Skip to main content

Advertisement

SpringerLink
Log in

\(nD-pD\) Dimensional reduction of micromagnetic structures

  • Published:
Ricerche di Matematica Aims and scope Submit manuscript

Abstract

Starting from a \(nD, n\ge 2\), non-convex and nonlocal micromagnetic energy, we determine, via an asymptotic analysis, the free energy of a \(pD\) ferromagnetic domain, \(1\le p<n\).

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. Alouges, F., Labbé, S.: Convergence of a ferromagnetic film model. C. R. Math. Acad. Sci. Paris 344(2), 77–82 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  2. Alouges, F., Rivière, T., Serfaty, S.: Néel and cross-tie wall energies for planar micromagnetic configurations. A tribute to J. L. Lions. ESAIM Control Optim. Calc. Var. 8, 31–68 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  3. Ammari, H., Halpern, L., Hamdache, K.: Asymptotic behavior of thin ferromagnetic films. Asymptot. Anal. 24, 277–294 (2000)

    MATH  MathSciNet  Google Scholar 

  4. Brown, W.F.: Micromagnetics. Wiley, New York (1963)

    Google Scholar 

  5. Carbou, G.: Thin layers in micromagnetism. \(M^3AS\). Math. Models Methods Appl. Sci. 11(9), 1529–1546 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  6. Carbou, P.G., Labbé, S.: Stabilization of walls for nano-wire of finite lenght. ESAIM Control Optim. Calc. Var. 18, 1–21 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  7. Ciarlet, P.C., Destuynder, P.: A justification of the two-dimensional linear plate model. J. Mécanique 18(2), 315–344 (1979)

    MATH  MathSciNet  Google Scholar 

  8. Deny, J., Lions, L.-L.: Les espaces du type de Beppo Levi. Ann. Inst. Fourier 5, 305–370 (1954)

    Article  MATH  MathSciNet  Google Scholar 

  9. Desimone, A., Kohn, R., Muller, S., Otto, F.: A reduced theory for thin-film micromagnetics. Commun. Pure Appl. Math. 55, 1408–1460 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  10. Gaudiello, A., Hadiji, R.: Asymptotic analysis, in a thin multidomain, of minimizing maps with values in S2. Ann. Inst. H. Poincaré Anal. Non Lineaire 26, 59–80 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  11. Gaudiello, A., Hadiji, R.: Junction of one-dimensional minimization problems involving \(S^2\) valued maps. Adv. Differ. Equ. 13(9–10), 935–958 (2008)

    MATH  MathSciNet  Google Scholar 

  12. Gaudiello, A., Hadiji, R.: Junction of ferromagnetic thin films. Calc. Var. Partial Differ. Equ. 39(3–4), 593–619 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  13. Gaudiello, A., Hadiji, R.: Ferromagnetic thin multi-structures. J. Differ. Equ. 257, 1591–1622 (2014)

  14. Gaudiello, A., Hamdache, K.: The polarization in a ferroelectric thin film: local and nonlocal limit problems. ESAIM Control Optim. Calc. Var. 19, 657–667 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  15. Gaudiello, A., Sili, A.: Asymptotic analysis of the eigenvalues of an elliptic problem in an anisotropic thin multidomain. Proc. R. Soc. Edinb. Sect. A 141(4), 739–754 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  16. Gioia, G., James, R.D.: Micromagnetics of very thin films. Proc. R. Lond. A 453, 213–223 (1997)

    Article  Google Scholar 

  17. Hadiji, R., Shirakawa, K.: Asymptotic analysis of micromagnetics on thin films governed by indefinite material coefficients. Commun. Pure Appl. Anal. 9(5), 1345–1361 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  18. Hadiji, R., Shirakawa, K.: 3D–2D Asymptotic observation for minimization problems associated with degenerative energy-coefficients. Discrete Contin. Dyn. Syst. Suppl. I , 624–633 (2011)

    MathSciNet  Google Scholar 

  19. Hadiji, R., Zhou, F.: Regularity of \(\int _\Omega \mid \nabla u \mid ^2 + \lambda \int _\Omega \mid u - f \mid ^2\) and some gap phenomenon. Potential Anal. 1(4), 385–400 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  20. Hubert, A., Schafer, R.: Magnetic Domains: The Analysis of Magnetic Microstructures. Springer, Berlin (1998)

    Google Scholar 

  21. James, R.D., Kinderlehrer, D.: Frustration in ferromagnetic materials. Contin. Mech. Thermodyn. 2, 215–239 (1990)

    Article  MathSciNet  Google Scholar 

  22. Khon, R.V., Slastikov, V.V.: Another thin-film limit of micromagnetics. Arch. Ration. Mech. Anal. 178, 227–245 (2005)

    Article  MathSciNet  Google Scholar 

  23. Landau, L.D., Lifshitz, E.M.: On the theory of the dispersion of magnetic perme- ability in ferromagnetic bodies, Phy. Z. Sowjetunion 8, 153 (1935) [ter Haar, D. (eds.): Reproduced in Collected Papers of L. D. Landau, pp. 101–114, New York: Pergamon Press (1965)]

  24. Rivière, T., Serfaty, S.: Limiting domain wall energy for a problem related to micromagnetics. Commun. Pure Appl. Math. 54(3), 294–338 (2001)

    Article  MATH  Google Scholar 

  25. Sanchez, D.: Behaviour of the Landau–Lifshitz equation in a ferromagnetic wire. Math. Methods Appl. Sci. 32(2), 167–205 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  26. Schwartz, L.: Théorie des distributions. Hermann, Paris (1996)

    Google Scholar 

  27. Slastikov, V.V., Sonnenberg, C.: Reduced models for ferromagnetic nanowires. J. Appl. Math. 77, 220–235 (2012)

    MATH  MathSciNet  Google Scholar 

  28. Visintin, A.: On Landau–Lifschitz, equations for ferromagnetism. Jpn. J. Appl. Math. 2, 69–84 (1985)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. LAMA, Laboratoire d’Analyse et de Mathématiques Appliquées, UMR 8050, UPEC, Université Paris-Est, 94010 , Créteil, France

    Salwa Soueid

Authors
  1. Salwa Soueid
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Salwa Soueid.

Additional information

Communicated by L.Carbone.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Soueid, S. \(nD-pD\) Dimensional reduction of micromagnetic structures. Ricerche mat. 64, 9–24 (2015). https://doi.org/10.1007/s11587-014-0186-8

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11587-014-0186-8

Keywords

Mathematics Subject Classification (2000)

Search

Navigation