{"id":"6c29b0da-d509-44dc-8325-cef3b2f92035","arxiv_id":"2411.12054","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":9,"one_line_summary":"Single-crystal measurements and a crystalline-electric-field model establish an easy-plane ground-state doublet and ferromagnetic exchange along both axes in CeCuSi, explaining the absence of hard-axis ordering.","lead":"CeCuSi single crystals were grown and found to order ferromagnetically at 15.5 K with magnetic moments in the basal plane. A crystal-field model built from susceptibility data also matches heat capacity, Raman, and magnetization, giving a rare clean test of how lattice anisotropy shapes a cerium ferromagnet.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Signs of λ∥ and λ⊥ are not secured: they come from an overparameterized fit with a negative χ⊥0 and overstated INS/Raman agreement.","rationale":"The paper has real strengths: single-crystal growth, direct magnetization showing the easy ab plane, Schottky anomaly, FM magnon gaps in Cp and resistivity, and Raman symmetry assignments. None of these are in question. The specific new claim that both exchange channels are ferromagnetic is not directly measured; it is a byproduct of the CEF+mean-field fit. The reader flagged the negative χ⊥0; I agree this is the weak point but would sharpen it: the problem is not only χ0 but the identifiability of the whole seven-parameter model. A negative χ0 is a symptom of overparameterization, and the discrepancy with prior INS (B34 nearly halved) and with the Raman peak energies shows that the CEF parameters can move substantially while still fitting the susceptibility. Because λ_i are determined jointly with the CEF parameters, a family of parameter sets likely exists in which one of the λ_i changes sign. A bootstrap with χ0 fixed and CEF energies constrained by Raman would settle this. If the signs survive, the paper's central claim is fine; if not, the conclusion should be softened to 'the data are consistent with FM exchange' rather than 'the interactions are ferromagnetic.' Thus the read does not change the reader's CONDITIONAL verdict; it makes the required condition concrete.","tokens_in":16285,"tokens_out":11953,"duration_ms":121719,"concrete_test":"Refit the inverse susceptibility (Fig. 2b) using Eq. A6 with χ⊥0 fixed to zero (or to an independently measured LaCuSi background), and with bootstrap resampling to obtain joint confidence intervals for λ∥ and λ⊥; additionally constrain the CEF splittings to the Raman-observed values (94 K and 129 K). If the 95% confidence interval for either λ∥ or λ⊥ includes zero or becomes negative, the 'ferromagnetic along both axes' claim is not settled by the present data.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that CeCuSi orders in the basal plane because the exchange is ferromagnetic along both axes depends entirely on the signs of λ∥ and λ⊥ obtained by fitting Eq. A6 to χ(T). This is the fragile link. The fit uses seven free parameters (B02, B04, B34, λ∥, λ⊥, χ∥0, χ⊥0) against two curves, and no error or correlation analysis is given. The fitted χ⊥0 = -8.21×10^-5 emu/mol is negative and is written off as a straw-mounting artifact; if it is wrong, λ⊥ can change. The problem is compounded by the fact that the CEF parameters themselves are not uniquely pinned: the 'agreement' with the previous INS parameters [16] is overstated—B02 changes from 2.43 to 4.42 K and B34 from 5.43 to 2.93 K—and the Raman CEF peaks (65 cm^-1 ≈ 94 K and 90 cm^-1 ≈ 129 K, Section III.E) do not match the fitted splittings Δ1 = 112 K and Δ2 = 122 K. Since the Van Vleck terms in Eqs. A3–A4 depend on the mixing angle α, and α is set by B34, a different α can be compensated by different λ_i. The directly measured c-axis saturation moment (0.18 μB, Fig. 2 inset) also sits well below the model's 0.26 μB from Eq. (1), further weakening the constraint on α. The easy-plane CEF ground state is robust (magnetization), but the novel 'FM along both axes' conclusion is an output of the same fit, not an independent result.