{"id":"719d5718-fe3c-4bf1-9bda-d632f824d4d9","arxiv_id":"2412.12263","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"In altermagnet CrSb, magnetoresistance and Hall resistivity obey extended Kohler scaling, and the nonlinear Hall effect arises from multi-band conduction, not an anomalous Hall effect.","lead":"A new study of the magnetic material CrSb shows that its large magnetoresistance and nonlinear Hall signals come from ordinary multi-band electron motion, not from its exotic altermagnetic order. The authors report the first scaling behavior of Hall resistivity in an altermagnet, a result that could reshape how such materials are evaluated for spintronics.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central interpretation rests on Boltzmann simulations using nonmagnetic band structure; without a check that AFM spin splitting does not alter the Fermi surface, the Lorentz-force/multi-band conclusion is unsupported.","rationale":"The reader identified the same load-bearing weakness: the simulations used to support the central claim are based on band structures without AFM order and assume a common relaxation time. My analysis agrees that this is the most important missing support. If the AFM spin splitting changes the Fermi surface or scattering, the agreement between experiment and the nonmagnetic simulation would not establish that transport is dominated by the Lorentz force or that the nonlinear Hall is multi-band rather than an altermagnetic AHE. The paper also lacks fit-quality metrics for the scaling analyses and for the three-band model, but those are secondary to the central interpretive claim. The concern is concrete and testable: rerun the transport simulation with the AFM band structure. Given that the reader already assigned CONDITIONAL, and my concern does not push the verdict further, the appropriate verdict is UNCHANGED: conditional acceptance pending the AFM-based simulation check.","tokens_in":10845,"tokens_out":6304,"duration_ms":61238,"concrete_test":"Repeat the WannierTools Boltzmann transport calculation using the collinear AFM band structure (with the experimentally constrained altermagnetic exchange splitting) instead of the nonmagnetic bands, keeping all other inputs fixed. Then compare the computed MR(H) and ρ_yx(H) curves to the experimental data using the same qualitative agreement criterion, and also report the Fermi-surface carrier densities for the NM and AFM calculations. If the AFM-based curves deviate from experiment substantially more than the NM-based curves, or if the carrier densities differ by more than ~50%, the nonmagnetic simulation's agreement cannot support the Lorentz-force/multi-band conclusion.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's main conclusion—that magneto-transport in CrSb originates from the intrinsic electronic structure and is dominated by the Lorentz force, and that nonlinear Hall is due to multi-band structure rather than AHE—is supported primarily by numerical simulations described as based on 'the band structures without considering AFM order' (Fig. 3(b) caption) and implicitly assuming a common relaxation time. This is the load-bearing joint: if the altermagnetic spin splitting, predicted to reach 1.2 eV near E_F, significantly reconstructs the Fermi surface or changes carrier balance, then the agreement between experiment and this nonmagnetic simulation does not establish the Lorentz-force interpretation or exclude an altermagnetic AHE. The text states only that simulations 'almost reproduce' the main characteristics of MR, with no quantitative comparison, error bars, or discussion of how the spin splitting affects the computed conductivities. The paper provides no direct check of whether the nonmagnetic band structure is an adequate proxy for the AFM one. This missing support is structurally distinct from the claim itself and is the weakest point in the argument.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript reports the growth of high-quality CrSb single crystals and a combined experimental and computational study of magnetotransport in this altermagnet. The authors measure magnetization, longitudinal resistivity, magnetoresistance (MR), and Hall resistivity as functions of temperature and magnetic field, and they perform DFT band-structure, Fermi-surface, and Boltzmann-transport simulations. They confirm an antiferromagnetic transition at TN = 712 K, observe a non-saturating positive MR (52.6% at 6 K, 7 T), and find a nonlinear Hall resistivity at low temperatures. The experimental MR and Hall data are claimed to collapse onto universal scaling curves when a temperature-dependent factor nT is introduced, extending Kohler's rule. The authors conclude that the magnetotransport is dominated by the Lorentz force and originates from the intrinsic electronic structure, and that the nonlinear Hall effect is due to a multi-band structure rather than an anomalous