{"id":"95ad792a-4284-4374-be71-189d897bcf16","arxiv_id":"2608.09533","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A parameter-free relation, xi = (R - R0)/(R1 - R0), makes longitudinal resistance a quantitative probe of spin polarization in two-dimensional electron liquids.","lead":"This experimental paper reports that the longitudinal resistance of a two-dimensional electron liquid gives a direct measure of its spin polarization, with electrically detected spin resonance used as the supporting check. The result would let researchers map the magnetic state of correlated electron systems using only resistance measurements.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The collapse test for Eq. (14) only establishes a factorized dR/dxi(B,T)=h(B)k(T), not the B-independence required to derive Eq. (7); the reconstructed 'polarization' may be xi(B)h(B)/h(B1).","rationale":"The reader identifies Supp. Eq. (14) as the weakest assumption, and I agree that this is the load-bearing point. The reader's phrasing emphasizes the self-referentiality of the normalization to an assumed xi(B). The more fundamental logical gap is that the experimental collapse of the temperature dependence of A/xi at a handful of fields establishes factorization in B and T, not the absence of B dependence. If dR/dxi(B,T)=h(B)k(T), every subsequent equation in the paper—Eqs. (4)–(7)—goes through with the same formal structure, but the reconstructed quantity is xi(B)h(B)/h(B1). The comparison with ESR amplitude cannot rescue this, because A is proportional to exactly the same contaminated combination. The only way to break the degeneracy is either an independent measurement of xi, or a quantitative comparison of absolute A/xi values across fields, which is not reported. The additional complication that R1 is taken at 1.2Bc with orbital magnetoresistance present further weakens the quantitative normalization. These concerns do not prove the relation false; they show that the central claim is underdetermined by the presented data. A conditional acceptance with a clear requirement for an external polarization check (or a decisive internal cross-check) is appropriate. The reader's CONDITIONAL verdict is therefore unchanged.","tokens_in":12493,"tokens_out":10119,"duration_ms":97936,"concrete_test":"Using the already-normalized ESR data at B/Bc = 0.3, 0.5, and 1.2, compute A(B,T)/xi_eq7(B) at fixed temperature without any per-curve vertical rescaling. If Eq. (14) is correct, the three curves must coincide at each T within the stated 10% uncertainty. If they are offset by a B-dependent factor, then dR/dxi retains B dependence, and the quantity extracted by Eq. (7) is xi(B)h(B)/h(B1), not xi(B). Alternatively, measure the actual spin polarization on the same sample (e.g., torque magnetometry or NMR Knight shift) and compare directly with Eq. (7).","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central result Eq. (7) is derived from Supplementary Eq. (14), which asserts dR/dxi(B,T)=dR/dxi(T). The experimental evidence cited for Eq. (14) is the near-identical temperature dependence of A/xi at B/Bc = 0.3, 0.5, and 1.2 (Fig. 2a). This observation, however, only establishes that A/xi factorizes into a product of a B-dependent and a T-dependent function. Since A ∝ xi dR/dxi, factorization is equally compatible with dR/dxi(B,T)=h(B)k(T) for any h(B); it does not force h(B)=const. The self-consistent replacement of the initial xi(B)=B/Bc by the reconstructed xi from Eq. (7) cannot resolve this degeneracy, because any factorized form survives the rescaling. If h(B) is not constant, integrating R(B,T)-R0(T)=xi(B)h(B)k(T) yields Eq. (7) only with xi replaced by xi(B)h(B)/h(B1). The comparison of A with the reconstructed xi in Fig. 1f is also insensitive to this ambiguity: A ∝ xi(B)h(B)k(T) is proportional to the contaminated quantity xi_eq7(B) times a constant. Additionally, the reference resistance R1 is taken at B1≈1.2Bc, where the paper itself notes orbital magnetoresistance contributes to R; this adds a non-spin term to the denominator of Eq. (7) and shifts the polarization scale. A direct, independent polarization measurement (or an absolute comparison of A/xi across fields) is required before Eq. (7) can be called parameter-free.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper claims to establish a parameter-free relation between the longitudinal resistance of a two-dimensional electron liquid and its spin polarization, given by Eq. (7): ξ(B) = [R(B,T) - R0(T)]/[R1(T) - R0(T)]. The relation is derived from a proposed field-independence of the spin sensitivity of the resistance, ∂R/∂ξ (Supplementary Eq. 14), which is inferred from the collapse of the temperature dependence of the ESR amplitude normalized by the spin polarization at three magnetic fields. The authors validate Eq. (7) by comparing the reconstructed polarization with the measured ESR amplitude and by demonstrating a temperature-independent collapse of the reconstructed ξ in Fig. 2b. They then fit the field dependence to an empirical