Domain structure of ultrathin ferromagnetic elements in the presence of Dzyaloshinskii-Moriya interaction

TL;DR

This paper investigates how Dzyaloshinskii-Moriya interaction influences the structure of domain walls in ultrathin ferromagnetic nanostructures using micromagnetic modeling and $ ext{Γ}$-convergence analysis.

Contribution

It provides explicit constructions of chiral domain wall minimizers and analyzes their asymptotic behavior in large samples with weak magnetic fields.

Findings

Explicit one-dimensional domain wall solutions for various parameters.

Asymptotic analysis of two-dimensional magnetization patterns.

Demonstration of DMI's impact on domain wall structure.

Abstract

Recent advances in nanofabrication make it possible to produce multilayer nanostructures composed of ultrathin film materials with thickness down to a few monolayers of atoms and lateral extent of several tens of nanometers. At these scales, ferromagnetic materials begin to exhibit unusual properties, such as perpendicular magnetocrystalline anisotropy and antisymmetric exchange, also referred to as Dzyaloshinskii-Moriya interaction (DMI), because of the increased importance of interfacial effects. The presence of surface DMI has been demonstrated to fundamentally alter the structure of domain walls. Here we use the micromagnetic modeling framework to analyse the existence and structure of chiral domain walls, viewed as minimizers of a suitable micromagnetic energy functional. We explicitly construct the minimizers in the one-dimensional setting, both for the interior and edge walls, for a broad range of parameters. We then use the methods of {$\Gamma$}-convergence to analyze the asymptotics of the two-dimensional mag- netization patterns in samples of large spatial extent in the presence of weak applied magnetic fields.