Pith. sign in

REVIEW 2 major objections 6 minor 63 references

Symmetry Breaking by Interfacial Dead Layers: Observation of Forbidden Self-Induced Spin-Orbit Torque in Symmetric Ferromagnets

T0 review · 2 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

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

Pith's one-line read Forbidden spin-orbit torque observed in a symmetric ferromagnet trilayer.

desk verdict Robust self-torque in a symmetric trilayer is a real observation, but the dead-layer attribution is underdetermined by the data and the paper's own DFT section admits an alternative symmetry breaker. read the letter →

arxiv 2608.09614 v1 pith:DVOHY7CR submitted 2026-08-10 cond-mat.mes-hall

Athira Ravindran K , Raghvendra Posti , Manish Kumar Mohanta , Abhishek Kumar , Damanpreet Kaur , Alberto Anadón , Sebastien Petit-Watelot , Juan-Carlos Rojas-Sánchez
show 3 more authors
Michel Hehn Puru Jena Debangsu Roy
This is my paper · ORCID
classification cond-mat.mes-hall
keywords spin-orbittorqueself-inducedmagneticdeadlayerNiFeMgO/NiFe/MgOharmonicHallmeasurementspinconductivityheavy-metal-freespintronics
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 reports that a nominally symmetric MgO/NiFe/MgO trilayer, a structure where a net spin-orbit torque is forbidden by inversion symmetry, nonetheless shows a clear damping-like torque with magnitude comparable to heavy-metal/ferromagnet bilayers. The symmetry-breaking agent is identified as a naturally formed magnetic dead layer about 1.8 nm thick at the bottom NiFe/MgO interface, seen in magnetization and photoemission depth profiles. Fitting the thickness dependence of the torque to the drift-diffusion model of [1] yields a dead-layer thickness of about 1.2 nm, in quantitative agreement with the structural estimate. Density-functional calculations give NiFe an intrinsic spin Hall conductivity large enough to supply the observed spin currents. If correct, the result converts an interface defect usually treated as parasitic into a functional element that can generate heavy-metal-free spin-orbit torques in standard magnetic stacks.

What carries the argument

The carrying mechanism is the drift-diffusion model of [1] applied to a single ferromagnetic layer, expressed in the fitting formula H_AD(t) = C_self / t_eff x Re[((g_top - g_bot) lambda_F tanh(t_eff / 2 lambda_F)) / ((g_top + g_bot) lambda_F coth(t_eff / lambda_F) + K)]. Here g_top and g_bot are the spin-absorption conductances of the two interfaces, and their difference is the source of the net torque: a spin current generated by the ferromagnet's intrinsic spin Hall effect precesses while diffusing, then reflects differently at the two interfaces so the top and bottom accumulations do not cancel. The magnetic dead layer is the physical object that makes g_top and g_bot unequal: a roughly 1.8 nm oxidized, magnetically inert region at the bottom interface detected by SQUID and XPS. In the experiment, this formula converts the measured thickness dependence into a dead-layer thickness and matches the structural value. The DFT calculation supplies the complementary ingredient, showing that the Ni3Fe(111) surface and the MgO/Ni3Fe(111) interface have an intrinsic spin Hall conductivity large enough to generate the required spin current.

What would settle it

A direct test is to make the two interfaces chemically and magnetically equivalent, for example by eliminating the bottom dead layer or by forming an identical dead layer at the top interface, and check whether the damping-like torque vanishes; a second test is high-resolution structural imaging of the (111) terminations to see whether they are equivalent.

