  We study the heterogeneous nucleation of Ising model on complex networks
under a non-equilibrium situation where the impurities perform degree-biased
motion controlled by a parameter \alpha. Through the forward flux sampling and
detailed analysis on the nucleating clusters, we find that the nucleation rate
shows a nonmonotonic dependence on \alpha for small number of impurities, in
which a maximal nucleation rate occurs at \alpha=0 corresponding to the
degree-uncorrelated random motion. Furthermore, we demonstrate the distinct
features of the nucleating clusters along the pathway for different preference
of impurities motion, which may be used to understand the resonance-like
dependence of nucleation rate on the motion bias of impurities. Our theoretical
analysis shows that the nonequilibrium diffusion of impurities can always
induce a positive energy flux that can facilitate the barrier-crossing
nucleation process. The nonmonotonic feature of the average value of the energy
flux with \alpha may be the origin of our simulation results.
