pith. machine review for the scientific record.
sign in

arxiv: 2510.16248 · v2 · submitted 2025-10-17 · ❄️ cond-mat.str-el · cond-mat.mtrl-sci

Cavity-induced coherent magnetization and polaritons in altermagnets

Pith reviewed 2026-05-18 05:35 UTC · model grok-4.3

classification ❄️ cond-mat.str-el cond-mat.mtrl-sci
keywords altermagnetsoptical cavitycoherent magnetizationpolaritonsd-wave symmetryLindblad analysisspin imbalancespintronics
0
0 comments X

The pith

Placing a d-wave altermagnet inside a driven optical cavity induces tunable magnetization via selective photon coupling to sublattices.

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

The paper shows that embedding a two-dimensional d-wave altermagnet in a driven optical cavity produces a finite, tunable magnetization. Coherent photon driving interacts selectively with the electronic sublattices because of the altermagnet's symmetry-broken spin texture, creating a steady-state spin imbalance. The same cavity setup leaves conventional antiferromagnets without any net magnetization. A mean-field Lindblad analysis establishes that quadratic couplings dominate, and strong photon-matter coupling produces distinct polariton signatures in the magnetization dynamics. This cavity approach supplies a route to manipulate altermagnetic order for spintronic uses.

Core claim

Embedding a two-dimensional d-wave altermagnet in a driven optical cavity induces a finite, tunable magnetization. Coherent photon driving couples selectively to electronic sublattices, and the resulting altermagnets' symmetry-broken spin texture yields a pronounced steady-state spin imbalance -- coherent magnetization -- absent in conventional antiferromagnets for the same lattice configuration.

What carries the argument

Selective coherent coupling of driven cavity photons to altermagnet sublattices within a mean-field Lindblad treatment, where quadratic interactions dominate and generate polariton features in the steady-state magnetization.

If this is right

  • The magnitude of induced magnetization scales directly with cavity drive strength.
  • Strong-coupling conditions produce observable polariton signatures in the steady-state magnetization.
  • The spin imbalance does not appear when the identical cavity setup is applied to conventional antiferromagnets.
  • Cavity driving offers a field-free method to control altermagnetic spin textures.

Where Pith is reading between the lines

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

  • The effect could be tested in candidate d-wave altermagnetic materials to measure the predicted magnetization.
  • The cavity control scheme may extend to g-wave or i-wave altermagnets with appropriate parameter adjustments.
  • Time-resolved measurements beyond the steady state could reveal additional routes for coherent spin manipulation.

Load-bearing premise

The mean-field Lindblad analysis accurately captures the dominance of quadratic over linear couplings and the emergence of distinct polariton signatures in the steady state of induced magnetization.

What would settle it

An experiment that measures zero net magnetization in the cavity-embedded altermagnet or finds identical spin balance in a conventional antiferromagnet under the same driving would disprove the selective induction of coherent magnetization.

Figures

Figures reproduced from arXiv: 2510.16248 by James K. Freericks, Libor \v{S}mejkal, Mohsen Yarmohammadi.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic illustration of a laser-driven cavity setup [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Time evolution of the spin imbalance [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Time-averaged cavity-induced magnetization in the [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
read the original abstract

Altermagnets feature antiparallel spin sublattices with $d$-, $g$-, or $i$-wave spin order, yielding nonrelativistic spin splitting without net magnetization. We show that embedding a two-dimensional $d$-wave altermagnet in a driven optical cavity induces a finite, tunable magnetization. Coherent photon driving couples selectively to electronic sublattices, and the resulting altermagnets' symmetry-broken spin texture yields a pronounced steady-state spin imbalance -- coherent magnetization -- absent in conventional antiferromagnets for the same lattice configuration. A mean-field Lindblad analysis reveals the dominance of quadratic over linear couplings. In the strong-coupling regime, distinct polariton signatures emerge in the steady state of induced magnetization. This work demonstrates cavity control of altermagnets for spintronic applications.

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 / 1 minor

Summary. The paper claims that embedding a two-dimensional d-wave altermagnet in a driven optical cavity induces a finite, tunable magnetization via coherent photon driving that couples selectively to electronic sublattices. This produces a steady-state spin imbalance (coherent magnetization) that is absent in conventional antiferromagnets with the same lattice configuration. A mean-field Lindblad analysis is used to establish the dominance of quadratic over linear couplings, with distinct polariton signatures appearing in the steady state of the induced magnetization in the strong-coupling regime.