Hall effect. The latter conclusion is supported by a magnetic-point-group symmetry argument and by a three-band model fit.","tokens_in":11073,"tokens_out":3411,"duration_ms":32712,"significance":"If the conclusions hold, the paper provides a useful counterpoint to recent altermagnet transport studies: it shows that ordinary multi-band magnetotransport can reproduce the scaling behavior in CrSb without invoking an anomalous Hall effect, and it reports the first scaling behavior of Hall resistivity in an altermagnet. The experimental data are of good quality (RRR ≈ 9, well-characterized crystals, high-temperature susceptibility), and the symmetry-based exclusion of an AHE is a solid contribution. The numerical simulations are based on standard, reproducible tools (VASP, Wannier90, WannierTools). However, the central interpretation rests on two pillars that are not fully demonstrated: (i) the Boltzmann simulations deliberately use the band structure without AFM order, although CrSb is predicted to have a spin splitting up to 1.2 eV near the Fermi level; and (ii) the scaling collapses are produced by freely adjusting nT at each temperature with no reported fit residuals or error bars. These issues currently limit the strength of the Lorentz-force/multi-band claim.","major_comments":[{"comment":"The numerical simulations that are used to conclude that magnetotransport 'originates from the intrinsic electronic structure and is dominated by the Lorentz force' are, by the authors' own statement, based on 'the band structures without considering AFM order.' Since CrSb is predicted to have a spin splitting of up to 1.2 eV near the Fermi level, the nonmagnetic Fermi surface may differ substantially from the altermagnetic one. Without a quantitative comparison of the nonmagnetic and AFM band structures/Fermi surfaces, or a calculation using the AFM spin configuration, the agreement between experiment and this nonmagnetic simulation does not establish the Lorentz-force origin. This is a load-bearing step for the paper's main conclusion and needs to be either fixed by calculation or explicitly justified as an approximation with supporting evidence.","section":"Fig. 3(b) and the paragraph beginning 'Figure 3(b) displays...'"},{"comment":"The scaling collapse is achieved by choosing a temperature-dependent constant nT for each temperature, with nT = 1 defined at 40 K, and then plotting MR and Hall data in the rescaled variables. No error bars, residuals, or goodness-of-fit statistics are reported for the collapsed curves, and no independent determination of nT is provided. Since any smooth family of curves can often be made to collapse by tuning one parameter per curve, the demonstration would be much stronger if the nT values were independently constrained—for example, from Hall coefficient measurements or from the carrier densities extracted from the three-band model—and if the collapse quality were quantified.","section":"Figs. 3(d) and 4(d) with insets"},{"comment":"Equation (1) is presented as a scaling law where n and m are the carrier density and effective mass, and the condition is that all charge carriers share the same temperature-dependent relaxation time. However, in the analysis the authors replace n and m by a single temperature-dependent nT and plot ρyx/(nT ρ0) against H/(nT ρ0), effectively absorbing the effective mass into nT without comment. The physical interpretation of nT is therefore ambiguous: it could represent carrier density, mobility, or a combination. The authors should state clearly whether Eq. (1) is being used in its full form or in a reduced, empirical form, and should discuss whether the fitted nT values are consistent with the stated condition of a common relaxation time.","section":"Eq. (1) and the Hall scaling analysis"}],"minor_comments":[{"comment":"The phrase 'band structures without considering AFM order' appears in both the main text and the caption; this is an unusual choice for a paper whose central subject is an altermagnet, and it should be flagged and explained more prominently in the text.","section":"Fig. 3(b) caption and text"},{"comment":"The three-band model used to fit ρyx(H) (2 electron pockets and 1 hole pocket) is mentioned, but no fit curves, parameters, or residuals are shown in the main text or referenced in the Supplemental Material. Since this fit is part of the evidence for the multi-band interpretation, a brief summary of its quality and parameters would be appropriate.","section":"The paragraph discussing Fig. 4(a)"},{"comment":"The direction of the current relative to the crystal axes is not specified for the MR and Hall measurements. The band structure and Fermi surface are anisotropic, so the orientation of the current and field relative to the crystallographic axes is important for comparing experiment with simulation.","section":"Experimental methods"},{"comment":"The sentence 'the scaling law can very well describe