  The nonequilibrium magnetic domain structure of growing ultrathin
ferromagnetic films with a realistic atomic structure is studied as a function
of coverage and temperature. We apply a kinetic Monte Carlo method to a
micromagnetic model describing the transition from superparamagnetic islands at
low coverages to a closed ferromagnetic film. The magnetic relaxation and the
island growth happen simultaneously. Near the percolation threshold a
metastable magnetic domain structure is obtained with an average domain area
ranging between the area of individual magnetic islands and the area of the
large domains observed for thicker ferromagnetic films. We conclude that this
micro-domain structure is controlled and stabilized by the nonuniform atomic
nanostructure of the ultrathin film, causing a random interaction between
magnetic islands with varying sizes and shapes. The average domain area and
domain roughness are determined. A maximum of the domain area and a minimum of
the domain roughness are obtained as a function of the temperature.
