{"id":"2c513c36-296b-45af-9fad-3ed452888f10","arxiv_id":"2412.10148","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"NMR linewidth analysis in H||[110] reveals a c-axis-oriented internal field at the As(2) site, proposing a q=0 A-type antiferromagnetic order with moments parallel to the c-axis in CeRh2As2.","lead":"75As-NMR measurements on the heavy-fermion superconductor CeRh2As2 with the field along [110] show that the internal magnetic field in the antiferromagnetic state points along the c axis. This indicates a q=0 A-type antiferromagnetic order with c-axis moments, an important clue for understanding the material's unusual superconducting multiphase.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The q=0 A-type proposal is not uniquely established because it relies on the Ref.","rationale":"Read in good faith, the manuscript is an honest experimental report: the NMR data are analyzed carefully, the spin-singlet conclusion is supported by the behavior of K at the As(1) site, and the authors explicitly flag the early-stage sample, the muSR discrepancy, and the need for further experiments (Secs. IV and V). The proposed q=0 A-type structure is plausible, but it is not directly measured. It is reached by two inference steps. The first step, that the internal field at As(2) is c-axis oriented, is reasonably supported by the strong anisotropy of the As(2) linewidth and by the absence of a comparable site-dependent excess in H||[110], although no explicit control for vortex-lattice or quadrupolar/mosaic broadening is provided. The second step, selecting the q=0 A-type structure over the helical q=(pi,pi,pi) candidate, is the weakest link: it depends entirely on the prior classification in Ref. [20] of As(1)-cancelling structures and on that classification being exhaustive. The paper does not reproduce or independently verify that symmetry analysis. The muSR result pointing to a different magnetic structure, together with the use of an early-stage sample, makes either a classification-specific gap or a sample-dependent difference a real possibility. This is a concrete correctness risk for the headline claim, not a disagreement with consensus or an ad hominem concern. The reader's CONDITIONAL verdict already captures this uncertainty; the present concern reinforces that condition without moving the verdict, so UNCHANGED is recommended.","tokens_in":10665,"tokens_out":13138,"duration_ms":147901,"concrete_test":"Enumerate all magnetic structures compatible with P4/nmm CeRh2As2 (space group 129) that give zero internal field at As(1) and a nonzero field along c at As(2), using a magnetic representation/symmetry search such as ISODISTORT or the same method as Ref. [20]. If more than the q=0 A-type structure satisfies both constraints, repeat the NMR linewidth analysis on a high-quality crystal (Refs. [15, 27]) at H||[110], H||[100], and one intermediate angle, to separate an intrinsic c-axis internal field from sample-dependent or vortex-lattice contributions.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is the q=0 A-type antiferromagnet with moments along c. The new NMR data directly establish only that, below TSC, the As(2) linewidth excess in H||c is larger than in H||[110], which the authors interpret as a c-axis internal field. That interpretation already assumes the entire As(2)-minus-As(1) linewidth excess in H||c is a static staggered field rather than an orientation-dependent vortex, diamagnetic, or mosaic contribution (Sec. IV, Figs. 3(b) and 3(c)). More load-bearing is the step from 'c-axis internal field at As(2)' to 'q=0 A-type'. That step uses the As(1)-cancellation classification from Ref. [20], which is cited but not re-derived, and the paper does not show that the classification is exhaustive under the present constraints. The paper itself notes that muSR on higher-quality samples reports a weakly anisotropic structure with comparable in-plane and c-axis components (Sec. V, Ref. [26]), and that the present crystal is an early-stage sample. If the Ref. [20] enumeration missed a c-axis-moment structure that also cancels at As(1), the proposed q=0 structure would not be uniquely selected by the NMR data; if the early-stage sample differs from the intrinsic material, the claim is sample-specific. These limitations are honestly stated, but they make the headline conclusion conditional rather than established.