Skip to main content
SpringerLink
Log in

Stability and Lifetimes of Magnetic States of Nano- and Microstructures (Brief Review)

  • CONDENSED MATTER
  • Published:
JETP Letters Aims and scope Submit manuscript

A statistical approach is presented to estimate the stability of magnetic states of nano- and microstructures to thermal fluctuations and random external actions. It implies the construction of the multidimensional energy surface of a system, search for the minimum energy paths between locally stable states on this surface, and calculation of rates of magnetic transitions between corresponding magnetic configurations at arbitrary temperatures in the harmonic approximation of the transition state theory. Lifetimes of quasi-two-dimensional topologically protected magnetic structures have been studied. The effect of magnetic characteristics of a medium limited by the geometry of a sample, nonmagnetic defects, and external magnetic field on the lifetimes of topological magnetic states has been shown.

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.

Similar content being viewed by others

REFERENCES

  1. A. A. Belavin and A. M. Polyakov, JETP Lett. 22, 245 (1975).

    ADS  Google Scholar 

  2. A. N. Bogdanov and D. A. Yablonskii, Sov. Phys. JETP 68, 101 (1989).

    Google Scholar 

  3. N. Nagaosa and Y. Tokura, Nat. Nanotechnol. 8, 899 (2013).

    Article  ADS  Google Scholar 

  4. G. Finocchio, F. Büttner, R. Tomasello, M. Carpentieri, and M. Kläui, J. Phys. D: Appl. Phys. 49, 423001 (2016).

  5. A. Fert, N. Reyren, and V. Cros, Nat. Rev. Mater. 2, 1 (2017).

    Article  Google Scholar 

  6. S. Krause, G. Herzog, T. Stapelfeldt, L. Berbil-Bautista, M. Bode, E. Y. Vedmedenko, and R. Wiesendanger, Phys. Rev. Lett. 103, 127202 (2009).

  7. W. T. Coffey, D. A. Garanin, and D. J. McCarthy, Adv. Chem. Phys. 117, 483 (2001).

    Google Scholar 

  8. P. F. Bessarab, V. M. Uzdin, and H. Jónsson, Phys. Rev. B 85, 184409 (2012).

  9. P. Hänggi, P. Talkner, and M. Borkovec, Rev. Mod. Phys. 62, 251 (1990).

    Article  ADS  Google Scholar 

  10. A. F. Voter and J. D. Doll, J. Chem. Phys. 82, 80 (1985).

    Article  ADS  Google Scholar 

  11. G. Fiedler, J. Fidler, J. Lee, T. Schrefl, R. L. Stamps, H. B. Braun, and D. Suess, J. Appl. Phys. 111, 093917 (2012).

  12. P. F. Bessarab, V. M. Uzdin, and H. Jónsson, Phys. Rev. Lett. 110, 020604 (2013).

  13. L. Desplat, D. Suess, J. V. Kim, and R. L. Stamps, Phys. Rev. B 98, 134407 (2018).

  14. A. S. Varentcova, S. von Malottki, M. N. Potkina, G. Kwiatkowski, S. Heinze, and P. F. Bessarab, npj Comput. Mater. 6, 193 (2020).

    Google Scholar 

  15. I. S. Lobanov, M. N. Potkina, V. M. Uzdin, and H. Jónsson, Nanosyst.: Phys., Chem., Math. 8, 586 (2017).

    Google Scholar 

  16. G. P. Müller, P. F. Bessarab, S. M. Vlasov, F. Lux, N. S. Kiselev, S. Blügel, V. M. Uzdin, and H. Jónsson, Phys. Rev. Lett. 121, 197202 (2018).

