Magnetization switching on small ferromagnetic ellipsoidal samples
ESAIM: Control, Optimisation and Calculus of Variations, Tome 15 (2009) no. 3, pp. 676-711.

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 inside the magnetic sample is of particular relevance. We here investigate mathematically this problem by considering the full partial differential model of Landau-Lifschitz equations triggered by a uniform (in space) external magnetic field.

DOI : 10.1051/cocv:2008047
Classification : 49J15, 35A05, 35A07, 35D05, 35K20, 35K55, 35Q60
Mots-clés : Landau-Lifschitz equation, micromagnetics, stabilization 
@article{COCV_2009__15_3_676_0,
     author = {Alouges, Fran\c{c}ois and Beauchard, Karine},
     title = {Magnetization switching on small ferromagnetic ellipsoidal samples},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {676--711},
     publisher = {EDP-Sciences},
     volume = {15},
     number = {3},
     year = {2009},
     doi = {10.1051/cocv:2008047},
     mrnumber = {2542578},
     zbl = {1167.49003},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/cocv:2008047/}
}
TY  - JOUR
AU  - Alouges, François
AU  - Beauchard, Karine
TI  - Magnetization switching on small ferromagnetic ellipsoidal samples
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 2009
SP  - 676
EP  - 711
VL  - 15
IS  - 3
PB  - EDP-Sciences
UR  - http://archive.numdam.org/articles/10.1051/cocv:2008047/
DO  - 10.1051/cocv:2008047
LA  - en
ID  - COCV_2009__15_3_676_0
ER  - 
%0 Journal Article
%A Alouges, François
%A Beauchard, Karine
%T Magnetization switching on small ferromagnetic ellipsoidal samples
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2009
%P 676-711
%V 15
%N 3
%I EDP-Sciences
%U http://archive.numdam.org/articles/10.1051/cocv:2008047/
%R 10.1051/cocv:2008047
%G en
%F COCV_2009__15_3_676_0
Alouges, François; Beauchard, Karine. Magnetization switching on small ferromagnetic ellipsoidal samples. ESAIM: Control, Optimisation and Calculus of Variations, Tome 15 (2009) no. 3, pp. 676-711. doi : 10.1051/cocv:2008047. http://archive.numdam.org/articles/10.1051/cocv:2008047/

[1] F. Alouges and A. Soyeur, On global weak solutions for Landau Lifschitz equations: existence and nonuniqueness. Nonlinear Anal. Theory Meth. Appl. 18 (1992) 1071-1084. | MR | Zbl

[2] M. Bauer, J. Fassbender, B. Hillebrands and R.L. Stamps, Switching behavior of a Stoner particle beyond the relaxation time limit. Phys. Rev. B 61 (2000) 3410-3416.

[3] G. Bertotti and I. Mayergoyz, The Science of Hysteresis. Academic Press (2006). | Zbl

[4] W.F. Brown, Micromagnetics. Interscience Publishers (1963). | Zbl

[5] G. Carbou and P. Fabrie, Regular solutions for Landau-Lifschitz equation in a bounded domain. Diff. Integral Eqns. 14 (2001) 219-229. | MR | Zbl

[6] G. Carbou, S. Labbé and E. Trélat, Control of travelling walls in a ferromagnetic nanowire. Discrete Contin. Dyn. Syst. Ser. S 1 (2008) 51-59. | MR | Zbl

[7] K.-C. Chang, W.Y. Ding and R. Ye, Finite-time blow-up of the heat flow of harmonic maps from surfaces. J. Differ. Geom. 36 (1992) 507-515. | MR | Zbl

[8] J.-M. Coron, Nonuniqueness for the heat flow of harmonic maps. Ann. Inst. H. Poincaré Anal. Non Linéaire 7 (1992) 335-344. | EuDML | Numdam | MR | Zbl

[9] J.-M. Coron and J.-M. Ghidaglia, Explosion en temps fini pour le flot des applications harmoniques. C. R. Acad. Sci. Paris Sér. I Math. 308 (1989) 339-344. | MR | Zbl

[10] A. Desimone, Hysteresis and imperfection sensitivity in small ferromagnetic particles. Meccanica 30 (1995) 591-603. | MR | Zbl

[11] A. Freire, Uniqueness for the harmonic map flow in two dimensions. Calc. Var. Partial Differential Equations 3 (1995) 95-105. | MR | Zbl

[12] A. Hubert and R. Schäfer, Magnetic Domains: The Analysis of Magnetic Microstructures. Springer (1998).

[13] J. Jost, Ein Existenzbeweis für harmonische Abbildungen, die ein Dirichletproblem lösen, mittels der Methode des Wärmeflusses. Manuscripta Math. 34 (1981) 17-25. | MR | Zbl

[14] R. Kikuchi, On the minimum of magnetization reversal time. J. Appl. Phys. 27 (1956) 1352-1357.

[15] S. Labbé, Simulation numérique du comportement hyperfréquence des matériaux ferromagnétiques. Ph.D. thesis, Université Paris XIII, France (1998).

[16] J.C. Mallinson, Damped gyromagnetic switching. IEEE Trans. Magn. 36 (2000) 1976-1981.

[17] J.-C. Mitteau, Sur les applications harmoniques. J. Differ. Geom. 9 (1974) 41-54. | MR | Zbl

[18] A. Visintin, On Landau-Lifschitz equations for ferromagnetism. Japan J. Appl. Math. 2 (1985) 69-84. | MR | Zbl

Cité par Sources :