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Spin wave freezing in Re/Co/Pt multilayers

Jan Kisielewski1,*, Kilian Lenz2, Pawel Gruszecki3, Ryszard Gieniusz1, Urszula Guzowska1, Marek Kisielewski1, Artem Lynnyk4, Aleksiej Pietruczik4, Andrzej Wawro4 et al.

Andrzej Maziewski1

  • *Contact author: jankis@uwb.edu.pl
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Phys. Rev. B 114, 134406 – Published 8 September, 2026

DOI: https://doi.org/10.1103/grf5-33qc

Abstract

The phenomenon of spin wave (SW) freezing occurs in the Damon-Eshbach mode in thin film magnetic systems, when SW phase and group velocities both go to zero, and the wave ceases to oscillate and move, preserving its shape as a domain structure pattern. This effect is related to the spin reorientation transition, where the magnetization configuration changes between the homogeneous in-plane state and domain structure with the out-of-plane magnetization component state. Here we study the SW freezing effect in [Re/Co/Pt]20 magnetic multilayers, induced by varying the in-plane external magnetic field. The studies were performed on nanostructures with the quality factor Q (ratio of uniaxial anisotropy to demagnetization energies) greater and smaller than one. Domain structures with an out-of-plane magnetization component were observed in these multilayers. The critical field, visible as the saturation field Hs|| in the parallel static magnetization curve measured by superconducting quantum interference device (SQUID), is also manifested in the field-dependent vector-network-analyzer ferromagnetic resonance (VNA-FMR) experiment, which measures the homogeneous magnetization oscillations. Brillouin Light Scattering (BLS) spectra, recorded for several values of wave vectors and several field values, probed the field-evolution of the dispersion relation. Micromagnetic simulations allow one to obtain a full dispersion, in good agreement with VNA-FMR and BLS results. Around Hs|| the simulated dispersion relations approach the conditions for SW freezing. Below Hs|| low- and high-frequency VNA-FMR modes are related to magnetization oscillations inside domain walls and within domains, respectively. The experimental results of static and dynamic behavior, together with micromagnetic simulations, create an overall consistent picture of the investigated multilayers.

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References (37)

