{"id":"d6399dbd-f5a7-4586-b077-d079e475fb07","arxiv_id":"2501.09864","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"In Co/Pt/Cu* stacks, damping-like torque has a spin channel from orbit-to-spin conversion in Pt at small Co thickness and a long-range orbital channel acting over several nanometers of Co at larger thickness.","lead":"This paper measures how current-generated orbital and spin currents push magnetization in thin cobalt films capped with platinum and oxidized copper. It reports that a long-range orbital contribution extends several nanometers into cobalt and attributes it to an interface effect in naturally oxidized copper.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Missing control for Co's own bulk orbital Hall effect: the linear ξDL(tCo) rise appears in the Cu*-free reference, so it cannot uniquely evidence Cu* OREE injection; a bulk Co OHE term would reproduce the same slope and is not in Eq. (6).","rationale":"The paper contains credible harmonic-Hall measurements and a consistent set of extracted parameters; the proposed orbital-torque interpretation is plausible and connects to an active literature. However, the central quantitative claim—that the linear rise of ξDL with tCo isolates a pure orbital current injected from Cu*/Pt—rests on a subtraction that is not performed. The reference stack without Cu* already exhibits the same rise, which means the effect is not interfacial-Cu* specific. The only candidate that naturally produces a long-lasting linear torque over several nanometers in a ferromagnet is a bulk orbital (or equivalent) self-torque in Co, because spin diffusion in Co is short (λ ~ 1.4–1.8 nm) and would saturate. Since Eq. (6) includes no bulk Co OHE term, and the fit window at tCo < 2 nm can absorb a linear-in-tCo contribution into the tanh onset, the model cannot distinguish injected orbital current from bulk Co OHE. A Co-only control is the decisive experiment. This does not invalidate the paper's measurement but makes the headline conclusion conditional until such a control is provided; the reader's CONDITIONAL verdict is therefore unchanged.","tokens_in":15079,"tokens_out":10464,"duration_ms":118482,"concrete_test":"Fabricate a control series Co(tCo)|insulator (e.g., 2-3 nm MgO or SiN capping, no Pt, no Cu) and repeat the same second-harmonic Hall protocol. If ξDL(tCo) still rises linearly for tCo ≥ 2 nm with a slope comparable to the Co|Pt reference slope, the linear term is a bulk self-torque of Co (orbital Hall or equivalent) and the assignment to injected Cu*/Pt orbital currents collapses. If the slope is zero or negative, the control supports the injection interpretation. To separate bulk Co OHE in the actual stacks, also compute the expected ξDL from the known orbital Hall conductivity of Co and subtract it before attributing the residual to Cu* OREE.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section IV fits Eq. (6), a spin-only model, to tCo < 2 nm and assigns the excess linear increase of ξDL for tCo ≥ 2 nm to 'pure orbital injection' from Pt OHE and/or Cu* OREE. This inference requires that no other torque channel grows linearly with tCo in that window. The paper's own reference Co(tCo)|Pt(3) series shows the same linear rise (Fig. 4b), so the rise is not specific to Cu*. A candidate omitted channel is the bulk orbital Hall effect (OHE) of Co itself: a charge current in Co generates an orbital current inside Co, which is converted to a spin torque by Co's spin-orbit coupling. Integrated over thickness, this produces ξDL ∝ tCo as long as tCo remains below the orbital decoherence length. Eq. (6) contains no such self-torque term, and the fit window at tCo < 2 nm cannot distinguish it from the linear onset of tanh(tCo/λ*) in the model. Thus the attribution of the slope to orbital currents injected from Cu* is underdetermined. Moreover, the Cu*-source claim is not established by the Co-thickness data: Fig. 6 fixes tCo = 2 nm and probes only the total torque at the boundary of the linear regime, not the propagation of a Cu*-generated current through several nm of Co. The control Co|Pt with no Cu* provides the same long-range slope, so an interfacial Cu* OREE is not uniquely required.