Spin Wave Eigenmodes of Dzyaloshinskii Domain Walls

A theory for the spin wave eigenmodes of a Dzyaloshinskii domain wall is presented. These walls are N'eel-type domain walls that can appear in perpendicularly-magnetized ultrathin ferromagnets in the presence of a sizeable Dzyaloshinskii-Moriya interaction. The mode frequencies for spin waves propagating parallel and perpendicular to the domain wall are computed using a continuum approximation. In contrast to Bloch-type walls, it is found that the spin wave potential associated with Dzyaloshinskii domain walls is not reflectionless, which leads to a finite scattering cross-section for interactions between spin waves and domain walls. A gap produced by the Dzyaloshinskii interaction emerges, and consequences for spin wave driven domain wall motion and band structures arising from periodic wall arrays are discussed.