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arxiv: 2507.22884 · v2 · submitted 2025-07-30 · ❄️ cond-mat.mes-hall

Floquet Spin Splitting and Spin Generation in Antiferromagnets

Bo Li , Ding-Fu Shao , Alexey A. Kovalev This is my paper

Pith reviewed 2026-05-19 02:37 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords antiferromagnetsFloquet engineeringspin currentsEdelstein effectspintronicsoptical drivingthermal bathspin splitting
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0 comments X

The pith

An optical field induces Floquet spin splitting in antiferromagnets, enabling pure spin currents and net spin accumulation via thermal bath engineering without spin-orbit coupling.

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

The paper proposes driving antiferromagnets with an optical field to create a dynamical spin splitting. Coupling this driven system to a thermal bath produces steady-state pure spin currents and both longitudinal and transverse spin currents in linear response. Thermal bath engineering then generates a net spin accumulation through a nonrelativistic Edelstein effect. A sympathetic reader would care because the method supplies a tunable, nonrelativistic route to spin control that sidesteps the usual reliance on spin-orbit coupling in antiferromagnetic spintronics.

Core claim

In antiferromagnets an optical field produces a dynamical Floquet spin splitting. When the driven system couples to a thermal bath, steady-state pure spin currents appear together with linear-response longitudinal and transverse spin currents. Thermal bath engineering enables a nonrelativistic Edelstein effect that generates net spin accumulation without spin-orbit coupling.

What carries the argument

Floquet spin splitting induced by an optical field, which dynamically lifts spin degeneracy and, when combined with engineered thermal bath coupling, generates spin currents and accumulation.

If this is right

  • Steady-state pure spin currents emerge in the optically driven antiferromagnetic system.
  • Linear-response longitudinal and transverse spin currents appear under the same driving and bath conditions.
  • A nonrelativistic Edelstein effect produces net spin accumulation without any spin-orbit coupling.
  • The approach supplies a broadly applicable and experimentally tunable method for spin generation and manipulation in antiferromagnetic spintronics.

Where Pith is reading between the lines

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

  • The same optical driving plus bath engineering might extend to other collinear or noncollinear magnetic orders to produce spin currents.
  • Device geometries that combine optical access with separate thermal reservoirs could test the predicted spin accumulation directly.
  • Varying the bath coupling strength offers a route to optimize the magnitude of the generated spin currents in future experiments.

Load-bearing premise

An external optical field can be applied to real antiferromagnetic materials to produce controllable Floquet spin splitting while allowing independent engineering of thermal bath coupling without dominant competing effects such as heating or decoherence.

What would settle it

Observation of net spin accumulation or pure spin currents in an optically driven antiferromagnet coupled to a controlled thermal bath, measured in a material where spin-orbit coupling is negligible.

Figures

Figures reproduced from arXiv: 2507.22884 by Alexey A. Kovalev, Bo Li, Ding-Fu Shao.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Quasi-energy band structure in honeycomb-lattice [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Steady-state population for the lower quasi-energy [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) Steady state spin current with [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Spin accumulation by contacting the system to elec [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Quasi-band structure in the first Floquet Brillouin [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 1
Figure 1. Figure 1: FIG. 1. Comparison between spin-up and down bands along diffe [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Net spin accumulation when the system is coupled to a fe [PITH_FULL_IMAGE:figures/full_fig_p016_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The honeycomb antiferromagnet is contacted to two metal [PITH_FULL_IMAGE:figures/full_fig_p018_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Left: the unit cell of the square-lattice antiferromagnet [PITH_FULL_IMAGE:figures/full_fig_p020_4.png] view at source ↗
read the original abstract

In antiferromagnetic spintronics, accessing the spin degree of freedom is essential for generating spin currents and manipulating magnetic order, which generally requires lifting spin degeneracy. This is typically achieved through relativistic spin-orbit coupling or non-relativistic spin splitting in altermagnets. Here, we propose an alternative approach: a dynamical spin splitting induced by an optical field in antiferromagnets. By coupling the driven system to a thermal bath, we demonstrate the emergence of steady-state pure spin currents, as well as linear-response longitudinal and transverse spin currents. Crucially, thermal bath engineering enables a nonrelativistic Edelstein effect--the generation of a net spin accumulation--without relying on spin-orbit coupling. Our results provide a broadly applicable and experimentally tunable route to control spins in antiferromagnets, offering new opportunities for spin generation and manipulation in antiferromagnetic spintronics.