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper presents second-harmonic Hall measurements of current-induced torques in Co(tCo)|Pt(3), Co(tCo)|Pt(3)|Cu(3)*, and Co(tCo)|Pt(4)|Cu(3)* stacks, plus Cu* thickness series at fixed tCo = 2 nm. The authors extract damping-like and field-like effective fields, normalize by electric field, and convert them into effective spin-Hall conductivities xi_DL and xi_FL. For tCo < 2 nm they fit a spin-only model (Eq. (6)) and extract short spin decoherence lengths (1.4-1.9 nm). For tCo >= 2 nm they observe a linear increase of xi_DL in all three Co-thickness series and assign this excess to pure orbital currents, claiming interfacial generation at the oxidized Cu interface and a long orbital decoherence length of several nanometers in Co. The Cu* thickness dependence in Section V is used to support the interfacial OREE origin. The paper's stated major result is the linear increase of xi_DL for tCo >= 2 nm assigned to pure orbital injection and interactions in Co.","tokens_in":15439,"tokens_out":4110,"duration_ms":48110,"significance":"If the central attribution were established, the work would provide a quantitative separation of spin and orbital torque channels and evidence for long-range orbital torque propagation in a 3d ferromagnet, which is of genuine interest for orbitronics. The experimental methodology has real strengths: the second-harmonic analysis follows standard practice, the thermal background is removed through field dependence, the results are cross-checked against previous work on equivalent samples, and the use of electric-field normalization addresses current-shunting concerns. The paper is also careful to compare with a reference Co|Pt series. However, the central attribution of the long-range torque to Cu*-generated orbital currents is not supported by the data as presented, because the Cu*-free reference exhibits the same linear increase and the Cu* thickness measurements do not probe propagation through Co.","major_comments":[{"comment":"The linear increase of xi_DL for tCo >= 2 nm is present in the Cu*-free reference Co(tCo)|Pt(3) (black diamonds in Fig. 4b) with the same qualitative behavior as the Cu*-containing series. The Co-thickness dependence therefore cannot by itself demonstrate that the long-range torque originates at the Cu* interface. Since Eq. (6) is a spin-only model and the fit is restricted to tCo < 2 nm under the stated assumption that \"in the limit of small tCo, region wherein the orbital torque is negligible\", the residual at larger tCo is assigned to injected orbital current by construction, but the identical residual in the Cu*-free series shows that this excess is not Cu*-specific. A bulk orbital Hall self-torque in Co, which would grow approximately linearly with tCo below its orbital decoherence length, is an omitted channel that could reproduce the observed slope and is not included in Eq. (6). The authors need to include or quantitatively rule out this channel before assigning the linear increase to interfacial Cu* OREE.","section":"Section IV, Fig. 4b, Eq. (6)"},{"comment":"The Cu* thickness dependence is measured at a fixed Co thickness of 2 nm, which lies at the onset of the linear regime, and it probes only the total damping-like torque at that single thickness. Such data cannot track the propagation of a Cu*-generated orbital current through several nanometers of Co, so it cannot support the abstract's claim that the Co-thickness series \"clearly demonstrates the interfacial generation of the orbital currents in Cu*\". The roughly constant xi_DL versus tCu* in Co|Pt|Cu* may indicate an interfacial contribution at tCo = 2 nm, but it does not establish that this contribution survives over the long lengthscale inferred from the Co-thickness dependence, since the Cu*-free reference shows the same long-range slope.","section":"Section V, Fig. 6"},{"comment":"Eq. (6) and the surrounding derivation describe absorption of a transverse spin current in Co and contain no orbital current degree of freedom, yet the paper's central conclusion introduces a \"pure orbital injection\" term as the difference between the data and the spin-only fit. The linear excess is not derived from a model that includes orbital current generation in Pt or Cu*, transport across the interface, and conversion in Co. To separate the spin channel, the Pt OHE channel, the Cu* OREE channel, and a possible Co bulk OHE self-torque, a quantitative model with all these terms (or a control experiment that isolates them) is required. As it stands, the assignment of the residual to one particular orbital source is underdetermined.","section":"Section IV, model completeness"}],"minor_comments":[{"comment":"The phrase \"One one hand\" at the start of the paragraph discussing coherence lengths contains a duplicate word.","section":"Introduction"},{"comment":"The sentence \"In tat case, the current density in Cu*...