Watch

Extended reading notes

Core claim

The central claim is that self-induced spin-orbit torque does not require a broken bulk or an engineered gradient: asymmetry in interfacial spin absorption alone can make the torque finite in a symmetric ferromagnet. In MgO(2)/NiFe(t)/MgO(3.5) trilayers with t from 4.5 to 14.4 nm, harmonic Hall measurements find a damping-like effective field that rises, peaks, and falls with thickness, the signature of a bulk spin current that precesses and diffuses before accumulating at the interfaces. X-ray photoemission shows Ni and Fe oxides only at the bottom NiFe/MgO interface, and SQUID magnetometry gives a magnetic dead layer of about 1.8 nm; fitting the torque data to the drift-diffusion equation of [1] with unequal top and bottom spin absorption yields about 1.2 nm. The paper therefore claims the first explicit confirmation that an interfacial dead layer creates the spin-absorption asymmetry required for a net self-torque, and that NiFe's intrinsic spin Hall conductivity, around 3 x $10^{2}$ (hbar/e) S/cm in the DFT (111)-surface calculation, an order below Pt, is sufficient to drive it. The field-like torque is non-negligible and roughly thickness-independent, consistent with the same model's prediction of transverse torques from spin precession even without interfacial asymmetry.

Load-bearing premise

The argument depends on the magnetic dead layer at the bottom interface being the only meaningful difference between the two interfaces; if the top and bottom (111) Ni3Fe surfaces are intrinsically inequivalent, the torque could come from that structural asymmetry alone.

Editorial extensions

If this is right

  • Standard MgO/NiFe/MgO films, which contain no heavy metal, can produce damping-like torques at a magnitude comparable to Pt/ferromagnet bilayers.
  • The torque magnitude can be predicted from the stack's dead-layer thickness through the drift-diffusion formula, making structure-to-function mapping quantitative.
  • Interfacial oxidation, normally avoided in device growth, becomes a controllable parameter for engineering self-torques.
  • The measured field-like torque confirms that spin precession inside an ordinary ferromagnet yields transverse torque even without interfacial asymmetry.
  • Because the effect requires only a common ferromagnet and oxide barriers, existing oxide/ferromagnet/oxide stacks may already contain hidden self-torques that standard symmetry arguments would miss.

Reading between the lines

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

  • If the dead-layer mechanism holds, past control samples with nominally symmetric oxide/ferromagnet/oxide stacks may deserve re-examination, since hidden self-torques could have been subtracted or dismissed as artifacts.
  • A direct testable extension is to tune the bottom interface by controlled oxygen exposure or an ultrathin inserted oxide layer and map the torque against dead-layer thickness; the drift-diffusion formula makes the predicted curve quantitative.
  • Because NiFe's intrinsic spin Hall conductivity is an order below Pt yet still yields a measurable torque, the result suggests that modest spin Hall materials can be sufficient once interface absorption is asymmetric.
  • The finding implies that torque cancellation in symmetric ferromagnetic stacks is the exception rather than the rule whenever the two interfaces differ chemically or magnetically, even unintentionally.
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.

Referee Report

2 major / 6 minor

Summary. The paper reports observation of a nonzero damping-like spin-orbit torque in a nominally symmetric MgO/NiFe/MgO trilayer, where conventional symmetry arguments forbid a net self-torque. Harmonic Hall measurements on a thickness wedge (4.5–14.4 nm) yield a DL effective field that peaks and then decreases with thickness. SQUID magnetometry and XPS depth profiling identify a ~1.8 nm magnetically dead layer at the bottom NiFe/MgO interface. The authors fit the thickness dependence with the Kim–Lee drift-diffusion expression, extracting a dead-layer thickness of ~1.2 nm, and support the mechanism with DFT calculations of the intrinsic spin Hall conductivity of Ni3Fe(111) and MgO/Ni3Fe interfaces. The central claim is that the naturally formed dead layer is the symmetry-breaking element that enables the forbidden self-torque.

Significance. If the causal attribution holds, the result is significant: it would provide a direct experimental validation of the Kim–Lee prediction that interfacial asymmetry in spin absorption alone can produce a net self-torque in a single ferromagnet, and it would reframe magnetic dead layers as functional spintronic elements. The experimental dataset is substantial and the paper does several things well: the harmonic Hall analysis includes a symmetry decomposition and explicit accounting for thermoelectric contributions; the dead-layer evidence from SQUID and XPS is independent of the transport model; and the thickness-series measurement is a suitable test of the Kim–Lee formalism. The main weakness is that the paper's own DFT discussion concedes an alternative symmetry-breaking source—intrinsic top/bottom (111) termination inequivalence—so the data do not uniquely identify the dead layer as the origin of the torque. The quantitative fit to Eq. 6 also lacks the parameter constraints needed to support the specific '1.2 nm vs 1.8 nm' agreement claimed in the abstract.

