pith. sign in

arxiv: 2511.09511 · v3 · submitted 2025-11-12 · ❄️ cond-mat.mes-hall

Spin and orbital-to-charge conversion in noncentrosymmetric materials: Hall versus Rashba-Edelstein effects

Diego Garcia Ovalle , Aurelien Manchon This is my paper

Pith reviewed 2026-05-17 22:09 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords Rashba-Edelstein effectspin Hall effectorbital Hall effectnoncentrosymmetricGeTedrift-diffusion modelcharge conversionbroken inversion symmetry
0
0 comments X

The pith

The Rashba-Edelstein effect primarily governs charge current generation from spin and orbital conversion in noncentrosymmetric materials.

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

This paper develops a general formalism using macroscopic observables to describe spin and orbital to charge conversion in materials with broken inversion symmetry. It treats the Hall effect and Rashba-Edelstein effect equally. In a case study of ferroelectric GeTe the fitted Rashba parameter is smaller than earlier reports. When fed into a drift-diffusion model the charge current turns out to be driven mainly by the Rashba-Edelstein effect instead of spin or orbital Hall effects.

Core claim

We investigate spin- and orbital-to-charge conversion phenomena in nonmagnetic materials with broken inversion symmetry, treating the contributions from the Hall effect and the Rashba-Edelstein effect on an equal footing. We develop a general formalism for this interconversion based solely on macroscopic observables. The theory is validated through a case study of ferroelectric GeTe, where we find that the effective Rashba parameter obtained is smaller than previously reported values for the same material. Incorporating these parameters into a drift-diffusion model, we show that the generated charge current is primarily governed by the Rashba-Edelstein effect, rather than by the spin or orb

What carries the argument

General formalism based on macroscopic observables that places Hall and Rashba-Edelstein contributions on equal footing for conversion analysis.

If this is right

  • The generated charge current is primarily governed by the Rashba-Edelstein effect.
  • The effective Rashba parameter for GeTe is smaller than previously reported.
  • Drift-diffusion models can predict the relative importance of different conversion mechanisms using fitted parameters.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same macroscopic approach could be applied to other noncentrosymmetric materials to identify dominant conversion channels.
  • Device design in spintronics might benefit from emphasizing interface Rashba effects over bulk Hall responses.
  • Further experiments on GeTe could verify if the smaller Rashba value holds across different conditions.

Load-bearing premise

The macroscopic observables formalism accurately captures the interconversion without needing microscopic band-structure details and the fitted Rashba parameter for GeTe transfers to the drift-diffusion model.

What would settle it

A measurement of the charge current in GeTe under spin or orbital current injection that does not match the drift-diffusion model prediction based on the reported Rashba parameter would disprove the primary governance by the Rashba-Edelstein effect.

Figures

Figures reproduced from arXiv: 2511.09511 by Aurelien Manchon, Diego Garcia Ovalle.

Figure 1
Figure 1. Figure 1: FIG. 1. (Color online) Sketch of the spin-to-charge conversion [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (Color online) Crystal structure and band structure [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (Color online) (a) Longitudinal conductivity (black [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. (Color online) (a) charge-to-spin (red) and charge-to [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. (Color online) (a) Density of states coefficient, mod [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗
read the original abstract

We investigate spin- and orbital-to-charge conversion phenomena in nonmagnetic materials with broken inversion symmetry, treating the contributions from the Hall effect and the Rashba-Edelstein effect on an equal footing. We develop a general formalism for this interconversion based solely on macroscopic observables. The theory is validated through a case study of ferroelectric GeTe, where we find that the effective Rashba parameter obtained is smaller than previously reported values for the same material. Incorporating these parameters into a drift-diffusion model, we show that the generated charge current is primarily governed by the Rashba-Edelstein effect, rather than by the spin or orbital Hall effects.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript develops a general formalism for spin- and orbital-to-charge conversion in noncentrosymmetric materials, treating Hall and Rashba-Edelstein contributions on equal footing and relying solely on macroscopic observables. Validation is performed via a case study on ferroelectric GeTe, yielding an effective Rashba parameter smaller than prior reports. These parameters are then inserted into a drift-diffusion model, from which the authors conclude that the generated charge current is primarily governed by the Rashba-Edelstein effect rather than spin or orbital Hall effects.

