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arxiv: 2510.02451 · v2 · submitted 2025-10-02 · ❄️ cond-mat.mtrl-sci · cond-mat.mes-hall· cond-mat.str-el

Slow-phonon control of spin Edelstein effect in Rashba d-wave altermagnets

Mohsen Yarmohammadi , Jacob Linder , James K. Freericks This is my paper

Pith reviewed 2026-05-18 10:11 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci cond-mat.mes-hallcond-mat.str-el
keywords d-wave altermagnetsspin Edelstein effectelectron-phonon couplingRashba spin-orbitFermi surface collapsepiezomagnetic strainspintronics
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The pith

Slow phonons suppress and fully depolarize the spin Edelstein effect in strained Rashba d-wave altermagnets by collapsing the Fermi surface.

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

The paper establishes that in two-dimensional d-wave altermagnets with added Rashba spin-orbit coupling, static electron-phonon interactions from slow lattice vibrations progressively reduce the spin polarization generated by electric fields, reaching complete suppression at a critical coupling strength. This occurs specifically when a piezomagnetic strain breaks the material's C4T symmetry, shifting electron energies so that the Fermi surface vanishes and eliminates available states for spin response. A sympathetic reader would care because altermagnets promise efficient spin-based electronics without net magnetization losses, and phonon-based control could enable reversible on-off switching of spin signals. The altermagnetic order turns the depolarization anisotropic and breaks the spin susceptibility antisymmetry typical of pure Rashba systems, while the effect stays isotropic without altermagnetism.

Core claim

In a Rashba continuum model of d-wave altermagnets, electron-phonon coupling treated at the static Holstein level and analyzed via Kubo linear response shows that a piezomagnetically active strain breaking C4T symmetry causes moderate-to-strong coupling to suppress induced spin polarization through intraband and interband channels, with a threshold coupling producing complete spin Edelstein depolarization. The mechanism is phonon-induced energy renormalization that collapses the Fermi surface. Depolarization can occur even without altermagnetism but remains isotropic; altermagnetism makes it anisotropic and breaks conventional antisymmetry between spin susceptibilities.

What carries the argument

Static Holstein electron-phonon coupling in the strained Rashba d-wave altermagnet continuum model, which renormalizes electron energies and drives complete Fermi surface collapse to suppress spin responses.

If this is right

  • The suppression acts through both intraband and interband channels and reaches full depolarization at a threshold coupling.
  • Altermagnetism renders the depolarization anisotropic while breaking the antisymmetry of spin susceptibilities found in pure spin-orbit coupling.
  • The depolarization threshold can be tuned by varying phonon coupling strength, Rashba spin-orbit strength, and carrier doping.
  • Static phononic effects enable reversible switching between spin-polarized and depolarized states for spintronic applications.

Where Pith is reading between the lines

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

  • Phonon-induced Fermi surface collapse might interact with external fields or dynamic lattice effects to produce hybrid control protocols in real devices.
  • The anisotropy from altermagnetism could be leveraged to design direction-selective spin filters that respond to lattice strain.
  • Similar renormalization mechanisms may appear in related systems with different lattice symmetries or higher dimensions, offering broader routes to phononic spin control.

Load-bearing premise

The static Holstein approximation for electron-phonon coupling together with Kubo linear response is enough to capture the phonon-driven energy renormalization and Fermi surface collapse without dynamic phonon or higher-order scattering effects.

What would settle it

An experiment or calculation that increases electron-phonon coupling strength in a strained d-wave altermagnet sample and checks whether the spin Edelstein polarization vanishes completely above a specific threshold tied to Fermi surface disappearance.

Figures

Figures reproduced from arXiv: 2510.02451 by Jacob Linder, James K. Freericks, Mohsen Yarmohammadi.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Real-space representation of the staggered spin [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) Components of the spin Edelstein susceptibility tensor, [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Minimum of the lower spin-split band, [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: presents the DOS D(E) along the high￾symmetry Γ → X and Γ → Y directions for various val￾ues of the EPC g. At weak coupling [ [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. (a) Transverse spin Edelstein susceptibility [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. (a) Transverse susceptibility [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. (a) Transverse spin Edelstein susceptibility [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Transverse spin Edelstein susceptibility [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
read the original abstract

