Tunable spin and orbital torques in Cu-based magnetic heterostructures

Can O. Avci; Silvia Damerio

REVIEW 3 major objections 6 minor 8 references

Tunable spin and orbital torques in Cu-based magnetic heterostructures

T0 review · 3 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Naturally oxidized Cu is claimed to generate damping-like orbital torque rivaling Pt, with sign and amplitude set by solid-state gating.

desk verdict Solid orbital-torque study with a nice Py-thickness series, but the headline gating result lacks direct chemical-state evidence and is undercut by the authors' own CoOx control. read the letter →

arxiv 2501.09458 v1 pith:7QWLM7SU submitted 2025-01-16 cond-mat.mtrl-sci

Silvia Damerio , Can O. Avci This is my paper · ORCID

classification cond-mat.mtrl-sci

keywords spin-orbittorquesorbitalHalleffectcurrentscopperoxidesolid-stategatingharmonicmeasurementsmagneto-ionicsspin-orbitronics

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper sets out to show that naturally oxidized copper, a light and abundant 3d metal, can generate current-induced torques on adjacent magnetic films as effectively as the heavy-metal standard platinum, and that the torque can be switched and tuned electrically. Its central experimental claim is that the damping-like torque in Co/CuOx and Py/CuOx bilayers has the opposite sign to that from metallic Cu and Pt, grows with ferromagnet thickness in a way that signals an orbital origin, and in Py/CuOx reaches an efficiency comparable to Py/Pt and greater than Co/Pt. The paper further claims reversible sign control of the damping-like torque in Co/CuOx/GdOx devices by solid-state gating, where voltage-driven oxygen-ion migration oxidizes or reduces the Cu layer. If these claims hold, cheap and sustainable Cu-based layers become viable torque sources for gate-tunable spintronic memory and logic.

What carries the argument

The load-bearing mechanism is the orbital Hall effect (OHE) in oxidized Cu: an electric current drives a transverse flow of orbital angular momentum in CuOx, and because orbital moments do not exchange-couple directly to the magnetization, the accumulated orbital angular momentum must be converted into a spin current in the adjacent ferromagnet via its orbital-to-spin conversion coefficient eta_FM. Harmonic Hall measurements separate the damping-like and field-like torque components through their different angular dependences in the second-harmonic signal, and the FM-thickness dependence distinguishes bulk orbital accumulation, which needs several nanometres of FM to convert, from interfacial effects. The gating demonstration uses an applied voltage to move O2- ions across a GdOx barrier, changing the Cu oxidation state and thereby turning the orbital-Hall contribution on, off, or reversed in sign.

What would settle it

A decisive test: grow Py(5)/CuOx(t) with CuOx thickness t from about 0.5 to 10 nm under the same natural-oxidation protocol and measure xi_E_DL; if the negative damping-like torque does not increase with CuOx thickness and saturate, the bulk orbital Hall effect is not the dominant source.

Watch

Extended reading notes

Core claim

Using harmonic Hall measurements on Co(t)/NM and Py(t)/NM bilayers with NM = Pt, Cu, and naturally oxidized CuOx, the paper reports that the damping-like effective field (BDL) in FM/CuOx is negative, opposite to both metallic Cu and Pt, and grows in magnitude with FM thickness, contrary to the usual 1/tFM scaling of spin-Hall torques. The efficiency xi_E_DL in Py/CuOx rises sharply up to tPy approximately 5 nm and then saturates at a value comparable to Py/Pt and above Co/Pt; the authors attribute this thickness behavior to an orbital accumulation in CuOx that converts to a spin torque in the first nanometres of the ferromagnet, with Py's larger orbital-to-spin conversion coefficient accounting for the difference from Co. In solid-state gated Co(5)/CuOx(3)/GdOx/Pt devices, applying +3 V reduces CuOx toward metallic Cu and flips the damping-like torque from negative to positive, while subsequent -3 V reoxidizes the Cu and restores the negative sign; intermediate gating partially suppresses the torque. The authors conclude that the orbital Hall effect in naturally oxidized Cu is large enough to be useful and can be electrically controlled, while cautioning that the exact sign depends on the orbital texture and oxidation conditions.

Load-bearing premise

The paper assumes that the negative damping-like torque in FM/CuOx comes from a bulk orbital Hall effect in the oxidized copper, not from interfacial orbital Rashba-Eдельstein effects or from partial oxidation of the ferromagnet, and that voltage gating changes mainly the Cu oxidation state; if either assumption fails, the orbital-Hall interpretation and the gate-tuning conclusion would both be weakened.

