{"id":"b7f2c2c2-57df-4065-ae50-c218952c7af2","arxiv_id":"2411.18540","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"In CeCo0.5Rh0.5In5, in-plane magnetic fields raise the magnetic ordering temperature, create block magnetic order, and eventually replace commensurate order with weakly incommensurate order once superconductivity is suppressed.","lead":"Neutron measurements show that magnetic fields applied within the crystal planes of the superconductor CeCo0.5Rh0.5In5 change its magnetic order, while fields along the c-axis do nothing. The results map how magnetism and superconductivity compete in this heavy-fermion material.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central incommensurate-order claim rests on 0.002–0.006 r.l.u. peak shifts that could be absorbed by asymmetric line-shape parameters or unresolved ±δq domains; the paper does not report the width or two-peak fits needed to exclude this.","rationale":"The reader's weakest assumption is exactly where the paper's novel claim hinges. The authors themselves flag the smallness of the shift and discuss mechanical artifacts in Section III.D, which is good. But the two instruments disagree in the field onset (RITA2: near Hc2; FLEXX: lower), and the paper attributes this to field inhomogeneity and temperature. That admission means the extracted L0(H) is not purely an intrinsic property; field gradients can create a distribution of propagation vectors, and the single-peak fits may be averaging over that distribution. The absence of a reported width or line-shape analysis prevents the reader from distinguishing a true single-domain incommensurate phase from an unresolved superposition of commensurate and incommensurate components or a small-angle artifact. This concern does not invalidate the block order at L=1/4, the anisotropic TN behaviour, or the linear intensity increase at low field; those are supported by separate observations. No change to the reader's CONDITIONAL verdict is needed: the claim is plausible but requires either the two-peak/width re-analysis proposed above or a dedicated high-resolution field-dependent diffraction measurement. I agree with the reader's identification of the weakest assumption.","tokens_in":20676,"tokens_out":9540,"duration_ms":94772,"concrete_test":"Re-analyze the raw RITA2 and FLEXX scans at fields above Hc2 with two models: (i) the published single asymmetric peak with L0 free and gamma/sigma fixed at their zero-field values, and (ii) a pair of resolution-limited satellites at 1.5±δq with field-independent widths and floating relative intensities, using the zero-field scan as the resolution reference. If model (ii) gives a significantly better fit (e.g., Δχ2/ndof or BIC), or if model (i) requires a field-dependent gamma/sigma to reproduce the data, the single-domain incommensurate interpretation is not established. Also report the fitted FWHM of the high-field peak at 14.5 T; if it exceeds the zero-field resolution width, unresolved splitting or field-gradient broadening is present.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The claim that the normal state above Hc2 is incommensurate along L (Section IV) depends on the small field-induced shift of the magnetic peak near L=1.5 in Figs. 5(c) and 6(c). The shifts are 0.002–0.006 r.l.u., comparable to the momentum resolution of a cold triple-axis spectrometer. The authors correctly note that a sample rotation would move the peak in A3, not A4, and that nuclear Bragg peaks are stationary, which addresses mechanical motion. What is not addressed is that a single peak center can shift systematically if the line shape changes with field. The FLEXX data are fit with an asymmetric resolution function containing a free skew parameter gamma; if gamma (or sigma) is allowed to vary with field, part of the apparent shift can be absorbed by the line shape rather than by L0. Also, for a commensurate-to-incommensurate transition, the expected response is two satellites at L=1.5±δq with domain populations. The authors argue for a single domain by analogy with CeRhIn5, but they did not test whether a two-peak model with equal or unequal intensities fits the high-field data as well as or better than a single shifted peak. Field inhomogeneity (which they invoke to explain the FLEXX/RITA2 difference) would also produce a distribution of q and hence a broadened, not simply shifted, peak; the paper does not report whether the high-field peak remains resolution limited. If the shift arises from any of these effects, the headline claim of field-induced incommensurate normal-state order loses support, though the block-order and intensity-scaling observations would remain.