{"id":"468a13a0-8a1e-4f6b-9688-9e107cc8983f","arxiv_id":"2608.06700","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"Magnetoresistance in four layered palladium metals follows a universal power-law scaling with residual resistivity ratio, with exponent 1.2 to 1.3, instead of the quadratic law of compensated semimetals.","lead":"The paper measures how the electrical resistance of four layered palladium compounds changes in a magnetic field, and finds all four follow the same simple power-law rule set by a single sample-quality number called the residual resistivity ratio. A smart generalist might care because it suggests large magnetoresistance is not restricted to specialized semimetals, which broadens the search for materials in magnetic sensors and high-mobility electronics.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"RRR-to-mobility mapping across compounds is not established; without carrier-density normalization, equal-RRR comparisons do not isolate mobility or spin-orbit scattering.","rationale":"The reader's weakest-assumption diagnosis is correct and is the most load-bearing issue in the paper. The empirical MR-RRR scaling may well be real, but the paper's physical interpretation depends on RRR being a direct proxy for carrier mobility across different materials. That identification is not justified, and the manuscript actually undermines it by attributing inter-compound RRR differences to band-structure and effective-mass effects. Because RRR mixes n and mu, the equal-RRR comparison in Fig. 5 does not cleanly isolate mobility, and the claimed suppression of MR in the noncentrosymmetric compound by SOC-induced scattering becomes an inference rather than a demonstrated result. The proposed Hall/quantum-oscillation measurement is a direct, feasible check that would settle whether the scaling survives when plotted against true mobility. This does not reject the paper's empirical findings or internal consistency; it instead identifies the specific missing measurement that separates an interesting empirical correlation from the claimed universal mobility-control mechanism. The reader's CONDITIONAL verdict remains appropriate, conditional on this test and on providing either a derivation or a quantitative fit of Eq. (3).","tokens_in":19900,"tokens_out":4336,"duration_ms":48832,"concrete_test":"Measure the low-field Hall coefficient and, where possible, use quantum-oscillation or DFT carrier counts to determine the total carrier density n for each compound, and record rho_300 for each crystal. Compute the transport mobility mu = 1/(n e rho_0) = RRR/(rho_300 n e) for every sample. Replot Fig. 5 as MR(2 K, 7 T) versus mu and refit MR = B' mu^{b'}. If b'_CS ~ b'_NCS and B'_CS > B'_NCS persist, the mobility interpretation survives. If the exponent changes or the CS/NCS ordering flips, the RRR-based scaling conflates carrier density and effective mass with mobility, and the SOC-scattering conclusion is unsupported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that MR at fixed field follows MR ~ (mu_ave H)^n with n ~ 1.2-1.3, and that centrosymmetric and noncentrosymmetric compounds differ only through a prefactor that reflects SOC-induced scattering. This rests on identifying RRR with mu_ave, stated in Section V as 'RRR is approximately proportional to mu_ave' and used to write Eq. (5), MR ~ (RRR x H)^n. In Drude theory, however, rho_0 = m*/(n e^2 tau), so RRR = rho_300/rho_0 = (rho_300 e^2) * n * mu, not mu itself. Within a single compound, n and rho_300 are fixed, so RRR is a valid mobility proxy; across PdTe2, PdPb2, beta-PdBi2, and alpha-PdBi, the paper itself argues that inter-compound RRR differences are set by effective mass and band dispersion, not by impurity content, and it provides no carrier densities or room-temperature resistivities. The asserted Eq. (3) is also not derived, so the step from a two-band expression to a clean power law with exponent 1.2-1.3 is unquantified. Consequently, the Fig. 5 CS/NCS prefactor separation could reflect differences in carrier density, effective mass, or compensation rather than SOC scattering channels.