We introduce in the diffusion-limited aggregation model an internal degree of freedom, i.e., a spin taking two states (up and down) with power-law Ising interaction. The fractal aggregation of magnetic particles with different ranges of interaction is investigated by Monte Carlo simulation. The simulation shows that for the antiferromagnetic coupling, the spins of the particles in the aggregates tend to be oriented alternately. For the ferromagnetic coupling, however, the spin orientation distribution of the aggregates depends on the interaction range: for the short-range interaction, domains with different sizes are observed in the aggregates, i.e., the aggregates exhibit ferromagnetic structure; for the long-range interaction, during the earlier stage of the growth process, the aggregates exhibit approximately antiferromagnetic structure, then, in subsequent growth of the outer part of the aggregates, the spin states of all particles are similar. The morphology and magnetization of the magnetic fractal aggregates as well as their evolutions with different ranges of interaction are also studied.
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