Significance. If the central claim is robust, the work supplies a macroscopic route to separating conversion mechanisms that avoids full microscopic band-structure input, which could streamline analysis of spin-orbit phenomena in polar materials. The reported smaller Rashba parameter for GeTe and the resulting dominance of Rashba-Edelstein conversion would refine expectations for device-relevant current generation in similar systems.

major comments (2)
  1. [Abstract / GeTe case study] Abstract and GeTe case study: the central claim that Rashba-Edelstein dominates rests on extracting a fitted effective Rashba parameter from the macroscopic formalism and inserting it unchanged into the drift-diffusion model. The manuscript provides no explicit test of whether this parameter remains valid once k-dependent orbital textures or scattering channels (omitted or averaged in the macroscopic treatment) are restored at the drift-diffusion level; without such a consistency check the dominance conclusion risks being an artifact of inconsistent modeling levels.
  2. [Drift-diffusion modeling] Drift-diffusion modeling section: the relative weighting of Rashba-Edelstein versus Hall contributions is reported to favor the former, yet the text does not quantify the sensitivity of this ordering to the precise value of the fitted Rashba parameter (including its uncertainty relative to earlier literature values). Because the ordering is the load-bearing result, a parameter-variation or error-propagation analysis is required to establish that the conclusion is not driven by the particular fitted number.
minor comments (2)
  1. [Formalism] Notation for the macroscopic observables (e.g., the precise definitions of the effective conversion coefficients) should be collected in a single table or appendix for clarity.
  2. [GeTe case study] A brief comparison table of the new Rashba parameter against the range of previously reported values for GeTe would help readers assess the magnitude of the reported reduction.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thorough review and constructive feedback on our manuscript. We address the two major comments point by point below, providing our reasoning and indicating where revisions will be made to strengthen the presentation.

read point-by-point responses

  1. Referee: [Abstract / GeTe case study] Abstract and GeTe case study: the central claim that Rashba-Edelstein dominates rests on extracting a fitted effective Rashba parameter from the macroscopic formalism and inserting it unchanged into the drift-diffusion model. The manuscript provides no explicit test of whether this parameter remains valid once k-dependent orbital textures or scattering channels (omitted or averaged in the macroscopic treatment) are restored at the drift-diffusion level; without such a consistency check the dominance conclusion risks being an artifact of inconsistent modeling levels.

    Authors: We appreciate the referee raising this consistency concern. Our macroscopic formalism is deliberately constructed to produce effective parameters that already incorporate averaged contributions from orbital and spin textures, without explicit k-dependence. The subsequent drift-diffusion model operates at a comparable phenomenological level and is intended to employ precisely these effective quantities derived from macroscopic observables. By design, the two stages remain consistent within the effective-description framework that forms the core of the work; restoring full microscopic k-dependent details would require a separate band-structure calculation outside the stated scope. We therefore do not consider the procedure an artifact. To improve clarity we will insert a short explanatory paragraph in the revised manuscript justifying the use of the effective Rashba parameter across both stages. revision: partial

  2. Referee: [Drift-diffusion modeling] Drift-diffusion modeling section: the relative weighting of Rashba-Edelstein versus Hall contributions is reported to favor the former, yet the text does not quantify the sensitivity of this ordering to the precise value of the fitted Rashba parameter (including its uncertainty relative to earlier literature values). Because the ordering is the load-bearing result, a parameter-variation or error-propagation analysis is required to establish that the conclusion is not driven by the particular fitted number.

    Authors: The referee correctly identifies that a sensitivity analysis would make the dominance conclusion more robust. In the revised version we will add a dedicated subsection (or appendix) that varies the effective Rashba parameter over the range of its fitted uncertainty and compares it with the spread of previously reported values for GeTe. We will show that the Rashba-Edelstein contribution remains the leading term throughout this interval. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation remains self-contained

full rationale

The paper develops a new general formalism for spin/orbital-to-charge conversion based on macroscopic observables, validates it on ferroelectric GeTe by extracting an effective Rashba parameter (reported smaller than prior values), and then inserts those parameters into a standard drift-diffusion model to conclude Rashba-Edelstein dominance. No step reduces by construction to its own inputs: the formalism is presented as independent of microscopic band details, the parameter extraction is a validation step rather than a self-referential fit, and the drift-diffusion conclusion follows from applying the extracted values rather than re-deriving them tautologically. No self-citations are load-bearing for the central claim, no ansatz is smuggled, and no uniqueness theorem is invoked from prior author work. The derivation chain is therefore independent of the target result.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Based solely on the abstract, the central claim rests on the transferability of a fitted Rashba parameter and the assumption that macroscopic observables suffice without microscopic input.

