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Stabilization of walls for nano-wires of finite length

Published online by Cambridge University Press:  02 December 2010

Gilles Carbou  and
Stéphane Labbé
Gilles Carbou
Affiliation:
MAB, UMR 5466, CNRS, Université Bordeaux 1, 351 cours de la Libération, 33405 Talence Cedex, France. carbou@math.u-bordeaux1.fr
Stéphane Labbé
Affiliation:
Université Joseph Fourier, Laboratoire Jean Kuntzmann, CNRS, UMR 5224, 51 rue des Mathématiques, B.P. 53, 38041 Grenoble Cedex 9, France; stephane.labbe@imag.fr
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Abstract

In this paper we study a one dimensional model of ferromagnetic nano-wires of finite length. First we justify the model by Γ-convergence arguments. Furthermore we prove the existence of wall profiles. These walls being unstable, we stabilize them by the mean of an applied magnetic field.

Keywords

Landau-Lifschitz equationcontrolstabilization
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 18 , Issue 1 , January 2012 , pp. 1 - 21
Copyright
© EDP Sciences, SMAI, 2010

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References

Alouges, F., Rivière, T. and Serfaty, S., Néel and cross-tie wall energies for planar micromagnetic configurations. ESAIM : COCV 8 (2002) 31–68. Google Scholar
W.F. Brown, Micromagnetics. Interscience Publisher, John Willey and Sons, New York (1963).
Carbou, G., Regularity for critical points of a nonlocal energy. Calc. Var. 5 (1997) 409–433. Google Scholar
Carbou, G., Thin layers in micromagnetism. Math. Models Methods Appl. Sci. 11 (2001) 1529–1546. Google Scholar
Carbou, G. and Fabrie, P., Time average in micromagnetism. J. Differ. Equ. 147 (1998) 383–409. Google Scholar
Carbou, G. and Fabrie, P., Regular solutions for Landau-Lifschitz equation in a bounded domain. Differential Integral Equations 14 (2001) 213–229. Google Scholar
Carbou, G. and Fabrie, P., Regular solutions for Landau-Lifschitz equation in R3. Commun. Appl. Anal. 5 (2001) 17–30. Google Scholar
Carbou, G. and Labbé, S., Stability for static walls in ferromagnetic nanowires. Discrete Continous Dyn. Syst. Ser. B 6 (2006) 273–290. Google Scholar
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. Google Scholar
A. DeSimone, R.V. Kohn, S. Müller and F. Otto, Magnetic microstructures – a paradigm of multiscale problems, in ICIAM 99 (Edinburgh), Oxford Univ. Press, Oxford (2000) 175–190.
Halpern, L. and Labbé, S., Modélisation et simulation du comportement des matériaux ferromagnétiques. Matapli 66 (2001) 70–86. Google Scholar
Kapitula, T., Multidimensional stability of planar travelling waves. Trans. Amer. Math. Soc. 349 (1997) 257–269. Google Scholar
Kühn, K., Travelling waves with a singularity in magnetic nanowires. Commun. Partial Diff. Equ. 34 (2009) 722–764. Google Scholar
S. Labbé, Simulation numérique du comportement hyperfréquence des matériaux ferromagnétiques. Thèse de l’Université Paris 13, Paris (1998).
Labbé, S. and Bertin, P.-Y., Microwave polarisability of ferrite particles with non-uniform magnetization. J. Magn. Magn. Mater. 206 (1999) 93–105. Google Scholar
Rivière, T. and Serfaty, S., Compactness, kinetic formulation, and entropies for a problem related to micromagnetics. Commun. Partial Diff. Equ. 28 (2003) 249–269. Google Scholar
D. Sanchez, Méthodes asymptotiques en ferromagnétisme. Thèse de l’Université Bordeaux 1, Bordeaux (2004).
Thiaville, A., Garcia, J.M. and Miltat, J., Domain wall dynamics in nanowires. J. Magn. Magn. Mater. 242–245 (2002) 1061–1063. Google Scholar
Visintin, A., On Landau Lifschitz equation for ferromagnetism. Japan Journal of Applied Mathematics 1 (1985) 69–84. Google Scholar
H. Wynled, Ferromagnetism, Encyclopedia of Physics XVIII/2. Springer-Verlag, Berlin (1966).