The magnetization reversal in perpendicular applied magnetic fields in low-temperature grown Fe/Cu(100) ultrathin films was studied in situ by magneto-optical Kerr effect, Kerr-microscopy, and scanning tunneling microscopy. It was found that the onset of long-range ferromagnetic order at \ensuremath{\cong}0.9 monolayers (ML) is related to the coalescence of bilayer islands of Fe. Below 3.8 ML, the magnetization-reversal process takes place in a narrow field range and is characterized by domain-wall motion. While the domain boundaries are rather smooth at thin films, domains get increasingly irregularly shaped above 3 ML, which is assigned to a decrease of the domain-wall energy. At the spin-reorientation transition from out-of-plane to in-plane magnetization at \ensuremath{\cong}3.8 ML, two coexisting metastable spin configurations are found.
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