  1. G. Leaf, H. Kaper, M. Yan, V. Novosad, P. Vavassori, R. E. Camley, and M. Grimsditch, Dynamic origin of stripe domains, Phys. Rev. Lett. 96, 017201 (2006).
  2. J. Kisielewski, P. Gruszecki, M. Krawczyk, V. Zablotskii, and A. Maziewski, Between waves and patterns: Spin wave freezing in films with Dzyaloshinskii-Moriya interaction, Phys. Rev. B 107, 134416 (2023).
  3. P. Contreras-Gallardo, J. Jiménez-Bustamante, N. Vidal-Silva, F. Brevis, J. W. González, O. Hellwig, J. Lindner, and R. A. Gallardo, Spin-wave softening and the emergence of stripe domains in synthetic antiferromagnetic multilayers, Phys. Rev. B 112, 224435 (2025).
  4. M. Cepeda-Arancibia, F. Brevis, S. J. R. Holt, D. Cortés-Ortuño, H. Fangohr, and P. Landeros, Micromagnetics of conical-helix textures in thin films with different kinds of Dzyaloshinskii-Moriya interactions, npj Comput. Mater. 12, 55 (2026).
  5. R. Battistelli, L. Körber, K. Litzius, M. Grelier, K. P. Joy, M. Schneider, S. Wittrock, D. Metternich, T. Karaman, L.-M. Kern, C. Klose, S. Finizio, J. Fuchs, C. M. Günther, T. A. Butcher, K. Prokeš, R. Boltje, M. Patra, S. Wintz, M. Weigand, et al., A fluctuation-free pathway for a topological magnetic phase transition, arXiv:2512.22947.
  6. K. Sobucki and P. Gruszecki, Temporal magnetic interfaces reveal damping-induced spin-wave amplification near the stripe-domain transition in ultrathin films with DMI, npj Comput. Mater. (to be published).
  7. N. Leśniewski, Y. Dadoenkova, F. F. L. Bentivegna, and P. Gruszecki, Perpendicular magnetic anisotropy in thin films enables extraordinary spin-wave phenomena: Anti-Larmor precession, negative reflection and refraction, multireflection and multirefraction, ACS Appl. Mater. Interfaces 18, 10539 (2026).
  8. K. Szulc, S. Tacchi, A. Hierro-Rodríguez, J. Díaz, P. Gruszecki, P. Graczyk, C. Quirós, D. Markó, J. I. Martín, M. Vélez, D. S. Schmool, G. Carlotti, M. Krawczyk, and L. M. Álvarez Prado, Reconfigurable magnonic crystals based on imprinted magnetization textures in hard and soft dipolar-coupled bilayers, ACS Nano 16, 14168 (2022).
  9. C. Banerjee, P. Gruszecki, J. W. Klos, O. Hellwig, M. Krawczyk, and A. Barman, Magnonic band structure in a Co/Pd stripe domain system investigated by Brillouin light scattering and micromagnetic simulations, Phys. Rev. B 96, 024421 (2017).
  10. Z.-X. Li, X. Guang Wang, D. Wei Wang, Y. Zhuang Nie, W. Tang, and G. Hua Guo, Reconfigurable magnonic crystal consisting of periodically distributed domain walls in a nanostrip, J. Magn. Magn. Mater. 388, 10 (2015).
  11. M. Grassi, M. Geilen, K. A. Oukaci, Y. Henry, D. Lacour, D. Stoeffler, M. Hehn, P. Pirro, and M. Bailleul, Higgs and Goldstone spin-wave modes in striped magnetic texture, Phys. Rev. B 105, 094444 (2022).
  12. A. K. Dhiman, N. Leśniewski, R. Gieniusz, J. Kisielewski, P. Mazalski, Z. Kurant, M. Matczak, F. Stobiecki, M. Krawczyk, A. Lynnyk, A. Maziewski, and P. Gruszecki, Reconfigurable magnonic crystals: Spin wave propagation in Pt/Co multilayer in saturated and stripe domain phase, APL Mater. 12, 111106 (2024).
  13. R. Allenspach and A. Bischof, Magnetization direction switching in Fe/Cu(100) epitaxial films: Temperature and thickness dependence, Phys. Rev. Lett. 69, 3385 (1992).
  14. M. Kisielewski, A. Maziewski, M. Tekielak, A. Wawro, and L. T. Baczewski, New possibilities for tuning ultrathin cobalt film magnetic properties by a noble metal overlayer, Phys. Rev. Lett. 89, 087203 (2002).
  15. A. Maziewski, J. Fassbender, J. Kisielewski, M. Kisielewski, Z. Kurant, P. Mazalski, F. Stobiecki, A. Stupakiewicz, I. Sveklo, M. Tekielak, A. Wawro, and V. Zablotskii, Magnetization states and magnetization processes in nanostructures: From a single layer to multilayers, physica status solidi (a) 211, 1005 (2014).
  16. A. Belabbes, G. Bihlmayer, F. Bechstedt, S. Blügel, and A. Manchon, Hund's rule-driven Dzyaloshinskii-Moriya interaction at 3d−5d interfaces, Phys. Rev. Lett. 117, 247202 (2016).
  17. A. Dhiman, M. Matczak, R. Gieniusz, I. Sveklo, Z. Kurant, U. Guzowska, F. Stobiecki, and A. Maziewski, Thickness dependence of interfacial Dzyaloshinskii-Moriya interaction, magnetic anisotropy and spin waves damping in Pt/Co/Ir and Ir/Co/Pt trilayers, J. Magn. Magn. Mater. 519, 167485 (2021).
  18. S. Woo, K. Litzius, B. Krüger, M. Y. Im, L. Caretta, K. Richter, M. Mann, A. Krone, R. M. Reeve, M. Weigand, P. Agrawal, I. Lemesh, M. A. Mawass, P. Fischer, M. Kläui, and G. S. D. Beach, Observation of room-temperature magnetic skyrmions and their current-driven dynamics in ultrathin metallic ferromagnets, Nat. Mater. 15, 501 (2016).