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reports the first single-crystal growth of CeCuSi and a multi-probe study (structural, magnetic, transport, heat capacity, Raman) of its magnetic properties. CeCuSi orders ferromagnetically at 15.5 K with the easy magnetization direction in the basal plane. The authors perform a crystalline-electric-field (CEF) analysis of the anisotropic susceptibility using a molecular-field correction and residual susceptibility terms, obtaining a CEF ground-state doublet with moment primarily in the basal plane and positive molecular-field parameters along both the c axis and the ab plane. They interpret the positive parameters as ferromagnetic exchange along both directions, explaining the absence of hard-axis ordering. Independent checks from the Schottky anomaly, Raman-active CEF excitations, and saturation moments are presented as support.","tokens_in":16661,"tokens_out":4398,"duration_ms":44595,"significance":"If the central claim holds, the paper provides a concrete counterexample within the CeTX family to the tendency of Kondo-lattice ferromagnets to order along the CEF hard axis, and it demonstrates the importance of simultaneous CEF analysis of anisotropic data. The paper also provides useful single-crystal data for a material previously studied only in polycrystalline form. Its main strengths are the multiple independent probes and the explicit treatment of the CEF contribution to the susceptibility and heat capacity. However, the most novel conclusion — that the exchange is ferromagnetic along both axes — rests on a seven-parameter mean-field fit whose stability is not demonstrated. The overall significance is therefore conditional on a robustness analysis of that fit.","major_comments":[{"comment":"The signs of λ∥ and λ⊥, which are the basis of the statement that the interactions are ferromagnetic along both directions, come from a fit with seven free parameters (B0_2, B0_4, B3_4, λ∥, λ⊥, χ∥0, χ⊥0) against two susceptibility curves, with no reported uncertainties or parameter-correlation analysis. The fitted χ⊥0 = -8.21×10^-5 emu/mol is attributed to a straw-mounting artifact; if this background is incorrect, or if a different trade-off between χ⊥0, the mixing angle α, and λ⊥ exists, the sign of λ⊥ is not secured. I request a robustness analysis: report error bars and correlations, or repeat the fit with χ⊥0 fixed to zero and with the CEF parameters fixed to the values of Ref. [16], and show whether λ⊥ remains positive.","section":"Section III.C and Table III, Eq. (A6)"},{"comment":"The agreement with previous inelastic neutron scattering and with the Raman data is overstated. The fitted B0_2 = 4.42 K and B3_4 = 2.93 K differ substantially from Ref. [16]'s values of 2.43 K and 5.43 K, and the Raman peaks at 94 K and 129 K are 18 K and 7 K away from Δ1 = 112 K and Δ2 = 122 K, respectively. Because α in Eqs. (A3)–(A4) controls the Van Vleck terms and is set by B3_4, the CEF parameters are not uniquely pinned. The paper should quantify these discrepancies and, ideally, constrain the CEF parameters with a combined fit to susceptibility, heat capacity, and Raman peak positions.","section":"Section III.C, III.E, and Table III"},{"comment":"The calculated c-axis saturation moment (0.26 μB) is 44% larger than the measured value (0.18 μB) shown in the inset of Fig. 2. This is a direct test of the ground-state wavefunction, and the discrepancy weakens the quantitative determination of the mixing angle α on which the Van Vleck terms and hence λ∥ and λ⊥ depend. Please discuss whether this discrepancy is within the expected accuracy of the model and how it affects the inferred signs of the molecular-field parameters.","section":"Section III.B and Eq. (1)"}],"minor_comments":[{"comment":"The phrase 'the highest in the CeTX family' should be qualified to make clear it refers to the compounds discussed in this work rather than an exhaustive statement about all CeTX materials.","section":"Section I"},{"comment":"The notation in Eq. (A6) is confusing: the left side is χ_i^{-1} while the right side is ( ... )^{-1}; please clarify that the residual susceptibility is added to the molecular-field-corrected susceptibility before taking the inverse.","section":"Eq. (A6)"},{"comment":"The caption states that the inverse susceptibility was 'fitted to Curie-Weiss law and the CEF model'; these are two separate fits with different functional forms, so the wording should distinguish them.","section":"Fig. 2(b) caption"},{"comment":"For CePtAl4Ge2 the mixing angle α is listed as N/A even though B3_4 ≈ 0; please explain why α is not defined or not reported for that compound.","section":"Table IV"},{"comment":"When claiming that the Raman energies 'agree reasonably well' with the CEF splittings, please include the numeric comparison (94 K vs 112 K and 129 K vs 122 K) so that readers can judge the level of agreement directly.","section":"Section III.E"},{"comment":"The single-crystal residual resistivity (241 μΩ cm) is much larger than that of the polycrystalline sample (9 μΩ cm); because the transport-derived magnon gap is extracted from this sample, the possible influence of micro-cracks on the fit should be discussed.","section":"Section III.F"}],"recommendation":"major_revision","confidential_remarks":"The paper is suitable for a condensed-matter journal and reports valuable single-crystal data. The main concern is that the central 'ferromagnetic interaction along both axes' claim is an output of a highly parameterized fit without robustness checks. I would encourage the editor to ask for error bars and at least one alternative fit (e.g., fixing χ⊥0 = 0 or using the INS CEF parameters) in the revision. The authors' claim of agreement with previous INS and Raman data should also be made quantitative, as the current text overstates the agreement."