Skip to main content
SpringerLink
Log in

Asymptotic analysis of a multiferroic model

  • Published:
Theoretical and Mathematical Physics Aims and scope Submit manuscript

Abstract

We consider a system of nonlinear autonomous differential equations that describe the orientation of the antiferromagnetic vector in a multiferroic film and find the conditions for the existence of spatially modulated structures of the cycloid type. We investigate the stability of such structures under spatial perturbations.

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

Similar content being viewed by others

References

  1. Y. Tokura and S. Seki, “Multiferroics with spiral spin order,” Adv. Mater.22, 1554–1565 (2010).

    Article  Google Scholar 

  2. N. A. Spaldin and R. Ramesh, “Advances in magnetoelectric multiferroics,” Nature Mater.18, 203–212 (2019).

    Article  Google Scholar 

  3. I. Sosnowska, T. Neumaier, and E. Steichele, “Spiral magnetic ordering in bismuth ferrite,” J. Phys. C15, 4835–4846 (1982).

    Article  ADS  Google Scholar 

  4. Yu. A. Izyumov, Neutron Diffraction in Long-Periodic Structures [in Russian], Energoatomizdat, Moscow (1987).

    Google Scholar 

  5. V. V. Nemytskii and V. V. Stepanov, Qualitative Theory of Differential Equations [in Russian], OGIZ, Moscow (1947); English transl., Princeton Univ. Press, Princeton, N. J. (1960).

    MATH  Google Scholar 

  6. C. Lanczos, The Variational Principles of Mechanics (Math. Expos., Vol. 4), Univ. of Toronto Press, Toronto (1952).

    MATH  Google Scholar 

  7. E. M. Galeev and V. M. Tikhomirov, Optimization: Theory, Examples, Problems [in Russian], Editorial URSS, Moscow (2000).

    Google Scholar 

  8. B. M. Levitan and V. V. Zhikov, Almost Periodic Functions and Differential Equations [in Russian], Moscow Univ. Press, Moscow (1978); English transl., Cambridge Univ. Press, London (1982).

    MATH  Google Scholar 

  9. N. I. Akhiezer, Lectures on Approximation Theory [in Russian], Nauka, Moscow (1965).

    Google Scholar 

  10. N. E. Kulagin, A. F. Popkov, and A. K. Zvezdin, “Spatially modulated antiferromagnetic structures in an easy-plane multiferroic,” Phys. Solid State53, 970–977 (2011).

    Article  ADS  Google Scholar 

  11. N. E. Kulagin, A. F. Popkov, S. V. Solov’yov, and A. K. Zvezdin, Phys. Solid State, 61, 108–116 (2019).

    Article  ADS  Google Scholar 

  12. M. V. Fedoryuk, Saddle-Point Method [in Russian], Nauka, Moscow (1977).

    MATH  Google Scholar 

  13. V. A. Yakubovich and V. M. Starzhinskii, Linear Differential Equations with Periodic Coefficients and Their Application [in Russian], Nauka, Moscow (1972)

    Google Scholar 

  14. V. A. Yakubovich and V. M. Starzhinskii, English transl.: Linear Differential Equations with Periodic Coefficients, John Wiley, New York (1975).

    Google Scholar 

  15. A. P. Shvartsman, “On the problem of boundedness of solutions of the differential equation y” + p(x)y = 0,” J. Appl. Math. Mech.18, 464–468 (1954).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics with Computing Centre - Subdivision of the Ufa Federal Research Centre of the Russian Academy of Science, Ufa, Russia

    L. A. Kalyakin

  2. Prokhorov General Physics Institute, RAS, Moscow, Russia

    A. K. Zvezdin

  3. National Research University “Higher School of Economics,”, Moscow, Russia

    A. K. Zvezdin

  4. Institute of Molecule and Crystal Physics, Ufa Science Center, RAS, Ufa, Russia

    Z. V. Gareeva

Authors
  1. L. A. Kalyakin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. K. Zvezdin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Z. V. Gareeva
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to L. A. Kalyakin.

Ethics declarations

The authors declare no conflicts of interest.

Additional information

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 203, No. 1, pp. 26–39, April, 2020.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kalyakin, L.A., Zvezdin, A.K. & Gareeva, Z.V. Asymptotic analysis of a multiferroic model. Theor Math Phys 203, 457–468 (2020). https://doi.org/10.1134/S0040577920040030

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0040577920040030

Keywords

Search

Navigation