  Recently it was suggested that stationary spin supercurrents (spin
superfluidity) are possible in the magnon condensate observed in
yttrium-iron-garnet (YIG) magnetic films under strong external pumping. Here we
analyze this suggestion. From topology of the equilibrium order parameter in
YIG one must not expect energetic barriers making spin supercurrents
metastable. However some small barriers of dynamical origin are possible
nevertheless. The critical phase gradient (analog of the Landau critical
velocity in superfluids) is proportional to intensity of the coherent spin wave
(number of condensed magnons). The conclusion is that although spin
superfluidity in YIG films is possible in principle, the published claim of its
observation is not justified.
  The analysis revealed that the widely accepted spin-wave spectrum in YIG
films with magnetostatic and exchange interaction required revision. This led
to revision of non-linear corrections, which determine stability of the magnon
condensate with and without spin supercurrents.
