We present a theory of the magnetic properties of the A-B phase bounda
ry propagating in He-3 under conditions of low temperature and therefo
re with slow magnetic relaxation. Owing to the difference in susceptib
ility between the phases, a nonequilibrium magnetization appears behin
d the moving boundary. This magnetization is transported in the form o
f step solitons into the bulk A and B phases by a new spin supercurren
t mode, related to the longitudinal NMR, which explains the experiment
ally observed magnetic precursor travelling ahead of the boundary.