{"id":"2f03a73a-292a-4f85-bb7c-311762373e76","arxiv_id":"2501.00403","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"An out-of-plane harmonic Hall measurement geometry quantitatively extracts spin-orbit and orbital torques in in-plane magnetized films and reproduces the two-fold torque enhancement from a Cu/CuOx interface.","lead":"Researchers present and test a new way to measure spin and orbital torques in magnetic multilayer films using an out-of-plane rotation of the magnetic field, which simplifies torque extraction and separates heating effects. Applied to a CuOx-capped sample, it confirms about twice the damping-like torque compared to an AlOx reference, pointing to orbital current generation at the oxidized copper interface.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The OOP method's quantitative torque extraction rests on an unverified single-term anomalous-Nernst model; at high fields the DLT and FLT angular signatures are degenerate, so unmodeled thermoelectric/MMR backgrounds could bias the reported HDL values.","rationale":"The paper's derivation of Eq. (8) is internally consistent, and the OOP/IP agreement in Fig. 4(b) is genuine supporting evidence for the central claim, as is the measured field-independence of TOOP/TIP in Fig. 3(b). The concern is therefore not that the method is wrong, but that it is under-constrained: the thermal model excludes, by assertion, terms that have angular signatures overlapping with the torque terms, and the claimed high-field separation of HDL and HFL is mathematically degenerate. This is exactly the condition under which systematic artifacts can bias a quantitative torque extraction by tens of percent. The proposed control experiment and expanded fitting test would settle whether unmodeled backgrounds are present. Because the issue is addressable and does not, on current evidence, contradict the OOP/IP agreement, the conditional verdict is unchanged.","tokens_in":10229,"tokens_out":19645,"duration_ms":199643,"concrete_test":"Re-analyze the existing OOP V2ω angular data with an expanded model that adds (i) a field-independent constant offset and (ii) a cosθM/Hext background term that is not assigned to torque. If the fitted HDL for the CuOx sample shifts by more than ~20% (or outside the quoted error bars) when these terms are included, the single-ANE-term model is incomplete and the twofold claim is compromised. A complementary experimental control: measure the same OOP angular scans on an identical stack with a 10 nm Cu spacer inserted between Co and Pt to suppress SOT; any residual fitted HDL above noise would directly indicate a thermal or MMR artifact.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that Eq. (8) quantitatively extracts HDL and HFL requires that the only non-torque 2ω background is the anomalous Nernst term I0α(TOOP cosθM + TIP sinθM) with field-independent TOOP/TIP, and that magnon magnetoresistance (MMR) is absent. The paper's MMR exclusion ('injected angular momentum being always transverse to the magnetization') is not demonstrated: in the OOP geometry the spin accumulation is transverse to M for all θM, so current-induced magnon processes can be θ-independent rather than absent. More concretely, for Hext ≫ Hk, θM ≈ θH and the DLT term (-1/2 I0 RAHE cosθM HDL/Heff) and FLT term (-I0 RPHE cos²θM (HFL+HOe)/(Hext cosθH)) have the identical angular shape cosθH/Hext; only the known RAHE/RPHE ratio separates them. Any unmodeled cosθH/Hext-like background (e.g., a field-dependent thermopower or an MMR term with a field-dependent amplitude) is therefore absorbed directly into HDL or HFL. The authors themselves note that the TOOP and HDL curves resemble each other at 35-40 kOe and that HDL extraction is unreliable there. Agreement with the IP geometry is reassuring but not decisive, because the same thermoelectric/MMR ambiguities (Refs. 41,42) affect both geometries.