{"id":"52015371-edc8-48a6-98b5-3eb92df54a10","arxiv_id":"2608.05709","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"EuRhGe3 is reported as the first helimagnet exhibiting the full field-driven sequence from a circular helix to an elliptic conical (xyz-fan) state and finally a planar xy-fan.","lead":"Resonant X-ray diffraction experiments clarify the zero-field helical order and field-induced phase sequence of the noncentrosymmetric tetragonal magnet EuRhGe3. The authors report the first observation of a complete sequence from a circular helix, through a locked-in soliton lattice, to a spin-flop xyz-fan (elliptic conical) state and a planar xy-fan state.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The xyz-fan identification for phase IV rests on a 4%-contamination subtraction in §3.5; if m_c vanishes, the claimed first full sequence collapses.","rationale":"I agree with the reader's weakest assumption: the load-bearing point is the phase IV assignment. The rest of the paper (helicity, lock-in, 2q) is well supported by the data. My concern is not that the authors are wrong, but that the evidence for m_c is too slender to carry the “first full sequence” claim. They are honest about this in the text, but the abstract asserts it more strongly than the body. I therefore keep the verdict at CONDITIONAL, same as the reader. The proposed tests are feasible with the existing setup and would either confirm or remove the m_c requirement.","tokens_in":19525,"tokens_out":2548,"duration_ms":26524,"concrete_test":"Re-measure the (−2,0,8−q) and (2,0,8−q) integrated intensities at 6 T as a function of temperature with enough counting time to make Poisson errors <5%, fit both with a single model containing m_b(T) and m_c(T), and test whether m_c is statistically significant (≥5σ). Then repeat the (−2,0,8−q) measurement at a different azimuth (or with a different analyzer channel) so the m_b contamination changes; a genuine m_c signal must be azimuth-independent.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The advertised full sequence—helix → soliton lattice → lock-in → xyz-fan → planar xy-fan—depends entirely on phase IV being an elliptic conical (xyz) state. The evidence for m_c is the temperature dependence of the (−2,0,8−q) reflection at 6 T (Fig. 7b): the mb-only model predicts a steep drop on entering phase IV, whereas the data stay flat. But that reflection is said to contain only 96% m_c and 4% m_b, meaning the “excess” is the difference between two small intensities, each subject to counting statistics, sample absorption, and the assumed 4% leakage. The model also assumes the mb(T) extracted from (2,0,8−q) is perfectly transferable to the (−2,0,8−q) geometry. The authors themselves write in §3.5 that the analysis “does not constitute a rigorous proof of the existence of mc.” No error bars are shown on the critical Fig. 7(b) points, no correction for multiple scattering or Debye–Waller anisotropy is discussed, and no independent check (e.g., a reflection with a different m_b/m_c ratio) is presented. If the flat intensity arises from a weak parasitic scattering, a small q shift changing the resolution correction, or a slight change in domain populations, the m_c component disappears and phase IV is just a planar fan; then the claimed first observation of the full sequence is not established.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript reports resonant X-ray diffraction measurements of EuRhGe3 in magnetic fields applied along the a axis. The authors identify the zero-field state as an equal-amplitude incommensurate ab-plane helix with q=(0,0,0.809), document the growth of a 2q component with field and a lock-in transition to q=0.8 at about 3.8 T, and propose that the high-field phases I and IV are planar xy-fan and xyz-fan (elliptic conical) structures, respectively. The paper argues that EuRhGe3 realizes the full theoretically predicted sequence helix → soliton lattice → lock-in → xyz-fan → planar xy-fan.","tokens_in":19794,"tokens_out":5611,"duration_ms":58079,"significance":"If the full sequence is confirmed, EuRhGe3 would be a rare clean experimental realization of the predicted helix-to-fan evolution including an intermediate elliptic conical phase, valuable for helimagnet theory. The zero-field helix and the field-induced 2q and lock-in behaviour are directly supported by the diffraction data, including the helicity dependence and the resonance at the Eu L2 edge. The main weakness is that the xyz-fan assignment rests on an indirect subtraction analysis that the authors themselves state is not rigorous.","major_comments":[{"comment":"The central claim of an xyz-fan phase in phase IV rests on the inference of mc from the temperature dependence of the (-2,0,8-q) reflection at 6 T. The mb-only prediction (dashed line in Fig. 7(b)) is obtained by transferring mb(T) extracted from (2,0,8-q) to a different scattering geometry, and the mc signal is the difference between a measured intensity and a prediction that contains a 4% mb contamination; no error bars are shown on the data points. The authors explicitly write