  17. I. S. Lobanov and V. M. Uzdin, arXiv: 2008.06754v1 [cond-mat.mtrl-sci].

  18. F. N. Rybakov, A. B. Borisov, S. Blügel, and N. S. Kiselev, Phys. Rev. Lett. 115, 117201 (2015).

  19. A. V. Ivanov, V. M. Uzdin, and H. Jónsson, Comput. Phys. Commun. 260, 107749 (2020).

  20. F. Büttner, I. Lemesh, and G. S. Beach, Sci. Rep. 8, 4464 (2018).

    Article  ADS  Google Scholar 

  21. I. S. Lobanov, V. M. Uzdin, and H. Jónsson, Phys. Rev. B 94, 174418 (2016).

  22. P. F. Bessarab, V. M. Uzdin, and H. Jónsson, Comput. Phys. Commun. 196, 335 (2015).

    Article  ADS  Google Scholar 

  23. G. Henkelman and H. Jónsson, J. Chem. Phys. 113, 9978 (2000).

    Article  ADS  Google Scholar 

  24. G. Henkelman, B. P. Uberuaga, and H. Jónsson, J. Chem. Phys. 113, 9901 (2000).

    Article  ADS  Google Scholar 

  25. A. V. Ivanov, D. Dagbartsson, J. Tranchida, V. M. Uzdin, and H. Jónsson, J. Phys.: Condens. Matter 32, 345901 (2020).

  26. P. F. Bessarab, V. M. Uzdin, and H. Jónsson, Phys. Rev. B 89, 214424 (2014).

  27. A. Ivanov, P. F. Bessarab, V. M. Uzdin, and H. Jónsson, Nanoscale 9, 13320 (2017).

    Article  Google Scholar 

  28. V. M. Uzdin, M. N. Potkina, I. S. Lobanov, P. F. Bessarab, and H. Jónsson, J. Magn. Magn. Mater. 459, 236 (2018).

    Article  ADS  Google Scholar 

  29. V. M. Uzdin, M. N. Potkina, I. S. Lobanov, P. F. Bessarab, and H. Jónsson, Phys. B (Amsterdam, Neth.) 549, 6 (2018).

  30. D. Cortés-Ortuno, W. Wang, M. Beg, R. A. Pepper, M. A. Bisotti, R. Carey, M. Vousden, T. Kluyver, O. Hovorka, and H. Fangohr, Sci. Rep. 7, 4060 (2017).

    Article  ADS  Google Scholar 

  31. S. von Malottki, B. Dupé, P. F. Bessarab, A. Delin, and S. Heinze, Sci. Rep. 7, 12299 (2017).

    Article  ADS  Google Scholar 

  32. P. F. Bessarab, G. P. Müller, I. S. Lobanov, F. N. Rybakov, N. S. Kiselev, H. Jónsson, V. M. Uzdin, S. Blügel, L. Bergqvist, and A. Delin, Sci. Rep. 8, 3433 (2018).

