{"id":"737ed572-1293-4772-b4fd-539d86626940","arxiv_id":"2412.19247","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"Nonlinear SMR in YIG/Pt reveals that interfacial spin-flip scattering is dominated by subthermal magnons, making the spin conductance gs strongly field- and thickness-dependent, with an inferred 30x enhancement at 10 nm YIG.","lead":"Measurements of harmonic Hall response in YIG/Pt bilayers show that the spin-flip scattering efficiency at the interface, gs, depends strongly on magnetic field and YIG thickness. The authors attribute this to deep subthermal magnons dominating spin-flip scattering at room temperature, and report about a 30-fold increase in gs when the YIG thickness is reduced from 100 to 10 nm.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central field-suppression claim depends on subtracting SSE and FL backgrounds from the 2nd-harmonic Hall signal using assumed field dependences; a mis-specified SSE(B) could create the apparent subthermal-magnon decay.","rationale":"The reader's weakest assumption correctly identifies the harmonic-Hall decomposition as the most fragile step. The central claims that spin-flip scattering is dominated by subthermal magnons and that g_s is exponentially suppressed by field rest on the field dependence of R_xy,SMR^{2ω} extracted from Eq. (3). Since the angular basis in Eq. (3) has two independent coefficients but three contributions, the result is only as good as the assumed field dependences of R_xy,FL^{2ω} and R_xy,SSE^{2ω}. The FL dependence is supported by the extracted Oersted field (0.22 mT vs 0.25 mT expected), but the SSE dependence is delegated to the missing Supplemental Material. The longitudinal R_xx^{2ω} analysis is also cited as consistent but not available for checking. Therefore, the conditional verdict is appropriate: the qualitative thickness trend is likely robust, but the quantitative field-suppression exponent and the factor-30 g_s enhancement cannot be fully accepted until the decomposition is validated against direct SSE measurements or the supplemental data are provided. This aligns with the reader's assessment, so no change to the verdict is needed.","tokens_in":10674,"tokens_out":18880,"duration_ms":197320,"concrete_test":"Re-fit the raw R_xy^{2ω}(φ,B) scans for the 10-nm YIG film at I=4 mA using Eq. (3) under alternative, defensible priors for the SSE background: (i) R_xy,SSE^{2ω} = constant, (ii) R_xy,SSE^{2ω} ∝ 1/B, and (iii) R_xy,SSE^{2ω}(B) taken from direct SSE measurements on a reference stack where the magnon-creation SMR^{2ω} is negligible (e.g., 100-nm YIG at high field), while keeping R_xy,FL^{2ω} ∝ 1/B. If the resulting R_xy,SMR^{2ω}(B) no longer exhibits a clear power-law decay with an exponent within ~0.15 of the reported γ, or if it no longer becomes negligible at 400 mT, the field-suppression and subthermal-magnon conclusions are artifacts of the SSE(B) model. If the extracted R_xy,SMR^{2ω}(B) is stable under all three priors, the decomposition is validated.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Eq. (3) decomposes R_xy^{2ω}(φ) into cosφ and cos^3φ terms, but contains three unknowns: R_xy,SMR^{2ω}, R_xy,FL^{2ω}, and R_xy,SSE^{2ω}. The extraction of R_xy,SMR^{2ω}(B) is therefore underdetermined unless R_xy,FL^{2ω}(B) ∝ 1/B and R_xy,SSE^{2ω}(B) is modeled, here as following R_xy,SMR^{1ω}(B). The headline observations—that R_xy,SMR^{2ω} vanishes by 400 mT and that ΔM/M_s follows B^{-γ} with γ≈0.70–0.83—are exactly the residual field dependence left after these two subtractions. If the true SSE^{2ω}(B) has a different form (for example ∝1/B or a different power law), the extracted R_xy,SMR^{2ω}(B) could be a fitting artifact rather than a magnon-generation signal. The paper states that field-dependent SSE is 'further confirmed by independent measurements' and that the longitudinal R_xx^{2ω} analysis gives consistent results, but both checks are deferred to the Supplemental Material, which is not included in the arXiv version. This is the most load-bearing assumption because it underlies both the 'subthermal magnons' interpretation and the empirical B^{-γ} law from which g_s(B) is inferred. Note also that B^{-γ} is a power law, not an exponential decay as stated in the abstract.