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 / 2 minor

Summary. The manuscript proposes a dynamical approach to spin splitting in antiferromagnets via a time-periodic optical field that induces Floquet states. Coupling the driven system to an engineered thermal bath is claimed to produce steady-state pure spin currents, linear-response longitudinal and transverse spin currents, and a nonrelativistic Edelstein effect that generates net spin accumulation without spin-orbit coupling.

Significance. If the central claims are substantiated, the work offers an experimentally tunable route to spin generation and manipulation in antiferromagnets that bypasses both relativistic SOC and the specific symmetries required for altermagnets. The combination of Floquet driving with bath engineering could expand the parameter space for antiferromagnetic spintronics.

major comments (3)
  1. [Model Hamiltonian and Floquet states] The derivation of the Floquet Hamiltonian and the resulting spin splitting (likely in the section presenting the model Hamiltonian) must be shown explicitly, including the explicit time-periodic term and the quasienergy spectrum. Without this, it is impossible to verify that the splitting is purely dynamical and symmetry-allowed in the antiferromagnet.
  2. [Bath coupling and master equation] In the treatment of the thermal bath (Floquet-Markov master equation or rate equations), the spin-dependent relaxation rates must be derived from a microscopic, spin-conserving Hamiltonian. The claim of an SOC-free Edelstein effect is load-bearing on this point; any momentum- or spin-mixing rates not derivable from the bare model would introduce effective symmetry breaking equivalent to SOC.
  3. [Spin currents and Edelstein effect] The linear-response spin currents and steady-state accumulation calculations (likely in the results section on currents and Edelstein effect) should include explicit checks that the bath engineering preserves the underlying antiferromagnetic symmetries while still producing net spin polarization. The current presentation leaves open whether the effect reduces to a hidden relativistic mechanism.
minor comments (2)
  1. [Figures] Figure captions and axis labels for the quasienergy bands and current plots should explicitly state the driving parameters and bath coupling strengths used.
  2. [Discussion] Add a short discussion of competing effects such as heating or decoherence under realistic optical driving to strengthen the experimental feasibility section.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful review and constructive feedback on our manuscript. The comments highlight important points for improving clarity and rigor, particularly regarding explicit derivations and symmetry checks. We address each major comment below and will revise the manuscript to incorporate additional details and explicit calculations as outlined.

read point-by-point responses

  1. Referee: [Model Hamiltonian and Floquet states] The derivation of the Floquet Hamiltonian and the resulting spin splitting (likely in the section presenting the model Hamiltonian) must be shown explicitly, including the explicit time-periodic term and the quasienergy spectrum. Without this, it is impossible to verify that the splitting is purely dynamical and symmetry-allowed in the antiferromagnet.

    Authors: We agree that an explicit derivation is essential for verification. In the revised manuscript, we will add a dedicated subsection in the model section that presents the full time-periodic Hamiltonian, including the explicit optical driving term. We will derive the Floquet Hamiltonian using the standard high-frequency expansion or exact diagonalization in the extended Hilbert space, and we will show the quasienergy spectrum to demonstrate the dynamical spin splitting. This will confirm that the effect is purely dynamical and respects the antiferromagnetic symmetries without requiring additional assumptions. revision: yes

  2. Referee: [Bath coupling and master equation] In the treatment of the thermal bath (Floquet-Markov master equation or rate equations), the spin-dependent relaxation rates must be derived from a microscopic, spin-conserving Hamiltonian. The claim of an SOC-free Edelstein effect is load-bearing on this point; any momentum- or spin-mixing rates not derivable from the bare model would introduce effective symmetry breaking equivalent to SOC.

    Authors: We thank the referee for emphasizing this key requirement. The relaxation rates are obtained from a microscopic spin-conserving system-bath interaction Hamiltonian coupled to the bare antiferromagnetic model (no SOC terms present). Using the Floquet-Markov master equation, the rates follow from Fermi's golden rule applied to the time-periodic system. In the revision, we will explicitly derive these rates in the main text or supplementary material, showing that they remain spin-conserving and do not introduce momentum- or spin-mixing equivalent to SOC. This preserves the nonrelativistic nature of the claimed Edelstein effect. revision: yes

  3. Referee: [Spin currents and Edelstein effect] The linear-response spin currents and steady-state accumulation calculations (likely in the results section on currents and Edelstein effect) should include explicit checks that the bath engineering preserves the underlying antiferromagnetic symmetries while still producing net spin polarization. The current presentation leaves open whether the effect reduces to a hidden relativistic mechanism.

