Calculus of Variations and Geometric Measure Theory

M. Morini - C. Muratov - M. Novaga - V. Slastikov

Transverse domain walls in thin ferromagnetic strips

created by novaga on 02 Jun 2021
modified on 30 May 2023


Published Paper

Inserted: 2 jun 2021
Last Updated: 30 may 2023

Journal: Arch. Rat. Mech. Anal.
Volume: 247
Number: 3
Pages: Article 59
Year: 2023
Doi: 10.1007/s00205-023-01868-7

ArXiv: 2106.01338 PDF


We present a characterization of the domain wall solutions arising as minimizers of an energy functional obtained in a suitable asymptotic regime of micromagnetics for infinitely long thin film ferromagnetic strips in which the magnetization is forced to lie in the film plane. For the considered energy, we provide existence, uniqueness, monotonicity, and symmetry of the magnetization profiles in the form of 180$^\circ$ and 360$^\circ$ walls. We also demonstrate how this energy arises as a $\Gamma$-limit of the reduced two-dimensional thin film micromagnetic energy that captures the non-local effects associated with the stray field, and characterize its respective energy minimizers.