free parameters (1)
  • effective Rashba parameter for GeTe
    Obtained from the case study and stated to be smaller than previously reported; used as input to the drift-diffusion model.
axioms (1)
  • domain assumption Macroscopic observables fully capture spin- and orbital-to-charge conversion without microscopic band details
    Invoked to justify the general formalism in noncentrosymmetric materials.

pith-pipeline@v0.9.0 · 5410 in / 1266 out tokens · 21442 ms · 2026-05-17T22:09:58.360649+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

80 extracted references · 80 canonical work pages

  1. [1]

    The direct SHE is definedJ α s,γ =σ γ αβEβ, where J α s,γ is the spin Hall current and E β is the electric field

    Inverse spin Hall effect Since thedirectSHE is driven by the charge chemical potential gradient and theinverseSHE is driven by the spin chemical potential gradient, the spin-to-charge and charge-to-spin conductivities are simply equal to each other. The direct SHE is definedJ α s,γ =σ γ αβEβ, where J α s,γ is the spin Hall current and E β is the electric ...

    work page

  2. [2]

    (12) directly

    Inverse Rashba-Edelstein effect Let us now consider the direct SRE and inverse SRE, expressed respectively as S=η c→sz×J c,(10) Jc =η s→cz×S.(11) The direct SRE coefficient,η c→s (in units of A −1·m−1), is given by the spin-current correlation function, readily computed using the Kubo formula [50] ηc→s =− eτ σxx Z BZ d3k (2π)3 X n snk,xvnk,y∂ϵnk fnk,(12) ...

    work page 2030

  3. [3]

    W. Han, Y. Otani, and S. Maekawa, Quantum materials for spin and charge conversion, npj Quantum Materials 3, 27 (2018)

    work page 2018

  4. [4]

    M. I. D’yakonov and V. I. Perel’, Possibility of orienting electron spins with current, JETP Letters , 467 (1971)

    work page 1971

  5. [5]

    Sinova, S

    J. Sinova, S. O. Valenzuela, J. Wunderlich, C. H. Back, and T. Jungwirth, Spin hall effects, Rev. Mod. Phys.87, 1213 (2015)

    work page 2015

  6. [6]

    Edelstein, Spin polarization of conduction electrons induced by electric current in two-dimensional asymmet- ric electron systems, Solid State Communications73, 233 (1990)

    V. Edelstein, Spin polarization of conduction electrons induced by electric current in two-dimensional asymmet- ric electron systems, Solid State Communications73, 233 (1990)

    work page 1990

  7. [7]

    Bihlmayer, P

    G. Bihlmayer, P. No¨ el, D. V. Vyalikh, E. V. Chulkov, and A. Manchon, Rashba-like physics in condensed matter, Nature Reviews Physics4, 642 (2022)

    work page 2022

  8. [8]

    Mosendz, V

    O. Mosendz, V. Vlaminck, J. E. Pearson, F. Y. Fradin, G. E. W. Bauer, S. D. Bader, and A. Hoffmann, Detection and quantification of inverse spin hall effect from spin pumping in permalloy/normal metal bilayers, Phys. Rev. B82, 214403 (2010)

    work page 2010

  9. [9]

    Ando and E

    K. Ando and E. Saitoh, Inverse spin-Hall effect in palla- dium at room temperature, Journal of Applied Physics 108, 113925 (2010)

    work page 2010

  10. [10]

    Mosendz, J

    O. Mosendz, J. E. Pearson, F. Y. Fradin, G. E. W. Bauer, S. D. Bader, and A. Hoffmann, Quantifying spin hall an- gles from spin pumping: Experiments and theory, Phys. Rev. Lett.104, 046601 (2010)

    work page 2010

  11. [11]

    C.-F. Pai, L. Liu, Y. Li, H. W. Tseng, D. C. Ralph, and R. A. Buhrman, Spin transfer torque devices utilizing the giant spin Hall effect of tungsten, Applied Physics Letters 101, 122404 (2012)

    work page 2012

  12. [12]

    Jiao and G

    H. Jiao and G. E. W. Bauer, Spin backflow and ac voltage generation by spin pumping and the inverse spin hall effect, Phys. Rev. Lett.110, 217602 (2013)

    work page 2013

  13. [13]

    Y. Wang, P. Deorani, X. Qiu, J. H. Kwon, and H. Yang, Determination of intrinsic spin Hall angle in Pt, Applied Physics Letters105, 152412 (2014)

    work page 2014

  14. [14]