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript reports harmonic Hall measurements on Pt/YIG bilayers with YIG thickness 10-100 nm and interprets the second-harmonic transverse response as arising from magnon creation/annihilation processes, parametrized by the interfacial spin conductance g_s. The authors claim that decreasing the YIG thickness from 100 to 10 nm increases g_s by a factor ~30 and that the magnon generation efficiency is exponentially (actually power-law B^{-\\gamma}) suppressed with magnetic field, which they attribute to the dominant role of deep subthermal magnons at room temperature. They also report that the critical current for damping compensation is reached in 10-nm continuous YIG films and increases roughly linearly with field up to ~40 mT. The central modeling elements are: (i) decomposition of the 2nd-harmonic Hall signal into SMR, field-like torque (1/B), and SSE components via angular dependence of Eq. (3); (ii) extraction of Delta M/M_s = R_xy,SMR^2w/(2 R_xy,SMR^1w); (iii) a relaxation-time model leading to Eq. (4) for Delta M/M_s(I) with critical current I_c; and (iv) a scaling argument Eq. (5) attributing the thickness dependence of Delta M to the ratio S_12 ≈ g_{s,1}/g_{s,2}, assuming kappa and n0 are thickness-independent.","tokens_in":11020,"tokens_out":4097,"duration_ms":34262,"significance":"If the main claims hold, the work would establish that the interfacial spin-flip conductance in YIG/Pt is not a thermal-equilibrium constant but is strongly field- and thickness-dependent, with practical implications for spin-orbit-torque devices and magnon condensation in thin films. The paper also makes a falsifiable prediction-like statement: the field suppression exponent gamma increases with decreasing thickness and increasing current, consistent with trends in unidirectional spin Hall magnetoresistance. Strengths: the manuscript presents a relatively simple closed-form model for the current dependence (Eq. 4) that yields fits with physically sensible critical currents, an independent check via the longitudinal 2nd harmonic is mentioned (though deferred to Supplemental Material), and the Oersted-field consistency check for the field-like torque (B_FL = 0.22±0.03 mT vs 0.25 mT) is a nice internal calibration. The significance is potentially high, but the load-bearing decomposition currently rests on assumptions deferred to the Supplemental Material, which is not included in the preprint.","major_comments":[{"comment":"The extraction of R_xy,SMR^2w(B) is underdetermined unless R_xy,FL^2w(B) ∝ 1/B and R_xy,SSE^2w(B) ∝ R_xy,SMR^1w(B) are assumed; the headline B^{-gamma} decay and the vanishing of R_xy,SMR^2w above ~400 mT are precisely the residual field dependences left after subtracting these modeled backgrounds. A mis-specification of the SSE(B) or FL(B) functional form could convert a background into the apparent subthermal-magnon signal. The manuscript states that the SSE form is \"further confirmed by independent measurements\" and that the longitudinal analysis gives consistent results, but both are deferred to the Supplemental Material and are not verifiable in this preprint. This is the most load-bearing assumption and needs to be either fully documented (data and fit residuals) in the main text or the key conclusions should be relaxed.","section":"Harmonic Hall measurements; Eq. (3) and Fig. 2"},{"comment":"The identification of the nonlinear SMR term with magnon creation/annihilation and the extraction of I_c from Delta M/M_s(I) fits assumes that the second-harmonic signal at the first harmonic frequency is entirely due to the current-induced change in the static magnetization M(I) = M_s + Delta M(I) sin(phi), with Delta M linear in I. However, Eq. (4) itself yields Delta M ∝ I/[1-(I/I_c)^2], i.e., a nonlinear-in-I magnetization change that then enters the SMR expression; the manuscript does not show that higher-order terms in the expansion of cos(phi) sin[phi + Delta M(I) sin(phi)] do not contribute to the 2nd-harmonic angular decomposition at the same order. The angular decomposition Eq. (3) is written for a generic second-harmonic response, but the mapping from Delta M/M_s in Fig. 3 to a current-dependent R_xy,SMR^2w via Eq. (2) assumes the second-harmonic SMR term is linear in the current-induced magnetization change; this should be stated explicitly and justified with the truncation order.","section":"Eqs. (2)-(4) and Fig. 3"},{"comment":"The claim that g_s increases by a factor ~30 when thickness decreases from 100 to 10 nm relies on the assumption that alpha*t and (1-kappa) n0 are approximately thickness-independent. The text gives arguments that kappa and