\" contains a typo: \"tat\" should be \"that\".","section":"Section V"},{"comment":"The caption uses the shorthand \"Co(t)\" while the text and axes use \"Co(tCo)\"; the notation should be made consistent.","section":"Fig. 4 caption"},{"comment":"The denominator in the first term appears to be formatted ambiguously; it should be clear that the DL term is proportional to HDL/(HK + Hext).","section":"Eq. (2)"},{"comment":"References [17] and [58] are the same paper (Salemi and Oppeneer), and references [29] and [37] are the same paper (An et al.); these duplicates should be consolidated.","section":"References"},{"comment":"The conclusion states that the orbital current is \"generated by OREE at the Cu|CuOx interface and partially transmitted through Pt until Co\", but the evidence for transmission through Pt and subsequent propagation through Co is not separated from the Co|Pt reference data; the wording should be moderated to match what the data actually constrain.","section":"General"}],"recommendation":"major_revision","confidential_remarks":"The paper contains a careful torque measurement campaign with good internal consistency checks, but the central claim overreaches the control data. The key issue is that the Cu*-free reference shows the same linear xi_DL(tCo) rise, so the Co-thickness series cannot uniquely fingerprint Cu* OREE as the source of the long-range orbital torque. This is fixable in principle by adding a Co bulk OHE self-torque term to the model, by using the reference as a baseline, or by reframing the conclusion as evidence for long-range orbital torque without a Cu* source attribution. I would not reject the manuscript, but the revision needs to be substantial rather than cosmetic."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Read the paper. The second-harmonic work is careful: three Co-thickness series, a Cu-thickness series, thermal-background subtraction, and a spin-only fit that gives plausible decoherence lengths. The new numbers are the xi_DL values and the extracted lambda_perp for Co|Pt|Cu* stacks, and the linear rise of xi_DL with tCo up to 10 nm is a useful confirmation of long-range orbital torque in 3d ferromagnets.\n\nThe soft spot is the attribution of that rise to Cu* OREE. The reference Co|Pt series shows the same linear slope--the authors admit this--so the Co-thickness data cannot uniquely evidence Cu* injection. They assign the reference slope to Pt OHE, but then the Cu* claim rests on the Cu-thickness series at fixed tCo=2 nm, which shows only an interfacial enhancement, not propagation through several nm of Co. The abstract oversells this. Also, the fit window tCo<2 nm is defined by assuming orbital torque is negligible there, and no term for Co's own bulk orbital Hall effect is included. A Co self-torque could generate a similar linear rise; without that control, the extraction of a Cu*-specific long-range channel is underdetermined.\n\nNone of this invalidates the data. The spin-channel parameters are in line with prior work, and the long-range component is real regardless of Cu*. But the interpretation needs work: add a Co-bulk-OHE control, or soften the claim that Cu* is the source of the several-nanometer torque. Recommendation: send to peer review--the measurements deserve referee time--but expect the reviewers to ask for exactly that control before the central claim can stand.","headline":"Careful torque data with new thickness series, but the long-range torque is not specifically tied to Cu*: the Co|Pt control shows the same slope, so the central attribution needs an extra control.","tokens_in":15996,"tokens_out":4716,"would_cite":true,"duration_ms":46997,"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 paper's measurements show that in Co|Pt|Cu* stacks the damping-like torque contains a pure orbital contribution that grows linearly with cobalt thickness beyond 2 nm, indicating orbital currents generated at the oxidized copper…","keywords":["orbital torque","orbital Rashba-Edelstein effect","spin-orbit torque","orbit-to-spin conversion","second harmonic Hall","decoherence length","cobalt thin films","copper oxide interface"],"falsifier":"Replace the Pt spacer in Co|Pt|Cu* with a light metal of negligible spin Hall effect but comparable orbital transparency (e.g., Cu or Al): if the linear rise of $\\xi_{\\mathrm{DL}}$ for $t_{\\mathrm{Co}} > 2$ nm persists, the thick-cobalt torque is a pure orbital channel; if it disappears, the long-range torque required the Pt spin Hall effect.","tokens_in":14887,"feed_emoji":"🧲","tokens_out":10363,"duration_ms":102365,"temperature":0.7,"pith_summary":"This paper tries to establish that the current-induced torque on a thin cobalt film in Co|Pt|Cu* stacks carries two distinct angular-momentum currents: the familiar spin current from the platinum spin Hall effect and a separate orbital current generated at the surface of the naturally oxidized copper layer. Using second-harmonic Hall measurements on cobalt-thickness series from sub-nanometer