    Article  ADS  Google Scholar 

  33. M. Hoffmann, G. P. Müller, and S. Blügel, Phys. Rev. Lett. 124, 247201 (2020).

  34. S. Rohart, J. Miltat, and A. Thiaville, Phys. Rev. B 93, 214412 (2016).

  35. E.Weinan, W. Ren, and E. Vanden-Eijnden, Phys. Rev. B 66, 052301 (2002).

  36. P. Heistracher, C. Abert, F. Bruckner, C. Vogler, and D. Suess, IEEE Trans. Magn. 54, 7206105 (2018).

  37. R. A. Olsen, G. J. Kroes, G. Henkelman, A. Arnaldsson, and H. Jónsson, J. Chem. Phys. 121, 9776 (2004).

    Article  ADS  Google Scholar 

  38. G. H. Golub and C. F. van Loan, Matrix Computations (JHU press, Baltimore, 2013), Vol. 3.

    Book  MATH  Google Scholar 

  39. G. Henkelman and H. Jónsson, J. Chem. Phys. 111, 7010 (1999).

    Article  ADS  Google Scholar 

  40. M. Moskalenko, P. F. Bessarab, V. M. Uzdin, and H. Jónsson, AIP Adv. 6, 025213 (2016).

  41. N. Romming, A. Kubetzka, C. Hanneken, K. von Bergmann, and R. Wiesendanger, Phys. Rev. Lett. 114, 177203 (2015).

  42. O. Boulle, J. Vogel, H. Yang, et al., Nat. Nanotech. 11, 449 (2016).

    Article  ADS  Google Scholar 

  43. P. F. Bessarab, V. M. Uzdin, and H. Jónsson, Z. Phys. Chem. 227, 1543 (2013).

    Google Scholar 

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

    Article  ADS  Google Scholar 

  45. A. Fert, V. Cros, and J. Sampaio, Nat. Nanotechnol. 8, 152 (2013).

    Article  ADS  Google Scholar 

  46. Z. R. Yan, Y. Z Liu, Y. Guang, J. F. Feng, R. K. Lake, G. O. Yu, and X. F. Han, Phys. Rev. Appl. 14, 044008 (2020).

  47. H. Zhang, D. Zhu, W. Kang, Y. Zhang, and W. Zhao, Phys. Rev. Appl. 13, 054049 (2020).

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

    Article  ADS  Google Scholar 

  49. V. L. Carvalho-Santos, M. A. Castro, D. Salazar-Aravena, D. Laroze, R. M. Corona, S. Allende, and D. Altbir, Appl. Phys. Lett. 118, 172407 (2021).

  50. Y. Zhou and M. Ezawa, Nat. Commun. 5, 4652 (2014).

    Article  ADS  Google Scholar 

  51. D. Suess, C. Vogler, F. Bruckner, P. Heistracher, and F. Slanovc, Sci. Rep. 9, 4827 (2019).

    Article  ADS  Google Scholar 

  52. M. N. Potkina, I. S. Lobanov, and V. M. Uzdin, Nanosyst.: Phys., Chem., Math. 11, 628 (2020).

    Google Scholar 

  53. J. Sampaio, V. Cros, S. Rohart, A. Thiaville, and F. Fert, Nat. Nanotechnol. 8, 839 (2013).

    Article  ADS  Google Scholar 

  54. J. Hagemeister, N. Romming, K. von Bergmann, E. V. Vedmedenko, and R. Wiesendanger, Nat. Commun. 6, 8455 (2015).

    Article  ADS  Google Scholar 

  55. K. S. Denisov, I. V. Rozhansky, M. N. Potkina, I. S. Lobanov, E. Lähderanta, and V. M. Uzdin, Phys. Rev. B 98, 214407 (2018).

  56. S. M. Vlasov, P. F. Bessarab, I. S. Lobanov, M. N. Potkina, V. M. Uzdin, and H. Jónsson, New J. Phys. 22, 083013 (2020).

  57. V. M. Kuchkin, B. Barton-Singer, F. N. Rybakov, S. Blügel, B. J. Schroers, and N. S. Kiselev, Phys. Rev. B 102, 144422 (2020).

  58. L. Caretta, M. Mann, F. Büttner, K. Ueda, B. Pfau, C. M. Günther, P. Hessing, A. Churikova, C. Klose, M. Schneider, and D. Engel, Nat. Nanotechnol. 13, 1154 (2018).

    Article  ADS  Google Scholar 

  59. S. Woo, K. M. Song, X. Zhang, et al., Nat. Commun. 9, 959 (2018).

    Article  ADS  Google Scholar 

  60. K. Litzius, I. Lemesh, B. Krüger, et al., Nat. Phys. 13, 170 (2017).

    Article  Google Scholar 

  61. J. Barker and O. A. Tretiakov, Phys. Rev. Lett. 116, 147203 (2016).

  62. X. Zhang, Y. Zhou, and M. Ezawa, Sci. Rep. 6, 24795 (2016).

    Article  ADS  Google Scholar 

  63. R. A. Duine, K. J. Lee, S. S. P. Parkin, and V. D. Stiles, Nat. Phys. 14, 217 (2018).

    Article  Google Scholar 

  64. W. Legrand, D. Maccariello, F. Ajejas, S. Collin, A. Vecchiola, K. Bouzehouane, N. Reyren, V. Cros, and A. Fert, Nat. Mater. 19, 34 (2020).

    Article  ADS  Google Scholar 

  65. P. F. Bessarab, D. Yudin, D. R. Gulevich, P. Wadley, M. Titov, and O. A. Tretiakov, Phys. Rev. B 99, 140411 (2019).

  66. M. N. Potkina, I. S. Lobanov, H. Jónsson, and V. M. Uzdin, J. Appl. Phys. 127, 213906 (2020).

  67. W. Koshibae and N. Nagaosa, Nat. Commun. 7, 10542 (2016).

    Article  ADS  Google Scholar 

  68. A. K. Nayak, V. Kumar, T. Ma, P. Werner, E. Pippel, R. Sahoo, F. Damay, U. K. Rößler, C. Felser, and S. S. P. Parkin, Nature (London, U.K.) 548, 561 (2017).