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript reports a magnetotransport study of four layered Pd-based metals (PdTe2, PdPb2, β-PdBi2, and α-PdBi), including an α-PdBi crystal with RRR≈660. The central empirical claims are: (i) MR follows a sub-quadratic power law in field, MR=A H^a with a≈1.2–1.3; (ii) MR at 2 K and 7 T follows a power law in RRR with a compatible exponent, separately for centrosymmetric and noncentrosymmetric compounds; (iii) high-RRR crystals satisfy Kohler scaling; and (iv) the centrosymmetric/noncentrosymmetric families differ only through the prefactor, which the authors attribute to extra scattering channels from spin-orbit-induced band splitting. The theoretical rationalization in Section V invokes an asserted two-band-type expression, Eq. (3), and uses RRR as a proxy for mobility.","tokens_in":20244,"tokens_out":6075,"duration_ms":59072,"significance":"The empirical portion is potentially valuable: it extends large-MR phenomenology beyond compensated semimetals, introduces a record-quality α-PdBi crystal, and provides a nontrivial internal consistency check in the agreement between field and RRR exponents. The Kohler collapse for high-RRR crystals, if quantified, would support an effective single-scattering-time description in a multiband metal. However, the two load-bearing interpretive steps are not yet established: Eq. (3) is asserted rather than derived, and the mapping between RRR and carrier mobility across different compounds is not supported by the data presented. Because these steps support the symmetry-based (CS vs NCS) conclusion, the manuscript requires revision before the universal-scaling interpretation can be accepted.","major_comments":[{"comment":"The expression MR ∼ (μ_ave H)^2 / [1 + (ΔN/N)^2 (μ_ave H)^2] is introduced without derivation, and it contains no variable representing the mobility distribution that the text invokes in the same paragraph. Since Eq. (3) is the only theoretical justification for the intermediate exponent in Eq. (4), please derive it from a specified multiband or two-band model, or replace it with a direct numerical evaluation; otherwise the claim that the observed exponent n≈1.2–1.3 is explained by imperfect compensation and mobility spread is unquantified and cannot be checked.","section":"Section V, Eq. (3)"},{"comment":"The identification of RRR with μ_ave across compounds is not justified. In a simple Drude picture, RRR ∝ ρ_300 n μ_ave (up to geometric factors), so Eq. (5) requires that n and ρ_300 be approximately constant among PdTe2, PdPb2, β-PdBi2, and α-PdBi. The manuscript itself states that inter-compound RRR differences are set by effective mass and band dispersion rather than impurity content (Section III and Section V), which makes this assumption non-trivial. Without Hall carrier densities and room-temperature resistivities for each compound, the equal-RRR comparison in Fig. 5 cannot separate the proposed SOC-induced scattering-channel effect from differences in carrier density, band mass, or compensation. Please supply the missing transport parameters or reframe the CS/NCS prefactor conclusion as a correlation.","section":"Section V, paragraph on RRR"},{"comment":"The robustness of the universal RRR exponent is not demonstrated. The centrosymmetric fit uses one crystal each of β-PdBi2, PdTe2, and PdPb2 (three points for a two-parameter fit), while the noncentrosymmetric fit uses only α-PdBi crystals; the quoted errors (b_CS=1.30±0.17, b_NCS=1.18±0.11) overlap, and no goodness-of-fit or confidence intervals are given. The claim that the scaling exponent is common across material families therefore rests on wide overlapping error bars rather than on a statistically meaningful test. Please add more crystals per compound or use a fitting procedure that pools data with stated uncertainties.","section":"Section IV.D, Fig. 5"},{"comment":"The Kohler-scaling claim is based on visual collapse of log-scale plots. Because this is central evidence for the single-scattering-time interpretation, please provide a quantitative collapse metric (e.g., residuals from a common curve or a normalized scatter measure) and state the temperature and field ranges over which the collapse holds. This is particularly important because β-PdBi2 is presented as a breakdown case and the high-RRR panels use different axis ranges.","section":"Section IV.C, Figs. 4(e)-(h)"}],"minor_comments":[{"comment":"The phrase 'electronic structuret' should be 'electronic structures'.","section":"Section I, third paragraph"},{"comment":"The panels display the fitted parameters A and a without explicit error bars, and the units of A are not stated; please add them.","section":"Section IV.B, Fig. 3(b)"},{"comment":"The caption says symbol colors correspond to each material, but the figure does not identify which color or symbol corresponds to which compound; please add a legend or explicit labels.","section":"Figure 5"},{"comment":"The