in §3.5 that the analysis does not constitute a rigorous proof of the existence of mc. This is a load-bearing limitation, because if mc=0, phase IV is a planar fan and the claimed first observation of the full sequence collapses. I ask the authors to either (i) provide a direct measurement of mc, e.g., using a reflection whose intensity is dominated by mc with negligible mb admixture, or a full polarization and azimuthal analysis that separates mb and mc, and to quantify systematic uncertainties such as multiple scattering, Debye-Waller anisotropy, and domain populations; or (ii) revise the abstract and discussion to present the xyz-fan assignment as tentative and not claim that the full sequence is experimentally established.","section":"3.5, Fig. 7"},{"comment":"The abstract states that a spin-flop xyz-fan state is realized and that EuRhGe3 provides a prototypical example exhibiting the full sequence, which has been theoretically predicted. However, §3.5 says the mc analysis is not rigorous and §4.2 says phase IV is most likely an elliptic-conical state. This inconsistency is problematic because the reader receives a definitive claim in the abstract that is stronger than the body's own assessment. The wording should be aligned, e.g., by saying the data are consistent with an xyz-fan but that a planar fan in phase IV cannot be excluded.","section":"Abstract and Sec. 4.2"},{"comment":"The fan structure model in Eq. (5) introduces parameters mc and α that are not constrained by the data except by the upper limit on the 2q intensity; the statement that the actual structure may be described as this form is therefore not a tested model. I recommend either performing a full refinement of the fan structure using all available reflections or clearly labeling the illustrations in Fig. 8 as schematic. This does not affect the phase II and III results but bears on the interpretation of phases I and IV.","section":"Sec. 4.2, Eq. (5)"}],"minor_comments":[{"comment":"The turn angle is given as 145.8° in the abstract and 145.6° in Sec. 4.1; please reconcile the two values.","section":"Abstract and Sec. 4.1"},{"comment":"In the last paragraph, 'an spin flop xyz-fan phase' should read 'a spin-flop xyz-fan phase'.","section":"Summary"},{"comment":"The sentence 'The vanishing of ma indicates that only the component perpendicular to the applied field survives in phase IV above 5 T' is slightly misleading because ma also vanishes at the II-I boundary at 8 K; please specify that this statement refers to the 2 K measurements.","section":"Sec. 3.2"},{"comment":"The measured helicity ratio differs between two sample regions (9:1 versus 6:4), yet the zero-field structure is described as a helix with a well-defined helicity in each domain; please clarify how the helicity is defined and whether the domain population affects the quantitative polarization analysis.","section":"Sec. 3.3"},{"comment":"The coexistence of incommensurate and commensurate peaks at 3.5 T is described qualitatively; a two-peak fit with residuals would make the lock-in transition more convincing.","section":"Fig. 5(a)"}],"recommendation":"major_revision","confidential_remarks":"The stress-test concern about circularity is unfounded: the analysis is a standard refinement of Fourier components from measured intensities and does not assume the conclusion. The more serious issue is the gap between the abstract's definitive language and the body's careful 'most likely' assessment. I recommend that the editor require either a softening of the title and abstract or additional data directly establishing the c-axis component in phase IV before acceptance. The phase II and III results are solid and would support a publication focused on the helix-to-lock-in evolution."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper is an RXD study of EuRhGe3. What is actually new and solid: the zero-field ab-plane helix with q=(0,0,0.809) is directly established through energy resonance, polarization analysis, and helicity measurements. The field-induced 2q magnetic peak and the lock-in to q=0.8 at 3.8 T are also on firm ground. Those results alone make this a useful experimental contribution to the EuTGe3 family.\n\nThe soft spot is phase IV. The claim that this is an xyz-fan (elliptic conical) state with a small c-axis component rests on the temperature dependence of one weak reflection, (−2,0,8−q), shown in Fig. 7(b). The mb-only model predicts a steep drop at the phase boundary; the data stay flat. The authors infer mc from that excess, and they state plainly that this is not rigorous proof. The stress-test note is correct: that reflection is said to be 96% mc and 4% mb, so the excess is a difference between two small intensities, no error bars are given, and there is no independent check from a reflection with a different mb/mc ratio. The abstract overstates the case by asserting phase IV \"is realized\" as an xyz-fan; the body says \"most likely\" and \"consistent with.\" If mc is an artifact, the full sequence collapses to helix → soliton lattice → lock-in → planar fan, which is still a decent result but not the first realization of the predicted xyz-fan sequence.