Altermagnets have zero net magnetization yet feature spin-split bands. Here, we investigate how slow lattice vibrations (phonons) influence both the intrinsic and externally induced spin polarizations in two-dimensional $d$-wave altermagnets. For the induced spin polarization, we employ a Rashba continuum model with electron-phonon coupling (EPC) treated at the static Holstein level and analyze the spin Edelstein effect using the Kubo linear-response formalism to probe EPC-induced contributions. We find that, under a specific symmetry-lowering pattern such as a piezomagnetically active strain that explicitly breaks the inherent $C_4 \mathcal{T}$ symmetry, moderate-to-strong EPC progressively suppresses the induced polarization via both intraband and interband channels, with a threshold coupling marking the onset of complete spin Edelstein depolarization. The depolarization arises from a phonon-induced energy renormalization that leads to a complete collapse of the Fermi surface. While depolarization can occur even in the Rashba non-altermagnetic phase, it remains isotropic. The presence of altermagnetism makes it anisotropic and breaks the conventional antisymmetry between spin susceptibilities that occurs with pure spin-orbit coupling, rendering the effect highly relevant for spintronic applications. We further investigate how the phonon coupling to the altermagnetic order, Rashba spin-orbit strength, and carrier doping collectively tune the depolarization. Our findings demonstrate that static phononic effects offer a powerful means for on-demand control of spin polarization, enabling reversible switching between spin-polarized and depolarized states--a key functionality for advancing spin logic architectures and optimizing next-generation spintronic devices.

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

3 major / 3 minor

Summary. The paper claims that in two-dimensional Rashba d-wave altermagnets, a piezomagnetically active strain breaking C4T symmetry allows slow phonons (treated via static Holstein EPC) to suppress the induced spin polarization through both intraband and interband channels in the Kubo linear-response formalism, with a threshold EPC strength triggering complete spin Edelstein depolarization via phonon-induced Fermi-surface collapse. Altermagnetism renders the depolarization anisotropic and breaks the conventional antisymmetry of spin susceptibilities seen in pure Rashba systems; the threshold can be tuned by EPC strength, Rashba SOC, and carrier doping, enabling reversible spin-polarized to depolarized switching.

Significance. If the central results hold, the work identifies a phononic route to on-demand control of spin polarization in altermagnets, with direct relevance to spintronic device architectures that require reversible switching. The explicit breaking of C4T symmetry and the resulting anisotropy in the spin susceptibilities constitute a clear advance over pure Rashba or non-altermagnetic cases. No machine-checked proofs or fully parameter-free derivations are provided, but the falsifiable prediction of strain-tunable, anisotropic depolarization offers a concrete experimental test.

major comments (3)
  1. [Model Hamiltonian and Self-Energy sections] The headline result of a sharp EPC threshold for complete Fermi-surface collapse and depolarization rests on the static Holstein self-energy producing a rigid band shift that drives the chemical potential through a van-Hove or band-edge singularity. Because the phonons are explicitly labeled “slow,” the adiabatic replacement is the least secure step: a frequency-dependent phonon propagator would generate a retarded self-energy whose real part is suppressed near the Fermi level and whose imaginary part adds scattering, either of which can keep states at the chemical potential and block the asserted collapse. This approximation is load-bearing for the threshold claim and requires either analytic justification or a dynamic-phonon benchmark. (Model Hamiltonian and Self-Energy sections)
  2. [Kubo Formalism and Numerical Results sections] In the Kubo bubble evaluation of the spin Edelstein conductivity on the EPC-renormalized bands, it is unclear whether the chemical potential is readjusted self-consistently after the static self-energy shift or held fixed at its bare value. The former is necessary for a true Fermi-surface collapse; the latter would leave a finite density of states at the Fermi level even after the nominal threshold. This distinction directly affects both the intraband and interband suppression channels. (Kubo Formalism and Numerical Results sections)
  3. [Results and Discussion sections] The depolarization threshold is identified by post-hoc numerical variation of the EPC strength inside the Rashba-Holstein-Kubo framework. An analytic estimate of the critical coupling (e.g., in terms of the van-Hove energy, Rashba parameter, and doping) or an explicit demonstration that the threshold survives modest dynamic corrections would strengthen the central claim. (Results and Discussion sections)
minor comments (3)
  1. [Abstract and Introduction] The abstract and introduction use “slow-phonon control” without a concise statement of the adiabaticity criterion (e.g., phonon frequency versus Fermi energy or bandwidth) that justifies the static approximation.
  2. [Figures] Figure captions and axis labels for the polarization-versus-EPC plots should explicitly mark the reported threshold value and indicate whether the curves are for fixed or self-consistent chemical potential.
  3. [Model and Analytic Expressions] Notation for the altermagnetic order parameter, Rashba strength, and EPC coupling should be unified between the Hamiltonian definition and the subsequent analytic expressions for the spin susceptibilities.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major point below and indicate revisions to be incorporated in the next version.

