[go: up one dir, main page]
Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Soliton-pair dynamics in patterned ferromagnetic ellipses

Nature Physics volume 1, pages 172–176 (2005)Cite this article

Abstract

Confinement alters the energy landscape of nanoscale magnets, leading to the appearance of unusual magnetic states, such as vortices, for example. Many basic questions concerning dynamical and interaction effects remain unanswered, and nanomagnets are convenient model systems for studying these fundamental physical phenomena. A single vortex in restricted geometry, also known as a non-localized soliton, possesses a characteristic translational excitation mode that corresponds to spiral-like motion of the vortex core around its equilibrium position. Here, we investigate, by a microwave reflection technique, the dynamics of magnetic soliton pairs confined in lithographically defined, ferromagnetic Permalloy ellipses. Through a comparison with micromagnetic simulations, the observed strong resonances in the subgigahertz frequency range can be assigned to the translational modes of vortex pairs with parallel or antiparallel core polarizations. Vortex polarizations play a negligible role in the static interaction between two vortices, but their effect dominates the dynamics.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on SpringerLink
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Figure 1: MFM and simulations of the two-vortex remanent states.
Figure 2: Experimentally measured vortex-pair resonance frequencies.
Figure 3: Diagrams of the magnetization configurations and dynamic modes for two magnetic vortices confined in an ellipse.
Figure 4: Micromagnetic simulation results showing the excitation frequencies as a function of H.

Similar content being viewed by others

References

  1. Russell, J. S. in Report of the Fourteenth Meeting of the British Association for the Advancement of Science 311–390 (Murray, London, 1844).

    Google Scholar 

  2. Manton, N. & Sutcliffe, P. Topological Solitons (Cambridge Univ. Press, Cambridge, 2004).

    Book  Google Scholar 

  3. Khaykovich, L. et al. Formation of a matter-wave bright soliton. Science 296, 1290–1293 (2002).

    Article  ADS  Google Scholar 

  4. Strecker, K. E., Partridge, G. B., Truscott, A. G. & Hulet, R. G. Formation and propagation of matter-wave soliton trains. Nature 417, 150–153 (2002).

    Article  ADS  Google Scholar 

  5. Nakazawa, M., Yamada, E. & Kubota, H. Coexistence of self-induced transparency soliton and nonlinear Schrödinger soliton. Phys. Rev. Lett. 66, 2625–2628 (1991).

    Article  ADS  Google Scholar 

  6. Matthews, M. R. et al. Vortices in a Bose-Einstein condensate. Phys. Rev. Lett. 83, 2498–2501 (1999).

    Article  ADS  Google Scholar 

  7. Lamb, H. Hydrodynamics (Dover, New York, 1945).

    MATH  Google Scholar 

  8. Kosevich, A. M., Ivanov, B. A. & Kovalev, A. S. Magnetic solitons. Phys. Rep. 194, 117–238 (1990).

    Article  ADS  Google Scholar 

  9. Saitoh, E., Miyajima, H., Yamaoka, T. & Tatara, G. Current-induced resonance and mass determination of a single magnetic domain wall. Nature 432, 203–206 (2004).

    Article  ADS  Google Scholar 

  10. Argyle, B. E., Terrenzio, E. & Slonczewski, J. C. Magnetic vortex dynamics using the optical Cotton-Mouton effect. Phys. Rev. Lett. 53, 190–193 (1984).

    Article  ADS  Google Scholar 

  11. Shinjo, T., Okuno, T., Hassdorf, R., Shigeto, K. & Ono, T. Magnetic vortex core observation in circular dots of Permalloy. Science 289, 930–932 (2000).

    Article  ADS  Google Scholar 

  12. Wachowiak, A. et al. Direct observation of internal spin structure of magnetic vortex cores. Science 298, 577–580 (2002).

    Article  ADS  Google Scholar 

  13. Guslienko, K. Yu., Novosad, V., Otani, Y., Shima, H. & Fukamichi, K. Magnetization reversal due to vortex nucleation, displacement, and annihilation in submicron ferromagnetic dot arrays. Phys. Rev. B 65, 024414 (2002).

    Article  ADS  Google Scholar 

  14. Cowburn, R. P., Koltsov, D. K., Adeyeye, A. O., Welland, M. E. & Tricker, D. M. Single-domain circular nanomagnets. Phys. Rev. Lett. 83, 1042–1045 (1999).

    Article  ADS  Google Scholar 

  15. Thiele, A. A. Steady-state motion of magnetic domains. Phys. Rev. Lett. 30, 230–233 (1973).

    Article  ADS  Google Scholar 

  16. Huber, D. L. Dynamics of spin vortices in two-dimensional planar magnets. Phys. Rev. B 26, 3758 (1982).

    Article  ADS  Google Scholar 

  17. Guslienko, K. Yu. et al. Eigenfrequencies of vortex state excitations in magnetic submicron-size disks. J. Appl. Phys. 91, 8037–8039 (2002).

    Article  ADS  Google Scholar 

  18. Usov, N. A. & Kurkina, L. G. Magnetodynamics of vortex in thin cylindrical platelet. J. Magn. Magn. Mater. 242, 1005–1008 (2002).

