We have simulated the magnetic relaxation (M(t)) and the nucleation of
magnetic domains in the presence of magnetic field in thin films with
anisotropy perpendicular to the film plane. We have used Monte Carlo
simulations based on the two-dimensional classical Ising model includi
ng the long-range dipole-dipole and Zeeman interactions. Domains nucle
ated during the magnetic relaxation exhibit very rough interfaces. We
analyze the roughness and the M(t) as a function of the relative stren
gth of dipole-dipole and Zeeman terms.