩/⟨S_z⟩ ≈ 32(2)%. Unpolarized l-scans at Q=(2/3,2/3,l) are fitted with interlayer correlation parameters A_nm, showing a change in the dominant stacking from A_03 at 0.5 K to A_02 at 0.06 K. Inelastic neutron scattering at l=0 and l=3.5 finds a suppression of spectral weight at large l stronger than expected from the magnetic form factor alone, which is interpreted as evidence that low-energy fluctuations are predominantly longitudinal. The paper concludes that the supersolid state survives in the near-Ising regime, with a small transverse moment and longitudinal-dominated dynamics.","tokens_in":14319,"tokens_out":9833,"duration_ms":92286,"significance":"If the quantitative claims hold, this is an important experimental benchmark: direct detection of a small transverse ordered moment in a near-Ising triangular-lattice antiferromagnet (J_xy/J_z ≈ 0.07) would confirm the existence of BEC-type supersolid order in a regime where some numerical methods predict its absence. The observation of longitudinal-dominated low-energy fluctuations would also impose strong constraints on theories of the XXZ triangular lattice. The paper uses a clever combination of polarized diffraction and unpolarized inelastic scattering, with data collected on multiple instruments (CORELLI, ZEBRA, IN12, AMATERAS), and the raw data are deposited at ILL, which is a strength for reproducibility. The qualitative flipping-ratio drop at T_BKT,3 is a relatively model-independent signature. However, the quantitative extraction of the moment ratio and the decomposition of the inelastic spectrum rely on nontrivial factorization and calibration assumptions that are not fully tested in the present dataset. In particular, the common-interlayer-correlation assumption for S_zz and S_perp, and the assumed l-independence of the inelastic structure factor, are load-bearing and n","major_comments":[{"comment":"The conversion S_perp/S_zz = 0.017(2) → m_perp/m_z ≈ 11% uses |⟨m_perp(Q)⟩|² = 3m_perp² and |⟨m_z(Q)⟩|² = (9/4)m_z², which presupposes that the longitudinal and transverse components share the same interlayer correlation function G(l). The paper's own l-scan fits, however, show that the dominant interlayer correlations change at T_BKT,3: A_03 = -0.029(4) at 0.5 K but A_02 = 0.022(4) at 0.06 K. Since S_perp appears only below T_BKT,3, there is no evidence that the transverse order parameter has the same stacking sequence as the longitudinal one. If the transverse component orders with a different G_perp(l), then the measured S_perp/S_zz at l=0 is not simply the ratio of Fourier components of the ordered moments, and the quoted 11% and 32% ratios are not the true ordered-moment ratios. This is a central quantitative claim. The authors should either provide a symmetry argument for common G(","section":"Polarized diffraction and conversion to m_perp/m_z (Fig. 2 and the S(Q)∝G(l)S_2D discussion)"},{"comment":"The beam-polarization fraction alpha = 0.9628(5) is fixed from the average flipping ratio between 0.5 and 2 K, assuming S_perp = 0 in that temperature window. A constant flipping ratio in this range is also consistent with a constant nonzero S_perp/S_zz, since the flipping ratio depends on the ratio of the two channels, not on their absolute magnitudes. Any finite transverse contribution in the calibration window would directly bias the extracted S_zz, S_perp, and hence the reported S_perp/S_zz at all temperatures. The authors should quantify the sensitivity of the final ratio to this assumption, for example by fitting alpha and S_perp/S_zz simultaneously over the full temperature range, or by placing an upper bound on S_perp above 0.5 K from the data themselves.","section":"Alpha calibration (Fig. 2(c) inset and the NSF/SF intensity equations)"},{"comment":"The extraction of the two-dimensional longitudinal and transverse dynamical structure factors from I(l=0) and I(l=3.5) assumes the inelastic intensity factorizes as |F(Q)|²[(1/2)(1+Q_z²/Q²)S_perp_2D + (1-Q_z²/Q²)S_zz_2D], with S_2D independent of l. This 'largely uncorrelated' interlayer assumption is imported from Ref. [26] and is not verified in the present data. If there are finite interlayer correlations in the excitation spectrum, l-dependent interference terms could suppress intensity at l=3.5 even for transverse fluctuations, and the extracted C_zz and C_perp maps in Fig. 4 would not represent the true 2D correlations. The authors should test the assumed l-dependence by fitting