read point-by-point responses

  1. Referee: [Model Hamiltonian and Self-Energy sections] The headline result of a sharp EPC threshold for complete Fermi-surface collapse and depolarization rests on the static Holstein self-energy producing a rigid band shift that drives the chemical potential through a van-Hove or band-edge singularity. Because the phonons are explicitly labeled “slow,” the adiabatic replacement is the least secure step: a frequency-dependent phonon propagator would generate a retarded self-energy whose real part is suppressed near the Fermi level and whose imaginary part adds scattering, either of which can keep states at the chemical potential and block the asserted collapse. This approximation is load-bearing for the threshold claim and requires either analytic justification or a dynamic-phonon benchmark.

    Authors: We agree that the static Holstein approximation for slow phonons requires careful justification. In the manuscript the static limit is adopted because the phonon frequency is taken to be much smaller than the electronic bandwidth and Fermi energy, rendering retardation effects subdominant near the Fermi level. The real part of the self-energy remains approximately constant while the imaginary part (scattering rate) is negligible at the low temperatures considered. We will add an explicit paragraph in the Model Hamiltonian section deriving this regime of validity from the phonon propagator and showing that the Fermi-surface collapse is preserved to leading order. A full frequency-dependent benchmark lies beyond the present scope but is noted as a natural extension. revision: partial

  2. Referee: [Kubo Formalism and Numerical Results sections] In the Kubo bubble evaluation of the spin Edelstein conductivity on the EPC-renormalized bands, it is unclear whether the chemical potential is readjusted self-consistently after the static self-energy shift or held fixed at its bare value. The former is necessary for a true Fermi-surface collapse; the latter would leave a finite density of states at the Fermi level even after the nominal threshold. This distinction directly affects both the intraband and interband suppression channels.

    Authors: We thank the referee for highlighting this ambiguity. In all calculations the chemical potential is readjusted self-consistently after the static self-energy shift so that the integrated density of states matches the fixed carrier density. This procedure is performed numerically at each EPC strength by solving for μ in the renormalized dispersion. We will insert a concise description of this self-consistent step, together with a short appendix illustrating the resulting density-of-states evolution, in the revised Kubo Formalism section. revision: yes

  3. Referee: [Results and Discussion sections] The depolarization threshold is identified by post-hoc numerical variation of the EPC strength inside the Rashba-Holstein-Kubo framework. An analytic estimate of the critical coupling (e.g., in terms of the van-Hove energy, Rashba parameter, and doping) or an explicit demonstration that the threshold survives modest dynamic corrections would strengthen the central claim.

    Authors: We concur that an analytic estimate would strengthen the presentation. In the revised Results section we will derive a simple closed-form expression for the critical EPC strength by setting the renormalized band edge (or van-Hove singularity) equal to the self-consistently determined chemical potential; the resulting formula depends explicitly on the bare van-Hove energy, Rashba SOC amplitude, and doping. Regarding dynamic corrections, we will add a brief remark that the leading real-part renormalization responsible for the collapse remains dominant for slow phonons, while scattering effects are suppressed at low T; a quantitative dynamic benchmark is left for future work. revision: partial

Circularity Check

0 steps flagged

No significant circularity; result follows from model computation

full rationale

The derivation applies the Rashba continuum model, static Holstein EPC self-energy, and Kubo linear response to compute spin Edelstein polarization as a function of EPC strength. The threshold for complete depolarization is obtained by solving the renormalized bands and response functions, yielding FS collapse at a critical coupling value. This is a direct numerical/analytical outcome of the equations rather than a self-definitional fit, renamed prediction, or load-bearing self-citation. No uniqueness theorem or prior ansatz from the same authors is invoked to force the result. The central claim retains independent content from the explicit model evaluation.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 0 invented entities

The central claim rests on the standard Kubo formalism and the static Holstein approximation for EPC; the coupling strength, Rashba parameter, and doping level are varied as control parameters rather than fitted to external data.

free parameters (3)
  • electron-phonon coupling strength
    Varied across moderate-to-strong regimes to locate the depolarization threshold.
  • Rashba spin-orbit strength
    Tuned collectively with phonon coupling and doping to explore depolarization.
  • carrier doping
    Adjusted to modulate the Fermi surface and depolarization behavior.
axioms (2)
  • standard math Kubo linear-response formalism accurately computes the spin Edelstein effect in the presence of EPC.
    Used to probe both intrinsic and externally induced spin polarizations.
  • domain assumption Static Holstein treatment of electron-phonon coupling captures the essential renormalization physics.
    Employed for the Rashba continuum model analysis.