    Article  ADS  Google Scholar 

  19. Ivanov, B. A. & Zaspel, C. E. High frequency modes in vortex-state nanomagnets. Phys. Rev. Lett. 94, 027205 (2005).

    Article  ADS  Google Scholar 

  20. Park, J. P., Eames, P., Engebretson, D. M., Berezovsky, J. & Crowell, P. A. Imaging of spin dynamics in closure domain and vortex structures. Phys. Rev. B 67, 020403 (2003).

    Article  ADS  Google Scholar 

  21. Buess, M. et al. Fourier transform imaging of spin vortex eigenmodes. Phys. Rev. Lett. 93, 077207 (2004).

    Article  ADS  Google Scholar 

  22. Zaspel, C. E., Ivanov, B. A., Park, J. P. & Crowell, P. A. Excitations in vortex-state Permalloy dots. Phys. Rev. B 50, 24427 (2005).

    Article  Google Scholar 

  23. Puzic, A. et al. Spatially resolved ferromagnetic resonance: Imaging of ferromagnetic eigenmodes. J. Appl. Phys. 97, 10E704 (2005).

    Article  Google Scholar 

  24. Choe, S. B. et al. Vortex core-driven magnetization dynamics. Science 304, 420–422 (2004).

    Article  ADS  Google Scholar 

  25. Novosad, V. et al. Spin excitations of magnetic vortices in ferromagnetic nanodots. Phys. Rev. B 66, 052407 (2002).

    Article  ADS  Google Scholar 

  26. Giovannini, L. et al. Spin excitations of nanometric cylindrical dots in vortex and saturated magnetic states. Phys. Rev. B 70, 172404 (2004).

    Article  ADS  Google Scholar 

  27. Hillebrands, B. & Ounadjela, K. Spin Dynamics in Confined Magnetic Structures I (Topics in Applied Physics, Vol. 83, Springer, Berlin, 2002).

    Book  Google Scholar 

  28. Voelkel, A. R., Mertens, F. G., Bishop, A. R. & Wysin, G. M. Motion of vortex pairs in the ferromagnetic and antiferromagnetic Heisenberg model. Phys. Rev. B 43, 5992–6005 (1991).

    Article  ADS  Google Scholar 

  29. Voelkel, A. R., Wysin, G. M., Mertens, F. G., Bishop, A. R. & Schnitzer, H. J. Collective-variable approach to the dynamics of nonlinear magnetic excitations with application to vortices. Phys. Rev. B 50, 12711–12720 (1994).

    Article  ADS  Google Scholar 

  30. Kovalev, A. S., Komineas, S. & Mertens, F. G. Scattering of vortex pairs in 2d easy-plane ferromagnets. Eur. Phys. J. B 25, 89–100 (2002).

    ADS  Google Scholar 

  31. Guslienko, K. Yu., Buchanan, K. S., Bader, S. D. & Novosad, V. Dynamics of coupled vortices in layered magnetic nanodots. Appl. Phys. Lett. 86, 223112 (2005).

    Article  ADS  Google Scholar 

  32. Shibata, J. & Otani, Y. Magnetic vortex dynamics in a two-dimensional square lattice of ferromagnetic nanodisks. Phys. Rev. B 70, 12404 (2004).

    Article  ADS  Google Scholar 

  33. Usov, N. A., Chang, C. R. & Wei, Z. H. Buckling instability in thin soft elliptical particles. Phys. Rev. B 66, 184431 (2002).

    Article  ADS  Google Scholar 

  34. Vavassori, P. et al. Magnetization reversal via single and double vortex states in submicron Permalloy ellipses. Phys. Rev. B 69, 214404 (2004).

    Article  ADS  Google Scholar 

  35. Novosad, V. et al. Magnetic vortex resonance in patterned ferromagnetic dots. Phys. Rev. B 72, 024455 (2005).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We thank Y. Otani and J. Pearson for stimulating discussions and R. Divan for lithography support. This work was supported by the US Department of Energy, Basic Energy Sciences, Material Sciences under Contract No. W-31-109-ENG-38. K.S.B. thanks NSERC of Canada for a fellowship. P.E.R. acknowledges support from the Swedish Research Council and Swedish Foundation for Strategic Research.

Author information

Authors and Affiliations

  1. Materials Science Division and Center for Nanoscale Materials, Argonne National Laboratory, Argonne, Illinois, 60439, USA

    Kristen S. Buchanan, Pierre E. Roy, Marcos Grimsditch, Frank Y. Fradin, Konstantin Yu. Guslienko, Sam D. Bader & Valentyn Novosad

  2. Department of Engineering Science, Uppsala University, Box 534, SE-751 21, Uppsala, Sweden

    Pierre E. Roy

Authors
  1. Kristen S. Buchanan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pierre E. Roy
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Marcos Grimsditch
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Frank Y. Fradin
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Konstantin Yu. Guslienko
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Sam D. Bader
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Valentyn Novosad
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Valentyn Novosad.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Rights and permissions

Reprints and permissions

About this article

Cite this article

Buchanan, K., Roy, P., Grimsditch, M. et al. Soliton-pair dynamics in patterned ferromagnetic ellipses. Nature Phys 1, 172–176 (2005). https://doi.org/10.1038/nphys173

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nphys173

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing