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Advances in coherent magnonics

Abstract

Magnonics addresses the dynamic excitations of a magnetically ordered material. These excitations, referred to as spin waves and their quanta, magnons, are a powerful tool for information transport and processing on the microscale and nanoscale. The physics of spin waves is very rich, ranging from a coexistence between dipole–dipole interaction and symmetric and antisymmetric exchange interaction, to various types of interface effects, anisotropies and spin torques. Spin waves are easily driven into the nonlinear regime. They can be confined and guided, and they can be amplified. Spin waves may be generated with varying degrees of coherency, depending on the excitation method, and transport mechanisms range from diffusive to ballistic. In this Review, we address specifically coherent spin waves. Coherency enables, for instance, the design of interference-based, wave processing spin-wave devices. Thus, the field of magnonics is well suited for the implementation of wave-based computing devices, combining the excellent versatility, smallness, nonlinearity and external control it affords. Novel coherent states of matter, such as magnon Bose–Einstein condensates, enable a broad range of additional applications.

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Fig. 1: SW band structures in YIG thin films and magnonic crystals.
Fig. 2: SW optics.
Fig. 3: Guided SW bullet.
Fig. 4: Magnon-based signal processing and computing.
Fig. 5: Quantum magnonics.
Fig. 6: Magnon BECs and supercurrents.

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References

  1. Kruglyak, V. V., Demokritov, S. O. & Grundler, D. Magnonics. J. Phys. D Appl. Phys. 43, 264001 (2010).

    Article  Google Scholar 

  2. Serga, A. A., Chumak, A. V. & Hillebrands, B. YIG magnonics. J. Phys. D Appl. Phys 43, 264002 (2010).

    Article  Google Scholar 

  3. Chumak, A. V., Vasyuchka, V. I., Serga, A. A. & Hillebrands, B. Magnon spintronics. Nat. Phys. 11, 453–461 (2015).

    Article  CAS  Google Scholar 

  4. Khitun, A., Bao, M. & Wang, K. L. Magnonic logic circuits. J. Phys. D Appl. Phys. 43, 264005 (2010).

    Article  Google Scholar 

  5. Han, W., Maekawa, S. & Xie, X.-C. Spin current as a probe of quantum materials. Nat. Mater. 19, 139–152 (2020).

    Article  CAS  Google Scholar 

  6. Sander, D. et al. The 2017 magnetism roadmap. J. Phys. D Appl. Phys. 50, 363001 (2017).

    Article  Google Scholar 

  7. Gurevich, A. G. & Melkov, G. A. Magnetization Oscillations and Waves (CRC, 1996).

  8. Kreil, A. J. E. et al. Tunable space-time crystal in room-temperature magnetodielectrics. Phys. Rev. B 100, 020406 (2019).

    Article  CAS  Google Scholar 

  9. Haidar, M. et al. A single layer spin-orbit torque nano-oscillator. Nat. Commun. 10, 2362 (2019).

    Article  Google Scholar 

  10. Collet, M. et al. Generation of coherent spin-wave modes in yttrium iron garnet microdiscs by spin–orbit torque. Nat. Commun. 7, 10377 (2016).

    Article  CAS  Google Scholar 

  11. Nowik-Boltyk, P., Dzyapko, O., Demidov, V. E., Berloff, N. G. & Demokritov, S. O. Spatially non-uniform ground state and quantized vortices in a two-component Bose-Einstein condensate of magnons. Sci. Rep. 2, 482 (2012).

    Article  CAS  Google Scholar 

  12. Bozhko, D. A. et al. Bogoliubov waves and distant transport of magnon condensate at room temperature. Nat. Commun. 10, 2460 (2019).

    Article  Google Scholar 

  13. Pirro, P. et al. Interference of coherent spin waves in micron-sized ferromagnetic waveguides. Phys. Stat. Sol. 248, 2404–2408 (2011).

    Article  CAS  Google Scholar 

  14. Csaba, G., Papp, Á. & Porod, W. Perspectives of using spin waves for computing and signal processing. Phys. Lett. A 381, 1471–1476 (2017).

    Article  CAS  Google Scholar 

  15. Mahmoud, A. et al. Introduction to spin wave computing. J. Appl. Phys. 128, 161101 (2020).

    Article  CAS  Google Scholar 

  16. Li, Y. et al. Hybrid magnonics: physics, circuits, and applications for coherent information processing. J. Appl. Phys. 128, 130902 (2020).

    Article  CAS  Google Scholar 

  17. Skarsvåg, H., Holmqvist, C. & Brataas, A. Spin superfluidity and long-range transport in thin-film ferromagnets. Phys. Rev. Lett. 115, 237201 (2015).

    Article  Google Scholar 

  18. Bauer, G. E. W., Saitoh, E. & van Wees, B. J. Spin caloritronics. Nat. Mater. 11, 391–399 (2012).

    Article  CAS  Google Scholar 

  19. Cornelissen, L. J., Liu, J., Duine, R. A., Youssef, J. B. & van Wees, B. J. Long-distance transport of magnon spin information in a magnetic insulator at room temperature. Nat. Phys. 11, 1022–1026 (2015).

    Article  CAS  Google Scholar 

  20. Lenk, B., Ulrichs, H., Garbs, F. & Münzenberg, M. The building blocks of magnonics. Phys. Rep. 507, 107–136 (2011).

    Article  Google Scholar 

  21. Chumak, A. V., Serga, A. A. & Hillebrands, B. Magnon transistor for all-magnon data processing. Nat. Commun. 5, 4700 (2014).

    Article  CAS  Google Scholar 

  22. Sulymenko, O. R., Prokopenko, O. V., Tyberkevych, V. S., Slavin, A. N. & Serga, A. A. Bullets and droplets: two-dimensional spin-wave solitons in modern magnonics. Low Temp. Phys. 44, 602–617 (2018).

    Article  CAS  Google Scholar 

  23. Shindou, R., Matsumoto, R., Murakami, S. & Ohe, J. Topological chiral magnonic edge mode in a magnonic crystal. Phys. Rev. B 87, 174427 (2013).

    Article  Google Scholar 

  24. Chumak, A. V. et al. All-linear time reversal by a dynamic artificial crystal. Nat. Commun. 1, 141 (2010).

    Article  Google Scholar 

  25. Wang, Q. et al. Spin pinning and spin-wave dispersion in nanoscopic ferromagnetic waveguides. Phys. Rev. Lett. 122, 247202 (2019).

    Article  CAS  Google Scholar 

  26. Tabuchi, Y. et al. Coherent coupling between a ferromagnetic magnon and a superconducting qubit. Science 349, 405–408 (2015).

    Article  CAS  Google Scholar 

  27. Longhi, S. Quantum-optical analogies using photonic structures. Laser Photonics Rev. 3, 243–261 (2009).

    Article  CAS  Google Scholar 

  28. Demokritov, S. O. et al. Bose–Einstein condensation of quasi-equilibrium magnons at room temperature under pumping. Nature 443, 430–433 (2006).

    Article  CAS  Google Scholar 

  29. Safranski, C. et al. Spin caloritronic nano-oscillator. Nat. Commun. 8, 117 (2017).

    Article  CAS  Google Scholar 

  30. Bozhko, D. A. et al. Supercurrent in a room-temperature Bose–Einstein magnon condensate. Nat. Phys. 12, 1057–1062 (2016).

    Article  CAS  Google Scholar 

  31. Nakata, K., Simon, P. & Loss, D. Magnon transport through microwave pumping. Phys. Rev. B 92, 014422 (2015).

    Article  Google Scholar 

  32. Sonin, E. B. Spin currents and spin superfluidity. Adv. Phys. 59, 181–255 (2010).

    Article  Google Scholar 

  33. Flebus, B., Bender, S. A., Tserkovnyak, Y. & Duine, R. A. Two-fluid theory for spin superfluidity in magnetic insulators. Phys. Rev. Lett. 116, 117201 (2016).

    Article  CAS  Google Scholar 

  34. Harris, V. G. Modern microwave ferrites. IEEE Trans. Magn. 48, 1075–1104 (2012).

    Article  CAS  Google Scholar 

  35. Cherepanov, V., Kolokolov, I. & L’vov, V. The saga of YIG: spectra, thermodynamics, interaction and relaxation ofmagnons in a complex magnet. Phys. Rep. 229, 81–144 (1993).

