Magnetization switching on small ferromagnetic ellipsoidal samples

François Alouges; Karine Beauchard

ESAIM: Control, Optimisation and Calculus of Variations (2009)

  • Volume: 15, Issue: 3, page 676-711
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Alouges, François, and Beauchard, Karine. "Magnetization switching on small ferromagnetic ellipsoidal samples." ESAIM: Control, Optimisation and Calculus of Variations 15.3 (2009): 676-711. <http://eudml.org/doc/245147>.

@article{Alouges2009,
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 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.},
author = {Alouges, François, Beauchard, Karine},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Landau-Lifschitz equation; micromagnetics; stabilization},
language = {eng},
number = {3},
pages = {676-711},
publisher = {EDP-Sciences},
title = {Magnetization switching on small ferromagnetic ellipsoidal samples},
url = {http://eudml.org/doc/245147},
volume = {15},
year = {2009},
}

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
PB - EDP-Sciences
VL - 15
IS - 3
SP - 676
EP - 711
AB - 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.
LA - eng
KW - Landau-Lifschitz equation; micromagnetics; stabilization
UR - http://eudml.org/doc/245147
ER -

References

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  1. [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. Zbl0788.35065MR1167422
  2. [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. [3] G. Bertotti and I. Mayergoyz, The Science of Hysteresis. Academic Press (2006). Zbl1117.34047
  4. [4] W.F. Brown, Micromagnetics. Interscience Publishers (1963). 
  5. [5] G. Carbou and P. Fabrie, Regular solutions for Landau-Lifschitz equation in a bounded domain. Diff. Integral Eqns. 14 (2001) 219–229. Zbl1161.35421MR1797387
  6. [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. Zbl1310.82059MR2375581
  7. [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. Zbl0765.53026MR1180392
  8. [8] J.-M. Coron, Nonuniqueness for the heat flow of harmonic maps. Ann. Inst. H. Poincaré Anal. Non Linéaire 7 (1992) 335–344. Zbl0707.58017MR1067779
  9. [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. Zbl0679.58017MR992088
  10. [10] A. DeSimone, Hysteresis and imperfection sensitivity in small ferromagnetic particles. Meccanica 30 (1995) 591–603. Zbl0836.73060MR1360973
  11. [11] A. Freire, Uniqueness for the harmonic map flow in two dimensions. Calc. Var. Partial Differential Equations 3 (1995) 95–105. Zbl0814.35057MR1384838
  12. [12] A. Hubert and R. Schäfer, Magnetic Domains: The Analysis of Magnetic Microstructures. Springer (1998). 
  13. [13] J. Jost, Ein Existenzbeweis für harmonische Abbildungen, die ein Dirichletproblem lösen, mittels der Methode des Wärmeflusses. Manuscripta Math. 34 (1981) 17–25. Zbl0459.58013MR614386
  14. [14] R. Kikuchi, On the minimum of magnetization reversal time. J. Appl. Phys. 27 (1956) 1352–1357. 
  15. [15] S. Labbé, Simulation numérique du comportement hyperfréquence des matériaux ferromagnétiques. Ph.D. thesis, Université Paris XIII, France (1998). 
  16. [16] J.C. Mallinson, Damped gyromagnetic switching. IEEE Trans. Magn. 36 (2000) 1976–1981. 
  17. [17] J.-C. Mitteau, Sur les applications harmoniques. J. Differ. Geom. 9 (1974) 41–54. Zbl0281.35034MR345129
  18. [18] A. Visintin, On Landau-Lifschitz equations for ferromagnetism. Japan J. Appl. Math. 2 (1985) 69–84. Zbl0613.35018MR839320

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