    Authors: We appreciate the suggestion to strengthen the symmetry analysis. In the revised results section, we will add explicit checks demonstrating that the bath engineering respects the antiferromagnetic symmetries (e.g., by verifying invariance under relevant symmetry operations such as combined spin and lattice transformations). We will show that the net spin accumulation and currents arise from the combination of Floquet driving and engineered dissipation without introducing any effective relativistic terms, as the underlying Hamiltonian contains no SOC. These checks will be presented alongside the linear-response and steady-state calculations. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation relies on standard Floquet theory and open-system master equation applied to a proposed model

full rationale

The paper proposes a time-periodic optical drive to induce Floquet spin splitting in an antiferromagnet, then couples the system to a thermal bath via a standard Floquet-Markov master equation to obtain steady-state currents and a nonrelativistic Edelstein effect. No step reduces a prediction to a fitted parameter by construction, nor does any load-bearing claim rest solely on a self-citation whose content is unverified or equivalent to the target result. The central claims are framed as numerical or analytical demonstrations from the driven Hamiltonian plus bath, which are independent of the final observables once the microscopic model is specified. External benchmarks (Floquet formalism and Lindblad-type baths) are standard and not derived from the present results.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides insufficient detail to enumerate specific free parameters or axioms; the proposal implicitly relies on standard Floquet theory and thermal bath models from prior literature.

pith-pipeline@v0.9.0 · 5678 in / 1052 out tokens · 41423 ms · 2026-05-19T02:37:50.026608+00:00 · methodology

discussion (0)

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Forward citations

Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

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  2. Tunable Odd-Parity Spin Splittings in Altermagnets

    cond-mat.mes-hall 2026-05 unverdicted novelty 7.0

    Collinear altermagnets can exhibit tunable mixed-parity spin textures and new dissipationless spin Hall responses when driven by two-color light or coupled to P-odd loop-current order, creating (P,T)=(-,-) or (+,+) states.

  3. Odd-Parity Altermagnetism Originated from Orbital Orders

    cond-mat.mes-hall 2025-08 conditional novelty 7.0

    A symmetry-based stacking strategy with layer-flip realizes odd-parity altermagnetism from nonrelativistic orbital orders, hosting quantum spin Hall phases with helical edge states.

  4. Light-induced Odd-parity Magnetism in Conventional Collinear Antiferromagnets

    cond-mat.mtrl-sci 2025-07 unverdicted novelty 6.0

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Reference graph

Works this paper leans on

56 extracted references · 56 canonical work pages · cited by 4 Pith papers

  1. [1]

    Floquet Brillouin zone

    has a dual symmetry between the two spin sectors, arising from an inversion operation, i.e., τxH↑ [k + A(t)]τx =H↓ [− k − A(t)]. (3) This leads to a dual relation between quasi-energies: ε↑ u,d (k) = ε↓ u,d (− k) [e.g., see Fig. 1 (c)], where u,d re- fer to the up and down bands in the FBZ. Notice that in Fig. 1 the equivalence among valleys is absent bec...

    work page 2021

  2. [4]

    Co- herent antiferromagnetic spintronics,

    J. Han, R. Cheng, L. Liu, H. Ohno, and S. Fukami, “Co- herent antiferromagnetic spintronics,” Nature Materials 22, 684 (2023)

    work page 2023

  3. [5]

    The multiple directions of antiferromagnetic spintronics,

    T. Jungwirth, J. Sinova, A. Manchon, X. Marti, J. Wun- derlich, and C. Felser, “The multiple directions of antiferromagnetic spintronics,” Nature Physics 14, 200 (2018)

    work page 2018

  4. [6]

    Topological antiferromagnetic spintronics,

    L. ˇSmejkal, Y. Mokrousov, B. Yan, and A. H. MacDon- ald, “Topological antiferromagnetic spintronics,” Nature Physics 14, 242 (2018)

    work page 2018

  5. [7]

    Antiferromagnetic spintronics,

    T. Jungwirth, X. Marti, P. Wadley, and J. Wunderlich, “Antiferromagnetic spintronics,” Nature Nanotechnology 11, 231 (2016)

    work page 2016

  6. [8]

