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Relaxation of ferromagnetic domains in a disordered lattice in 2D

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.