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript reports 75As-NMR measurements on CeRh2As2 with the magnetic field applied along [110] inside the superconducting phase. By comparing the NMR linewidth at the two As sites with earlier H||c data, the authors find that the excess field distribution below TSC at the As(2) site is much smaller for H||[110] than for H||c, and they interpret this as an internal magnetic field oriented along the c axis with magnitude about 16 mT. Combining this with the As(1)-site cancellation classification of Ref. [20], they propose a q=0 A-type antiferromagnetic structure with moments parallel to c. The paper also uses the Knight-shift decrease to argue for spin-singlet pairing, while noting that a substantial part of the As(2) shift change below TSC is caused by a frequency shift from the internal-field tilt. The authors explicitly acknowledge that recent muSR results on higher-quality samples suggest a different, weakly anisotropic structure, and that the present sample is an early-stage crystal.","tokens_in":10905,"tokens_out":3483,"duration_ms":35777,"significance":"If the proposed magnetic structure is correct, this would be a rare example of an odd-parity magnetic multipole (magnetic monopole) state coexisting with superconductivity, with direct relevance to the field-induced SC multiphase of CeRh2As2. The experimental strategy of comparing linewidths at the same nuclei in two field orientations is sound, and the paper is commendably honest in stating the sample limitations and the conflict with muSR. However, the central structural conclusion is conditional on the attribution of all excess linewidth to a static staggered field, on the exhaustiveness of a classification taken from Ref. [20], and on the representativeness of the early-stage sample; the spin-singlet evidence is also weakened by the internal-field correction to the As(2) Knight shift.","major_comments":[{"comment":"The inference that the internal field at the As(2) site is oriented along the c axis assumes that the entire excess linewidth below TSC is caused by the static staggered internal field. Orientation-dependent contributions from vortex-lattice disorder, SC diamagnetic shielding, or mosaic spread could also differ between H||[110] and H||c, but no quantitative estimate of these effects is provided. Please estimate these contributions or give an additional test (for example, the field dependence of the excess linewidth at fixed temperature) that separates the static staggered-field broadening from other sources.","section":"IV, Figs. 3(b) and 3(c)"},{"comment":"The step from 'c-axis internal field at As(2)' to 'q=0 A-type AFM with moments parallel to c' relies entirely on the two-structure classification of Ref. [20] and on the cancellation of the internal field at the As(1) site. This classification is cited but not re-derived, and the paper does not demonstrate that no other c-axis-moment structure could also cancel at As(1). If uniqueness is claimed, please include the symmetry enumeration or group-theoretical argument; alternatively, explicitly state that the q=0 A-type structure is the most plausible candidate rather than the uniquely determined one.","section":"IV, Ref. [20]"},{"comment":"The spin-singlet claim is weakened by the later analysis in the same section. The observed As(2) Knight-shift reduction of about 0.4% is shown to be largely accounted for by an 11.5 kHz frequency shift arising from the 16 mT c-axis internal field, corresponding to about 0.43% in shift. After this correction, the extracted spin susceptibility reduction at the As(2) site may be comparable to the error bar. Please present the corrected δK_As2 with its uncertainty and state clearly whether spin-singlet pairing is still established without relying on the As(2) shift.","section":"IV, Eq. (3) and following"},{"comment":"The paper acknowledges that muSR on higher-quality crystals detects static magnetic order with comparable in-plane and c-axis components, and that the present NMR sample is an early-stage crystal. This is an honest statement, but it makes the headline structure conditional on sample quality. To strengthen the paper, please discuss which of the NMR constraints would change if the muSR structure were realized, or propose a discriminating measurement (for example, NMR on the higher-quality samples) that could resolve the discrepancy.","section":"V, Ref. [26]"}],"minor_comments":[{"comment":"There is a typo in the title: 'sta te' should be 'state'.","section":"Title and abstract"},{"comment":"'Temeperature' in the caption for Fig. 2(e) should be 'Temperature'.","section":"Fig. 2 caption"},{"comment":"The formula for Kdia contains an unusual typographical combination 