Editorial extensions

If this is right

Py/CuOx bilayers offer torque efficiencies on par with Py/Pt, meaning a light-metal oxide can replace a heavy metal for current-induced torque generation.
The torque sign is determined by the Cu oxidation state, so a small gate voltage can reverse the torque direction without changing the magnetic layer.
Solid-state gating through GdOx works at room temperature with negligible gate leakage, offering a microelectronics-compatible route to tune orbital currents.
The FM thickness data identify Py as an efficient orbital-to-spin converter, making ferromagnet choice and interface quality central design levers.
The reduced-Cu torque state remains stable for at least the measurement time after gating, pointing toward non-volatile or semi-non-volatile operation.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A CuOx thickness series at fixed Py thickness would test the bulk-OHE picture: a bulk signal should grow and saturate with CuOx thickness, while an interface signal should saturate immediately.
The sign of the torque appears sensitive to oxidation conditions, so engineering the Cu oxidation state (for example Cu2O versus CuO) rather than merely having an oxide may allow deliberate sign selection.
The long gating times reported here, hundreds to thousands of seconds, suggest that immediate device use would target write-once or slowly refreshed configurations; faster ion conductors or thinner barriers could bring the effect closer to practical switching.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Good to talk. I've read the Damerio/Avci paper on Cu-based orbital torques. Short take: the ungated half of the paper is a solid, careful study that gives the field a useful Py-thickness series and a clean comparison between Cu, CuOx, and Pt. The gated half is an inventive proof-of-concept but the mechanism is not closed, and their own control data cuts against their interpretation.

What's genuinely new: the Py(t)/CuOx thickness dependence, with xi_DL rising to Pt-like values at tPy ~ 5 nm, and the solid-state GdOx gating that reversibly flips the sign of the damping-like torque. The harmonic Hall analysis is standard but done carefully; they include self-torque controls, inverted stack checks, and a parallel-resistor Oersted subtraction, and they are refreshingly explicit about what they cannot explain (e.g., the BFL sign crossover at large tPy, the device-to-device variability in gating).

The soft spots are in the interpretation. The orbital-origin claim is inferred from the thickness dependence and sign reversal rather than directly evidenced; the authors acknowledge this. That would be acceptable for a first report, but the gating story has a bigger problem. The negative-bias state is assumed to oxidize Cu while leaving Co intact. The XPS showing no CoOx was done on the ungated stack, not on actual gated devices. Resistance changes and AHE loop shapes are indirect. More damaging, their own SI Note 5 control shows that intentionally forming interfacial CoOx produces a damping-like torque with the same sign as the claimed CuOx torque, yet in SI Note 8 they argue CoOx 'enhances but does not change sign.' That is inconsistent. If negative gating forms a sub-nm CoOx at the Co/Cu interface, it alone could reproduce the observed sign change, with no CuOx-to-Cu conversion needed.

I don't think this kills the paper. The Py/CuOx efficiency result and the thickness dependence stand independently of the gating mechanism. But the paper's most novel claim - full electrical tunability via Cu oxidation - remains mechanistically open.

My recommendation: send it to peer review, and if I were the editor I'd ask for direct chemical state analysis (XPS or EELS) of the gated stack in pristine, +V, and -V states, or at least a recognition that CoOx formation is a viable competing explanation. As it stands, it's a conditional accept at best.

I'd cite the Py/CuOx thickness data in my own work. Take it to reading group if you want to discuss what counts as evidence for OHE in oxides.

Referee Report

3 major / 6 minor

Summary. The paper reports harmonic Hall measurements of current-induced spin and orbital torques in Co and Ni80Fe20 (Py) films adjacent to Cu, naturally oxidized CuOx, and Pt layers. The main experimental findings are: (i) FM/CuOx bilayers exhibit a damping-like torque with sign opposite to that of FM/Cu and FM/Pt references; (ii) the damping-like torque efficiency grows with FM thickness in CuOx systems, with Py/CuOx reaching values comparable to Py/Pt and exceeding Co/Pt at tPy = 5 nm; and (iii) solid-state gating through a GdOx layer can reversibly change the sign and magnitude of the damping-like torque in Co(5)/CuOx(3), attributed to voltage-driven oxygen migration that switches Cu between oxidized and metallic states. The manuscript includes supporting thickness series, XPS characterization, control experiments for self-torques, and fits of orbital diffusion lengths.