Significance. If the central results hold, the work demonstrates a mechanism for cavity control of altermagnets, enabling induction of net magnetization in systems that otherwise exhibit zero net magnetization due to their symmetry. This could have implications for spintronic applications by providing tunable, light-mediated spin imbalance and polariton features not accessible in equilibrium or in standard antiferromagnets.

major comments (2)
  1. [Mean-field Lindblad analysis (as described in the abstract and main text)] The mean-field Lindblad treatment is asserted to show quadratic-coupling dominance and distinct steady-state polariton signatures, but in a 2D driven-dissipative setting the approximation may miss fluctuation corrections and cavity-mediated correlations that renormalize the induced spin imbalance (especially since the altermagnetic order parameter is itself cavity-induced rather than pre-existing). An explicit check that the truncation remains controlled in the reported strong-coupling regime is required to support the central claim of tunable magnetization absent in conventional AFMs.
  2. [Symmetry analysis and comparison to antiferromagnets] The symmetry argument for selective sublattice coupling and the resulting absence of the effect in conventional antiferromagnets for the same lattice configuration is central to the claim; however, without a direct side-by-side comparison (e.g., via explicit calculation of the steady-state magnetization for both cases under identical driving), it is unclear whether the distinction arises purely from the d-wave spin texture or from other details of the model.
minor comments (1)
  1. [Abstract] The abstract provides a high-level outline but contains no equations, parameter values, or quantitative measures of the induced magnetization or polariton splitting, which limits immediate assessment of the results.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major point below, providing clarifications and indicating where revisions will be made to strengthen the presentation.

read point-by-point responses
  1. Referee: [Mean-field Lindblad analysis (as described in the abstract and main text)] The mean-field Lindblad treatment is asserted to show quadratic-coupling dominance and distinct steady-state polariton signatures, but in a 2D driven-dissipative setting the approximation may miss fluctuation corrections and cavity-mediated correlations that renormalize the induced spin imbalance (especially since the altermagnetic order parameter is itself cavity-induced rather than pre-existing). An explicit check that the truncation remains controlled in the reported strong-coupling regime is required to support the central claim of tunable magnetization absent in conventional AFMs.

    Authors: We agree that fluctuation corrections merit explicit discussion in driven-dissipative settings. Our mean-field Lindblad treatment is applied in the regime where coherent driving dominates dissipation, yielding quadratic-coupling dominance and stable polariton features as reported. To address the concern directly, the revised manuscript will include a dedicated subsection estimating fluctuation effects via a perturbative expansion around the mean-field solution and finite-size scaling arguments. These estimates show that cavity-mediated correlations produce only quantitative renormalizations without altering the qualitative induction of net magnetization or the distinction from conventional antiferromagnets. We therefore maintain that the truncation is controlled for the parameters and conclusions presented. revision: yes

  2. Referee: [Symmetry analysis and comparison to antiferromagnets] The symmetry argument for selective sublattice coupling and the resulting absence of the effect in conventional antiferromagnets for the same lattice configuration is central to the claim; however, without a direct side-by-side comparison (e.g., via explicit calculation of the steady-state magnetization for both cases under identical driving), it is unclear whether the distinction arises purely from the d-wave spin texture or from other details of the model.

    Authors: The absence of induced magnetization in conventional antiferromagnets follows directly from their spin symmetry, which enforces equal coupling to both sublattices and thus cancels any net imbalance under the same cavity drive. While the symmetry argument is model-independent for the lattice configuration considered, we recognize that an explicit numerical comparison would make the distinction more transparent. The revised manuscript will therefore add a direct side-by-side calculation of the steady-state magnetization for both the d-wave altermagnet and a conventional antiferromagnet, using identical driving amplitudes, cavity parameters, and lattice geometry. This will confirm that the net magnetization remains zero in the antiferromagnetic case, isolating the role of the d-wave spin texture. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected; derivation remains self-contained

full rationale

The paper constructs a microscopic model of a 2D d-wave altermagnet coupled to a driven cavity, then solves the resulting mean-field Lindblad master equation to obtain the steady-state spin imbalance. The induced magnetization follows directly from the selective photon-sublattice coupling and the altermagnetic symmetry breaking, without any reduction of the central prediction to a fitted parameter, self-definition, or load-bearing self-citation. Symmetry arguments and the explicit master-equation treatment supply independent content that can be checked against the stated Hamiltonian and truncation assumptions.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard open-quantum-system assumptions and mean-field approximations typical for cavity QED; no new free parameters or invented entities are declared in the abstract.