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Works this paper leans on

94 extracted references · 94 canonical work pages

  1. [1]

    Šmejkal, J

    L. Šmejkal, J. Sinova, and T. Jungwirth, Emerging re- search landscape of altermagnetism, Phys. Rev. X12, 040501 (2022)

    work page 2022

  2. [2]

    Mazin (The PRX Editors), Editorial: Altermagnetism—a new punch line of fundamental magnetism, Phys

    I. Mazin (The PRX Editors), Editorial: Altermagnetism—a new punch line of fundamental magnetism, Phys. Rev. X12, 040002 (2022)

    work page 2022

  3. [3]

    Šmejkal, J

    L. Šmejkal, J. Sinova, and T. Jungwirth, Beyond conven- tional ferromagnetism and antiferromagnetism: A phase with nonrelativistic spin and crystal rotation symmetry, Phys. Rev. X12, 031042 (2022)

    work page 2022

  4. [4]

    Hayami, Y

    S. Hayami, Y. Yanagi, and H. Kusunose, Momentum- dependent spin splitting by collinear antiferromagnetic ordering, Journal of the Physical Society of Japan88, 123702 (2019)

    work page 2019

  5. [5]

    Šmejkal, A

    L. Šmejkal, A. B. Hellenes, R. González-Hernández, J. Sinova, and T. Jungwirth, Giant and tunneling mag- netoresistance in unconventional collinear antiferromag- nets with nonrelativistic spin-momentum coupling, Phys. Rev. X12, 011028 (2022)

    work page 2022

  6. [6]

    L.-D. Yuan, Z. Wang, J.-W. Luo, E. I. Rashba, and 12 A. Zunger, Giant momentum-dependent spin splitting in centrosymmetric low-zantiferromagnets, Phys. Rev. B 102, 014422 (2020)

    work page 2020

  7. [7]

    K.-H. Ahn, A. Hariki, K.-W. Lee, and J. Kuneš, Antifer- romagnetisminRuO 2 asd-wavepomeranchukinstability, Phys. Rev. B99, 184432 (2019)

    work page 2019

  8. [8]

    L.-D. Yuan, Z. Wang, J.-W. Luo, and A. Zunger, Predic- tion of low-Z collinear and noncollinear antiferromagnetic compounds having momentum-dependent spin splitting even without spin-orbit coupling, Phys. Rev. Mater.5, 014409 (2021)

    work page 2021

  9. [9]

    I. I. Mazin, K. Koepernik, M. D. Johannes, R. González- Hernández, and L. Šmejkal, Prediction of unconventional magnetism in doped FeSb2, Proceedings of the National Academy of Sciences118, e2108924118 (2021)

    work page 2021

  10. [10]

    H. Bai, Y. C. Zhang, Y. J. Zhou, P. Chen, C. H. Wan, L. Han, W. X. Zhu, S. X. Liang, Y. C. Su, X. F. Han, F. Pan, and C. Song, Efficient spin-to-charge conversion via altermagnetic spin splitting effect in antiferromagnet RuO2, Phys. Rev. Lett.130, 216701 (2023)

    work page 2023

  11. [11]

    X. Feng, H. Bai, X. Fan, M. Guo, Z. Zhang, G. Chai, T. Wang, D. Xue, C. Song, and X. Fan, Incommensurate spin density wave in antiferromagnetic RuO2 evinced by abnormal spin splitting torque, Phys. Rev. Lett.132, 086701 (2024)

    work page 2024

  12. [12]

    P. A. McClarty and J. G. Rau, Landau theory of alter- magnetism, Phys. Rev. Lett.132, 176702 (2024)

    work page 2024

  13. [13]

    M. Vila, V. Sunko, and J. E. Moore, Orbital-spin lock- ing and its optical signatures in altermagnets, (2024), arXiv:2410.23513

    work page arXiv 2024

  14. [14]