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes an out-of-plane (OOP) angular harmonic Hall measurement technique for extracting damping-like and field-like spin-orbit torque effective fields in in-plane magnetized samples. The authors derive the second-harmonic Hall voltage expression (Eq. (8)) that includes both torque terms and a two-component anomalous Nernst thermal background, then validate the method on Co(2)/Pt(4)/AlOx(3) and Co(2)/Pt(4)/CuOx(3) stacks. They report that the OOP geometry separates thermal effects from torques, requires no complete field sweep, and gives accurate DL/FL separation under favorable conditions. The measured damping-like fields show consistency with the in-plane geometry and corroborate a twofold enhancement in the CuOx-capped sample, attributed to orbital currents from the Cu|CuOx interface.","tokens_in":10513,"tokens_out":10204,"duration_ms":93613,"significance":"If validated, this would be a useful extension of harmonic Hall metrology: the analytical derivation is careful, the 1st-harmonic fits determine the magnetization direction self-consistently, the multi-field data allow scaling checks (1/(Hext+Hk) for DL, 1/Hext for FL), and the agreement between OOP and IP geometries is a genuine strength. The corroboration of the orbital-torque enhancement in CuOx-capped samples is also of interest. However, the quantitative extraction depends heavily on the assumption that all non-torque 2ω backgrounds are captured by a single anomalous-Nernst term with field-independent coefficients. The paper does not demonstrate the absence of magnon magnetoresistance or other thermoelectric backgrounds, and at high fields the DL and FL angular signatures become degenerate. The method is promising, but its error budget is not yet fully established.","major_comments":[{"comment":"The quantitative extraction of HDL and HFL from V2ω rests on the assumption that all non-torque 2ω backgrounds are described by the single anomalous Nernst term I0α(TOOP cosθM + TIP sinθM) with field-independent TOOP and TIP. The statement that MMR 'should be discarded' because the injected angular momentum is always transverse to the magnetization is not demonstrated; current-induced magnon processes can produce θ-independent or field-dependent resistivity contributions rather than vanishing identically. Since the antisymmetric part of V2ω is fitted with HDL, HFL, and TOOP as free parameters, any unmodeled background with a similar angular dependence will be absorbed into the torque values. The authors should provide a quantitative bound on such backgrounds, for example by varying the field at fixed θM or by performing a control experiment with a non-magnetic stack.","section":"Eq. (8) and fitting description in experimental section"},{"comment":"For Hext ≫ Hk, θM≈θH and the DL and FL terms in Eq. (8) have the same angular shape (both ∝ cosθH/Hext), so their separation is possible only through the prescribed RAHE/RPHE ratio and the thermal model. The authors themselves note that at 35–40 kOe the TOOP curve resembles the HDL signal and that the HDL extraction is unreliable there. The claim of 'greater accuracy in properly separating and quantifying' the two torque components should therefore be restricted to fields where Heff is sufficiently nonlinear, and the manuscript should specify the field window over which the separation is reliable.","section":"High-field regime, Fig. 3(a) and text after Fig. 2"},{"comment":"The statement that the OOP approach 'does not require a complete set of measurements at different magnetic fields' is overstated. Although the angular dependence of Eq. (8) can in principle separate the terms at a single field, the presented extraction requires an accurate Hk value from fitting V1ω over multiple fields, and the validation shown in Fig. 3(a) uses data from the whole field window. The manuscript should state the minimal set of measurements needed for a standalone determination of HDL and HFL and demonstrate it with a single-field example; otherwise the claimed advantage over the IP geometry is not established.","section":"Introduction, claim 'does not require a complete set of measurements at different magnetic fields'"}],"minor_comments":[{"comment":"The sentence 'Eq. (3) requires the information from the 1st harmonic signal' is confusing because Eq. (3) directly gives ΔθM; the 1st harmonic is actually used to determine Hk and the θM(θH) relation. Please rephrase.","section":"Experimental section, near Eq. (3)"},{"comment":"The reference list contains duplicates: Refs. 27 and 35 are the same paper (El Hamdi et al.), Refs. 34 and 36 are the same paper (Santos et al.), and Refs. 13 and 33 are the same paper (Lee et al.).","section":"References"},{"comment":"The linear fit of V2ω versus 1/(Hext+Hk) neglects the FL term, which scales as 1/Hext and is not strictly negligible at the lower fields included; the fit would benefit from a statement of the resulting systematic error or from a two-parameter fit.","section":"Fig. 2(a)"},{"comment":"Figure 