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nYou should know two things about this paper. First, it's the first single-crystal study of CeCuSi and it offers a CEF scheme that is cross-checked across susceptibility, heat capacity, Raman, and magnetization. Second, the abstract's central claim—that exchange is ferromagnetic along both crystallographic axes, explaining why CeCuSi orders in the easy plane rather than the hard axis—is much less secure than the paper's tone suggests. That conclusion rests on a seven-parameter fit to two susceptibility curves, with no reported error bars, and one fitted background term, χ⊥0, that is negative and physically unexplained.\n\nWhat's genuinely new: the single-crystal growth, the structure confirmation, and the explicit multi-probe consistency. The easy-plane doublet ground state is well supported by the quick basal-plane saturation of 1.25 μB, the small c-axis moment, and the Schottky anomaly that peaks near the fitted splittings. The Raman spectra show E_g excitations at energies close to the model, though not exactly (94 K vs 112 K for the first level). The comparison table with other trigonal Ce compounds is useful.\n\nThe soft spots are real but not fatal. Appendix A's fit, with B02, B04, B34, λ∥, λ⊥, χ∥0, χ⊥0 against two curves, is overparameterized for the claims made off it. No uncertainty or correlation analysis is given. The negative χ⊥0 is explained as a straw-mounting artifact, but without further evidence it's precisely the kind of term that can trade off against λ⊥ and flip its sign. The agreement with prior INS parameters is overstated: B02 goes from 2.43 to 4.42 K and B34 from 5.43 to 2.93 K—large changes, though the splitting energies stay close. The measured c-axis saturation moment, 0.18 μB, sits 30% below the model's 0.26 μB, and that discrepancy is noted but not addressed. None of this undermines the easy-plane ground state, but it does mean the \"ferromagnetic along both directions\" should be presented as a plausible interpretation, not as a settled result.\n\nI'd send this to peer review. The experiments are careful and the model is worth discussing. I'd ask the referee to require an error analysis of the fit, a physical accounting of χ⊥0, and a more measured comparison with the neutron data. I'd cite it for the single-crystal properties and the CEF scheme, not for the sign of the exchange along both axes.","headline":"Solid single-crystal study of a triangular-lattice Ce ferromagnet with a plausible CEF scheme, but the 'ferromagnetic along both axes' claim is not as secure as the abstract implies.","tokens_in":17228,"tokens_out":3399,"would_cite":true,"duration_ms":43118,"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":"CeCuSi is a Kondo-lattice ferromagnet whose easy-plane order follows from ferromagnetic exchange along both crystallographic directions.","keywords":["CeCuSi","Kondo lattice ferromagnet","crystalline electric field","easy-plane magnetic ordering","triangular lattice","molecular-field parameters","ferromagnetic magnon gap","single-crystal growth"],"falsifier":"A low-temperature neutron diffraction and inelastic neutron scattering study on CeCuSi single crystals could settle the claim directly: if the ordered moment is found to have a dominant $c$-axis component, or if the measured CEF excitations require a level scheme whose simultaneous susceptibility fit yields a negative $\\lambda$ in either direction, the paper's explanation of easy-plane order would fail.","tokens_in":16100,"feed_emoji":"🧲","tokens_out":6065,"duration_ms":60591,"temperature":0.7,"pith_summary":"The paper reports the first single-crystal growth of CeCuSi and uses susceptibility, heat capacity, Raman, and resistivity data to determine why this Kondo-lattice ferromagnet orders in the hexagonal basal plane rather than along the crystallographic hard axis. The central claim is that the Ce$^{3+}$ crystalline-electric-field ground state is a doublet with the moment largely confined to the basal plane, and that the molecular-field exchange is ferromagnetic both parallel and perpendicular to the $c$ axis. On that picture, the negative Curie--Weiss temperature along $c$ comes from the crystal field rather than from