# Magnetization switching on small ferromagnetic ellipsoidal samples

François Alouges; Karine Beauchard

ESAIM: Control, Optimisation and Calculus of Variations (2008)

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

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topAlouges, François, and Beauchard, Karine. "Magnetization switching on small ferromagnetic ellipsoidal samples." ESAIM: Control, Optimisation and Calculus of Variations 15.3 (2008): 676-711. <http://eudml.org/doc/90932>.

@article{Alouges2008,

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},

month = {7},

number = {3},

pages = {676-711},

publisher = {EDP Sciences},

title = {Magnetization switching on small ferromagnetic ellipsoidal samples},

url = {http://eudml.org/doc/90932},

volume = {15},

year = {2008},

}

TY - JOUR

AU - Alouges, François

AU - Beauchard, Karine

TI - Magnetization switching on small ferromagnetic ellipsoidal samples

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2008/7//

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/90932

ER -

## References

top- 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. Zbl0788.35065
- M. Bauer, J. Fassbender, B. Hillebrands and R.L. Stamps, Switching behavior of a Stoner particle beyond the relaxation time limit. Phys. Rev. B61 (2000) 3410–3416.
- G. Bertotti and I. Mayergoyz, The Science of Hysteresis. Academic Press (2006). Zbl1117.34047
- W.F. Brown, Micromagnetics. Interscience Publishers (1963).
- G. Carbou and P. Fabrie, Regular solutions for Landau-Lifschitz equation in a bounded domain. Diff. Integral Eqns.14 (2001) 219–229. Zbl1161.35421
- G. Carbou, S. Labbé and E. Trélat, Control of travelling walls in a ferromagnetic nanowire. Discrete Contin. Dyn. Syst. Ser. S1 (2008) 51–59. Zbl1310.82059
- 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.
- J.-M. Coron, Nonuniqueness for the heat flow of harmonic maps. Ann. Inst. H. Poincaré Anal. Non Linéaire7 (1992) 335–344. Zbl0707.58017
- 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. Zbl0679.58017
- A. DeSimone, Hysteresis and imperfection sensitivity in small ferromagnetic particles. Meccanica30 (1995) 591–603. Zbl0836.73060
- A. Freire, Uniqueness for the harmonic map flow in two dimensions. Calc. Var. Partial Differential Equations3 (1995) 95–105. Zbl0814.35057
- A. Hubert and R. Schäfer, Magnetic Domains: The Analysis of Magnetic Microstructures. Springer (1998).
- J. Jost, Ein Existenzbeweis für harmonische Abbildungen, die ein Dirichletproblem lösen, mittels der Methode des Wärmeflusses. Manuscripta Math.34 (1981) 17–25. Zbl0459.58013
- R. Kikuchi, On the minimum of magnetization reversal time. J. Appl. Phys.27 (1956) 1352–1357.
- S. Labbé, Simulation numérique du comportement hyperfréquence des matériaux ferromagnétiques. Ph.D. thesis, Université Paris XIII, France (1998).
- J.C. Mallinson, Damped gyromagnetic switching. IEEE Trans. Magn.36 (2000) 1976–1981.
- J.-C. Mitteau, Sur les applications harmoniques. J. Differ. Geom.9 (1974) 41–54. Zbl0281.35034
- A. Visintin, On Landau-Lifschitz equations for ferromagnetism. Japan J. Appl. Math.2 (1985) 69–84. Zbl0613.35018

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