    Rojas-S´ anchez, N

    J.-C. Rojas-S´ anchez, N. Reyren, P. Laczkowski, W. Savero, J.-P. Attan´ e, C. Deranlot, M. Jamet, J.-M. George, L. Vila, and H. Jaffr` es, Spin pumping and in- verse spin hall effect in platinum: The essential role of spin-memory loss at metallic interfaces, Phys. Rev. Lett. 112, 106602 (2014)

    work page 2014

  15. [15]

    Isasa, E

    M. Isasa, E. Villamor, L. E. Hueso, M. Gradhand, and F. Casanova, Temperature dependence of spin diffusion length and spin hall angle in au and pt, Phys. Rev. B91, 024402 (2015)

    work page 2015

  16. [16]

    R. Yu, B. F. Miao, L. Sun, Q. Liu, J. Du, P. Omelchenko, B. Heinrich, M. Wu, and H. F. Ding, Determina- tion of spin hall angle and spin diffusion length inβ- phase-dominated tantalum, Phys. Rev. Mater.2, 074406 (2018)

    work page 2018

  17. [17]

    Manchon, S

    A. Manchon, S. Shi, and H. Yang, Spin current leakage and onsager reciprocity in interfacial spin-charge inter- conversion, Phys. Rev. B109, 094424 (2024)

    work page 2024

  18. [19]

    Zhang and A

    S. Zhang and A. Fert, Conversion between spin and charge currents with topological insulators, Phys. Rev. B94, 184423 (2016)

    work page 2016

  19. [20]

    Rojas-S´ anchez, S

    J.-C. Rojas-S´ anchez, S. Oyarz´ un, Y. Fu, A. Marty, C. Vergnaud, S. Gambarelli, L. Vila, M. Jamet, Y. Oht- subo, A. Taleb-Ibrahimi, P. Le F` evre, F. Bertran, N. Reyren, J.-M. George, and A. Fert, Spin to charge conversion at room temperature by spin pumping into a new type of topological insulator:α-sn films, Phys. Rev. Lett.116, 096602 (2016)

    work page 2016

  20. [21]

    Lesne, Y

    E. Lesne, Y. Fu, S. Oyarzun, J. C. Rojas-S´ anchez, D. C. Vaz, H. Naganuma, G. Sicoli, J.-P. Attan´ e, M. Jamet, E. Jacquet, J.-M. George, A. Barth´ el´ emy, H. Jaffr` es, A. Fert, M. Bibes, and L. Vila, Highly efficient and tun- able spin-to-charge conversion through rashba coupling at oxide interfaces, Nature Materials15, 1261 (2016)

    work page 2016

  21. [22]

    Y. Wang, R. Ramaswamy, M. Motapothula, K. Narayanapillai, D. Zhu, J. Yu, T. Venkatesan, and H. Yang, Room-temperature giant charge-to-spin conversion at the srtio3–laalo3 oxide interface, Nano Letters17, 7659 (2017)

    work page 2017

  22. [23]

    D. C. Vaz, P. No¨ el, A. Johansson, B. G¨ obel, F. Y. Bruno, G. Singh, S. McKeown-Walker, F. Trier, L. M. Vicente- Arche, A. Sander, S. Valencia, P. Bruneel, M. Vivek, M. Gabay, N. Bergeal, F. Baumberger, H. Okuno, A. Barth´ el´ emy, A. Fert, L. Vila, I. Mertig, J.-P. Attan´ e, and M. Bibes, Mapping spin–charge conversion to the band structure in a topolo...

    work page 2019

  23. [24]

    No¨ el, F

    P. No¨ el, F. Trier, L. M. V. Arche, J. Br´ ehin, D. C. Vaz, V. Garcia, S. Fusil, A. Barth´ el´ emy, L. Vila, M. Bibes, and J. philippe Attan´ e, Non-volatile electric control of spin – charge conversion in a srtio 3 rashba system, Nature580, 483 (2020)

    work page 2020

  24. [25]

    L. M. Vicente-Arche, J. Br´ ehin, S. Varotto, M. Cosset- Cheneau, S. Mallik, R. Salazar, P. No¨ el, D. C. Vaz, F. Trier, S. Bhattacharya, A. Sander, P. Le F` evre, F. Bertran, G. Saiz, G. M´ enard, N. Bergeal, A. Barth´ el´ emy, H. Li, C.-C. Lin, D. E. Nikonov, I. A. Young, J. E. Rault, L. Vila, J.-P. Attan´ e, and M. Bibes, Spin–charge interconversion in...

