{"id":"dedd2122-f20a-4399-8737-b1b1ef297988","arxiv_id":"2412.03149","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"Neutron diffraction reveals a Y-like ground state and a c-axis collinear intermediate phase in the spin-5/2 triangular-lattice antiferromagnet Na2BaMn(PO4)2, with two successive transitions at 1.13 K and 1.28 K.","lead":"Neutron diffraction shows that the manganese magnet Na2BaMn(PO4)2 adopts a Y-shaped spin arrangement at very low temperature and a simpler up-down arrangement at slightly higher temperature. The result gives a classical-spin comparison point for the exotic quantum spin states seen in related cobalt and nickel compounds.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The intermediate-phase c-axis collinear assignment rests on a single-temperature powder refinement where the c-axis and Y-like models differ by only ~1% in Rwp; without error bars or a free in-plane refinement, the absence of in-plane order is not established.","rationale":"The reader's weakest assumption identifies exactly the same concern: the intermediate-phase assignment to a purely c-axis collinear structure is inferred from a single powder pattern at 1.25 K, where the Y-like and c-axis models are nearly indistinguishable. This is the most load-bearing point because the paper's two-transition scenario depends on the in-plane moment vanishing below TN1 while the c-axis moment persists to TN2. The concern does not overturn the ground-state Y-like structure, which is more strongly supported by the 67 mK refinements and the low-Q peak comparisons; those show clear failures of the single-IR in-plane and c-axis models. However, the intermediate-phase assignment is not positively established by the evidence presented. The reader's CONDITIONAL verdict remains appropriate: the paper should either demonstrate with error-propagated free refinements that the in-plane component is consistent with zero across the intermediate phase, or soften the intermediate-phase structural claim. Therefore the recommended verdict is UNCHANGED relative to the reader's CONDITIONAL assessment, with the concrete free-refinement test as the condition for resolution.","tokens_in":12159,"tokens_out":5627,"duration_ms":56423,"concrete_test":"Reanalyze the existing 1.25 K, λ = 2.45 Å NPD pattern with FULLPROF by refining all three irreducible-representation coefficients (Γ1, Γ2, Γ3) independently, including covariances, and report the in-plane moment m_ab with a 2σ confidence interval. If the interval contains zero and its upper bound is below ~0.2 μB, the c-axis assignment is supported; if it contains zero but the upper bound is large, the data are inconclusive and the intermediate phase should be labeled unassigned; if it excludes zero, the c-axis collinear model is falsified. A companion check is to refine the same free model at 1.15 K and 1.30 K to confirm that the in-plane component is systematically zero throughout the intermediate phase, not merely at one temperature.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing weak point is the assignment of the TN1<T<TN2 phase as purely c-axis collinear (Section III, Figs. 5 and 6). This is the evidence that TN1 corresponds to loss of in-plane order while out-of-plane order persists. The paper's own comparison near Fig. 5(e) says the difference between the c-axis collinear and Y-like refinements is 'quite marginal' and that adding in-plane components does not improve the fit. That is then interpreted as showing the in-plane moment is zero. But Rwp differences of ~0.2-1% between models with different parameter counts are not meaningful unless accompanied by uncertainties, and a non-detection of in-plane magnetic intensity in a powder pattern is not equivalent to m_ab = 0, especially when candidate reflections overlap or are weak. Refined in-plane moments in Fig. 6(c) are shown without error bars, so the claim that the Mn2 in-plane component 'tends to vanish at TN1' cannot be tested. If the intermediate phase actually retains a small in-plane component or has a different symmetry, the two-step ordering scenario might still be qualitatively valid, but the specific c-axis collinear structure would be wrong. Since the paper's central structural claim for the intermediate phase rests at this point, the concern is load-bearing.