    Article  CAS  Google Scholar 

  36. Hirohata, A. et al. Roadmap for emerging materials for spintronic device applications. IEEE Trans. Magn. 51, 0800511 (2015).

    Article  Google Scholar 

  37. Manna, K., Sun, Y., Muechler, L., Kübler, J. & Felser, C. Heusler, Weyl and Berry. Nat. Rev. Mater. 3, 244–256 (2018).

    Article  CAS  Google Scholar 

  38. Mihalceanu, L. et al. Temperature dependent relaxation of dipolar-exchange magnons in yttrium iron garnet films. Phys. Rev. B 97, 214405 (2018).

    Article  CAS  Google Scholar 

  39. Guillemard, C. et al. Ultralow magnetic damping in Co2Mn-based Heusler compounds: promising materials for spintronics. Phys. Rev. Appl. 11, 064009 (2019).

    Article  CAS  Google Scholar 

  40. Stancil, D. D. & Prabhakar, A., Spin Waves: Theory and Applications (Springer, 2009).

  41. Chumak, A. V., Neumann, T., Serga, A. A., Hillebrands, B. & Kostylev, M. P. A current-controlled, dynamic magnonic crystal. J. Phys. D Appl. Phys. 42, 205005 (2009).

    Article  Google Scholar 

  42. Kostylev, M. P. Non-reciprocity of dipole-exchange spin waves in thin ferromagnetic films. J. Appl. Phys. 113, 053907 (2013).

    Article  Google Scholar 

  43. Mohseni, M. et al. Backscattering immunity of dipole-exchange magnetostatic surface spin waves. Phys. Rev. Lett. 122, 197201 (2019).

    Article  CAS  Google Scholar 

  44. Gladii, O., Haidar, M., Henry, Y., Kostylev, M. & Bailleul, M. Frequency nonreciprocity of surface spin wave in permalloy thin films. Phys. Rev. B 93, 054430 (2016).

    Article  Google Scholar 

  45. Nembach, H. T., Silva, T. J., Shaw, J. M., Weiler, M. & Jué, E. Linear relation between Heisenberg exchange and interfacial Dzyaloshinskii-Moriya interaction in metal films. Nat. Phys. 11, 825–829 (2015).

    Article  CAS  Google Scholar 

  46. Zakeri, K. et al. Asymmetric spin-wave dispersion on Fe(110): direct evidence of the Dzyaloshinskii-Moriya interaction. Phys. Rev. Lett. 104, 137203 (2010).

    Article  Google Scholar 

  47. Wang, H. et al. Chiral spin-wave velocities induced by all-garnet interfacial Dzyaloshinskii-Moriya interaction in ultrathin yttrium iron garnet films. Phys. Rev. Lett. 124, 027203 (2020).

    Article  CAS  Google Scholar 

  48. Seki, S. et al. Propagation dynamics of spin excitations along skyrmion strings. Nat. Commun. 11, 256 (2020).

    Article  CAS  Google Scholar 

  49. Seki, S. et al. Magnetochiral nonreciprocity of volume spin wave propagation in chiral-lattice ferromagnets. Phys. Rev. B 93, 235131 (2016).

    Article  Google Scholar 

  50. Gubbiotti, G. (ed.) Three-Dimensional Magnonics: Layered, Micro- and Nanostructures (Jenny Stanford Publishing, 2019).

  51. Chumak, A. V. et al. Spin-wave propagation in a microstructured magnonic crystal. Appl. Phys. Lett. 95, 262508 (2009).

    Article  Google Scholar 

  52. Obry, B. et al. A micro-structured ion-implanted magnonic crystal. Appl. Phys. Lett. 102, 202403 (2013).

    Article  Google Scholar 

  53. Troncoso, R. E., Ulloa, C., Pesce, F. & Nunez, A. S. Antiferromagnetic magnonic crystals. Phys. Rev. B 92, 224424 (2015).

    Article  Google Scholar 

  54. Ustinov, A. B. et al. Dynamic electromagnonic crystal based on artificial multiferroic heterostructure. Comm. Phys. 2, 137 (2019).

    Article  Google Scholar 

  55. Chumak, A. V., Serga, A. A. & Hillebrands, B. Magnonic crystals for data processing. J. Phys. D Appl. Phys. 50, 244001 (2017).

    Article  Google Scholar 

  56. Nikitov, S. A., Tailhades, P. & Tsai, C. S. Spin waves in periodic magnetic structures — magnonic crystals. J. Magn. Magn. Mater. 236, 320–330 (2001).

    Article  CAS  Google Scholar 

  57. Vogel, M. et al. Optically reconfigurable magnetic materials. Nat. Phys. 11, 487–491 (2015).

    Article  CAS  Google Scholar 

  58. Krawczyk, M. & Grundler, D. Review and prospects of magnonic crystals and devices with reprogrammable band structure. J. Phys. Condens. Matter 26, 123202 (2014).

    Article  CAS  Google Scholar 

  59. Ordóñez-Romero, C. L. et al. Mapping of spin wave propagation in a one-dimensional magnonic crystal. J. Appl. Phys. 120, 043901 (2016).

    Article  Google Scholar 

  60. Kłos, J. W., Kumar, D., Krawczyk, M. & Barman, A. Magnonic band engineering by intrinsic and extrinsic mirror symmetry breaking in antidot spin-wave waveguides. Sci. Rep. 3, 2444 (2013).

    Article  Google Scholar 

  61. Kruglyak, V. V. et al. Formation of the band spectrum of spin waves in 1D magnonic crystals with different types of interfacial boundary conditions. J. Phys. D Appl. Phys. 50, 094003 (2017).

    Article  Google Scholar 

  62. Chumak, A. V., Serga, A. A., Wolff, S., Hillebrands, B. & Kostylev, M. P. Scattering of surface and volume spin waves in a magnonic crystal. Appl. Phys. Lett. 94, 172511 (2009).

    Article  Google Scholar 

  63. Mruczkiewicz, M. et al. Nonreciprocity of spin waves in metallized magnonic crystal. New J. Phys. 15, 113023 (2013).

    Article  Google Scholar 

  64. Mruczkiewicz, M. et al. Observation of magnonic band gaps in magnonic crystals with nopnreciprocal dispersion relation. Phys. Rev. B 90, 174416 (2014).

    Article  Google Scholar 

  65. Gallardo, R. A. et al. Flat bands, indirect gaps, and unconventional spin-wave behavior induced by a periodic Dzyaloshinskii-Moriya interaction. Phys. Rev. Lett. 122, 067204 (2019).

    Article  CAS  Google Scholar 

  66. Rychły, J. et al. Magnonic crystals — Prospective structures for shaping spin waves in nanoscale. Low Temp. Phys. 41, 745–759 (2015).

    Article  Google Scholar 

  67. Kakazei, G. N., Liu, X. M., Ding, J. & Adeyeye, A. O. Ni80Fe20 film with periodically modulated thickness as a reconfigurable one-dimensional magnonic crystal. Appl. Phys. Lett. 104, 042403 (2014).

    Article  Google Scholar 

  68. Kakazei, G. N. et al. Large four-fold magnetic anisotropy in two-dimensional modulated Ni80Fe20 films. Appl. Phys. Lett. 107, 232402 (2015).

    Article  Google Scholar 

  69. Karenowska, A. et al. Oscillatory energy exchange between waves coupled by a dynamic artificial crystal. Phys. Rev. Lett. 108, 015505 (2012).

    Article  CAS  Google Scholar 

  70. Chumak, A. V., Dhagat, P., Jander, A., Serga, A. A. & Hillebrands, B. Reverse Doppler effect of magnons with negative group velocity scattered from a moving Bragg grating. Phys. Rev. B 81, 140404 (2010).

    Article  Google Scholar 

  71. Kryshtal, R. G. & Medved, A. V. Nonlinear spin waves in dynamic magnonic crystals created by surface acoustic waves in yttrium iron garnet films. J. Phys. D Appl. Phys. 50, 495004 (2017).

    Article  Google Scholar 

  72. Dobrovolskiy, O. V. et al. Magnon–fluxon interaction in a ferromagnet/superconductor heterostructure. Nat. Phys. 15, 477–482 (2019).

