Quantitative analysis of vectorial torques in thin 3d Co ferromagnet using orbital-spin conversion

A. Fert; B. Bony; H. Jaffr\`es; J.-M. George; M. Viret; S. Collin; S. Krishnia; V. Cros; Y. Xu

REVIEW 3 major objections 6 minor 59 references

Quantitative analysis of vectorial torques in thin 3d Co ferromagnet using orbital-spin conversion

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

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read 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…

desk verdict 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. read the letter →

arxiv 2501.09864 v1 pith:WMQ5JV3C submitted 2025-01-16 cond-mat.mtrl-sci cond-mat.mes-hall

B. Bony , S. Krishnia , Y. Xu , S. Collin , A. Fert , J.-M. George , M. Viret , V. Cros

show 1 more author

H. Jaffrès

This is my paper · ORCID

classification cond-mat.mtrl-scicond-mat.mes-hall

keywords orbitaltorqueRashba-Edelsteineffectspin-orbitorbit-to-spinconversionsecondharmonicHalldecoherencelengthcobaltthinfilmscopperoxideinterface

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

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.

What carries the argument

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.

What would settle it

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.

Watch

Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

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.

Reading between the lines

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

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.

Share X Bluesky LinkedIn Reddit HN

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

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.

The 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.

None 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.

Referee Report

3 major / 6 minor

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.

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 (3)

[Section IV, Fig. 4b, Eq. (6)] 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 V, Fig. 6] 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 IV, model completeness] 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.

minor comments (6)

[Introduction] The phrase "One one hand" at the start of the paragraph discussing coherence lengths contains a duplicate word.
[Section V] The sentence "In tat case, the current density in Cu*..." contains a typo: "tat" should be "that".
[Fig. 4 caption] The caption uses the shorthand "Co(t)" while the text and axes use "Co(tCo)"; the notation should be made consistent.
[Eq. (2)] 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).
[References] 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.
[General] 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.

Circularity Check

1 steps flagged · score 4.0 of 10

Central 'pure orbital injection' claim is the residual of a spin-only fit performed over a window defined by assuming orbital torque is negligible; the Cu*-free reference shows the same linear rise.

fitted input called prediction [Section IV, fitting of Eq. (6); Fig. 4b; Section V]
"we detail our quantitative model describing the spin-orbit torque arising from spin only in the limit of small tCo, region wherein the orbital torque is negligible. ... The major result of this paper is the linear increase of ξDL for tCo ≥ 2 nm assigned to pure orbital injection and interactions in Co."

Eq. (6) is a spin-only torque expression. The fit is restricted to tCo < 2 nm by the paper's own premise that orbital torque is negligible there, so any excess at tCo ≥ 2 nm is, by construction, classified as 'pure orbital injection'. The claimed long orbital decoherence length is not extracted from an independent orbital-transport model; it is the linear residual left after subtracting the spin-only fit. Because the Co(tCo)|Pt(3) reference without Cu* exhibits the same linear rise (Fig. 4b), the residual cannot uniquely identify Cu* interfacial OREE: a bulk orbital Hall self-torque in Co, absent from Eq. (6), would produce the same slope. The 'orbital' conclusion is thus the leftover of the fitted model rather than a parameter-free prediction.

full rationale

The paper contains original harmonic-Hall measurements and an independent spin-transport expression, Eq. (6), so the analysis is not globally circular. Fitting parameters such as G↑↓rPt_s and λPt_sf are imported from prior work of the same group, but they are not the target result and the torque data are new. The mild circular loop is in the interpretive step: the spin-only model is fit only in the tCo < 2 nm window defined as 'region wherein the orbital torque is negligible', and the linear rise beyond 2 nm is then assigned to 'pure orbital injection'. That assignment is fixed once the model and window are chosen. The Co|Pt reference without Cu* shows the same linear rise, so the excess is not specific to Cu*; an omitted bulk orbital-Hall self-torque in Co would mimic it. This is a fitted residual called a conclusion (score 4) rather than a definitional identity; an independent orbital-transport model or a control suppressing bulk Co OHE would be needed to break the loop.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central torque claim depends on a spin-only transport fit in a restricted thickness window, on prior material parameters, and on the assumption that OREE at the Cu interface generates the orbital current. The AHE and shunt analysis also uses material parameters taken from earlier work, but those affect normalizations rather than the main torque attribution. No new entities are introduced.