Significance. If the central claims hold, this work would establish naturally oxidized Cu as a practical, low-cost, and voltage-switchable source of orbital torques, which is significant for the development of orbitronic devices using earth-abundant elements. The paper's strengths are its systematic thickness-dependent data, use of established harmonic Hall analysis, explicit control experiments for self-induced torques, and honest reporting of limitations (e.g., large device-to-device variability and possible Co oxidation). However, the most novel claim—full electrical tunability of the orbital torque via controlled oxidation of Cu—is not directly verified: the chemical state of the gated devices is inferred from resistance changes rather than measured, and the authors' own control experiments show that interfacial CoOx can produce the same sign of damping-like torque. The orbital-origin interpretation for the ungated CuOx bilayers is reasonable but not unique, as interface effects such as orbital Rashba-Edelstein or unintended FM oxidation could contribute. For these reasons, the paper is promising yet not definitive in its current form.

major comments (3)

[SI Note 8 and main-text 'Solid-state gated devices' (Fig. 4-5)]
[Figure 5 and 'Electrical control of orbital torques']
[Figure 3c and accompanying text]

minor comments (6)

[SI Note 4]
[SI Note 8]
[Main text, 'Solid-state gated devices' section]
[Main text, conclusion]
[SI Note 8, last paragraph]
[SI Note 6]

Circularity Check

0 steps flagged · score 2.0 of 10

No circularity in the derivation; the main claims are direct measurements, with only minor self-citations and transparently fitted diffusion lengths that are not load-bearing.

full rationale

The central results—the opposite-sign damping-like torque in FM/CuOx bilayers, the FM-thickness dependence, and the gate-induced sign reversal—are obtained from direct harmonic-Hall measurements and are not derived from fitted parameters or from prior work by the same authors. The orbital diffusion lengths in SI Note 6 are obtained by fitting the same thickness-dependent torque data that they interpret, but they are presented as fits and are not used to force the sign or efficiency claims; the sign and efficiency statements stand on the raw measured fields. The gating interpretation uses resistance changes and AHE saturation-field monitoring as independent proxies in addition to the torque sign; the statement in SI Note 8 that 'the sign change of the torque indicates which species (Cu or CuOx) predominates' is an interpretive shortcut rather than a mathematical reduction. Self-citations (harmonic-Hall method references and the CoOx reference that includes one of the present authors) are methodological or corroborating, and they are accompanied by independent citations and by the paper's own control experiments; they do not carry the argument alone. The possible interfacial CoOx alternative, acknowledged in SI Note 8 and supported by the SI Note 5 control, is a scientific-interpretation risk rather than a circularity of the derivation chain.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central claims rest on standard harmonic-Hall analysis, a mechanism attribution to the orbital Hall effect in CuOx that is inferred rather than directly measured, and the assumption that gating changes Cu oxidation without strongly altering the Co interface. No new entities are introduced.

free parameters (3)

orbital diffusion length in Py (lambda_Py) = ~4 nm
Fitted from Py thickness dependence of xi_DL using y=A*tanh(x/B+C)+D with C=1.5 nm fixed (SI Note 6). Used to support the orbital-current interpretation.
orbital diffusion length lower limit in Co (lambda_Co) = >=4.5 nm (lower limit)
Tentative fit to Co thickness dependence; authors acknowledge it is unreliable because no saturation observed (SI Note 6).
spin diffusion length in Pt (lambda_Pt) = 1.56 nm
Fit to Co/Pt thickness dependence; used only as a reference, not central.

assumptions (5)

standard math Harmonic Hall analysis correctly separates damping-like and field-like torques from thermoelectric contributions (Eqs. 1-4).
The analysis relies on established formalism (Refs. 30,32,33) without re-derivation; assumes thermal terms R_delta_T are properly accounted for.
domain assumption The orbital-to-spin conversion coefficient eta is significantly larger in Py and Ni than in Co (Refs. 9,36).
Used to explain why Py/CuOx torque is larger than Co/CuOx; this assumption is imported from literature.
ad hoc to paper The orbital Hall effect in naturally oxidized Cu produces an orbital accumulation that converts to a damping-like torque in the adjacent ferromagnet.
Central interpretation; invoked in 'The negative sign of xi_DL...' paragraph and used to attribute the sign and thickness dependence.
ad hoc to paper Voltage-driven oxygen migration alters the Cu oxidation state without significantly oxidizing the Co interface.
Required for the gating demonstration; the authors present indirect evidence and admit 'minor oxidation of Co close to the Cu interface is possible' (SI Note 8).
domain assumption Parallel resistor model accurately describes current distribution in the multilayer for Oersted-field subtraction.
Used to compute B_Oe; relies on bulk resistivities of single-layer films, which may differ from those in the stack.