the experimental data ... consistent very well with the numerical simulation results' is stronger than the evidence presented, because the simulation agreement is described elsewhere only as 'almost reproduce the main characteristics.' The wording should be adjusted to match the actual quantitative comparison.","section":"The concluding paragraph"}],"recommendation":"major_revision","confidential_remarks":"The central issue is that the main claim—that magnetotransport in CrSb is governed by the Lorentz force and the nonlinear Hall effect is of multi-band origin—relies on Boltzmann simulations that intentionally ignore the AFM order. This is a correctable but substantive gap: the authors should either run the same calculations with the AFM spin configuration or provide a clear quantitative argument that the nonmagnetic Fermi surface is adequate. The scaling analysis is also presented in a way that could be viewed as a fitting exercise rather than a prediction; adding error bars and an independent extraction of nT would materially strengthen the paper. The novelty relative to Refs. [44] and [46] should be clarified, since Ref. [44] is also on CrSb transport and Eq. (1) is taken from Ref. [46]."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe genuinely new thing here is the first observation of Hall-resistivity scaling in an altermagnet, plus a clean symmetry-based argument that CrSb's nonlinear Hall is not an anomalous Hall effect. The MR and Hall data are careful, the crystal quality looks good, and the three-band model plus Boltzmann transport simulation capture the qualitative trends. The authors do not claim a new scaling law; they apply known extended Kohler's rule and the Hall scaling from their own prior work, which is fine.\n\nThe soft spot is exactly where the stress-test note points. The central claim—that transport is Lorentz-force dominated and the nonlinear Hall is multi-band, not AHE—leans on a simulation done with band structures 'without considering AFM order.' If the altermagnetic spin splitting (up to 1.2 eV predicted near E_F) reconstructs the Fermi surface or changes carrier balance, the agreement between experiment and nonmagnetic simulation does not establish the interpretation. The paper never checks whether the AFM band structure gives a meaningfully different FS or transport. That is a load-bearing gap, and it is addressable: run the same Boltzmann calculation with the AFM band structure and show the MR and Hall curves barely change.\n\nSecond, the scaling collapse is a fitting exercise. n_T is adjusted at each temperature to force the collapse of both MR and Hall data, with no error bars or fit statistics. That does not refute the interpretation—the n_T values are consistent between longitudinal and transverse channels, which is internally supportive—but it weakens the claim that the scaling is a nontrivial law rather than a re-parameterization. The authors should report residuals or an unbiased collapse metric, and ideally show that the fitted n_T tracks an independently measured carrier density.\n\nOn the citation pattern: heavy self-citation is present, but the cited scaling laws (Refs 45, 46) are real and directly relevant. Not a flaw per se.\n\nWho gets value: the altermagnet and magneto-transport communities, especially those working on CrSb and similar NiAs-type magnets. It is a useful material-specific data set and a reasonable caution against misreading nonlinear Hall as AHE. It deserves a serious referee—the core interpretation is plausible and the experiment looks solid, but the nonmagnetic simulation gap should be fixed before publication. I would send it to review.\n\nBest,\n[Your name]","headline":"Solid magneto-transport study of CrSb with a first Hall-scaling observation in an altermagnet, but the load-bearing simulation uses a nonmagnetic band structure and the scaling collapse is fitting-driven.","tokens_in":11651,"tokens_out":614,"would_cite":true,"duration_ms":7006,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["72.15.Gd","75.50.Ee","71.18.+y"],"model":"deepseek-v4-flash","headline":"This paper argues that CrSb's large magnetoresistance and nonlinear Hall resistivity come from ordinary multi-band Lorentz-force transport, not from its altermagnetic order.","keywords":["altermagnet","CrSb","magnetoresistance","Hall resistivity","extended Kohler's rule","multi-band transport","Lorentz force","scaling law"],"falsifier":"Compute the magneto-transport from a DFT band structure that explicitly includes CrSb's antiferromagnetic order and spin splitting, using the same relaxation-time model; if those curves match the measured magnetoresistance and Hall resistivity better than the nonmagnetic simulation does, the paper's conclusion that transport is dominated by the ordinary, nonmagnetic electronic structure fails.","tokens_in":10674,"feed_emoji":"🧲","tokens_out":11034,"duration_ms":83437,"temperature":0.7,"pith_summary":"This