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reports a combined thermodynamic and neutron powder diffraction study of the spin-5/2 triangular-lattice antiferromagnet Na2BaMn(PO4)2. Specific heat and dc magnetization show two successive transitions at TN1 ≈ 1.13 K and TN2 ≈ 1.28 K. At 67 mK, refinement of the NPD data favors a Y-like magnetic structure with both in-plane and c-axis Mn2+ moment components, with Rwp = 5.77 versus 9.62 and 9.72 for the in-plane 120° and c-axis collinear alternatives. Between TN1 and TN2, the magnetic propagation vector changes, most notably kz, and the authors assign a c-axis collinear structure based on refinements at a single temperature, 1.25 K, where the c-axis collinear model and the Y-like model give similar Rwp values. The paper interprets the two transitions as separate ordering of the out-of-plane and in-plane spin components, in line with easy-axis triangular-lattice XXZ expectations, and notes incommensurate kz as evidence of interlayer coupling.","tokens_in":12403,"tokens_out":4209,"duration_ms":38232,"significance":"If the ground-state Y structure and the two-step ordering scenario are correct, this is a valuable experimental realization of the classical spin-5/2 limit of the easy-axis triangular-lattice XXZ model, complementing the quantum spin-1/2 and spin-1 compounds in the same phosphate family. The ground-state assignment is well supported: the Y-like refinement gives a substantially lower Rwp than the single-IR alternatives, and the comparison shown in Fig. 3(e) directly demonstrates systematic intensity mismatches for the competing models. The paper also benefits from being grounded in externally established structural results and theoretical predictions from Refs. [28,29]. The intermediate-phase assignment, however, rests on weaker evidence, and the central claim of the paper depends on that assignment; the analysis needs quantitative uncertainty handling before the result can be regarded as conclusive.","major_comments":[{"comment":"The assignment of the intermediate phase (TN1 < T < TN2) as purely c-axis collinear is not established by the evidence presented. The refinement comparison at 1.25 K is made at a single temperature, and the text itself states that the difference between the c-axis collinear and Y-like models is 'quite marginal' and that adding in-plane components does not improve the fit. Non-improvement of Rwp with additional parameters is not equivalent to a zero in-plane moment, particularly in powder data where the relevant magnetic reflections are weak or overlapping. To support the claim, the authors should provide error bars on the refined moments and either a statistical comparison (e.g., a Hamilton test or equivalent) or an explicit sensitivity estimate that quantifies the upper bound on an in-plane component compatible with the 1.25 K pattern. If such an analysis is not possible, the intermediate-phase structure should be presented as one plausible model rather than as the determined structure.","section":"Section III, Figs. 5 and 6"},{"comment":"The temperature dependence of the moment sizes is central to the two-step-ordering scenario, but Fig. 6(c) reports refined out-of-plane and in-plane moments without error bars and with only one intermediate temperature point (1.25 K). The statement that the in-plane moment 'tends to vanish at TN1 already' therefore cannot be quantitatively tested, and the continuity or discontinuity of the in-plane order parameter across TN1 is not resolved. The authors should add refinement uncertainties and, if feasible, additional temperatures around TN1, or they should explicitly restrict the claim to consistency rather than determination.","section":"Section III, Fig. 6(c)"}],"minor_comments":[{"comment":"The sentence 'two sharp anomalies can be observed at TN1 ∼ 1.13 K at TN2 ∼ 1.28 K' appears to have a typo; 'at' before TN2 should presumably be 'and'.","section":"Introduction, paragraph 4"},{"comment":"The abstract says the magnetic propagation vector shows a dramatic change, but the reported evidence concerns specifically kz; please state this explicitly to avoid overstating the change in the full vector.","section":"Abstract and Section III"},{"comment":"The figure caption says panels (a) and (b) are fitted with a c-axis collinear structure, while the main text says panels (b), (c), and (d) use c-axis collinear, in-plane 120°, and Y-like structures respectively; the description of the panels should be made consistent.","section":"Figure 5 caption and main text"},{"comment":"The phrase 'the mixture were pelletized' should be 'the mixture was pelletized'.","section":"Section II, sample synthesis"},{"comment":"Even if error bars are added in a revision, the figure would benefit from a legend distinguishing the three Mn sites in the triangular unit, because the text refers to Mn1, Mn2, and Mn3 but the symbols are not defined in the caption.","section":"Section III, Fig. 6(c)"}],"recommendation":"major_revision","confidential_remarks":"The paper is within the scope of the journal and the ground-state result is likely to be of interest. The main risk is that the intermediate-phase structure is underdetermined by the current single-temperature powder refinement, and the authors' own wording concedes the marginal nature of the fit difference. I would support publication after the authors either provide a quantitative error analysis for the in-plane moment or explicitly soften the intermediate-phase claim. I do not see any concern about overlap with the authors' prior Ref. [24]; the neutron diffraction data presented here are a distinct contribution."