    Article  CAS  Google Scholar 

  73. Frey, P. et al. Reflection-less width-modulated magnonic crystal. Commun. Phys. 3, 17 (2020).

    Article  Google Scholar 

  74. Inoue, M. et al. Investigating the use of magnonic crystals as extremely sensitive magnetic field sensors at room temperature. Appl. Phys. Lett. 98, 132511 (2011).

    Article  Google Scholar 

  75. Metaxas, P. J. et al. Sensing magnetic nanoparticles using nano-confined ferromagnetic resonances in a magnonic crystal. Appl. Phys. Lett. 106, 232406 (2015).

    Article  Google Scholar 

  76. Chumak, A. V. et al. Storage-recovery phenomenon in magnonic crystal. Phys. Rev. Lett. 108, 257207 (2012).

    Article  CAS  Google Scholar 

  77. Ding, J., Kostylev, M. & Adeyeye, A. O. Realization of a mesoscopic reprogrammable magnetic logic based on a nanoscale reconfigurable magnonic crystal. Appl. Phys. Lett. 100, 073114 (2012).

    Article  Google Scholar 

  78. Nikitin, A. A. et al. A spin-wave logic gate based on a width-modulated dynamic magnonic crystal. Appl. Phys. Lett. 106, 102405 (2015).

    Article  Google Scholar 

  79. Li, Y. et al. Nutation spectroscopy of a nanomagnet driven into deeply nonlinear ferromagnetic resonance. Phys. Rev. X 9, 041036 (2019).

    CAS  Google Scholar 

  80. Heyroth, F. et al. Monocrystalline freestanding three-dimensional yttrium-iron-garnet magnon nanoresonators. Phys. Rev. Appl. 12, 054031 (2019).

    Article  CAS  Google Scholar 

  81. Zingsem, B. W. et al. Biologically encoded magnonics. Nat. Commun. 10, 4345 (2019).

    Article  Google Scholar 

  82. Haldar, A., Kumar, D. & Adeyeye, A. O. A reconfigurable waveguide for energy-efficient transmission and local manipulation of information in a nanomagnetic device. Nat. Nanotechnol. 11, 437–443 (2016).

    Article  CAS  Google Scholar 

  83. Pirro, P. et al. Spin-wave excitation and propagation in microstructured waveguides of yttrium iron garnet/Pt bilayers. Appl. Phys. Lett. 104, 012402 (2014).

    Article  Google Scholar 

  84. Collet, M. et al. Spin-wave propagation in ultra-thin YIG based waveguides. Appl. Phys. Lett. 110, 092408 (2017).

    Article  Google Scholar 

  85. Evelt, M. et al. High-efficiency control of spin-wave propagation in ultra-thin yttrium iron garnet by the spin-orbit torque. Appl. Phys. Lett. 108, 172406 (2016).

    Article  Google Scholar 

  86. Klingler, S. et al. Design of a spin-wave majority gate employing mode selection. Appl. Phys. Lett. 105, 152410 (2014).

    Article  Google Scholar 

  87. Klingler, S. et al. Spin-wave logic devices based on isotropic forward volume magnetostatic waves. Appl. Phys. Lett. 106, 212406 (2015).

    Article  Google Scholar 

  88. Heinz, B. et al. Propagation of coherent spin waves in individual nano-sized yttrium iron garnet magnonic conduits. Nano Lett. 20, 4220–4227 (2020).

    Article  CAS  Google Scholar 

  89. Wang, Q. et al. Reconfigurable nanoscale spin-wave directional coupler. Sci. Adv. 4, e1701517 (2018).

    Article  Google Scholar 

  90. Wang, Q. et al. A magnonic directional coupler for integrated magnonic half-adders. Nat. Electron. 3, 765–774 (2020).

    Article  Google Scholar 

  91. Bergmann, K. et al. Roadmap on STIRAP applications. J. Phys. B At. Mol. Opt. Phys. 52, 202001 (2019).

    Article  CAS  Google Scholar 

  92. Wagner, K. et al. Magnetic domain walls as reconfigurable spin-wave nanochannels. Nat. Nanotechnol. 11, 432–436 (2016).

    Article  CAS  Google Scholar 

  93. Sluka, V. et al. Emission and propagation of 1D and 2D spin waves with nanoscale wavelengths in anisotropic spin textures. Nat. Nanotechnol. 14, 328–333 (2019).

    Article  CAS  Google Scholar 

  94. Albisetti, E. et al. Nanoscale spin-wave circuits based on engineered reconfigurable spin-textures. Commun. Phys. 1, 56 (2018).

    Article  Google Scholar 

  95. Albisetti, E. et al. Nanopatterning reconfigurable magnetic landscapes via thermally assisted scanning probe lithography. Nat. Nanotechnol. 11, 545–551 (2016).

    Article  CAS  Google Scholar 

  96. Liu, C. et al. Current-controlled propagation of spin waves in antiparallel, coupled domains. Nat. Nanotechnol. 14, 691–697 (2019).

    Article  CAS  Google Scholar 

  97. Hertel, R., Wulfhekel, W. & Kirschner, J. Domain-wall induced phase shifts in spin waves. Phys. Rev. Lett. 93, 257202 (2004).

    Article  Google Scholar 

  98. Pirro, P. et al. Experimental observation of the interaction of propagating spin waves with Néel domain walls in a Landau domain structure. Appl. Phys. Lett. 106, 232405 (2015).

    Article  Google Scholar 

  99. Hämäläinen, S. J., Madami, M., Qin, H., Gubbiotti, G. & van Dijken, S. Control of spin-wave transmission by a programmable domain wall. Nat. Commun. 9, 4853 (2018).

    Article  Google Scholar 

  100. Holländer, R. B., Müller, C., Schmalz, J., Gerken, M. & Mccord, J. Magnetic domain walls as broadband spin wave and elastic magnetisation wave emitters. Sci. Rep. 8, 13871 (2018).

    Article  Google Scholar 

  101. Albisetti, E. et al. Optically inspired nanomagnonics with nonreciprocal spin waves in synthetic antiferromagnets. Adv. Mater. 32, e1906439 (2020).

    Article  Google Scholar 

  102. Han, J., Zhang, P., Hou, J. T., Siddiqui, S. A. & Liu, L. Mutual control of coherent spin waves and magnetic domain walls in a magnonic device. Science 366, 1121–1125 (2019).

    Article  CAS  Google Scholar 

  103. Diaz, S. A., Hirosawa, T., Klinovaja, J. & Loss, D. Chiral magnonic edge states in ferromagnetic skyrmion crystals controlled by magnetic fields. Phys. Rev. Res. 2, 013231 (2020).

    Article  CAS  Google Scholar 

  104. Roldán-Molina, A., Nunez, A. S. & Fernández-Rossier, J. Topological spin waves in the atomic-scale magnetic skyrmion crystal. New J. Phys. 18, 045015 (2016).

    Article  Google Scholar 

  105. Garst, M., Waizner, J. & Grundler, D. Collective spin excitations of helices and magnetic skyrmions: review and perspectives of magnonics in non-centrosymmetric magnets. J. Phys. D Appl. Phys. 50, 293002 (2017).

    Article  Google Scholar 

  106. Katsura, H., Nagaosa, N. & Lee, P. A. Theory of the thermal Hall effect in quantum magnets. Phys. Rev. Lett. 104, 066403 (2010).

    Article  Google Scholar 

  107. Onose, Y. et al. Observation of the magnon Hall effect. Science 329, 297–299 (2010).

    Article  CAS  Google Scholar 

  108. Zhang, L., Ren, J., Wang, J.-S. & Li, B. Topological magnon insulator in insulating ferromagnet. Phys. Rev. B 87, 144101 (2013).

    Article  Google Scholar 

  109. Okamoto, A. & Murakami, S. Berry curvature for magnons in ferromagnetic films with dipole-exchange interactions. Phys. Rev. B 96, 174437 (2017).

    Article  Google Scholar 

  110. Mook, A., Henk, J. & Mertig, I. Tunable magnon Weyl points in ferromagnetic pyrochlores. Phys. Rev. Lett. 117, 157204 (2016).