    work page 2021

  25. [26]

    Varotto, A

    S. Varotto, A. Johansson, B. G¨ obel, L. M. Vicente-Arche, S. Mallik, J. Br´ ehin, R. Salazar, F. Bertran, P. L. F` evre, N. Bergeal, J. Rault, I. Mertig, and M. Bibes, Direct vi- sualization of rashba-split bands and spin/orbital-charge interconversion at ktao3 interfaces, Nature Communica- tions13, 6165 (2022)

    work page 2022

  26. [27]

    Sharma, F.-X

    P. Sharma, F.-X. Xiang, D.-F. Shao, D. Zhang, E. Y. Tsymbal, A. R. Hamilton, and J. Seidel, A room-temperature ferroelectric semimetal, Science Advances5, eaax5080 (2019), https://www.science.org/doi/pdf/10.1126/sciadv.aax5080

    work page doi:10.1126/sciadv.aax5080 2019

  27. [28]

    Ishizaka, M

    K. Ishizaka, M. S. Bahramy, H. Murakawa, M. Sakano, T. Shimojima, T. Sonobe, K. Koizumi, S. Shin, H. Miyahara, A. Kimura, K. Miyamoto, T. Okuda, H. Namatame, M. Taniguchi, R. Arita, N. Nagaosa, K. Kobayashi, Y. Murakami, R. Kumai, Y. Kaneko, Y. Onose, and Y. Tokura, Giant rashba-type spin split- ting in bulk bitei, Nature materials10, 521 (2011), 10.1038/nmat3051

    work page doi:10.1038/nmat3051 2011

  28. [29]

    Varotto, L

    S. Varotto, L. Nessi, S. Cecchi, J. S lawi´ nska, P. No¨ el, 8 S. Petr` o, F. Fagiani, A. Novati, M. Cantoni, D. Petti, E. Albisetti, M. Costa, R. Calarco, M. Buon- giorno Nardelli, M. Bibes, S. Picozzi, J.-P. Attan´ e, L. Vila, R. Bertacco, and C. Rinaldi, Room-temperature ferroelectric switching of spin-to-charge conversion in ger- manium telluride, Nat...

    work page 2021

  29. [30]

    Calavalle, M

    F. Calavalle, M. Su´ arez-Rodr´ ıguez, B. Mart´ ın-Garc´ ıa, A. Johansson, D. C. Vaz, H. Yang, I. V. Maznichenko, S. Ostanin, A. Mateo-Alonso, A. Chuvilin, I. Mertig, M. Gobbi, F. Casanova, and L. E. Hueso, Gate-tuneable and chirality-dependent charge-to-spin conversion in tel- lurium nanowires, Nature Materials21, 526 (2022)

    work page 2022

  30. [31]

    M. S. Bahramy, R. Arita, and N. Nagaosa, Origin of giant bulk rashba splitting: Application to bitei, Phys. Rev. B 84, 041202 (2011)

    work page 2011

  31. [32]

    Di Sante, P

    D. Di Sante, P. Barone, R. Bertacco, and S. Picozzi, Elec- tric control of the giant rashba effect in bulk gete, Ad- vanced Materials25, 509 (2013)

    work page 2013

  32. [33]

    Jafari, A

    H. Jafari, A. Roy, and J. S lawi´ nska, Ferroelectric control of charge-to-spin conversion in wte 2, Phys. Rev. Mater. 6, L091404 (2022)

    work page 2022

  33. [34]

    L. Cai, C. Yu, W. Zhao, Y. Li, H. Feng, H.-A. Zhou, L. Wang, X. Zhang, Y. Zhang, Y. Shi, J. Zhang, L. Yang, and W. Jiang, The giant spin-to-charge conversion of the layered rashba material bitei, Nano Letters22, 7441 (2022)

    work page 2022

  34. [35]

    Tenzin, A

    K. Tenzin, A. Roy, H. Jafari, B. Banas, F. T. Cera- soli, M. Date, A. Jayaraj, M. Buongiorno Nardelli, and J. S lawi´ nska, Analogs of rashba-edelstein effect from den- sity functional theory, Phys. Rev. B107, 165140 (2023)

    work page 2023

  35. [36]

    D. Go, D. Jo, C. Kim, and H. W. Lee, Intrinsic spin and orbital hall effects from orbital texture, Physical Review Letters121, 086602 (2018)

    work page 2018

  36. [37]

    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, Observation of the orbital hall effect in a light metal ti, Nature619, 52 (2023)

    work page 2023

  37. [38]

