Xiao, D., Chang, M.-C. & Niu, Q. Berry section results on digital properties. Rev. Mod. Phys. 82, 1959 (2010).
Nagaosa, N. & Tokura, Y. Emergent electromagnetism in solids. Phys. Scr. T146, 014020 (2012).
El-Ganainy, R. et al. Non-hermitian physics and PT symmetry. Nat. Phys. 14, 11–19 (2018).
Yu, T., Zou, J., Zeng, B., Rao, J. & Xia, Ok. Non-hermitian topological magnonics. Phys. Rep. 1062, 1–86 (2024).
Ladd, T. D. et al. Quantum computer systems. Nature 464, 45–53 (2010).
Yuan, H., Cao, Y., Kamra, A., Duine, R. A. & Yan, P. Quantum magnonics: when magnon spintronics meets quantum data science. Phys. Rep. 965, 1–74 (2022).
Kittel, C. On the idea of ferromagnetic resonance absorption. Phys. Rev. 73, 155 (1948).
Keffer, F. & Kittel, C. Principle of antiferrornagnetic resonance. Phys. Rev. 85, 329 (1952).
Chumak, A. V., Vasyuchka, V. I., Serga, A. A. & Hillebrands, B. Magnon spintronics. Nat. Phys. 11, 453–461 (2015).
Duine, R. A., Lee, Ok.-J., Parkin, S. S. P. & Stiles, M. D. Artificial antiferromagnetic spintronics. Nat. Phys. 14, 217–219 (2018).
Pirro, P., Vasyuchka, V. I., Serga, A. A. & Hillebrands, B. Advances in coherent magnonics. Nat. Rev. Mater. 6, 1114–1135 (2021).
Yang, S.-H., Naaman, R., Paltiel, Y. & Parkin, S. S. P. Chiral spintronics. Nat. Rev. Phys. 3, 328–343 (2021).
Han, J., Cheng, R., Liu, L., Ohno, H. & Fukami, S. Coherent antiferromagnetic spintronics. Nat. Mater. 22, 684–695 (2023).
Zhang, Y. et al. Switchable long-distance propagation of chiral magnonic edge states. Nat. Mater. 24, 69–75 (2025).
Liu, C. et al. Correlated spin-wave technology and domain-wall oscillation in a topologically textured magnetic movie. Nat. Mater. 24, 406–413 (2025).
Grünberg, P. Magnetostatic spinwave modes of a ferromagnetic double layer. J. Appl. Phys. 51, 4338–4341 (1980).
Grünberg, P. Magnetostatic spin-wave modes of a heterogeneous ferromagnetic double layer. J. Appl. Phys. 52, 6824–6829 (1981).
Grünberg, P., Schreiber, R. & Pang, Y. Layered magnetic constructions: proof for antiferromagnetic coupling of Fe layers throughout Cr interlayers. Phys. Rev. Lett. 57, 2442 (1986).
Krebs, J. J., Lubitz, P., Chaiken, A. & Prinz, G. A. Magnetic resonance deterination of the antiferromagnetic coupling of Fe layers by means of Cr. Phys. Rev. Lett. 63, 1645 (1989).
Heinrich, B. et al. Dynamic alternate coupling in magnetic bilayers. Phys. Rev. Lett. 90, 187601 (2003).
Klingler, S. et al. Spin-torque excitation of perpendicular standing spin waves in coupled YIG/Co heterostructures. Phys. Rev. Lett. 120, 127201 (2018).
Chen, J. et al. Sturdy interlayer magnon–magnon coupling in magnetic metal-insulator hybrid nanostructures. Phys. Rev. Lett. 120, 217202 (2018).
MacNeill, D. et al. Gigahertz frequency antiferromagnetic resonance and powerful magnon–magnon coupling within the layered crystal CrCl3. Phys. Rev. Lett. 123, 047204 (2019).
Barman, A. et al. The 2021 magnonics roadmap. J. Phys. Condens. Matter 33, 413001 (2021).
Liu, H. et al. Remark of outstanding factors in magnonic parity-time symmetry units. Sci. Adv. 5, eaax9144 (2019).
Hu, B., Xie, Z.-Ok., Lu, J. & He, W. Exploring wavefunction hybridization of magnon–magnon hybrid state. Preprint at https://arxiv.org/abs/2308.14463 (2023).
Wang, Y. et al. Ultrastrong to just about deep-strong magnon–magnon coupling with a excessive diploma of freedom in artificial antiferromagnets. Nat. Commun. 15, 2077 (2024).
Zhang, X., Zou, C.-L., Jiang, L. & Tang, H. X. Strongly coupled magnons and cavity microwave photons. Phys. Rev. Lett. 113, 156401 (2014).
Tabuchi, Y. et al. Coherent coupling between a ferromagnetic magnon and a superconducting qubit. Science 349, 405–408 (2015).
Lachance-Quirion, D. et al. Entanglement-based single-shot detection of a single magnon with a superconducting qubit. Science 367, 425–428 (2020).