paper sets out to show that the large magnetoresistance and nonlinear Hall resistivity measured in the altermagnet CrSb -- a magnetic material with zero net magnetization but spin-split electronic bands -- are ordinary Lorentz-force magneto-transport, not signatures of the material's altermagnetic order. The authors grew CrSb single crystals, confirmed the antiferromagnetic transition at $T_N = 712$ K, and measured longitudinal and Hall resistivity in fields up to 7 T between 6 K and 150 K. They find that both transport channels obey scaling laws -- an extended Kohler's rule with a temperature-dependent carrier-density factor $n_T$ for the magnetoresistance and a parallel scaling relation for the Hall resistivity -- and that numerical simulation from the calculated band structure reproduces the data. The central conclusion is that the nonlinear Hall response comes from a three-band (two electron, one hole) Fermi surface rather than from an anomalous Hall effect (a magnetization-related Hall voltage), so altermagnetic spin splitting does not dominate these transport coefficients.","feed_headline":"CrSb's magnetoresistance and Hall effect are ordinary transport","feed_subtitle":"Lorentz-force dominance means the transport probes ordinary electrons, not the altermagnetic spin-split bands.","key_machinery":"The argument is carried by three connected tools. The extended Kohler's rule $MR = \\alpha(H/n_T\\rho_0)^m$, with a temperature-dependent carrier-density factor $n_T$, absorbs the change of carrier density with temperature and collapses the longitudinal magnetoresistance data onto one curve. The Hall-resistivity scaling law $\\rho_{yx}/(n\\rho_0/m) = h(B/(n\\rho_0/m))$, derived under the condition that all charge carriers share the same temperature-dependent relaxation time, collapses the transverse data using the same $n_T$ values. A three-band model with two electron pockets and one hole pocket, together with Boltzmann-transport simulation of the calculated band structure, reproduces the measurements and identifies the nonlinear Hall response as a multi-band effect rather than an anomalous Hall effect; the magnetic point group $\\overline{6}'/m'mm'$ of CrSb is what rules out the anomalous Hall interpretation.","core_discovery":"The central claim is that in CrSb, a bulk g-wave altermagnet with Néel temperature $T_N = 712$ K and predicted spin splitting up to 1.2 eV, the measured magneto-transport is governed by the Lorentz force acting on ordinary carriers of the intrinsic band structure. Longitudinal magnetoresistance reaches 52.6% at 6 K and 7 T without saturating, and the data collapse under the extended Kohler's rule $MR = \\alpha(H/n_T\\rho_0)^m$ with $m = 1.42$ and $n_T$ varying from 0.8 at 6 K to 1.72 at 150 K. The Hall resistivity is nonlinear below 150 K, dips and changes sign below 60 K, yet a scaling plot of $\\rho_{yx}/(n_T\\rho_0)$ against $H/(n_T\\rho_0)$ collapses all temperatures onto one curve with the same $n_T$ values used for the longitudinal magnetoresistance. The authors attribute the nonlinearity to a three-band model with two electron pockets and one hole pocket, and they argue from the magnetic point group $\\overline{6}'/m'mm'$ that an anomalous Hall effect is not allowed. Numerical Boltzmann-transport simulation using the band structure without antiferromagnetic order almost reproduces the measured curves, which the paper takes as evidence that the transport is intrinsic and Lorentz-force dominated.","pith_inferences":["A sharper test of the Lorentz-force claim than the paper's simulation would be to repeat the calculation with the antiferromagnetic order and spin splitting included; the paper's match with experiment does not by itself identify which Fermi surface is active.","If the same analysis were applied to MnTe, where an anomalous Hall effect has been reported, subtracting the multi-band background would show whether a genuine altermagnetic Hall response remains; the paper does not make that comparison.","The success of the scaling suggests that other altermagnets could be analyzed the same way, but the extracted $n_T$ values are model-dependent and should be cross-checked against quantum-oscillation or thermoelectric measurements of the carrier density.","One consequence the authors leave implicit: if CrSb's transport is purely Lorentz-force in all field geometries, spintronic readout schemes for this altermagnet would have to rely on spin currents or other responses rather than on an anomalous Hall signal."],"forward_implications":["Nonlinear Hall resistivity in CrSb should not be taken as evidence of an altermagnetic anomalous Hall effect; the paper attributes it to multi-band transport.","The same temperature-dependent $n_T$ collapses both longitudinal magnetoresistance and Hall resistivity, so the two scaling analyses are tied to one carrier-density or relaxation-time scale.","Magneto-transport computed from