    D. Jo, D. Go, and H. woo Lee, Gigantic intrinsic orbital hall effects in weakly spin-orbit coupled metals, Physical Review B98, 214405 (2018)

    work page 2018

  38. [39]

    A. Pezo, D. G. Ovalle, and A. Manchon, Orbital hall effect in crystals: inter-atomic versus intra-atomic con- tributions, Physical Review B106, 104414 (2022)

    work page 2022

  39. [40]

    D. Go, J. philipp Hanke, P. M. Buhl, F. Freimuth, G. Bihlmayer, H. woo Lee, Y. Mokrousov, and S. Bl¨ ugel, Toward surface orbitronics : giant orbital magnetism from the orbital rashba effect at the surface of sp-metals, Scientific Reports7, 46742 (2017)

    work page 2017

  40. [41]

    Tserkovnyak, A

    Y. Tserkovnyak, A. Brataas, and G. E. W. Bauer, Spin pumping and magnetization dynamics in metallic multi- layers, Physical Review B66, 224403 (2002)

    work page 2002

  41. [42]

    Brataas, Y

    A. Brataas, Y. Tserkovnyak, G. E. W. Bauer, and B. Halperin, Spin battery operated by ferromagnetic res- onance, Physical Review B66, 060404 (2002)

    work page 2002

  42. [43]

    Shchelushkin and A

    R. Shchelushkin and A. Brataas, Spin hall effects in diffu- sive normal metals, Physical Review B71, 045123 (2005)

    work page 2005

  43. [44]

    Picozzi, Ferroelectric rashba semiconductors as a novel class of multifunctional materials, Frontiers in Physics2, 1 (2014)

    S. Picozzi, Ferroelectric rashba semiconductors as a novel class of multifunctional materials, Frontiers in Physics2, 1 (2014)

    work page 2014

  44. [45]

    Liebmann, C

    M. Liebmann, C. Rinaldi, D. D. Sante, J. Kellner, C. Pauly, R. N. Wang, J. E. Boschker, A. Gius- sani, S. Bertoli, M. Cantoni, L. Baldrati, M. Asa, I. Vobornik, G. Panaccione, D. Marchenko, J. S´ anchez- Barriga, O. Rader, R. Calarco, S. Picozzi, R. Bertacco, and M. Morgenstern, Giant rashba-type spin splitting in ferroelectric gete(111), Advanced Materia...

    work page 2016

  45. [46]

    S. Han, H. W. Ko, J. H. Oh, H. W. Lee, K. J. Lee, and K. W. Kim, Orbital pumping incorporating both orbital angular momentum and position, Physical Review Let- ters134, 036305 (2025)

    work page 2025

  46. [47]

    D. Go, K. Ando, A. Pezo, S. Bl¨ ugel, A. Manchon, and Y. Mokrousov, Orbital pumping by magnetization dy- namics in ferromagnets, Physical Review B111, L140409 (2025)

    work page 2025

  47. [48]

    A. Pezo, D. Go, Y. Mokrousov, H. Jaffr` es, and A. Man- chon, Adiabatic spin and orbital pumping in metallic het- erostructures, Physical Review B111, 134424 (2025)

    work page 2025

  48. [49]

    Onsager, Reciprocal relations in irreversible processes

    L. Onsager, Reciprocal relations in irreversible processes. i., Phys. Rev.37, 405 (1931)

    work page 1931

  49. [50]

    Onsager, Reciprocal relations in irreversible processes

    L. Onsager, Reciprocal relations in irreversible processes. ii., Phys. Rev.38, 2265 (1931)

    work page 1931

  50. [51]

    J. Qiao, J. Zhou, Z. Yuan, and W. Zhao, Calculation of intrinsic spin hall conductivity by wannier interpolation, Phys. Rev. B98, 214402 (2018)

    work page 2018

  51. [52]

    Zhong, J

    S. Zhong, J. E. Moore, and I. Souza, Gyrotropic magnetic effect and the magnetic moment on the fermi surface, Phys. Rev. Lett.116, 077201 (2016)

    work page 2016

  52. [53]

    K. Shen, G. Vignale, and R. Raimondi, Microscopic the- ory of the inverse edelstein effect, Phys. Rev. Lett.112, 096601 (2014)

    work page 2014

  53. [54]

    Pezo, J.-M

    A. Pezo, J.-M. George, and H. Jaffr` es, Theory of spin and orbital charge conversion at the surface states of bi1−xsbx topological insulator, Phys. Rev. Res.6, 043332 (2024)

    work page 2024

  54. [55]

