Resonant translational, breathing and twisting modes of pinned transverse magnetic domain walls

TL;DR

This paper investigates the resonant modes of pinned transverse magnetic domain walls in ferromagnetic nanostrips, revealing how different modes respond to notch characteristics and approaching depinning.

Contribution

It provides a detailed analysis of how various resonant modes of domain walls are affected by notch geometry and pinning potential, including a harmonic oscillator model for depinning behavior.

Findings

Translational mode frequency drops near zero at depinning.

Lateral motion modes are highly sensitive to notch depth.

Breathing mode remains relatively insensitive to notch size.

Abstract

We study translational, breathing and twisting resonant modes of transverse magnetic domain walls pinned at notches in ferromagnetic nanostrips. We demonstrate that a mode's sensitivity to notches depends strongly on the characteristics of that particular resonance. For example, the frequencies of modes involving lateral motion of the wall are the ones which are most sensitive to changes in the notch intrusion depth (especially at the narrower, more strongly confined end of the domain wall). In contrast, the breathing mode, whose dynamics are concentrated away from the notches is relatively insensitive to changes in the notches' sizes. We also demonstrate a sharp drop in the translational mode's frequency towards zero when approaching depinning which is found, using a harmonic oscillator model, to be consistent with a reduction in the local slope of the notch-induced confining potential at its edge.