    Antiferromagnetic spintronics,

    V. Baltz, A. Manchon, M. Tsoi, T. Moriyama, T. Ono, and Y. Tserkovnyak, “Antiferromagnetic spintronics,” Rev. Mod. Phys. 90, 015005 (2018)

    work page 2018

  7. [9]

    Momentum- dependent spin splitting by collinear antiferromagnetic ordering,

    S. Hayami, Y. Yanagi, and H. Kusunose, “Momentum- dependent spin splitting by collinear antiferromagnetic ordering,” Journal of the Physical Society of Japan 88, 123702 (2019) , https://doi.org/10.7566/JPSJ.88.123702

    work page doi:10.7566/jpsj.88.123702 2019

  8. [10]

    Giant momentum-dependent spin splitting in centrosymmetric low- z antiferromagnets,

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

    work page 2020

  9. [11]

    Prediction of low-z collinear and noncollinear antiferro- magnetic compounds having momentum-dependent spin splitting even without spin-orbit coupling,

    L.-D. Yuan, Z. Wang, J.-W. Luo, and A. Zunger, “Prediction of low-z collinear and noncollinear antiferro- magnetic compounds having momentum-dependent spin splitting even without spin-orbit coupling,” Phys. Rev. 6 Mater. 5, 014409 (2021)

    work page 2021

  10. [12]

    Crystal time-reversal symmetry breaking and spontaneous hall effect in collinear antiferromagnets,

    L. ˇSmejkal, R. Gonz´ alez-Hern´ andez, T. Jungwirth, and J. Sinova, “Crystal time-reversal symmetry breaking and spontaneous hall effect in collinear antiferromagnets,” Science Advances 6, eaaz8809 (2020)

    work page 2020

  11. [13]

    Beyond con- ventional ferromagnetism and antiferromagnetism: A phase with nonrelativistic spin and crystal rotation sym- metry,

    L. ˇSmejkal, J. Sinova, and T. Jungwirth, “Beyond con- ventional ferromagnetism and antiferromagnetism: A phase with nonrelativistic spin and crystal rotation sym- metry,” Phys. Rev. X 12, 031042 (2022)

    work page 2022

  12. [14]

    Editorial: Altermagnetism—a new punch line of fundamental magnetism,

    I. Mazin (The PRX Editors), “Editorial: Altermagnetism—a new punch line of fundamental magnetism,” Phys. Rev. X 12, 040002 (2022)

    work page 2022

  13. [15]

    Spin-split collinear antiferromagnets: A large-scale ab-initio study,

    Y. Guo, H. Liu, O. Janson, I. C. Fulga, J. van den Brink, and J. I. Facio, “Spin-split collinear antiferromagnets: A large-scale ab-initio study,” Materials Today Physics 32, 100991 (2023)

    work page 2023

  14. [16]

    Bottom-up de- sign of spin-split and reshaped electronic band structures in antiferromagnets without spin-orbit coupling: Proce- dure on the basis of augmented multipoles,

    S. Hayami, Y. Yanagi, and H. Kusunose, “Bottom-up de- sign of spin-split and reshaped electronic band structures in antiferromagnets without spin-orbit coupling: Proce- dure on the basis of augmented multipoles,” Phys. Rev. B 102, 144441 (2020)

    work page 2020

  15. [17]

    Efficient electrical spin splitter based on nonrelativis- tic collinear antiferromagnetism,

    R. Gonz´ alez-Hern´ andez, L.ˇSmejkal, K. V´ yborn´ y, Y. Ya- hagi, J. Sinova, T. c. v. Jungwirth, and J. ˇZelezn´ y, “Efficient electrical spin splitter based on nonrelativis- tic collinear antiferromagnetism,” Phys. Rev. Lett. 126, 127701 (2021)

    work page 2021

  16. [18]

    Spin- group symmetry in magnetic materials with negligible spin-orbit coupling,

    P. Liu, J. Li, J. Han, X. Wan, and Q. Liu, “Spin- group symmetry in magnetic materials with negligible spin-orbit coupling,” Phys. Rev. X 12, 021016 (2022)

    work page 2022

  17. [19]

    Emerging re- search landscape of altermagnetism,

    L. ˇSmejkal, J. Sinova, and T. Jungwirth, “Emerging re- search landscape of altermagnetism,” Phys. Rev. X 12, 040501 (2022)

    work page 2022

  18. [20]