n0 are weakly thickness-dependent, but the ratio S_12 is then entirely attributed to g_s; given that the extracted gamma and the empirical Delta R_xy,SMR^1w(B) are used to infer g_s(B) in the penultimate paragraph before Conclusions, the thickness dependence of g_s is not independently measured but inferred from the same nonlinear SMR data. This is internally consistent but should be flagged as a model-dependent rather than direct measurement, and the sensitivity of the factor-30 estimate to the assumed alpha*t, kappa, and n0 variations should be quantified.","section":"Modelling Delta M/M_s; Eq. (5)"},{"comment":"The abstract and several passages state that the magnetic field \"exponentially suppresses the magnon generation efficiency\", but the data are fitted to a power law B^{-gamma} with gamma ≈ 0.70-0.83 (Fig. 2a) and Delta M/M_s ∝ B^{-gamma} (Figs. 2b, 4). A power law is not an exponential decay; the terminology should be corrected consistently, or the functional form should be analyzed as an exponential (e.g., exp(-B/B0)) and shown to be inferior, before the current claim is stated.","section":"Abstract; Figs. 2-4"}],"minor_comments":[{"comment":"The blue line is described as a fit to B^{-gamma} with gamma = 1.00, but the text earlier states R_xy,FL^2w follows 1/B; using the same notation B^{-gamma} with gamma = 1.00 for the FL torque is fine but the caption should explicitly distinguish this from the extracted SMR gamma values.","section":"Fig. 2(a) caption"},{"comment":"The term \"exponential\" is also used for Delta R_xy,SMR^1w(B) of the form B^{-eta}; the authors should use \"power-law\" throughout.","section":"Penultimate paragraph before Conclusions"},{"comment":"Eq. (4) has no explicit proportionality constant or definition of the prefactor relating Delta M/M_s to n0 I/I_c; the text states \"proportional\" but the fits in Fig. 3(a) use an amplitude prefactor that is not specified. Adding the prefactor expression (e.g., in terms of g_s, alpha, and magnon density) would make the scaling argument in Eq. (5) more transparent.","section":"Eq. (4)"},{"comment":"The open symbols for B >= 100 mT are described as unreliable estimates because Delta M/M_s(I) is flat; these points appear to be included in the claim of a linear increase with field, which should be clarified or removed.","section":"Fig. 3(b)"},{"comment":"The GGG substrate formula is written as Ga5Gd3O12, which is likely a typo for Gd3Ga5O12.","section":"Samples preparation"},{"comment":"The companion work by Nöel et al. is mentioned as arXiv:2411.07991 but is not cited as a numbered reference; the reference numbering should be checked.","section":"Bibliography"},{"comment":"The Supplemental Material is referenced as [21] but is not included in the arXiv version; the authors should either include it as ancillary material or clearly state which key measurements are deferred.","section":"Supplemental Material reference [21]"},{"comment":"The estimate of the number of occupied magnon bands n = 1 + int(t/pi sqrt(k_B T_eff/(hbar gamma_m D))) uses a formula without derivation or reference; give a citation or derivation in the Supplemental Material.","section":"Magnon band occupation paragraph"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is potentially interesting, but the central field- and thickness-dependence of g_s is built on a 2nd-harmonic decomposition whose key validation (SSE field dependence, longitudinal consistency) is promised in the Supplemental Material, which is not provided in this preprint. As a referee for a journal that will receive the full version, I would expect the Supplemental Material to be included in the review package. The revision is major rather than reject because the experimental claims are specific and the model is testable; the authors need to make the decomposition assumptions falsifiable by showing residuals and independent checks. The power-law vs exponential terminology should also be fixed. I do not see evidence of a novelty or attribution problem, but the connection to the companion paper arXiv:2411.07991 should be clarified in the final version."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"First thing you should know: this is a real experimental effect. The 2nd-harmonic SMR in YIG/Pt grows by roughly two orders of magnitude when the YIG thickness drops from 100 to 10 nm, and it is strongly suppressed by fields of a few hundred mT. That is surprising and worth taking seriously. The paper's interpretation—that spin-flip scattering is dominated by deep subthermal magnons, making g_s a function of field and thickness—is plausible and consistent with earlier work on subthermal magnon transport.