Daniels, M. W., Cheng, R., Yu, W., Xiao, J. & Xiao, D. Nonabelian magnonics in antiferromagnets. Phys. Rev. B 98, 134450 (2018).
Wimmer, T. et al. Remark of antiferromagnetic magnon pseudospin dynamics and the Hanle impact. Phys. Rev. Lett. 125, 247204 (2020).
Kamra, A., Wimmer, T., Huebl, H. & Althammer, M. Antiferromagnetic magnon pseudospin: dynamics and diffusive transport. Phys. Rev. B 102, 174445 (2020).
Ishibashi, M. et al. Switchable large nonreciprocal frequency shift of propagating spin waves in artificial antiferromagnets. Sci. Adv. 6, eaaz6931 (2020).
Hu, B., Xie, Z.-Ok., Lu, J. & He, W. Mapping the magnon–magnon hybrid state onto the Bloch sphere. Appl. Phys. Lett. 124, 232402 (2024).
Acremann, Y. et al. Imaging precessional movement of the magnetization vector. Science 290, 492–495 (2000).
Enviornment, D. A., Vescovo, E., Kao, C.-C., Guan, Y. & Bailey, W. E. Weakly coupled movement of particular person layers in ferromagnetic resonance. Phys. Rev. B 74, 064409 (2006).
van der Laan, G. Time-resolved X-ray detected ferromagnetic resonance of spin currents. J. Electron Spectrosc. Relat. Phenom. 220, 137–146 (2017).
Donnelly, C. et al. Time-resolved imaging of three-dimensional nanoscale magnetization dynamics. Nat. Nanotechnol. 15, 356–360 (2020).
Girardi, D. et al. Three-dimensional spin-wave dynamics, localization and interference in an artificial antiferromagnet. Nat. Commun. 15, 3057 (2024).
Wintz, S. et al. Magnetic vortex cores as tunable spin-wave emitters. Nat. Nanotechnol. 11, 948–953 (2016).
Donnelly, C. et al. Tomographic reconstruction of a three-dimensional magnetization vector area. New J. Phys. 20, 083009 (2018).
Donnelly, C. et al. Complicated free-space magnetic area textures induced by three-dimensional magnetic nanostructures. Nat. Nanotechnol. 17, 136–142 (2022).
Rana, A. et al. Three-dimensional topological magnetic monopoles and their interactions in a ferromagnetic meta-lattice. Nat. Nanotechnol. 18, 227–232 (2023).
Neethirajan, J. et al. Gentle X-ray section nanomicroscopy of micrometer-thick magnets. Phys. Rev. X 14, 031028 (2024).
Burn, D. M. et al. Depth-resolved magnetization dynamics revealed by X-ray reflectometry ferromagnetic resonance. Phys. Rev. Lett. 125, 137201 (2020).
Mazzoli, C. et al. Disentangling multipole resonances by means of a full X-ray polarization evaluation. Phys. Rev. B 76, 195118 (2007).
Zhang, S. L., van der Laan, G. & Hesjedal, T. Direct experimental willpower of the topological winding variety of skyrmions in Cu2OSeO3. Nat. Commun. 8, 14619 (2017).
Zhang, S., van der Laan, G., Wang, W., Haghighirad, A. & Hesjedal, T. Direct remark of twisted floor skyrmions in bulk crystals. Phys. Rev. Lett. 120, 227202 (2018).
Guang, Y. et al. Superposition of emergent monopole and antimonopole in CoTb skinny movies. Phys. Rev. Lett. 127, 217201 (2021).
Li, M., Lu, J. & He, W. Symmetry breaking induced magnon–magnon coupling in artificial antiferromagnets. Phys. Rev. B 103, 064429 (2021).
Vogel, Ok. & Risken, H. Willpower of quasiprobability distributions when it comes to chance distributions for the rotated quadrature section. Phys. Rev. A 40, 2847 (1989).
Yi, C.-R. et al. Extracting the quantum geometric tensor of an optical raman lattice by bloch-state tomography. Phys. Rev. Res. 5, L032016 (2023).
Sharma, S., Viola Kusminskiy, S. & Bittencourt, V. A. S. V. Quantum tomography of magnons utilizing brillouin mild scattering. Phys. Rev. B 110, 014416 (2024).
Shiota, Y., Taniguchi, T., Ishibashi, M., Moriyama, T. & Ono, T. Tunable magnon–magnon coupling mediated by dynamic dipolar interplay in artificial antiferromagnets. Phys. Rev. Lett. 125, 017203 (2020).
Sud, A. et al. Tunable magnon–magnon coupling in artificial antiferromagnets. Phys. Rev. B 102, 100403 (2020).
Comstock, A. H. et al. Hybrid magnonics in hybrid perovskite antiferromagnets. Nat. Commun. 14, 1834 (2023).
Jin, H. Uncooked information for the article: resolving the magnon eigenfunctions by X-ray magnetic vector chronoscopy. Zenodo https://doi.org/10.5281/zenodo.18028719 (2025).
