- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Applied

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Editors' Suggestion
  • Open Access

Roles of quadratic and biquadratic couplings in the spin-wave modes of Co−Fe/Ru/Ni−Fe artificial spin ices

Riccardo Fornari1,2,*, Mohammad Tomal Hossain3, Raffaele Silvani1,2, Vinayak Shantaram Bhat3, Rawnak Sultana3, M. Benjamin Jungfleisch3,†, and Gianluca Gubbiotti2,‡

  • *Contact author: riccardo.fornari@dottorandi.unipg.it
  • †Contact author: mbj@udel.edu
  • ‡Contact author: gianluca.gubbiotti@cnr.it
PDF

Phys. Rev. Applied 26, 034063 – Published 25 September, 2026

DOI: https://doi.org/10.1103/5c9l-5w7v

Abstract

We investigate the interplay between quadratic and biquadratic exchange coupling in an exchange-coupled Co−Fe/Ru/Ni−Fe synthetic ferrimagnetic structure and compare its behavior to that of the same trilayer, patterned into an artificial spin ice (ASI). The static and dynamic properties are investigated by vibrating-sample magnetometry and Brillouin light-scattering spectroscopy and interpreted using MuMax3 micromagnetic simulations. Following this combined experimental and computational approach, we quantify the quadratic and biquadratic interfacial coupling terms and reveal their impact on magnetization reversal and layer-resolved spin-wave dynamics in the CoFe and NiFe layers. Furthermore, simulations of the evolution of the static configurations of the ASI system as a function of the applied magnetic field reveal the significant role played by the quadratic and biquadratic coupling terms in determining the equilibrium configurations of the nanoislands, in competition with the magnetostatic interactions imposed by the shape anisotropy of the nanoelements. This competition promotes mutually orthogonal layer magnetizations and may give rise to frustrated equilibrium states in which the magnetization aligns along the hard axis of the nanoelements. Our results suggest artificial spin lattices as promising reconfigurable magnonic devices where magnetic ground-state tunability may enable field-controlled magnonic crystals, spin-wave filters, and artificial spin-ice metamaterials with switchable dynamic properties.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (37)