\n\nWhat is new: the thickness series itself and the explicit claim that g_s is enhanced by vertical confinement. The authors connect their data to a previous model (Eq. 4) and provide a scaling relation (Eq. 5) to isolate the g_s contribution. The harmonic measurements look careful: they fit the angular dependence, check the FL torque against the Oersted field, and cite consistent longitudinal analysis. The paper is honest about what is assumed.\n\nWhere it gets soft: the extraction of R_xy,SMR^2ω(B) depends on subtracting SSE and FL contributions using assumed field dependences—SSE following R_SMR^1ω(B) and FL following 1/B. If the SSE's true field dependence is different, the apparent power-law suppression of the magnon signal could be an artifact. The stress-test note is correct that the headline 'exponential suppression' is actually a power law B^{-γ} (γ≈0.7–0.83), and the abstract's wording is sloppy. The key supporting analyses (field-dependent SSE measurements, longitudinal cross-check, ΔR_SMR^1ω(B) analysis) are all deferred to a Supplemental Material not included in the arXiv version. That makes it impossible to fully verify the central quantitative claim from the preprint alone. The factor-30 increase in g_s also assumes α*t is roughly constant and that κ and n0 do not vary with thickness; the paper argues for this but again the details are in the supplement.\n\nIs the central observation broken? No. The raw data show a large, field-dependent, thickness-dependent 2nd-harmonic SMR. But the quantitative conclusions—factor 30, exponential g_s(B)—are model-dependent and not independently verified here. The gamma exponent is fitted, not predicted, and the g_s(B) attribution is a consistency argument, not a direct measurement.\n\nBottom line: this deserves a serious referee. The experimental trend is likely real and important for the magnonics community. The referee should insist on seeing the Supplemental Material and a frank discussion of the SSE subtraction. I would cite the raw trend in my own work, but hesitate to cite the factor-30 number until it survives review. For a reading group, it's a good paper to discuss because the gap between the data and the interpretation is instructive.","headline":"A clear and reproducible experimental trend—huge thickness- and field-dependent 2nd-harmonic SMR in YIG/Pt—but the quantitative claims (factor 30, exponential field suppression) rest on a decomposition whose assumptions are deferred to the Supplemental Material.","tokens_in":11561,"tokens_out":1792,"would_cite":true,"duration_ms":17223,"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":"The interfacial spin conductance of YIG/Pt is not a constant: subthermal magnons make it a strong function of magnetic field and film thickness.","keywords":["spin conductance","subthermal magnons","harmonic Hall magnetoresistance","magnon creation and annihilation","YIG/Pt interfaces","vertical confinement","damping compensation","spin Hall magnetoresistance"],"falsifier":"Measure $\\Delta$ M/M_s in the same YIG/Pt films using an independent probe that does not require the spin Seebeck and field-like torque subtraction, for example nonlocal magnon transport or spin-torque ferromagnetic resonance, and compare its field and thickness dependence with the harmonic-Hall g_s(B,t). Alternatively, repeat the harmonic-Hall measurement with the Pt layer on a nonmagnetic control film such as GGG/Pt to characterize the spin Seebeck and Oersted-field baselines directly; if the extracted magnon signal does not vanish in a geometry where no magnons exist, the exponential field dependence is called into question.","tokens_in":10409,"feed_emoji":"🧲","tokens_out":6047,"duration_ms":59173,"temperature":0.7,"pith_summary":"The paper argues that the interfacial spin conductance $g_s$ of YIG/Pt, usually treated as a constant set by thermal magnons, is instead dominated by deep subthermal magnons at room temperature and depends strongly on magnetic field and YIG thickness. It supports this with second-harmonic Hall measurements on YIG films from 10 to 100 nm thick: reducing thickness from 100 to 10 nm raises the extracted spin-flip efficiency by a factor of about 30, and the magnon generation efficiency falls exponentially with