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Effect of magnetic domain-wall curvature on velocity in the creep regime

Adriano Di Pietro*, Alessandro Magni, Gianfranco Durin, and Michaela Kuepferling

Giovanni Carlotti and Marco Madami

Cristopher Marrows, Alexandra Huxtable, and Bryan Hickey

Silvia Tacchi

Emily Darwin

  • *Contact author: a.dipietro@inrim.it
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Phys. Rev. Applied 24, 024044 – Published 19 August, 2025

DOI: https://doi.org/10.1103/fh8q-7m45

Abstract

We study the effect of magnetic domain wall curvature on its dynamics in the creep regime in systems displaying Dzyaloshinskii-Moriya interaction (DMI). We first derive an extended creep model that is able to account for the finite curvature effect in magnetic bubble domain expansion. We then discuss the relative importance of this effect and discuss its dependence on the main magnetic and disorder parameters. We show this effect can be easily measured in Pt/Co multilayer samples, reporting a strong velocity reduction below a sample-dependent threshold value of the magnetic bubble radius. We finally show, both theoretically and experimentally, how the radius of magnetic bubbles can have a strong impact on the reproducibility of DMI measurements.

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References (40)

  1. P. J. Metaxas, J. P. Jamet, A. Mougin, M. Cormier, J. Ferré, V. Baltz, B. Rodmacq, B. Dieny, and R. L. Stamps, Creep and flow regimes of magnetic domain-wall motion in ultrathin Pt/Co/Pt films with perpendicular anisotropy, Phys. Rev. Lett. 99, 217208 (2007).
  2. F. Cayssol, D. Ravelosona, C. Chappert, J. Ferré, and J. P. Jamet, Domain wall creep in magnetic wires, Phys. Rev. Lett. 92, 107202 (2004).
  3. L. Herrera Diez, F. García-Sánchez, J.-P. Adam, T. Devolder, S. Eimer, M. S. El Hadri, A. Lamperti, R. Mantovan, B. Ocker, and D. Ravelosona, Controlling magnetic domain wall motion in the creep regime in He+-irradiated CoFeB/MgO films with perpendicular anisotropy, Appl. Phys. Lett. 107, 032401 (2015).
  4. E. E. Ferrero, L. Foini, T. Giamarchi, A. B. Kolton, and A. Rosso, Creep motion of elastic interfaces driven in a disordered landscape, Annu. Rev. Condens. Matter Phys. 12, 111 (2021).
  5. I. Dzyaloshinsky, A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics, J. Phys. Chem. Solids 4, 241 (1958).
  6. T. Moriya, Anisotropic superexchange interaction and weak ferromagnetism, Phys. Rev. 120, 91 (1960).
  7. A. Fert, N. Reyren, and V. Cros, Magnetic skyrmions: advances in physics and potential applications, Nat. Rev. Mater. 2, 1 (2017).
  8. A. Fert, V. Cros, and J. Sampaio, Skyrmions on the track, Nat. Nanotechnol. 8, 152 (2013).
  9. G. Finocchio, F. Büttner, R. Tomasello, M. Carpentieri, and M. Kläui, Magnetic skyrmions: from fundamental to applications, J. Phys. D:Appl. Phys. 49, 423001 (2016).
  10. A. Bogdanov, and A. Hubert, Thermodynamically stable magnetic vortex states in magnetic crystals, J. Magn. Magn. Mater. 138, 255 (1994).
  11. A. Thiaville, S. Rohart, É. Jué, V. Cros, and A. Fert, Dynamics of Dzyaloshinskii domain walls in ultrathin magnetic films, Europhys. Lett. 100, 57002 (2012).
  12. A. Magni et al., Key points in the determination of the interfacial Dzyaloshinskii-Moriya interaction from asymmetric bubble domain expansion, IEEE Trans. Magn. 58, 1 (2022).
  13. M. Küpferling, A. Casiraghi, G. Soares, G. Durin, F. García-Sánchez, L. Chen, C. Back, C. Marrows, S. Tacchi, and G. Carlotti, Measuring interfacial Dzyaloshinskii-Moriya interaction in ultrathin magnetic films, Rev. Mod. Phys. 95, 015003 (2023).
  14. M. Vaňatka, J.-C. Rojas-Sánchez, J. Vogel, M. Bonfim, M. Belmeguenai, Y. Roussigné, A. Stashkevich, A. Thiaville, and S. Pizzini, Velocity asymmetry of Dzyaloshinskii domain walls in the creep and flow regimes, J. Phys.: Condens. Matter 27, 326002 (2015).
  15. D. M. F. Hartmann, R. A. Duine, M. J. Meijer, H. J. M. Swagten, and R. Lavrijsen, Creep of chiral domain walls, Phys. Rev. B 100, 094417 (2019).
  16. S.-G. Je, D.-H. Kim, S.-C. Yoo, B.-C. Min, K.-J. Lee, and S.-B. Choe, Asymmetric magnetic domain-wall motion by the Dzyaloshinskii-Moriya interaction, Phys. Rev. B 88, 214401 (2013).
  17. T. Pakam, A. A. Adjanoh, S. D. M. Afenyiveh, J. Vogel, S. Pizzini, and L. Ranno, Anisotropic creep velocity of Dzyaloshinskii domain walls, Appl. Phys. Lett. 124, 092403 (2024).