'βλ d√ eξ'; please clarify the expression, e.g., by inserting appropriate parentheses in the logarithm.","section":"Eq. (2)"},{"comment":"The text uses '3He-4He' with hyphens; please use the standard en-dash notation '3He–4He'.","section":"Sec. II"},{"comment":"Reference [34] is listed as 'Phys. Rev. Lett. (unpublished)'; please update it with the arXiv number or provide the publication status.","section":"Ref. [34]"}],"recommendation":"major_revision","confidential_remarks":"The paper is a careful NMR study, but the headline structural conclusion depends on several assumptions that are acknowledged but not fully resolved. The authors' willingness to state the muSR conflict and the early-stage sample is a strength, yet it also means the conclusion is currently conditional. I would encourage the editor to consider this as a major-revision case rather than reject, because the linewidth comparison is a genuine and useful result, and the missing pieces (quantification of non-staggered broadening, an explicit enumeration of allowed structures, and corrected Knight-shift values) appear addressable within the manuscript's scope."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper adds a genuinely new data point to the CeRh2As2 puzzle—the first 75As-NMR in H || [110]—and it uses a sensible linewidth comparison to argue that the internal field at the As(2) site points along c. That is a real step forward, and the spin-singlet interpretation, while not airtight, is consistent with earlier work from the same group. But the headline structure (q=0 A-type, moments along c) is conditional: it leans on the enumeration of allowed structures from their earlier NQR paper (Ref. [20]), which is cited but not re-derived here, and it sits uneasily with the recent muSR result (Ref. [26]). None of that makes the paper wrong; it makes the structural conclusion provisional.\n\nWhat's good: the new in-plane field data are reported cleanly. The site-dependent broadening is a nice piece of evidence: As(2) broadens much more in H || c than in H || [110], while As(1) is similar in both orientations, which would be hard to explain if the extra broadening came from vortex-lattice disorder or sample mosaicity rather than a site-specific internal field. The estimate of the ordered moment (~0.1 μB) is consistent with the absence of static magnetic scattering in neutron work. The authors also flag the internal-field correction to the As(2) Knight shift honestly—it complicates the spin-singlet claim, but they don't hide it.\n\nSoft spots in proportion. The step from 'c-axis internal field at As(2)' to 'q=0 A-type' is a two-part argument. The first part, orientation, is well supported. The second part relies on the two-structure classification from Ref. [20] being exhaustive; that classification is not re-examined here, and a paper that takes it as given cannot fully exclude a different structure that also cancels at As(1) but has a c-axis moment. The muSR discrepancy is handled responsibly—different samples and conditions—but it means the proposed structure is not the last word. And the sample is an early-stage crystal, which the authors acknowledge; a cleaner sample might change the linewidth picture.\n\nBottom line: this is a careful experimental paper that deserves refereeing. The new data are valuable even if the magnetic structure is not uniquely pinned down. A referee should ask the authors to justify the exhaustiveness of the structure enumeration more explicitly, and to discuss what could distinguish their structure from a canted or multi-component one. I would accept the paper as a solid contribution with the structural conclusion clearly marked as provisional. It is for people working on CeRh2As2, heavy-fermion superconductors, multipole order, and NMR studies of superconductivity coexisting with magnetism.","headline":"Careful NMR study that narrows the CeRh2As2 magnetic structure to a c-axis internal field at As(2), but the q=0 A-type conclusion is provisional rather than nailed down.","tokens_in":11474,"tokens_out":3746,"would_cite":true,"duration_ms":35649,"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":"NMR measurements place the antiferromagnetic order in superconducting CeRh2As2 at a q=0 A-type structure with moments along the c axis, and confirm spin-singlet pairing.","keywords":["CeRh2As2","heavy-fermion superconductor","antiferromagnetic order","NMR linewidth","Knight shift","spin-singlet superconductivity","odd-parity multipole","magnetic structure"],"falsifier":"A direct measurement of the ordered