    H. Bai, L. Han, X. Y. Feng, Y. J. Zhou, R. X. Su, Q. Wang, L. Y. Liao, W. X. Zhu, X. Z. Chen, F. Pan, X. L. Fan, and C. Song, Observation of spin splitting torque in a collinear antiferromagnet RuO2, Phys. Rev. Lett.128, 197202 (2022)

    work page 2022

  15. [15]

    Karube, T

    S. Karube, T. Tanaka, D. Sugawara, N. Kadoguchi, M. Kohda, and J. Nitta, Observation of spin-splitter torque in collinear antiferromagnetic RuO2, Phys. Rev. Lett.129, 137201 (2022)

    work page 2022

  16. [16]

    X. Duan, J. Zhang, Z. Zhu, Y. Liu, Z. Zhang, I. Žutić, and T. Zhou, Antiferroelectric altermagnets: Antiferro- electricity alters magnets, Phys. Rev. Lett.134, 106801 (2025)

    work page 2025

  17. [17]

    M. Gu, Y. Liu, H. Zhu, K. Yananose, X. Chen, Y. Hu, A. Stroppa, and Q. Liu, Ferroelectric switchable alter- magnetism, Phys. Rev. Lett.134, 106802 (2025)

    work page 2025

  18. [18]

    Werner, M

    P. Werner, M. Lysne, and Y. Murakami, High harmonic generation in altermagnets, Phys. Rev. B110, 235101 (2024)

    work page 2024

  19. [19]

    J. A. Ouassou, A. Brataas, and J. Linder, dc Joseph- son effect in altermagnets, Phys. Rev. Lett.131, 076003 (2023)

    work page 2023

  20. [20]

    C. Sun, A. Brataas, and J. Linder, Andreev reflection in altermagnets, Phys. Rev. B108, 054511 (2023)

    work page 2023

  21. [21]

    Papaj, Andreev reflection at the altermagnet- superconductor interface, Phys

    M. Papaj, Andreev reflection at the altermagnet- superconductor interface, Phys. Rev. B108, L060508 (2023)

    work page 2023

  22. [22]

    Zhu, Z.-Y

    D. Zhu, Z.-Y. Zhuang, Z. Wu, and Z. Yan, Topological superconductivity in two-dimensional altermagnetic met- als, Phys. Rev. B108, 184505 (2023)

    work page 2023

  23. [23]

    Brekke, A

    B. Brekke, A. Brataas, and A. Sudbø, Two-dimensional altermagnets: Superconductivity in a minimal micro- scopic model, Phys. Rev. B108, 224421 (2023)

    work page 2023

  24. [24]

    Zhang, L.-H

    S.-B. Zhang, L.-H. Hu, and T. Neupert, Finite- momentum Cooper pairing in proximitized altermagnets, Nature Communications15, 1801 (2024)

    work page 2024

  25. [25]

    Li, Realizing tunable higher-order topological su- perconductors with altermagnets, Phys

    Y.-X. Li, Realizing tunable higher-order topological su- perconductors with altermagnets, Phys. Rev. B109, 224502 (2024)

    work page 2024

  26. [26]

    Li and C.-C

    Y.-X. Li and C.-C. Liu, Majorana corner modes and tun- able patterns in an altermagnet heterostructure, Phys. Rev. B108, 205410 (2023)

    work page 2023

  27. [27]

    A. Bose, N. J. Schreiber, R. Jain, D.-F. Shao, H. P. Nair, J. Sun, X. S. Zhang, D. A. Muller, E. Y. Tsymbal, D. G. Schlom, and D. C. Ralph, Tilted spin current generated by the collinear antiferromagnet ruthenium dioxide, Na- ture Electronics5, 267 (2022)

    work page 2022

  28. [28]

    González-Hernández, L

    R. González-Hernández, L. Šmejkal, K. Výborný, Y. Ya- hagi, J. Sinova, T. c. v. Jungwirth, and J. Železný, Efficient electrical spin splitter based on nonrelativis- tic collinear antiferromagnetism, Phys. Rev. Lett.126, 127701 (2021)

    work page 2021

  29. [29]

    L. Han, X. Fu, R. Peng, X. Cheng, J. Dai, L. Liu, Y. Li, Y. Zhang, W. Zhu, H. Bai, Y. Zhou, S. Liang, C. Chen, Q. Wang, X. Chen, L. Yang, Y. Zhang, C. Song, J. Liu, and F. Pan, Electrical 180°switching of Néel vec- tor in spin-splitting antiferromagnet, Science Advances 10, eadn0479 (2024)

    work page 2024

  30. [30]

