Skip to main content
SpringerLink
Log in

Stability of Asymptotic Approximation in Models of Multiferroics

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

We consider a system of nonlinear differential equations describing the antiferromagnetism victor in a ferrite film. The system contains two parameters and admits a family of exact solutions with plane phase trajectories. Perturbation of such solutions leads to the Hill equation with periodic coefficient. We study the stability of the equilibrium state of the Hill equation.

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. L. A. Kalyakin, A. K. Zvezdin, and Z. V. Gareva, “Asymptotic analysis of multiferroic model,” Theor. Math. Phys 203, No. 1, 457-468 (2020).

    Article  MathSciNet  Google Scholar 

  2. Z. V. Gareva, L. A. Kalyakin, I. P. Kayumov, and A. K. Zvezdin, “Spin-reorientation transitions in multiferroics with cycloidal spin ordering,” Phys. Metals Metallography 121, No. 4, 310–315 (2020).

    Article  Google Scholar 

  3. A. K. Zvezdin and A. P. Pyatakov, “Phase transitions and the giant magnetoelectric effect in multiferroics,” Phys. Usp. 47, No. 4, 416–422 (2004).

    Article  Google Scholar 

  4. N. A. Spaldin and R. Ramesh, “Advances in magnetoelectric multiferroics,” Nat. Mater. 18, No. 3, 203–212 (2019).

    Article  Google Scholar 

  5. I. Sosnowska and A. Zvezdin, “Origin of the Long Period Magnetic Ordering in BiFeO3,” J. Magn. Magn. Mater. 140, 167–168 (1995).

    Article  Google Scholar 

  6. N. E. Kulagin, A. F. Popkov, and A. K. Zvezdin, “Spatially modulated antiferromagnetic structures in an easy-plane multiferroic,” Phys. Solid State 53, No. 5, 970–977 (2011).

    Article  Google Scholar 

  7. N. E. Kulagin, A. F. Popkov, S. V. Solov’ev, and A. K. Zvezdin, “Field-induced spin-modulated transitions in epitaxial (001) BiFeO3 films,” Phys. Solid State 61, No. 2, 108–116 (2019).

    Article  Google Scholar 

  8. V. A. Yakubovich and V. M. Starzhinskij, Linear Differential Equations with Periodic Coefficients, John Wiley, New York etc. (1975).

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, UFRC RAS, 112, Chernyshevsky St., Ufa, 450008, Russia

    L. A. Kalyakin

  2. Prokhorov General Physics Institute RAS, 38, Vavilova St., Moscow, 117942, Russia

    A. K. Zvezdin

  3. Institute of Molecule and Crystal Physics RAS, 151, Oktyabrya Pr., Ufa, 450075, 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.

Additional information

Translated from Problemy Matematicheskogo Analiza 108, 2021, pp. 83-97.

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. Stability of Asymptotic Approximation in Models of Multiferroics. J Math Sci 255, 444–458 (2021). https://doi.org/10.1007/s10958-021-05383-6

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-021-05383-6

Search

Navigation