moment direction—for example, neutron diffraction or muon spin rotation on the same crystals—that finds a dominant in-plane component, or an NMR measurement at an intermediate field angle that does not show the linewidth anisotropy predicted for a c-axis internal field, would refute the proposed q=0 A-type structure.","tokens_in":1673,"feed_emoji":"🧲","tokens_out":2817,"duration_ms":58880,"temperature":0.7,"pith_summary":"This paper tries to identify the magnetic structure of the antiferromagnetic state that coexists with superconductivity in CeRh2As2, a heavy-fermion superconductor with a field-induced superconducting multiphase. By comparing 75As-NMR linewidths between magnetic fields applied along the c axis and along [110], the authors find that the internal magnetic field at the As(2) site points along the c axis. Combined with the earlier observation that the internal field cancels at the As(1) site, this selects a q=0 A-type antiferromagnet with moments parallel to c. The same data show a reduction of the spin susceptibility in all directions, indicating spin-singlet pairing in the low-field superconducting phase. If correct, this settles a long-open question and connects the magnetism to odd-parity multipolar order.","feed_headline":"NMR pins CeRh2As2's hidden magnetism to c-axis moments","feed_subtitle":"Linewidth comparison in two field orientations selects a q=0 A-type structure and confirms spin-singlet pairing.","key_machinery":"The argument rests on comparing NMR linewidth broadening in two field geometries: $H \\parallel c$ and $H \\parallel [110]$. Since broadening from a staggered internal field is largest when the internal field is parallel to the applied field, the observation that the As(2) site's field distribution is much larger for $H \\parallel c$ than for $H \\parallel [110]$ locates the internal field along the c axis. To convert linewidth to field distribution in the $H \\parallel [110]$ geometry, the paper numerically diagonalizes the nuclear Hamiltonian including quadrupolar coupling, obtaining an effective gyromagnetic ratio for each arsenic site. The q=0 A-type antiferromagnet is the structure in which ferromagnetic planes are antiferromagnetically stacked along c, so the dipolar field cancels at As(1) but not at As(2).","core_discovery":"The paper claims that the internal magnetic field sensed by arsenic nuclei at the As(2) site in the superconducting phase of CeRh2As2 points along the tetragonal c axis. This orientation, together with the previously observed cancellation of the field at the As(1) site, selects the q=0 A-type antiferromagnetic structure with ordered moments parallel to c. From the magnitude of the field distribution, the ordered moment is estimated to be on the order of 0.1 $\\mu_B$. The paper also reports a decrease of the spin susceptibility in all measured field directions below the superconducting transition, demonstrating that the low-field superconducting state is spin-singlet.","pith_inferences":["If the q=0 A-type structure is correct, the antiferromagnetic order breaks global inversion symmetry, and CeRh2As2 becomes a testbed for cross-correlated responses such as magnetoelectric effects in a superconductor.","The comparison with zero-field NQR data suggests that the ordered moment is suppressed by a c-axis magnetic field; a systematic field-dependence study could map how the moment weakens as the system approaches the high-field superconducting phase.","The discrepancy with recent μSR results, which find comparable in-plane and c-axis components, might be resolved by measuring the same high-quality crystals with both techniques, since sample quality and field conditions differ between the two experiments.","Extending the Knight-shift measurements to other in-plane field orientations could sharpen the spin-singlet conclusion and test for a possible nodal or anisotropic gap."],"forward_implications":["The antiferromagnetic order in the low-field superconducting phase has c-axis-oriented moments, resolving the magnetic structure as q=0 A-type.","The spin susceptibility decreases in every measured field direction below the superconducting transition, confirming spin-singlet pairing in the low-field superconducting state.","The ordered moment is small (about 0.1 $\\mu_B$), consistent with the absence of static magnetic scattering in neutron diffraction experiments.","The excess Knight-shift reduction at the As(2) site in $H \\parallel [110]$ is quantitatively explained by the 16 mT internal field tilting the effective field, rather than by a change