Abstract
The high density of states corresponding to photonic flat bands offers a unique avenue for enhancing light–matter interactions, but despite their potential, flat-band continuous modes have largely focused on the weak-coupling or Purcell regimes. Here, we report experimentally achieve strong coupling between the photonic flat-band mode and a magnon mode in a ferrimagnetic spin ensemble. By using one-dimensional Lieb photonic lattices, we reveal that, in the strong-coupling regime, the mechanism underlying flat-band-enhanced interaction is analogous to Dicke superradiance. A localized bright mode is obtained by coherent combination of N degenerate flat-band modes, yielding an enhancement of coupling strength proportional to \(\sqrt{N}\), compared to systems without photonic flat bands. Remarkably, we observe flat-band-induced protection of the strong coupling against lattice-size scaling, an effect we term “coupling pinning”. Further enhancement is achieved by sandwiching the spin ensemble between two stacked Lieb layers, resulting in the hybridization of bright modes. Our results establish photonic flat bands as a promising and scalable platform for achieving and sustaining strong light–matter interactions, with potential for large-scale photonic integration and flat-band-enabled functionalities in hybrid systems.
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References
Lieb, E. H. Two theorems on the Hubbard model. Phys. Rev. Lett. 62, 1201–1204 (1989).
Mielke, A. Ferromagnetic ground states for the Hubbard model on line graphs. J. Phys. A Math. Gen. 24, L73 (1991).
Flach, S., Leykam, D., Bodyfelt, J. D., Matthies, P. & Desyatnikov, A. S. Detangling flat bands into Fano lattices. Europhys. Lett. 105, 30001 (2014).
Rhim, J.-W. & Yang, B.-J. Classification of flat bands according to the band-crossing singularity of Bloch wave functions. Phys. Rev. B 99, 045107 (2019).
Balents, L., Dean, C. R., Efetov, D. K. & Young, A. F. Superconductivity and strong correlations in moiré flat bands. Nat. Phys. 16, 725–733 (2020).
Yin, J.-X., Lian, B. & Hasan, M. Z. Topological kagome magnets and superconductors. Nature 612, 647–657 (2022).
Wilson, S. D. & Ortiz, B. R. AV3Sb5 kagome superconductors. Nat. Rev. Mater. 9, 420–432 (2024).
Checkelsky, J. G., Bernevig, B. A., Coleman, P., Si, Q. & Paschen, S. Flat bands, strange metals and the Kondo effect. Nat. Rev. Mater. 9, 509–526 (2024).
Lin, Z. et al. Flatbands and emergent ferromagnetic ordering in \({{{{\rm{Fe}}}}}_{3}{{{{\rm{Sn}}}}}_{2}\) kagome lattices. Phys. Rev. Lett. 121, 096401 (2018).
Sharpe, A. L. et al. Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene. Science 365, 605–608 (2019).
Yin, J.-X. et al. Negative flat band magnetism in a spin-orbit-coupled correlated kagome magnet. Nat. Phys. 15, 443–448 (2019).
Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018).
Cao, Y. et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556, 80–84 (2018).
Wakefield, J. P. et al. Three-dimensional flat bands in pyrochlore metal CaNi2. Nature 623, 301–306 (2023).
Leykam, D., Alexei, A. & Flach, S. Artificial flat band systems: from lattice models to experiments. Adv. Phys. X 3, 1473052 (2018).
Vicencio Poblete, R. A. Photonic flat band dynamics. Adv. Phys. X 6, 1878057 (2021).
Vicencio, R. A. et al. Observation of localized states in Lieb photonic lattices. Phys. Rev. Lett. 114, 245503 (2015).
Mukherjee, S. et al. Observation of a localized flat-band state in a photonic Lieb lattice. Phys. Rev. Lett. 114, 245504 (2015).
Xia, S. et al. Unconventional flatband line states in photonic Lieb lattices. Phys. Rev. Lett. 121, 263902 (2018).
Mukherjee, S., Di Liberto, M., Öhberg, P., Thomson, R. R. & Goldman, N. Experimental observation of Aharonov-Bohm cages in photonic lattices. Phys. Rev. Lett. 121, 075502 (2018).