  19. P. Jadaun, L. Register, and S. Banerjee, The microscopic origin of DMI in magnetic bilayers and prediction of giant DMI in new bilayers, npj Comput Mater 6, 88 (2020).
  20. R. S. A. Hubert, Magnetic Domains: The Analysis of Magnetic Microstructures (Springer, Berlin, Heidelberg, 1998).
  21. N. Vukadinovic, O. Vacus, M. Labrune, O. Acher, and D. Pain, Magnetic excitations in a weak-stripe-domain structure: A 2D dynamic micromagnetic approach, Phys. Rev. Lett. 85, 2817 (2000).
  22. N. Vukadinovic, H. L. Gall, J. Gehanno, B. Y. V., A. Marty, Y. Samson, and B. Gilles, Magnetization dynamics and relaxation in epitaxial FePd thin films with a stripe domain structure, Eur. Phys. J. B 13, 445 (2000).
  23. Y. Talbi, P. Djemia, Y. Roussigné, J. BenYoussef, N. Vukadinovic, and M. Labrune, Magnetic excitation in weak stripe domains: Ferromagnetic resonance and Brillouin light sattering studies, J. Phys.: Conf. Ser. 200, 072107 (2010).
  24. I. S. Camara, S. Tacchi, L.-C. Garnier, M. Eddrief, F. Fortuna, G. Carlotti, and M. Marangolo, Magnetization dynamics of weak stripe domains in Fe-N thin films: A multi-technique complementary approach, J. Phys.: Condens. Matter 29, 465803 (2017).
  25. R. Gieniusz, P. Gruszecki, J. Kisielewski, A. Dhiman, M. Matczak, Z. Kurant, I. Sveklo, U. Guzowska, M. Tekielak, M. Krawczyk, F. Stobiecki, and A. Maziewski, Spin wave frequency hysteresis in Ir/Co/Pt multilayers with Dzyaloshinskii-Moriya interaction, Phys. Rev. B 110, 184410 (2024).
  26. G. Gubbiotti, G. Carlotti, S. Tacchi, M. Madami, T. Ono, T. Koyama, D. Chiba, F. Casoli, and M. G. Pini, Spin waves in perpendicularly magnetized Co/Ni(111) multilayers in the presence of magnetic domains, Phys. Rev. B 86, 014401 (2012).
  27. S. Tacchi, S. Fin, G. Carlotti, G. Gubbiotti, M. Madami, M. Barturen, M. Marangolo, M. Eddrief, D. Bisero, A. Rettori, and M. G. Pini, Rotatable magnetic anisotropy in a Fe0.8Ga0.2 thin film with stripe domains: Dynamics versus statics, Phys. Rev. B 89, 024411 (2014).
  28. S. K. Jena, J. Kisielewski, U. Guzowska, A. K. Dhiman, R. Gieniusz, A. Lynnyk, P. Dłużewski, R. Minikayev, A. Pietruczik, A. Maziewski, and A. Wawro, Field angular dependence of stable remnant bubble lattice formation in Re/Co/Pt multilayers, Appl. Surf. Sci. 731, 166460 (2026).
  29. S. K. Jena, K. Lenz, M. Zelent, M. Moalic, A. Lynnyk, A. Pietruczik, P. Aleszkiewicz, E. Milińska, J. Lindner, and A. Wawro, Angle-dependent resonant dynamics of stripes and skyrmions in Re/Co/Pt multilayers, Phys. Rev. B 113, 214403 (2026).
  30. 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).
  31. A. Bonda, L. Uba, S. Uba, A. Wawro, Z. Kurant, and A. Maziewski, Enhanced spin pumping in asymmetric Co/Re/Co trilayers with antiferromagnetic coupling and mixed magnetic anisotropy, Phys. Rev. B 113, 184414 (2026).
  32. A. Kumar Dhiman, A. Fakhredine, R. Gieniusz, Z. Kurant, I. Sveklo, P. Dłużewski, W. Dobrogowski, S. Jena, A. Pietruczik, C. Autieri, A. Wawro, and A. Maziewski, Evolution of static and dynamic magnetic properties of Re/Co/Pt and Pt/Co/Re trilayers with enhanced Dzyaloshinskii-Moriya interaction, Appl. Surf. Sci. 679, 161151 (2025).
  33. M. T. Johnson, P. J. H. Bloemen, F. J. A. den Broeder, and J. J. de Vries, Magnetic anisotropy in metallic multilayers, Rep. Prog. Phys. 59, 1409 (1996).
  34. G. G. Scott, Gyromagnetic ratios of the iron-nickel alloys, Phys. Rev. 103, 561 (1956).
  35. A. Fakhredine, A. Wawro, and C. Autieri, Huge Dzyaloshinskii-Moriya interactions in Pt/Co/Re thin films, J. Appl. Phys. 135, 035303 (2024).
  36. W. Legrand, J.-Y. Chauleau, D. Maccariello, N. Reyren, S. Collin, K. Bouzehouane, N. Jaouen, V. Cros, and A. Fert, Hybrid chiral domain walls and skyrmions in magnetic multilayers, Sci. Adv. 4, eaat0415 (2018).
  37. S. A. Montoya, S. Couture, J. J. Chess, J. C. T. Lee, N. Kent, M.-Y. Im, S. D. Kevan, P. Fischer, B. J. McMorran, S. Roy, V. Lomakin, and E. E. Fullerton, Resonant properties of dipole skyrmions in amorphous Fe/Gd multilayers, Phys. Rev. B 95, 224405 (2017).

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Phys. Rev. B 114, 134406– Published 8 September, 2026
  • Received 31 March 2026
  • Revised 9 July 2026
  • Accepted 4 August 2026
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