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Cite this review

Pith. "Pith review of Tunable spin and orbital torques in Cu-based magnetic heterostructures." pith.science (2026). https://pith.science/paper/7QWLM7SU

@misc{pith2026250109458,
  author       = {Pith},
  title        = {Pith review of: Tunable spin and orbital torques in Cu-based magnetic heterostructures},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7QWLM7SU}},
  note         = {Machine review of arXiv:2501.09458}
}

read the original abstract

Current-induced torques originating from earth-abundant 3d elements offer a promising avenue for low-cost and sustainable spintronic memory and logic applications. Recently, orbital currents -- transverse orbital angular momentum flow in response to an electric field -- have been in the spotlight since they allow current-induced torque generation from 3d transition metals. Here, we report a comprehensive study of the current-induced spin and orbital torques in Cu-based magnetic heterostructures. We show that high torque efficiencies can be achieved in engineered Ni80Fe20/Cu bilayers where Cu is naturally oxidized, exceeding the ones found in the archetypical Co/Pt. Furthermore, we demonstrate sign and amplitude control of the damping-like torque by manipulating the oxidation state of Cu via solid-state gating. Our findings provide insights into the interplay between charge, spin, and orbital transport in Cu-based heterostructures and open the door to the development of gate-tunable spin-orbitronic devices.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

8 extracted references · 8 canonical work pages

[1]

Methods Sample Preparation. Bilayers of Co/Cu, Co/Pt, Py/Cu and Py/Pt with in-plane mag- netic anisotropy were deposited on thermally oxidized Si(001)/SiO2 substrates at room temperature by DC magnetron sputtering with 3 mTorr Ar. The deposition rates of Co, Py, Cu and Pt were 0.104 nms −1 at 200 W , 0.0568 nms −1 at 100 W, 0.0675 nm nms−1 at 50 W and 0.1...

work page 2022
[2]

XPS analysis To characterize the composition of our materials, the oxidation state of Ti, O, Cu and Co was investigated by X-ray Photoelectron spectroscopy (XPS). We prepared three different samples: 1 - Ti(1.5)/Co(5)/CuOX (3), where CuO X was obtained by natural oxidation of Cu, 2 - Ti(1.5)/Co(5)/Cu(3)/Ti(1.5) and 3- Ti(1.5)/CoOX(6)/Cu/Ti(1.5), where CuO...

work page
[3]

Magnetism and Magnetic Materials

VSM measurements The magnetic properties of the FM(t)/Cu(3) bilayers were studied by means of vibrating sample magnetometry in a Quantum Design Physical Property Measurement System (PPMS). Figure S3a shows the in-plane magnetic hysteresis loops of Co samples with variable thickness. The saturation magnetization MS of Co ranges from 1.17×106 A/m for the 1....

work page 2010
[4]

These values are comparable with what previously obtained for films of comparable thickness [Y

Parallel resistor model of current density The resistivity of Co, Py, Cu and Pt are measured from reference single -layer samples and result to be 37.2 μΩ/cm, 51.8 μΩ/ cm, 8.8 μΩ/ cm and 50 μΩ/ cm respectively. These values are comparable with what previously obtained for films of comparable thickness [Y. Ke, et al., Phys. Rev. B 79, 155406 (2009), Nguyen...

work page 2009
[5]

Ochoa, R

Self-induced torques Spin accumulations can also be generated by spin -polarized currents in metallic ferromagnets without the active intervention of adjacent normal metals [H. Ochoa, R. Zarzuela, and Y. Tserkovnyak, J. Magn. Magn. Mater. 538, 168262 (2021) ]. To estimate the magnitude of the self-induced torque in Co and Py we measured single- layer film...

work page 2021
[6]

Figure S6.1a shows a plot of the damping-like component of the torque as a function of Pt thickness ( tPt), which increases steeply for the first few nm and saturates above 3 nm

Spin and orbital diffusion length To quantify the spin diffusion length in Pt ( λPt) we studied the SOT in Co(5)/Pt( t) bilayers. Figure S6.1a shows a plot of the damping-like component of the torque as a function of Pt thickness ( tPt), which increases steeply for the first few nm and saturates above 3 nm. From the fit of the experimental points with an ...

work page 2024
[7]

Therefore , we attempted to measure the orbital torques in Ni/CuOx bilayers

Spin transparency at the FM/NM interface It is well -known that the bulk of Ni is more efficient than Py in the orbital -to-spin conversion. Therefore , we attempted to measure the orbital torques in Ni/CuOx bilayers. Figure S 7a shows the damping -like torque efficiency ( ξDL) measured in different FM/NM bilayers. Surprisingly, the absolute value of ξDL ...

work page
[8]

Upon applying a negative VG, the Cu present in the stack gets oxidized and the resistance increases (light blue in Figure S8.1a)

Voltage-driven ion migration in Cu An indirect proof of the formation of metallic Cu via ion-migration upon gating with a positive gate voltage ( VG) comes from following the resistance ( RL) of the stack during the gating experiment. Upon applying a negative VG, the Cu present in the stack gets oxidized and the resistance increases (light blue in Figure ...

work page 2020

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.

[1] [1]

Methods Sample Preparation. Bilayers of Co/Cu, Co/Pt, Py/Cu and Py/Pt with in-plane mag- netic anisotropy were deposited on thermally oxidized Si(001)/SiO2 substrates at room temperature by DC magnetron sputtering with 3 mTorr Ar. The deposition rates of Co, Py, Cu and Pt were 0.104 nms −1 at 200 W , 0.0568 nms −1 at 100 W, 0.0675 nm nms−1 at 50 W and 0.1...

work page 2022

[2] [2]

XPS analysis To characterize the composition of our materials, the oxidation state of Ti, O, Cu and Co was investigated by X-ray Photoelectron spectroscopy (XPS). We prepared three different samples: 1 - Ti(1.5)/Co(5)/CuOX (3), where CuO X was obtained by natural oxidation of Cu, 2 - Ti(1.5)/Co(5)/Cu(3)/Ti(1.5) and 3- Ti(1.5)/CoOX(6)/Cu/Ti(1.5), where CuO...

work page

[3] [3]

Magnetism and Magnetic Materials

VSM measurements The magnetic properties of the FM(t)/Cu(3) bilayers were studied by means of vibrating sample magnetometry in a Quantum Design Physical Property Measurement System (PPMS). Figure S3a shows the in-plane magnetic hysteresis loops of Co samples with variable thickness. The saturation magnetization MS of Co ranges from 1.17×106 A/m for the 1....

work page 2010

[4] [4]

These values are comparable with what previously obtained for films of comparable thickness [Y

Parallel resistor model of current density The resistivity of Co, Py, Cu and Pt are measured from reference single -layer samples and result to be 37.2 μΩ/cm, 51.8 μΩ/ cm, 8.8 μΩ/ cm and 50 μΩ/ cm respectively. These values are comparable with what previously obtained for films of comparable thickness [Y. Ke, et al., Phys. Rev. B 79, 155406 (2009), Nguyen...

work page 2009

[5] [5]

Ochoa, R

Self-induced torques Spin accumulations can also be generated by spin -polarized currents in metallic ferromagnets without the active intervention of adjacent normal metals [H. Ochoa, R. Zarzuela, and Y. Tserkovnyak, J. Magn. Magn. Mater. 538, 168262 (2021) ]. To estimate the magnitude of the self-induced torque in Co and Py we measured single- layer film...

work page 2021

[6] [6]

Figure S6.1a shows a plot of the damping-like component of the torque as a function of Pt thickness ( tPt), which increases steeply for the first few nm and saturates above 3 nm

Spin and orbital diffusion length To quantify the spin diffusion length in Pt ( λPt) we studied the SOT in Co(5)/Pt( t) bilayers. Figure S6.1a shows a plot of the damping-like component of the torque as a function of Pt thickness ( tPt), which increases steeply for the first few nm and saturates above 3 nm. From the fit of the experimental points with an ...

work page 2024

[7] [7]

Therefore , we attempted to measure the orbital torques in Ni/CuOx bilayers

Spin transparency at the FM/NM interface It is well -known that the bulk of Ni is more efficient than Py in the orbital -to-spin conversion. Therefore , we attempted to measure the orbital torques in Ni/CuOx bilayers. Figure S 7a shows the damping -like torque efficiency ( ξDL) measured in different FM/NM bilayers. Surprisingly, the absolute value of ξDL ...

work page

[8] [8]

Upon applying a negative VG, the Cu present in the stack gets oxidized and the resistance increases (light blue in Figure S8.1a)

Voltage-driven ion migration in Cu An indirect proof of the formation of metallic Cu via ion-migration upon gating with a positive gate voltage ( VG) comes from following the resistance ( RL) of the stack during the gating experiment. Upon applying a negative VG, the Cu present in the stack gets oxidized and the resistance increases (light blue in Figure ...

work page 2020