\n\nThe authors are honest about the limitation, which counts in their favor. The paper also has no public data, and several model parameters are fitted rather than constrained, but that is typical for this kind of work.\n\nThis paper deserves a serious referee. The direct diffraction results justify referee time, and a referee can ask for error bars, an additional reflection with different sensitivity, or a direct check of mc. I would read it for the helix and lock-in results, and I would cite it with the phase IV caveat clearly attached.","headline":"Careful diffraction study that solidly establishes the zero-field helix, the 2q soliton-lattice distortion, and the lock-in at q=0.8, but the advertised xyz-fan phase IV rests on an explicitly non-rigorous subtraction analysis.","tokens_in":20378,"tokens_out":2432,"would_cite":true,"duration_ms":27225,"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":"EuRhGe3 shows the full field-driven sequence of magnetic structures, from a circular helix to a planar fan, passing through a spin-flop xyz-fan phase.","keywords":["EuRhGe3","helimagnetism","resonant X-ray diffraction","magnetic phase diagram","soliton lattice","xyz-fan structure","elliptic conical structure","noncentrosymmetric magnet"],"falsifier":"Measure the (-2,0,8-q) reflection in phase IV with a full linear-polarization analysis at several fields between 5 and 8 T at 2 K: if the inferred m_c does not appear as a distinct polarization signature, or if a direct measurement in a geometry that isolates the c-axis component finds m_c = 0, the xyz-fan identification fails. A single-crystal neutron diffraction experiment in magnetic field would settle the issue directly by mapping all three moment components.","tokens_in":19321,"feed_emoji":"🧲","tokens_out":8232,"duration_ms":86769,"temperature":0.7,"pith_summary":"EuRhGe3, a noncentrosymmetric tetragonal magnet with S=7/2 Eu moments, is claimed to show the full set of field-induced magnetic structures that theory predicts for a helimagnet whose spins prefer to lie in a plane. Using resonant X-ray diffraction with polarization and helicity analysis, the paper identifies the zero-field state as an equal-amplitude ab-plane helix with q=(0,0,0.809), follows its distortion into a soliton-lattice-like structure and a lock-in at q=0.8, and then a phase in which the spins flop partly out of the plane (an xyz-fan, or elliptic conical state) before settling into a planar xy-fan. If the identification of the c-axis component in the intermediate fan is right, EuRhGe3 is the first helimagnet in which this theoretically predicted sequence has been observed in one material.","feed_headline":"X-rays map the full helix-to-fan sequence in EuRhGe3","feed_subtitle":"A spin-flop xyz-fan phase appears between a lock-in helix and the planar fan, confirming theory.","key_machinery":"The load-bearing probe is resonant X-ray diffraction at the Eu L2 edge with controlled incident polarization and a polarization analyzer. The scattering amplitude $F_{\\varepsilon\\varepsilon'} = (\\varepsilon'^*\\times\\varepsilon)\\cdot m_q$ lets the Fourier components $m_a$, $m_b$, and $m_c$ of the magnetic structure be extracted separately from the $\\pi$–$\\pi'$ and $\\pi$–$\\sigma'$ channels, while circular-polarization scans determine the helicity of the spiral. The appearance and disappearance of the $2q$ reflection tracks the soliton-lattice distortion, and the comparison of reflections with different sensitivity to $m_b$ and $m_c$ is what supports the xyz-fan assignment in phase IV.","core_discovery":"On the paper's own terms, the central discovery is that EuRhGe3 realizes, in a single field sweep at 2 K, the complete helical-to-fan evolution predicted for a planar helimagnet: a circular helix with moments rotating in the ab plane at a constant turn angle of 145.8°, a field-distorted helix of soliton-lattice type marked by a resonant second-harmonic 2q reflection, a commensurate lock-in at q=0.8, then a spin-flop xyz-fan state in which the dominant oscillation is along the b axis but a small c-axis component appears, and finally a planar xy-fan with no c-axis component. The paper argues that phase IV is distinguished from the high-temperature planar fan by an excess intensity in the (-2,0,8-q) reflection that cannot be explained by the b-axis component alone, and it claims this is the first experimental establishment of the full theoretically predicted sequence. The paper is careful to note that the xyz-fan assignment is not rigorously proven by the subtraction analysis.","pith_inferences":["If the sequence is generic, other EuTGe3 helimagnets with weaker in-plane anisotropy should show a wider xyz-fan window; the differences already seen in EuIrGe3 and EuNiGe3 offer a controlled family for testing that anisotropy dependence.","The absence of a detectable 2q peak in the fan phases suggests the fan is amplitude-modulated rather than equal-moment, which could be connected to the unresolved flat specific-heat anomaly below TN by measuring whether the moment