Skip to main content
SpringerLink
Log in

Ferromagnetic spin waves in nanostriped magnonic crystals with quasiperiodic vertical development

  • Regular Article
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

A theoretical analysis is reported for the spin waves in ferromagnetically-ordered magnonic crystals consisting of lateral periodic arrays of composite nanowires. The structure of each nanowire is a vertically-developed multilayer built up according to a quasiperiodic Fibonacci sequence. Each nanowire is separated by a non-magnetic spacer in either direction. The quasiperiodicity in these composite nanowires is addressed in two ways: the geometric variation in a single-component (permalloy) structure and the compositional variation (using cobalt and permalloy). These composite nanowire structures are compared and contrasted with one another. A microscopic approach is used to calculate the spectra of spin-wave bands and band gaps for several generation numbers of the Fibonacci sequence. Comparison of the density of states for these structures is made with that for the periodic cases, which highlights distinct characteristics of the quasiperiodicity. The fractal-like scaling properties of the modes show characteristics analogous to some complex biological systems.

Graphical abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  3. S.O. Demokritov, A.N. Slavin,Magnonics: from Fundamentals to Applications (Springer, Berlin, 2013)

  4. G. Gubbiotti,Three-Dimensional Magnonics (Jenny Stanford, Singapore, 2019)

  5. B. Hillebrands, K. Ounadjela,Spin Dynamics in Confined Magnetic Structures I (Springer, Berlin, 2003)

  6. M. Krawczyk, D. Grundler, J. Phys. Condens. Matter 26, 123202 (2014)

    Google Scholar 

  7. J.D. Joannopoulos, S.G. Johnson, J.N. Winn, R.D. Meade,Photonic Crystals: Molding the Flow of Light, 2nd edn. (Princeton University Press, Princeton, 2008)

  8. F. Capolino,Theory and phenomena of metamaterials (CRC Press, Boca Raton, 2009)

  9. M. Kohmoto, L.P. Kadanoff, C. Tang, Phys. Rev. Lett. 50, 1870 (1983)

    ADS  MathSciNet  Google Scholar 

  10. Q. Niu, F. Nori, Phys. Rev. Lett. 57, 2057 (1986)

    ADS  Google Scholar 

  11. J.P. Lu, T. Odagaki, J.L. Birman, Phys. Rev. B 33, 4809 (1986)

    ADS  Google Scholar 

  12. J.A. Ashraff, R.B. Stinchcombe, Phys. Rev. B 37, 5723 (1988)

    ADS  MathSciNet  Google Scholar 

  13. A. Chakrabarti, S.N. Karmakar, R.K. Moitra, Phys. Rev. B 39, 9730 (1989)

    ADS  Google Scholar 

  14. S.J. Xiong, J. Phys. C Solid State Phys. 20, L167 (1987)

    Google Scholar 

  15. G.-D. Pang, F.-C. Pu, Phys. Rev. B 38, 12649 (1988)

    ADS  Google Scholar 

  16. R. Merlin, K. Bajema, R. Clarke, F.-Y. Juang, P.K. Bhattacharya, Phys. Rev. Lett. 55, 1768 (1985)

    ADS  Google Scholar 

  17. Z.V. Vardeny, A. Nahaha, A. Agarwal, Nat. Photon 7, 177 (2013)

    ADS  Google Scholar 

  18. W. Steurer, D. Sutter-Widmer, J. Phys. D Appl. Phys. 40, R229 (2007)

    ADS  Google Scholar 

  19. D. Shechtman, I. Blech, D. Gratias, J.W. Cahn, Phys. Rev. Lett. 53, 1951 (1984)

    ADS  Google Scholar 

  20. J.R. Dutcher, S. Lee, B. Hillebrands, G.J. McLaughlin, B.G. Nickel, G.I. Stegeman, Phys. Rev. Lett. 68, 2464 (1992)

    ADS  Google Scholar 

  21. V.L. Zhang, C.G. Hou, H.H. Pan, F.S. Ma, M.H. Kuok, H.S. Lim, S.C. Ng, M.G. Cottam, M. Jamali, H. Yang, Appl. Phys. Lett. 101, 053102 (2012)