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The ground-state result is the real news here, and it is well supported. Refinements at 67 mK clearly favor the Y-like structure over the in-plane 120° and c-axis collinear alternatives: Rwp of 5.77 versus 9.62 and 9.72, and the visual difference in the low-Q magnetic peaks is convincing. That nails the zero-field magnetic structure of Na2BaMn(PO4)2 as the classical counterpart to the quantum spin supersolid in Na2BaCo(PO4)2, which is a genuinely useful data point for the field. I also like that the paper is careful to compare against explicit model candidates from representation analysis, and that the thermodynamic measurements agree with earlier single-crystal work.\n\nThe intermediate phase between TN1 and TN2 is where I part company with the paper's confidence. The authors themselves say the difference between the c-axis collinear and Y-like refinements at 1.25 K is 'quite marginal,' yet they assign the collinear structure because it has higher symmetry and the Y-like model does not improve the fit. That is a reasonable working hypothesis, but it is not a determination. Rwp differences of about a percent between models with different parameter counts are not meaningful without uncertainties, and powder-averaged non-detection of in-plane intensity is not the same as m_ab = 0. The refined in-plane moments in Fig. 6(c) have no error bars, so the claim that the in-plane component vanishes at TN1 is not testable from the paper as written. I would not call this fatal, but I would call it the load-bearing weak point for the 'successive ordering' narrative: if the intermediate phase retains a small in-plane component, the two-step scenario is still qualitatively right but the specific collinear structure is not established.\n\nOther soft spots are minor by comparison: raw data are not deposited, refined moments lack uncertainties throughout, and there is a small internal inconsistency in calling the 1.25 K comparison 'marginal' while also listing visibly different R factors. None of these affect the ground-state conclusion.\n\nOverall this is a straightforward, honest experimental paper that delivers one solid result and one plausible but under-supported secondary claim. It deserves a serious referee: the ground-state structure alone is worth publishing, and the intermediate phase can be tightened with error analysis or single-crystal data. Send it to review, but expect the referee to push on the 1.25 K assignment.","headline":"A solid neutron-diffraction determination of the Y-like ground state in a classical spin-5/2 triangular antiferromagnet, with the intermediate-phase structure plausible but not nailed down.","tokens_in":12981,"tokens_out":1048,"would_cite":true,"duration_ms":11106,"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":"The zero-field ground state of the spin-5/2 triangular-lattice antiferromagnet Na2BaMn(PO4)2 is a Y-like spin configuration, with a c-axis collinear phase between two successive transitions at 1.13 K and 1.28 K.","keywords":["triangular lattice antiferromagnet","spin-5/2","neutron powder diffraction","magnetic structure","successive magnetic transitions","Y-like spin configuration","easy-axis anisotropy","Na2BaMn(PO4)2"],"falsifier":"A single-crystal neutron diffraction experiment at a temperature between $T_{N1}$ and $T_{N2}$ that resolves magnetic intensity requiring an in-plane moment component, or a powder measurement at several temperatures in that window showing nonzero in-plane scattering, would falsify the c-axis collinear assignment. Conversely, measuring the in-plane moment to remain zero throughout the window while the $c$-axis moment orders at $T_{N2}$ would confirm it.","tokens_in":11945,"feed_emoji":"🧲","tokens_out":6717,"duration_ms":59699,"temperature":0.7,"pith_summary":"Na$_2$BaMn(PO$_4$)$_2$, the spin-5/2 member of a triangular-lattice phosphate family whose lighter members show quantum spin states, orders in two steps in zero field. Neutron powder diffraction shows that below $T_{N1}\\approx1.13$ K the ground state is a Y-like configuration in which Mn$^{2+}$ moments have both in-plane and $c$-axis components. Between $T_{N1}$ and $T_{N2}\\approx1.28$ K the magnetic structure becomes a $c$-axis collinear arrangement with only out-of-plane moments, an assignment the paper makes at 1.25 K. Both phases share an incommensurate