  1. J. Sklenar, S. Lendinez, and M. B. Jungfleisch, Dynamics in artificial spin ice and magnetic metamaterials, Solid State Physics (Academic Press, New York, NY, USA, 2019), Vol. 70, pp. –.
  2. L. J. Heyderman and R. L. Stamps, Artificial ferroic systems: Novel functionality from structure, interactions and dynamics, J. Phys.: Condens. Matter 25, 363201 (2013).
  3. R. Sultana, A. K. Mondal, V. S. Bhat, K. Stenning, Y. Li, D. M. Arroo, A. Vasdev, M. R. McCarter, L. E. De Long, J. T. Hastings, J. C. Gartside, and M. B. Jungfleisch, Ice sculpting: An artificial spin ice tutorial on controlling microstate and geometry for magnonics and neuromorphic computing, J. Appl. Phys. 138, 061101 (2025).
  4. S. H. Skjærvø, C. H. Marrows, R. L. Stamps, and L. J. Heyderman, Advances in artificial spin ice, Nat. Rev. Phys. 2, 13 (2020).
  5. S. Gliga, E. Iacocca, and O. G. Heinonen, Dynamics of reconfigurable artificial spin ice: Toward magnonic functional materials, APL Mater. 8, 040911 (2020).
  6. E. Iacocca, S. Gliga, R. L. Stamps, and O. Heinonen, Reconfigurable wave band structure of an artificial square ice, Phys. Rev. B 93, 134420 (2016).
  7. M. B. Jungfleisch, W. Zhang, E. Iacocca, J. Sklenar, J. Ding, W. Jiang, S. Zhang, J. E. Pearson, V. Novosad, J. B. Ketterson, O. Heinonen, and A. Hoffmann, Dynamic response of an artificial square spin ice, Phys. Rev. B 93, 100401(R) (2016).
  8. E. Iacocca, S. Gliga, and O. G. Heinonen, Tailoring spin-wave channels in a reconfigurable artificial spin ice, Phys. Rev. Appl. 13, 044047 (2020).
  9. F. Montoncello, M. T. Kaffash, H. Carfagno, M. F. Doty, G. Gubbiotti, and M. B. Jungfleisch, A brillouin light scattering study of the spin-wave magnetic field dependence in a magnetic hybrid system made of an artificial spin-ice structure and a film underlayer, J. Appl. Phys. 133, 083901 (2023).
  10. V. S. Bhat, F. Heimbach, I. Stasinopoulos, and D. Grundler, Magnetization dynamics of topological defects and the spin solid in a kagome artificial spin ice, Phys. Rev. B 93, 140401(R) (2016).
  11. V. S. Bhat, S. Watanabe, K. Baumgaertl, A. Kleibert, M. A. W. Schoen, C. A. F. Vaz, and D. Grundler, Magnon modes of microstates and microwave-induced avalanche in kagome artificial spin ice with topological defects, Phys. Rev. Lett. 125, 117208 (2020).
  12. W. Bang, J. Sturm, R. Silvani, M. T. Kaffash, A. Hoffmann, J. B. Ketterson, F. Montoncello, and M. B. Jungfleisch, Influence of the vertex region on spin dynamics in artificial kagome spin ice, Phys. Rev. Appl. 14, 014079 (2020).
  13. T. Dion, W. Zhang, M. B. Jungfleisch, Y.-L. Wang, P. Schiffer, and A. Hoffmann, Tunable magnetization dynamics in artificial spin ice via shape anisotropy modification, Phys. Rev. B 100, 054433 (2019).
  14. V. S. Bhat, J. Sklenar, B. Farmer, J. Woods, J. T. Hastings, S. J. Lee, J. B. Ketterson, and L. E. De Long, Controlled magnetic reversal in permalloy films patterned into artificial quasicrystals, Phys. Rev. Lett. 111, 077201 (2013).
  15. V. S. Bhat and M. B. Jungfleisch, Dynamic fingerprint of controlled structural disorder in artificial spin lattices, arXiv:2506.07007.
  16. Y. Li, G. Gubbiotti, F. Casoli, F. J. T. Gonçalves, S. A. Morley, M. C. Rosamond, E. H. Linfield, C. H. Marrows, S. McVitie, and R. L. Stamps, Brillouin light scattering study of magnetic-element normal modes in a square artificial spin ice geometry, J. Phys. D 50, 015003 (2017).
  17. J. C. Gartside, K. D. Stenning, A. Vanstone, H. H. Holder, D. M. Arroo, T. Dion, F. Caravelli, H. Kurebayashi, and W. R. Branford, Reconfigurable training and reservoir computing in an artificial spin-vortex ice via spin-wave fingerprinting, Nat. Nanotechnol. 17, 460 (2022).
  18. X. Zhou, G.-L. Chua, N. Singh, and A. O. Adeyeye, Large area artificial spin ice and anti-spin ice Ni80Fe20 structures: Static and dynamic behavior, Adv. Funct. Mater. 26, 1616 (2016).
  19. S. Lendinez, M. T. Kaffash, O. G. Heinonen, S. Gliga, E. Iacocca, and M. B. Jungfleisch, Nonlinear multi-magnon scattering in artificial spin ice, Nat. Commun. 14, 720 (2023).
  20. M. T. Kaffash, S. Lendinez, and M. B. Jungfleisch, Nanomagnonics with artificial spin ice, Phys. Lett. A 402, 127364 (2021).
