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REVIEW 3 major objections 4 minor 91 references

Magnetic field tuned superconducting and normal phase magnetism in CeCo$_{0.5}$Rh$_{0.5}$In$_{5}$

T0 review · 3 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read 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.

desk verdict 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. read the letter →

arxiv 2411.18540 v1 pith:3C5Y3CRK submitted 2024-11-27 cond-mat.str-el cond-mat.supr-con

A. Howell , M. Songvilay , J. A. Rodriguez-Rivera , Ch. Niedermayer , Z. Husges , P. Manuel , S. Saha , C. Eckberg
show 2 more authors
J. Paglione C. Stock
This is my paper · ORCID
classification cond-mat.str-elcond-mat.supr-con
keywords heavyfermionCeCo0.5Rh0.5In5neutrondiffractionmagneticfieldcommensurateantiferromagnetismincommensurateordersuperconductivityvortexstate
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

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.

What carries the argument

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.

What would settle it

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.

Watch

Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

  • 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.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • 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.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

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.

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 (3)
  1. [§III.D, Figs. 5(c) and 6(c)] 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.
  2. [§III.D and §IV] 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.
  3. [§III.A, Fig. 2(b)] 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.
minor comments (4)
  1. [§III.C, Fig. 4(a)] 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.
  2. [§III.A and figure captions] 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.
  3. [§III.D] 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.
  4. [§III.B, Fig. 3(c)] 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.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the central claims are direct neutron diffraction observations, not outputs of a fitted model or self-citation chain.

full rationale

The paper's central claims—zero-field commensurate order at Q=(1/2,1/2,1/2), field-induced block order at L=1/4, and the small shift of the magnetic peak along L above Hc2—are measured Bragg intensities and peak positions. They are not derived from a fitted parameter or from an imported uniqueness theorem. The only model comparison, the DSZ curve in Fig. 4(a), is explicitly a fit with theta=6.8±1.0 and Hc2 fixed, and the authors state that the logarithmic form 'may not be appropriate' above ~2 T; it is not presented as a prediction, and the paper's claims do not rest on it. Self-citations (Stock et al. for CeRhIn5 spin resonance, langasite single domains, and YbRh2Si2) are used as analogies and background, and are not load-bearing; the single-domain interpretation is supported by the direct absence of peak splitting and by citations to non-overlapping groups such as Marty et al. and Qureshi et al. The high-field incommensurate claim depends on a small peak shift (0.002–0.006 r.l.u.), which raises a data-analysis robustness concern about resolution and line-shape absorption, not a circularity. No equation in the paper defines a predicted quantity in terms of the same data used to test it, and no fitted quantity is renamed as a prediction.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The central claims are experimental. The only fitted theoretical parameter is theta in the DSZ comparison, plus the order-parameter exponent beta and cross-instrument normalizations. The load-bearing assumptions concern sample homogeneity, field/domain artifacts, and the applicability of a cuprate vortex-core model.

free parameters (3)
  • theta in Demler-Sachdev-Zhang vortex-core fit = 6.8 +/- 1.0
    Fitted to the low-field intensity growth in Fig. 4(a); the predicted value is about 3 for square or triangular vortex lattices, and the authors note the fit is poor above 2 T.
  • Critical exponent beta for the magnetic order parameter = 0.65 +/- 0.03 (0 T), 0.44 +/- 0.03 (6.5 T, [1,-1,0])
    Fitted to power-law I(T) near TN in Fig. 2(b); the authors note the value depends on the temperature range chosen, so the fitted beta is not a rigorous critical exponent.
  • Relative normalization between RITA2 and FLEXX datasets = not quoted, chosen to overlap 5-9 T data
    Fig. 2(c) merges data from two instruments with different temperatures and resolutions; the overlap scaling is a free choice that affects the apparent field dependence.
assumptions (6)
  • domain assumption Magnetic Bragg intensity is proportional to the square of the ordered moment, and the observed peaks are magnetic in origin.
    Used throughout the paper; magnetic nature is supported by absence at high temperature, but no polarization analysis was performed for this sample.
  • domain assumption The sample is homogeneous at nominal composition x=0.5, so measured magnetic phases are intrinsic bulk properties.
    The sharp TN is cited as evidence of homogeneity in Section III, but Co/Rh substitution disorder is not directly measured.
  • domain assumption The field was only changed in the normal state, so the sample did not move or twist in the beam during field sweeps.
    Section III.D uses this to argue the small peak shift is not a sample-twisting artifact; nuclear peaks also showed no shift.
  • domain assumption The incommensurate scattering at high field is a single magnetic domain rather than unresolved ±δq splitting.
    Discussed in Section III.D; authors note single-domain states exist in related langasites and CeRhIn5, but do not measure domain populations.
  • domain assumption The H/Hc2 ln(theta Hc2/H) model for spin-density-wave order near vortices applies to this material.
    Section III.C fits this cuprate-derived model with theta=6.8±1.0; the authors acknowledge the fit fails above about 2 T and theta is anomalously large.
  • standard math Field along [1,-1,0] preserves a twofold rotation, so any field-induced intensity change from static magnetism alone should be even in H.
    Used in Section III.C to argue the linear increase is unusual and implies coupling to the superconducting order parameter.