free parameters (4)

G↑↓r_s^Pt (spin mixing conductance times Pt spin resistance) = ≈ 2
Used in Eq. (6) to fit the spin-only torque and extract decoherence lengths; value taken from prior work by the same group [22,27], not measured here.
λ_sf^Pt (spin diffusion length in Pt) = 1.75 ± 0.05 nm
Input to Eq. (6) from Refs [22,27]; quoted uncertainty is not propagated into the final spin versus orbital decomposition.
λ_F^{⊥,Re} decoherence lengths for the three series = 1.40±0.16, 1.85±0.20, 1.67±0.10 nm
Central outputs from fitting Eq. (6) to the tCo < 2 nm data; values depend on the model and on the two input parameters above.
σ_SHE^eff (effective spin Hall conductivity for torque) = 1600, 2090, 2860 (ℏ/e)(Ω cm)^-1
Fit results for Co|Pt, Co|Pt(3)|Cu* and Co|Pt(4)|Cu* respectively; used to quantify enhancement and to support the second spin channel claim.

assumptions (5)

standard math Complex Boltzmann equation with spin-mixing conductance at Co|Pt describes spin transport in Co.
Underlies Eqs. (5)-(6); accepted background transport theory, not derived in the paper.
domain assumption Orbital torque is negligible for tCo < 2 nm, allowing a spin-only fit.
Section IV explicitly limits the model to 'the limit of small tCo, region wherein the orbital torque is negligible'; this defines the fit window and is the gate for the claim that the thick-Co residual is orbital.
ad hoc to paper Perfect electronic reflection at the back end of the thin Co layer.
Assumption in the derivation of Eq. (6); non-perfect reflection at Co/SiO2 would change the extracted spin channel and the residual orbital contribution.
domain assumption OREE at the Cu|CuO_x interface is the source of the orbital current.
Taken from Refs [13,20,22,28-33] and used in Eq. (3) and Section V; the paper's own Co|Cu* data show increasing ξDL with tCu, so the interfacial conclusion is not self-evident from this paper alone.
domain assumption The linear increase of ξDL for tCo ≥ 2 nm is caused by pure orbital current inside Co.
Assigned with Refs [33,47,54]; no direct orbital-current probe is used, and the stated origin changes within the paper (Pt in Section III A, Cu* in Section V and the Conclusions).

how reviews work

0 comments

Cite this review

Pith. "Pith review of Quantitative analysis of vectorial torques in thin 3d Co ferromagnet using orbital-spin conversion." pith.science (2026). https://pith.science/paper/WMQ5JV3C

@misc{pith2026250109864,
  author       = {Pith},
  title        = {Pith review of: Quantitative analysis of vectorial torques in thin 3d Co ferromagnet using orbital-spin conversion},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WMQ5JV3C}},
  note         = {Machine review of arXiv:2501.09864}
}

read the original abstract

Recent findings in orbitronics pointed out large current-induced torques originating, in the current understanding, from incident orbital currents. These are generated by orbital Rashba-Edelstein effect (OREE) produced at the interface between some light metal and oxides films e.g. by naturally oxidized copper layer (Cu*). In the present work, by using second harmonic Hall techniques, we determine the ratio of orbital vs spin currents exerting torques on thin transition metals Co ferromagnet in systems using an orbit-to-spin Pt converter as interlayer with Cu*. Our results quantifying damping like torques show that both orbital and spin currents are enhanced in these systems. Moreover, the experimental determination of the decoherence length in a sample series with varying Co thickness clearly demonstrates the interfacial generation of the orbital currents in Cu* by Orbital Rashba-Edelstein effects (REE) leading to subsequent magnetic torque in Co over a typical lengthscale of several nanometers

Figures

Figures reproduced from arXiv: 2501.09864 by the authors.