propagation vector $k=(1/3,1/3,k_z)$ with $k_z\\approx0.187$ at base temperature and $k_z\\approx0.139$ at 1.25 K, which the authors read as evidence of interlayer coupling. The result matters because it places a classical, high-spin system in the same theoretical family as the quantum spin-supersolid and two-magnon condensate compounds, and it matches the two-step ordering scenario predicted for an easy-axis triangular antiferromagnet.","feed_headline":"Neutrons reveal two-step ordering in a spin-5/2 triangular magnet","feed_subtitle":"Y-like ground state below 1.13 K, c-axis collinear phase up to 1.28 K, matching easy-axis theory.","key_machinery":"The analysis is carried by irreducible-representation decomposition of the magnetic representation for the Mn$^{2+}$ site, which splits into three representations: $\\Gamma_1$ (spins along $c$, cosinusoidally modulated by the incommensurate $k_z$), and $\\Gamma_2,\\Gamma_3$ (coplanar $120^\\circ$ structures of opposite in-plane chirality). The Y ground state is the superposition of all three with the $\\Gamma_2:\\Gamma_3$ coefficients fixed at 1:$-1$, while the intermediate phase is modeled by $\\Gamma_1$ alone. Neutron powder diffraction at 67 mK and 1.25 K discriminates among these models: at 67 mK the single-representation models misfit the magnetic reflection intensities, while at 1.25 K the in-plane components refine to zero and the higher-symmetry $\\Gamma_1$ model fits as well as the Y model. The temperature dependence of the integrated magnetic reflection intensity and the refined moment components then ties the two macroscopic anomalies in specific heat and magnetization to the in-plane and out-of-plane ordering separately.","core_discovery":"The paper reports that the zero-field magnetic ground state of Na$_2$BaMn(PO$_4$)$_2$ is a Y-like spin structure, not a simple $120^\\circ$ or $c$-axis collinear state: refinement of the 67 mK powder patterns requires the superposition of the $c$-axis collinear irreducible representation with the two in-plane $120^\\circ$ representations, with the in-plane pair entered in a 1:$-1$ ratio. On warming through $T_{N1}\\approx1.13$ K, the in-plane moment components vanish and the remaining $c$-axis moments stay ordered up to $T_{N2}\\approx1.28$ K, giving a $c$-axis collinear intermediate phase with U(1) spin-rotation symmetry preserved. The magnetic propagation vector is incommensurate in both phases, and its $c$-axis component jumps between the two phases, which the authors attribute to the different interlayer spin arrangements. The paper interprets the two transitions as the separate ordering of the out-of-plane and in-plane moment components of an easy-axis triangular-lattice antiferromagnet, with the intermediate collinear phase stabilized by thermal fluctuations rather than by quantum fluctuations.","pith_inferences":["If single-crystal neutron diffraction confirms the intermediate phase, Na$_2$BaMn(PO$_4$)$_2$ could serve as a clean classical reference for the easy-axis XXZ triangular lattice, where temperature rather than quantum fluctuations selects the collinear state.","The jump in $k_z$ between the two phases suggests the interlayer registry, not just the intralayer spin pattern, changes at $T_{N1}$; a microscopic model fit to the two measured $k_z$ values could constrain the interlayer exchange ratio.","One could test the thermal-fluctuation interpretation by measuring the intermediate phase under applied magnetic field: a field along $c$ should compete with the collinear state and may reveal whether the collinear phase is a robust thermodynamic phase or a narrow fluctuation-stabilized window.","Given the marginal difference between the collinear and Y fits at 1.25 K in powder data, the claim would be sharpened by measurements at several temperatures within $T_{N1}<T<T_{N2}$ rather than a single temperature."],"forward_implications":["Above $T_{N1}$ the in-plane moments are zero while $c$-axis moments remain ordered, so the two anomalies at $T_{N1}$ and $T_{N2}$ are the separate ordering temperatures of the in-plane and out-of-plane spin components.","The $c$-axis collinear intermediate phase must be an amplitude-modulated antiferromagnet, not the field-induced up-up-down ferrimagnet, because the propagation vector has incommensurate $k_z$ and no $k=0$ ferromagnetic intensity appears at 1.25 K.","The incommensurate $k_z$ and resolution-limited magnetic Bragg peaks imply the interlayer couplings are not negligible, so a purely two-dimensional model will miss part of the physics.","The Y ground state in this $S=5/2$ system shows that the Y-like configuration is not a purely quantum effect, extending the spin-supersolid-like spin pattern to the classical limit.","The success of the same irreducible representations at