3 shows error bars described as variations, but no statistical uncertainties are given for the fitted parameters in Eq. (8); reporting standard errors or confidence intervals would strengthen the metrological claim.","section":"Fig. 3"},{"comment":"There is a typo in the sample name 'Co(2)|Pt(4)|AlOx x(3)' in the experimental section; the extra 'x' should be removed.","section":"Experimental section, sample description"}],"recommendation":"major_revision","confidential_remarks":"The paper is within scope and the method is potentially useful. The main risk is that the harmonic Hall community will push back on the single-term anomalous-Nernst assumption and on the dismissal of magnon magnetoresistance; the authors should address this directly rather than asserting absence. The orbital-torque enhancement is a corroboration of prior work by the same group (Ref. 39), which is acceptable but should be positioned accordingly. The duplicate references and the minor clarity issues should be easy to fix."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"You asked about Xu et al., arXiv:2501.00403. The paper reports an out-of-plane (OOP) harmonic Hall geometry for spin-orbit torque measurements in in-plane magnetized samples. What is newly added is the analytical derivation of the second-harmonic response in OOP geometry (Eqs. 7–8), including a two-term anomalous Nernst contribution, and the demonstration that this geometry separates thermal terms without requiring a full multi-field scan.\n\nTo its credit, the paper does the right control checks. The extracted damping-like field scales as 1/(Hext+Hk) and the field-like part as 1/Hext at θH=0, as expected. The OOP results for both an AlOx and a CuOx sample agree with in-plane harmonic measurements from the same group, which is a meaningful internal consistency check. The twofold enhancement of HDL in the CuOx sample corroborates earlier work on the same stacks. I have no problem with the self-citation; it anchors the method to a known system.\n\nThe soft spots are proportionate to their impact. The thermal model assumes a single anomalous Nernst term with field-independent coefficients TOOP and TIP. The data do show these coefficients roughly constant with field, which supports the assumption, but the paper does not experimentally rule out other spin-caloritronic or magnon magnetoresistance (MMR) backgrounds. The argument that MMR is absent in OOP because the injected spin is always transverse to the magnetization is plausible but not proven; the transverse accumulation could still alter magnon populations via current-induced torques. Even if MMR is negligible, the more serious issue is the angular degeneracy between the DLT and FLT terms at fields well above Hk: both go as cosθH/Hext. Any unmodeled background with that shape will be absorbed into the fitted torque fields. The authors notice this at 35–40 kOe and exclude those data, but they do not quantify how sensitive the averaged HDL values are to the assumed thermal model across the whole field range. I would also want a proper error propagation from the raw data and multi-parameter fits, which is missing.\n\nNone of these break the central claim. The OOP method is a plausible extension of standard harmonic Hall, the derivation is internally consistent, and the torque values agree with the IP geometry. The claim that it offers 'greater accuracy' in separating DL and FL components is qualified: it holds at low and intermediate fields, not at high fields.\n\nThis paper is aimed at spintronics metrology specialists working on spin and orbital torques, and it deserves a serious referee. I would send it out, with requests to refine the thermal-model sensitivity analysis and to provide error estimates on the extracted fields.","headline":"Useful OOP harmonic Hall metrology advance with an internally consistent derivation and good cross-checks; the thermal-model assumptions and high-field degeneracy need tightening, but the core claim holds.","tokens_in":11141,"tokens_out":4673,"would_cite":true,"duration_ms":48391,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"An out-of-plane angular harmonic Hall geometry quantitatively separates damping-like and field-like spin-orbit torques and reveals a twofold damping-like enhancement from a naturally oxidized copper interface.","keywords":["spin-orbit torque","harmonic Hall voltage","orbital torque","damping-like torque","field-like torque","magnon magnetoresistance","anomalous