    Chakraborty, R

    A. Chakraborty, R. González Hernández, L. Šmejkal, and J. Sinova, Strain-induced phase transition from antiferro- magnettoaltermagnet,Phys.Rev.B109,144421(2024)

    work page 2024

  31. [31]

    V. M. Edelstein, Spin polarization of conduction elec- trons induced by electric current in two-dimensional asymmetric electron systems, Solid State Communica- tions73, 233 (1990)

    work page 1990

  32. [32]

    D. S. Smirnov and L. E. Golub, Electrical spin orien- tation, spin-galvanic, and spin-Hall effects in disordered two-dimensional systems, Phys. Rev. Lett.118, 116801 (2017)

    work page 2017

  33. [33]

    Chakraborty, A

    A. Chakraborty, A. Birk Hellenes, R. Jaeschke-Ubiergo, T. Jungwirth, L. Šmejkal, and J. Sinova, Highly efficient non-relativistic Edelstein effect in nodalp-wave magnets, Nature Communications16, 7270 (2025)

    work page 2025

  34. [34]

    N. A. A. Pari, R. Jaeschke-Ubiergo, A. Chakraborty, L. Šmejkal, and J. Sinova, Nonrelativistic linear Edel- steineffectinhelicalEuin 2As2,Phys.Rev.B112,024404 (2025)

    work page 2025

  35. [35]

    Salemi, M

    L. Salemi, M. Berritta, A. K. Nandy, and P. M. Op- peneer, Orbitally dominated Rashba-Edelstein effect in noncentrosymmetric antiferromagnets, Nature Commu- nications10, 5381 (2019)

    work page 2019

  36. [36]

    Johansson, Theory of spin and orbital Edelstein ef- fects, Journal of Physics: Condensed Matter36, 423002 (2024)

    A. Johansson, Theory of spin and orbital Edelstein ef- fects, Journal of Physics: Condensed Matter36, 423002 (2024)

    work page 2024

  37. [37]

    L.Salemi, M.Berritta,andP.M.Oppeneer,Quantitative comparison of electrically induced spin and orbital po- larizations in heavy-metal/3d-metal bilayers, Phys. Rev. Mater.5, 074407 (2021)

    work page 2021

  38. [38]

    Salemi and P

    L. Salemi and P. M. Oppeneer, First-principles theory of intrinsicspinandorbitalHallandNernsteffectsinmetal- lic monoatomic crystals, Phys. Rev. Mater.6, 095001 (2022)

    work page 2022

  39. [39]

    L. E. Golub and L. Šmejkal, Spin orientation by electric current in altermagnets, (2025), arXiv:2503.12203

    work page arXiv 2025

  40. [40]

    M. Hu, O. Janson, C. Felser, P. McClarty, J. van den Brink, and M. G. Vergniory, Spin Hall and Edelstein ef- fects in chiral non-collinear altermagnets, Nature Com- munications16, 8529 (2025). 13

    work page 2025

  41. [41]

    Yarmohammadi, U

    M. Yarmohammadi, U. Zülicke, J. Berakdar, J. Linder, and J. K. Freericks, Anisotropic light-tailored RKKY in- teraction in two-dimensionald-wave altermagnets, Phys. Rev. B111, 224412 (2025)

    work page 2025

  42. [42]

    Amundsen, A

    M. Amundsen, A. Brataas, and J. Linder, RKKY interac- tion in Rashba altermagnets, Phys. Rev. B110, 054427 (2024)

    work page 2024

  43. [43]

    Mazin, R

    I. Mazin, R. González-Hernández, and L. Šmejkal, In- duced monolayer altermagnetism in MnP(S,Se) 3 and FeSe, (2023), arXiv:2309.02355

    work page arXiv 2023

  44. [44]

    Trama, I

    M. Trama, I. Gaiardoni, C. Guarcello, J. I. Facio, A. Maiellaro, F. Romeo, R. Citro, and J. van den Brink, Non-linear anomalous Edelstein response at altermag- netic interfaces, (2024), arXiv:2410.18036

    work page arXiv 2024

  45. [45]

    A. B. Hellenes, T. Jungwirth, R. Jaeschke-Ubiergo, A. Chakraborty, J. Sinova, and L. Šmejkal, P-wave mag- nets, (2024), arXiv:2309.01607

    work page arXiv 2024

  46. [46]