the full l-scan of Fig. 3(d) (and, if possible, additional l values at several (h,k) points) to the form-factor/polarization-factor expression, rather than comparing only two l values.","section":"INS decomposition into C_zz and C_perp (Eq. for I(Q,ω) and Fig. 4)"}],"minor_comments":[{"comment":"The phrase 'consistence check' should be 'consistency check'; 'based sorely' should be 'based solely'.","section":"Supplemental material"},{"comment":"In the main text, A_nm is defined as ⟨Ŝ_nŜ_m⟩/⟨Ŝ_n²⟩, while in the Supplemental Material it is defined as ⟨η_n η_m⟩. These are equivalent only if the denominator is assumed constant. Please use one consistent definition throughout.","section":"Notation for A_nm"},{"comment":"The equation for I(Q,ω) in the INS section omits the g-factor factors that appear in the Fig. 4 caption (I ∝ g_zz² C_zz + g_perp² (1/2) C_perp). Including g_zz² and g_perp² explicitly in the main equation, or stating that the 2D structure factors absorb them, would remove ambiguity.","section":"INS equation and Fig. 4"},{"comment":"The text states S_perp/S_zz = |⟨m_perp⟩/⟨m_z⟩|², but the inset in Fig. 2(d) labels the vertical axis as 'm_perp/m_z'. Since the ratio is a squared quantity, the plot and the text should be explicitly reconciled to avoid confusion about which quantity is plotted.","section":"Fig. 2(d) inset and text"},{"comment":"The red solid line is described as the intensity drop due to the squared magnetic form factor alone. If the longitudinal interpretation is intended, the comparison should include the polarization factor for a longitudinal-only spectrum; please specify exactly what functional form is plotted.","section":"Fig. 3(d)"}],"recommendation":"major_revision","confidential_remarks":"The paper builds heavily on Refs. [24–26] from the same group, and the present manuscript is essentially an extension of that program. The qualitative observation of a flipping-ratio drop at T_BKT,3 is solid and likely correct. However, the headline quantitative conclusions (11%/32% moment ratio and predominantly longitudinal dynamics) depend on factorization and calibration assumptions that are not directly verified. I would encourage the editor to request the additional checks described in the major comments; if those cannot be supplied from existing data, the quantitative claims should be softened accordingly."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Bottom line: a genuinely new experimental result with one load-bearing soft spot. The new thing is the direct, polarization-resolved observation of a transverse ordered moment in K2Co(SeO3)2 below about 0.35 K, plus the attempt to split the low-energy spin fluctuations into longitudinal and transverse channels. The flipping-ratio drop at T_BKT,3 is a clean signature; the SF/NSF separation is internally consistent; and the extracted S_perp/S_zz ~ 0.017 at base temperature is small but nonzero. If that holds, the near-Ising supersolid survives, and the DMRG/ED debate gets a genuinely sharp experimental constraint.\n\nThe soft spot is exactly the stress-test concern. The polarized-diffraction extraction of S_perp/S_zz assumes one common interlayer correlation factor multiplies both the zz and perp contributions. The paper's own l-fits show the interlayer correlations change across T_BKT,3 (A_03 = -0.029(4) at 0.5 K, A_02 = 0.022(4) at 0.06 K), so it is entirely plausible that the transverse and longitudinal components stack differently below that transition. If they do, the quoted 11% (and the g-corrected 32%) is not simply the ordered-moment ratio. The second headline — longitudinal fluctuations — rests on the same kind of assumption, imported from a prior paper: that inelastic scattering is largely uncorrelated between layers. That is not verified in these data. With only l = 0 and l = 3.5, any l-dependent interlayer interference could suppress intensity regardless of the polarization factor. So the qualitative conclusion that low-energy fluctuations are predominantly longitudinal is plausible and consistent with the earlier QMC work, but the quantitative decomposition in Fig. 4 is not uniquely determined by what is shown.\n\nI do not think these concerns sink the central claim of transverse order — that seems robust. But they do mean the quantitative benchmarks and the longitudinal-fluctuation decomposition should be treated as model-dependent until a two-component stacking analysis is done, or until l-scans at intermediate l validate the uncorrelated-layer assumption.