major comments (2)
  1. [DFT Analysis, final paragraph before Conclusions] The manuscript explicitly concedes that 'the (111) Ni3Fe surface terminations at the top and bottom interfaces may not be equivalent' because of the ABC stacking sequence, with different bonding configurations and electronic hybridization, and that 'confirming the exact atomic terminations... lies beyond the scope of this work.' Since the Kim–Lee mechanism requires only an asymmetry in interfacial spin absorption (g_top ≠ g_bot), a purely structural/electronic interface asymmetry could produce the observed net damping-like torque without any magnetic dead layer. No control sample in which the dead layer is suppressed, moved to the top interface, or varied independently is reported. The wording in the abstract and the XPS/SQUID section—'we identify the symmetry-breaking origin' and 'we therefore attribute the observed self-torque to the interfacial asymmetry arising from the magnetic dead layer'—therefore overstates what the data establish. The authors should either provide such controls or reframe the central claim as demonstrating a self-torque consistent with dead-layer-induced asymmetry rather than uniquely identifying that mechanism.
  2. [Eq. 6 and Fig. 3(d)] The claimed quantitative agreement between the fitted dead-layer thickness (~1.2 nm) and the independently measured value (~1.8 nm) is not demonstrated in the main text. Equation (6) contains at least C_self, g_top, g_bot, λ_F, K, and the dead-layer correction entering through t_eff as adjustable parameters, yet no fixed values, constraints, starting points, parameter uncertainties, or uniqueness/identifiability analysis are reported. A correlated multi-parameter fit of a non-monotonic thickness dependence can easily absorb a 0.6 nm shift in the effective thickness. To make this point load-bearing, the authors must report the full parameter set with confidence intervals, a fit in which t_dead is fixed to the SQUID value of 1.8 nm with a comparison of goodness of fit, and a sensitivity analysis. As it stands, the 'agreement' between 1.2 nm and 1.8 nm is suggestive but does not constitute the quantitative validation claimed in the abstract.
minor comments (6)
  1. [Introduction, paragraph after Eq. 6] The phrase 'This mechanism provides direct evidence for substantial self-torque' overstates the inferential strength of a fit with unconstrained parameters; 'is consistent with' would be more appropriate.
  2. [Fig. 3(c)] The linear fit of magnetic moment per area versus NiFe thickness used to extract the 1.8 nm dead layer should report the fit parameters, uncertainties, and the criterion used to identify the thickness intercept as the dead layer.
  3. [DFT Analysis, Fig. 4] The DFT calculations are performed on an ordered Ni3Fe(111) surface, whereas the measured films are polycrystalline Ni80Fe20; a brief justification of the transferability of the computed spin Hall conductivity to the polycrystalline experimental system would strengthen the argument.
  4. [Fig. 2(e)–(f) and text] The statement that the damping-like torque is 'comparable to HM-based systems' would be more convincing with a direct numerical benchmark against specific Pt/FM values cited in the references, rather than a qualitative comparison.
  5. [Equation (6)] All symbols in Eq. (6), especially C_self, K, λ_F, and t_eff, should be defined in the main text rather than only in the supplementary information.
  6. [References] Several references are missing journal identifiers (e.g., [5], [21], [35], [45], [50]); these should be completed before publication.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the dead-layer comparison rests on an independent structural benchmark, and the Kim-Lee theory is external to the authors.