    Jungwirth, R

    T. Jungwirth, R. M. Fernandes, E. Fradkin, A. H. Mac- Donald, J. Sinova, and L. Šmejkal, Altermagnetism: An unconventional spin-ordered phase of matter, Newton1, 10.1016/j.newton.2025.100162 (2025)

    work page doi:10.1016/j.newton.2025.100162 2025

  47. [47]

    Giustino, Electron-phonon interactions from first prin- ciples, Rev

    F. Giustino, Electron-phonon interactions from first prin- ciples, Rev. Mod. Phys.89, 015003 (2017)

    work page 2017

  48. [48]

    Lihm and C.-H

    J.-M. Lihm and C.-H. Park, Phonon-induced renormal- ization of electron wave functions, Phys. Rev. B101, 121102 (2020)

    work page 2020

  49. [49]

    Shang and J

    H. Shang and J. Yang, The electron–phonon renormal- ization in the electronic structure calculation: Funda- mentals, current status, and cHallenges, The Journal of Chemical Physics158, 130901 (2023)

    work page 2023

  50. [50]

    L. Wang, H. Wang, R. Nughays, W. Ogieglo, J. Yin, L. Gutiérrez-Arzaluz, X. Zhang, J.-X. Wang, I. Pinnau, O. M. Bakr, and O. F. Mohammed, Phonon-driven tran- sient bandgap renormalization in perovskite single crys- tals, Mater. Horiz.10, 4192 (2023)

    work page 2023

  51. [51]

    D. I. Badrtdinov, M. I. Katsnelson, and A. N. Rudenko, Phonon-induced renormalization of exchange interac- tions in metallic two-dimensional magnets, Phys. Rev. B110, L060409 (2024)

    work page 2024

  52. [52]

    Lafuente-Bartolome, C

    J. Lafuente-Bartolome, C. Lian, W. H. Sio, I. G. Gur- tubay, A. Eiguren, and F. Giustino, Unified approach to polarons and phonon-induced band structure renormal- ization, Phys. Rev. Lett.129, 076402 (2022)

    work page 2022

  53. [53]

    Tse and S

    W.-K. Tse and S. Das Sarma, Phonon-induced many- body renormalization of the electronic properties of graphene, Phys. Rev. Lett.99, 236802 (2007)

    work page 2007

  54. [54]

    Garate, Phonon-induced topological transitions and crossovers in Dirac materials, Phys

    I. Garate, Phonon-induced topological transitions and crossovers in Dirac materials, Phys. Rev. Lett.110, 046402 (2013)

    work page 2013

  55. [55]

    Antonius, S

    G. Antonius, S. Poncé, E. Lantagne-Hurtubise, G. Au- clair, X.Gonze,andM.Côté,Dynamicalandanharmonic effects on the electron-phonon coupling and the zero- point renormalization of the electronic structure, Phys. Rev. B92, 085137 (2015)

    work page 2015

  56. [56]

    Emeis, S

    C. Emeis, S. Jauernik, S. Dahiya, Y. Pan, C. E. Jensen, P. Hein, M. Bauer, and F. Caruso, Coherent phonons and quasiparticle renormalization in semimetals from first principles, Phys. Rev. X15, 021039 (2025)

    work page 2025

  57. [57]

    C. E. Patrick and F. Giustino, Unified theory of elec- tron–phonon renormalization and phonon-assisted opti- cal absorption, Journal of Physics: Condensed Matter 26, 365503 (2014)

    work page 2014

  58. [58]

    I. V. Iorsh, Electron pairing by dispersive phonons in altermagnets: Reentrant superconductivity and continu- oustransitiontofinitemomentumsuperconductingstate, Phys. Rev. B111, L220503 (2025)

    work page 2025

  59. [59]

    Leraand, K

    K. Leraand, K. Mæland, and A. Sudbø, Phonon- mediated spin-polarized superconductivity in altermag- nets, Phys. Rev. B112, 104510 (2025)

    work page 2025

  60. [60]

    C. R. W. Steward, R. M. Fernandes, and J. Schmalian, Dynamic paramagnon-polarons in altermagnets, Phys. Rev. B108, 144418 (2023)

    work page 2023

  61. [61]

    E. W. Hodt, A. Qaiumzadeh, and J. Linder, Phonon- enhanced optical spin-conductivity and spin-splitter ef- fect in altermagnets, (2025), arXiv:2507.03571

    work page arXiv 2025

  62. [62]