both temperatures means the exchange anisotropy and symmetry constraints of the $P\\bar{3}$ structure are sufficient to describe the ordered phases within the tested model space."],"supporting_citations":[{"why":"Supplies the theoretical prediction that an easy-axis triangular-lattice Heisenberg antiferromagnet orders the out-of-plane and in-plane spin components at two separate transitions.","marker":"[28]"},{"why":"Provides the theoretical expectation of a c-axis collinear intermediate phase stabilized by thermal fluctuations.","marker":"[29]"},{"why":"Reports the earlier thermodynamic evidence for two magnetic transitions and the field-induced up-up-down plateau in single crystals, the phenomena this paper explains microscopically.","marker":"[18]"},{"why":"Establishes the P-3 space group and prior magnetic characterization of Na2BaMn(PO4)2 used as the structural starting model for the refinements.","marker":"[24]"},{"why":"Gives the quantum phase diagram of the triangular-lattice XXZ model, supporting identification of the Y-like ground state.","marker":"[30]"},{"why":"Documents the spin-supersolid Y-like ground state in the quantum spin-1/2 counterpart, the comparison motivating this classical spin-5/2 study.","marker":"[13]"}],"fun_headline_variants":["Two magnetic transitions in spin-5/2 triangular antiferromagnet","Y-like spin order emerges below 1.13 K in Na2BaMn(PO4)2","Neutron study maps Y-shape to collinear transition in easy-axis magnet","Spin-5/2 triangular magnet orders in two steps: Y then c-axis","Easy-axis triangular magnet shows successive Y and collinear phases"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the single 1.25 K powder pattern, in which the in-plane magnetic intensities refine to zero, proves the intermediate phase has exactly zero in-plane moment; if powder averaging or the limited set of tested models hides a small in-plane component, the two-step picture would need revision.","fun_headline_variants_meta":{"raw":{"variants":["Two magnetic transitions in spin-5/2 triangular antiferromagnet","Y-like spin order emerges below 1.13 K in Na2BaMn(PO4)2","Neutron study maps Y-shape to collinear transition in easy-axis magnet","Spin-5/2 triangular magnet orders in two steps: Y then c-axis","Easy-axis triangular magnet shows successive Y and collinear phases"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000208,"raw_usage":{"total_tokens":1492,"prompt_tokens":1124,"completion_tokens":368,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":740,"completion_tokens_details":{"reasoning_tokens":264}},"tokens_in":740,"tokens_out":368,"duration_ms":3847,"temperature":1.0,"reasoning_tokens":264,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T22:42:25.724886+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A single-crystal neutron diffraction experiment at a temperature between $T_{N1}$ and $T_{N2}$ that resolves magnetic intensity requiring an in-plane moment component, or a powder measurement at several temperatures in that window showing nonzero in-plane scattering, would falsify the c-axis collinear assignment. Conversely, measuring the in-plane moment to remain zero throughout the window while the $c$-axis moment orders at $T_{N2}$ would confirm it.","supporting_citations":[{"cited_title":"Rodríguez-Carvajal, Recent advances in magnetic structure determination by neutron powder diffraction, Physica B 192, 55 (1993)","cited_arxiv_id":null,"evidence_quote":"Supplies the theoretical prediction that an easy-axis triangular-lattice Heisenberg antiferromagnet orders the out-of-plane and in-plane spin components at two separate transitions."},{"cited_title":"Miyashita and H","cited_arxiv_id":null,"evidence_quote":"Provides the theoretical expectation of a c-axis collinear intermediate phase stabilized by thermal fluctuations."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Reports the earlier thermodynamic evidence for two magnetic transitions and the field-induced up-up-down plateau in single crystals, the phenomena this paper explains microscopically."},{"cited_title":"Zhang, J","cited_arxiv_id":null,"evidence_quote":"Establishes the P-3 space group and prior magnetic characterization of Na2BaMn(PO4)2 used as the structural starting model for the refinements."},{"cited_title":"Miyashita, Magnetic properties of Ising-like Heisenberg an- tiferromagnets on the triangular lattice, J","cited_arxiv_id":null,"evidence_quote":"Gives the quantum phase diagram of the triangular-lattice XXZ model, supporting identification of the Y-like ground state."},{"cited_title":"Xiang, C","cited_arxiv_id":null,"evidence_quote":"Documents the spin-supersolid Y-like ground state in the quantum spin-1/2 counterpart, the comparison motivating this classical spin-5/2 study."}],"review_version":1}