The magnetic Fe nanostructures formed on a Cu(111) surface were simulated by the kinetic Monte Carlo (kMC) method, in which the substrate-mediated long-range interactions between Fe adatoms are involved. The dependence of coverage and temperature on the formation of local nanostructures was investigated to reveal the microprocess of Fe nanostructures formed on a Cu(111) substrate. The simulation results show that the long-range interactions between Fe adatoms lead first to the formation of short linear chains and then to locally ordered nanostructures when they become steady at low coverages between 10 and 18 K. Based on the analysis of the formation mechanism of the Fe superlattice, it is found that the size of the repulsive ring, the distance to the first minimum potential and the diffusion barrier are the important parameters for Fe adatoms to form a superlattice on the Cu(111) surface.
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