    Observation of spin splitting torque in a collinear antiferromagnet ruo 2,

    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 ruo 2,” Phys. Rev. Lett. 128, 197202 (2022)

    work page 2022

  19. [21]

    Observation of spin-splitter torque in collinear antiferromagnetic ruo 2,

    S. Karube, T. Tanaka, D. Sugawara, N. Kadoguchi, M. Kohda, and J. Nitta, “Observation of spin-splitter torque in collinear antiferromagnetic ruo 2,” Phys. Rev. Lett. 129, 137201 (2022)

    work page 2022

  20. [22]

    An anomalous hall effect in altermagnetic ruthenium dioxide,

    Z. Feng, X. Zhou, L. ˇSmejkal, L. Wu, Z. Zhu, H. Guo, R. Gonz´ alez-Hern´ andez, X. Wang, H. Yan, P. Qin, X. Zhang, H. Wu, H. Chen, Z. Meng, L. Liu, Z. Xia, J. Sinova, T. Jungwirth, and Z. Liu, “An anomalous hall effect in altermagnetic ruthenium dioxide,” Nature Electronics 5, 735 (2022)

    work page 2022

  21. [23]

    Chiral magnons in altermagnetic ruo 2,

    L. ˇSmejkal, A. Marmodoro, K.-H. Ahn, R. Gonz´ alez- Hern´ andez, I. Turek, S. Mankovsky, H. Ebert, S. W. D’Souza, O. c. v. ˇSipr, J. Sinova, and T. c. v. Jungwirth, “Chiral magnons in altermagnetic ruo 2,” Phys. Rev. Lett. 131, 256703 (2023)

    work page 2023

  22. [24]

    Altermagnetic anomalous hall effect emerging from electronic correlations,

    T. Sato, S. Haddad, I. C. Fulga, F. F. Assaad, and J. van den Brink, “Altermagnetic anomalous hall effect emerging from electronic correlations,” Phys. Rev. Lett. 133, 086503 (2024)

    work page 2024

  23. [25]

    Floquet engineering of quan- tum materials,

    T. Oka and S. Kitamura, “Floquet engineering of quan- tum materials,” Annual Review of Condensed Matter Physics 10, 387 (2019)

    work page 2019

  24. [26]

    Band structure engi- neering and non-equilibrium dynamics in floquet topolog- ical insulators,

    M. S. Rudner and N. H. Lindner, “Band structure engi- neering and non-equilibrium dynamics in floquet topolog- ical insulators,” Nature Reviews Physics 2, 229 (2020)

    work page 2020

  25. [27]

    Persistence of magnetism in atomically thin MnPS3 crystals,

    G. Long, H. Henck, M. Gibertini, D. Dumcenco, Z. Wang, T. Taniguchi, K. Watanabe, E. Giannini, and A. F. Morpurgo, “Persistence of magnetism in atomically thin MnPS3 crystals,” Nano. Lett. 20, 2452 (2020)

    work page 2020

  26. [28]

    Exploring the magnetic ordering in atomically thin antiferromagnetic mnpse3 by raman spectroscopy,

    P. Liu, Z. Xu, H. Huang, J. Li, C. Feng, M. Huang, M. Zhu, Z. Wang, Z. Zhang, D. Hou, Y. Lu, and B. Xi- ang, “Exploring the magnetic ordering in atomically thin antiferromagnetic mnpse3 by raman spectroscopy,” Jour- nal of Alloys and Compounds 828, 154432 (2020)

    work page 2020

  27. [29]

    Prob- ing ultrafast photo-induced dynamics of the exchange en- ergy in a heisenberg antiferromagnet,

    G. Batignani, D. Bossini, N. Di Palo, C. Ferrante, E. Pon- tecorvo, G. Cerullo, A. Kimel, and T. Scopigno, “Prob- ing ultrafast photo-induced dynamics of the exchange en- ergy in a heisenberg antiferromagnet,” Nature Photonics 9, 506 (2015)

    work page 2015

  28. [30]

    The antiferromagnetic phase of the floquet-driven hubbard model,

    N. Walldorf, D. M. Kennes, J. Paaske, and A. J. Mil- lis, “The antiferromagnetic phase of the floquet-driven hubbard model,” Phys. Rev. B 100, 121110 (2019)

    work page 2019

  29. [31]