modulation grows as the xyz-fan phase is approached.","A quantitative check of the phase-IV assignment would be to compare the (0,0,8+q) and (-2,0,8-q) intensities as functions of field inside phase IV: the model predicts the inferred m_c contribution should scale with distance from the II/III-IV boundary, not simply with the b-axis component."],"forward_implications":["The zero-field order is an equal-amplitude ab-plane helix with q=(0,0,0.809), and the constant turn angle of 145.8° follows directly from the measured Fourier components.","Field along the a axis at 2 K first distorts the helix into a soliton-lattice-like state signaled by a growing 2q reflection, then locks it into a commensurate q=0.8 helix between about 4 and 5 T.","Above 5 T the a-axis oscillation vanishes, the spins flop partly out of the ab plane, and a small c-axis component produces the xyz-fan (elliptic conical) phase IV.","At higher fields the system enters a planar xy-fan without a c-axis component, and at temperatures above roughly 5 K the intermediate xyz-fan phase is skipped entirely.","EuRhGe3 is claimed to be the first helimagnet in which the full theoretically predicted helix-to-xyz-fan-to-xy-fan sequence is experimentally realized."],"supporting_citations":[{"why":"Provides the bulk phase diagram and magnetization/resistivity data that define phases I-IV and the boundaries onto which the diffraction results are mapped.","marker":"[33]"},{"why":"Supplies the irreducible-representation analysis showing that the zero-field xy helix with q=(0,0,zeta) is symmetry-allowed in the I4mm space group.","marker":"[36]"},{"why":"Is the theoretical prediction of helical-to-fan transitions and the xyz-fan (elliptic conical) state.","marker":"[42]"},{"why":"Calculates zero-temperature phase diagrams as a function of magnetic anisotropy that include the xyz-fan intermediary.","marker":"[43]"},{"why":"Provides the theoretical framework for fan and conical states in helimagnets that the observed phase sequence is compared with.","marker":"[44]"},{"why":"Supplies both the chiral-soliton-lattice comparison for the 2q behavior and the Stokes-parameter fitting function used for the helicity scans.","marker":"[45]"}],"fun_headline_variants":["EuRhGe3 shows full helix-to-fan sequence under field","Complete magnetic morphing: helix to fan in EuRhGe3","Spin-flop xyz-fan seen between lock-in and planar fan in EuRhGe3","Helix, lock-in, xyz-fan, planar: field maps EuRhGe3"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that phase IV really has a small c-axis component: it is inferred only from the excess intensity of one reflection over what a b-only model predicts, and the paper admits this is not rigorous proof.","fun_headline_variants_meta":{"raw":{"variants":["EuRhGe3 shows full helix-to-fan sequence under field","Complete magnetic morphing: helix to fan in EuRhGe3","Spin-flop xyz-fan seen between lock-in and planar fan in EuRhGe3","Helix, lock-in, xyz-fan, planar: field maps EuRhGe3"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000822,"raw_usage":{"total_tokens":3661,"prompt_tokens":1077,"completion_tokens":2584,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":693,"completion_tokens_details":{"reasoning_tokens":2497}},"tokens_in":693,"tokens_out":2584,"duration_ms":21763,"temperature":1.0,"reasoning_tokens":2497,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-08T00:39:21.569505+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the (-2,0,8-q) reflection in phase IV with a full linear-polarization analysis at several fields between 5 and 8 T at 2 K: if the inferred m_c does not appear as a distinct polarization signature, or if a direct measurement in a geometry that isolates the c-axis component finds m_c = 0, the xyz-fan identification fails. A single-crystal neutron diffraction experiment in magnetic field would settle the issue directly by mapping all three moment components.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the bulk phase diagram and magnetization/resistivity data that define phases I-IV and the boundaries onto which the diffraction results are mapped."},{"cited_title":"Matsumura, M","cited_arxiv_id":null,"evidence_quote":"Supplies the irreducible-representation analysis showing that the zero-field xy helix with q=(0,0,zeta) is symmetry-allowed in the I4mm space group."},{"cited_title":"Nagamiya, K","cited_arxiv_id":null,"evidence_quote":"Is the theoretical prediction of helical-to-fan transitions and the xyz-fan (elliptic conical) state."},{"cited_title":"Kurauchi, T","cited_arxiv_id":null,"evidence_quote":"Calculates zero-temperature phase diagrams as a function of magnetic anisotropy that include the xyz-fan intermediary."},{"cited_title":"Utsumi, I","cited_arxiv_id":null,"evidence_quote":"Provides the theoretical framework for fan and conical states in helimagnets that the observed phase sequence is compared with."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies both the chiral-soliton-lattice comparison for the 2q behavior and the Stokes-parameter fitting function used for the helicity scans."}],"review_version":1}