field. If correct, this changes how electrically driven magnon generation is modeled and suggests that thin-film confinement can substantially lower the current needed for damping compensation and magnon condensation.","feed_headline":"YIG/Pt spin-flip efficiency jumps 30-fold when YIG thins to 10 nm","feed_subtitle":"Second-harmonic Hall data tie spin conductance to deep subthermal magnons, so thin films amplify magnon generation.","key_machinery":"The central object is the spin conductance $g_s$, which sets the interfacial efficiency of spin-flip scattering. The measurement machinery is the angular dependence of the second-harmonic Hall resistance $R_{xy}^{2\\omega}(\\phi)$, decomposed into spin Hall magnetoresistance, field-like torque, and spin Seebeck contributions with distinct field dependences, leaving $R_{xy,\\mathrm{SMR}}^{2\\omega}$ as the magnon-creation signal. The model for the magnon spectral density $n(\\omega,I)=n_0/(1-I/I_c)$ connects $\\Delta M/M_s$ to $I/I_c$, where $I_c$ is the critical current for damping compensation. Thickness enters through a factor $g_s/t$ and through vertical confinement: for subthermal magnons the number of occupied bands $n = 1 + \\mathrm{int}\\left(\\frac{t}{\\pi}\\sqrt{\\frac{k_B T_{\\mathrm{eff}}}{\\hbar \\gamma_m D}}\\right)$ drops to a few, with the three-dimensional-to-two-dimensional crossover length $\\lambda_{T_{\\mathrm{eff}}} \\sim 10\\,\\mathrm{nm}$ for $T_{\\mathrm{eff}} \\sim 10\\,\\mathrm{K}$.","core_discovery":"On the authors' terms, the central discovery is that current-driven spin-flip scattering at the YIG/Pt interface is not governed by the thermal magnon bath but by a small population of deep subthermal magnons (GHz frequencies, effective temperatures of order Kelvin) whose occupation is easily altered by field and confinement. The extracted spin conductance $g_s(B,t)$ therefore becomes a tunable quantity: magnetic field exponentially suppresses it, and reducing YIG thickness from 100 nm to 10 nm increases it by roughly a factor 30. The authors attribute the thickness dependence to vertical confinement, which leaves only a few occupied magnon bands in films thinner than about 10 nm; their estimates relate the transition to the subthermal magnon wavelength. They further report that in 10 nm films the critical current for damping compensation is reached in continuous films, and that the field dependence of $g_s$ tracks the field dependence of the transverse magnetization fluctuations $\\langle M_\\perp^2 \\rangle$ inferred from the first-harmonic spin Hall magnetoresistance.","pith_inferences":["If the confinement picture is right, $g_s$ could be tuned by engineering the magnon band bottom (strain, anisotropy, or thickness) rather than only by interface quality, because shifting the band edge changes the number of occupied subthermal bands and hence the net spin-flip efficiency.","The model implies a specific temperature signature: cooling should alter the effective magnon temperature and the number of occupied bands, so $g_s(B,t)$ in ultrathin films should deviate from the usual thermal-magnon scaling; the paper does not report temperature dependence.","A decisive independent check would be comparing the field exponent $\\gamma$ from harmonic Hall with the field dependence of nonlocal magnon transport in identical films; the paper notes nonlocal signals scale as $g_s^2$ but does not perform this comparison."],"forward_implications":["Because nonlocal magnon transport signals depend on $g_s^2$, their measured amplitudes should show the same exponential field suppression and thickness enhancement as the harmonic-Hall data.","Damping compensation in continuous 10-nm YIG/Pt films occurs at accessible currents, so spin-orbit-torque nano-oscillators may not require patterned magnetic structures in this thickness range.","Magnon Bose-Einstein condensation thresholds should drop when the YIG thickness approaches the subthermal-magnon confinement length, making nanoscale condensate experiments realistic.","Models that treat $g_s$ as a thermal-only constant will overestimate magnon generation at high fields and underestimate it in thin films; $g_s(B,t)$ should be treated as a material parameter."],"supporting_citations":[{"why":"Introduces the nonlinear magnetoresistive response from magnon creation/annihilation that this paper extends to thickness- and field-dependent g_s.","marker":"[13]"},{"why":"Supplies the magnon chemical potential framework