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REVIEW 3 major objections 6 minor 71 references

Negative $c$-axis longitudinal magnetoresistance in FeSe

T0 review · 3 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Below the structural transition at 90 K, FeSe develops a negative longitudinal magnetoresistance of about 15% at 10 K and 16 T when current and field are both along the c-axis, which the authors attribute to field-modified…

desk verdict A credible first observation of negative c-axis longitudinal magnetoresistance in FeSe, with the main caveat being the unquantified low-temperature contact leakage. read the letter →

arxiv 2412.02677 v1 pith:GV3FQZZC submitted 2024-12-03 cond-mat.supr-con cond-mat.str-el

M. Lourdes Amigó , Jorge I. Facio , Gladys Nieva This is my paper · ORCID
classification cond-mat.supr-concond-mat.str-el
keywords FeSenegativelongitudinalmagnetoresistancenematicphasespinfluctuationsc-axistransportiron-basedsuperconductorsCorbinocontact
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 reports that in single-crystal FeSe, below the structural transition at $T_s=90$ K, the longitudinal magnetoresistance for current and magnetic field both aligned along the c-axis becomes negative, reaching roughly $-15\%$ at 10 K and 16 T. This is opposite to the well-known positive transverse magnetoresistance in the ab-plane and is the first report of negative longitudinal magnetoresistance in FeSe. The authors argue that the Lorentz force cannot produce a longitudinal magnetoresistance, so the effect must reflect a field-induced change in scattering; they identify scattering from short-range anisotropic spin fluctuations, which strengthen below $T_s$, as the origin. If correct, the result would make c-axis magnetotransport a direct probe of spin-fluctuation physics in the nematic phase of a superconductor that lacks long-range magnetic order.

What carries the argument

The load-bearing mechanism is the field dependence of scattering from antiferromagnetic spin fluctuations, described by the s-d model in which the external field enhances the uniform $q=0$ spin mode at the expense of the staggered $q=Q$ mode, reducing the resistivity. The paper fits the data to $\Delta\rho/\rho = [\Delta_0 + \nu (T_s - T)^\beta]H^2$ with $\beta = 1.3(4)$, a form that mirrors the growth of the spin-fluctuation contribution as the temperature approaches $T_s$ from below. The contact geometry that isolates the c-axis channel, validated by the condition that $T_c^{\rm max}$ stays near 229 K, is the experimental key that makes the observation possible.

What would settle it

A geometry-independent test would be to pattern a focused-ion-beam microbridge along the c-axis of a FeSe crystal and measure longitudinal magnetoresistance with current and field exactly parallel; if the negative ~15% signal at 10 K and 16 T does not reproduce, the contact-alignment explanation would be called into question. Alternatively, a measurement of the spin-fluctuation spectrum under a 16 T field along c, via inelastic neutron scattering, could test whether the $q=Q$ spectral weight actually shifts to $q=0$ by the amount needed to produce the observed resistance drop.

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Extended reading notes

Core claim

The central discovery is that FeSe's c-axis resistivity falls when a magnetic field is applied along the same direction, but only in the nematic phase below $T_s$. The magnetoresistance is essentially zero above $T_s$, then grows negative on cooling, reaching about $-15\%$ at 10 K and $\mu_0H=16$ T, with an approximately quadratic field dependence. The authors show that the effect is sensitive to contact geometry: a misalignment that shifts the c-axis resistivity maximum $T_c^{\rm max}$ by only 5 K turns the signal positive, because it mixes in the ab-plane magnetoresistance. They interpret the negative longitudinal magnetoresistance as the signature of the magnetic field suppressing the spin-fluctuation scattering contribution to the c-axis resistivity, connecting the transport to the enhanced anisotropic spin fluctuations observed in the nematic phase.

Load-bearing premise

The entire observation depends on the c-axis contact alignment being accurate enough that the measurement is not contaminated by the positive ab-plane magnetoresistance; the authors themselves note that a misalignment shifting the resistivity maximum by just 5 K erases the negative signal.