axioms (1)
  • domain assumption Mean-field approximation suffices for the Lindblad master equation describing the driven cavity-altermagnet system
    Invoked to obtain the steady-state spin imbalance and polariton signatures.

pith-pipeline@v0.9.0 · 5684 in / 1159 out tokens · 35610 ms · 2026-05-18T05:35:25.301521+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]

    Šmejkal, J

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

  2. [2]

    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)

  3. [3]

    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)

  4. [4]

    Šmejkal, R

    L. Šmejkal, R. González-Hernández, T. Jungwirth, and J. Sinova, Crystal time-reversal symmetry breaking and spontaneousHalleffectincollinearantiferromagnets,Sci- ence Advances6, eaaz8809 (2020)

  5. [5]

    I. I. Mazin, K. Koepernik, M. D. Johannes, R. González-Hernández, and L. Šmejkal, Pre- diction of unconventional magnetism in doped fesb<sub>2</sub>, Proceedings of the National Academy of Sciences118, e2108924118 (2021), https://www.pnas.org/doi/pdf/10.1073/pnas.2108924118

  6. [6]

    Krempaský, L

    J. Krempaský, L. Šmejkal, S. W. D’Souza, M. Ha- jlaoui, G. Springholz, K. Uhlířová, F. Alarab, P. C. Constantinou, V. Strocov, D. Usanov, W. R. Pudelko, R. González-Hernández, A. Birk Hellenes, Z. Jansa, H. Reichlová, Z. Šobáň, R. D. Gonzalez Betancourt, P. Wadley, J. Sinova, D. Kriegner, J. Minár, J. H. Dil, and T. Jungwirth, Altermagnetic lifting of Kra...

  7. [7]

    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)

  8. [8]

    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)

  9. [9]

    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)

  10. [10]

    D. Jo, D. Go, Y. Mokrousov, P. M. Oppeneer, S.-W. Cheong, and H.-W. Lee, Weak ferromagnetism in alter- magnets from alternatingg-tensor anisotropy, Phys. Rev. Lett.134, 196703 (2025)

  11. [11]

    M. Vila, V. Sunko, and J. E. Moore, Orbital-spin locking and its optical signatures in altermagnets, Phys. Rev. B 112, L020401 (2025)

  12. [12]

    Z. Feng, X. Zhou, L. Šmejkal, L. Wu, Z. Zhu, H. Guo, R. González-Hernández, 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 Elec- tronics5, 735 (2022)

  13. [13]

    P.-H. Fu, Q. Lv, Y. Xu, J. Cayao, J.-F. Liu, and X.- L. Yu, All-electrically controlled spintronics in altermag- netic heterostructures, (2025), arXiv:2506.05504

  14. [14]

    Šmejkal, Y

    L. Šmejkal, Y. Mokrousov, B. Yan, and A. H. Mac- Donald, Topological antiferromagnetic spintronics, Na- ture Physics14, 242 (2018)

  15. [15]

    K. V. Yershov, O. Gomonay, J. Sinova, J. van den Brink, and V. P. Kravchuk, Curvature-induced magnetization of altermagnetic films, Phys. Rev. Lett.134, 116701 (2025)

  16. [16]

    E. W. Hodt, P. Sukhachov, and J. Linder, Interface- induced magnetization in altermagnets and antiferro- magnets, Phys. Rev. B110, 054446 (2024)

  17. [17]

    N. N. Orlova, V. D. Esin, A. V. Timonina, N. N. Kolesnikov, and E. V. Deviatov, Magnetization symme- try for the altermagnetic candidate MnTe, Phys. Rev. B 111, 224414 (2025)

  18. [18]

    Furuya and K

    G. Furuya and K. Hattori, Order parameter fluctuation effects on current-induced magnetization, Phys. Rev. B 112, 035171 (2025)

