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Homogenization of ferromagnetic multilayersinthe presence of surface energies

Published online by Cambridge University Press:  12 May 2007

Kévin Santugini-Repiquet
Kévin Santugini-Repiquet*
Affiliation:
UNIGE, Section de mathématiques, Genève, Switzerland; [email protected]
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Abstract

We study the homogenization process of ferromagnetic multilayers in the presence of surface energies:super-exchange, also called interlayer exchange coupling,and surface anisotropy. The two main difficulties are the non-linearity of the Landau-Lifshitz equation and the absence of a good sequenceof extension operators for the multilayer geometry.First, we consider the case when surface anisotropy is the dominant term, then the case when the magnitude of the super-exchange interaction is inversely proportional to the interlayer distance. We establishthe homogenized equation in these two situations.

Keywords

FerromagnetismmultilayersLandau-Lifshitz equationmicromagnetic model
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 13 , Issue 2 , April 2007 , pp. 305 - 330
Copyright
© EDP Sciences, SMAI, 2007

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References

A. Aharoni, Introduction to the theory of ferromagnetism. Oxford Science Publication (1996).
Allaire, G., Homogenization and two-scale convergence. SIAM J. Math. Anal. 23 (1992) 1482–1518. CrossRef
G. Allaire, A. Damlamian and U. Hornung, Two-scale convergence on periodic surfaces and applications, in Proc. of the International Conference on Mathematical Modelling of Flow through Porous Media, Singapore, May 1995, A. Bourgeat et al. Eds., World Scientific Pub., 15–25.
Alouges, F. and Soyeur, A., On global weak solutions for Landau-Lifshitz equations: existence and nonuniqueness. Nonlinear Anal. Theory Methods Appl. 18 (1992) 1071–1084. CrossRef
W.F. Brown, Micromagnetics. Interscience Publishers (1963).
Friedman, M.J., Mathematical study of the nonlinear singular integral magnetic field equation I. SIAM J. Appl. Math. 39 (1980) 14–20. CrossRef
H. Haddar and P. Joly, Homogenized model for a laminar ferromagnetic medium. Proc. Roy. Soc. Edinburgh Sect. A 133, (2003) 567–598.
Halpern, L. and Labbé, S., La théorie du micromagnétisme. Modélisation et simulation du comportement des matériaux magnétiques. Matapli 66 (2001) 77–92.
K. Hamdache, Homogenization of layered ferromagnetic media. Preprint 495, CMAP Polytechnique, UMR CNRS 7641, Palaiseau, France (2002).
Kirilyuk, A., Ferré, J., Grolier, V., Jamet, J. and Renard, D.. Magnetization reversal in ultrathin ferromagetic films with perpendicular anisotropy. J. Magn. Magn. Mater. 171 (1997) 45–63. CrossRef
Labrune, M. and Miltat, J., Wall structure in ferro / antiferromagnetic exchange-coupled bilayers: a numerical micromagnetic approach. J. Magn. Magn. Mater. 151 (1995) 231–245. CrossRef
Landau, L.D. and Lifshitz, E.M., On the theory of the dispersion of magnetic permeability in ferromagnetic bodies. Phys. Z. Sowjetunion 8 (1935) 153–169.
M. Neuss-Radu, Homogenization techniques. Diplomaarbeit, University of Heidelberg (1992).
Neuss-Radu, M., Some extensions of two-scale convergence. C. R. Acad. Sci. Paris Sér. I Math. 322 (1996) 899–904.
Santugini-Repiquet, K., Solutions to the Landau-Lifshitz system with nonhomogeneous Neumann boundary conditions arising from surface anisotropy and super-exchange interactions in a ferromagnetic media. Nonlinear Anal. 65 (2006) 129–158. CrossRef
J. Simon, Compact sets in the space $\mathrm{L}^p(0,T;B)$ . Ann. Mat. Pura Appl. 146 (1987) 66–96.
É. Trémolet de Lacheisserie, editor. Magnétisme: Fondements, Collection Grenoble Sciences, Vol. I, EDP Sciences (2000).
É. Trémolet de Lacheisserie, editor. Magnétisme: Matériaux et applications, Collection Grenoble Sciences, Vol. II, EDP Sciences (2000).