  A domain wall in a magnet with easy-axis anisotropy is shown to harbor spin
superfluid associated with its spontaneous breaking of the U(1) spin-rotational
symmetry. The spin superfluid is shown to have several topological properties,
which are absent in conventional superfluids. First, the associated phase slips
create and destroy skyrmions to obey the conservation of the total skyrmion
charge, which allows us to use a domain wall as a generator and detector of
skyrmions. Secondly, the domain wall engenders the emergent magnetic flux for
magnons along its length, which are proportional to the spin supercurrent
flowing through it, and thereby provides a way to manipulate magnons. Thirdly,
the spin supercurrent can be driven by the magnon current traveling across it
owing to the spin transfer between the domain wall and magnons, leading to the
magnonic manipulation of the spin superfluid. The theory for superfluid spin
transport within the domain wall is confirmed by numerical simulations.