    Article  Google Scholar 

  111. Chen, L. et al. Topological spin excitations in honeycomb ferromagnet CrI3. Phys. Rev. X 8, 041028 (2018).

    CAS  Google Scholar 

  112. Chisnell, R. et al. Topological magnon bands in a kagome lattice ferromagnet. Phys. Rev. Lett. 115, 147201 (2015).

    Article  CAS  Google Scholar 

  113. Owerre, S. A. Floquet topological magnons. J. Phys. Commun. 1, 021002 (2017).

    Article  Google Scholar 

  114. Li, Y.-M., Xiao, J. & Chang, K. Topological magnon modes in patterned ferrimagnetic insulator thin films. Nano Lett. 18, 3032 (2018).

    Article  CAS  Google Scholar 

  115. Yamamoto, K. et al. Topological characterization of classical waves: the topological origin of magnetostatic surface spin waves. Phys. Rev. Lett. 122, 217201 (2019).

    Article  CAS  Google Scholar 

  116. Wang, X. S., Zhang, H. W. & Wang, X. R. Topological magnonics: a paradigm for spin-wave manipulation and device design. Phys. Rev. Appl. 9, 024029 (2018).

    Article  Google Scholar 

  117. Davies, C. S. et al. Towards graded-index magnonics: steering spin waves in magnonic networks. Phys. Rev. B 92, 020408 (2015).

    Article  Google Scholar 

  118. Reshetnyak, S. A. Refraction of surface spin waves in spatially inhomogeneous ferrodielectrics with biaxial magnetic anisotropy. Phys. Solid State 46, 1061 (2004).

    Article  CAS  Google Scholar 

  119. Gorobets, Y. I. & Reshetnyak, S. A. Reflection and refraction of spin waves in uniaxial magnets in the geometrical-optics approximation. Tech. Phys. 43, 188–191 (1998).

    Article  Google Scholar 

  120. Loayza, N., Jungfleisch, M. B., Hoffmann, A., Bailleul, M. & Vlaminck, V. Fresnel diffraction of spin waves. Phys. Rev. B 98, 144430 (2018).

    Article  CAS  Google Scholar 

  121. Vashkovskii, A., Stal’makhov, A. & Shakhnazaryan, D. Formation, reflection, and refraction of magnetostatic wave beams. Sov. Phys. J. 31, 908–915 (1988).

    Article  Google Scholar 

  122. Yu, W., Lan, J., Wu, R. & Xiao, J. Magnetic Snell’s law and spin-wave fiber with Dzyaloshinskii-Moriya interaction. Phys. Rev. B 94, 140410 (2016).

    Article  Google Scholar 

  123. Xing, X. & Zhou, Y. Fiber optics for spin waves. NPG Asia Mater. 8, e246 (2016).

    Article  Google Scholar 

  124. Whitehead, N. J., Horsley, S. A. R., Philbin, T. G. & Kruglyak, V. V. Graded index lenses for spin wave steering. Phys. Rev. B 100, 094404 (2019).

    Article  CAS  Google Scholar 

  125. Csaba, G., Papp, A. & Porod, W. Spin-wave based realization of optical computing primitives. J. Appl. Phys. 115, 17C741 (2014).

    Article  Google Scholar 

  126. Papp, Á., Porod, W., Csurgay, Á. I. & Csaba, G. Nanoscale spectrum analyzer based on spin-wave interference. Sci. Rep. 7, 9245 (2017).

    Article  Google Scholar 

  127. Whitehead, N. J., Horsley, S. A. R., Philbin, T. G. & Kruglyak, V. V. A Luneburg lens for spin waves. Appl. Phys. Lett. 113, 212404 (2018).

    Article  Google Scholar 

  128. Minzioni, P. et al. Roadmap on all-optical processing. J. Opt. 21, 063001 (2019).

    Article  CAS  Google Scholar 

  129. Lock, E. H. The properties of isofrequency dependences and the laws of geometrical optics. Phys. Usp. 51, 375–393 (2008).

    Article  Google Scholar 

  130. Kim, J.-V., Stamps, R. L. & Camley, R. E. Spin wave power flow and caustics in ultrathin ferromagnets with the Dzyaloshinskii-Moriya interaction. Phys. Rev. Lett. 117, 197204 (2016).

    Article  Google Scholar 

  131. Mulkers, J. et al. Tunable Snell’s law for spin waves in heterochiral magnetic films. Phys. Rev. B 97, 104422 (2018).

    Article  CAS  Google Scholar 

  132. Kim, S. K. et al. Negative refraction of dipole-exchange spin waves through a magnetic twin interface in restricted geometry. Appl. Phys. Lett. 92, 212501 (2008).

    Article  Google Scholar 

  133. Vashkovskii, A. V. & Lock, E. H. Negative refractive index for a surface magnetostatic wave propagating through the boundary between a ferrite and ferrite-insulator-metal media. Phys. Usp. 47, 601 (2004).

    Article  CAS  Google Scholar 

  134. Veerakumar, V. & Camley, R. E. Magnon focusing in thin ferromagnetic films. Phys. Rev. B 74, 214401 (2006).

    Article  Google Scholar 

  135. Annenkov, A. Y., Gerus, S. V. & Lock, E. H. Superdirectional beam of surface spin wave. Europhys. Lett. 123, 44003 (2018).

    Article  Google Scholar 

  136. Schneider, T. et al. Nondiffractive subwavelength wave beams in a medium with externally controlled anisotropy. Phys. Rev. Lett. 104, 197203 (2010).

    Article  CAS  Google Scholar 

  137. Stigloher, J. et al. Snell’s law for spin waves. Phys. Rev. Lett. 117, 037204 (2016).

    Article  CAS  Google Scholar 

  138. Hata, H. et al. Micromagnetic simulation of spin wave propagation in a ferromagnetic film with different thicknesses. J. Magn. Soc. Jpn. 39, 151–155 (2015).

    Article  Google Scholar 

  139. Toedt, J.-N., Mundkowski, M., Heitmann, D., Mendach, S. & Hansen, W. Design and construction of a spin-wave lens. Sci. Rep. 6, 33169 (2016).

    Article  CAS  Google Scholar 

  140. Papp, A. & Csaba, G. Lens design for computing with anisotropic spin waves. IEEE Magn. Lett. 9, 3706405 (2018).

    Article  CAS  Google Scholar 

  141. Slawinski, M. & Slawinski, R. Energy partition at the boundary between anisotropic media; Part one: generalized Snell’s law. CREWES Res. Rep. 6, 9 (1994).

    Google Scholar 

  142. Madami, M. et al. Nonreciprocity of backward volume spin wave beams excited by the curved focusing transducer. Appl. Phys. Lett. 113, 152403 (2018).

    Article  Google Scholar 

  143. Vogel, M., Pirro, P., Hillebrands, B. & von Freymann, G. Optical elements for anisotropic spin-wave propagation. Appl. Phys. Lett. 116, 262404 (2020).

    Article  CAS  Google Scholar 

  144. Dzyapko, O., Borisenko, I. V., Demidov, V. E., Pernice, W. & Demokritov, S. O. Reconfigurable heat-induced spin wave lenses. Appl. Phys. Lett. 109, 232407 (2016).

    Article  Google Scholar 

  145. Vogel, M. et al. Control of spin-wave propagation using magnetisation gradients. Sci. Rep. 8, 11099 (2018).

    Article  Google Scholar 

  146. Serga, A. A., Neumann, T., Chumak, A. V. & Hillebrands, B. Generation of spin-wave pulse trains by current-controlled magnetic mirrors. Appl. Phys. Lett. 94, 112501 (2009).

    Article  Google Scholar 

  147. Kostylev, M. et al. Resonant and nonresonant scattering of dipole-dominated spin waves from a region of inhomogeneous magnetic field in a ferromagnetic film. Phys. Rev. B 76, 184419 (2007).

    Article  Google Scholar 

  148. Gruszecki, P. et al. Goos-Hänchen effect and bending of spin wave beams in thin magnetic films. Appl. Phys. Lett. 105, 242406 (2014).

    Article  Google Scholar 

  149. Stigloher, J. et al. Observation of a Goos-Hänchen-like phase shift for magnetostatic spin waves. Phys. Rev. Lett. 121, 137201 (2018).

    Article  CAS  Google Scholar 

  150. Kłos, J. W. et al. Hartman effect for spin waves in exchange regime. Sci. Rep. 8, 17944 (2018).

    Article  Google Scholar 

  151. Gołębiewski, M., Gruszecki, P., Krawczyk, M. & Serebryannikov, A. E. Spin-wave Talbot effect in a thin ferromagnetic film. Phys. Rev. B 102, 134402 (2020).

    Article  Google Scholar 

  152. Demidov, V. E. et al. Radiation of spin waves from the open end of a microscopic magnetic-film waveguide. Phys. Rev. B 80, 014429 (2009).

    Article  Google Scholar 

  153. Gieniusz, R. et al. Single antidot as a passive way to create caustic spin-wave beams in yttrium iron garnet films. Appl. Phys. Lett. 102, 102409 (2013).

    Article  Google Scholar 

  154. Sebastian, T. et al. Nonlinear emission of spin-wave caustics from an edge mode of a microstructured Co2Mn0.6Fe0.4Si waveguide. Phys. Rev. Lett. 110, 067201 (2013).

    Article  CAS  Google Scholar 

  155. Heussner, F. et al. Frequency-division multiplexing in magnonic logic networks based on caustic-like spin-wave beams. Phys. Status Solidi RRL 12, 1800409 (2018).

    Article  Google Scholar 

  156. Muralidhar, S. et al. Femtosecond laser pulse driven caustic spin wave beams. Phys. Rev. Lett. 126, 037204 (2021).

    Article  CAS  Google Scholar 

  157. Kostylev, M. P., Serga, A. A. & Hillebrands, B. Radiation of caustic beams from a collapsing bullet. Phys. Rev. Lett. 106, 134101 (2011).

    Article  CAS  Google Scholar 

  158. Heussner, F., Serga, A. A., Brächer, T., Hillebrands, B. & Pirro, P. A switchable spin-wave signal splitter for magnonic networks. Appl. Phys. Lett. 111, 122401 (2017).

    Article  Google Scholar 

  159. Heussner, F. et al. Experimental realization of a passive GHz frequency-division demultiplexer for magnonic logic networks. Phys. Status Solidi RRL 14, 1900695 (2020).

    Article  CAS  Google Scholar 

  160. Serga, A. A., Kostylev, M. P. & Hillebrands, B. Formation of guided spin-wave bullets in ferrimagnetic film stripes. Phys. Rev. Lett. 101, 137204 (2008).

    Article  CAS  Google Scholar 

  161. Demokritov, S. O., Hillebrands, B. & Slavin, A. N. Brillouin light scattering studies of confined spin waves: linear and nonlinear confinement. Phys. Rep. 348, 441–489 (2001).

    Article  CAS  Google Scholar 

  162. Kalinikos, B. A., Scott, M. M. & Patton, C. E. Self-generation of fundamental dark solitons in magnetic films. Phys. Rev. Lett. 84, 4697 (2000).

    Article  CAS  Google Scholar 

  163. Ustinov, A. B., Kondrashov, A. V., Nikitin, A. A. & Kalinikos, B. A. Self-generation and management of spin-electromagnetic wave solitons and chaos. Appl. Phys. Lett. 104, 234101 (2014).

    Article  Google Scholar 

  164. Richardson, D., Kalinikos, B. A., Carr, L. D. & Wu, M. Spontaneous exact spin-wave fractals in magnonic crystals. Phys. Rev. Lett. 121, 107204 (2018).

    Article  CAS  Google Scholar 

  165. Demokritov, S. O. et al. Experimental observation of symmetry breaking nonlinear modes in an active ring. Nature 426, 159–162 (2003).

    Article  CAS  Google Scholar 

  166. Serga, A. A., Demokritov, S. O., Hillebrands, B. & Slavin, A. N. Self-generation of two-dimensional spin-wave bullets. Phys. Rev. Lett. 92, 117203 (2004).

    Article  CAS  Google Scholar 

  167. Divinskiy, B. et al. Magnetic droplet solitons generated by pure spin currents. Phys. Rev. B 96, 224419 (2017).

    Article  Google Scholar 

  168. Mohseni, M. et al. Propagating magnetic droplet solitons as moveable nanoscale spin-wave sources with tunable direction of emission. Phys. Rev. Appl. 13, 024040 (2020).

    Article  CAS  Google Scholar 

  169. Melkov, G. A., Kobljanskyj, Y. V., Serga, A. A., Tiberkevich, V. S. & Slavin, A. N. Nonlinear amplification and compression of envelope solitons by localized nonstationary parametric pumping. J. Appl. Phys. 89, 6689 (2001).

    Article  CAS  Google Scholar 

  170. Serga, A. A. et al. Parametric generation of forward and phase-conjugated spin-wave bullets in magnetic films. Phys. Rev. Lett. 94, 167202 (2005).

    Article  CAS  Google Scholar 

  171. Bir, A. S. & Grishin, S. V. Generation of dark multisoliton complexes in a magnonic ring resonator with dispersion management and competing nonlinear spin-wave interactions. JETP Lett. 110, 364–369 (2019).

    Article  CAS  Google Scholar 

  172. Wu, M., Kalinikos, B. A., Carr, L. D. & Patton, C. E. Observation of spin-wave soliton fractals in magnetic film active feedback rings. Phys. Rev. Lett. 96, 187202 (2006).

    Article  Google Scholar 

  173. Inglis, A. & Gregg, J. F. Onset of spin wave time-domain fractals in a dynamic artificial crystal. J. Magn. Magn. Mater. 495, 165868 (2020).

    Article  CAS  Google Scholar 

  174. Anderson, J. Q., Ryan, R. A., Wu, M. & Carr, L. D. Complex solitary wave dynamics, pattern formation and chaos in the gain–loss nonlinear Schrödinger equation. New J. Phys. 16, 023025 (2014).

    Article  Google Scholar 

  175. Nikitov, S. A. et al. Magnonics: a new research area in spintronics and spin wave electronics. Phys. Usp. 58, 1002–1028 (2015).

    Article  CAS  Google Scholar 

  176. Melkov, G. A., Vasyuchka, V. I., Kobljanskyj, Yu. V. & Slavin, A. N. Wave-front reversal in a medium with inhomogeneities and an anisotropic wave spectrum. Phys. Rev. B 70, 224407 (2004).

    Article  Google Scholar 

  177. Dobrovolskiy, O. V. et al. Spin-wave phase inverter upon a single nanodefect. ACS Appl. Mater. Interfaces 11, 17654–17662 (2019).

    Article  CAS  Google Scholar 

  178. Sadovnikov, A. V. et al. Magnonic beam splitter: the building block of parallel magnonic circuitry. Appl. Phys. Lett. 106, 192406 (2015).

    Article  Google Scholar 

  179. Brächer, T., Pirro, P. & Hillebrands, B. Parallel pumping for magnon spintronics: amplification and manipulation of magnon spin currents on the micron-scale. Phys. Rep. 699, 1–34 (2017).

    Article  Google Scholar 

  180. Khitun, A., Nikonov, D. E. & Wang, K. L. Magnetoelectric spin wave amplifier for spin wave logic circuits. J. Appl. Phys. 106, 123909 (2009).

    Article  Google Scholar 

  181. Wang, Z., Sun, Y., Wu, M., Tiberkevich, V. & Slavin, A. Control of spin waves in a thin film ferromagnetic insulator through interfacial spin scattering. Phys. Rev. Lett. 107, 146602 (2011).

    Article  Google Scholar 

  182. Sebastian, T., Schultheiss, K., Obry, B., Hillebrands, B. & Schultheiss, H. Micro-focused Brillouin light scattering: imaging spin waves at the nanoscale. Front. Phys. 3, 35 (2015).

    Article  Google Scholar 

  183. Brächer, T. & Pirro, P. An analog magnon adder for all-magnonic neurons. J. Appl. Phys. 124, 152119 (2018).

    Article  Google Scholar 

  184. Lee, K.-S. & Kim, S.-K. Conceptual design of spin wave logic gates based on a Mach–Zehnder-type spin wave interferometer for universal logic functions. J. Appl. Phys. 104, 053909 (2008).