in spin susceptibility.","The proposed structure corresponds to magnetic monopole order, making CeRh2As2 a rare platform for studying superconductivity coexisting with odd-parity multipoles."],"supporting_citations":[{"why":"Establishes the superconducting multiphase and provides the basic thermodynamic parameters (Hc, Hc2, etc.) used in the Pauli-limit estimate.","marker":"[8]"},{"why":"NQR observation of antiferromagnetic order and identification of the two candidate magnetic structures that cancel at the As(1) site.","marker":"[20]"},{"why":"Earlier NMR study in H||c that supplies the field-distribution data this paper compares against to determine the internal field direction.","marker":"[21]"},{"why":"Provides hyperfine coupling constants and characterizes the two-dimensional XY-type magnetic fluctuations of CeRh2As2.","marker":"[28]"},{"why":"Determines the hyperfine coupling constants of the As sites used to estimate the ordered moment from the 16 mT internal field.","marker":"[29]"},{"why":"Reports the absence of static magnetic scattering in neutron diffraction, used to argue that the ordered moment is small.","marker":"[34]"},{"why":"Recent μSR results that find a weakly anisotropic magnetic structure with an in-plane component, discussed as a contrasting observation.","marker":"[26]"}],"fun_headline_variants":["NMR finds c-axis moments in CeRh2As2's hidden AFM state","CeRh2As2's AFM order pinned to c-axis moments by NMR","NMR reveals c-axis moments in CeRh2As2's odd-parity AFM state","NMR identifies q=0 A-type AFM with c-axis moments in CeRh2As2","NMR shows spin-singlet pairing and c-axis moments in CeRh2As2"],"cache_read_input_tokens":13568,"weakest_assumption_plain":"The conclusion hinges on the assumption that the NMR linewidth increase below the superconducting transition is caused entirely by the staggered internal field, with no comparable contribution from vortex disorder or sample inhomogeneity, and that the two candidate structures from the earlier NQR work are the only possibilities.","fun_headline_variants_meta":{"raw":{"variants":["NMR finds c-axis moments in CeRh2As2's hidden AFM state","CeRh2As2's AFM order pinned to c-axis moments by NMR","NMR reveals c-axis moments in CeRh2As2's odd-parity AFM state","NMR identifies q=0 A-type AFM with c-axis moments in CeRh2As2","NMR shows spin-singlet pairing and c-axis moments in CeRh2As2"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001176,"raw_usage":{"total_tokens":4838,"prompt_tokens":903,"completion_tokens":3935,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":519,"completion_tokens_details":{"reasoning_tokens":3819}},"tokens_in":519,"tokens_out":3935,"duration_ms":27766,"temperature":1.0,"reasoning_tokens":3819,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T16:16:39.170901+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A direct measurement of the ordered moment direction—for example, neutron diffraction or muon spin rotation on the same crystals—that finds a dominant in-plane component, or an NMR measurement at an intermediate field angle that does not show the linewidth anisotropy predicted for a c-axis internal field, would refute the proposed q=0 A-type structure.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Establishes the superconducting multiphase and provides the basic thermodynamic parameters (Hc, Hc2, etc.) used in the Pauli-limit estimate."},{"cited_title":"Such a small ordered moment is consis- tent with the absence of the static magnetic scattering in elastic neutron diffraction measurements [34]","cited_arxiv_id":null,"evidence_quote":"NQR observation of antiferromagnetic order and identification of the two candidate magnetic structures that cancel at the As(1) site."},{"cited_title":"Schmidt and P","cited_arxiv_id":null,"evidence_quote":"Earlier NMR study in H||c that supplies the field-distribution data this paper compares against to determine the internal field direction."},{"cited_title":"Chajewski, D","cited_arxiv_id":null,"evidence_quote":"Determines the hyperfine coupling constants of the As sites used to estimate the ordered moment from the 16 mT internal field."},{"cited_title":"Momma and F","cited_arxiv_id":null,"evidence_quote":"Reports the absence of static magnetic scattering in neutron diffraction, used to argue that the ordered moment is small."},{"cited_title":"Szabo and A","cited_arxiv_id":null,"evidence_quote":"Recent μSR results that find a weakly anisotropic magnetic structure with an in-plane component, discussed as a contrasting observation."}],"review_version":1}