    Colloquium: Nonther- mal pathways to ultrafast control in quantum materials,

    A. de la Torre, D. M. Kennes, M. Claassen, S. Gerber, J. W. McIver, and M. A. Sentef, “Colloquium: Nonther- mal pathways to ultrafast control in quantum materials,” Rev. Mod. Phys. 93, 041002 (2021)

    work page 2021

  30. [33]

    Transport properties of nonequilibrium systems under the application of light: Photoinduced quantum hall in- sulators without landau levels,

    T. Kitagawa, T. Oka, A. Brataas, L. Fu, and E. Demler, “Transport properties of nonequilibrium systems under the application of light: Photoinduced quantum hall in- sulators without landau levels,” Phys. Rev. B 84, 235108 (2011)

    work page 2011

  31. [34]

    Periodically driven quan- tum systems: Effective hamiltonians and engineered gauge fields,

    N. Goldman and J. Dalibard, “Periodically driven quan- tum systems: Effective hamiltonians and engineered gauge fields,” Phys. Rev. X 4, 031027 (2014)

    work page 2014

  32. [35]

    Phonons in carbon nanotubes,

    M. S. Dresselhaus and P. C. Eklund, “Phonons in carbon nanotubes,” Advances in Physics 49, 705 (2000)

    work page 2000

  33. [36]

    Phonons and electron-phonon scattering in carbon nanotubes,

    H. Suzuura and T. Ando, “Phonons and electron-phonon scattering in carbon nanotubes,” Phys. Rev. B 65, 235412 (2002)

    work page 2002

  34. [37]

    Out-of-equilibrium electrons and the hall conductance of a floquet topologi- cal insulator,

    H. Dehghani, T. Oka, and A. Mitra, “Out-of-equilibrium electrons and the hall conductance of a floquet topologi- cal insulator,” Phys. Rev. B 91, 155422 (2015)

    work page 2015

  35. [38]

    Optical hall conductivity of a floquet topological insulator,

    H. Dehghani and A. Mitra, “Optical hall conductivity of a floquet topological insulator,” Phys. Rev. B 92, 165111 (2015)

    work page 2015

  36. [39]

    Statistical mechanics of floquet systems: The pervasive problem of near degeneracies,

    D. W. Hone, R. Ketzmerick, and W. Kohn, “Statistical mechanics of floquet systems: The pervasive problem of near degeneracies,” Phys. Rev. E 79, 051129 (2009)

    work page 2009

  37. [40]

    See the Supplementary Materials at [URL will be inserted by publisher] for details of calculation

    work page

  38. [41]

    Floquet band struc- ture of a semi-dirac system,

    Q. Chen, L. Du, and G. A. Fiete, “Floquet band struc- ture of a semi-dirac system,” Phys. Rev. B 97, 035422 (2018)

    work page 2018

  39. [42]

    Photovoltaic hall effect in graphene,

    T. Oka and H. Aoki, “Photovoltaic hall effect in graphene,” Phys. Rev. B 79, 081406 (2009)

    work page 2009

  40. [43]

    Floquet-Engineering Weyl Points and Linked Fermi Arcs from Straight Nodal Lines,

    D. Liu, Z.-Y. Zhuang, and Z. Yan, “Floquet-Engineering Weyl Points and Linked Fermi Arcs from Straight Nodal Lines,” arXiv e-prints , arXiv:2507.04489 (2025)

    work page arXiv 2025

  41. [44]

    Nuclear electric resonance and orientation of carrier spins by an electric field,

    A. G. Aronov and Y. B. Lyanda-Geller, “Nuclear electric resonance and orientation of carrier spins by an electric field,” Soviet Journal of Experimental and Theoretical Physics Letters 50, 431 (1989)

    work page 1989

  42. [45]

    Spin polarization of conduction electron s induced by electric current in two-dimensional asymmet- ric electron systems,

    V. Edelstein, “Spin polarization of conduction electron s induced by electric current in two-dimensional asymmet- ric electron systems,” Solid State Communications 73, 233 (1990)

    work page 1990

  43. [46]

    Probing topological floque t states in wse2 using circular dichroism in time- and angle- 7 resolved photoemission spectroscopy,

    M. Sch¨ uler and S. Beaulieu, “Probing topological floque t states in wse2 using circular dichroism in time- and angle- 7 resolved photoemission spectroscopy,” Communications Physics 5, 164 (2022)

    work page 2022

  44. [47]