in which g_s is conventionally taken as a thermal-only constant.","marker":"[4]"},{"why":"Provides the YIG film growth and magnon diffusion length characterization used for the same sample family.","marker":"[10]"},{"why":"Gives the relation g_s proportional to the average squared transverse magnetization, used to connect field-dependent disorder to g_s(B).","marker":"[15]"},{"why":"Provides the spin-flip scattering rate and spectral-density model leading to the expression for Delta M/M_s.","marker":"[16,17]"},{"why":"Supplies the 1/B field dependence of field-like torques used to separate that contribution from the magnon signal.","marker":"[18]"},{"why":"Documents the field-dependent spin Seebeck baseline, Gilbert damping, and magnon band-occupation estimates that support the decomposition.","marker":"[21]"},{"why":"Reports exponential field dependence in unidirectional spin Hall magnetoresistance, used as a comparative trend for the measured exponent gamma.","marker":"[28]"}],"fun_headline_variants":["Subthermal magnons boost YIG/Pt spin-flip 30x at 10 nm","YIG/Pt spin conductance tunable: field and thickness control","Deep subthermal magnons dominate YIG/Pt spin-flip scattering","Thin YIG boosts spin-flip efficiency 30-fold via confinement","Vertical confinement magnifies magnon generation in YIG/Pt"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is the decomposition of the second-harmonic Hall signal: the spin Seebeck part is assumed to follow the same field dependence as the first-harmonic spin Hall magnetoresistance, and the field-like torque is assumed to fall as 1/B, so every remaining field dependence in the extracted magnon signal is assigned to g_s(B). If those two background contributions have different field dependences, the apparent exponential suppression of magnon generation could be an artifact.","fun_headline_variants_meta":{"raw":{"variants":["Subthermal magnons boost YIG/Pt spin-flip 30x at 10 nm","YIG/Pt spin conductance tunable: field and thickness control","Deep subthermal magnons dominate YIG/Pt spin-flip scattering","Thin YIG boosts spin-flip efficiency 30-fold via confinement","Vertical confinement magnifies magnon generation in YIG/Pt"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000219,"raw_usage":{"total_tokens":1450,"prompt_tokens":960,"completion_tokens":490,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":576,"completion_tokens_details":{"reasoning_tokens":392}},"tokens_in":576,"tokens_out":490,"duration_ms":4274,"temperature":1.0,"reasoning_tokens":392,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T00:48:07.399091+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure $\\Delta$ M/M_s in the same YIG/Pt films using an independent probe that does not require the spin Seebeck and field-like torque subtraction, for example nonlocal magnon transport or spin-torque ferromagnetic resonance, and compare its field and thickness dependence with the harmonic-Hall g_s(B,t). Alternatively, repeat the harmonic-Hall measurement with the Pt layer on a nonmagnetic control film such as GGG/Pt to characterize the spin Seebeck and Oersted-field baselines directly; if the extracted magnon signal does not vanish in a geometry where no magnons exist, the exponential field dependence is called into question.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the magnon chemical potential framework in which g_s is conventionally taken as a thermal-only constant."},{"cited_title":"Schlitz, S","cited_arxiv_id":null,"evidence_quote":"Provides the YIG film growth and magnon diffusion length characterization used for the same sample family."},{"cited_title":"Vélez, V","cited_arxiv_id":null,"evidence_quote":"Gives the relation g_s proportional to the average squared transverse magnetization, used to connect field-dependent disorder to g_s(B)."},{"cited_title":"Manchon, I","cited_arxiv_id":null,"evidence_quote":"Supplies the 1/B field dependence of field-like torques used to separate that contribution from the magnon signal."},{"cited_title":"The Supplementary Material includes Refs","cited_arxiv_id":null,"evidence_quote":"Documents the field-dependent spin Seebeck baseline, Gilbert damping, and magnon band-occupation estimates that support the decomposition."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Reports exponential field dependence in unidirectional spin Hall magnetoresistance, used as a comparative trend for the measured exponent gamma."}],"review_version":1}