full rationale

The derivation chain is not circular. The central quantitative claim—that a fitted magnetic dead-layer thickness of ~1.2 nm agrees with an independently measured value of ~1.8 nm—is a parameter comparison, not an identity. The transport fit uses the measured thickness dependence of the damping-like torque (Eq. 6, Fig. 2e), while the SQUID/XPS dead layer is obtained from the intercept of moment/area versus thickness (Fig. 3c) and from oxide core-level depth profiles. Neither quantity is constructed from the other, so the agreement is not forced by construction. The Kim-Lee drift-diffusion theory [1] is external to the present authors, and the DFT spin-Hall-conductivity calculation is a separate first-principles computation rather than a recycled input. The only self-citations (Refs. 9-10) are background references on heavy-metal/ferromagnet SOTs and are not load-bearing. The paper does concede, in the DFT section, that "the (111) Ni3Fe surface terminations at the top and bottom interfaces may not be equivalent" and that confirming exact terminations "lies beyond the scope of this work." This is a genuine limitation: the causal attribution to the dead layer is underdetermined relative to an intrinsic interface asymmetry. However, underdetermination of mechanism is not circularity—no equation reduces to its own input, and the matching structural measurement is independent. Therefore the paper is self-contained against its external benchmarks and warrants a score of 0.

Assumptions & free parameters 6 free parameters · 4 assumptions · 0 invented entities

The central claim depends on a handful of fit parameters in the Kim-Lee model (C_self, g_top, g_bot, lambda_F, K) and on the assumption that the fitted interfacial conductance asymmetry can be converted into a dead-layer thickness. The dead-layer thickness measured by SQUID/XPS is independent; the one from the transport fit is a derived fit quantity, not a free-floating prediction.

free parameters (6)
  • C_self
    Overall amplitude prefactor in Eq 6, adjusted to match the DL torque magnitude; value not stated in main text.
  • g_top
    Spin-mixing conductance of the top MgO/NiFe interface in Eq 6; the asymmetry (g_top - g_bot) is used to infer the dead-layer thickness.
  • g_bot
    Spin-mixing conductance of the bottom NiFe/MgO interface in Eq 6; its difference from g_top encodes the dead-layer effect.
  • lambda_F
    Spin diffusion length in NiFe used in the drift-diffusion model; likely taken from literature or fitted; not stated in main text.
  • K
    Dimensionless constant in the denominator of Eq 6; part of the model fit.
  • dead_layer_thickness_from_fit = ~1.2 nm
    The value presented as the theoretical extraction, but it is a derived quantity from the fitted conductance asymmetry, not an independent prediction.
assumptions (4)
  • domain assumption The Kim-Lee drift-diffusion formalism with asymmetric interfacial spin absorption rates accurately describes the torque in NiFe.
    The paper fits the thickness dependence of H_AD to Eq 6, which is based on this model (Refs [1,53]). If the model is inapplicable, the extracted dead-layer thickness has no meaning.
  • domain assumption The harmonic Hall analysis correctly separates SOT contributions from thermoelectric (ANE, PNE) and Oersted effects.
    The extraction of H_AD,y and H_FL,y relies on the angular decomposition in Eqs 2-3 and the symmetrization procedure described in the supplement. Misassignment of thermal signals to SOT would bias the effective fields.
  • ad hoc to paper The intrinsic spin Hall conductivity of the fcc Ni3Fe (111) surface is representative of the polycrystalline Ni80Fe20 in the experiment.
    The DFT calculations use an ordered Ni3Fe (111) slab, while the measured films are polycrystalline Ni80Fe20 with unknown texture. The paper claims the SHC is sufficient but does not fully justify the transfer.
  • domain assumption The macrospin approximation for the magnetization dynamics in the harmonic Hall analysis is valid for these in-plane films.
    The fitting equation Eq 2 assumes coherent rotation of magnetization and uniform current density; the paper notes minor deviations near zero field in M-H loops.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Symmetry Breaking by Interfacial Dead Layers: Observation of Forbidden Self-Induced Spin-Orbit Torque in Symmetric Ferromagnets." pith.science (2026). https://pith.science/paper/DVOHY7CR

@misc{pith2026260809614,
  author       = {Pith},
  title        = {Pith review of: Symmetry Breaking by Interfacial Dead Layers: Observation of Forbidden Self-Induced Spin-Orbit Torque in Symmetric Ferromagnets},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DVOHY7CR}},
  note         = {Machine review of arXiv:2608.09614}
}
read the original abstract