Rakich, P. T. et al. Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal. Nat. Mater. 5, 93–96 (2006).
Settle, M. et al. Flatband slow light in photonic crystals featuring spatial pulse compression and terahertz bandwidth. Opt. Express 15, 219–226 (2007).
Li, J., White, T. P., O’Faolain, L., Gomez-Iglesias, A. & Krauss, T. F. Systematic design of flat band slow light in photonic crystal waveguides. Opt. Express 16, 6227–6232 (2008).
Mao, X.-R., Shao, Z.-K., Luan, H.-Y., Wang, S.-L. & Ma, R.-M. Magic-angle lasers in nanostructured moiré superlattice. Nat. Nanotechnol. 16, 1099–1105 (2021).
Luan, H.-Y., Ouyang, Y.-H., Zhao, Z.-W., Mao, W.-Z. & Ma, R.-M. Reconfigurable moiré nanolaser arrays with phase synchronization. Nature 624, 282–288 (2023).
Cui, J. et al. Ultracompact multibound-state-assisted flat-band lasers. Nat. Photonics 19, 643–649 (2025).
Yang, J. et al. Realization of all-band-flat photonic lattices. Nat. Commun. 15, 1484 (2024).
Ruggenthaler, M., Tancogne-Dejean, N., Flick, J., Appel, H. & Rubio, A. From a quantum-electrodynamical light-matter description to novel spectroscopies. Nat. Rev. Chem. 2, 0118 (2018).
Frisk Kockum, A., Miranowicz, A., De Liberato, S., Savasta, S. & Nori, F. Ultrastrong coupling between light and matter. Nat. Rev. Phys. 1, 19–40 (2019).
Gutzler, R., Garg, M., Ast, C. R., Kuhnke, K. & Kern, K. Light-matter interaction at atomic scales. Nat. Rev. Phys. 3, 441–453 (2021).
Fox, M. Quantum Optics: An Introduction (Oxford Academic, 2006).
Yang, Y. et al. Photonic flatband resonances for free-electron radiation. Nature 613, 42–47 (2023).
Wang, Y.-T. et al. Moiré cavity quantum electrodynamics. Sci. Adv. 11, eadv8115 (2025).
Yan, S. et al. Cavity quantum electrodynamics with moiré photonic crystal nanocavity. Nat. Commun. 16, 4634 (2025).
Dovzhenko, D. S., Ryabchuk, S. V., Rakovich, Y. P. & Nabiev, I. R. Light-matter interaction in the strong coupling regime: configurations, conditions, and applications. Nanoscale 10, 3589–3605 (2018).
Flick, J., Rivera, N. & Narang, P. Strong light-matter coupling in quantum chemistry and quantum photonics. Nanophotonics 7, 1479–1501 (2018).
Liu, X. et al. Strong light-matter coupling in two-dimensional atomic crystals. Nat. Photonics 9, 30–34 (2015).
Samak, M. M. & Bilal, O. R. Direct observation of all-flat bands phononic metamaterials. Phys. Rev. Lett. 133, 266101 (2024).
Song, L. et al. Topological flatband loop states in fractal-like photonic lattices. Laser Photonics Rev. 17, 2200315 (2023).
Baboux, F. et al. Bosonic condensation and disorder-induced localization in a flat band. Phys. Rev. Lett. 116, 066402 (2016).
Real, B. et al. Flat-band light dynamics in stub photonic lattices. Sci. Rep. 7, 15085 (2017).
Chisnell, R. et al. Topological magnon bands in a kagome lattice ferromagnet. Phys. Rev. Lett. 115, 147201 (2015).
Schnack, J., Schulenburg, J., Honecker, A. & Richter, J. Magnon crystallization in the kagome lattice antiferromagnet. Phys. Rev. Lett. 125, 117207 (2020).
Cheng, C. et al. Magnon flatband effect in antiferromagnetically coupled magnonic crystals. Appl. Phys. Lett. 122, 082401 (2023).
