  We investigate the relaxation process of ferromagnetic domains in 2D
subjected to the influence of both, static disorder of variable strength and
weak interactions. The domains are represented by a two species bosonic mixture
of $^{87}$Rb ultracold atoms, such that initially each specie lies on left and
right halves of a square lattice. The dynamics of the double domain is followed
by describing the two-component superfluid, at mean field level, through the
time dependent Gross-Pitaevskii coupled equations, considering values of the
intra and inter-species interaction, reachable in current experimental setups,
that guaranty miscibility of the components. A robust analysis for several
values inter-species interaction leads us to conclude that the presence of
structural disorder leads to slowdown the relaxation process of the initial
ferromagnetic order. As shown by our numerical experiments, magnetization is
maintained up to 60 percent of its initial value for the largest disorder
amplitude.