  19. [19]

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

  20. [20]

    D. Go, K. Ando, A. Pezo, S. Blügel, A. Manchon, and Y. Mokrousov, Orbital pumping by magnetization dy- namics in ferromagnets, Phys. Rev. B111, L140409 (2025)

  21. [21]

    Yao and S

    D. Yao and S. Murakami, Theory of spin magnetiza- tion driven by chiral phonons, Phys. Rev. B111, 134414 (2025)

  22. [22]

    Shaposhnikov, E

    L. Shaposhnikov, E. Barredo-Alamilla, F. Wilczek, and M. A. Gorlach, Probing ultrafast magnetization dynam- ics via synthetic axion fields, Phys. Rev. Lett.134, 246702 (2025)

  23. [23]

    P.-H. Fu, S. Mondal, J.-F. Liu, Y. Tanaka, and J. Cayao, Floquet engineering spin triplet states in unconventional magnets, (2025), arXiv:2505.20205

  24. [24]

    I.-T. Lu, D. Shin, M. K. Svendsen, S. Latini, H. Hübener, M. Ruggenthaler, and A. Rubio, Cavity engineering of solid-state materials without external driving, Adv. Opt. Photon.17, 441 (2025)

  25. [26]

    Shalabney, J

    A. Shalabney, J. George, J. Hutchison, G. Pupillo, C. Genet, and T. W. Ebbesen, Coherent coupling of molecular resonators with a microcavity mode, Nature Communications6, 5981 (2015)

  26. [27]

    D. N. Basov, A. Asenjo-Garcia, P. J. Schuck, X. Zhu, A. Rubio, A. Cavalleri, M. Delor, M. M. Fogler, and M. Liu, Polaritonic quantum matter 10.1515/nanoph- 2025-0001 (2025)

  27. [28]

    B. Kass, S. Talkington, A. Srivastava, and M. Claassen, Many-body photon blockade and quantum light gen- eration from cavity quantum materials, (2024), arXiv:2411.08964

  28. [29]

    Y. Yang, R. Chikkaraddy, Q. Lin, D. D. A. Clarke, D. Wigger, J. J. Baumberg, and O. Hess, Electrochemi- cally switchable multimode strong coupling in plasmonic nanocavities, Nano Letters24, 238 (2024)

  29. [30]

    Bujalance, L

    C. Bujalance, L. Caliò, D. N. Dirin, D. O. Tiede, J. F. Galisteo-López, J. Feist, F. J. García-Vidal, M. V. Ko- valenko, and H. Míguez, Strong light-matter coupling in lead halide perovskite quantum dot solids, ACS Nano18, 4922 (2024)

  30. [31]

    Keren, T

    I. Keren, T. A. Webb, S. Zhang, J. Xu, D. Sun, B. S. Y. Kim, D. Shin, S. S. Zhang, J. Zhang, G. Pereira, J. Yao, T. Okugawa, M. H. Michael, J. H. Edgar, S. Wolf, M. Ju- lian, R. P. Prasankumar, K. Miyagawa, K. Kanoda, G. Gu, M. Cothrine, D. Mandrus, M. Buzzi, A. Cavalleri, C. R. Dean, D. M. Kennes, A. J. Millis, Q. Li, M. A. Sen- tef, A. Rubio, A. N. Pasu...

  31. [32]

    Le Dé, C

    B. Le Dé, C. J. Eckhardt, D. M. Kennes, and M. A. Sentef, Cavity engineering of HubbardUvia phonon po- laritons, Journal of Physics: Materials5, 024006 (2022)

  32. [33]

    R.-C. Ge, S. R. Koshkaki, and M. H. Kolodrubetz, Cav- ity induced many-body localization, Phys. Rev. B111, 155416 (2025)

  33. [35]

    M. A. Sentef, M. Ruggenthaler, and A. Rubio, Cav- ity quantum-electrodynamical polaritonically enhanced electron-phonon coupling and its influence on supercon- ductivity, Science Advances4, eaau6969 (2018)

  34. [36]

    C. J. Eckhardt, G. Passetti, M. Othman, C. Karrasch, F. Cavaliere, M. A. Sentef, and D. M. Kennes, Quan- tum Floquet engineering with an exactly solvable tight- binding chain in a cavity, Communications Physics5, 122 (2022)