quantity ΔN/N is described only as the 'degree of imbalance' between electron and hole carriers; please define it in terms of the carrier densities n_e and n_h.","section":"Section V, second paragraph"}],"recommendation":"major_revision","confidential_remarks":"The manuscript has solid empirical content and the scaling observation is worth publishing if the interpretation is appropriately constrained. The main revision risk is over-interpretation of the CS/NCS prefactor difference; if the authors cannot provide Hall carrier densities and room-temperature resistivities, they should soften the SOC-scattering conclusion. The theoretical Eq. (3) should either be derived or presented as a phenomenological interpolation with a clear statement that it is not quantitatively tested."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper's real value is the systematic four-crystal dataset and the demonstration that, within each compound, MR tracks RRR with a robust exponent around 1.2-1.3, while the cleanest crystals obey Kohler's rule. That is a genuinely useful empirical contribution. The record RRR of 660 in alpha-PdBi is a materials achievement, and the within-compound RRR series for alpha-PdBi cleanly separates disorder from band-structure effects. The match between the field exponent and the RRR exponent is a nontrivial consistency check, and the paper deserves credit for that. The soft spots are real but fixable. First, Eq. (3) is asserted without derivation. The two-band rationalization with imperfect compensation is plausible, but it is not quantitatively tested, so it reads as a retrofit rather than a prediction. Second, and more importantly, the paper's RRR-to-mobility mapping does not hold across compounds. RRR = rho_300/rho_0 is proportional to n*mu under Drude assumptions, not to mu alone. Since the paper itself attributes the inter-compound RRR baseline to effective mass and band dispersion, the equal-RRR comparison between centrosymmetric and noncentrosymmetric compounds does not cleanly isolate SOC-induced scattering channels. The prefactor separation in Fig. 5 could partly reflect carrier-density or compensation differences. Third, the entire symmetry argument rests on a single noncentrosymmetric compound, alpha-PdBi. A second NCS member would make the case much stronger. Fourth, there are no raw data or error bars for the Kohler collapse, and the 7 T range is short for claiming non-saturating power laws. None of this kills the central empirical result. The within-compound scaling and the Kohler collapse seem solid as far as I can tell. The universal cross-compound statement and the SOC-prefactor interpretation are plausible but under-supported. A serious referee should ask for a derivation or direct test of Eq. (3), a discussion of the carrier-density confound in the RRR scaling, and either more NCS compounds or a clear admission of the single-member limitation. Data availability should also be required. Who gets value from this paper: experimentalists working on layered metals and large-magnetoresistance phenomenology, and theorists who want to test semiclassical multi-mobility transport models. It deserves peer review, but it needs revision before the universal claim is taken as established.","headline":"Useful dataset and a plausible empirical scaling, but the symmetry-dependent prefactor claim is shakier than the paper lets on.","tokens_in":667,"tokens_out":1001,"would_cite":true,"duration_ms":31736,"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":"This paper shows that large magnetoresistance in carrier-rich, multiband Pd-based metals follows a universal power-law scaling in residual resistivity ratio, with exponent about 1.2–1.3 and a symmetry-dependent prefactor.","keywords":["magnetoresistance","Kohler's rule","residual resistivity ratio","multiband metal","mobility scaling","noncentrosymmetric","PdBi","PdTe2"],"falsifier":"Measure the Hall mobility directly on the same crystals used for the scaling and check whether $\\mu_{\\mathrm{ave}}$ is proportional to RRR across all four compounds; if it is not, $MR = B \\times RRR^{b}$ is an empirical correlation rather than a mobility scaling law.","tokens_in":19685,"feed_emoji":"🧲","tokens_out":12142,"duration_ms":108622,"temperature":0.7,"pith_summary":"Large magnetoresistance is usually associated with compensated semimetals with near-perfect electron-hole balance. This paper argues that a different, simpler mechanism controls magnetoresistance in four carrier-rich, multiband Pd-based metals (PdTe2, PdPb2, β-PdBi2, and noncentrosymmetric α-PdBi): once crystals are clean enough, the magnetoresistance ratio collapses onto a single power-law scaling in the residual resistivity ratio, $MR = B \\times RRR^{b}$ with $b \\approx 1.2$–$1.3$, and the same exponent governs the field dependence. High-RRR crystals obey Kohler's rule, implying one effective scattering time despite complex Fermi surfaces. The symmetry of the crystal does not change the scaling exponent; it only changes the prefactor, with centrosymmetric compounds outperforming noncentrosymmetric α-PdBi at equal RRR. If correct, this establishes a mobility-controlled regime of large magnetoresistance beyond the compensated-semimetal picture and makes sample purity a quantitative predictor of magnetoresponse.","feed_headline":"Large magnetoresistance in Pd metals obeys one mobility law","feed_subtitle":"Clean multiband crystals scale as MR = B × RRR^1.2–1.3; crystal symmetry sets the prefactor.","key_machinery":"The load-bearing object is the pair of power-law scalings $MR = A H^{a}$ and $MR = B \\times RRR^{b}$ with a shared exponent $a \\approx b \\approx 1.2$–$1.3$, together with Kohler's rule, the statement that $MR$ is a universal function of $H/\\rho^{*}$ when a single scattering time controls transport. The paper uses the semiclassical interpolation $MR \\sim (\\mu_{\\mathrm{ave}} H)^{2}/[1 + (\\Delta N/N)^{2}(\\mu_{\\mathrm{ave}} H)^{2}]$ to show how imperfect carrier compensation and a spread of band mobilities turn the ideal quadratic dependence into a sub-quadratic power law. The residual resistivity ratio plays the role of an experimental proxy for the average mobility $\\mu_{\\mathrm{ave}}$, so Eq. (2) becomes a mobility scaling law, and the separation of centrosymmetric and noncentrosymmetric compounds into two curves with the same exponent but different prefactors is what carries the symmetry argument.","core_discovery":"The central claim is that magnetoresistance in clean, carrier-rich, multiband metals can be governed by a single effective carrier mobility even when the Fermi surface consists of many electron and hole pockets. For the four Pd-based compounds studied, the magnetoresistance ratio measured at fixed field and temperature follows $MR = B \\times RRR^{b}$, with exponents $b \\approx 1.30 \\pm 0.17$ for centrosymmetric β-PdBi2, PdTe2, and PdPb2 and $b \\approx 1.18 \\pm 0.11$ for noncentrosymmetric α-PdBi. The field dependence has the same sub-quadratic exponent, $a \\approx 1.2$–$1.3$, and high-RRR crystals show a collapse of all temperature-dependent curves onto one Kohler plot, evidence for an effective single scattering time. The intermediate exponent is attributed to imperfect carrier compensation combined with a distribution of mobilities, captured by the interpolation formula $MR \\sim (\\mu_{\\mathrm{ave}} H)^{2}/[1 + (\\Delta N/N)^{2}(\\mu_{\\mathrm{ave}} H)^{2}]$. The paper's comparison at equal RRR isolates the role of inversion symmetry: α-PdBi reaches 1500% at 2 K and 7 T because of its record RRR ≈ 660, yet its MR is smaller than the centrosymmetric compounds at the same RRR, which the paper interprets as extra spin-orbit-induced scattering channels in the noncentrosymmetric system.","pith_inferences":["The paper does not directly measure the mobility distribution, so Hall and quantum-oscillation measurements on the same crystals would be a natural next test of whether the exponent tracks the compensation ratio $\\Delta N/N$.","If the same exponent appears in other clean layered multiband metals, RRR could become a screening metric for high-field magnetotransport that does not require detailed band-structure calculation.","The equal-RRR comparison implies a sharp, testable extrapolation: growing centrosymmetric PdTe2 or PdPb2 with RRR near 660 should yield MR several times larger than α-PdBi, a prediction the paper does not state explicitly."],"forward_implications":["In clean multiband metals, RRR can be used as a quantitative predictor of low-field magnetoresistance through $MR = B \\times RRR^{b}$, without invoking carrier compensation.","A field exponent near 1.2–1.3 becomes a diagnostic for imperfect compensation with a spread of mobilities, separating this regime from the quadratic response of ideal two-band compensated semimetals and from linear-MR mechanisms.","Kohler scaling can survive a complex multiband Fermi surface in the clean limit, so a breakdown of Kohler's rule in a multiband metal may signal insufficient purity rather than intrinsic multiband physics.","Comparing