antiferromagnetism, and the absence of hard-axis ordering is natural. The paper also shows that the exponential resistivity and heat-capacity tails below $T_\\mathrm{C}$ follow a ferromagnetic magnon gap near 24--25 K.","feed_headline":"Ferromagnetic exchange both ways fixes easy-plane order in CeCuSi","feed_subtitle":"Single-crystal data place the Ce moment in the basal plane; positive exchange along both axes explains the 15.5 K order.","key_machinery":"The central object is the trigonal CEF Hamiltonian $H_\\mathrm{CEF} = B_2^0 O_2^0 + B_4^0 O_4^0 + B_4^3 O_4^3$ written in Stevens operators for a $J=5/2$ Ce$^{3+}$ ion, whose eigenstates are two mixed $|\\pm1/2\\rangle/|\\pm5/2\\rangle$ doublets and a pure $|\\pm3/2\\rangle$ doublet. The magnetic susceptibility is then dressed by a molecular field through $\\chi_i^{-1} = (\\chi_i^\\mathrm{CEF}/(1-\\lambda_i\\chi_i^\\mathrm{CEF}) + \\chi_i^0)^{-1}$, with $\\lambda_\\parallel$, $\\lambda_\\perp$, and small residual offsets $\\chi_i^0$ as parameters. This formula is what allows the authors to separate crystal-field anisotropy from exchange: the CEF parameters set the anisotropy, while the sign of $\\lambda$ sets whether the exchange is ferromagnetic along each direction. The simultaneous fit to both susceptibility axes, anchored by a $B_2^0$ estimate from the Curie--Weiss temperatures, is the load-bearing step that produces the easy-plane ground state and the positive $\\lambda$ values.","core_discovery":"The authors establish that CeCuSi, with Ce$^{3+}$ on a triangular lattice of $D_{3d}$ point symmetry, has a crystalline-electric-field ground state $\\Gamma_4^{(1)} = 0.257|\\pm 5/2\\rangle - 0.967|\\mp 1/2\\rangle$, which yields a saturation moment of about $1.20\\,\\mu_\\mathrm{B}$ in the basal plane versus $0.26\\,\\mu_\\mathrm{B}$ along $c$. Simultaneous fits of the inverse magnetic susceptibility along both axes to a trigonal CEF Hamiltonian with molecular-field terms give positive exchange parameters $\\lambda_\\parallel = 9.0$ and $\\lambda_\\perp = 5.2$ mol/emu, meaning the exchange interaction is ferromagnetic along both directions. The paper argues that this positive exchange is why CeCuSi orders along the easy plane, in contrast to many Kondo-lattice ferromagnets that order along the CEF hard axis. Supporting evidence includes the Schottky anomaly in specific heat, CEF excitations observed in Raman at energies consistent with the splittings $\\Delta_1 = 112$ K and $\\Delta_2 = 122$ K, and the magnon-gap behavior seen in heat capacity, resistivity, and Raman.","pith_inferences":["Editorial inference: applying the same simultaneous CEF-plus-molecular-field analysis to known hard-axis Kondo-lattice ferromagnets would directly test whether their in-plane exchange is actually antiferromagnetic; if so, hard-axis ordering becomes a fingerprint of competing exchange rather than of the CEF alone.","Editorial inference: because the magnon gap exceeds $T_\\mathrm{C}$, an in-plane magnetic field applied below $T_\\mathrm{C}$ should shift or soften the roughly 25 cm$^{-1}$ Raman magnon mode, and measuring that field dependence would independently check the magnon assignment.","Editorial inference: the fitted negative residual susceptibility $\\chi_{\\perp 0} = -8.21\\times10^{-5}$ emu/mol enters the fit as an offset, so re-measuring the in-plane susceptibility with a rigid sample holder or with oriented powder would test whether this offset is indeed a mounting artifact."],"forward_implications":["Below $T_\\mathrm{C}=15.5$ K, the ordered moment should point in the basal plane with a magnitude near $1.2\\,\\mu_\\mathrm{B}$ per Ce$^{3+}$, not along $c$.","The CEF scheme with $\\Delta_1=112$ K and $\\Delta_2=122$ K predicts specific CEF excitations and a Schottky anomaly, both of which the paper reports observing.","Because both $\\lambda_\\parallel$ and $\\lambda_\\perp$ are positive, no hard-axis ordering is expected, distinguishing CeCuSi from Kondo-lattice ferromagnets that order along the CEF hard axis.","The exponential low-temperature resistivity and heat capacity are signatures of a gapped ferromagnetic magnon branch with gap $\\Delta\\approx 24$--25 K, implying strong magnetic anisotropy.","The previous inelastic neutron scattering CEF parameters from polycrystalline CeCuSi agree with the single-crystal fit, so the CEF scheme is not an artifact of this particular sample batch."],"supporting_citations":[{"why":"Supplies the earlier polycrystalline result of collinear ferromagnetic ordering in an easy plane with a 1.25 $\\mu_\\mathrm{B}$ moment, which the single-crystal data reproduce.","marker":"[14]"},{"why":"Provides the previous inelastic neutron scattering CEF parameters and level