Editorial extensions

If this is right

  • The c-axis longitudinal magnetoresistance of FeSe is negative below $T_s$ and scales approximately as $H^2$, reaching about 15% at 10 K and 16 T.
  • Because the Lorentz force vanishes when current and field are parallel, the observation implies a field-dependent scattering mechanism, namely spin-fluctuation scattering, operates along the c-axis in the nematic phase.
  • The effect is tied to the nematic transition: it appears only below $T_s$ and grows as $(T_s - T)^\beta$, making c-axis transport a sensitive probe of nematic spin fluctuations.
  • The contact-alignment requirement, with $T_c^{\rm max}$ near 229 K and a 5 K shift erasing the signal, likely explains why the negative longitudinal magnetoresistance had not been seen before.

Reading between the lines

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

  • If the spin-fluctuation interpretation holds, the c-axis magnetoresistance should track the doping or pressure evolution of the nematic transition in FeSe$_{1-x}$S$_x$, providing a bulk transport signature of the fluctuation spectrum.
  • Extending the measurements to higher fields and lower temperatures near $T^* \sim 20$ K might reveal a change in the functional form of the magnetoresistance, which the authors note they cannot currently resolve.
  • The same field-suppression mechanism might be expected to appear in other iron-based systems with strong c-axis spin fluctuations, though the masking positive Lorentz contribution in transverse configurations may hide it.
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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 / 6 minor

Summary. This paper reports measurements of the c-axis longitudinal magnetoresistance in single-crystal FeSe using a modified Corbino contact configuration. The authors find that for H || I || c, the magnetoresistance becomes negative below the structural transition at Ts = 90 K, reaching approximately -15% at T = 10 K and 16 T, whereas the transverse in-plane magnetoresistance is positive. They attribute the negative longitudinal magnetoresistance to field-induced suppression of spin-fluctuation scattering. The manuscript presents data from three samples (S1-S3), an angular dependence showing negative magnetoresistance for a wide range of angles around H || c, and a fit of the magnetoresistance to the form Delta rho/rho = [Delta0 + nu(Ts - T)^beta] H^2.

Significance. If the observation is correct, this is the first report of negative c-axis longitudinal magnetoresistance in FeSe and would add a transport signature supporting the importance of spin fluctuations in the nematic phase. The paper has clear strengths: the result is reproduced in three single crystals, an angular dependence is provided, and the zero-field T_max_c diagnostic for contact alignment is a reasonable and well-motivated check. The interpretation is placed in the context of existing spin-fluctuation studies, and the comparison with prior work on Ba(Fe,Co)2As2 and LiFeAs is appropriate. The main limitation is that the quantitative claim of about 15% is made without an explicit uncertainty budget, and the contact-alignment diagnostic is only strictly validated at zero field near 229 K, not at the low temperatures and high fields where the effect is claimed. With additional validation of the contact geometry at low temperature and error bars on the magnetoresistance curves, this would be a valuable contribution to the transport phenomenology of FeSe.

