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Magnetization switching on small ferromagneticellipsoidal samples

Published online by Cambridge University Press:  19 July 2008

François Alouges  and
Karine Beauchard
François Alouges
Affiliation:
Laboratoire de Mathématiques, Bât. 425, Université Paris-Sud XI, 91405 Orsay Cedex, France. [email protected]
Karine Beauchard
Affiliation:
CMLA, ENS Cachan, CNRS, Universud, 61 Avenue du président Wilson, 94230 Cachan, France. [email protected]
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Abstract

The study of small magnetic particles has become a very important topic, in particular for the development of technological devices such as those used for magnetic recording. In this field, switching the magnetization insidethe magnetic sample is of particular relevance. We here investigate mathematicallythis problem by considering the full partial differential model of Landau-Lifschitzequations triggered by a uniform (in space) external magnetic field.

Keywords

Landau-Lifschitz equationmicromagneticsstabilization
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 15 , Issue 3 , July 2009 , pp. 676 - 711
Copyright
© EDP Sciences, SMAI, 2008

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References

Alouges, F. and Soyeur, A., On global weak solutions for Landau Lifschitz equations: existence and nonuniqueness. Nonlinear Anal. Theory Meth. Appl. 18 (1992) 1071–1084. CrossRef
Bauer, M., Fassbender, J., Hillebrands, B. and Stamps, R.L., Switching behavior of a Stoner particle beyond the relaxation time limit. Phys. Rev. B 61 (2000) 3410–3416. CrossRef
G. Bertotti and I. Mayergoyz, The Science of Hysteresis. Academic Press (2006).
W.F. Brown, Micromagnetics. Interscience Publishers (1963).
Carbou, G. and Fabrie, P., Regular solutions for Landau-Lifschitz equation in a bounded domain. Diff. Integral Eqns. 14 (2001) 219–229.
Carbou, G., Labbé, S. and Trélat, E., Control of travelling walls in a ferromagnetic nanowire. Discrete Contin. Dyn. Syst. Ser. S 1 (2008) 51–59.
Chang, K.-C., Ding, W.Y. and Finite-time, R. Ye blow-up of the heat flow of harmonic maps from surfaces. J. Differ. Geom. 36 (1992) 507–515. CrossRef
Coron, J.-M., Nonuniqueness for the heat flow of harmonic maps. Ann. Inst. H. Poincaré Anal. Non Linéaire 7 (1992) 335–344. CrossRef
Coron, J.-M. and Ghidaglia, J.-M., Explosion en temps fini pour le flot des applications harmoniques. C. R. Acad. Sci. Paris Sér. I Math. 308 (1989) 339–344.
DeSimone, A., Hysteresis and imperfection sensitivity in small ferromagnetic particles. Meccanica 30 (1995) 591–603. CrossRef
Freire, A., Uniqueness for the harmonic map flow in two dimensions. Calc. Var. Partial Differential Equations 3 (1995) 95–105. CrossRef
A. Hubert and R. Schäfer, Magnetic Domains: The Analysis of Magnetic Microstructures. Springer (1998).
Jost, J., Ein Existenzbeweis für harmonische Abbildungen, die ein Dirichletproblem lösen, mittels der Methode des Wärmeflusses. Manuscripta Math. 34 (1981) 17–25. CrossRef
Kikuchi, R., On the minimum of magnetization reversal time. J. Appl. Phys. 27 (1956) 1352–1357. CrossRef
S. Labbé, Simulation numérique du comportement hyperfréquence des matériaux ferromagnétiques. Ph.D. thesis, Université Paris XIII, France (1998).
Mallinson, J.C., Damped gyromagnetic switching. IEEE Trans. Magn. 36 (2000) 1976–1981. CrossRef
Mitteau, J.-C., Sur les applications harmoniques. J. Differ. Geom. 9 (1974) 41–54. CrossRef
Visintin, A., Landau-Lifschitz, On equations for ferromagnetism. Japan J. Appl. Math. 2 (1985) 69–84. CrossRef