    ADS  Google Scholar 

  22. M.G. Cottam, D.R. Tilley,Introduction to Surface and Superlattice Excitations (Cambridge University Press, Cambridge, 1989)

  23. G. Gubbiotti, S. Tacchi, G. Carlotti, N. Singh, S. Goolaup, A.O. Adeyeye, M. Kostylev, Appl. Phys. Lett. 90, 092503 (2007)

    ADS  Google Scholar 

  24. G. Gubbiotti, S. Tacchi, M. Madami, G. Carlotti, A.O. Adeyeye, M. Kostylev, J. Phys, D Appl. Phys. 43, 264003 (2010)

    ADS  Google Scholar 

  25. G. Gubbiotti, L.L. Xiong, F. Montoncello, A.O. Adeyeye, Appl. Phys. Lett. 111, 192403 (2017)

    ADS  Google Scholar 

  26. G. Gubbiotti, S. Tacchi, H.T. Nguyen, M. Madami, G. Carlotti, K. Nakono, T. Ono, M.G. Cottam, Phys. Rev. B 87, 094406 (2013)

    ADS  Google Scholar 

  27. S. Tacchi, M. Madami, G. Gubbiotti, S. Goolaup, A.O. Adeyeye, H.T. Nguyen, M.G. Cottam, J. Appl. Phys. 105, 07C102 (2009)

    Google Scholar 

  28. G. Gubbiotti, X. Zhou, Z. Haghshenasfard, M.G. Cottam, A.O. Adeyeye, Phys. Rev. B 97, 134428 (2018)

    ADS  Google Scholar 

  29. P. Lupo, Z. Haghshenasfard, M.G. Cottam, A.O. Adeyeye, Phys. Rev. B 118, 113902 (2016)

    Google Scholar 

  30. M.G. Cottam, Z. Haghshenasfard, A.O. Adeyeye, G. Gubbiotti, inThree-Dimensional Magnonics, edited by G. Gubbiotti (Jenny Stanford, Singapore, 2019), p. 1

  31. A.B. Kalinikos, Sov. J. Phys. 24, 718 (1981)

    Google Scholar 

  32. A.G. Gurevich, G.A. Melkov,Magnetization Oscillations and Waves (CRC Press, Boca Raton, 1996)

  33. M. Kostylev, J. Ding, E. Ivanov, S. Samarin, A.O. Adeyeye, J. Appl. Phys. 115, 173903 (2014)

    ADS  Google Scholar 

  34. M. Kostylev, Z. Yang, I.S. Maksymov, J. Ding, S. Samarin, A.O. Adeyeye, J. Appl. Phys. 119, 103903 (2016)

    ADS  Google Scholar 

  35. C.H.O. Costa, M.S. Vasconcelos, J. Phys. Condens. Matter 25, 286002 (2013)

    Google Scholar 

  36. T.S. Liu, G.Z. Wei, Phys. Rev. B 48, 7154 (1993)

    ADS  Google Scholar 

  37. C.H.O. Costa, P.H.R. Barbosa, F.F. Barbosa Filho, M.S. Vasconcelos, E.L. Albuquerque, Solid State Commun. 150, 2325 (2010)

    ADS  Google Scholar 

  38. C.H.O. Costa, M.S. Vasconcelos, P.H.R. Barbosa, F.F. Barbosa Filho, J. Magn. Magn. Mater. 324, 2315 (2012)

    ADS  Google Scholar 

  39. J. Rychly, J.W. Klos, M. Krawczyk, J. Phys. D Appl. Phys. 49, 175001 (2016)

    ADS  Google Scholar 

  40. E.L. Albuquerque, M.G. Cottam, Phys. Rep. 376, 225 (2003)

    ADS  Google Scholar 

  41. E.L. Albuquerque, M.G. Cottam,Polaritons in Periodic and Quasiperiodic Structures (Elsevier, Amsterdam, 2004)

  42. V.S. Bhat, J. Sklenar, B. Farmer, J. Woods, J.T. Hastings, S.J. Lee, J.B. Ketterson, L.E. De Long, Phys. Rev. Lett. 111, 077201 (2013)

