Static Theory for Planar Ferromagnets and Antiferromagnets

Abstract Here we generalize the "BBH"-asymptotic analysis to a simplified mathematical model for the planar ferromagnets and antiferromagnets. To develop such a static theory is a necessary step for a rigorous mathematical justification of dynamical laws for the magnetic vortices formally derived in [1] and [2].

[1]  C. B. Morrey.  Multiple Integrals in the Calculus of Variations , 1966 .

[2]  Fanghua Lin,et al.  Some Dynamical Properties of Ginzburg-Landau Vortices , 1996 .

[3]  Paul Baird,et al.  Harmonic maps with symmetry, harmonic morphisms, and deformations of metrics , 1983 .

[4]  N. Papanicolaou,et al.  Semitopological solitons in planar ferromagnets , 1999 .

[5]  Vortex dynamics in two-dimensional antiferromagnets , 1996, cond-mat/9612043.

[6]  Yuanlong Xin,et al.  Geometry of Harmonic Maps , 1996 .

[7]  S. Yau,et al.  Lectures on Harmonic Maps , 1997 .

[8]  Patrick S. Hagan,et al.  Spiral Waves in Reaction-Diffusion Equations , 1982 .

[9]  H. Brezis,et al.  Ginzburg-Landau Vortices , 1994 .

[10]  Charles M. Elliott,et al.  Shooting method for vortex solutions of a complex-valued Ginzburg–Landau equation , 1994, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[11]  F. Hélein,et al.  REGULARITE DES APPLICATIONS FAIBLEMENT HARMONIQUES ENTRE UNE SURFACE ET UNE VARIETE RIEMANNIENNE , 1991 .

[12]  D. Gilbarg,et al.  Elliptic Partial Differential Equa-tions of Second Order , 1977 .

[13]  Topology and dynamics in ferromagnetic media , 1995, cond-mat/9511126.

[14]  Michael Struwe,et al.  On the asymptotic behavior of minimizers of the Ginzburg-Landau model in $2$ dimensions , 1994, Differential and Integral Equations.

[15]  Petru Mironescu,et al.  On the Stability of Radial Solutions of the Ginzburg-Landau Equation , 1995 .

[16]  J. Slonczewski,et al.  Magnetic domain walls in bubble materials , 1979 .

[17]  Frédéric Hélein,et al.  Asymptotics for the minimization of a Ginzburg-Landau functional , 1993 .

[18]  F. Lin.  Static and moving vortices in Ginzburg-Landau theories , 1997 .

[19]  H. Brezis,et al.  Quantization effects for −Δu = u(1 − |u|2) in ℝ2 , 1994 .