Nernst effect","out-of-plane angular geometry"],"falsifier":"Measure the out-of-plane second-harmonic signal on a sample whose in-plane harmonic data show a clear magnon-magnetoresistance contribution; if the out-of-plane signal contains a comparable $\\cos^3$-type angular component, the claim that magnon magnetoresistance is absent in that geometry is falsified, while repeating the fits at several temperatures and bias currents would expose any unmodeled thermoelectric term.","tokens_in":9952,"feed_emoji":"🧲","tokens_out":13952,"duration_ms":116344,"temperature":0.7,"pith_summary":"This paper claims that rotating the magnetic field out of the sample plane during harmonic Hall measurements gives a direct, quantitative readout of spin-orbit torque effective fields in in-plane magnetized films, without the full field sweep normally required in the standard in-plane geometry. The analytical model for the second-harmonic voltage separates the damping-like term, the field-like term, and thermoelectric voltages by their distinct angular signatures, so the torque values are less contaminated by thermal artifacts and by the magnon-magnetoresistance terms that complicate in-plane measurements. Applied to Co(2)|Pt(4)|CuOx(3), the method yields a damping-like field of about 2.4 mT/($10^{11}$ A/m$^2$), twice the value for the AlOx reference stack, which the authors attribute to orbital current generated at the Cu|CuOx interface. If correct, the out-of-plane geometry is a reliable alternative metrology for spin and orbital torques and strengthens the case for oxidized copper as an orbital-torque source.","feed_headline":"New Hall geometry shows twofold orbital torque boost","feed_subtitle":"A rotated harmonic Hall measurement separates damping- and field-like torques without field sweeps or magnon corrections.","key_machinery":"The load-bearing element is Eq. (8), the analytical second-harmonic model for the out-of-plane geometry, together with the self-consistent equilibrium relation $\\tan\\theta_M = H_{\\rm ext}\\sin\\theta_H/(H_K\\cos\\theta_M + H_{\\rm ext}\\cos\\theta_H)$. Equation (8) decomposes $V_{2\\omega}$ into a damping-like term proportional to $1/[H_{\\rm ext}\\cos(\\theta_H-\\theta_M)+H_K\\cos(2\\theta_M)]$, a field-like term proportional to $1/(H_{\\rm ext}\\cos\\theta_H)$, and an anomalous-Nernst thermoelectric term $\\alpha(T_{OOP}\\cos\\theta_M + T_{IP}\\sin\\theta_M)$. The angular separation of these terms, symmetric versus antisymmetric around $\\theta_H=90^\\circ$, is what makes a single-field fit possible and what lets the method discard magnon magnetoresistance, whose in-plane $\\cos^3(\\varphi)$ signature is absent when injected angular momentum is transverse to the magnetization.","core_discovery":"The central discovery is that the out-of-plane angular second-harmonic Hall response of an in-plane magnetized sample can be written as a sum of three terms with distinct angular symmetries: a damping-like term proportional to $1/[H_{\\rm ext}\\cos(\\theta_H-\\theta_M)+H_K\\cos(2\\theta_M)]$, a field-like term proportional to $1/(H_{\\rm ext}\\cos\\theta_H)$, and a thermoelectric term $\\alpha(T_{OOP}\\cos\\theta_M + T_{IP}\\sin\\theta_M)$. Fitting this expression to a single angular scan at fixed field extracts the damping-like and field-like effective fields together with the two thermal coefficients, and the results agree with values obtained in the conventional in-plane geometry for the same stacks. The paper then uses the method to show that replacing the AlOx capping layer with naturally oxidized Cu doubles the damping-like field, from about 1.2 to 2.4 mT per $10^{11}$ A/m$^2$, a change it interprets as orbital torque from the Cu|CuOx interface rather than a thermal or magnon artifact.","pith_inferences":["A natural extension is to apply the out-of-plane protocol to samples with large anomalous Nernst responses, such as Bi-based or topological-insulator films, where the angular separation of thermal and torque terms could make quantitative SOT extraction feasible.","The claim that magnon magnetoresistance is absent in the out-of-plane geometry could be tested directly by measuring a film series where the in-plane magnon signature is known to grow; if out-of-plane values stay flat while in-plane values drift, the claim is supported.","If the CuOx enhancement reflects a real orbital-current source, then a simple naturally oxidized copper cap could serve as an efficient orbital-torque