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
Access Full Article
top
Abstract
topHow to cite
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 . 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).
Citations in EuDML Documents
topNotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.