    ADS  Google Scholar 

  43. S.V. Grishin, E.N. Beginin, Yu.P. Sharaevskii, S.A. Nikitov, Appl. Phys. Lett. 103, 022408 (2013)

    ADS  Google Scholar 

  44. B. Hussain, M.G. Cottam, J. Phys. D. Appl. Phys. 51, 355003 (2018)

    Google Scholar 

  45. B. Hussain, M.G. Cottam, J. Phys. D. Appl. Phys. 52, 095001 (2019)

    ADS  Google Scholar 

  46. K. Bajema, R. Merlin, Phys. Rev. Lett. 36, 4555 (1987)

    ADS  Google Scholar 

  47. J. Todd, R. Merlin, R. Clarke, K.M. Mohanty, J.D. Axe, Phys. Rev. Lett. 57, 1157 (1986)

    ADS  Google Scholar 

  48. Z. Cheng, R. Savit, R. Merlin, Phys. Rev. Lett. B 37, 4375 (1988)

    ADS  Google Scholar 

  49. M. Albrecht, G. Hu, A. Moser, O. Hellwig, B.D. Terris, J. Appl. Phys. 97, 103910 (2005)

    ADS  Google Scholar 

  50. J. Butler, M. Shachar, B. Lee, D. Garcia, B. Hu, J. Hong, N. Amos, S. Khizroev, J. Appl. Phys. 115, 163903 (2014)

    ADS  Google Scholar 

  51. S.M.M. Zanjani, M. Holt, M.M. Sadeghi, S. Rahimi, D. Akinwande, npj 2D Mater. Appl. 1, 36 (2017)

    Google Scholar 

  52. T.M. Nguyen, M.G. Cottam, Phys. Rev. B 71, 094406 (2005)

    ADS  Google Scholar 

  53. T.M. Nguyen, M.G. Cottam, Phys. Rev. B 72, 224415 (2005)

    ADS  Google Scholar 

  54. H.T. Nguyen, T.M. Nguyen, M.G. Cottam, Phys. Rev. B 76, 134413 (2007)

    ADS  Google Scholar 

  55. H.T. Nguyen, M.G. Cottam, J. Appl. Phys. 111, 07D122 (2012)

    Google Scholar 

  56. H.T. Nguyen, M.G. Cottam, J. Phys. D Appl. Phys. 44, 315001 (2011)

    ADS  Google Scholar 

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

  58. G.A. Losa, D. Merlini, T.F. Nonnenmacher, E.R. Wiebe, inFractals in Biology and Medicine (Birkhauser, Basel, 2005), Vol. 4

  59. G. Gubbiotti, X. Zhou, Z. Haghshenasfard, M.G. Cottam, A.O. Adeyeye, Nat. Sci. Rep. 9, 46172019 (2019)

    Google Scholar 

  60. L. Zhi-xiong, M.N. Wang, Y.Z. Nie, D.W. Wang, Q.L. Xia, W. Tang, Z.M. Zeng, G.H. Guo, J. Magn. Magn. Mater. 414, 49 (2016)

    ADS  Google Scholar 

  61. G. Gubbiotti, R. Silvani, S. Tacchi, M. Madami, G. Carlotti, Z. Yang, A.O. Adeyeye, M. Kostylev, J. Phys. D Appl. Phys. 50, 105002 (2017)

    ADS  Google Scholar 

  62. G. Gubbiotti, L.L. Xiong, F. Montoncello, L. Giovannini, A.O. Adeyeye, J. Appl. Phys. 124, 082903 (2018)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics and Astronomy, The University of Western Ontario, London, Ontario N6A 3K7, Canada

    Bushra Hussain, Zahra Haghshenasfard & Michael G. Cottam

Authors
  1. Bushra Hussain
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zahra Haghshenasfard
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Michael G. Cottam
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zahra Haghshenasfard.

Additional information

Publisher's Note

The EPJ Publishers remain neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hussain, B., Haghshenasfard, Z. & Cottam, M.G. Ferromagnetic spin waves in nanostriped magnonic crystals with quasiperiodic vertical development. Eur. Phys. J. B 93, 65 (2020). https://doi.org/10.1140/epjb/e2020-100491-1

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/e2020-100491-1

Keywords

Search

Navigation