Existence and the stability of minimizers in ferromagnetic nanowires

TL;DR

This paper proves the existence and stability of energy-minimizing magnetic domain walls in ferromagnetic nanowires with symmetric cross sections, and analyzes their behavior under asymmetry.

Contribution

It establishes the existence of global minimizers for micromagnetic energy in nanowires and demonstrates their stability under certain asymmetries of the cross section.

Findings

Existence of global minimizers for micromagnetic energy in nanowires.

Stability of minimizers under asymmetry of cross sections.

Close energy states imply proximity to a minimizer up to rotation and translation.

Abstract

We study static 180 degree domain walls in infinite magnetic wires with bounded, $C^1$ and rotationally symmetric cross sections. We prove an existence of global minimizers for the energy of micromagnetics for any bounded $C^1$ cross sections. Under some asymmetry of cross sections we prove a stability result for the minimizers, namely, we show that vectors of micromagnetics having an energy close to the minimal one, must be $H^1$ close to a minimizer of the limiting energy up to a rotation and a translation.