    Article  Google Scholar 

  185. Schneider, T. et al. Realization of spin-wave logic gates. Appl. Phys. Lett. 92, 022505 (2008).

    Article  Google Scholar 

  186. Kanazawa, N. et al. The role of Snell’s law for a magnonic majority gate. Sci. Rep. 7, 7898 (2017).

    Article  Google Scholar 

  187. Fischer, T. et al. Experimental prototype of a spin-wave majority gate. Appl. Phys. Lett. 110, 152401 (2017).

    Article  Google Scholar 

  188. Talmelli, G. et al. Reconfigurable submicrometer spin-wave majority gate with electrical transducers. Sci. Adv. 6, eabb4042 (2020).

    Article  CAS  Google Scholar 

  189. Kaganov, M. I., Pustyl’nik, N. B. & Shalaeva, T. I. Magnons, magnetic polaritons, magnetostatic waves. Phys. Usp. 167, 191 (1997).

    Article  CAS  Google Scholar 

  190. Holanda, J., Maior, D. S., Azevedo, A. & Rezende, S. M. Detecting the phonon spin in magnon–phonon conversion experiments. Nat. Phys. 14, 500–506 (2018).

    Article  CAS  Google Scholar 

  191. Lachance-Quirion, D., Tabuchi, Y., Gloppe, A., Usami, K. & Nakamura, Y. Hybrid quantum systems based on magnonics. Appl. Phys. Express 12, 70101 (2019).

    Article  CAS  Google Scholar 

  192. Li, Y. et al. Strong coupling between magnons and microwave photons in on-chip ferromagnet-superconductor thin-film devices. Phys. Rev. Lett. 123, 107701 (2019).

    Article  CAS  Google Scholar 

  193. Soykal, Ö. O. & Flatté, M. E. Strong field interactions between a nanomagnet and a photonic cavity. Phys. Rev. Lett. 104, 077202 (2010).

    Article  CAS  Google Scholar 

  194. Zare Rameshti, B. & Bauer, G. E. W. Indirect coupling of magnons by cavity photons. Phys. Rev. B 97, 014419 (2018).

    Article  CAS  Google Scholar 

  195. Cao, Y., Yan, P., Huebl, H., Goennenwein, S. T. B. & Bauer, G. E. W. Exchange magnon-polaritons in microwave cavities. Phys. Rev. B 91, 094423 (2015).

    Article  Google Scholar 

  196. Wolz, T. et al. Introducing coherent time control to cavity magnon-polariton modes. Commun. Phys. 3, 3 (2020).

    Article  Google Scholar 

  197. Tabuchi, Y. et al. Hybridizing ferromagnetic magnons and microwave photons in the quantum limit. Phys. Rev. Lett. 113, 083603 (2014).

    Article  CAS  Google Scholar 

  198. Goryachev, M. et al. High-cooperativity cavity QED with magnons at microwave frequencies. Phys. Rev. Appl. 2, 054002 (2014).

    Article  CAS  Google Scholar 

  199. Harder, M. et al. Level attraction due to dissipative magnon-photon coupling. Phys. Rev. Lett. 121, 137203 (2018).

    Article  CAS  Google Scholar 

  200. Huebl, H. et al. High cooperativity in coupled microwave resonator ferrimagnetic insulator hybrids. Phys. Rev. Lett. 111, 127003 (2013).

    Article  Google Scholar 

  201. Bourhill, J., Kostylev, N., Goryachev, M., Creedon, D. L. & Tobar, M. E. Ultrahigh cooperativity interactions between magnons and resonant photons in a YIG sphere. Phys. Rev. B 93, 144420 (2016).

    Article  Google Scholar 

  202. Zhang, X., Zou, C.-L., Jiang, L. & Tang, H. X. Strongly coupled magnons and cavity microwave photons. Phys. Rev. Lett. 113, 156401 (2014).

    Article  Google Scholar 

  203. Bhoi, B. et al. Study of photon-magnon coupling in a YIG-film split-ring resonant system. J. Appl. Phys. 116, 243906 (2014).

    Article  Google Scholar 

  204. Klingler, S. et al. Combined Brillouin light scattering and microwave absorption study of magnon-photon coupling in a split-ring resonator/YIG film system. Appl. Phys. Lett. 109, 072402 (2016).

    Article  Google Scholar 

  205. Morris, R. G. E., Van Loo, A. F., Kosen, S. & Karenowska, A. D. Strong coupling of magnons in a YIG sphere to photons in a planar superconducting resonator in the quantum limit. Sci. Rep. 7, 11511 (2017).

    Article  CAS  Google Scholar 

  206. Yang, Y. et al. Control of the magnon-photon level attraction in a planar cavity. Phys. Rev. Appl. 11, 054023 (2019).

    Article  CAS  Google Scholar 

  207. Bhoi, B. et al. Abnormal anticrossing effect in photon-magnon coupling. Phys. Rev. B 99, 134426 (2019).

    Article  CAS  Google Scholar 

  208. Tabuchi, Y. et al. Quantum magnonics: the magnon meets the superconducting qubit. C. R. Phys. 17, 729–739 (2016).

    Article  CAS  Google Scholar 

  209. Lachance-Quirion, D. et al. Entanglement-based single-shot detection of a single magnon with a superconducting qubit. Science 367, 425–428 (2020).

    Article  CAS  Google Scholar 

  210. Hisatomi, R. et al. Bidirectional conversion between microwave and light via ferromagnetic magnons. Phys. Rev. B 93, 174427 (2016).

    Article  Google Scholar 

  211. Osada, A. et al. Cavity optomagnonics with spin-orbit coupled photons. Phys. Rev. Lett. 116, 223601 (2016).

    Article  CAS  Google Scholar 

  212. Zhang, X., Zhu, N., Zou, C. L. & Tang, H. X. Optomagnonic whispering gallery microresonators. Phys. Rev. Lett. 117, 123605 (2016).

    Article  Google Scholar 

  213. Sharma, S., Blanter, Y. M. & Bauer, G. E. W. Light scattering by magnons in whispering gallery mode cavities. Phys. Rev. B 96, 094412 (2017).

    Article  Google Scholar 

  214. Kirilyuk, A., Kimel, A. V. & Rasing, T. Ultrafast optical manipulation of magnetic order. Rev. Mod. Phys. 82, 2731 (2010).

    Article  Google Scholar 

  215. Osada, A. et al. Brillouin light scattering by magnetic quasivortices in cavity optomagnonics. Phys. Rev. Lett. 120, 133602 (2018).

    Article  CAS  Google Scholar 

  216. Haigh, J. A. et al. Selection rules for cavity-enhanced Brillouin light scattering from magnetostatic modes. Phys. Rev. B 97, 214423 (2018).

    Article  CAS  Google Scholar 

  217. Lodahl, P. et al. Chiral quantum optics. Nature 541, 473–480 (2017).

    Article  CAS  Google Scholar 

  218. Graf, J., Pfeifer, H., Marquardt, F. & Kusminskiy, S. V. Cavity optomagnonics with magnetic textures: coupling a magnetic vortex to light. Phys. Rev. B 98, 241406 (2018).

    Article  CAS  Google Scholar 

  219. Zhang, X., Zou, C.-L., Jiang, L. & Tang, H. X. Cavity magnomechanics. Sci. Adv. 2, e1501286 (2016).

    Article  Google Scholar 

  220. Li, J., Zhu, S.-Y. & Agarwal, G. S. Squeezed states of magnons and phonons in cavity magnomechanics. Phys. Rev. A 99, 021801 (2019).

    Article  CAS  Google Scholar 

  221. Li, J., Zhu, S. Y. & Agarwal, G. S. Magnon-photon-phonon entanglement in cavity magnomechanics. Phys. Rev. Lett. 121, 203601 (2018).

    Article  CAS  Google Scholar 

  222. Kosen, S., van Loo, A. F., Bozhko, D. A., Mihalceanu, L. & Karenowska, A. D. Microwave magnon damping in YIG films at millikelvin temperatures. APL Mater. 7, 101120 (2019).

    Article  Google Scholar 

  223. Pfirrmann, M. et al. Magnons at low excitations: observation of incoherent coupling to a bath of two-level systems. Phys. Rev. Res. 1, 032023 (2019).

