A theory for the spin-wave eigenmodes of a Dzyaloshinskii domain wall is presented. These walls are Néel-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 perpendicular to the domain wall plane 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 band structures arising from periodic wall arrays are discussed
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