Conventionally, spin-orbit torques (SOTs) in ferromagnets require heavy-metal layers or engineered structural asymmetry to break inversion symmetry. In this work, we report the observation of robust, self-generated SOTs in a nominally symmetric, heavy-metal-free MgO/NiFe/MgO trilayer - a geometry where such torques are theoretically forbidden. By combining harmonic Hall measurements with SQUID magnetometry and X-ray photoelectron spectroscopy, we identify the symmetry-breaking origin: a 1.8 nm magnetic dead layer at the bottom interface. Crucially, we demonstrate a quantitative agreement between our data and the drift-diffusion theory predicted by Kim and Lee, yielding a theoretically extracted dead-layer thickness (1.2 nm) which matches structural characterization. Furthermore, density-functional calculations confirm that NiFe possesses sufficient intrinsic spin Hall conductivity to support the observed spin currents. These results reframe the parasitic dead layer as a functional spintronic component, establishing a universal, all-ferromagnetic route to SOTs in standard magnetic heterostructures.

Figures

Figures reproduced from arXiv: 2608.09614 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 5
Figure 5. FIG. 5. (a) Optimized atomic structure of MgO [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

63 extracted references · 63 canonical work pages

  1. [1]

    K. W. Kim and K. J. Lee, Phys. Rev. Lett. 125, 207205 (2020)

    work page 2020

  2. [2]

    X. Qiu, Z. Shi, W. Fan, S. Zhou, and H. Yang, Advanced Materials 30, 1705699 (2018)

    work page 2018

  3. [3]

    Brataas, A

    A. Brataas, A. D. Kent, and H. Ohno, Nature Materials 11, 372 (2012)

    work page 2012

  4. [4]

    Chappert, A

    C. Chappert, A. Fert, and F. N. Van Dau, Nature Materials 6, 813 (2007)

    work page 2007

  5. [5]

    J. Ryu, S. Lee, K.-J. Lee, and B.-G. Park, 32, 1907148 (2020)

    work page 2020

  6. [6]

    Manchon, J

    A. Manchon, J. Železný, I. M. Miron, T. Jungwirth, J. Sinova, A. Thiaville, K. Garello, and P. Gambardella, Reviews of Modern Physics 91, 035004 (2019)

    work page 2019

  7. [7]

    C. F. Pai, Y. Ou, L. H. Vilela-Leão, D. C. Ralph, and R. A. Buhrman, Phys. Rev. B 92, 064426 (2015)

    work page 2015

  8. [8]

    Posti, A

    R. Posti, A. Kumar, D. Tiwari, and D. Roy, Applied Physics Letters 121, 223502 (2022)

    work page 2022

Show all 63 references
  1. [9]

    Posti, A

    R. Posti, A. Kumar, M. Baghoria, B. Prakash, D. Tiwari, and D. Roy, Applied Physics Letters 122, 152405 (2023). 17

    2023

  2. [10]

    Posti, A

    R. Posti, A. Ravindran K, D. Tiwari, and D. Roy, ACS Applied Electronic Materials 7, 3955 (2025)

    2025

  3. [11]

    Davidson, V

    A. Davidson, V. P. Amin, W. S. Aljuaid, P. M. Haney, and X. Fan, Physics Letters A 384, 126228 (2020)

    2020

  4. [12]

    Kim, B.-G

    K.-W. Kim, B.-G. Park, and K.-J. Lee, npj Spintronics 2, 8 (2024)

    2024

  5. [13]

    V. P. Amin, J. Li, M. D. Stiles, and P. M. Haney, Physical Review B 99, 220405 (2019)

    2019

  6. [14]

    C. O. Pauyac, M. Chshiev, A. Manchon, and S. A. Nikolaev, Physical Review Letters 120, 176802 (2018)

    2018

  7. [15]

    Xue et al., Nature Communications 14, 3932 (2023)

    F. Xue et al., Nature Communications 14, 3932 (2023)

    2023

  8. [16]