**Figure 2.** FIG. 2. Cobalt thickness dependence for Co( [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** FIG. 3. a) Azimuthal angle [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: FIG. 4. Co thickness dependence for the Co( [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

**Figure 5.** Figure 5: FIG. 5. Co thickness dependence for the Co( [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

**Figure 6.** Figure 6: FIG. 6. Cu* thickness dependence DL effective field normalized by [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

59 extracted references · 55 canonical work pages

[1]

Manchon, J

A. Manchon, J. Zelezny, I. M. Miron, T. Jungwirth, J. Sinova, A. Thiaville, K. Garello, and P. Gambardella, Rev. Mod. Phys. 91, 035004 (2019)

work page 2019
[2]

Mihai Miron, G

I. Mihai Miron, G. Gaudin, S. Auffret, B. Rodmacq, A. Schuhl, S. Pizzini, J. V ogel, and P. Gambardella, Nature Materials 9, 230 (2010)

work page 2010
[3]

I. M. Miron, K. Garello, G. Gaudin, P.-J. Zermatten, M. V . Costache, S. Auffret, S. Bandiera, B. Rodmacq, A. Schuhl, and P. Gambardella, Nature 476, 189 (2011)

work page 2011
[4]

D. Lee, D. Go, H.-J. Park, W. Jeong, H.-W. Ko, D. Yun, D. Jo, S. Lee, G. Go, J. H. Oh, K.-J. Kim, B.-G. Park, B.-C. Min, H. C. Koo, H.-W. Lee, O. Lee, and K.-J. Lee, Nature Commu- nications 12, 6710 (2021)

work page 2021
[5]

D. Go, D. Jo, C. Kim, and H.-W. Lee, Physical Review Letters 121, 086602 (2018)

work page 2018
[6]

D. Go, F. Freimuth, J.-P. Hanke, F. Xue, O. Gomonay, K.-J. Lee, S. Blügel, P. M. Haney, H.-W. Lee, and Y . Mokrousov, Phys. Rev. Res. 2, 033401 (2020)

work page 2020
[7]

D. Go, D. Jo, H.-W. Lee, M. Kläui, and Y . Mokrousov, Euro- physics Letters 135, 37001 (2021)

work page 2021
[9]

Tang and G

P. Tang and G. E. W. Bauer, Phys. Rev. Lett. 133, 186302 (2024)

work page 2024

Show all 59 references

[10]

Y .-G. Choi, D. Jo, K.-H. Ko, D. Go, K.-H. Kim, H. G. Park, C. Kim, B.-C. Min, G.-M. Choi, and H.-W. Lee, Nature 619, 52 (2023)

2023
[11]

Go, J.-P

D. Go, J.-P. Hanke, P. M. Buhl, F. Freimuth, G. Bihlmayer, H.- W. Lee, Y . Mokrousov, and S. Blügel, Scientific Reports 7, 46742 (2017). 9

2017
[12]

Johansson, B

A. Johansson, B. Göbel, J. Henk, M. Bibes, and I. Mertig, Phys. Rev. Res. 3, 013275 (2021)

2021
[13]

S. Ding, Z. Liang, D. Go, C. Yun, M. Xue, Z. Liu, S. Becker, W. Yang, H. Du, C. Wang, Y . Yang, G. Jakob, M. Kläui, Y . Mokrousov, and J. Yang, Phys. Rev. Lett. 128, 067201 (2022)

2022
[14]

Leiva-Montecinos, J

S. Leiva-Montecinos, J. Henk, I. Mertig, and A. Johansson, Phys. Rev. Res. 5, 043294 (2023)

2023
[15]