universal form Eq. (8) and construct a spin-polarization map over density and magnetic field. The central claim is that magnetotransport alone can quantitatively determine the spin polarization of strongly correlated 2D electron systems.","tokens_in":12831,"tokens_out":5242,"duration_ms":47889,"significance":"If Eq. (7) is valid, the paper delivers a simple, transport-only probe of the magnetic state of strongly correlated two-dimensional electron systems, which would be of wide interest in condensed-matter physics. The experimental effort is substantial: broadband electrically detected ESR over four densities, careful intensity normalization, and a self-consistent reconstruction scheme. The paper also makes an explicit, falsifiable prediction (Eq. 8) and tests it against published data, though the latter is not documented in the manuscript. However, the significance is conditional on the validity of the central assumption and on the independence of the ESR calibration; both are currently subject to serious underdetermination. The strengths are the clear presentation of the experimental protocol and the honesty in labelling Supplementary Eq. (14) as the central assumption.","major_comments":[{"comment":"The inference of Supplementary Eq. (14), ∂R/∂ξ(B,T) = ∂R/∂ξ(T), from the collapse of A/ξ is logically insufficient. The observed near-identical temperature dependences at B/Bc = 0.3, 0.5, and 1.2 establish only the factorization A/ξ = f1(B)f2(T) (Supplementary Eq. 13), and the claim that f1(B) = 1 is not tested at intermediate fields. Since A ∝ ξ ∂R/∂ξ, the data are equally compatible with ∂R/∂ξ = h(B)k(T) for arbitrary h(B) as long as h(B) is the same at the three sampled fields. Under that alternative, integrating Eq. (5) gives (R - R0)/(R1 - R0) = ξ(B)h(B)/h(B1), so Eq. (7) does not measure the true polarization unless h(B) is constant over the whole field range. The self-consistent replacement of the initial ξ = B/Bc by the reconstructed ξ does not resolve this degeneracy, because the factorized form survives the rescaling. This is the load-bearing point: Eq. (7) is derived from Eq. (14), and the derivation as presented does not exclude the h(B) contamination.","section":"Supplementary Eq. (14) and Fig. 2a"},{"comment":"The claimed independent calibration of the spin state by ESR is not fully independent. Supplementary Eq. (10), A(B) ∝ ξ(B), is taken from previous work of the same group (refs. 23 and 38), not established here. Consequently, the validation in Fig. 1f, which compares the ESR amplitude with the reconstructed ξ, is sensitive only to the product ξ(B)h(B) that also enters Eq. (7) under the factorized alternative, and cannot distinguish ξ(B) from ξ(B)h(B)/h(B1). The agreement between A and the reconstructed ξ is therefore a consistency check, not an independent calibration of the polarization scale. An absolute calibration of the ESR amplitude against a known spin system, or an independent measurement of ξ (e.g., capacitance or NMR), is required to fix h(B).","section":"Supplementary Eq. (10) and Fig. 1f"},{"comment":"The reference resistance R1 in Eq. (7) is measured at B1 ≈ 1.2Bc, a field where the paper itself reports orbital magnetoresistance: Fig. 1d shows a suppression of the ESR amplitude above Bc, and the text attributes values of ξ formally exceeding unity to 'additional orbital magnetoresistance that lies outside the spin-only description'. The denominator R1 - R0 therefore contains a non-spin contribution, shifting the polarization scale. The low-field estimate of ∂R/∂ξ shown as the black curve in Fig. 2a, using R(0.2Bc) - R(0), is not the same quantity used in Eq. (7); the two definitions are consistent only if orbital effects are negligible at B1, which the paper's own discussion contradicts. This is a quantitative issue for the 'parameter-free' claim, not merely a cosmetic choice of B1.","section":"Eq. (7), R1 at B1 ≈ 1.2Bc"},{"comment":"The claim that Eq. (8) 'universally describes' the spin polarization reconstructed from published magnetotransport data for Si MOSFETs, SiGe/Si, AlAs/AlGaAs, ZnO/MgZnO, MoTe2, and MoSe2 is not substantiated in the manuscript. No data, fits, or fit parameters for the other material systems are shown, so the reader cannot assess the universality claim. Moreover, the phase map in Fig. 3 is constructed using Eq. (8) with the best-fit parameters a ≈ 2.2 and k ≈ 2.4 from the present ZnO samples, not directly from Eq. (7). Thus the final map depends on an empirical two-parameter fit and on an undocumented generalization to other materials, which weakens the claim that the spin polarization can be obtained from transport alone without adjustable parameters.","section":"Eq. (8) and Fig. 3"}],"minor_comments":[{"comment":"The phrase 'Land´ egfactor' in the line following Eq. (2) should read 'Landé g-factor'.","section":"Eq. (2)"},{"comment":"The sentence 'the equilibrium spin polarization effectively temperature independent' is missing the verb 'is'.","section":"Main text, page 2"},{"comment":"The notation for the normalized magnetic