    Article  ADS  Google Scholar 

  69. S. Huang, C. Zhou, G. Chen, H. Shen, A. K. Schmid, K. Liu, and Y. Wu, Phys. Rev. B 96, 144412 (2017).

  70. L. Camosi, N. Rougemaille, O. Fruchart, J. Vogel, and S. Rohart, Phys. Rev. B 97, 134404 (2018).

  71. M. N. Potkina, I. S. Lobanov, O. A. Tretiakov, H. Jónsson, and V. M. Uzdin, Phys. Rev. B 102, 134430 (2020).

  72. C. Hanneken, A. Kubetzka, K. von Bergmann, and R. Wiesendanger, New J. Phys. 18, 055009 (2016).

  73. I. L. Fernandes, J. Bouaziz, S. Blügel, and S. Lounis, Nat. Commun. 9, 4395 (2018).

    Article  ADS  Google Scholar 

  74. J. Müller and A. Rosch, Phys. Rev. B 91, 054410 (2015).

  75. J. Castell-Queralt, L. González-Gómez, N. Del-Valle, A. Sanchez, and C. Navau, Nanoscale 11, 12589 (2019).

    Article  Google Scholar 

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

  77. N. Romming, C. Hanneken, M. Menzel, J. E. Bickel, B. Wolter, K. von Bergmann, A. Kubetzka, and R. Wiesendanger, Science (Washington, DC, U. S.) 341, 636 (2013).

    Article  ADS  Google Scholar 

  78. V. E. Timofeev, A. O. Sorokin, and D. N. Aristov, JETP Lett. 109, 207 (2019).

    Article  ADS  Google Scholar 

  79. M. V. Sapozhnikov, O. V. Ermolaeva, E. V. Skorokhodov, N. S. Gusev, and M. N. Drozdov, JETP Lett. 107, 364 (2018).

    Article  ADS  Google Scholar 

  80. H. R. O. Sohn, S. M. Vlasov, V. M. Uzdin, A. O. Leonov, and I. I. Smalyukh, Phys. Rev. B 100, 104401 (2019).

  81. S. M. Vlasov, V. M. Uzdin, and A. O. Leonov, J. Phys.: Condens. Matter 32, 185801 (2020).

  82. A. O. Leonov, I. M. Tambovtcev, I. S. Lobanov, and V. M. Uzdin, Phys. Rev. B 102, 174415 (2020).

  83. A. V. Ivanov, P. F. Bessarab, E. V. Aksenova, V. P. Romanov, and V. M. Uzdin, Phys. Rev. E 93, 042708 (2016).

  84. S. S. Tenishchev, A. D. Kiselev, A. V. Ivanov, and V. M. Uzdin, Phys. Rev. E 100, 062704 (2019).

  85. S. S. Tenishchev, I. M. Tambovtcev, A. D. Kiselev, and V. M. Uzdin, J. Mol. Liq. 325, 115242 (2021).

Download references

Funding

This work was supported in part by the Russian Foundation for Basic Research (project nos. 18-02-00267-A and 19-32-90048-Aspiranty), by the Foundation for the Advancement of Theoretical Physics and Mathematics BASIS (project no. 19-1-1-12-1,2), and jointly by the Russian Science Foundation and Helmholtz Foundation (project no. 19-42-06302, development of methods of the calculation of lifetimes of magnetic states for systems with millions of degrees of freedom).

Author information

Authors and Affiliations

  1. Faculty of Physics, St. Petersburg State University, 199034, St. Petersburg, Russia

    I. S. Lobanov, M. N. Potkina & V. M. Uzdin

  2. Faculty of Physics, ITMO University, 197101, St. Petersburg, Russia

    I. S. Lobanov, M. N. Potkina & V. M. Uzdin

Authors
  1. I. S. Lobanov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. N. Potkina
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. V. M. Uzdin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. M. Uzdin.

Additional information

Translated by R. Tyapaev

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lobanov, I.S., Potkina, M.N. & Uzdin, V.M. Stability and Lifetimes of Magnetic States of Nano- and Microstructures (Brief Review). Jetp Lett. 113, 801–813 (2021). https://doi.org/10.1134/S0021364021120109

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0021364021120109

Search

Navigation