El Hamdi, J.-Y

A. El Hamdi, J.-Y . Chauleau, M. Boselli, C. Thibault, C. Gorini, A. Smogunov, C. Barreteau, S. Gariglio, J.-M. Triscone, and M. Viret, Nature Physics 19, 1855 (2023)

2023
[16]

Quantum kinetic theory of the linear response for weakly disordered multiband systems,

T. Valet and R. Raimondi, “Quantum kinetic theory of the linear response for weakly disordered multiband systems,” (2024), arXiv:2410.08975 [cond-mat.mes-hall]

2024 arXiv
[17]

Salemi and P

L. Salemi and P. M. Oppeneer, Phys. Rev. Mater. 6, 095001 (2022)

2022
[18]

D. Jo, D. Go, and H.-W. Lee, Phys. Rev. B 98, 214405 (2018)

2018
[19]

Sala and P

G. Sala and P. Gambardella, Phys. Rev. Res. 4, 033037 (2022)

2022
[20]

J. Kim, J. Uzuhashi, M. Horio, T. Senoo, D. Go, D. Jo, T. Sumi, T. Wada, I. Matsuda, T. Ohkubo, S. Mitani, H.-W. Lee, and Y . Otani, Phys. Rev. Mater.7, L111401 (2023)

2023
[21]

Lee, M.-G

S. Lee, M.-G. Kang, D. Go, D. Kim, J.-H. Kang, T. Lee, G.-H. Lee, J. Kang, N. J. Lee, Y . Mokrousov,et al., Communications Physics 4, 234 (2021)

2021
[22]

Krishnia, B

S. Krishnia, B. Bony, E. Rongione, L. M. Vicente-Arche, T. Denneulin, A. Pezo, Y . Lu, R. Dunin-Borkowski, S. Collin, A. Fert, et al., APL Materials 12 (2024)

2024
[23]

S. Ding, A. Ross, D. Go, L. Baldrati, Z. Ren, F. Freimuth, S. Becker, F. Kammerbauer, J. Yang, G. Jakob, Y . Mokrousov, and M. Kläui, Physical Review Letters 125, 177201 (2020)

2020
[24]

Santos, J

E. Santos, J. Abrão, D. Go, L. de Assis, Y . Mokrousov, J. Mendes, and A. Azevedo, Physical Review Applied 19, 014069 (2023)

2023
[25]

Gupta, C

R. Gupta, C. Bouard, F. Kammerbauer, J. O. Ledesma- Martin, A. Bose, I. Kononenko, S. Martin, P. Usé, G. Jakob, M. Drouard, and M. Kläui, Nature Communications 16, 130 (2025)

2025
[26]

S. A. Nikolaev, M. Chshiev, F. Ibrahim, S. Krishnia, N. Sebe, J.-M. George, V . Cros, H. Jaffrès, and A. Fert, Nano Letters24, 13465 (2024)

2024
[27]

Krishnia, Y

S. Krishnia, Y . Sassi, F. Ajejas, N. Sebe, N. Reyren, S. Collin, T. Denneulin, A. Kovács, R. E. Dunin-Borkowski, A. Fert, et al., Nano Letters 23, 6785 (2023)

2023
[28]

D. Go, D. Jo, T. Gao, K. Ando, S. Blügel, H.-W. Lee, and Y . Mokrousov, Physical Review B103, L121113 (2021)

2021
[29]

H. An, Y . Kageyama, Y . Kanno, N. Enishi, and K. Ando, Na- ture communications 7, 13069 (2016)

2016
[30]

J. Kim, D. Go, H. Tsai, D. Jo, K. Kondou, H.-W. Lee, and Y . Otani, Phys. Rev. B103, L020407 (2021)

2021
[31]

Huang, S

Q. Huang, S. Liu, T. Yang, R. Xie, L. Cai, Q. Cao, W. Lu, L. Bai, Y . Tian, and S. Yan, Nano Letters23, 11323 (2023)

2023
[32]

Ding, M.-G

S. Ding, M.-G. Kang, W. Legrand, and P. Gambardella, Phys. Rev. Lett. 132, 236702 (2024)

2024
[33]

