Nonreciprocal flexural dynamics of Dzyaloshinskii domain walls

We revisit the description of ferromagnetic domain wall dynamics through an extended one-dimensional model by allowing flexural distortions of the wall during its motion. This is taken into account by allowing the domain wall center and internal angle to be functions of position in the direction parallel to the wall. In the limit of small applied fields, this model accounts for the nonreciprocity in the propagation of wall modes and their stability in the presence of the Dzyaloshinskii-Moriya interaction and in-plane magnetic field.