    Antiferromagnetic topological insulator with nonsymmorphic protection in two dimensions,

    C. Niu, H. Wang, N. Mao, B. Huang, Y. Mokrousov, and Y. Dai, “Antiferromagnetic topological insulator with nonsymmorphic protection in two dimensions,” Phys. Rev. Lett. 124, 066401 (2020)

    work page 2020

  45. [48]

    Dirac semimetals in two dimensions,

    S. M. Young and C. L. Kane, “Dirac semimetals in two dimensions,” Phys. Rev. Lett. 115, 126803 (2015)

    work page 2015

  46. [49]

    Antiferromagnetic dirac semimetals in two di- mensions,

    J. Wang, “Antiferromagnetic dirac semimetals in two di- mensions,” Phys. Rev. B 95, 115138 (2017)

    work page 2017

  47. [50]

    Electric control of dirac quasiparticles by spin-orbit torque in an antiferromagnet,

    L. ˇSmejkal, J. ˇZelezn´ y, J. Sinova, and T. Jungwirth, “Electric control of dirac quasiparticles by spin-orbit torque in an antiferromagnet,” Phys. Rev. Lett. 118, 106402 (2017)

    work page 2017

  48. [51]

    Chiral photocurrent in parity-violating magnet and enhanced response in topological antiferromagnet,

    H. Watanabe and Y. Yanase, “Chiral photocurrent in parity-violating magnet and enhanced response in topological antiferromagnet,” Phys. Rev. X 11, 011001 (2021). Supplemental Material for “Floquet Spin Splitting and Spin Generation in Antiferromagnets” Bo Li, 1, ∗ Ding-Fu Shao, 2, † and Alexey A. Kovalev 3, ‡ 1MOE Key Laboratory for Nonequilibrium Synthes...

    work page 2021

  49. [52]

    (55) By setting ∂tρkα =Ikα = 0, we obtain ρkα = ∑ n Γ n kαf0(εkα +nω ) ∑ n Γ n kα

    On the other hand, the collision integral counting electrons tunnel ing into and out of the system is given by [5] Ikα = ∑ n Γ n kα [ (1− ρkα )f0(εkα +nω )− ρkα ( 1− f0(εkα +nω ) )] . (55) By setting ∂tρkα =Ikα = 0, we obtain ρkα = ∑ n Γ n kαf0(εkα +nω ) ∑ n Γ n kα . (56) In our study, we expect the fast drive can induce a net spin accumul ation in the st...

    work page

  50. [53]

    D. W. Hone, R. Ketzmerick, and W. Kohn, Phys. Rev. E 79, 051129 (2009), URL https://link.aps.org/doi/10.1103/ PhysRevE.79.051129

    work page 2009

  51. [54]

    M. S. Rudner and N. H. Lindner, The floquet engineer’s handbook (2020), 2003.08252, URL https://arxiv.org/abs/2003. 08252

    work page arXiv 2020

  52. [55]

    Kumar, M

    A. Kumar, M. Rodriguez-Vega, T. Pereg-Barnea, and B. Seradjeh, Phys. Rev. B 101, 174314 (2020), URL https://link. aps.org/doi/10.1103/PhysRevB.101.174314

    work page doi:10.1103/physrevb.101.174314 2020

  53. [56]

    Impurity spectra of graphene unde r electric and magnetic fields

    H. Dehghani, T. Oka, and A. Mitra, Phys. Rev. B 91, 155422 (2015), URL https://link.aps.org/doi/10.1103/PhysRevB. 91.155422

    work page doi:10.1103/physrevb 2015

  54. [57]

    K. I. Seetharam, C.-E. Bardyn, N. H. Lindner, M. S. Rudner, and G. Refael, Phys. Rev. X 5, 041050 (2015), URL https://link.aps.org/doi/10.1103/PhysRevX.5.041050

    work page doi:10.1103/physrevx.5.041050 2015

  55. [58]

    & Aoki, H

    T. Oka and H. Aoki, Phys. Rev. B 79, 081406 (2009), URL https://link.aps.org/doi/10.1103/PhysRevB.79.081406

    work page doi:10.1103/physrevb.79.081406 2009

  56. [59]

    Liu, Z.-Y

    D. Liu, Z.-Y. Zhuang, and Z. Yan, arXiv e-prints arXiv:2507.0 4489 (2025)

    work page 2025