We study the multiscale problem of a parametrized planar 180° rotation of magnetization states in a thin ferromagnetic film. In an appropriate scaling and when the film thickness is comparable to the Bloch line width, the underlying variational principle has the form
where the reduced stray-field operator 𝒮 Q approximates (−Δ)1/2 as the quality factor Q tends to zero. We show that the associated Néel wall profile u exhibits a very long logarithmic tail. The proof relies on limiting elliptic regularity methods on the basis of the associated Euler-Lagrange equation and symmetrization arguments on the basis of the variational principle. Finally we study the renormalized limit behavior as Q tends to zero.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
(Accepted October 29, 2002) Published online March 6, 2003
Communicated by F. Otto
Rights and permissions
About this article
Cite this article
Melcher, C. The Logarithmic Tail of Néel Walls. Arch. Rational Mech. Anal. 168, 83–113 (2003). https://doi.org/10.1007/s00205-003-0248-7
Issue Date:
DOI: https://doi.org/10.1007/s00205-003-0248-7