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

We study resonant translational, breathing, and twisting 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 mode's characteristics. For example, the frequencies of modes that involve lateral motion of the wall are the most sensitive to changes in the notch intrusion depth, especially at the narrow, 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 confirmed, using a harmonic oscillator model, to be consistent with a reduction in the local slope of the notch-induced confining potential at its edge.