    Giannozzi, S

    P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococ- cioni, I. Dabo, A. D. Corso, S. de Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C. Sbraccia, S. Sc...

    work page 2009

  55. [56]

    Giannozzi, O

    P. Giannozzi, O. Andreussi, T. Brumme, O. Bunau, M. B. Nardelli, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, M. Cococcioni, N. Colonna, I. Carnimeo, A. D. Corso, S. de Gironcoli, P. Delugas, R. A. DiStasio, A. Ferretti, A. Floris, G. Fratesi, G. Fugallo, R. Gebauer, U. Gerstmann, F. Giustino, T. Gorni, J. Jia, M. Kawa- mura, H.-Y. Ko, A. Kokalj, E. K¨...

    work page 2017

  56. [57]

    J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996)

    work page 1996

  57. [58]

    Pizzi, V

    G. Pizzi, V. Vitale, R. Arita, S. Bl¨ ugel, F. Freimuth, G. G´ eranton, M. Gibertini, D. Gresch, C. Johnson, T. Koretsune, J. Iba˜ nez-Azpiroz, H. Lee, J.-M. Lihm, D. Marchand, A. Marrazzo, Y. Mokrousov, J. I. Mustafa, Y. Nohara, Y. Nomura, L. Paulatto, S. Ponc´ e, T. Pon- weiser, J. Qiao, F. Th¨ ole, S. S. Tsirkin, M. Wierzbowska, 9 N. Marzari, D. Vander...

    work page 2020

  58. [59]

    S. S. Tsirkin, High performance wannier interpolation of berry curvature and related quantities with wannierberri code, npj Computational Materials7, 33 (2021)

    work page 2021

  59. [60]

    Momma and F

    K. Momma and F. Izumi,VESTA3for three-dimensional visualization of crystal, volumetric and morphology data, Journal of Applied Crystallography44, 1272 (2011)

    work page 2011

  60. [61]

    Zhang, Z

    W. Zhang, Z. Teng, H. Zeng, H. Zhang, J. ˇZelezn´ y, and W. Zhang, Tuning spin hall conductivity in gete by ferroelectric polarization, physica status solidi (b)257, 2000143 (2020)

    work page 2020

  61. [62]

    H. Wang, P. Gopal, S. Picozzi, S. Curtarolo, M. Buon- giorno Nardelli, and J. S lawi´ nska, Spin hall effect in pro- totype rashba ferroelectrics gete and snte, npj Computa- tional Materials6, 7 (2020)

    work page 2020

  62. [63]

    Rojas-S´ anchez, M

    J.-C. Rojas-S´ anchez, M. Cubukcu, A. Jain, C. Vergnaud, C. Portemont, C. Ducruet, A. Barski, A. Marty, L. Vila, J.-P. Attan´ e, E. Augendre, G. Desfonds, S. Gambarelli, H. Jaffr` es, J.-M. George, and M. Jamet, Spin pumping and inverse spin hall effect in germanium, Phys. Rev. B 88, 064403 (2013)

    work page 2013

  63. [64]

    H. J. Elmers, R. Wallauer, M. Liebmann, J. Kellner, M. Morgenstern, R. N. Wang, J. E. Boschker, R. Calarco, J. S´ anchez-Barriga, O. Rader, D. Kutnyakhov, S. V. Chernov, K. Medjanik, C. Tusche, M. Ellguth, H. Vol- fova, S. Borek, J. Braun, J. Min´ ar, H. Ebert, and G. Sch¨ onhense, Spin mapping of surface and bulk rashba states in ferroelectricα-gete(111)...

    work page 2016

  64. [65]

    Rinaldi, S

    C. Rinaldi, S. Varotto, M. Asa, J. S lawi´ nska, J. Fujii, G. Vinai, S. Cecchi, D. D. Sante, R. Calarco, I. Vobornik, G. Panaccione, S. Picozzi, and R. Bertacco, Ferroelectric control of the spin texture in gete, Nano Letters18, 2751 (2018)

    work page 2018

  65. [66]

    Leiva-Montecinos, L

    S. Leiva-Montecinos, L. Voj´ aˇ cek, J. Li, M. Chshiev, L. Vila, I. Mertig, and A. Johansson, Current-induced spin and orbital polarization in the ferroelectric rashba semiconductor gete, arXiv:2505.21340 (2025)

    work page arXiv 2025

  66. [67]