S. Ding, H. Wang, W. Legrand, P. Noël, and P. Gambardella, Nano Letters (2024)

2024
[34]

Otani, W

Y . Otani, W. Gao, L. Liao, H. Isshiki, J. Kim, D. Go, Y . Mokrousov, K. Lee, and H. Lee, (2024), 10.21203/rs.3.rs- 5107751/v1

2024 doi
[35]

J. A. Mendoza-Rodarte, M. Cosset-Chéneau, B. J. van Wees, and M. H. D. Guimarães, Phys. Rev. Lett. 132, 226704 (2024)

2024
[36]

Sahoo, S

A. Sahoo, S. Mallick, A. Rath, H. Ding, A. Azevedo, and S. Be- danta, Applied Physics Letters 125 (2024)

2024
[37]

H. An, Y . Kageyama, Y . Kanno, N. Enishi, and K. Ando, Na- ture Communications 7, 13069 (2016)

2016
[38]

Rang and P

M. Rang and P. J. Kelly, Phys. Rev. B 109, 214427 (2024)

2024
[39]

Hayashi, D

H. Hayashi, D. Jo, D. Go, T. Gao, S. Haku, Y . Mokrousov, H.- W. Lee, and K. Ando, Communications Physics 6, 32 (2023)

2023
[40]

Chiba, Y

S. Chiba, Y . Marui, H. Ohno, and S. Fukami, Nano Letters 24, 14028 (2024)

2024
[41]

D. Go, D. Jo, K.-W. Kim, S. Lee, M.-G. Kang, B.-G. Park, S. Blügel, H.-W. Lee, and Y . Mokrousov, (2022), arXiv:2106.07928 [cond-mat.mes-hall]

2022 arXiv
[42]

K.-J. Lee, V . Cros, and H.-W. Lee, Nature Materials 23, 1302 (2024)

2024
[43]

M. D. Stiles and A. Zangwill, Phys. Rev. B 66, 014407 (2002)

2002
[44]

Taniguchi, S

T. Taniguchi, S. Yakata, H. Imamura, and Y . Ando, IEEE Transactions on Magnetics 44, 2636 (2008)

2008
[45]

Ghosh, S

A. Ghosh, S. Auffret, U. Ebels, and W. Bailey, Physical review letters 109, 127202 (2012)

2012
[46]

S. Ding, P. Noël, G. K. Krishnaswamy, and P. Gambardella, Phys. Rev. Res. 4, L032041 (2022)

2022
[47]

Orbital hall effect in transition metals from first-principles scattering calculations,

M. Rang and P. J. Kelly, “Orbital hall effect in transition metals from first-principles scattering calculations,” (2024), arXiv:2409.20526 [cond-mat.mtrl-sci]

2024 arXiv
[48]

Inter- facial spin-orbitronic effects controlled with different oxidation levels at the co|al interface,

S. Krishnia, L. V ojá ˇcek, T. D. C. S. C. Gomes, N. Sebe, F. Ibrahim, J. Li, L. M. Vicente-Arche, S. Collin, T. Denneulin, R. E. Dunin-Borkowski, P. Ohresser, N. Jaouen, A. Thiaville, A. Fert, H. Jaffrès, M. Chshiev, N. Reyren, and V . Cros, “Inter- facial spin-orbitronic eff...

2024 arXiv
[49]

V . W. Guo, B. Lu, X. Wu, G. Ju, B. Valcu, and D. Weller, Journal of Applied Physics 99 (2006)

2006
[50]

T. H. Dang, Q. Barbedienne, D. Q. To, E. Rongione, N. Reyren, F. Godel, S. Collin, J. M. George, and H. Jaffrès, Phys. Rev. B 102, 144405 (2020)

2020
[51]

Alternative harmonic detection approach for quantitative determination of spin and orbital torques,

