The logarithmic tail of Neel walls

Journal article

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 Q ∥ m ∥Ḣ12 + ∥ u ∥L22 + 〈u|SQ|u〉 → min, m = (u, v) : ℝ → double-struck S sign1 with u(0) = 1, where the reduced stray-field operator SQ 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.

Authors: Melcher, C

• Publication status: Published
• Journal: ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
• Volume: 168
• Issue: 2
• Pages: 83-113
• Publication date: 2003-06-01
• DOI: 10.1007/s00205-003-0248-7
• EISSN: 1432-0673
• ISSN: 0003-9527
• Language: English