injector, potentially reducing the heavy-metal thickness needed in SOT devices."],"forward_implications":["A single angular scan in the out-of-plane geometry can supply quantitative damping-like and field-like effective fields without measuring at multiple applied fields, simplifying SOT characterization.","The same measurement reports the thermoelectric voltages $T_{OOP}$ and $T_{IP}$ while extracting torques, so the thermal background is characterized rather than assumed away.","Because magnon-magnetoresistance terms are discarded in the out-of-plane geometry, torque values from this method should not need the magnon corrections required for in-plane harmonic data.","The measured twofold increase in damping-like field for Co/Pt/CuOx compared with Co/Pt/AlOx confirms that the Cu|CuOx interface adds an orbital-torque contribution on top of the Co|Pt spin Hall source.","The out-of-plane results match the in-plane geometry values for the same stacks, cross-validating both harmonic Hall approaches for these samples."],"supporting_citations":[{"why":"Supplies the two sample stacks, the in-plane harmonic data used for cross-checking, and the resistivity/shunting calibration that converts measured fields to current-density efficiencies.","marker":"[39]"},{"why":"Establishes the harmonic Hall methodology and the anomalous-Nernst treatment of thermoelectric voltages that the out-of-plane model adapts.","marker":"[40]"},{"why":"Provides the field-derivative principle used to compute torque-induced magnetization oscillations in Eqs. (3) and (4).","marker":"[22]"},{"why":"Supplies the harmonic Hall formalism for spin-orbit torque measurements that the modulation expansion builds on.","marker":"[44]"},{"why":"Identifies the magnon-magnetoresistance angular signature in the in-plane geometry that the out-of-plane method is claimed to avoid.","marker":"[41]"},{"why":"Quantifies current-induced magnon effects that can contaminate in-plane SOT estimates, motivating the alternative geometry.","marker":"[42]"},{"why":"Establishes the orbital Rashba-Edelstein effect at light-metal/oxide interfaces, the mechanism invoked for the Cu|CuOx torque enhancement.","marker":"[32]"}],"fun_headline_variants":["Rotated Hall test doubles damping-like torque","New Hall geometry splits torque terms, doubles orbital effect","Harmonic Hall in OOP geometry yields twofold torque boost","No sweeps, no magnons: new Hall method doubles torque","Out-of-plane Hall angle doubles damping torque"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The extracted torque values assume that every non-torque contribution to the second-harmonic signal is captured by a single temperature-gradient term with two field-independent constants, and that magnon-related magnetoresistance never appears in the out-of-plane geometry.","fun_headline_variants_meta":{"raw":{"variants":["Rotated Hall test doubles damping-like torque","New Hall geometry splits torque terms, doubles orbital effect","Harmonic Hall in OOP geometry yields twofold torque boost","No sweeps, no magnons: new Hall method doubles torque","Out-of-plane Hall angle doubles damping torque"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000687,"raw_usage":{"total_tokens":3104,"prompt_tokens":928,"completion_tokens":2176,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":544,"completion_tokens_details":{"reasoning_tokens":2100}},"tokens_in":544,"tokens_out":2176,"duration_ms":17212,"temperature":1.0,"reasoning_tokens":2100,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T22:51:41.900793+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the out-of-plane second-harmonic signal on a sample whose in-plane harmonic data show a clear magnon-magnetoresistance contribution; if the out-of-plane signal contains a comparable $\\cos^3$-type angular component, the claim that magnon magnetoresistance is absent in that geometry is falsified, while repeating the fits at several temperatures and bias currents would expose any unmodeled thermoelectric term.","supporting_citations":[{"cited_title":"Ding , author M.-G","cited_arxiv_id":null,"evidence_quote":"Quantifies current-induced magnon effects that can contaminate in-plane SOT estimates, motivating the alternative geometry."},{"cited_title":"El Hamdi , author J.-Y","cited_arxiv_id":null,"evidence_quote":"Establishes the orbital Rashba-Edelstein effect at light-metal/oxide interfaces, the mechanism invoked for the Cu|CuOx torque enhancement."}],"review_version":1}