  35. [38]

    Zare Rameshti, S

    B. Zare Rameshti, S. Viola Kusminskiy, J. A. Haigh, K. Usami, D. Lachance-Quirion, Y. Nakamura, C.-M. Hu, H. X. Tang, G. E. Bauer, and Y. M. Blanter, Cav- ity magnonics, Physics Reports979, 1 (2022), cavity Magnonics

  36. [39]

    Viola Kusminskiy, H

    S. Viola Kusminskiy, H. X. Tang, and F. Marquardt, Coupled spin-light dynamics in cavity optomagnonics, Phys. Rev. A94, 033821 (2016)

  37. [40]

    C. A. Potts, E. Varga, V. A. S. V. Bittencourt, S. V. Kusminskiy, and J. P. Davis, Dynamical backaction mag- nomechanics, Phys. Rev. X11, 031053 (2021)

  38. [41]

    Białek, W

    M. Białek, W. Knap, and J.-P. Ansermet, Cavity- mediated coupling of terahertz antiferromagnetic res- onators, Phys. Rev. Appl.19, 064007 (2023)

  39. [42]

    Weber, K

    M. Weber, K. Leckron, L. Haag, R. Jaeschke-Ubiergo, L. Šmejkal, J. Sinova, and H. C. Schneider, Ultrafast electron dynamics in altermagnetic materials, (2024), arXiv:2411.08160

  40. [43]

    Rajpurohit, R

    S. Rajpurohit, R. Karaalp, Y. Ping, L. Z. Tan, T. Ogitsu, and P. E. Blöchl, Optical control of spin-splitting in an altermagnet, (2024), arXiv:2409.17718

  41. [44]

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

  42. [45]

    U. F. P. Seifert, M. Ye, and L. Balents, Ultrafast optical excitation of magnetic dynamics in van der waals mag- nets: Coherent magnons and BKT dynamics in NiPS3, Phys. Rev. B105, 155138 (2022)

  43. [46]

    Ruggenthaler, N

    M. Ruggenthaler, N. Tancogne-Dejean, J. Flick, H. Ap- pel, and A. Rubio, From a quantum-electrodynamical light-matter description to novel spectroscopies, Nature Reviews Chemistry2, 0118 (2018)

  44. [47]

    Frisk Kockum, A

    A. Frisk Kockum, A. Miranowicz, S. De Liberato, S. Savasta, and F. Nori, Ultrastrong coupling between light and matter, Nature Reviews Physics1, 19 (2019)

  45. [48]

    Hübener, U

    H. Hübener, U. De Giovannini, C. Schäfer, J. Andberger, M. Ruggenthaler, J. Faist, and A. Rubio, Engineering quantum materials with chiral optical cavities, Nature Materials20, 438 (2021)

  46. [49]

    Genet, J

    C. Genet, J. Faist, and T. W. Ebbesen, Inducing new ma- terial properties with hybrid light-matter states, Physics Today74, 42 (2021)

  47. [50]

    X. Li, M. Bamba, Q. Zhang, S. Fallahi, G. C. Gard- ner, W. Gao, M. Lou, K. Yoshioka, M. J. Manfra, and J. Kono, Vacuum Bloch–Siegert shift in Landau polari- tons with ultra-high cooperativity, Nature Photonics12, 324 (2018)

  48. [51]

    X. Wang, E. Ronca, and M. A. Sentef, Cavity quantum electrodynamical chern insulator: Towards light-induced quantized anomalous Hall effect in graphene, Phys. Rev. B99, 235156 (2019)

  49. [52]

    G. Kipp, H. M. Bretscher, B. Schulte, D. Herrmann, K. Kusyak, M. W. Day, S. Kesavan, T. Matsuyama, X. Li, S. M. Langner, J. Hagelstein, F. Sturm, A. M. Potts, C. J. Eckhardt, Y. Huang, K. Watanabe, T. Taniguchi, A. Rubio, D. M. Kennes, M. A. Sentef, E. Baudin, G. Meier, M. H. Michael, and J. W. McIver, Cavity electrodynamics of van der Waals heterostruc- ...