    Article  CAS  Google Scholar 

  224. Hou, J. T. & Liu, L. Strong coupling between microwave photons and nanomagnet magnons. Phys. Rev. Lett. 123, 107702 (2019).

    Article  CAS  Google Scholar 

  225. Hu, C.-M. Cavity spintronics gets more with less. Physics 12, 97 (2019).

    Article  Google Scholar 

  226. Sposito, A., May-Smith, T. C., Stenning, G. B. G., de Groot, P. A. J. & Eason, R. W. Pulsed laser deposition of high-quality μm-thick YIG films on YAG. Opt. Mater. Express 3, 624–632 (2013).

    Article  CAS  Google Scholar 

  227. Levy, M., Osgood, R., Rachford, F., Kumar, A. & Bakhru, H. Narrow-linewidth yttrium iron garnet films for heterogeneous integration. MRS Proc. 603, 119–122 (1999).

    Article  Google Scholar 

  228. Förster, J. et al. Nanoscale X-ray imaging of spin dynamics in yttrium iron garnet. J. Appl. Phys. 126, 173909 (2019).

    Article  Google Scholar 

  229. Danilov, V. V. & Nechiporuk, A. Y. Experimental investigation of the quantum amplification effect for magnetostatic waves in ferrite-paramagnet structures. Tech. Phys. Lett. 28, 369–370 (2002).

    Article  CAS  Google Scholar 

  230. Rezende, S. M. Theory of coherence in Bose-Einstein condensation phenomena in a microwave-driven interacting magnon gas. Phys. Rev. B 79, 174411 (2009).

    Article  Google Scholar 

  231. Bunkov, Yu. M. Spin superfluidity and coherent spin precession. J. Phys. Condens. Matter 21, 164201 (2009).

    Article  Google Scholar 

  232. Volovik, G. E. Twenty years of magnon Bose condensation and spin current superfluidity in 3He-B. J. Low Temp. Phys. 153, 266–284 (2008).

    Article  CAS  Google Scholar 

  233. Kalafati, Y. D. & Safonov, V. L. Theory of quasiequilibrium effects in a system of magnons excited by incoherent pumping. Sov. Phys. JETP 73, 836–841 (1991).

    Google Scholar 

  234. Bozhko, D. A. et al. Bottleneck accumulation of hybrid magnetoelastic bosons. Phys. Rev. Lett. 118, 237201 (2017).

    Article  Google Scholar 

  235. Serga, A. A. et al. Bose–Einstein condensation in an ultra-hot gas of pumped magnons. Nat. Commun. 5, 3452 (2014).

    Article  Google Scholar 

  236. Lavrinenko, A. V. et al. “Kinetic” instability of a strongly nonequilibrium system of spin waves and tunable radiation of a ferrite. Sov. Phys. JETP 54, 542–549 (1981).

    Google Scholar 

  237. Melkov, G. A. & Sholom, S. V. Kinetic instability of spin waves in thin ferrite films. Sov. Phys. JETP 72, 341–346 (1991).

    Google Scholar 

  238. Kreil, A. J. E. et al. From kinetic instability to Bose-Einstein condensation and magnon supercurrents. Phys. Rev. Lett. 121, 077203 (2018).

    Article  CAS  Google Scholar 

  239. Bender, S. A., Duine, R. A. & Tserkovnyak, Y. Electronic pumping of quasiequilibrium Bose-Einstein-condensed magnons. Phys. Rev. Lett. 108, 246601 (2012).

    Article  Google Scholar 

  240. Barker, J. & Bauer, G. E. W. Thermal spin dynamics of yttrium iron garnet. Phys. Rev. Lett. 117, 217201 (2016).

    Article  Google Scholar 

  241. Uchida, K., Kikkawa, T., Miura, A., Shiomi, J. & Saitoh, E. Quantitative temperature dependence of longitudinal spin Seebeck effect at high temperatures. Phys. Rev. X 4, 041023 (2014).

    CAS  Google Scholar 

  242. Schneider, M. et al. Bose-Einstein condensation of quasi-particles by rapid cooling. Nat. Nanotechnol. 15, 457–461 (2020).

    Article  CAS  Google Scholar 

  243. Bender, S. A., Duine, R. A., Brataas, A. & Tserkovnyak, Y. Dynamic phase diagram of dc-pumped magnon condensates. Phys. Rev. B 90, 094409 (2014).

    Article  CAS  Google Scholar 

  244. Rückriegel, A. & Kopietz, P. Rayleigh-Jeans condensation of pumped magnons in thin-film ferromagnets. Phys. Rev. Lett. 115, 157203 (2015).

    Article  Google Scholar 

  245. Takei, S. & Tserkovnyak, Y. Superfluid spin transport through easy-plane ferromagnetic insulators. Phys. Rev. Lett. 112, 227201 (2014).

    Article  Google Scholar 

  246. Nakata, K., van Hoogdalem, K. A., Simon, P. & Loss, D. Josephson and persistent spin currents in Bose-Einstein condensates of magnons. Phys. Rev. B 90, 144419 (2014).

    Article  Google Scholar 

  247. Mihalceanu, L. et al. Magnon Bose–Einstein condensate and supercurrents over a wide temperature range. Ukr. J. Phys. 64, 927 (2019).

    Article  Google Scholar 

  248. Schütz, F., Kollar, M. & Kopietz, P. Persistent spin currents in mesoscopic Heisenberg rings. Phys. Rev. Lett. 91, 017205 (2003).

    Article  Google Scholar 

  249. Aharonov, Y. & Casher, A. Topological quantum effects for neutral particles. Phys. Rev. Lett. 53, 319 (1984).

    Article  CAS  Google Scholar 

  250. Aharonov, Y. & Bohm, D. Significance of electromagnetic potentials in the quantum theory. Phys. Rev. 115, 485 (1959).

    Article  Google Scholar 

  251. Nakata, K., Simon, P. & Loss, D. Spin currents and magnon dynamics in insulating magnets. J. Phys. D Appl. Phys. 50, 114004 (2017).

    Article  Google Scholar 

  252. Loss, D. & Goldbart, P. M. Persistent currents from Berry’s phase in mesoscopic systems. Phys. Rev. B 45, 13544 (1992).

    Article  CAS  Google Scholar 

  253. Meier, F. & Loss, D. Magnetization transport and quantized spin conductance. Phys. Rev. Lett. 90, 167204 (2003).

    Article  Google Scholar 

  254. Nakata, K., Klinovaja, J. & Loss, D. Magnonic quantum Hall effect and Wiedemann-Franz law. Phys. Rev. B 95, 125429 (2017).

    Article  Google Scholar 

  255. Tserkovnyak, Y. & Kläui, M. Exploiting coherence in nonlinear spin-superfluid transport. Phys. Rev. Lett. 119, 187705 (2017).

    Article  Google Scholar 

  256. Dzyapko, O. et al. Magnon-magnon interactions in a room-temperature magnonic Bose-Einstein condensate. Phys. Rev. B 96, 064438 (2017).

    Article  Google Scholar 

  257. Tiberkevich, V. et al. Excitation of coherent second sound waves in a dense magnon gas. Sci. Rep. 9, 9063 (2019).

    Article  CAS  Google Scholar 

  258. Troncoso, R. E. & Núñez, Á. S. Josephson effects in a Bose–Einstein condensate of magnons. Ann. Phys. 346, 182–194 (2014).

    Article  CAS  Google Scholar 

  259. Rana, B. & Otani, Y. Towards magnonic devices based on voltage-controlled magnetic anisotropy. Commun. Phys. 2, 90 (2019).

    Article  Google Scholar 

  260. Yu, H. et al. Approaching soft X-ray wavelengths in nanomagnet-based microwave technology. Nat. Commun. 7, 11255 (2016).

    Article  CAS  Google Scholar 

  261. Förster, J. et al. Direct observation of coherent magnons with suboptical wavelengths in a single-crystalline ferrimagnetic insulator. Phys. Rev. B 100, 214416 (2019).

    Article  Google Scholar 

  262. Hashimoto, Y. et al. Frequency and wavenumber selective excitation of spin waves through coherent energy transfer from elastic waves. Phys. Rev. B 97, 140404 (2018).

