  We investigate the formation of lattice matched single-crystalline
Fe$_3$Si/GaAs(001) ferromagnet/semiconductor hybrid structures by Volmer-Weber
island growth, starting from the epitaxial growth of isolated Fe$_3$Si islands
up to the formation of continuous films as a result of island coalescence. We
find coherent defect-free layers exhibiting compositional disorder near the
Fe$_3$Si/GaAs-interface for higher growth rates, whereas they are fully ordered
for lower growth rates.
