Skip to main content
SpringerLink
Log in

Interaction of a Magnetic Vortex with Magnetic Anisotropy Nonuniformity

  • ORDER, DISORDER, AND PHASE TRANSITION IN CONDENSED SYSTEM
  • Published:
Journal of Experimental and Theoretical Physics Aims and scope Submit manuscript

Abstract

The problem of propagation of a magnetic inhomogeneity in the form of a magnetic vortex near a defect simulated by a crystallite with uniaxial anisotropy has been solved theoretically. The defect (crystallite) is implanted into a homogeneous 2D ferromagnetic matrix. Apart from the anisotropy energy, the term responsible for the existence of a centrosymmetric potential is included into the total energy. For calculations, we have used the method of collective variables (Thiele equation). We have considered the variants of bidirectional and unidirectional anisotropy of the crystallite. Analysis of the equations of motion for different directions of the anisotropy axis of the implanted defect has revealed the variety in the behavior of the vortex core as a quasiparticle. The vortex core can be trapped by the defect with equilibrium position of the vortex at rest directly on the crystallite or during its motion at a certain distance from it. It is shown that for a small damping parameter and in the case when the defect anisotropy axis lies in the plane of the magnet, the vortex moves so as if its core experiences the action of the repulsive axially symmetric potential.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.
Fig. 9.

Similar content being viewed by others

REFERENCES

  1. D. A. Allwood, G. Xiong, C. C. Faulkner, D. Atkinson, D. Petit, and R. P. Cowburn, Science (Washington, DC, U. S.) 309, 1688 (2005).

    Article  ADS  Google Scholar 

  2. M. Hayashi, L. Thomas, R. Moriya, Ch. Rettner, and S. S. P. Parkin, Science (Washington, DC, U. S.) 320, 209 (2008).

    Article  ADS  Google Scholar 

  3. S. S. P. Parkin, M. Hayashi, and L. Thomas, Science (Washington, DC, U. S.) 320, 190 (2008).

    Article  ADS  Google Scholar 

  4. W. Kang, Y. Huang, Ch. Zheng, W. Lv, N. Lei, Y. Zhang, X. Zhang, Y. Zhou, and W. Zhao, Sci. Rep. 6, 23164 (2016).

    Article  ADS  Google Scholar 

  5. A. S. Mel’nikov, A. V. Samokhvalov, and V. L. Vadimov, JETP Lett. 102, 775 (2015).

    Article  ADS  Google Scholar 

  6. J. Kim and S.-B. Choe, J. Magn. 12, 113 (2007).

    Article  Google Scholar 

  7. A. Puzic, B. van Waeyenberge, K. W. Chou, P. Fischer, H. Stoll, G. Schutz, T. Tyliszczak, K. Rott, H. Bruckl, G. Reiss, I. Neudecker, Th. Haug, M. Buess, and C. H. Back, J. Appl. Phys. 97, 10E704 (2005).

  8. B. Pigeau, G. de Loubens, O. Klein, A. Riegler, F. Lochner, G. Schmidt, L. W. Molenkamp, V. S. Tiberkevich, and A. N. Slavin, Appl. Phys. Lett. 96, 132506 (2010).

    Article  ADS  Google Scholar 

  9. K. Yu. Guslienko, V. Novosad, Y. Otani, H. Shima, and K. Fukamichi, Phys. Rev. B 65, 024414 (2001).

    Article  ADS  Google Scholar 

  10. A. K. Zvezdin and K. A. Zvezdin, J. Low Temp. Phys. 36, 826 (2010).

    Article  Google Scholar 

  11. S. V. Stepanov, A. E. Ekomasov, A. K. Zvezdin, and E. G. Ekomasov, Phys. Solid State 60, 1055 (2018).

    Article  ADS  Google Scholar 

  12. V. A. Orlov, R. Yu. Rudenko, A. V. Kobyakov, A. V. Lukyanenko, P. D. Kim, V. S. Prokopenko, and I. N. Orlova, J. Exp. Theor. Phys. 126, 523 (2018).