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reports neutron diffraction and spectroscopy on CeCo0.5Rh0.5In5, a 115 compound that coexists commensurate antiferromagnetism (Q=(1/2,1/2,1/2), TN=2.5 K) with superconductivity (Tc=1.3 K). The authors find that a magnetic field along the c-axis has no observable effect on the static magnetism, whereas a field within the a-b plane increases TN, changes the critical exponent, induces block order at L=1/4 in the vortex phase, and produces a small shift of the magnetic peak along L above Hc2=7.5 T. They interpret this last effect as field-induced incommensurate order in the normal phase that competes with commensurate magnetism in the superconducting and vortex phases. The paper also reports overdamped magnetic excitations at zero field and discusses possible instrumental artifacts, particularly sample rotation, field inhomogeneity, and domain splitting.","tokens_in":21014,"tokens_out":5568,"duration_ms":53879,"significance":"If the central claim is established, the result is significant for the 115 heavy-fermion family: it would document a field-driven competition between commensurate magnetism stabilized by superconductivity/vortices and weakly incommensurate order in the normal state, with a strong dependence on field orientation. The paper's strengths include direct diffraction measurements of Bragg intensities and peak positions on multiple instruments, an explicit discussion of potential artifacts such as sample rotation and domain formation, and a spectroscopic comparison with CeRhIn5. The main limitation is that the key incommensurate shift is very small (0.002-0.006 r.l.u.) and the current analysis does not yet exclude alternative explanations based on line-shape changes or unresolved domain splitting; this is a correctness risk rather than a circularity problem.","major_comments":[{"comment":"The field-induced incommensurate claim rests entirely on shifts of 0.002-0.006 r.l.u. along L, which are close to the momentum resolution of the cold triple-axis spectrometers, but the paper does not report the fitted peak widths or the asymmetry parameter for the representative scans. Because the FLEXX line shape contains a free skew parameter gamma, a field-dependent change in line shape can absorb part of the apparent shift without a real change in L0. The authors should report sigma(H) and gamma(H), and test whether a two-peak model with satellites at L=1.5±delta_q of unequal intensity fits the high-field data as well as or better than a single shifted peak; the single-domain analogy to CeRhIn5 is suggestive but is not a substitute for such a test on this sample.","section":"§III.D, Figs. 5(c) and 6(c)"},{"comment":"The claim that the incommensurate wavevector saturates in the normal state and shows 'little change' up to 14.5 T is based on comparing RITA2 data at T=100 mK with FLEXX data at T=300 mK, using different resolutions and different analysis functions. The authors attribute the smaller FLEXX shift to field inhomogeneity and higher temperature, but field inhomogeneity would broaden the peak as well as shift it, and the paper does not report whether the high-field peaks remain resolution-limited on either instrument. A common analysis of both datasets, including fitted widths, is needed to support the saturation statement and to rule out instrument-dependent line-shape effects.","section":"§III.D and §IV"},{"comment":"The conclusion that an a-b field induces a crossover to more anisotropic magnetism is supported partly by the decrease of the fitted critical exponent from beta=0.65±0.03 to beta=0.44±0.03, but these values come from power-law fits over 1 K < T < TN, far outside the asymptotic critical region. The authors acknowledge the range sensitivity, yet they still use the exponent change as evidence; they should report fits with the same temperature range for both field orientations, with TN treated consistently, and show the sensitivity of beta to the fitting window.","section":"§III.A, Fig. 2(b)"}],"minor_comments":[{"comment":"The comparison to the Demler-Sachdev-Zhang prediction should be de-emphasized or removed: theta is fitted to the data and comes out as 6.8±1.0 against a predicted value of about 3, and the authors themselves note a strong deviation above about 2 T. As presented, this fit does not provide quantitative support for the vortex-core scenario and mainly illustrates the field