materials at equal RRR isolates the role of crystal symmetry: the larger centrosymmetric prefactor implies that breaking inversion symmetry costs mobility through spin-orbit-split scattering channels."],"supporting_citations":[{"why":"Supplies Kohler's rule, the single-scattering-time scaling law the paper tests and confirms in high-RRR crystals.","marker":"[64]"},{"why":"Establishes WTe2 as the prototypical compensated semimetal whose large non-saturating and quadratic magnetoresistance the paper contrasts.","marker":"[6]"},{"why":"Provides the precedent that magnetoresistance scales with crystal quality in WTe2, motivating the MR-RRR analysis.","marker":"[7]"},{"why":"Gives InBi as a compensated-semimetal counterpart with extremely large MR, used to frame the comparison beyond two-band behavior.","marker":"[63]"},{"why":"Shows a correlation between RRR and magnetoresistance in MgB2, supporting the RRR-as-mobility proxy in a clean multiband superconductor.","marker":"[61]"},{"why":"Demonstrates large anisotropic magnetoresistance in clean MgB2 thin films, another carrier-rich multiband system with mobility-controlled response.","marker":"[62]"},{"why":"Documents the first-principles band-structure method used to establish the complex multiband Fermi surfaces.","marker":"[60]"},{"why":"Provides the crystal-growth route for α-PdBi that yielded the record-RRR samples underlying the scaling data.","marker":"[28]"}],"fun_headline_variants":["One mobility law rules magnetoresistance in layered Pd metals","Universal MR scaling emerges in multiband Pd compounds","Pd-based metals defy simple models yet obey one MR law","Complex Fermi surfaces, simple MR scaling: Pd metals","Mobility sets magnetoresistance in clean multiband Pd metals"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The argument assumes that the residual resistivity ratio is a faithful proxy for the carrier mobility entering the magnetoresistance formulas, so that RRR differences between compounds reflect band-structure-dependent effective mass rather than material-specific impurity levels.","fun_headline_variants_meta":{"raw":{"variants":["One mobility law rules magnetoresistance in layered Pd metals","Universal MR scaling emerges in multiband Pd compounds","Pd-based metals defy simple models yet obey one MR law","Complex Fermi surfaces, simple MR scaling: Pd metals","Mobility sets magnetoresistance in clean multiband Pd metals"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000221,"raw_usage":{"total_tokens":1570,"prompt_tokens":1188,"completion_tokens":382,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":804,"completion_tokens_details":{"reasoning_tokens":301}},"tokens_in":804,"tokens_out":382,"duration_ms":4306,"temperature":1.0,"reasoning_tokens":301,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T22:13:44.170477+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the Hall mobility directly on the same crystals used for the scaling and check whether $\\mu_{\\mathrm{ave}}$ is proportional to RRR across all four compounds; if it is not, $MR = B \\times RRR^{b}$ is an empirical correlation rather than a mobility scaling law.","supporting_citations":[{"cited_title":"Kohler, Zur magnetischen widerstands¨ anderung reiner metalle, Ann","cited_arxiv_id":null,"evidence_quote":"Supplies Kohler's rule, the single-scattering-time scaling law the paper tests and confirms in high-RRR crystals."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the precedent that magnetoresistance scales with crystal quality in WTe2, motivating the MR-RRR analysis."},{"cited_title":"Okawa, M","cited_arxiv_id":null,"evidence_quote":"Gives InBi as a compensated-semimetal counterpart with extremely large MR, used to frame the comparison beyond two-band behavior."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Shows a correlation between RRR and magnetoresistance in MgB2, supporting the RRR-as-mobility proxy in a clean multiband superconductor."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Demonstrates large anisotropic magnetoresistance in clean MgB2 thin films, another carrier-rich multiband system with mobility-controlled response."},{"cited_title":"Blaha, K","cited_arxiv_id":null,"evidence_quote":"Documents the first-principles band-structure method used to establish the complex multiband Fermi surfaces."},{"cited_title":"Okawa, M","cited_arxiv_id":null,"evidence_quote":"Provides the crystal-growth route for α-PdBi that yielded the record-RRR samples underlying the scaling data."}],"review_version":1}