    Article  CAS  Google Scholar 

  263. Lisenkov, I., Jander, A. & Dhagat, P. Magnetoelastic parametric instabilities of localized spin waves induced by traveling elastic waves. Phys. Rev. B 99, 184433 (2019).

    Article  CAS  Google Scholar 

  264. Satoh, T. et al. Directional control of spin-wave emission by spatially shaped light. Nat. Photonics 6, 662–666 (2012).

    Article  CAS  Google Scholar 

  265. Jackl, M. et al. Magnon accumulation by clocked laser excitation as source of long-range spin waves in transparent magnetic films. Phys. Rev. X 7, 021009 (2017).

    Google Scholar 

  266. Schlauderer, S. et al. Temporal and spectral fingerprints of ultrafast all-coherent spin switching. Nature 569, 383–387 (2019).

    Article  CAS  Google Scholar 

  267. Grollier, J. et al. Neuromorphic spintronics. Nat. Electron. 3, 360–370 (2020).

    Article  Google Scholar 

  268. Lebrun, R. et al. Tunable long-distance spin transport in a crystalline antiferromagnetic iron oxide. Nature 561, 222–225 (2018).

    Article  CAS  Google Scholar 

  269. Sando, D. et al. Crafting the magnonic and spintronic response of BiFeO3 films by epitaxial strain. Nat. Mater. 12, 641–646 (2013).

    Article  CAS  Google Scholar 

  270. Princep, A. J. et al. The full magnon spectrum of yttrium iron garnet. NPJ Quantum Mater. 2, 63 (2017).

    Article  Google Scholar 

  271. Petrenko, O. A., Paul, D. M., Ritter, C., Zeiske, T. & Yethiraj, M. Magnetic frustration and order in gadolinium gallium garnet. Phys. B Condens. Matter 266, 41–48 (1999).

    Article  CAS  Google Scholar 

  272. Delgado, A., Guerra, Y., Padrón-Hernández, E. & Peña-Garcia, R. Combining the sol gel method and spin coating to obtain YIG films with low FMR linewidth on silicon (100) substrate. Mater. Res. Express 5, 026419 (2018).

    Article  Google Scholar 

  273. Aldosary, M. et al. Platinum/yttrium iron garnet inverted structures for spin current transport. Appl. Phys. Lett. 108, 242401 (2016).

    Article  Google Scholar 

  274. Dubs, C. et al. Sub-micrometer yttrium iron garnet LPE films with low ferromagnetic resonance losses. J. Phys. D Appl. Phys. 50, 204005 (2017).

    Article  Google Scholar 

  275. Soumah, L. et al. Ultra-low damping insulating magnetic thin films get perpendicular. Nat. Commun. 9, 1505 (2018).

    Article  Google Scholar 

  276. Liu, H. et al. Organic-based magnon spintronics. Nat. Mater. 17, 308–312 (2018).

    Article  CAS  Google Scholar 

  277. Franson, A. et al. Low-damping ferromagnetic resonance in electron-beam patterned, high-Q vanadium tetracyanoethylene magnon cavities. APL Mater. 7, 121113 (2019).

    Article  Google Scholar 

  278. Flacke, L. et al. High spin-wave propagation length consistent with low damping in a metallic ferromagnet. Appl. Phys. Lett. 115, 122402 (2019).

    Article  Google Scholar 

  279. Gladii, O., Halley, D., Henry, Y. & Bailleul, M. Spin-wave propagation and spin-polarized electron transport in single-crystal iron films. Phys. Rev. B 96, 174420 (2017).

    Article  Google Scholar 

  280. Vlaminck, V. & Bailleul, M. Current-induced spin-wave Doppler shift. Science 322, 410–413 (2008).

    Article  CAS  Google Scholar 

  281. Kobljanskyj, Y. V., Melkov, G. A., Serga, A. A., Slavin, A. N. & Hillebrands, B. Detection of spin waves in Permalloy using planar Hall effect. Phys. Rev. Appl. 4, 014014 (2015).

    Article  Google Scholar 

  282. Hurben, M. J. & Patton, C. E. Theory of two magnon scattering microwave relaxation and ferromagnetic resonance linewidth in magnetic thin films. J. Appl. Phys. 83, 4344 (1998).

    Article  CAS  Google Scholar 

  283. Mathieu, C., Synogach, V. T. & Patton, C. E. Brillouin light scattering analysis of three-magnon splitting processes in yttrium iron garnet films. Phys. Rev. B 67, 104402 (2003).

    Article  Google Scholar 

  284. Ordóñez-Romero, C. L. et al. Three-magnon splitting and confluence processes for spin-wave excitations in yttrium iron garnet films: wave vector selective Brillouin light scattering measurements and analysis. Phys. Rev. B 79, 144428 (2009).

    Article  Google Scholar 

  285. Schultheiss, K. et al. Excitation of whispering gallery magnons in a magnetic vortex. Phys. Rev. Lett. 122, 097202 (2019).

    Article  CAS  Google Scholar 

  286. Cunha, R. O. et al. Nonlinear dynamics of three-magnon process driven by ferromagnetic resonance in yttrium iron garnet. Appl. Phys. Lett. 106, 192403 (2015).

    Article  Google Scholar 

  287. Anisimov, A. N. & Gurevich, A. G. Attenuation of spin waves due to four-magnon scattering. Sov. Phys. Solid State 18, 38–43 (1976).

    CAS  Google Scholar 

  288. Krivosik, P. & Patton, C. E. Hamiltonian formulation of nonlinear spin-wave dynamics: theory and applications. Phys. Rev. B 82, 184428 (2010).

    Article  Google Scholar 

  289. Streib, S., Vidal-Silva, N., Shen, K. & Bauer, G. E. W. Magnon-phonon interactions in magnetic insulators. Phys. Rev. B 99, 184442 (2019).

    Article  CAS  Google Scholar 

  290. Rückriegel, A., Kopietz, P., Bozhko, D. A., Serga, A. A. & Hillebrands, B. Magnetoelastic modes and lifetime of magnons in thin yttrium iron garnet films. Phys. Rev. B 89, 184413 (2014).

    Article  Google Scholar 

  291. Kasuya, T. & LeCraw, R. C. Relaxation mechanisms in ferromagnetic resonance. Phys. Rev. Lett. 6, 223 (1961).

    Article  CAS  Google Scholar 

  292. Kamberský, V. Spin-orbital Gilbert damping in common magnetic metals. Phys. Rev. B 76, 134416 (2007).

    Article  Google Scholar 

  293. Heinrich, B. in Ultrathin Magnetic Structures III Vol. 5 (eds Bland, J. A. C. & Heinrich, B.) 143–210 (Springer, 2005).

  294. Bunyaev, S. A. et al. Spin-wave relaxation by eddy currents in YIG-Pt bilayers and a way to suppress it. Phys. Rev. Appl. 14, 024094 (2020).

    Article  CAS  Google Scholar 

  295. Tserkovnyak, Y., Brataas, A. & Bauer, G. E. W. Spin pumping and magnetization dynamics in metallic multilayers. Phys. Rev. B 66, 224403 (2002).

    Article  Google Scholar 

  296. Vollmer, R., Etzkorn, M., Anil Kumar, P. S., Ibach, H. & Kirschner, J. Spin-polarized electron energy loss spectroscopy: a method to measure magnon energies. J. Mag. Mag. Mater. 272–276, 2126–2130 (2004).

    Article  Google Scholar 

  297. Plihal, M., Mills, D. L. & Kirschner, J. Spin wave signature in the spin polarized electron energy loss spectrum of ultrathin Fe films: theory and experiment. Phys. Rev. Lett. 82, 2579 (1999).

    Article  CAS  Google Scholar 

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Acknowledgements

The financial support of the European Research Council within the Advanced Grant 694709 SuperMagnonics — Supercurrents of Magnon Condensates for Advanced Magnonics and the funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) TRR 173 - 268565370: Spin in its Collective Environment (projects B01 and B04) are gratefully acknowledged. The authors are grateful to V. S. L’vov from the Weizmann Institute of Science (Rehovot, Israel) for the valuable discussions.

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Pirro, P., Vasyuchka, V.I., Serga, A.A. et al. Advances in coherent magnonics. Nat Rev Mater 6, 1114–1135 (2021). https://doi.org/10.1038/s41578-021-00332-w

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