  We report a stable magnetic domain wall in a uniform ferromagnetic spin-1
condensate, characterized by the magnetization having a dark soliton profile
with nonvanishing superfluid density. We find exact stationary solutions for a
particular ratio of interaction parameters with and without magnetic fields,
and develop an accurate analytic solution applicable to the whole ferromagnetic
phase. 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. Remarkably, 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 grow perpendicularly while leaving the domain
wall unchanged. Real time dynamics in the presence of white noise reveals that
this "spin twist" instability does not destroy the topological structure of the
magnetic domain wall.
