Skip to main content
Log in

Energy Barriers for the Spontaneous Magnetization Reversal of Atomic Co Chains on the Surface Pt(664) in the Model of Dzyaloshinskii–Moriya Interaction

  • Published:
Journal of Surface Investigation: X-ray, Synchrotron and Neutron Techniques Aims and scope Submit manuscript

Abstract

Within the framework of the continuous XY model, analytical expressions are derived to calculate the time of the spontaneous magnetization reversal of finite-length atomic chains on the surface of a metal. The interaction of magnetic moments of atoms is described by the classical Hamiltonian, which includes the Heisenberg exchange interaction, the Dzyaloshinskii–Moriya interaction, and the magnetic-anisotropy energy. Using the example of the Co/Pt(664) system, it is demonstrated that the proposed method exhibits good agreement with the results of numerical simulations for both short and long atomic chains. For atomic chains of intermediate length, it can be utilized to obtain an upper bound on the time of spontaneous magnetization reversal. We obtained dependences of the time of spontaneous magnetization reversal for finite-length Co atomic chains, taking into account the exchange integral, parameters characterizing the magnetic anisotropy, and the projection of the Dzyaloshinskii vector onto the axis perpendicular to the plane containing the magnetic moments of atoms. The proposed method is applicable over a wide range of temperatures and values of physical parameters that characterize the magnetic properties of atomic chains. Thus, it can be employed not only for the Co/Pt(664) system but also for other similar systems.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1.
Fig. 2.

REFERENCES

  1. I. Zutic, J. Fabian, and S. Das Sarma, Rev. Mod. Phys. 76, 323 (2004). https://www.doi.org/10.1103/RevModPhys.76.323

    Article  CAS  Google Scholar 

  2. N. D. Mermin, Quantum Computer Science: An Introduction (Cambridge Univ. Press, Cambridge, 2007).

    Book  Google Scholar 

  3. S. Bose, Phys. Rev. Lett. 91, 207901 (2003). https://www.doi.org/10.1103/PhysRevLett.91.207901

    Article  PubMed  Google Scholar 

  4. S. Bose, Contemp. Phys. 48, 13 (2007). https://www.doi.org/10.1080/00107510701342313

    Article  CAS  Google Scholar 

  5. H. Verma, L. Chotorlishvili, J. Berakdar, and S. K. Mishra, Europhys. Lett. 119, 30001 (2017). https://www.doi.org/10.1209/0295-5075/119/30001

    Article  Google Scholar 

  6. P. Gambardella, A. Dallmeyer, K. Maiti, M. C. Malagoli, W. Eberhardt, K. Kern, and C. Carbone, Nature 416, 301 (2002). https://www.doi.org/10.1038/416301a

    Article  CAS  PubMed  Google Scholar 

  7. P. Gambardella, S. Rusponi, M. Veronese, S. S. Dhesi, C. Grazioli, A. Dallmeyer, I. Cabria, R. Zeller, P. H. Dederichs, K. Kern, C. Carbone, and H. Brune, Science 300, 1130 (2003). https://www.doi.org/10.1126/science.1082857

    Article  CAS  PubMed  Google Scholar 

  8. I. Dzyaloshinsky, J. Phys. Chem. Solids 4, 241 (1958). https://www.doi.org/10.1016/0022-3697(58)90076-3

    Article  CAS  Google Scholar 

  9. T. Moriya, Phys. Rev. Lett. 4, 228 (1960). https://www.doi.org/10.1103/PhysRevLett.4.228

    Article  CAS  Google Scholar 

  10. D. J. Choi, N. Lorente, J. Wiebe, K. von Bergmann, A. F. Otte, and A. J. Heinrich, Rev. Mod. Phys. 91, 041001 (2019). https://www.doi.org/10.1103/RevModPhys.91.041001

    Article  CAS  Google Scholar 

  11. L. D. Landau and E. M. Lifshits, Electrodynamics of Continuous Media (Fizmatlit, Moscow, 2005) [in Russian].

    Google Scholar 

  12. H. T. Nembach, J. M. Shaw, M. Weiler, E. Jue, and T. J. Silva, Nat. Phys. 11, 825 (2015). https://www.doi.org/10.1038/nphys3418

    Article  CAS  Google Scholar 

  13. J. Cho, N.-H. Kim, S. Lee, J.-S. Kim, R. Lavrijsen, A. Solignac, Y. Yin, D.-S. Han, N. J. J. van Hoof, H. J. M. Swagten, B. Koopmans, and C.-Y. You, Nat. Commun. 6, 7635 (2015). https://www.doi.org/10.1038/ncomms8635