field is inconsistent: B||/Bc appears in the text, while the caption of Fig. 2 uses 'B ∥ = 0.5Bc' without the division by Bc. Please standardize the notation.","section":"Fig. 2 caption and text"},{"comment":"The black curve is described as showing ΔR ∝ Rxx(0.2Bc, T) - Rxx(0, T), but the text does not explicitly state that this quantity is proportional to ∂R/∂ξ under the low-field approximation and the linear-response assumption; adding that clarification would help the reader.","section":"Fig. 2a"},{"comment":"The stated measurement error of approximately 10% in the integrated ESR amplitude is not shown as error bars in the figures, which makes the claimed collapse at the three fields more difficult to assess quantitatively.","section":"Figs. 1f and 2a"},{"comment":"Reference [5] is an arXiv preprint; if it has been published or updated, please provide the journal reference. Please also check for consistency of reference formatting throughout.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The paper's central claim is interesting and potentially important, but the current evidence does not exclude the factorized alternative ∂R/∂ξ = h(B)k(T), which would invalidate Eq. (7) as a measure of the true polarization. The reliance on same-group prior work for the key proportionality A ∝ ξ (Supplementary Eq. 10) is a concern for the claimed independence of the calibration, though it is not a reason to question scientific integrity. The manuscript would be strengthened by an absolute calibration of the ESR amplitude or an independent determination of ξ at one or more fields, and by a quantitative estimate of the orbital contribution at B1."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Read this one if you care about whether magnetoresistance can be turned into a quantitative spin-polarization probe. The punchline: Eq. (7) is a nice empirical relation, but the paper's 'parameter-free' claim is not nailed down. The collapse of A/xi at three fields (Fig. 2a) establishes that the normalized ESR amplitude factorizes into field and temperature parts; it does not establish Eq. (14), that dR/dxi is independent of field. The supplementary even writes the factorization (Supp. Eq. 13) and then asserts f1(B)=1. That assertion is the load-bearing step, and the data shown don't force it. If dR/dxi = h(B)k(T), integrating gives an Eq. (7) where the right side is not xi but a field-distorted version of it. The comparison with A in Fig. 1f cannot see this, because A is proportional to the contaminated quantity as well.\n\nCredit where it's due: this is a careful experiment. Four densities, broad ESR frequency range, and the exclusion of bolometric detection at the metal–insulator transition (B = 0.5Bc, where dR/dT = 0) is genuinely clever. The supplementary is honest enough to name Eq. (14) as 'the central assumption.' The data in Fig. 2b showing a temperature collapse of Eq. (7) is a good internal consistency check.\n\nSoft spots beyond the main one. R1 is measured at 1.2Bc, where the paper itself says orbital magnetoresistance is already present; that puts a non-spin term in the denominator of Eq. (7) and shifts the polarization scale. It might be a few percent, but it isn't estimated. Eq. (8) is a two-parameter fit presented as universal across Si, SiGe, AlAs, ZnO, MoTe2, and MoSe2 without showing any of those comparisons. As written, that's a placeholder, not evidence.\n\nBottom line: if Eq. (14) were established by an external polarization measurement—one that doesn't assume A ∝ xi—the paper would be a solid methodological advance. As is, it's a well-executed experimental study with a central inference that is underdetermined. That's a major-revision situation, not a desk reject. It deserves a serious referee who understands both ESR and magnetotransport. I would not cite the parameter-free claim; I might cite the data and the empirical Eq. (8) once they appear in a stronger form.","headline":"Careful experiment, but the 'parameter-free' polarization relation rests on an underdetermined assumption; deserves serious review, not the claim as stated.","tokens_in":13418,"tokens_out":2939,"would_cite":false,"duration_ms":29301,"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":"Longitudinal resistance itself provides a direct, parameter-free measure of spin polarization in a strongly correlated two-dimensional electron liquid.","keywords":["spin polarization","two-dimensional electron liquid","longitudinal resistance","electrically detected electron spin resonance","ZnO/MgZnO heterostructures","interacting electron system","parallel magnetic field"],"falsifier":"Measure, on a single sample at fields where orbital magnetoresistance is negligible, both the longitudinal resistance and an independent spin polarization - for example the integrated ESR absorption intensity - over a range of temperatures and fields. If the quotient $[R(B,T)-R_0(T)]/[R_1(T)-R_0(T)]$ does not track the independently measured $\\xi(B,T)$, Eq. (7) is falsified; a second check is that the normalized ESR amplitude $A/\\xi$ would show different temperature dependences at two such fields if the central field-independence assumption fails.","tokens_in":12268,"feed_emoji":"🧲","tokens_out":15462,"duration_ms":125126,"temperature":0.7,"pith_summary":"The paper sets out to show that the longitudinal resistance of a strongly correlated two-dimensional electron liquid is itself a quantitative measure of its spin polarization. The central object is Eq. (7), the parameter-free quotient $\\xi(B) = [R(B,T)-R_0(T)]/[R_1(T)-R_0(T)]$, which turns a magnetoresistance curve into a polarization curve. The authors validate this relation with electrically detected electron spin resonance, whose integrated amplitude is proportional to $\\xi$ times the spin sensitivity of the resistance and therefore serves as an independent calibration of the magnetic state. Once validated, the relation means that conventional transport measurements alone can map the electron liquid's evolution from a partially polarized paramagnetic Fermi liquid to a fully spin-polarized one across densities and fields. This matters because spin polarization is otherwise hard to access directly, and a transport-only probe makes the magnetic state of interacting two-dimensional systems routinely measurable.","feed_headline":"Resistance ratio maps electron spin polarization directly","feed_subtitle":"A parameter-free quotient of longitudinal resistance, calibrated by ESR, turns transport into a spin-polarization probe.","key_machinery":"The load-bearing identity is Eq. (7), the resistance quotient $\\xi(B) = (R(B,T)-R_0(T))/(R_1(T)-R_0(T))$, obtained by integrating the spin sensitivity $\\partial R/\\partial \\xi$ across polarization under the assumption that this sensitivity is field-independent and depends only on temperature. The complementary experimental machinery is electrically detected electron spin resonance with an intensity-normalization and background-subtraction protocol, yielding the integrated ESR amplitude $A(B,T) \\propto I \\, \\xi(B) \\, \\partial R/\\partial \\xi(T)$. The observed collapse of $A/\\xi$ onto a single temperature curve at several fields is what licenses the field-independence assumption. A second compact object is the empirical relation $\\xi(B,n) = 1 - \\exp[-a (B/B_c(n))^k]$, which parameterizes the reconstructed polarization and is shown to fit published magnetoresistance data across multiple material families.","core_discovery":"Equation (7) is the central discovery: $\\xi(B) = [R(B,T)-R_0(T)]/[R_1(T)-R_0(T)]$, a direct, parameter-free relation between longitudinal resistance and equilibrium spin polarization. The derivation integrates the spin sensitivity $\\partial R/\\partial \\xi$ from the unpolarized state to full polarization, using the experimentally observed factorization that $\\partial R/\\partial \\xi$ depends on temperature but not on magnetic field. The paper validates the relation by comparing the polarization reconstructed from transport against the independently measured electrically detected ESR amplitude, obtaining quantitative agreement over two orders of magnitude of signal where orbital effects are weak. It also reports that the reconstructed polarization follows $\\xi(B) = 1 - \\exp[-a (B/B_c)^k]$ with $a \\simeq 2.2$ and $k \\simeq 2.4$ for the ZnO/MgZnO samples, and that the same formula describes published magnetotransport data from Si MOSFETs, SiGe/Si, AlAs/AlGaAs, MoTe2, and MoSe2. The strongly nonlinear field dependence is the paper's evidence that electron-electron interactions, not a non-interacting Fermi-gas redistribution, govern the magnetic response.","pith_inferences":["A natural extension is to use the same resistance quotient as a model-free spin-polarization probe in van der Waals heterostructures, where electron spin resonance is difficult; if Eq. (7) is generic, it would remove the main obstacle to spin-state mapping in those materials.","The universal form of Eq. (8) suggests that the parameters $a$ and $k$ encode the interaction strength; a quantitative theory connecting them to $r_s$ or the enhanced spin susceptibility would turn the empirical fit into a measurement of interaction effects.","Since $R_1$ is read at about $1.2B_c$ where orbital magnetoresistance is already present, a field-dependent correction for the orbital background could sharpen the reconstructed polarization near saturation and extend the method to higher fields."],"forward_implications":["Spin polarization can be extracted from ordinary longitudinal resistance measurements with no adjustable parameters, making the magnetic state of a two-dimensional electron liquid accessible to any lab with magnetotransport capability.","The reconstructed polarization quantitatively accounts for the field and temperature dependence of the electrically detected ESR signal, confirming that in this regime the ESR response is governed by spin polarization rather than resonant heating.","The spin polarization rises nonlinearly with magnetic field and is captured by $\\xi(B)=1-\\exp[-a(B/B_c)^k]$; the same functional