    Dc et al., Nature Materials 22, 591 (2023)

    M. Dc et al., Nature Materials 22, 591 (2023)

    2023

  9. [17]

    Zheng, J

    F. Zheng, J. Dong, Y. Song, M. Zhu, X. Li, and J. Zhang, Applied Physics Letters 126 (2025)

    2025

  10. [18]

    Wang et al., Physical Review Applied 17, 034026 (2022)

    W. Wang et al., Physical Review Applied 17, 034026 (2022)

    2022

  11. [19]

    MacNeill, G

    D. MacNeill, G. M. Stiehl, M. H. D. Guimaraes, R. A. Buhrman, J. Park, and D. C. Ralph, Nature Physics 13, 300 (2017)

    2017

  12. [20]

    Pandey et al., Nature Communications 16, 8722 (2025)

    L. Pandey et al., Nature Communications 16, 8722 (2025)

    2025

  13. [21]

    Q. Liu, X. Lin, A. Shaked, Z. Nie, G. Yu, and L. Zhu, 36, 2406552 (2024)

    2024

  14. [22]

    Safranski, E

    C. Safranski, E. A. Montoya, and I. N. Krivorotov, Nature Nanotechnology 14, 27 (2019)

    2019

  15. [23]

    E. A. Montoya, X. Pei, and I. N. Krivorotov, Nature Nanotechnology 20, 353 (2025)

    2025

  16. [24]

    T. C. Chuang, D. Qu, S. Y. Huang, and S. F. Lee, Physical Review Research 2, 032053 (2020)

    2020

  17. [25]

    Zheng, M

    F. Zheng, M. Zhu, J. Dong, X. Li, Y. Zhou, K. Wu, and J. Zhang, Physical Review B 109, 224401 (2024)

    2024

  18. [26]

    Wang et al., Nat

    W. Wang et al., Nat. Nanotechnol. 14, 819 (2019)

    2019

  19. [27]

    Seki, Y.-C

    T. Seki, Y.-C. Lau, S. Iihama, and K. Takanashi, Physical Review B 104, 094430 (2021)

    2021

  20. [28]

    R. E. Maizel et al., Physical Review Applied 22, 044052 (2024)

    2024

  21. [29]

    Fu et al., Physical Review B 105, 224417 (2022)

    Q. Fu et al., Physical Review B 105, 224417 (2022)

    2022

  22. [30]

    Hibino, T

    Y. Hibino, T. Taniguchi, K. Yakushiji, H. Kubota, and S. Yuasa, Physical Review B 109, L180409 (2024)

    2024

  23. [31]

    L. Zhu, X. Zhang, D. Muller, D. Ralph, and R. Buhrman, Advanced Functional Materials, 2020005201 (2020)

    2020

  24. [32]

    S. Park, K. J. Lee, S. Lee, X. Liu, M. Dobrowolska, and J. K. Furdyna, APL Materials 9 (2021)

    2021

  25. [33]

    Y. Du, R. Thompson, M. Kohda, and J. Nitta, AIP Advances 11, 025033 (2021)

    2021

  26. [34]

    Z. Luo, Q. Zhang, Y. Xu, Y. Yang, X. Zhang, and Y. Wu, Phys. Rev. Appl. 11, 064021 (2019)

    2019

  27. [35]

    Wang et al., 32, 2204212 (2022)

    W. Wang et al., 32, 2204212 (2022)

    2022

  28. [36]

    Haidar, A

    M. Haidar, A. A. Awad, M. Dvornik, R. Khymyn, A. Houshang, and J. Åkerman, Nature Communications 10, 2362 (2019)

    2019

  29. [37]

    M. Aoki, Y. Yin, S. Granville, Y. Zhang, N. V. Medhekar, L. Leiva, R. Ohshima, Y. Ando, and M. Shiraishi, Nano Letters 23, 6951 (2023)

    2023

  30. [38]

    Tsukahara, Y

    A. Tsukahara, Y. Ando, Y. Kitamura, H. Emoto, E. Shikoh, M. P. Delmo, T. Shinjo, and M. Shiraishi, Physical Review B 89, 235317 (2014)