    R. He, Z. Duan, B. Lei, N. Luo, J. Zeng, K.-Q. Chen, and L.-M. Tang, Crucial role of electron-phonon scattering in the spin-splitter effect, Phys. Rev. B112, 064423 (2025)

    work page 2025

  63. [63]

    Grimaldi, Large polaron formation induced by Rashba spin-orbit coupling, Phys

    C. Grimaldi, Large polaron formation induced by Rashba spin-orbit coupling, Phys. Rev. B81, 075306 (2010)

    work page 2010

  64. [64]

    Xu and Y

    J. Xu and Y. Ping, Substrate effects on spin relaxation in two-dimensionalDirac materialswith strong spin-orbit coupling, npj Computational Materials9, 47 (2023)

    work page 2023

  65. [65]

    Behin-Aein, D

    B. Behin-Aein, D. Datta, S. Salahuddin, and S. Datta, Proposal for an all-spin logic device with built-in mem- ory, Nature Nanotechnology5, 266 (2010)

    work page 2010

  66. [66]

    Holstein, Studies of polaron motion: Part i

    T. Holstein, Studies of polaron motion: Part i. the molecular-crystal model, Annals of Physics8, 325 (1959)

    work page 1959

  67. [67]

    Holstein, Studies of polaron motion: Part ii

    T. Holstein, Studies of polaron motion: Part ii. the “small” polaron, Annals of Physics8, 343 (1959)

    work page 1959

  68. [68]

    J. K. Freericks, V. Zlatić, and M. Jarrell, Approxi- mate scaling relation for the anharmonic electron-phonon problem, Phys. Rev. B61, R838 (2000)

    work page 2000

  69. [69]

    J. K. Freericks and M. Jarrell, Competition between electron-phonon attraction and weak Coulomb repulsion, Phys. Rev. Lett.75, 2570 (1995)

    work page 1995

  70. [70]

    M. D. Petrović, M. Weber, and J. K. Freericks, Theo- retical description of pump-probe experiments in charge- density-wave materials out to long times, Phys. Rev. X 14, 031052 (2024)

    work page 2024

  71. [71]

    Weber and J

    M. Weber and J. K. Freericks, Real-time evolution of static electron-phonon models in time-dependent electric fields, Phys. Rev. E105, 025301 (2022)

    work page 2022

  72. [72]

    Jeckelmann, C

    E. Jeckelmann, C. Zhang, and S. R. White, Metal- insulator transition in the one-dimensional Holstein model at half filling, Phys. Rev. B60, 7950 (1999)

    work page 1999

  73. [73]

    Werner and A

    P. Werner and A. J. Millis, Efficient dynamical mean field simulation of the Holstein-Hubbard model, Phys. Rev. Lett.99, 146404 (2007)

    work page 2007

  74. [74]

    Faúndez, R

    J. Faúndez, R. A. Fontenele, S. dos Anjos Sousa-Júnior, F. F. Assaad, and N. C. Costa, The two-dimensional Rashba-Holstein model, (2024), arXiv:2411.07119

    work page arXiv 2024

  75. [75]

    K. V. Yershov, V. P. Kravchuk, M. Daghofer, and J. van den Brink, Fluctuation-induced piezomagnetism in local moment altermagnets, Phys. Rev. B110, 144421 (2024)

    work page 2024

  76. [76]

    Aoyama and K

    T. Aoyama and K. Ohgushi, Piezomagnetic properties in altermagnetic MnTe, Phys. Rev. Mater.8, L041402 (2024)

    work page 2024

  77. [77]

    M. Naka, Y. Motome, T. Miyazaki, and H. Seo, Nonrel- ativistic piezomagnetic effect in an organic altermagnet, (2025), arXiv:2505.07327 [cond-mat.str-el]

    work page arXiv 2025

  78. [78]

    C. Chen, X. He, Q. Xiong, C. Quan, H. Hou, S. Ji, J. Yang, and X. Li, Strain-modulated valley polariza- tion and piezomagnetic effects in altermagnetic Cr2S2, Applied Physics Letters127, 102409 (2025)

    work page 2025

  79. [79]

    F. A. Lindemann, The calculation of molecular vibration frequencies, Phys. Z.11, 609 (1910). 14

    work page 1910

  80. [80]

    Doğan and F

    F. Doğan and F. Marsiglio, Self-consistent modification to the electron density of states due to electron-phonon coupling in metals, Phys. Rev. B68, 165102 (2003)

    work page 2003

Showing first 80 references.