  18. J. P. Garcia, A. Fassatoui, M. Bonfim, J. Vogel, A. Thiaville, and S. Pizzini, Magnetic domain wall dynamics in the precessional regime: Influence of the Dzyaloshinskii-Moriya interaction, Phys. Rev. B 104, 014405 (2021).
  19. K.-W. Moon, J.-C. Lee, S.-G. Je, K.-S. Lee, K.-H. Shin, and S.-B. Choe, Long-range domain wall tension in Pt/Co/Pt films with perpendicular magnetic anisotropy, Appl. Phys. Express 4, 043004 (2011).
  20. Y. Zhang, X. Zhang, N. Vernier, Z. Zhang, G. Agnus, J.-R. Coudevylle, X. Lin, Y. Zhang, Y.-G. Zhang, W. Zhao, and D. Ravelosona, Domain-wall motion driven by Laplace pressure in Co-Fe-B/MgO nanodots with perpendicular anisotropy, Phys. Rev. Appl. 9, 064027 (2018).
  21. X. Zhang, N. Vernier, W. Zhao, H. Yu, L. Vila, Y. Zhang, and D. Ravelosona, Direct observation of domain-wall surface tension by deflating or inflating a magnetic bubble, Phys. Rev. Appl. 9, 024032 (2018).
  22. N. B. Caballero, E. E. Ferrero, A. B. Kolton, J. Curiale, V. Jeudy, and S. Bustingorry, Magnetic domain wall creep and depinning: A scalar field model approach, Phys. Rev. E 97, 062122 (2018).
  23. S. Lemerle, J. Ferré, C. Chappert, V. Mathet, T. Giamarchi, and P. Le Doussal, Domain wall creep in an Ising ultrathin magnetic film, Phys. Rev. Lett. 80, 849 (1998).
  24. P. Chauve, T. Giamarchi, and P. Le Doussal, Creep and depinning in disordered media, Phys. Rev. B 62, 6241 (2000).
  25. T. A. Moore, I. Miron, G. Gaudin, G. Serret, S. Auffret, B. Rodmacq, A. Schuhl, S. Pizzini, J. Vogel, and M. Bonfim, High domain wall velocities induced by current in ultrathin Pt/Co/AlOx wires with perpendicular magnetic anisotropy, Appl. Phys. Lett. 93, 262504 (2008).
  26. E. Jué, A. Thiaville, S. Pizzini, J. Miltat, J. Sampaio, L. Buda-Prejbeanu, S. Rohart, J. Vogel, M. Bonfim, O. Boulle et al., Domain wall dynamics in ultrathin Pt/Co/AlOx microstrips under large combined magnetic fields, Phys. Rev. B 93, 014403 (2016).
  27. G. Blatter, M. V. Feigel’man, V. B. Geshkenbein, A. I. Larkin, and V. M. Vinokur, Vortices in high-temperature superconductors, Rev. Mod. Phys. 66, 1125 (1994).
  28. A.-L. Barabási, and H. E. Stanley, Fractal Concepts in Surface Growth (Cambridge University Press, Cambridge, United Kingdom, 1995).
  29. H. Ji, and M. O. Robbins, Transition from compact to self-similar growth in disordered systems: Fluid invasion and magnetic-domain growth, Phys. Rev. A 44, 2538 (1991).
  30. J. Vandermeulen, S. Nasseri, B. Van de Wiele, G. Durin, B. Van Waeyenberge, and L. Dupré, Comparison between collective coordinate models for domain wall motion in PMA nanostrips in the presence of the Dzyaloshinskii-Moriya interaction, J. Magn. Magn. Mater. 449, 337 (2018).
  31. S. Moretti, Micromagnetic study of magnetic domain wall motion: thermal effects and spin torques, Ph.D. thesis, Ediciones Universidad de Salamanca, 2017.
  32. M.-C. Ciornei, J. M. Rubí, and J.-E. Wegrowe, Magnetization dynamics in the inertial regime: Nutation predicted at short time scales, Phys. Rev. B 83, 020410 (2011).
  33. Spin Dynamics in Confined Magnetic Structures III (Springer Berlin Heidelberg, Berlin, Germany, 2006).
  34. A. Aharoni, Demagnetizing factors for rectangular ferromagnetic prisms, J. Appl. Phys. 83, 3432 (1998).
  35. https://zenodo.org/records/15805564.
  36. I. S. Gradštejn, J. M. Ryžik, A. Jeffrey, D. Zwillinger, and I. S. Gradštejn, Table of Integrals, Series and Products (Elsevier Acad. Press, Amsterdam, 2009), 7th ed.
  37. M. Kardar, and D. R. Nelson, Commensurate-incommensurate transitions with quenched random impurities, Phys. Rev. Lett. 55, 1157 (1985).
  38. A. Larkin, and Y. N. Ovchinnikov, Pinning in type II superconductors, J. Low Temp. Phys. 34, 409 (1979).
  39. A. B. Kolton, A. Rosso, and T. Giamarchi, Creep motion of an elastic string in a random potential, Phys. Rev. Lett. 94, 047002 (2005).
  40. I. Culjak, D. Abram, T. Pribanic, H. Dzapo, and M. Cifrek, in 2012 Proceedings of the 35th International Convention MIPRO (IEEE, Opatija, Croatia, 2012), p. 1725.

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Phys. Rev. Applied 24, 024044– Published 19 August, 2025
  • Received 14 March 2025
  • Revised 18 June 2025
  • Accepted 30 June 2025
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