Y . Xu, B. Bony, S. Krishnia, R. T. Victor, S. Collin, A. Fert, J. M. George, V . Cros, and H. Jaffrès, “Alternative harmonic detection approach for quantitative determination of spin and orbital torques,” (2024), arXiv:2501.00403 [cond-mat.mtrl- sci]

2024 arXiv
[52]

Hayashi, J

M. Hayashi, J. Kim, M. Yamanouchi, and H. Ohno, Phys. Rev. B 89, 144425 (2014)

2014
[53]

C. O. Avci, K. Garello, M. Gabureac, A. Ghosh, A. Fuhrer, S. F. Alvarado, and P. Gambardella, Phys. Rev. B 90, 224427 (2014)

2014
[54]

Tanaka, H

T. Tanaka, H. Kontani, M. Naito, T. Naito, D. S. Hirashima, K. Yamada, and J. Inoue, Phys. Rev. B 77, 165117 (2008)

2008
[55]

Ghosh, K

A. Ghosh, K. Garello, C. O. Avci, M. Gabureac, and P. Gam- bardella, Phys. Rev. Appl. 7, 014004 (2017)

2017
[56]

Petitjean, D

C. Petitjean, D. Luc, and X. Waintal, Phys. Rev. Lett. 109, 117204 (2012)

2012
[57]

Phenomenol- ogy of orbital torque, pumping and mixing conductance in metallic bilayers,

X. Ning, H. Jaffrès, W. Zhao, and A. Manchon, “Phenomenol- ogy of orbital torque, pumping and mixing conductance in metallic bilayers,” (2024), arXiv:2412.08340 [cond-mat.mes- hall]

2024 arXiv
[58]

D. Go, D. Jo, C. Kim, and H.-W. Lee, Phys. Rev. Lett. 121, 086602 (2018)

2018
[59]

Kim, Phys

K.-W. Kim, Phys. Rev. B 99, 224415 (2019)

2019
[60]

Salemi, M

L. Salemi, M. Berritta, and P. M. Oppeneer, Phys. Rev. Mater. 5, 074407 (2021)

2021

Pith tools

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

[1] [1]

Manchon, J

A. Manchon, J. Zelezny, I. M. Miron, T. Jungwirth, J. Sinova, A. Thiaville, K. Garello, and P. Gambardella, Rev. Mod. Phys. 91, 035004 (2019)

work page 2019

[2] [2]

Mihai Miron, G

I. Mihai Miron, G. Gaudin, S. Auffret, B. Rodmacq, A. Schuhl, S. Pizzini, J. V ogel, and P. Gambardella, Nature Materials 9, 230 (2010)

work page 2010

[3] [3]

I. M. Miron, K. Garello, G. Gaudin, P.-J. Zermatten, M. V . Costache, S. Auffret, S. Bandiera, B. Rodmacq, A. Schuhl, and P. Gambardella, Nature 476, 189 (2011)

work page 2011

[4] [4]

D. Lee, D. Go, H.-J. Park, W. Jeong, H.-W. Ko, D. Yun, D. Jo, S. Lee, G. Go, J. H. Oh, K.-J. Kim, B.-G. Park, B.-C. Min, H. C. Koo, H.-W. Lee, O. Lee, and K.-J. Lee, Nature Commu- nications 12, 6710 (2021)

work page 2021

[5] [5]

D. Go, D. Jo, C. Kim, and H.-W. Lee, Physical Review Letters 121, 086602 (2018)

work page 2018

[6] [6]

D. Go, F. Freimuth, J.-P. Hanke, F. Xue, O. Gomonay, K.-J. Lee, S. Blügel, P. M. Haney, H.-W. Lee, and Y . Mokrousov, Phys. Rev. Res. 2, 033401 (2020)

work page 2020

[7] [7]

D. Go, D. Jo, H.-W. Lee, M. Kläui, and Y . Mokrousov, Euro- physics Letters 135, 37001 (2021)

work page 2021

[8] [9]

Tang and G

P. Tang and G. E. W. Bauer, Phys. Rev. Lett. 133, 186302 (2024)

work page 2024