    Salemi and P

    L. Salemi and P. M. Oppeneer, First-principles theory of intrinsic spin and orbital hall and nernst effects in metallic monoatomic crystals, Physical Review Materials 6, 095001 (2022)

    work page 2022

  67. [68]

    Costa, B

    M. Costa, B. Focassio, L. M. Canonico, T. P. Cysne, G. R. Schleder, R. B. Muniz, A. Fazzio, and T. G. Rappoport, Connecting higher-order topology with the orbital hall effect in monolayers of transition metal dichalcogenides, Physical Review Letters130, 116204 (2023)

    work page 2023

  68. [69]

    Isshiki, P

    H. Isshiki, P. Muduli, J. Kim, K. Kondou, and Y. Otani, Phenomenological model for the direct and inverse edel- stein effects, Phys. Rev. B102, 184411 (2020)

    work page 2020

  69. [70]

    J. C. Rojas-S´ anchez, L. Vila, G. Desfonds, S. Gambarelli, J.-P. Attane, J. M. D. Teresa, C. Mag´ en, and A. Fert, Spin-to-charge conversion using rashba coupling at the interface between non-magnetic materials., Nature Com- munications4, 2944 (2013)

    work page 2013

  70. [71]

    Zhang and A

    S. Zhang and A. Fert, Conversion between spin and charge currents with topological insulators, Physical Re- view B94, 184423 (2016)

    work page 2016

  71. [72]

    G. Y. Guo, S. Murakami, T.-W. Chen, and N. Nagaosa, Intrinsic spin hall effect in platinum: First-principles cal- culations, Phys. Rev. Lett.100, 096401 (2008)

    work page 2008

  72. [73]

    Y. Sun, Y. Zhang, C. Felser, and B. Yan, Strong intrinsic spin hall effect in the taas family of weyl semimetals, Phys. Rev. Lett.117, 146403 (2016)

    work page 2016

  73. [74]

    Johansson, J

    A. Johansson, J. Henk, and I. Mertig, Edelstein effect in weyl semimetals, Phys. Rev. B97, 085417 (2018)

    work page 2018

  74. [75]

    J. B. S. Mendes, A. S. Vieira, R. O. Cunha, S. O. Ferreira, R. D. dos Reis, M. Schmidt, M. Nicklas, S. M. Rezende, and A. Azevedo, Efficient spin-to-charge interconversion in weyl semimetal tap at room temperature, Advanced Materials Interfaces9, 2201716 (2022)

    work page 2022

  75. [76]

    B. Zhao, D. Khokhriakov, Y. Zhang, H. Fu, B. Karpiak, A. M. Hoque, X. Xu, Y. Jiang, B. Yan, and S. P. Dash, Observation of charge to spin conversion in weyl semimetal wte2 at room temperature, Phys. Rev. Res.2, 013286 (2020)

    work page 2020

  76. [77]

    Jamali, J

    M. Jamali, J. S. Lee, J. S. Jeong, F. Mahfouzi, Y. Lv, Z. Zhao, B. Nikolic, K. A. Mkhoyan, N. Samarth, and J.- P. Wang, Giant spin pumping and inverse spin hall effect in the presence of surface spin-orbit coupling of topolog- ical insulator bi2se3, Nano Letters15, 7126 (2015)

    work page 2015

  77. [78]

    M.-Y. Liu, L. Gong, Y. He, and C. Cao, Tuning rashba ef- fect, band inversion, and spin-charge conversion of janus xsn2ymonolayers via an external field, Phys. Rev. B103, 075421 (2021)

    work page 2021

  78. [79]

    Chassot, A

    F. Chassot, A. Pulkkinen, G. Kremer, T. Zakusylo, G. Krizman, M. Hajlaoui, J. H. Dil, J. Krempask´ y, J. Min´ ar, G. Springholz, and C. Monney, Persistence of structural distortion and bulk band rashba splitting in snte above its ferroelectric critical temperature, Nano Letters24, 82 (2024)

    work page 2024

  79. [80]

    L. L. Tao, T. R. Paudel, A. A. Kovalev, and E. Y. Tsym- bal, Reversible spin texture in ferroelectric Hfo 2, Phys. Rev. B95, 245141 (2017)

    work page 2017

  80. [81]

    Zhang, X

    Q. Zhang, X. Chen, Y. Yu, H. Li, M. Dou, G. Gurung, X. Wang, and L. L. Tao, Spin Hall effect in doped fer- roelectric HfO2, Applied Physics Letters125, 032905 (2024)

    work page 2024