scheme for CeCuSi that the new single-crystal CEF fit is compared with and found to agree.","marker":"[16]"},{"why":"Documents the puzzling hard-axis ordering in Kondo-lattice ferromagnets, the key contrast that motivates the paper's explanation for the absence of such ordering in CeCuSi.","marker":"[19]"},{"why":"Supplies the trigonal CEF susceptibility expressions and the mixing-angle parameterization used to fit the anisotropic magnetic susceptibility.","marker":"[26]"},{"why":"Provides the ferromagnetic spin-wave gap expression used to fit the low-temperature heat capacity below $T_\\mathrm{C}$.","marker":"[34]"},{"why":"Provides the electron-magnon scattering expression used to fit the low-temperature resistivity and extract the magnon gap.","marker":"[41]"},{"why":"Gives the molecular-field plus residual susceptibility form used in Eq. (A6) for the inverse magnetic susceptibility.","marker":"[48]"},{"why":"Supplies the comparison example of CeAgSb$_2$, whose magnon gap and transport behavior support the strong-anisotropy interpretation of the CeCuSi gap.","marker":"[36]"}],"fun_headline_variants":["CeCuSi: easy-plane ferromagnet, exchange positive along both axes","CeCuSi orders in plane: ferromagnetic exchange along c and in-plane","CeCuSi: basal-plane moment, ferromagnetic exchange along c and ab","CeCuSi avoids hard-axis order via positive exchange; moment in plane"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"Everything rests on assuming that the exchange can be represented by temperature-independent molecular-field constants $\\lambda_\\parallel$ and $\\lambda_\\perp$ plus small residual susceptibility offsets, and that the fitted negative in-plane offset $\\chi_{\\perp 0} = -8.21\\times10^{-5}$ emu/mol is an unphysical mounting artifact.","fun_headline_variants_meta":{"raw":{"variants":["CeCuSi: easy-plane ferromagnet, exchange positive along both axes","CeCuSi orders in plane: ferromagnetic exchange along c and in-plane","CeCuSi: basal-plane moment, ferromagnetic exchange along c and ab","CeCuSi avoids hard-axis order via positive exchange; moment in plane"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000876,"raw_usage":{"total_tokens":3847,"prompt_tokens":1060,"completion_tokens":2787,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":676,"completion_tokens_details":{"reasoning_tokens":2705}},"tokens_in":676,"tokens_out":2787,"duration_ms":22693,"temperature":1.0,"reasoning_tokens":2705,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T17:58:05.371694+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A low-temperature neutron diffraction and inelastic neutron scattering study on CeCuSi single crystals could settle the claim directly: if the ordered moment is found to have a dominant $c$-axis component, or if the measured CEF excitations require a level scheme whose simultaneous susceptibility fit yields a negative $\\lambda$ in either direction, the paper's explanation of easy-plane order would fail.","supporting_citations":[{"cited_title":"Gignoux, D","cited_arxiv_id":null,"evidence_quote":"Supplies the earlier polycrystalline result of collinear ferromagnetic ordering in an easy plane with a 1.25 $\\mu_\\mathrm{B}$ moment, which the single-crystal data reproduce."},{"cited_title":"Sondezi-Mhlungu, D","cited_arxiv_id":null,"evidence_quote":"Provides the previous inelastic neutron scattering CEF parameters and level scheme for CeCuSi that the new single-crystal CEF fit is compared with and found to agree."},{"cited_title":"Hafner, B","cited_arxiv_id":null,"evidence_quote":"Documents the puzzling hard-axis ordering in Kondo-lattice ferromagnets, the key contrast that motivates the paper's explanation for the absence of such ordering in CeCuSi."},{"cited_title":"Banda, B","cited_arxiv_id":null,"evidence_quote":"Supplies the trigonal CEF susceptibility expressions and the mixing-angle parameterization used to fit the anisotropic magnetic susceptibility."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the ferromagnetic spin-wave gap expression used to fit the low-temperature heat capacity below $T_\\mathrm{C}$."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the electron-magnon scattering expression used to fit the low-temperature resistivity and extract the magnon gap."},{"cited_title":"Kabeya, S","cited_arxiv_id":null,"evidence_quote":"Gives the molecular-field plus residual susceptibility form used in Eq. (A6) for the inverse magnetic susceptibility."},{"cited_title":"Jobiliong, J","cited_arxiv_id":null,"evidence_quote":"Supplies the comparison example of CeAgSb$_2$, whose magnon gap and transport behavior support the strong-anisotropy interpretation of the CeCuSi gap."}],"review_version":1}