# Homogenization of ferromagnetic multilayers in the presence of surface energies

ESAIM: Control, Optimisation and Calculus of Variations (2007)

- Volume: 13, Issue: 2, page 305-330
- ISSN: 1292-8119

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topSantugini-Repiquet, Kévin. "Homogenization of ferromagnetic multilayers in the presence of surface energies." ESAIM: Control, Optimisation and Calculus of Variations 13.2 (2007): 305-330. <http://eudml.org/doc/249990>.

@article{Santugini2007,

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 sequence
of 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 establish
the homogenized equation in these two situations.
},

author = {Santugini-Repiquet, Kévin},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Ferromagnetism; multilayers; Landau-Lifshitz equation; micromagnetic model; interlayer exchange coupling; surface anisotropy},

language = {eng},

month = {5},

number = {2},

pages = {305-330},

publisher = {EDP Sciences},

title = {Homogenization of ferromagnetic multilayers in the presence of surface energies},

url = {http://eudml.org/doc/249990},

volume = {13},

year = {2007},

}

TY - JOUR

AU - Santugini-Repiquet, Kévin

TI - Homogenization of ferromagnetic multilayers in the presence of surface energies

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2007/5//

PB - EDP Sciences

VL - 13

IS - 2

SP - 305

EP - 330

AB -
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 sequence
of 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 establish
the homogenized equation in these two situations.

LA - eng

KW - Ferromagnetism; multilayers; Landau-Lifshitz equation; micromagnetic model; interlayer exchange coupling; surface anisotropy

UR - http://eudml.org/doc/249990

ER -

## References

top- A. Aharoni, Introduction to the theory of ferromagnetism. Oxford Science Publication (1996).
- G. Allaire, Homogenization and two-scale convergence. SIAM J. Math. Anal.23 (1992) 1482–1518.
- 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.
- F. Alouges and A. Soyeur, On global weak solutions for Landau-Lifshitz equations: existence and nonuniqueness. Nonlinear Anal. Theory Methods Appl.18 (1992) 1071–1084.
- W.F. Brown, Micromagnetics. Interscience Publishers (1963).
- M.J. Friedman, Mathematical study of the nonlinear singular integral magnetic field equation I. SIAM J. Appl. Math.39 (1980) 14–20.
- H. Haddar and P. Joly, Homogenized model for a laminar ferromagnetic medium. Proc. Roy. Soc. Edinburgh Sect. A133, (2003) 567–598.
- L. Halpern and S. Labbé, La théorie du micromagnétisme. Modélisation et simulation du comportement des matériaux magnétiques. Matapli66 (2001) 77–92.
- K. Hamdache, Homogenization of layered ferromagnetic media. Preprint 495, CMAP Polytechnique, UMR CNRS 7641, Palaiseau, France (2002).
- A. Kirilyuk, J. Ferré, V. Grolier, J. Jamet and D. Renard. Magnetization reversal in ultrathin ferromagetic films with perpendicular anisotropy. J. Magn. Magn. Mater.171 (1997) 45–63.
- M. Labrune and J. Miltat, Wall structure in ferro / antiferromagnetic exchange-coupled bilayers: a numerical micromagnetic approach. J. Magn. Magn. Mater.151 (1995) 231–245.
- L.D. Landau and E.M. Lifshitz, On the theory of the dispersion of magnetic permeability in ferromagnetic bodies. Phys. Z. Sowjetunion8 (1935) 153–169.
- M. Neuss-Radu, Homogenization techniques. Diplomaarbeit, University of Heidelberg (1992).
- M. Neuss-Radu, Some extensions of two-scale convergence. C. R. Acad. Sci. Paris Sér. I Math.322 (1996) 899–904.
- K. Santugini-Repiquet, 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.
- 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).

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