    Article  ADS  Google Scholar 

  13. J. C. Martinez and M. B. A. Jalil, New J. Phys. 18, 033008 (2016).

    Article  ADS  Google Scholar 

  14. L. Gonzalez-Gomez, J. Castell-Queralt, N. Del-Valle, A. Sanchez, and C. Navau, Phys. Rev. B 100, 054440 (2019).

    Article  ADS  Google Scholar 

  15. X. Liang, G. Zhao, L. Shen, J. Xia, Li Zhao, X. Zhang, and Y. Zhou, Phys. Rev. B 100, 144439 (2019).

    Article  ADS  Google Scholar 

  16. X. Gong, H. Y. Yuan, and X. R. Wang, arXiv:1911.01245v1 [cond-mat.mes-hall] (2019).

  17. C. Navau, N. Del-Valle, and A. Sanchez, J. Magn. Magn. Mater. 465, 709 (2018).

    Article  ADS  Google Scholar 

  18. H. C. Choi, S.-Z. Lin, and J.-X. Zhu, Phys. Rev. B 93, 115112 (2016).

    Article  ADS  Google Scholar 

  19. J. Muller and A. Rosch, Phys. Rev. B 91, 054410 (2015).

    Article  ADS  Google Scholar 

  20. J. A. J. Burgess, J. E. Losby, and M. R. Freeman, J. Magn. Magn. Mater. 361, 140 (2014).

    Article  ADS  Google Scholar 

  21. D. Stosic, T. B. Ludermir, and M. V. Milosevic, Phys. Rev. B 96, 214403 (2017).

    Article  ADS  Google Scholar 

  22. D. Stosic, Numerical Simulations of Magnetic Skyrmions in Atomically-thin Ferromagnetic Films (Univ. Fed. Pernambuco, Recife, 2018).

    Google Scholar 

  23. J. Iwasaki, M. Mochizuki, and N. Nagaosa, Nat. Commun. 4, 1463 (2012).

    Article  ADS  Google Scholar 

  24. R. Brearton, M. W. Olszewski, S. Zhang, M. R. Eskildsen, C. Reichhardt, C. J. O. Reichhardt, G. van der Laan, and T. Hesjedal, MRS Adv. (2019). https://doi.org/10.1557/adv.2019.43

  25. W. Legrand, D. Maccariello, N. Reyren, K. Garcia, C. Moutafis, C. Moreau-Luchaire, S. Collin, K. Bouzehouane, V. Cros, and A. Fert, Nano Lett. 17, 2703 (2017).

    Article  ADS  Google Scholar 

  26. J.-V. Kim and M.-W. Yoo, Appl. Phys. Lett. 110, 132404 (2017).

    Article  ADS  Google Scholar 

  27. C. Reichhardt, D. Ray, and C. J. Olson Reichhardt, Phys. Rev. Lett. 114, 217202 (2015).

    Article  ADS  Google Scholar 

  28. K. Zeissler, S. Finizio, C. Barton, A. J. Huxtable, J. Massey, J. Raabe, A. V. Sadovnikov, S. A. Nikitov, R. Brearton, T. Hesjedal, G. van der Laan, M. C. Rosamond, E. H. Linfield, G. Burnell, and C. H. Marrows, Nat. Commun. 11, 428 (2020).