to 10 nm, the authors find that the damping-like torque efficiency $\\xi_{\\mathrm{DL}}$ is well described by a spin-only model below about 2 nm but then increases linearly with cobalt thickness. They attribute that linear increase to pure orbital currents that travel several nanometers into cobalt before exerting torque, in contrast to spin currents whose decoherence length is only $\\approx 1.4$–$1.85$ nm. A complementary copper-thickness series shows the orbital source is interfacial, at the Cu|CuO$_x$ boundary, rather than in the bulk copper. If correct, this cleanly separates orbital from spin torques and shows that light-metal/oxide interfaces can compete with heavy-metal spin Hall layers.","feed_headline":"Orbital currents torque cobalt from nanometers away","feed_subtitle":"A cobalt-thickness series separates pure orbital torque from spin Hall torque, pointing to oxide interfaces as the orbital source.","key_machinery":"The central object is the thickness dependence of the damping-like torque, measured by second-harmonic Hall voltage analysis in the in-plane field-rotation geometry, which separates the damping-like component (proportional to $\\cos\\varphi$) from the field-like component (proportional to $2\\cos^3\\varphi - \\cos\\varphi$). The quantitative model is the spin-only formula for $\\sigma_{\\mathrm{SHE}}^{\\mathrm{eff}}$ in Eq. (6), derived from a complex Boltzmann equation with a complex decoherence length $\\lambda_F^*$; the real part controls the damping-like torque decay with ferromagnet thickness and fits the data for $t_{\\mathrm{Co}} \\le 2$ nm. The interpretive key is the contrast between the short spin decoherence length ($\\lambda_{\\perp,\\mathrm{Re}}^F \\approx 1.4$–$1.85$ nm) and the linearly rising $\\xi_{\\mathrm{DL}}$ up to $t_{\\mathrm{Co}} = 10$ nm, which is read as the fingerprint of a long-lived pure orbital channel. The orbital source is identified with the Orbital Rashba-Edelstein effect (OREE), the current-induced buildup of orbital angular momentum at a metal/oxide interface, located at the Cu|CuO$_x$ boundary by the Cu*-thickness series.","core_discovery":"On the authors' account, the effective damping-like torque efficiency $\\xi_{\\mathrm{DL}}$ in Co($t_{\\mathrm{Co}}$)|Pt|Cu* stacks is the sum of a spin channel and a pure orbital channel. For cobalt thinner than about 2 nm, the data are captured by a spin-only model with a complex spin-diffusion length giving $\\lambda_{\\perp,\\mathrm{Re}}^F \\approx 1.4$–$1.85$ nm across the three series; in this range the torque comes from the Pt spin Hall effect plus an orbit-to-spin conversion in Pt, which is why the Cu*-containing series saturate above the Co|Pt reference. For $t_{\\mathrm{Co}} \\geq 2$ nm, $\\xi_{\\mathrm{DL}}$ rises linearly with cobalt thickness instead of saturating, and the authors assign this non-saturating part to orbital currents generated by the Orbital Rashba-Edelstein effect at the Cu|CuO$_x$ interface, transmitted through Pt, and acting directly on the cobalt magnetization over a lengthscale of several nanometers. The copper-thickness series supports the interfacial picture: $\\xi_{\\mathrm{DL}}$ stays nearly constant in Co|Pt|Cu* as $t_{\\mathrm{Cu}^*}$ grows from 2 to 5 nm, whereas it rises in Co|Cu*, the opposite of what a bulk orbital Hall effect in metallic copper would produce.","pith_inferences":["Interpolating from the data, the linear rise of $\\xi_{\\mathrm{DL}}$ shows no sign of saturating by 10 nm; a direct measurement at larger $t_{\\mathrm{Co}}$ would yield the orbital decoherence length in cobalt, which the current series cannot fix.","The same thickness-series logic could be applied with the Cu* layer at the opposite interface to map the orbital torque sign and separate it from the spin Hall channel in a purely geometric way.","Comparing different oxides under the same cobalt thickness would test whether the strong orbital source is specific to the Cu|CuO$_x$ hybridization or a general metal/oxide interface effect.","The interpretation assumes the residual torque beyond the spin model is purely orbital; a measurement with a spin-sink layer between Pt and Co could directly test whether any spin-mediated component remains in the thick-cobalt regime."],"forward_implications":["The damping-like torque in Co|Pt|Cu* is the sum of a short-range spin contribution (Pt spin Hall effect plus orbit-to-spin conversion in Pt) and a long-range pure orbital contribution originating at the Cu|CuO$_x$ interface.","Because the orbital channel acts over several nanometers of cobalt, orbital currents can torque ferromagnetic layers far thicker than the roughly 1–2 nm reach of spin currents, potentially enabling manipulation of thicker storage layers.","The flat copper-thickness dependence in Co|Pt|Cu* versus the rising dependence in Co|Cu* places orbital-current generation at the interface, not in the metallic copper bulk, so oxide-interface engineering becomes a torque-design knob.","A light-element source Co(2)|Cu(5)* can exceed the torque efficiency of Co(2)|Pt(3), making orbitronic sources a credible alternative to heavy-metal spin Hall layers."],"supporting_citations":[{"why":"Characterizes the naturally oxidized Cu layer and quantifies the orbit-to-spin conversion enhancement that this paper builds on.","marker":"[22]"},{"why":"Provides the Co|Pt reference series and the complex-Boltzmann spin-only model used to fit the thin-cobalt data.","marker":"[27]"},{"why":"Introduced the cobalt-thickness method that assigns torque increase above spin decoherence to orbital effects in Pt.","marker":"[19]"},{"why":"Gives first-principles orbital Hall conductivities in transition metals, the theoretical basis for pure orbital torque in Pt.","marker":"[47]"},{"why":"Reported a linear increase of torque efficiency with ferromagnet thickness attributed to pure orbital torque, the precedent for the present interpretation.","marker":"[33]"},{"why":"Demonstrated current-induced orbital torque from a Cu|CuOx interface via OREE, supporting the interfacial generation claim.","marker":"[13]"},{"why":"Provides the O p–Cu d orbital hybridization model for OREE at the Cu|CuO interface, grounding the proposed source mechanism.","marker":"[28]"}],"fun_headline_variants":["Orbital currents, not spin, drive torque in Co films","Cobalt thickness test pinpoints interfacial orbital torque","Orbital torque from CuO interface acts over nanometers","Thin Co reveals orbital currents as torque source","Oxide interface feeds orbital torque into cobalt"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"For cobalt thinner than 2 nm the spin-only model is complete and orbital torque is negligible there, so the extra torque that appears only in thicker cobalt is interpreted as pure orbital injection instead of a thickness-dependent change in spin-transport parameters.","fun_headline_variants_meta":{"raw":{"variants":["Orbital currents, not spin, drive torque in Co films","Cobalt thickness test pinpoints interfacial orbital torque","Orbital torque from CuO interface acts over nanometers","Thin Co reveals orbital currents as torque source","Oxide interface feeds orbital torque into cobalt"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000205,"raw_usage":{"total_tokens":1425,"prompt_tokens":1008,"completion_tokens":417,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":624,"completion_tokens_details":{"reasoning_tokens":341}},"tokens_in":624,"tokens_out":417,"duration_ms":5217,"temperature":1.0,"reasoning_tokens":341,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T19:37:07.462677+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Replace the Pt spacer in Co|Pt|Cu* with a light metal of negligible spin Hall effect but comparable orbital transparency (e.g., Cu or Al): if the linear rise of $\\xi_{\\mathrm{DL}}$ for $t_{\\mathrm{Co}} > 2$ nm persists, the thick-cobalt torque is a pure orbital channel; if it disappears, the long-range torque required the Pt spin Hall effect.","supporting_citations":[{"cited_title":"Krishnia, B","cited_arxiv_id":null,"evidence_quote":"Characterizes the naturally oxidized Cu layer and quantifies the orbit-to-spin conversion enhancement that this paper builds on."},{"cited_title":"Krishnia, Y","cited_arxiv_id":null,"evidence_quote":"Provides the Co|Pt reference series and the complex-Boltzmann spin-only model used to fit the thin-cobalt data."},{"cited_title":"Sala and P","cited_arxiv_id":null,"evidence_quote":"Introduced the cobalt-thickness method that assigns torque increase above spin decoherence to orbital effects in Pt."},{"cited_title":"Orbital Hall effect in transition metals from first-principles scattering calculations","cited_arxiv_id":"2409.20526","evidence_quote":"Gives first-principles orbital Hall conductivities in transition metals, the theoretical basis for pure orbital torque in Pt."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Reported a linear increase of torque efficiency with ferromagnet thickness attributed to pure orbital torque, the precedent for the present interpretation."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Demonstrated current-induced orbital torque from a Cu|CuOx interface via OREE, supporting the interfacial generation claim."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the O p–Cu d orbital hybridization model for OREE at the Cu|CuO interface, grounding the proposed source mechanism."}],"review_version":1}