  50. [53]

    Passetti, C

    G. Passetti, C. J. Eckhardt, M. A. Sentef, and D. M. Kennes, Cavity light-matter entanglement through quan- tum fluctuations, Phys. Rev. Lett.131, 023601 (2023)

  51. [54]

    Rokaj, M

    V. Rokaj, M. Penz, M. A. Sentef, M. Ruggenthaler, and A. Rubio, Polaritonic Hofstadter butterfly and cavity control of the quantized Hall conductance, Phys. Rev. B105, 205424 (2022)

  52. [55]

    W. Qin, A. F. Kockum, C. S. Muñoz, A. Miranowicz, and F. Nori, Quantum amplification and simulation of strong and ultrastrong coupling of light and matter, Physics Re- ports1078, 1 (2024)

  53. [56]

    Z. Jin, H. Yang, Z. Zeng, Y. Cao, and P. Yan, Cavity- induced strong magnon-magnon coupling in altermag- nets, (2023), arXiv:2307.00909

  54. [57]

    Jiang, M

    B. Jiang, M. Hu, J. Bai, Z. Song, C. Mu, G. Qu, W. Li, W. Zhu, H. Pi, Z. Wei, Y.-J. Sun, Y. Huang, X. Zheng, Y. Peng, L. He, S. Li, J. Luo, Z. Li, G. Chen, H. Li, H. Weng, and T. Qian, A metallic room-temperatured- wave altermagnet, Nature Physics21, 754 (2025)

  55. [58]

    Zhang, X

    F. Zhang, X. Cheng, Z. Yin, C. Liu, L. Deng, Y. Qiao, Z. Shi, S. Zhang, J. Lin, Z. Liu, M. Ye, Y. Huang, X. Meng, C. Zhang, T. Okuda, K. Shimada, S. Cui, Y. Zhao, G.-H. Cao, S. Qiao, J. Liu, and C. Chen, Crystal-symmetry-paired spin–valley locking in a layered room-temperature metallic altermagnet candidate, Na- ture Physics21, 760 (2025)

  56. [59]

    M. Naka, S. Hayami, H. Kusunose, Y. Yanagi, Y. Mo- tome, and H. Seo, Spin current generation in organic an- tiferromagnets, Nature Communications10, 4305 (2019)

  57. [60]

    Weber, S

    M. Weber, S. Wust, L. Haag, A. Akashdeep, K. Leckron, C. Schmitt, R. Ramos, T. Kikkawa, E. Saitoh, M. Kläui, L. Šmejkal, J. Sinova, M. Aeschlimann, G. Jakob, B. Stadtmüller, and H. C. Schneider, All optical excita- tion of spin polarization ind-wave altermagnets, (2024), arXiv:2408.05187

  58. [61]

    Y. Noda, K. Ohno, and S. Nakamura, Momentum- dependent band spin splitting in semiconducting MnO2: a density functional calculation, Phys. Chem. Chem. Phys.18, 13294 (2016)

  59. [62]

    Šmejkal, A

    L. Šmejkal, A. H. MacDonald, J. Sinova, S. Nakatsuji, andT.Jungwirth,AnomalousHallantiferromagnets,Na- ture Reviews Materials7, 482 (2022)

  60. [63]

    The total pseudospin magnetization per unit cell is 8 defined asn↑ −n ↓ ∝ R BZ d2k (2π)2 ⟨σz⟩⃗k

    In our framework, we introduce the notion of spin magne- tizationusingthePaulimatrixσ z inorbitalspace, assign- ingσ z = +1to the first orbital andσ z =−1to the sec- ond. The total pseudospin magnetization per unit cell is 8 defined asn↑ −n ↓ ∝ R BZ d2k (2π)2 ⟨σz⟩⃗k. Due to the antisym- metry of the spin-splitting term,∆(kx,ky ) =−∆ (ky ,kx), under interc...

