{"id":"caef2793-0596-4e31-b333-09f3c56968e4","arxiv_id":"2412.02677","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"FeSe exhibits a sizable negative longitudinal magnetoresistance for current and field along the c-axis below its 90 K structural transition, which the authors link to field-modified spin-fluctuation scattering.","lead":"Measurements on FeSe crystals show that when electric current and magnetic field both point along the crystal's c-axis, the resistivity decreases with field below the 90 K structural transition, reaching about 15% at 10 K and 16 T. The authors attribute this negative longitudinal magnetoresistance to the field suppressing scattering from spin fluctuations, offering a new transport signature of nematic order in FeSe.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Contact-alignment diagnostic only checks zero field at 229 K; it does not rule out temperature/field-dependent ab-plane leakage at 10 K, where the NLMR claim lives.","rationale":"The paper reports a plausible and potentially important observation with real supporting evidence: three samples, an angular dependence study, and a clear awareness of the contact-alignment pitfall. That independent support is why I do not recommend moving the verdict toward REJECT. The weakest link is not the spin-fluctuation interpretation, which is explicitly qualitative and presented as a framework rather than a quantitative derivation. The weakest link is the measurement itself: the entire claim of negative c-axis longitudinal magnetoresistance depends on isolating the c-axis transport channel from ab-plane contamination. The reader's weakest_assumption identified the same broad concern, so I partially agree. My stress-test sharpens it: the T_max_c diagnostic is a zero-field, single-temperature check that does not bound the leakage fraction at 10 K and 16 T, where the effect is claimed. Because rho_ab has positive transverse magnetoresistance below Ts, even a small field-dependent admixture of ab-plane signal could partially cancel or amplify the c-axis signal. A finite-element current-flow simulation with the measured anisotropic resistivities and the actual contact geometry would settle whether realistic misalignment can produce or mask the 15% effect. Until that check is performed, CONDITIONAL is the appropriate verdict, and no verdict adjustment is needed beyond what the reader already recommended.","tokens_in":12835,"tokens_out":6656,"duration_ms":83408,"concrete_test":"Build a finite-element current-flow model of the modified Corbino geometry using the measured anisotropic resistivity tensor rho_ab(T,H) and rho_c(T,H), with realistic contact dimensions and plausible misalignment values. Require the model to reproduce three facts: T_max_c = 229 K in zero field, the sensitivity of T_max_c to a 5 K shift, and the observed angular dependence of the magnetoresistance at T=10 K and mu0H=16 T. If no physically reasonable epsilon(T,H) can reproduce the 15% negative longitudinal magnetoresistance while keeping T_max_c at 229 K, the alignment concern is resolved. If a small epsilon(T,H) can, the authors should repeat the measurement with an independent low-temperature alignment probe, such as a direct ab-plane monitor contact on the same crystal.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central observation is a negative longitudinal magnetoresistance of about 15% at T=10 K and mu0H=16 T for current and field along the c-axis. For this observation to be valid, the measured voltage must be dominated by the c-axis channel and not by ab-plane paths that exhibit positive transverse magnetoresistance. The paper's only quantitative alignment check is the zero-field position of the resistivity maximum T_max_c = 229(1) K, together with the assertion that a misalignment shifting T_max_c by only 5 K destroys the negative magnetoresistance (Section III). That diagnostic is performed near 229 K, in zero field, and on the zero-field resistivity. It does not quantitatively constrain the leakage fraction epsilon(T,H) at T=10 K under 16 T. In a layered anisotropic material, contact misalignment and finite contact geometry produce a temperature- and field-dependent mixture of rho_ab and rho_c. Since rho_ab has a large positive transverse magnetoresistance below Ts while the reported c-axis magnetoresistance is negative, an uncontrolled epsilon(T,H) can change the magnitude and even the sign of the measured Delta-rho/rho. The statement that a 5 K shift in T_max_c erases the effect calibrates sensitivity at 229 K, not at 10 K; thermal contraction, contact resistance, and field-dependent current redistribution could alter the effective mixing at low temperature. No error bars or raw data are provided, and no independent geometric validation, such as finite-element current-flow simulation or a deliberately misaligned control sample, is presented. The observation therefore still rests on an unquantified assumption about the low-temperature, high-field current path.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":13055,"tokens_out":7088,"duration_ms":78680,"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":[{"comment":"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.","section":"Section III, contact alignment diagnostic"},{"comment":"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.","section":"Section III, Figs. 1(d) and 3"},{"comment":"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.","section":"Section IV, Eq. (2), and Appendix A"}],"minor_comments":[{"comment":"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.","section":"Section III, Fig. 2"},{"comment":"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.","section":"Section II, modified Corbino geometry"},{"comment":"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.","section":"Section III, Fig. 1"},{"comment":"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.","section":"Section IV, Eq. (1)"},{"comment":"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.","section":"Appendix A, Fig. 6"},{"comment":"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.","section":"Section IV"}],"recommendation":"major_revision","confidential_remarks":"The manuscript reports a potentially interesting and novel transport observation, but the central claim rests on the absence of ab-plane leakage in a c-axis Corbino measurement. The current alignment diagnostic is not sufficient to rule out low-temperature field-dependent mixing. If the authors can provide a quantitative leakage estimate at the relevant field and temperature, or additional control experiments, I would be supportive of publication. I also recommend asking for error bars and raw data or an uncertainty budget, as the quantitative 15% claim is otherwise not verifiable."