range where block order appears.","section":"§III.C, Fig. 4(a)"},{"comment":"There are several typographical errors: 'normzlized' in the Fig. 2 caption, 'CoCoIn5' instead of 'CeCoIn5' in the discussion of critical exponents, and 'Lande' should be 'Landé'. Please correct these.","section":"§III.A and figure captions"},{"comment":"The sentence describing the domain-splitting expected at (1/2,1/2,3/2) as peaks 'originating from (0,0,1)+δq and (1,1,2)−δq' is confusing; please clarify that these are magnetic satellites around the (1/2,1/2,3/2) position, and define the sign convention for δq.","section":"§III.D"},{"comment":"The onset of the L=1/4 block order is stated as about 2.5 T, but the field dependence in Fig. 3(c) is difficult to read because of the vertical scale; adding a labeled onset marker or reporting the fitted onset field and uncertainty would make the claim more transparent.","section":"§III.B, Fig. 3(c)"}],"recommendation":"major_revision","confidential_remarks":"I recommend major revision rather than rejection because the needed controls, such as two-peak fits, width reporting, and a common analysis of the RITA2 and FLEXX data, are reanalyses of data the authors already have. The central physics is potentially important, but the current manuscript does not yet establish the headline incommensurate normal-state order with sufficient rigor. The authors should also reconsider the prominence of the DSZ comparison, which is not a strong quantitative test as it stands."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"First, the block order is real and new. CeCo0.5Rh0.5In5 shows a field-induced (1/2,1/2,1/4) peak for in-plane fields above about 2.5 T, it is resolution limited, it was seen on two instruments, and it does not appear for c-axis fields. That alone is a solid result. The paper also does good experimental bookkeeping: it checks nuclear peaks for sample rotation, discusses domain splitting explicitly, and is honest that the DSZ fit fails at higher fields and that the beta values depend on the fit range.\n\nThe weak spot is the headline claim about weakly incommensurate order in the normal state. The peak shift along L is 0.002 to 0.006 r.l.u., which is close to the resolution of the triple-axis spectrometers. The FLEXX line shape includes a free skew parameter gamma, and if gamma or sigma drifts with field, part of the apparent shift can be absorbed by the line shape rather than by L0. The authors argue against ±δq domains by analogy with CeRhIn5, but they never test whether a two-peak model fits the high-field data as well as a single shifted peak. Field inhomogeneity, which they invoke to explain the RITA2/FLEXX difference, would broaden the peak rather than simply shift it, and no width analysis is reported. So the incommensurate claim is plausible but not proven. The block order and the intensity scaling do not depend on this.\n\nMinor points: the beta fits are over an extended temperature range, which the authors acknowledge, and the DSZ curve in Fig. 4(a) has a fitted theta and is admitted to deviate above 2 T. These are caveats, not fatal flaws.\n\nWho is this for? The heavy-fermion and neutron scattering communities. It is a careful experimental study of one composition that extends the known CeRhIn5 and CeCoIn5 field behavior. It deserves a serious referee. The referee should ask for two-peak fits at high field, a check of whether gamma and sigma are field-dependent, and a statement of the resolution width of the high-field peak. The block order result will stand regardless.\n\nRecommendation: send it to peer review. It is not a desk reject. My own verdict would be conditional pending the line-shape analysis.","headline":"Solid field-dependent neutron study with a genuinely new block-order phase; the high-field incommensurate claim is plausible but rests on near-resolution peak shifts that need a two-peak test.","tokens_in":21632,"tokens_out":1413,"would_cite":true,"duration_ms":14557,"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":"An in-plane magnetic field that suppresses superconductivity in CeCo$_{0.5}$Rh$_{0.5}$In$_5$ also switches the magnetic order from commensurate to weakly incommensurate.","keywords":["heavy fermion","CeCo0.5Rh0.5In5","neutron diffraction","magnetic field","commensurate antiferromagnetism","incommensurate magnetic order","superconductivity","vortex state"],"falsifier":"A higher-resolution or polarized neutron diffraction measurement on the same compound above $H_{c2}$ with the field in the $a$-$b$ plane would settle the