form fits published data from several semiconductor and van der Waals systems, suggesting a common interaction-driven response.","The apparent temperature dependence of the magnetoresistance is fully absorbed by $R_0(T)$, $R_1(T)$, and the spin sensitivity, while $\\xi(B)$ itself is temperature independent in the studied regime, as shown by the collapse of polarization curves at different temperatures.","Deviations above $B_c$ identify orbital magnetoresistance from the finite layer thickness, with a strength that grows with electron density, so the spin-only relation cleanly separates spin and orbital contributions at lower fields."],"supporting_citations":[{"why":"Provides the Bc kink criterion in magnetotransport and the MoTe2 data that Eq. (8) is shown to describe.","marker":"[5]"},{"why":"Supplies the non-interacting Fermi-gas polarization xi = B/Bc and the critical-field definition used as the reference baseline.","marker":"[6]"},{"why":"Establishes the electrically detected ESR detection scheme and the proportionality of ESR amplitude to spin polarization used for calibration.","marker":"[23]"},{"why":"Supplies the intensity-normalization and background-subtraction protocol that makes ESR amplitudes quantitatively comparable.","marker":"[37]"},{"why":"Documents the A proportional to xi scaling in strongly correlated two-dimensional systems underlying Eq. (3).","marker":"[38]"},{"why":"Gives the kink criterion for locating Bc from the parallel-field magnetoresistance.","marker":"[41]"},{"why":"Identifies the metal-insulator transition where dR/dT = 0, the key control experiment that excludes resonant heating.","marker":"[44]"},{"why":"Provides SiGe/Si magnetotransport data that Eq. (8) is shown to describe.","marker":"[45]"},{"why":"Provides AlAs/AlGaAs magnetotransport data that Eq. (8) is shown to describe.","marker":"[46]"},{"why":"Provides MoSe2 magnetotransport data that Eq. (8) is shown to describe.","marker":"[47]"}],"fun_headline_variants":["Resistance alone reveals electron spin polarization","Spin polarization quantified by magnetotransport alone","ESR-calibrated resistance measures spin polarization","Parameter-free resistance quotient maps spin polarization"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing assumption is that the resistance response per unit change in spin polarization does not depend on magnetic field, only on temperature, so the same sensitivity factor $\\partial R/\\partial \\xi$ works at every field.","fun_headline_variants_meta":{"raw":{"variants":["Resistance alone reveals electron spin polarization","Spin polarization quantified by magnetotransport alone","ESR-calibrated resistance measures spin polarization","Parameter-free resistance quotient maps spin polarization"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000662,"raw_usage":{"total_tokens":2985,"prompt_tokens":867,"completion_tokens":2118,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":483,"completion_tokens_details":{"reasoning_tokens":2064}},"tokens_in":483,"tokens_out":2118,"duration_ms":18184,"temperature":1.0,"reasoning_tokens":2064,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T04:14:14.018118+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure, on a single sample at fields where orbital magnetoresistance is negligible, both the longitudinal resistance and an independent spin polarization - for example the integrated ESR absorption intensity - over a range of temperatures and fields. If the quotient $[R(B,T)-R_0(T)]/[R_1(T)-R_0(T)]$ does not track the independently measured $\\xi(B,T)$, Eq. (7) is falsified; a second check is that the normalized ESR amplitude $A/\\xi$ would show different temperature dependences at two such fields if the central field-independence assumption fails.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the non-interacting Fermi-gas polarization xi = B/Bc and the critical-field definition used as the reference baseline."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Establishes the electrically detected ESR detection scheme and the proportionality of ESR amplitude to spin polarization used for calibration."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the intensity-normalization and background-subtraction protocol that makes ESR amplitudes quantitatively comparable."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Gives the kink criterion for locating Bc from the parallel-field magnetoresistance."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Identifies the metal-insulator transition where dR/dT = 0, the key control experiment that excludes resonant heating."},{"cited_title":"Okamoto, M","cited_arxiv_id":null,"evidence_quote":"Provides SiGe/Si magnetotransport data that Eq. (8) is shown to describe."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides AlAs/AlGaAs magnetotransport data that Eq. (8) is shown to describe."},{"cited_title":"Larentis, H","cited_arxiv_id":null,"evidence_quote":"Provides MoSe2 magnetotransport data that Eq. (8) is shown to describe."}],"review_version":1}