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, \(1\le p<n\).
Similar content being viewed by others
References
Alouges, F., Labbé, S.: Convergence of a ferromagnetic film model. C. R. Math. Acad. Sci. Paris 344(2), 77–82 (2007)
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)
Ammari, H., Halpern, L., Hamdache, K.: Asymptotic behavior of thin ferromagnetic films. Asymptot. Anal. 24, 277–294 (2000)
Brown, W.F.: Micromagnetics. Wiley, New York (1963)
Carbou, G.: Thin layers in micromagnetism. \(M^3AS\). Math. Models Methods Appl. Sci. 11(9), 1529–1546 (2001)
Carbou, P.G., Labbé, S.: Stabilization of walls for nano-wire of finite lenght. ESAIM Control Optim. Calc. Var. 18, 1–21 (2012)
Ciarlet, P.C., Destuynder, P.: A justification of the two-dimensional linear plate model. J. Mécanique 18(2), 315–344 (1979)
Deny, J., Lions, L.-L.: Les espaces du type de Beppo Levi. Ann. Inst. Fourier 5, 305–370 (1954)
Desimone, A., Kohn, R., Muller, S., Otto, F.: A reduced theory for thin-film micromagnetics. Commun. Pure Appl. Math. 55, 1408–1460 (2002)
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)
Gaudiello, A., Hadiji, R.: Junction of one-dimensional minimization problems involving \(S^2\) valued maps. Adv. Differ. Equ. 13(9–10), 935–958 (2008)
Gaudiello, A., Hadiji, R.: Junction of ferromagnetic thin films. Calc. Var. Partial Differ. Equ. 39(3–4), 593–619 (2010)
Gaudiello, A., Hadiji, R.: Ferromagnetic thin multi-structures. J. Differ. Equ. 257, 1591–1622 (2014)
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)
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)
Gioia, G., James, R.D.: Micromagnetics of very thin films. Proc. R. Lond. A 453, 213–223 (1997)
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)
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)
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)
Hubert, A., Schafer, R.: Magnetic Domains: The Analysis of Magnetic Microstructures. Springer, Berlin (1998)
James, R.D., Kinderlehrer, D.: Frustration in ferromagnetic materials. Contin. Mech. Thermodyn. 2, 215–239 (1990)
Khon, R.V., Slastikov, V.V.: Another thin-film limit of micromagnetics. Arch. Ration. Mech. Anal. 178, 227–245 (2005)
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)]
Rivière, T., Serfaty, S.: Limiting domain wall energy for a problem related to micromagnetics. Commun. Pure Appl. Math. 54(3), 294–338 (2001)
Sanchez, D.: Behaviour of the Landau–Lifshitz equation in a ferromagnetic wire. Math. Methods Appl. Sci. 32(2), 167–205 (2009)
Schwartz, L.: Théorie des distributions. Hermann, Paris (1996)
Slastikov, V.V., Sonnenberg, C.: Reduced models for ferromagnetic nanowires. J. Appl. Math. 77, 220–235 (2012)
Visintin, A.: On Landau–Lifschitz, equations for ferromagnetism. Jpn. J. Appl. Math. 2, 69–84 (1985)
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by L.Carbone.
Rights and permissions
About this article
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
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11587-014-0186-8