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"First observation of negative c-axis longitudinal magnetoresistance in FeSe is a real, useful result. The paper does the important work of checking contact alignment, shows the effect in three samples, and the angular dependence makes it hard to brush off as a wiring artifact. Credit where it's due: the modified Corbino setup is the right tool, and the fact that misalignment shifting Tmax_c by 5 K erases the effect is a meaningful diagnostic, though it is a zero-field, high-temperature check.\n\nThe soft spots are the ones the reader flagged. The ~15% at 10 K and 16 T has no error bars, and there is no raw data deposit, so the quantitative claim can't be independently verified. More pointedly, the alignment test is done at 229 K in zero field, not at 10 K under 16 T; in a layered material, the effective mixing of rho_ab and rho_c can be temperature- and field-dependent. The stress-test note is right about this. It is not fatal, because the angular dependence and the three-sample repeatability make a pure leakage artifact less likely, but it is an unquantified assumption. The authors could kill it with a finite-element current-flow calculation or a deliberately misaligned control sample.\n\nThe spin-fluctuation interpretation is plausible and consistent with prior INS and NMR work, but it's a qualitative attribution. The fit to Eq. 2 is a three-parameter empirical function, not a FeSe-specific derivation; the paper honestly says it's a foundational framework.\n\nOverall: this is a solid experimental paper for the FeSe community. It reports a new observable, handles the main experimental pitfall, and the interpretation is reasonable. It deserves a serious referee. My own verdict is conditional: the observation is likely real, but the quantitative claim needs error bars and the low-temperature alignment question needs a quantitative answer. I'd send it to review.","headline":"A credible first observation of negative c-axis longitudinal magnetoresistance in FeSe, with the main caveat being the unquantified low-temperature contact leakage.","tokens_in":13672,"tokens_out":2057,"would_cite":true,"duration_ms":22197,"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":"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…","keywords":["FeSe","negative longitudinal magnetoresistance","nematic phase","spin fluctuations","c-axis transport","iron-based superconductors","Corbino contact"],"falsifier":"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.","tokens_in":12586,"feed_emoji":"🧲","tokens_out":5872,"duration_ms":54672,"temperature":0.7,"pith_summary":"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.","feed_headline":"In FeSe's nematic phase, c-axis field lowers c-axis resistance","feed_subtitle":"The drop reaches roughly 15% at 10 K and 16 T, implicating spin-fluctuation scattering.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Provides the s-d model formula for negative magnetoresistance from antiferromagnetic spin fluctuations that the paper uses as its interpretive framework.","marker":"[52]"},{"why":"Reports negative longitudinal magnetoresistance in Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ and LiFeAs and supplies the comparable fitting forms and the precedent for spin-fluctuation-driven NLMR.","marker":"[49]"},{"why":"Shows the enhancement of stripe spin fluctuations below $T_s$ in FeSe, the experimental basis for expecting field-modified scattering.","marker":"[23]"},{"why":"Reports anisotropic spin fluctuations in FeSe that are stronger along the c-axis, supporting the direction dependence of the effect.","marker":"[37]"},{"why":"Provides the earlier c-axis resistivity data showing the $T_c^{\\rm max}$ feature used to validate the contact alignment.","marker":"[38]"},{"why":"Describes the crystal growth and the multiband ab-plane magnetoresistance characterization of the same crystals, used as the in-plane baseline.","marker":"[30]"}],"fun_headline_variants":["FeSe's c-axis resistance drops under c-axis field","Negative c-axis magnetoresistance in FeSe nematic phase","Magnetic field quells c-axis spin scattering in FeSe","In FeSe, c-axis field cuts c-axis resistivity"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["FeSe's c-axis resistance drops under c-axis field","Negative c-axis magnetoresistance in FeSe nematic phase","Magnetic field quells c-axis spin scattering in FeSe","In FeSe, c-axis field cuts c-axis resistivity"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000344,"raw_usage":{"total_tokens":1842,"prompt_tokens":849,"completion_tokens":993,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":465,"completion_tokens_details":{"reasoning_tokens":924}},"tokens_in":465,"tokens_out":993,"duration_ms":9877,"temperature":1.0,"reasoning_tokens":924,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T23:10:50.409862+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"Resistance anomaly near the su- perconducting transition temperature in short aluminum wires,","cited_arxiv_id":null,"evidence_quote":"Provides the s-d model formula for negative magnetoresistance from antiferromagnetic spin fluctuations that the paper uses as its interpretive framework."},{"cited_title":"Nonmonotonic pressure evolution of the upper critical field in superconducting FeSe,","cited_arxiv_id":null,"evidence_quote":"Reports negative longitudinal magnetoresistance in Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ and LiFeAs and supplies the comparable fitting forms and the precedent for spin-fluctuation-driven NLMR."},{"cited_title":"Lifting of xz/yz orbital de- generacy at the structural transition in detwinned FeSe,","cited_arxiv_id":null,"evidence_quote":"Shows the enhancement of stripe spin fluctuations below $T_s$ in FeSe, the experimental basis for expecting field-modified scattering."},{"cited_title":"Nematic pairing from orbital-selective spin fluctuations in FeSe,","cited_arxiv_id":null,"evidence_quote":"Reports anisotropic spin fluctuations in FeSe that are stronger along the c-axis, supporting the direction dependence of the effect."},{"cited_title":"Field-induced supercon- ducting phase of FeSe in the BCS-BEC cross-over,","cited_arxiv_id":null,"evidence_quote":"Provides the earlier c-axis resistivity data showing the $T_c^{\\rm max}$ feature used to validate the contact alignment."},{"cited_title":"Origin of the tetragonal-to-orthorhombic phase transition in FeSe: A combined thermodynamic and NMR study of nematicity,","cited_arxiv_id":null,"evidence_quote":"Describes the crystal growth and the multiband ab-plane magnetoresistance characterization of the same crystals, used as the in-plane baseline."}],"review_version":1}