    2014

  31. [39]

    Gladii et al., Physical Review B 100, 174409 (2019)

    O. Gladii et al., Physical Review B 100, 174409 (2019)

    2019

  32. [40]

    Liu, Y.-H

    Y.-T. Liu, Y.-H. Huang, C.-C. Huang, Y.-C. Li, C.-L. Cheng, and C.-F. Pai, Physical Review Applied 18, 034019 (2022)

    2022

  33. [41]

    Huang et al., ACS nano 16, 12462 (2022)

    Q. Huang et al., ACS nano 16, 12462 (2022)

    2022

  34. [42]

    R. Q. Zhang et al., Physical Review B 101, 214418 (2020)

    2020

  35. [43]

    Chen et al., Applied Physics Express 14, 033002 (2021)

    Z. Chen et al., Applied Physics Express 14, 033002 (2021)

    2021

  36. [44]

    Liu et al., Nature Communications 13, 3539 (2022)

    L. Liu et al., Nature Communications 13, 3539 (2022)

    2022

  37. [45]

    Tang et al., 32, 2002607 (2020)

    M. Tang et al., 32, 2002607 (2020)

    2020

  38. [46]

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

    2014

  39. [47]

    Hayashi, J

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

    2014

  40. [48]

    Y. Wen, J. Wu, P. Li, Q. Zhang, Y. Zhao, A. Manchon, J. Q. Xiao, and X. Zhang, Physical Review B 95, 104403 (2017)

    2017

  41. [49]

    N. Soya, M. Yamada, K. Hamaya, and K. Ando, Physical Review Letters 131, 076702 (2023)

    2023

  42. [50]

    Q. Liu, X. Lin, and L. Zhu, 10, 2301409 (2023)

    2023

  43. [51]

    M. Aoki, E. Shigematsu, R. Ohshima, T. Shinjo, M. Shiraishi, and Y. Ando, Phys. Rev. B 106, 174418 (2022)

    2022

  44. [52]

    Choi et al., Nature Communications 16, 5859 (2025)

    W.-Y. Choi et al., Nature Communications 16, 5859 (2025)

    2025

  45. [53]

    E.-S. Park, D. Lee, O. Lee, B.-C. Min, H. C. Koo, K.-W. Kim, and K.-J. Lee, Physical Review B 103, 134405 (2021). 18

    2021

  46. [54]

    Hu, Y.-F

    C.-Y. Hu, Y.-F. Chiu, C.-C. Tsai, C.-M. Lee, M.-Y. Song, S.-J. Lin, X. Bao, and C.-F. Pai, ACS Applied Electronic Materials 5, 968 (2023)

    2023

  47. [55]

    Lau and M

    Y.-C. Lau and M. Hayashi, Japanese Journal of Applied Physics 56, 0802B5 (2017)

    2017

  48. [56]

    M. S. Gabor, M. Belmeguenai, and I. M. Miron, Physical Review B 109, 104407 (2024)

    2024

  49. [57]

    L. Liu, T. Moriyama, D. C. Ralph, and R. A. Buhrman, Physical Review Letters 106, 036601 (2011)

    2011

  50. [58]

    C.-F. Pai, Y. Ou, L. H. Vilela-Leão, D. C. Ralph, and R. A. Buhrman, Physical Review B 92, 064426 (2015)

    2015

  51. [59]

    Tanaka, H

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

    2008

  52. [60]

    Musha, Y

    A. Musha, Y. Kanno, and K. Ando, Physical Review Materials 3, 054411 (2019)

    2019

  53. [61]

    J. Qiao, J. Zhou, Z. Yuan, and W. Zhao, Physical Review B 98, 214402 (2018)

    2018

  54. [62]

    M. K. Mohanta and P. Jena, Physical Review B 108, 085432 (2023)

    2023

  55. [63]

    Jo et al., Nano Letters 24, 7100 (2024)

    Y. Jo et al., Nano Letters 24, 7100 (2024)

    2024

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.