major comments (3)
  1. [Section III, contact alignment diagnostic] The alignment test based on T_max_c = 229(1) K is performed in zero field and at high temperature; it does not provide a quantitative bound on the fraction of ab-plane signal that can enter the measured voltage at T = 10 K and H = 16 T. Because the ab-plane transverse magnetoresistance of FeSe is large and positive below Ts while the reported c-axis longitudinal magnetoresistance is negative, an uncontrolled temperature- and field-dependent mixing of the two channels can change both the magnitude and the sign of Delta rho/rho. The statement that a misalignment shifting T_max_c by only 5 K destroys the negative magnetoresistance is useful, but it calibrates the sensitivity at 229 K, not at 10 K. Please provide a quantitative low-temperature leakage estimate (for example, finite-element simulation of the current flow in the modified Corbino geometry) or a control experiment with a deliberately misaligned contact at the same temperature and field.
  2. [Section III, Figs. 1(d) and 3] The central quantitative claim of about 15% negative magnetoresistance at T = 10 K and mu0H = 16 T is presented without error bars or an uncertainty budget. The values in Figure 3(b) and the quoted magnitude in the abstract require a measurement uncertainty statement covering voltage noise, field-angle reproducibility, and the normalization procedure. Without this, the reader cannot assess the significance of the 15% figure or the differences among samples S1-S3 in Figure 6.
  3. [Section IV, Eq. (2), and Appendix A] The fit of Eq. (2) is a central element of the spin-fluctuation interpretation, but the manuscript does not report fit quality (e.g., R^2 or chi^2) or the temperature range included in the fit. The large uncertainties on the fitted parameters (beta = 1.3(4), nu = -1.9(5) x 10^-6 T^-2 K^-1.3 for S1) make it difficult to assess the significance of the power-law form. In addition, Appendix A reports Delta0 = +6(1) x 10^-6 T^-2 for sample S2, while the main text states that Delta0 'accounts for a very small NLMR above Ts,' which is inconsistent in sign. Please clarify the interpretation of Delta0 and specify the fitting procedure and range.
minor comments (6)
  1. [Section III, Fig. 2] The angular dependence curves for different temperatures in Figure 2(b) are plotted without distinct symbols or labels for each temperature; please use distinguishable markers or explicit labels to improve readability.
  2. [Section II, modified Corbino geometry] The description of the modified Corbino configuration would benefit from quantitative details: contact diameters, sample thickness, and the area of the top and bottom gold patterns. These parameters are important for assessing possible ab-plane current contributions.
  3. [Section III, Fig. 1] The normalized resistivity curves in Figure 1 would be clearer if the values of T_max_ab and T_max_c were marked on the plots or stated in the figure caption, since these temperatures are central to the alignment test.
  4. [Section IV, Eq. (1)] The relation between the exponent alpha in Eq. (1) and the power-law exponent beta in Eq. (2) is not discussed; please clarify how the temperature dependence of a(T) maps to the fitted (Ts - T)^beta form.
  5. [Appendix A, Fig. 6] The curves in Figure 6 are vertically shifted by an unspecified factor for clarity; please state the shift or plot the MR values on a common scale so that the sample-to-sample magnitude comparison is transparent.
  6. [Section IV] The interpretation would be strengthened by a brief discussion of alternative mechanisms that can produce negative longitudinal magnetoresistance, such as weak-localization corrections or orbital effects, even if they are considered less plausible for FeSe.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the NLMR measurement is an independent observable, and the spin-fluctuation interpretation rests on external prior work rather than on the paper's own fitted equations.

full rationale

The paper's central claim is an experimental observation: a negative longitudinal magnetoresistance of about 15% at T=10 K and mu0H=16 T for H parallel to I parallel to the c-axis in FeSe below Ts. This quantity is measured directly and is not constructed from, or defined in terms of, the model used later. Equation 2 is explicitly presented as a fit to the observed data ('the observed NLMR can be effectively fitted with ...'), with parameters beta, nu, and Delta0 obtained from that fit; the fit does not generate the data and is not used to define the measured magnetoresistance. The spin-fluctuation interpretation is imported from external literature (Refs. 51-52, the Usami-Moriya s-d model, and Ref. 49 for comparison with Ba(Fe1-xCox)2As2 and LiFeAs), not from a self-citation chain. The paper's self-citations (Refs. 30 and 41) concern crystal growth and prior characterization of the same samples, and they are not load-bearing for the NLMR claim. The contact-alignment diagnostic based on T_max_c = 229 K is an experimental validation using an independently known feature of the c-axis resistivity, not a circular argument. The skeptical concern that ab-plane leakage could contaminate the c-axis measurement is a question about experimental robustness and interpretation, but it does not amount to the paper deriving its conclusion from its own inputs. No step in the derivation chain reduces to a fitted parameter renamed as a prediction, a uniqueness theorem imported from the authors' own prior work, or a self-referential definition. Accordingly, the circularity score is 0.