\n\nWho gets value: specialists in frustrated magnetism and neutron scattering, and theorists working on the XXZ triangular-lattice phase diagram. It deserves a serious referee; the right referee will ask for error bars on the flipping ratio and a direct test of the G(l) factorization. I would send it to review rather than desk reject, and I would cite it — with a caveat.","headline":"The paper credibly detects a transverse ordered moment in the near-Ising supersolid, but both headline numbers — the 11% moment ratio and the longitudinal-fluctuation decomposition — rest on an interlayer-correlation factorization that the paper never actually tests.","tokens_in":14811,"tokens_out":4198,"would_cite":true,"duration_ms":40875,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"In the near-Ising triangular antiferromagnet K2Co(SeO3)2, the supersolid state survives with a transverse ordered moment only about 11% of the longitudinal one, and low-energy spin fluctuations are predominantly longitudinal.","keywords":["spin supersolid","triangular lattice antiferromagnet","XXZ model","near-Ising anisotropy","BKT transitions","polarized neutron diffraction","longitudinal spin fluctuations","K2Co(SeO3)2"],"falsifier":"A polarized inelastic neutron scattering measurement at Q=(1/6,1/6,l) with energy transfer near 0.3 meV, resolving spin-flip and non-spin-flip channels at l=0 and l=3.5, would directly measure S_perp(Q,omega) and S_zz(Q,omega). If the transverse channel is found to contribute a significant fraction of the spectral weight at l=3.5, the paper's central claim that low-energy fluctuations are predominantly longitudinal fails. Alternatively, if the l-dependence looks different in a material with the same in-plane exchange but a different stacking sequence, the assumption of negligible interlayer co","tokens_in":13877,"feed_emoji":"🧲","tokens_out":7149,"duration_ms":64937,"temperature":0.7,"pith_summary":"The paper sets out to settle whether the spin supersolid state survives in a triangular-lattice antiferromagnet very close to the Ising limit, where several recent calculations predict the transverse (Bose-condensed) order parameter should vanish. Using polarized neutron diffraction on K2Co(SeO3)2, it shows that a small transverse ordered moment appears only below the lowest of three BKT-type transitions, reaching about 11% of the longitudinal moment at 0.035 K. It further shows, from the momentum-transfer dependence of inelastic neutron scattering, that the low-energy spin fluctuations are predominantly longitudinal, not transverse as conventional spin-wave theory would expect. If correct, this provides direct experimental evidence that supersolidity persists at J_xy/J_z approximately 0.07 and sets a quantitative benchmark for microscopic theories of the easy-axis XXZ model.","feed_headline":"A near-Ising magnet hosts a spin supersolid after all","feed_subtitle":"Polarized neutrons find a transverse ordered moment only ~11% of the longitudinal one, with mostly longitudinal spin fluctuations.","key_machinery":"The load-bearing tool is polarization-resolved neutron diffraction: with incident polarization perpendicular to the scattering plane, the non-spin-flip and spin-flip channels probe different combinations of the longitudinal static structure factor S_zz and the transverse S_perp (the Fourier transforms of the out-of-plane and in-plane spin correlation functions), so the temperature dependence of the flipping ratio isolates the onset of transverse order. The companion tool is the polarization factor in the unpolarized neutron cross section, I proportional to (1 - Q_z^2/Q^2) S_zz + 1/2(1+Q_z^2/Q^2) S_perp, which makes the l-dependence of the inelastic intensity at fixed (h,k) a filter for longi","core_discovery":"On the paper's own account, the central discovery is that in K2Co(SeO3)2 the supersolid state is real even in the near-Ising regime: the transverse ordered moment emerges only below T_BKT,3 approximately 0.35 K, coinciding with a change in interlayer correlations, and reaches S_perp/S_zz approximately 0.017, i.e. m_perp/m_z approximately 11(1)% (a spin ratio <S_perp>/<S_z> approximately 32(2)% after g-factor correction) at the lowest measured temperature. At the same time, the low-energy excitation spectrum is dominated by longitudinal spin fluctuations, as shown by a suppression of spectral weight with out-of-plane momentum transfer