A two-dimensional cluster model in which the morphology of clusters depends on power-law magnetic interactions that decay with distance r as a r(-alpha) law is introduced. The growth algorithm is a generalization of diffusion-limited aggregation ( DLA) model. The particles with spin degree diffuse on a square lattice and each spin is allowed to flip under a Monte Carlo probability. The simulation shows that, for the antiferromagnetic coupling, the spins of the particles in clusters tend to be oriented alternately. For the ferromagnetic coupling, however, the spin distribution depends on the exponent alpha: for large value of alpha, domains with different sizes are observed in the clusters; while for small alpha, during the earlier stage of the growth process, the clusters exhibit approximately antiferromagnetic structure, then, in subsequent growth of the outer part of the clusters, the spin states of all particles are similar. The magnetization and system energy of the clusters as well as their evolutions with the growth parameters are also studied in detail. (c) 2007 Elsevier B. V. All rights reserved.