    Article  ADS  Google Scholar 

  29. J. Castell-Queralt, L. Gonzalez-Gomez, N. Del-Valle, A. Sanchez, and C. Navau, Nanoscale 11, 12589 (2019).

    Article  Google Scholar 

  30. A. Salimath, A. Abbout, A. Brataas, and A. Manchon, Phys. Rev. B 99, 104416 (2019).

    Article  ADS  Google Scholar 

  31. J. Iwasaki, M. Mochizuki, and N. Nagaosa, Nat. Nanotechnol. 8, 742 (2013).

    Article  ADS  Google Scholar 

  32. H. T. Fook, W. L. Gan, and W. S. Lew, Sci. Rep. 6, 21099 (2016).

    Article  ADS  Google Scholar 

  33. M. Rahm, J. Biberger, V. Umansky, and D. Weiss, J. Appl. Phys. 93, 7429 (2003).

    Article  ADS  Google Scholar 

  34. I. L. Fernandes, J. Bouaziz, S. Blugel, and S. Lounis, Sci. Rep. 9, 4395 (2018).

    Google Scholar 

  35. R. L. Compton and P. A. Crowell, Phys. Rev. Lett. 97, 137202 (2006).

    Article  ADS  Google Scholar 

  36. T. Y. Chen, M. J. Erickson, and P. A. Crowell, Phys. Rev. Lett. 109, 097202 (2012).

    Article  ADS  Google Scholar 

  37. C. Hanneken, New J. Phys. 18, 055009 (2016).

    Article  ADS  Google Scholar 

  38. A. Thiele, Phys. Rev. Lett. 30, 230 (1973).

    Article  ADS  Google Scholar 

  39. K. Yu. Guslienko, B. A. Ivanov, V. Novosad, Y. Otani, H. Shima, and K. Fukamichi, J. Appl. Phys. 91, 8037 (2002).

    Article  ADS  Google Scholar 

  40. P. D. Kim, V. A. Orlov, V. S. Prokopenko, S. S. Zamai, V. Ya. Prints, R. Yu. Rudenko, and T. V. Rudenko, Phys. Solid State 57, 30 (2015).

    Article  ADS  Google Scholar 

  41. D. Reitz, A. Ghosh, and O. Tchernyshyov, Phys. Rev. B 97, 054424 (2018).

    Article  ADS  Google Scholar 

  42. X. Zhang, J. Müller, J. Xia, M. Garst, X. Liu, and Y. Zhou, New J. Phys. 10, 065001 (2017).

    Article  Google Scholar 

  43. K. Yu. Guslienko, X. F. Han, D. J. Keavney, R. Divan, and S. D. Bader, Phys. Rev. Lett. 96, 067205 (2006).

    Article  ADS  Google Scholar 

  44. M. Wolf, U. K. Robler, and R. Schafer, J. Magn. Magn. Mater. 314, 105 (2007).

    Article  ADS  Google Scholar 

  45. W. Scholz, K. Yu. Guslienko, V. Novosad, D. Suess, T. Schrefl, R. W. Chantrell, and J. Fidler, J. Magn. Magn. Mater. 266, 155 (2003).

    Article  ADS  Google Scholar 

  46. V. A. Orlov and P. D. Kim, J. Sib. Fed. Univ. Math. Phys. 6, 86 (2013).

    Google Scholar 

  47. V. P. Kravchuk and D. D. Sheka, Phys. Solid State 49, 1923 (2007).

    Article  ADS  Google Scholar 

  48. N. A. Usov and S. E. Peschany, J. Magn. Magn. Mater. 118, L290 (1993).

    Article  ADS  Google Scholar 

  49. A. Aharoni, J. Appl. Phys. 68, 2892 (1990).

    Article  ADS  Google Scholar 

  50. A. Wachowiak, J. Wiebe, M. Bode, O. Pietzsch, M. Morgenstern, and R. Wiesendanger, Science (Washington, DC, U. S.) 298, 577 (2002).

    Article  ADS  Google Scholar 

  51. E. Feldtkeller and H. Thomas, Phys. Kond. Mater. 4, 8 (1965).

    Google Scholar 

Download references

Funding

This study was supported by the Russian Foundation for Basic Research (project no. 18-02-00161).

Author information

Authors and Affiliations

  1. Siberian Federal University, 660041, Krasnoyarsk, Russia

    V. A. Orlov & G. S. Patrin

  2. Kirensky Institute of Physics, Federal Research Center “Krasnoyarsk Scientific Center,” Siberian Branch, Russian Academy of Sciences, 660036, Krasnoyarsk, Russia

    V. A. Orlov & G. S. Patrin

  3. Astaf’ev Krasnoyarsk State Pedagogical University, 660049, Krasnoyarsk, Russia

    I. N. Orlova

Authors
  1. V. A. Orlov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. S. Patrin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. I. N. Orlova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. A. Orlov.

Additional information

Translated by N. Wadhwa

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Orlov, V.A., Patrin, G.S. & Orlova, I.N. Interaction of a Magnetic Vortex with Magnetic Anisotropy Nonuniformity. J. Exp. Theor. Phys. 131, 589–599 (2020). https://doi.org/10.1134/S1063776120090071

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063776120090071

Search

Navigation