  21. S. Sahoo, A. May, A. van Den Berg, A. K. Mondal, S. Ladak, and A. Barman, Observation of coherent spin waves in a three-dimensional artificial spin ice structure, Nano Lett. 21, 4629 (2021).
  22. A. Talapatra, N. Singh, and A. O. Adeyeye, Magnetic tunability of permalloy artificial spin ice structures, Phys. Rev. Appl. 13, 014034 (2020).
  23. F. Montoncello, L. Giovannini, W. Bang, J. B. Ketterson, M. B. Jungfleisch, A. Hoffmann, B. W. Farmer, and L. E. De Long, Mutual influence between macrospin reversal order and spin-wave dynamics in isolated artificial spin-ice vertices, Phys. Rev. B 97, 014421 (2018).
  24. T. Dion, K. D. Stenning, A. Vanstone, H. H. Holder, R. Sultana, G. Alatteili, V. Martinez, M. T. Kaffash, T. Kimura, R. F. Oulton, W. R. Branford, H. Kurebayashi, E. Iacocca, M. B. Jungfleisch, and J. C. Gartside, Ultrastrong magnon-magnon coupling and chiral spin-texture control in a dipolar 3d multilayered artificial spin-vortex ice, Nat. Commun. 15, 4077 (2024).
  25. S. Lendinez, M. Taghipour Kaffash, and M. B. Jungfleisch, Observation of mode splitting in artificial spin ice: A comparative ferromagnetic resonance and brillouin light scattering study, Appl. Phys. Lett. 118, 162407 (2021).
  26. V. S. Bhat and M. B. Jungfleisch, Magnon signatures of multidimensional reconfigurations in multilayer square artificial spin ices, Appl. Phys. Lett. 126, 022406 (2025).
  27. M. T. Hossain, H. Chen, S. Bhatt, M. Taghipour Kaffash, J. Q. Xiao, J. Sklenar, and M. B. Jungfleisch, Broken intrinsic symmetry induced magnon-magnon coupling in synthetic ferrimagnets, Phys. Rev. Appl. 25, 044018 (2026).
  28. A. Vansteenkiste, J. Leliaert, M. Dvornik, J. Helsen, F. Garcia-Sanchez, and B. Van Waeyenberge, Mumax3 (2014). https://mumax.github.io/.
  29. J. R. Sandercock, Light scattering in solids, Light Scattering in Solids III, Springer Series in Topics in Applied Physics, edited by M. Cardona and G. Guntherodt (Springer-Verlag, Berlin, 1982), p. 173.
  30. P. Grünberg, R. Schreiber, Y. Pang, M. B. Brodsky, and H. Sowers, Layered magnetic structures: Evidence for antiferromagnetic coupling of Fe layers across Cr interlayers, Phys. Rev. Lett. 57, 2442 (1986).
  31. M. Belmeguenai, T. Martin, G. Woltersdorf, M. Maier, and G. Bayreuther, Frequency- and time-domain investigation of the dynamic properties of interlayer-exchange coupled Ni81Fe19/Ru/Ni81Fe19 thin films, Phys. Rev. B 76, 104414 (2007).
  32. M. Belmeguenai, T. Martin, G. Woltersdorf, G. Bayreuther, V. Baltz, A. K. Suszka, and B. J. Hickey, Microwave spectroscopy with vector network analyzer for interlayer exchange-coupled symmetrical and asymmetrical NiFe/Ru/NiFe, J. Phys. Condens. Matter. 20, 345206 (2008).
  33. X. M. Liu, H. T. Nguyen, J. Ding, M. G. Cottam, and A. O. Adeyeye, Interlayer coupling in Ni80Fe20/Ru/Ni80Fe20 multilayer films: Ferromagnetic resonance experiments and theory, Phys. Rev. B 90, 064428 (2014).
  34. P. A. Grünberg, Nobel lecture: From spin waves to giant magnetoresistance and beyond, Rev. Mod. Phys. 80, 1531 (2008).
  35. S. M. Rezende, C. Chesman, M. A. Lucena, A. Azevedo, F. M. de Aguiar, and S. S. P. Parkin, Studies of coupled metallic magnetic thin-film trilayers, J. Appl. Phys. 84, 958 (1998).
  36. Y. Li, G. Gubbiotti, F. Casoli, S. A. Morley, F. J. T. Gonçalves, M. C. Rosamond, E. H. Linfield, C. H. Marrows, S. McVitie, and R. L. Stamps, Thickness dependence of spin wave excitations in an artificial square spin ice-like geometry, J. Appl. Phys. 125, 220901 (2017), https://pubs.aip.org/aip/jap/article/121/10/103903/974035/Thickness-dependence-of-spin-wave-excitations-in.
  37. R. Negrello, F. Montoncello, M. T. Kaffash, M. B. Jungfleisch, and G. Gubbiotti, Dynamic coupling and spin-wave dispersions in a magnetic hybrid system made of an artificial spin-ice structure and an extended NiFe underlayer, APL Mater. 10, 091115 (2022).

Outline

Information

Phys. Rev. Applied 26, 034063– Published 25 September, 2026
  • Received 10 June 2026
  • Revised 25 July 2026
  • Accepted 29 July 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation