Stability of Static Walls for a three dimensional Model of Ferromagnetic Material

In this paper we consider a three dimensional model of ferromagnetic material. We deal with the static domain wall configuration calculated by Walker. We prove the stability of this configuration for the Landau-Lifschitz equation with a simplified expression of the demagnetizing field.

[1]  Gilles Carbou,et al.  Time Average in Micromagnetism , 1998 .

[2]  Stéphane Labbé,et al.  Fast Computation for Large Magnetostatic Systems Adapted for Micromagnetism , 2005, SIAM J. Sci. Comput..

[3]  François Alouges,et al.  Néel and Cross-Tie Wall Energies for Planar Micromagnetic Configurations , 2002 .

[4]  T. Kapitula Multidimensional stability of planar travelling waves , 1997 .

[5]  Mark S. C. Reed,et al.  Method of Modern Mathematical Physics , 1972 .

[6]  Stéphane Labbé A preconditioning strategy for microwave susceptibility in ferromagnets , 2007, Adv. Eng. Softw..

[7]  J. Xin Multidimensional Stability of Traveling Waves in a Bistable Reaction–Diffusion Equation, I , 1992 .

[8]  M. Reed Methods of Modern Mathematical Physics. I: Functional Analysis , 1972 .

[9]  François Alouges,et al.  On global weak solutions for Landau-Lifshitz equations: existence and nonuniqueness , 1992 .

[10]  N. L. Schryer,et al.  The motion of 180° domain walls in uniform dc magnetic fields , 1974 .

[11]  Andreas Prohl,et al.  A Convergent Implicit Finite Element Discretization of the Maxwell-Landau-Lifshitz-Gilbert Equation , 2008, SIAM J. Numer. Anal..

[12]  Jonathan Goodman Stability of viscous scalar shock fronts in several dimensions , 1989 .

[13]  W. D. Evans,et al.  PARTIAL DIFFERENTIAL EQUATIONS , 1941 .

[14]  Stéphane Labbé,et al.  Simulation numérique du comportement hyperfrequence des matériaux ferromagnétiques , 1998 .

[15]  Gilles Carbou,et al.  Control of travelling walls in a ferromagnetic nanowire , 2006, math/0609231.

[16]  Sylvia Serfaty,et al.  Limiting domain wall energy for a problem related to micromagnetics , 2001 .

[17]  Gilles Carbou,et al.  Stability for static walls in ferromagnetic nanowires , 2005 .

[18]  On the Stability of Traveling Waves in Weighted L∞ Spaces , 1994 .

[19]  Barry Simon,et al.  Analysis of Operators , 1978 .

[20]  Gilles Carbou,et al.  Regular solutions for Landau-Lifschitz equation in a bounded domain , 2001, Differential and Integral Equations.

[21]  Guo Boling,et al.  Global Weak Solution for the Landau–Lifshitz–Maxwell Equation in Three Space Dimensions , 1997 .

[22]  Augusto Visintin,et al.  On Landau-Lifshitz’ equations for ferromagnetism , 1985 .

[23]  Robert V. Kohn,et al.  Two–dimensional modelling of soft ferromagnetic films , 2000, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[24]  Robert V. Kohn,et al.  Repulsive Interaction of Néel Walls, and the Internal Length Scale of the Cross-Tie Wall , 2003, Multiscale Model. Simul..

[25]  Stéphane Labbé,et al.  Microwave polarizability of ferrite particles with non-uniform magnetization , 1999 .

[26]  N. Vukadinovic,et al.  3D Dynamic Micromagnetic Simulations of Susceptibility Spectra in Soft Ferromagnetic Particles , 2008 .

[27]  B. Guo,et al.  Global existence of weak solutions for Landau-Lifshitz-Maxwell equations , 2007 .

[28]  Gilles Carbou,et al.  On the Ferromagnetism equations in the non static case , 2004 .