claim: if the Bragg peak splits into two peaks around $L=1/2$, or remains at $L=1/2$ within resolution, then the reported normal-state incommensurate order is not established.","tokens_in":20484,"feed_emoji":"🧲","tokens_out":7543,"duration_ms":65179,"temperature":0.7,"pith_summary":"The paper uses neutron diffraction to ask what magnetic order is left behind when superconductivity is switched off by a magnetic field in the heavy-fermion compound CeCo$_{0.5}$Rh$_{0.5}$In$_5$, which at zero field hosts both superconductivity ($T_c=1.3$ K) and commensurate antiferromagnetism ($T_N=2.5$ K). It finds that the answer depends sharply on field direction. Fields along the $c$-axis leave the static magnetism untouched, while fields within the $a$-$b$ plane first strengthen the commensurate order, then induce a block $\\uparrow\\uparrow\\downarrow\\downarrow$ phase at intermediate fields, and finally, once the field exceeds the upper critical field $H_{c2}=7.5$ T, replace the commensurate peak with weakly incommensurate order along the $c$-axis. The paper takes this as evidence that superconductivity actively stabilizes commensurate magnetism, and that a long-wavelength incommensurate magnetic phase competes with it in the normal state. A sympathetic reader would care because it maps the magnetic competitor that superconductivity must suppress, using fields modest enough for neutron experiments.","feed_headline":"Magnetic field flips a superconductor's magnetism to incommensurate","feed_subtitle":"Neutron data show the shift only for in-plane fields, tying superconductivity to commensurate order.","key_machinery":"The experimental engine is field-controlled neutron triple-axis diffraction on single crystals, measuring the intensity, width, and position of magnetic Bragg peaks of the form $(1/2,1/2,L)$ as functions of temperature and applied field. The magnetic propagation vector is the central object: commensurate $L=1/2$ order (doubled unit cell), block $L=1/4$ order (fourfold periodicity along $c$), and a weakly incommensurate shift $\\delta L\\approx 0.002$--$0.006$ r.l.u. above $H_{c2}$. Field orientation matters because vertical and horizontal magnet geometries let the authors apply the field either along $c$ or within the $a$-$b$ plane, and the contrast between those geometries is what isolates the anisotropic competition.","core_discovery":"The central claim, stated in Section IV, is that incommensurate magnetic order at high magnetic fields in the normal phase competes with commensurate magnetism in the superconducting and vortex phases of CeCo$_{0.5}$Rh$_{0.5}$In$_5$, and that this competition is only switched on by fields applied within the $a$-$b$ plane. In zero field the magnetic Bragg peaks are resolution-limited at $\\vec{Q}=(1/2,1/2,1/2)$, corresponding to a doubling of the unit cell with $\\uparrow\\downarrow\\uparrow\\downarrow$ spin order. As an $a$-$b$ field is applied, the $(1/2,1/2,3/2)$ intensity grows linearly at low fields in the vortex state, then at fields around 2.5 T a second commensurate peak at $(1/2,1/2,5/4)$ appears, interpreted as $\\uparrow\\uparrow\\downarrow\\downarrow$ block order. Above $H_{c2}=7.5$ T, the main peak shifts along $L$ by a small amount, from $L=1/2$ to a weakly incommensurate position, and this shift saturates and persists to 14.5 T. The same measurements with the field along $c$ show none of these effects, which the authors tie to the strong in-plane magnetic anisotropy of the Ce$^{3+}$ crystal-field environment.","pith_inferences":["A testable extension follows from the claim that superconductivity stabilizes commensurate order: suppressing superconductivity by tuning Rh/Co substitution closer to the magnetic/superconducting boundary, or by pressure, should restore or strengthen the incommensurate wavevector in a way that mirrors the field effect.","The reported shift is only 0.002--0.006 r.l.u., near the resolution of triple-axis spectrometers, so a single-domain or polarized diffraction measurement on the same compound above $H_{c2}$ would decide whether the normal state is truly a single-$q$ incommensurate helix or a finely split multi-domain state.","The normal-state incommensurate order along $L$ is distinct from the in-plane Q-phase of CeCoIn$_5$, suggesting at least two different field-induced magnetic instabilities in the 115 family; mapping their field and temperature boundaries could reveal a general competition between superconductivity and incommensurate magnetism."],"forward_implications":["If the claim is right, superconductivity