the nonmagnetic band structure predicts the measured curves, so the predicted 1.2 eV spin splitting does not produce a detectable transport anomaly in this field and temperature range.","The extended Kohler scaling framework, previously applied to semimetals, now applies to an altermagnet, and Hall-resistivity scaling is reported in an altermagnetic material for the first time."],"supporting_citations":[{"why":"Defines altermagnetism and identifies CrSb as a candidate with substantial spin splitting near the Fermi level.","marker":"[2]"},{"why":"Provides the neutron-diffraction magnetic structure of CrSb that fixes the antiferromagnetic order and the high Néel temperature.","marker":"[18]"},{"why":"Predicts the up-to-1.2 eV spin splitting near the Fermi level that motivates the transport study.","marker":"[20]"},{"why":"Supplies the Boltzmann-transport and DFT framework used for the numerical magneto-transport simulations.","marker":"[22]"},{"why":"Provides the simulation code used to compute Fermi surfaces and magneto-transport from the tight-binding model.","marker":"[26]"},{"why":"Gives the three-band (two electron, one hole) model the paper uses to describe the nonlinear Hall resistivity.","marker":"[44]"},{"why":"Derives the Hall-resistivity scaling law used to collapse the transverse data under a common temperature-dependent relaxation time.","marker":"[46]"},{"why":"Excludes a spontaneous or field-induced anomalous Hall effect in CrSb by magnetic point group analysis.","marker":"[48]"},{"why":"Gives the symmetry condition that an antisymmetric Hall conductivity is allowed only in ferromagnetism-compatible magnetic point groups.","marker":"[49]"},{"why":"Shows that CrSb's magnetic point group is incompatible with ferromagnetism, ruling out the simple anomalous Hall interpretation.","marker":"[50]"}],"fun_headline_variants":["Lorentz force rules CrSb's transport, not altermagnetism","CrSb: Hall scaling first seen in an altermagnet","CrSb's magnetotransport: intrinsic, Lorentz-driven","Altermagnet CrSb: ordinary carriers, no anomalous Hall effect","Scaling of magnetoresistance and Hall in CrSb: Lorentz force"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The numerical simulations that anchor the Lorentz-force conclusion use the band structure without antiferromagnetic order and assume a shared or constant relaxation time; if the altermagnetic spin splitting or band-dependent scattering changes the Fermi surface enough, the match with experiment would not prove that the transport is ordinary.","fun_headline_variants_meta":{"raw":{"variants":["Lorentz force rules CrSb's transport, not altermagnetism","CrSb: Hall scaling first seen in an altermagnet","CrSb's magnetotransport: intrinsic, Lorentz-driven","Altermagnet CrSb: ordinary carriers, no anomalous Hall effect","Scaling of magnetoresistance and Hall in CrSb: Lorentz force"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000157,"raw_usage":{"total_tokens":1264,"prompt_tokens":1033,"completion_tokens":231,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":649,"completion_tokens_details":{"reasoning_tokens":141}},"tokens_in":649,"tokens_out":231,"duration_ms":2958,"temperature":1.0,"reasoning_tokens":141,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T14:14:52.468413+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the magneto-transport from a DFT band structure that explicitly includes CrSb's antiferromagnetic order and spin splitting, using the same relaxation-time model; if those curves match the measured magnetoresistance and Hall resistivity better than the nonmagnetic simulation does, the paper's conclusion that transport is dominated by the ordinary, nonmagnetic electronic structure fails.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the neutron-diffraction magnetic structure of CrSb that fixes the antiferromagnetic order and the high Néel temperature."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Predicts the up-to-1.2 eV spin splitting near the Fermi level that motivates the transport study."},{"cited_title":"Zhang, Q","cited_arxiv_id":null,"evidence_quote":"Supplies the Boltzmann-transport and DFT framework used for the numerical magneto-transport simulations."},{"cited_title":"Nonlinear field dependence of Hall effect and high-mobility multi-carrier transport in an altermagnet CrSb","cited_arxiv_id":"2409.14855","evidence_quote":"Gives the three-band (two electron, one hole) model the paper uses to describe the nonlinear Hall resistivity."},{"cited_title":"Zhang, Z","cited_arxiv_id":null,"evidence_quote":"Derives the Hall-resistivity scaling law used to collapse the transverse data under a common temperature-dependent relaxation time."},{"cited_title":"ˇSmejkal, R","cited_arxiv_id":null,"evidence_quote":"Gives the symmetry condition that an antisymmetric Hall conductivity is allowed only in ferromagnetism-compatible magnetic point groups."}],"review_version":1}