  61. [64]

    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)

  62. [65]

    F. P. Bonafé, E. I. Albar, S. T. Ohlmann, V. P. Koshel- eva, C. M. Bustamante, F. Troisi, A. Rubio, and H. Ap- pel,FullminimalcouplingMaxwell-TDDFT:Anab initio framework for light-matter interaction beyond the dipole approximation, Phys. Rev. B111, 085114 (2025)

  63. [66]

    While laser pulses could also excite cavity photons and potentially induce magnetization over very short timescales, our focus here is on creating NESS, allowing the induced magnetization to be sustained and probed over extended timescales

  64. [67]

    Weber, E

    L. Weber, E. Viñas Boström, M. Claassen, A. Rubio, and D. M. Kennes, Cavity-renormalized quantum criti- cality in a honeycomb bilayer antiferromagnet, Commu- nications Physics6, 247 (2023)

  65. [68]

    V. Leeb, A. Mook, L. Šmejkal, and J. Knolle, Sponta- neous formation of altermagnetism from orbital ordering, Phys. Rev. Lett.132, 236701 (2024)

  66. [69]

    Lindblad, On the generators of quantum dynamical semigroups, Comm

    G. Lindblad, On the generators of quantum dynamical semigroups, Comm. Math. Phys.48, 119 (1976)

  67. [70]

    Xiang and W

    B. Xiang and W. Xiong, Molecular polaritons for chem- istry, photonics and quantum technologies, Chemical Re- views124, 2512 (2024)

  68. [71]

    Schwennicke, N

    K. Schwennicke, N. C. Giebink, and J. Yuen-Zhou, Ex- tracting accurate light-matter couplings from disordered polaritons, Nanophotonics13, 2469 (2024)

  69. [72]

    F. J. García-Vidal, C. Ciuti, and T. W. Ebbesen, Ma- nipulating matter by strong coupling to vacuum fields, Science373, eabd0336 (2021)

  70. [73]

    Y.Luo, J.Zhao, A.Fieramosca, Q.Guo, H.Kang, X.Liu, T. C. H. Liew, D. Sanvitto, Z. An, S. Ghosh, Z. Wang, H. Xu, and Q. Xiong, Strong light-matter coupling in van der Waals materials, Light: Science & Applications13, 203 (2024)

  71. [74]

    F. Tay, A. Mojibpour, S. Sanders, S. Liang, H. Xu, G. C. Gardner, A. Baydin, M. J. Manfra, A. Alabas- tri, D. Hagenmüller, and J. Kono, Multimode ultrastrong coupling in three-dimensional photonic-crystal cavities, Nature Communications16, 3603 (2025)

  72. [75]

    See the video at http://xxx.yyy.zzz for the response of the other driving amplitudes and frequencies

  73. [76]

    T. W. Ebbesen, Hybrid light-matter states in a molecular and material science perspective, Accounts of Chemical Research49, 2403 (2016)

  74. [77]

    Schlawin, D

    F. Schlawin, D. M. Kennes, and M. A. Sentef, Cavity quantum materials, Applied Physics Reviews9, 011312 (2022)

  75. [78]

    Since our proposal relies on a weak continuous-wave laser and weak cavity-altermagnet coupling, the energy input remains well below the lattice-melting threshold and is balanced by dissipation, ensuring a stable NESS

  76. [79]

    Kawaguchi, K

    K. Kawaguchi, K. Kuroda, Z. Zhao, S. Tani, A. Hara- sawa, Y. Fukushima, H. Tanaka, R. Noguchi, T. Iimori, K. Yaji, M. Fujisawa, S. Shin, F. Komori, Y. Kobayashi, and T. Kondo, Time-, spin-, and angle-resolved photoe- mission spectroscopy with a 1-MHz 10.7-eV pulse laser, Review of Scientific Instruments94, 083902 (2023)

  77. [80]

    A.Kirilyuk, A.V.Kimel,andT.Rasing,Ultrafastoptical manipulation of magnetic order, Rev. Mod. Phys.82, 2731 (2010)

  78. [81]

    Yarmohammadi, P

    M. Yarmohammadi, P. M. Oppeneer, and J. K. Freericks, Cavity-assisted magnetization switching in a quantum spin-phonon chain, Phys. Rev. B112, 094445 (2025)

  79. [82]

    Yarmohammadi, M

    M. Yarmohammadi, M. Bukov, V. Oganesyan, and M. H. Kolodrubetz, Laser-enhanced magnetism in SmFeO 3, Phys. Rev. B109, 224417 (2024)

  80. [83]

    Yarmohammadi, L

    M. Yarmohammadi, L. Šmejkal, and J. K. Freericks, Zen- odo: Dataset, (2025)