Tacchi, S. et al. Experimental observation of flat bands in one-dimensional chiral magnonic crystals. Nano Lett. 23, 6776–6783 (2023).
Riberolles, S. X. M. et al. Chiral and flat-band magnetic quasiparticles in ferromagnetic and metallic kagome layers. Nat. Commun. 15, 1592 (2024).
Rojas-Rojas, S., Morales-Inostroza, L., Vicencio, R. A. & Delgado, A. Quantum localized states in photonic flat-band lattices. Phys. Rev. A 96, 043803 (2017).
Slot, M. R. et al. Experimental realization and characterization of an electronic Lieb lattice. Nat. Phys. 13, 672–676 (2017).
Drost, R., Ojanen, T., Harju, A. & Liljeroth, P. Topological states in engineered atomic lattices. Nat. Phys. 13, 668–671 (2017).
Zhang, D. et al. Cavity quantum electrodynamics with ferromagnetic magnons in a small yttrium-iron-garnet sphere. npj Quantum Inf. 1, 15014 (2015).
Zare Rameshti, B. et al. Cavity magnonics. Phys. Rep. 979, 1–61 (2022).
Yu, T., Zou, J., Zeng, B., Rao, J. & Xia, K. Non-Hermitian topological magnonics. Phys. Rep. 1062, 1–86 (2024).
Goryachev, M. et al. High-cooperativity cavity QED with magnons at microwave frequencies. Phys. Rev. Appl. 2, 054002 (2014).
Tabuchi, Y. et al. Coherent coupling between a ferromagnetic magnon and a superconducting qubit. Science 349, 405–408 (2015).
Bai, L. et al. Spin pumping in electrodynamically coupled magnon-photon systems. Phys. Rev. Lett. 114, 227201 (2015).
Bhoi, B., Kim, B., Kim, J., Cho, Y.-J. & Kim, S.-K. Robust magnon-photon coupling in a planar-geometry hybrid of inverted split-ring resonator and YIG film. Sci. Rep. 7, 11930 (2017).
Hou, J. T. & Liu, L. Strong coupling between microwave photons and nanomagnet magnons. Phys. Rev. Lett. 123, 107702 (2019).
Lachance-Quirion, D. et al. Entanglement-based single-shot detection of a single magnon with a superconducting qubit. Science 367, 425–428 (2020).
Wang, Z.-Q. et al. Giant spin ensembles in waveguide magnonics. Nat. Commun. 13, 7580 (2022).
Rao, Z. et al. Braiding reflectionless states in non-Hermitian magnonics. Nat. Phys. 20, 1904–1911 (2024).
Wang, Y.-P. et al. Bistability of cavity magnon polaritons. Phys. Rev. Lett. 120, 057202 (2018).
Wang, Y.-P. et al. Nonreciprocity and unidirectional invisibility in cavity magnonics. Phys. Rev. Lett. 123, 127202 (2019).
Shen, R.-C., Li, J., Fan, Z.-Y., Wang, Y.-P. & You, J. Mechanical bistability in Kerr-modified cavity magnomechanics. Phys. Rev. Lett. 129, 123601 (2022).
Xu, D. et al. Quantum control of a single magnon in a macroscopic spin system. Phys. Rev. Lett. 130, 193603 (2023).
Wang, C. et al. Enhancement of magnonic frequency combs by exceptional points. Nat. Phys. 20, 1139–1144 (2024).
Xiong, Y. et al. Magnon-photon coupling in an opto-electro-magnonic oscillator. npj Spintron. 2, 9 (2024).
Li, W. et al. Topological surface magnon-polariton in an insulating canted antiferromagnet https://arxiv.org/abs/2510.08334 (2025).
Chen, P. J., Iunin, Y. L., Cheng, S. F. & Shull, R. D. Underlayer effect on perpendicular magnetic anisotropy in Co20Fe60B20/MgO films. IEEE Trans. Magn. 52, 1–4 (2016).
Shen, R.-C. et al. Long-time memory and ternary logic gate using a multistable cavity magnonic system. Phys. Rev. Lett. 127, 183202 (2021).