that is stronger than the magnetic form factor alone can e","pith_inferences":["A natural extension would be to measure the superfluid (transverse) stiffness directly, for example via the field-dependence of the transverse moment; the BEC picture predicts a specific response to a small in-plane field that distinguishes it from a classical canted state.","Because the g-factor anisotropy is large (g_z/g_perp approximately 2.9), comparisons with theory should always use spin ratios rather than moment ratios; the paper's approximately 32% spin ratio makes the near-Ising model less extreme than the 11% moment ratio suggests.","The longitudinal-fluctuation signature could be tested in the sister compound Rb2Co(SeO3)2: if the same l-dependent suppression appears despite different interlayer stacking, the interpretation in terms of intrinsic longitudinal dynamics would be strengthened.","If the longitudinal-dominance result holds generally, roton-like minima in other triangular supersolid candidates may be density modes rather than magnons, changing how those materials are modeled."],"forward_implications":["The BEC order parameter is nonzero at J_xy/J_z approximately 0.07, so the easy-axis triangular XXZ model supports supersolidity in the near-Ising regime; theories that predict a vanishing transverse moment there are contradicted by this experiment.","The successive-ordering scenario is confirmed: longitudinal order sets in near 10 K and 0.8 K, while transverse order condenses only at T_BKT,3 approximately 0.35 K, accompanied by a switch in dominant interlayer correlations.","The measured spin ratio <S_perp>/<S_z> approximately 32(2)% is substantially larger than a recent DMRG estimate of about 5%, so microscopic calculations must be revised to reproduce the robustness of transverse order.","The low-energy dynamics being predominantly longitudinal explains why quantum Monte Carlo simulations based on longitudinal fluctuations reproduce the continuum and roton features; linear spin-wave theory, which predicts transverse excitations, does not apply to this regime.","The change of interlayer stacking across T_BKT,3 is a measurable correlate of the transverse condensation and can serve as a thermodynamic marker in other quasi-2D supersolid candidates."],"fun_headline_variants":["Spin supersolid survives the near-Ising limit","Near-Ising magnet reveals a stubborn spin supersolid","Tiny transverse moment still means supersolid","Longitudinal spins dominate near-Ising supersolid","Supersolid order in a near-Ising triangular antiferromagnet"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The claim that the low-energy excitations are predominantly longitudinal rests on treating the out-of-plane momentum dependence of the inelastic intensity as coming only from the magnetic form factor and the polarization factor; if interlayer correlations significantly reshape the spectrum along l — an ingredient taken from earlier work rather than verified in these data — the longitudinal conclusion would not follow.","fun_headline_variants_meta":{"raw":{"variants":["Spin supersolid survives the near-Ising limit","Near-Ising magnet reveals a stubborn spin supersolid","Tiny transverse moment still means supersolid","Longitudinal spins dominate near-Ising supersolid","Supersolid order in a near-Ising triangular antiferromagnet"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000291,"raw_usage":{"total_tokens":1517,"prompt_tokens":708,"completion_tokens":809,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":452,"completion_tokens_details":{"reasoning_tokens":729}},"tokens_in":452,"tokens_out":809,"duration_ms":8111,"temperature":1.0,"reasoning_tokens":729,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-02T04:35:35.923891+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A polarized inelastic neutron scattering measurement at Q=(1/6,1/6,l) with energy transfer near 0.3 meV, resolving spin-flip and non-spin-flip channels at l=0 and l=3.5, would directly measure S_perp(Q,omega) and S_zz(Q,omega). If the transverse channel is found to contribute a significant fraction of the spectral weight at l=3.5, the paper's central claim that low-energy fluctuations are predominantly longitudinal fails. Alternatively, if the l-dependence looks different in a material with the same in-plane exchange but a different stacking sequence, the assumption of negligible interlayer co","supporting_citations":[],"review_version":1}