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

The central claim rests on the experimental transport data and on prior theoretical and experimental assumptions about spin fluctuations in FeSe. No new entities are introduced. The free parameters are the three coefficients of the empirical fit in Eq.2, which are used to describe the temperature and field dependence of the observed magnetoresistance.

free parameters (3)
  • beta = 1.3(4)
    Power-law exponent in Eq.2, fitted to the temperature dependence of the negative longitudinal magnetoresistance at 16 T for three samples.
  • nu = -1.9(5) x 10^-6 T^-2 K^-1.3 for sample S1; -2.4(7) x 10^-6 and -1.5(5) x 10^-6 for S2 and S3 in Appendix A
    Prefactor of the (Ts-T)^beta term in Eq.2, fitted to the data for each sample.
  • Delta0 = -1.8(5) x 10^-5 T^-2 for sample S1; 6(1) x 10^-6 and -1.5(5) x 10^-5 for S2 and S3 in Appendix A
    Field-quadratic coefficient accounting for the small negative magnetoresistance above Ts, fitted in Eq.2.
assumptions (3)
  • domain assumption The spin-fluctuation scattering mechanism of Usami and Moriya, giving Delta rho = -a(T) H^2, applies to FeSe in the nematic phase.
    Used in Section IV to interpret the observed negative longitudinal magnetoresistance; the model is cited from Refs. [51,52], not re-derived for FeSe, and its applicability to this multiband material is asserted qualitatively.
  • domain assumption Short-range spin fluctuations in FeSe are enhanced below Ts and are anisotropic, with a stronger component along the c-axis.
    Invoked in Section IV to explain why negative longitudinal magnetoresistance appears only for H parallel to c; based on INS and NMR studies [19,20,23,37], not measured in this work.
  • domain assumption The modified Corbino contact configuration measures intrinsic c-axis resistivity, and the shift of T_max_c is a valid diagnostic of contact misalignment.
    Methodology assumption in Sections II and III; the authors use T_max_c to detect ab-plane admixture, but this diagnostic is not independently calibrated.

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Pith. "Pith review of Negative $c$-axis longitudinal magnetoresistance in FeSe." pith.science (2026). https://pith.science/paper/GV3FQZZC

@misc{pith2026241202677,
  author       = {Pith},
  title        = {Pith review of: Negative $c$-axis longitudinal magnetoresistance in FeSe},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GV3FQZZC}},
  note         = {Machine review of arXiv:2412.02677}
}
abstract

Below the structural transition occurring at $T_s=90$\,K, FeSe exhibits positive transverse magnetoresistance when the current is applied parallel to the $ab$-plane. In this study, we show that, in contrast, when both the magnetic field and the current are aligned along the $c$-axis, the magnetotransport changes significantly. In this configuration, FeSe develops a sizable negative longitudinal magnetoresistance ($\sim$15\% at $T$=10\,K and $\mu_0H$=16\,T) in the nematic phase. We attribute this finding to the effect of the applied magnetic field on the scattering from spin fluctuations. Our observations reflect the intricate interplay between spin and orbital degrees of freedom in the nematic phase of FeSe.

Figures

Figures reproduced from arXiv: 2412.02677 by the authors.

Figure 1
Figure 1. FIG. 1. Temperature dependence of the normalized resistivity with the current applied (a) in the [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. a) Angular dependence of the resistivity with the [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 5
Figure 5. FIG. 5. Angular dependence of the magnetoresistance for [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Temperature dependence of the normalized magne [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Temperature dependence of the magnetoresistance [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]

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Reference graph

Works this paper leans on

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    6 0 50 100 150 200 250 300 ρc/ρ c(T =290 K) T (K) S1 µ 0H=0 S1 µ 0H=16 T S2 µ 0H=0 S2 µ 0H=16 T S3 µ 0H=0 S3 µ 0H=16 T FIG. 4. Temperature dependence of the normalized magne- toresistance for µ0H∥c=0 and 16 T. The curves for each sam- ple are vertically shifted with the same factor. Additionally, figure 5 presents the angular dependence for the current al...

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