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Pith. "Pith review of Magnetic field tuned superconducting and normal phase magnetism in CeCo$_{0.5}$Rh$_{0.5}$In$_{5}$." pith.science (2026). https://pith.science/paper/3C5Y3CRK

@misc{pith2026241118540,
  author       = {Pith},
  title        = {Pith review of: Magnetic field tuned superconducting and normal phase magnetism in CeCo$_0.5$Rh$_0.5$In$_5$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3C5Y3CRK}},
  note         = {Machine review of arXiv:2411.18540}
}
abstract

By tuning superconductivity with an applied magnetic field, we use neutrons to compare the magnetic ordered phases in superconducting and normal states of CeCo$_{0.5}$Rh$_{0.5}$In$_{5}$. At zero field, CeCo$_{0.5}$Rh$_{0.5}$In$_{5}$ displays both superconductivity ($T_{c}$=1.3 K) and spatially long-ranged commensurate $\uparrow\downarrow\uparrow\downarrow$ antiferromagnetism ($T_{N}$=2.5 K, $\vec{Q}_{0}=({1\over 2}, {1\over 2}, {1\over 2})$). Neutron spectroscopy fails to measure propagating magnetic excitations with only temporally overdamped fluctuations observable. On applying a magnetic field we find anisotropic behavior in the static magnetism. When the field is along the crystallographic $c$-axis, no change in the static magnetic response is observable. However when the field is oriented within the $a-b$ plane, an increase in $T_{N}$ and change in the critical response are measured. At low temperatures in the superconducting phase, the elastic magnetic intensity increases linearly ($\propto |H|$) with small $a-b$ oriented fields. However, this trend is interrupted at intermediate fields where commensurate block $\uparrow\uparrow\downarrow\downarrow$ magnetism with propagation vector $\vec{Q}=({1\over 2}, {1\over 2}, {1\over 4})$ forms. For large applied fields in the [1 $\overline{1}$ 0] direction which completely suppresses superconductivity, weakly incommensurate magnetic order along $L$ is observed to replace the commensurate response present in the superconducting and vortex phases. We suggest field-induced incommensurate static magnetism, present in the normal state of superconducting and antiferromagnetic CeCo$_{0.5}$Rh$_{0.5}$In$_{5}$ for $a-b$ plane oriented magnetic fields. We speculate that these field dependent properties are tied to the field induced anisotropy associated with the local Ce$^{3+}$ crystal field environment of the tetragonal `115' structure.

Figures

Figures reproduced from arXiv: 2411.18540 by the authors.

Figure 1
Figure 1. FIG. 1. The magnetic and superconducting phase diagram [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Temperature and applied field dependent mag ⃗ [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 4
Figure 4. FIG. 4. Magnetic field dependence using vertical fields at ⃗ [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figures from the paper (3 more)
Figure 5
Figure 5. Figure 5: FIG. 5. Magnetic diffraction near [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Magnetic diffraction near [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Magnetic spectroscopy at zero applied field prob [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]

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