    Article  PubMed  Google Scholar 

  14. A. Fert, N. Reyren, and V. Cros, Nat. Rev. Mater. 2, 17031 (2017). https://www.doi.org/10.1038/natrevmats.2017.31

    Article  CAS  Google Scholar 

  15. A. Soumyanarayanan, N. Reyren, A. Fert, and C. Panagopoulos, Nature 539, 509 (2016). https://www.doi.org/10.1038/nature19820

    Article  CAS  PubMed  Google Scholar 

  16. M. Garst, J. Waizner, and D. Grundler, J. Phys. D: App-l. Phys. 50, 293002 (2017). https://www.doi.org/10.1088/1361-6463/aa7573

    Article  Google Scholar 

  17. R. Mazzarello and E. Tosatti, Phys. Rev. B 79, 134402 (2009). https://www.doi.org/10.1103/PhysRevB.79.134402

    Article  Google Scholar 

  18. M. Menzel, Y. Mokrousov, R. Wieser, J. E. Bickel, E. Vedmedenko, S. Blügel, S. Heinze, K. von Bergmann, A. Kubetzka, and R. Wiesendanger, Phys. Rev. Lett. 108, 197204 (2012).

    Article  PubMed  Google Scholar 

  19. M. Heide, G. Bihlmayer, and S. Blügel, Phys. Rev. B 78, 140403 (2008). https://www.doi.org/10.1103/PhysRevB.78.140403

    Article  Google Scholar 

  20. B. Schweflinghaus, B. Zimmermann, M. Heide, G. Bihlmayer, and S. Blügel, Phys. Rev. B 94, 024403 (2016). https://www.doi.org/10.1103/PhysRevB.94.024403

    Article  Google Scholar 

  21. L. Chotorlishvili, X. Wang, A. Dyrdal, G. Guo, V. K. Dugaev, J. Barna’s, and J. Berakdar, Phys. Rev. B 106, 014417 (2022). https://www.doi.org/10.1103/PhysRevB.106.014417

    Article  CAS  Google Scholar 

  22. S. V. Kolesnikov and E. S. Sapronova, IEEE Magn. Lett. 13, 2505905 (2022). https://www.doi.org/10.1109/LMAG.2022.3226656

  23. P. F. Bessarab, V. M. Uzdin, and H. Jonsson, Comp. Phys. Commun. 196, 335 (2015). https://www.doi.org/10.1016/j.cpc.2015.07.001

  24. E. M. Chudnovsky and L. Gunther, Phys. Rev. Lett. 60, 661 (1988). https://www.doi.org/10.1103/PhysRevLett.60.661

    Article  CAS  PubMed  Google Scholar 

  25. A. S. Smirnov, N. N. Negulyaev, W. Hergert, A. M. Saletsky, and V. S. Stepanyuk, New J. Phys. 11, 063004 (2009). https://www.doi.org/10.1088/1367-2630/11/6/063004

    Article  Google Scholar 

  26. A. P. Popov, A. Rettori, and M. G. Pini, Phys. Rev. B 90, 134418. https://www.doi.org/10.1103/PhysRevB.90.134418

  27. S. V. Kolesnikov and E. S. Sapronova, J. Exp. Theor. Phys. 135 (5), 690 (2022). https://www.doi.org/10.1134/s1063776122110097

  28. S. V. Kolesnikov and I. N. Kolesnikova, J. Exp. Theor. Phys. 125 (4), 644 (2017). https://www.doi.org/10.1134/s1063776117090060

Download references

Funding

S.V. Kolesnikov is grateful to the Russian Science Foundation for the support (grant no. 21-72-20 034). E.S. Sapronova is a fellow of the Foundation for the Advancement of Theoretical Physics and Mathematics “BASIS.”

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to S. V. Kolesnikov.

Ethics declarations

The authors of this work declare that they have no conflicts of interest.

Additional information

Translated by O. Zhukova

Publisher’s Note.

Pleiades Publishing remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kolesnikov, S.V., Sapronova, E.S. Energy Barriers for the Spontaneous Magnetization Reversal of Atomic Co Chains on the Surface Pt(664) in the Model of Dzyaloshinskii–Moriya Interaction. J. Surf. Investig. 18, 150–155 (2024). https://doi.org/10.1134/S1027451024010282

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1027451024010282

Keywords:

Navigation