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Walls in infinite bent ferromagnetic nanowires
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 27 (2018) no. 5, pp. 897-924.

We study a one-dimensional model for a bent ferromagnetic nanowire. We prove the existence of static solutions describing either one domain or two domains separated by a wall. We address the stability of these solutions. In particular, we show that the asymptotically stable wall profiles are pinned at the bend even in presence of a small applied magnetic field.

Dans cet article, on étudie un modèle monodimensionnel de fil ferromagnétique présentant un coude. On explicite toutes les solutions stationnaires décrivant soit un domaine soit deux domaines séparés par un mur. On étudie ensuite la stabilité de ces solutions. On montre en particulier que certains profils de murs sont asymptotiquement stables, l’interprétation physique de ce résultat étant que les murs restent bloqués au niveau du coude, et ce même en présence d’un champ magnétique appliqué.

Received:
Accepted:
Published online:
DOI: 10.5802/afst.1587
Classification: 35K55,  35Q60
Keywords: ferromagnetism, Landau–Lifschitz equation, stability, domain walls
Abdel Kader Al Sayed 1; Gilles Carbou 1

1 CNRS / Université de Pau et des Pays de l’Adour, LMAP - UMR CNRS 5142, IPRA, E2S UPPA, Avenue de l’Université - BP 1155, 64013 PAU, France
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     title = {Walls in infinite bent ferromagnetic nanowires},
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     pages = {897--924},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
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Abdel Kader Al Sayed; Gilles Carbou. Walls in infinite bent ferromagnetic nanowires. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 27 (2018) no. 5, pp. 897-924. doi : 10.5802/afst.1587. https://afst.centre-mersenne.org/articles/10.5802/afst.1587/

[1] Serge Alinhac; Patrick Gérard Pseudo-differential operators and the Nash-Moser theorem, Graduate Studies in Mathematics, Volume 82, American Mathematical Society, 2007, vii+168 pages (Translated from the 1991 French original by Stephen S. Wilson) | Zbl: 1121.47033

[2] Sergiy M. Bokoch; Gilles Carbou; Stéphane Labbé Circuits ferromagnetic of nano wires (in preparation)

[3] William F. Brown Micromagnetics, John Wiley & Sons, 1963

[4] Gilles Carbou; Rida Jizzini Domain walls dynamics in a nanowire subject to an electric current, J. Differ. Equations, Volume 258 (2015) no. 8, pp. 2941-2965 | Zbl: 1321.35219

[5] Gilles Carbou; Stéphane Labbé Stability for static walls in ferromagnetic nanowires, Discrete Contin. Dyn. Syst, Volume 6 (2006) no. 2, pp. 273-290 | Zbl: 1220.82163

[6] Gilles Carbou; Stéphane Labbé Stabilization of Walls for Nano-Wires of Finite Length, ESAIM, Control Optim. Calc. Var., Volume 18 (2012) no. 1, pp. 1-21 | Zbl: 1235.35029

[7] Gilles Carbou; Stéphane Labbé; Emmanuel Trélat Control of traveling walls in a ferromagnetic nanowire, Discrete Contin. Dyn. Syst (2007)

[8] C. L. Chien; Daniel H. Reich; Daniel M. Silevitch; Marius Tanase Magnetotransport properties of bent ferromagnetic nanowires, J. Appl. Phys., Volume 93 (2003), 7616, 9 pages (Art. ID 7616) | Article

[9] C. L. Chien; Daniel H. Reich; Daniel M. Silevitch; Marius Tanase Room temperature Domain Wall Pinning in Bent Ferromagnetic Nanowires (2003) (https://arxiv.org/abs/cond-mat/0308579)

[10] Rida Jizzini Optimal stability criterion for a wall in ferromagnetic wire submitted to a magnetic field, J. Differ. Equations, Volume 250 (2011) no. 8, pp. 3349-3361 | Zbl: 1211.35039

[11] Stéphane Labbé; Yannick Privat; Emmanuel Trélat Stability properties of steady-states for a network of ferromagnetic nanowires, J. Differ. Equations, Volume 253 (2012) no. 6, pp. 1709-1728 | Zbl: 1247.35173

[12] L. Landau; E. Lifschitz Electrodynamique des milieux continues, Physique Théorique, Volume VIII, Editions de Moscou, 1969

[13] Stuart S. P. Parkin; Masamitsu Hayashi; Luc Thomas Magnetic Domain-Wall Racetrack Memory, Science, Volume 320 (2008), pp. 190-194 | Article

[14] Valeriy V. Slatiskov; Charles Sonnenberg Reduce models for ferromagnetic nanowires, IMA J. Appl. Math., Volume 77 (2012) no. 2, pp. 220-235 | Zbl: 1243.78013

[15] Keisuke Takasao Stability of travelling wave solutions for the Landau-Lifshitz equation, Hiroshima Math. J., Volume 41 (2011) no. 3, pp. 367-388 | Zbl: 1235.35031

[16] André Thiaville; Yoshinobu Nakatani Domain wall dynamics in nanowires and nanostrips, Spin Dynamics in Confined Magnetic Structures III (Topics in Applied Physics) Volume 101, Springer, 2006, pp. 161-206 | Article

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