is not merely coexisting with commensurate magnetism in this compound; it is actively favoring the commensurate wavevector over the incommensurate one that appears in the normal state.","The linear growth of the magnetic Bragg intensity in the vortex state provides a direct, if approximate, measure of the coupling between the superconducting and magnetic order parameters near the magnetic/superconducting boundary.","The appearance of block $\\uparrow\\uparrow\\downarrow\\downarrow$ order around 2.5 T means the field-temperature phase diagram contains at least three magnetic regimes, not a single order parameter smoothly suppressed by the field.","Because the incommensurate shift is along $L$ and only appears for $a$-$b$ fields, the normal-state magnetic instability is tied to the two-dimensional in-plane magnetic anisotropy rather than to an isotropic response."],"supporting_citations":[{"why":"Supplies the CeCo$_x$Rh$_{1-x}$In$_5$ phase diagram that places the x=0.5 sample at the coexistence of superconductivity and antiferromagnetism.","marker":"Ref. 33"},{"why":"Documents the competition between unconventional superconductivity and incommensurate antiferromagnetic order across the same series, providing the interpretive frame for the competing orders observed here.","marker":"Ref. 34"},{"why":"Reports the coexistence of incommensurate and commensurate magnetic order near x=0.4, the concentration boundary that motivates looking for both types of order in the x=0.5 sample.","marker":"Ref. 43"},{"why":"Discovered the low-field sinusoidal magnetic order with propagation vector $(1/2,1/2,3/4)$ in CeRhIn$_5$, which directly motivated the search for block $L=1/4$ order in the present compound.","marker":"Ref. 52"},{"why":"Provides the analogous observation of field-enhanced long-range magnetic order in superconducting La$_2$CuO$_{4+y}$, the model used for the vortex-state intensity increase.","marker":"Ref. 58"},{"why":"Gives the theoretical $H/H_{c2}\\ln(\\theta H_{c2}/H)$ scaling for proximate spin-density-wave and superconducting orders, which is fitted to the low-field intensity data.","marker":"Ref. 59"},{"why":"Defines the low-temperature magnetic structure and in-plane field anisotropy of parent antiferromagnet CeRhIn$_5$, serving as the main comparator for the incommensurate order and anisotropy found here.","marker":"Ref. 27"},{"why":"Demonstrates single-domain helical magnetic order in CeRhIn$_5$, the precedent used to argue that the unsplit shifted peak above $H_{c2}$ could be a genuine single-domain incommensurate state.","marker":"Ref. 30"}],"fun_headline_variants":["In-plane field drives superconducting CeCoRhIn5 to incommensurate order","Magnetic field direction tunes order in superconducting CeCoRhIn5","Neutrons show in-plane field turns magnetism incommensurate in superconductor","CeCoRhIn5: field within a-b plane makes magnetic order incommensurate","Superconducting magnetism reorders under in-plane field in CeCoRhIn5"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The claim stands on the assumption that the small shift of the magnetic peak along $L$ above 7.5 T is a true single-domain incommensurate propagation vector, not the result of unresolved splitting into $\\pm\\delta q$ domains, sample motion, or field inhomogeneity.","fun_headline_variants_meta":{"raw":{"variants":["In-plane field drives superconducting CeCoRhIn5 to incommensurate order","Magnetic field direction tunes order in superconducting CeCoRhIn5","Neutrons show in-plane field turns magnetism incommensurate in superconductor","CeCoRhIn5: field within a-b plane makes magnetic order incommensurate","Superconducting magnetism reorders under in-plane field in CeCoRhIn5"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001132,"raw_usage":{"total_tokens":4877,"prompt_tokens":1295,"completion_tokens":3582,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":911,"completion_tokens_details":{"reasoning_tokens":3476}},"tokens_in":911,"tokens_out":3582,"duration_ms":23806,"temperature":1.0,"reasoning_tokens":3476,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T11:06:00.230201+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A higher-resolution or polarized neutron diffraction measurement on the same compound above $H_{c2}$ with the field in the $a$-$b$ plane would settle the claim: if the Bragg peak splits into two peaks around $L=1/2$, or remains at $L=1/2$ within resolution, then the reported normal-state incommensurate order is not established.","supporting_citations":[],"review_version":1}