Zhang, D., Luo, X.-Q., Wang, Y.-P., Li, T.-F. & You, J. Q. Observation of the exceptional point in cavity magnon-polaritons. Nat. Commun. 8, 1368 (2017).
Qian, J., Li, J., Zhu, S.-Y., You, J. & Wang, Y.-P. Probing PT-symmetry breaking of non-Hermitian topological photonic states via strong photon-magnon coupling. Phys. Rev. Lett. 132, 156901 (2024).
Huebl, H. et al. High cooperativity in coupled microwave resonator ferrimagnetic insulator hybrids. Phys. Rev. Lett. 111, 127003 (2013).
Tabuchi, Y. et al. Hybridizing ferromagnetic magnons and microwave photons in the quantum limit. Phys. Rev. Lett. 113, 083603 (2014).
Zhang, X., Zou, C.-L., Jiang, L. & Tang, H. X. Strongly coupled magnons and cavity microwave photons. Phys. Rev. Lett. 113, 156401 (2014).
Zhang, X. et al. Magnon dark modes and gradient memory. Nat. Commun. 6, 8914 (2015).
Dicke, R. H. Coherence in spontaneous radiation processes. Phys. Rev. 93, 99–110 (1954).
Tavis, M. & Cummings, F. W. Exact solution for an N-molecule-radiation-field Hamiltonian. Phys. Rev. 170, 379–384 (1968).
Borjans, F., Croot, X. G., Mi, X., Gullans, M. J. & Petta, J. R. Resonant microwave-mediated interactions between distant electron spins. Nature 577, 195–198 (2020).
Lin, R., Tai, T., Li, L. & Lee, C. H. Topological non-hermitian skin effect. Front. Phys. 18, 53605 (2023).
El-Ganainy, R. et al. Non-hermitian physics and PT symmetry. Nat. Phys. 14, 11–19 (2018).
Li, A. et al. Exceptional points and non-hermitian photonics at the nanoscale. Nat. Nanotechnol. 18, 706–720 (2023).
Nakata, Y., Okada, T., Nakanishi, T. & Kitano, M. Observation of flat band for terahertz spoof plasmons in a metallic kagomé lattice. Phys. Rev. B 85, 205128 (2012).
Yamaguchi, K., Nakajima, M. & Suemoto, T. Coherent control of spin precession motion with impulsive magnetic fields of half-cycle terahertz radiation. Phys. Rev. Lett. 105, 237201 (2010).
Seifert, T. S. et al. Femtosecond formation dynamics of the spin Seebeck effect revealed by terahertz spectroscopy. Nat. Commun. 9, 2899 (2018).
Ye, Z. et al. Excitation-polarization-dependent dynamics of polariton condensates in the ZnO microwire at room temperature. J. Phys. Condens. Matter 34, 22LT01 (2022).
Acknowledgements
This work was supported by the National Key Research and Development Program of China (Nos. 2022YFA1405200 and 2023YFA1406703 to Y.P.W.; No. 2022YFA1404900 to Y.H.Y.), the Zhejiang Provincial Natural Science Foundation of China (No. LR26A040001 to Y.P.W.), the National Natural Science Foundation of China (No. 92265202 to Y.P.W.), and the Fundamental Research Funds for the Central Universities (No. 2024FZZX02-01-02 to Y.P.W.).
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Y.P.W. and Q.H. conceived the idea and initiated the research project. Q.H. designed the samples and performed the experiments with input from Y.P.W. and Y.H.Y. Q.H. carried out the data analysis under the discussion with Y.P.W. and Y.H.Y. Q.H., Y.P.W., and Y.H.Y. drafted the manuscript. J.Q. and F.J.C. were involved in the discussion of results and the final manuscript editing. Y.P.W. supervised the project.
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Hong, Q., Qian, J., Chen, F. et al. Strong magnon–photon coupling enhanced by photonic lattice flat-bands. Nat Commun (2026). https://doi.org/10.1038/s41467-026-69326-y
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DOI: https://doi.org/10.1038/s41467-026-69326-y
