Dark-soliton-like magnetic domain walls in a two-dimensional ferromagnetic superfluid

We report a magnetic domain wall in a uniform ferromagnetic spin-1 condensate, a stable topological excitation characterized by the magnetization having a dark soliton profile with nonvanishing superfluid density. In the absence of magnetic fields, this domain wall relates various distinct solitary excitations in binary condensates through $\textrm{SO}(3)$ spin rotations, which otherwise are unconnected. We find an exact solution for a particular ratio of interaction parameters, and develop an accurate analytic solution applicable to the whole ferromagnetic phase. Studying the dynamics of a quasi-two-dimensional (quasi-2D) system we show that standing wave excitations of the domain wall oscillate without decay, being stable against the snake instability. The domain wall is dynamically unstable to modes that cause the magnetization to twist. However, dynamics in the presence of noise reveals that this "spin twist" instability does not destroy the topological structure of the magnetic domain wall.