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Hybridization of semiconducting and magnetic materials into a single heterostructure is believed to be potentially applicable to the design of novel functional spintronic devices. In the present work we report epitaxial stabilization of four magnetically ordered iron oxide phases (Fe3O4, {\gamma}-Fe2O3, {\alpha}-Fe2O3 and most exotic metastable {\epsilon}-Fe2O3) in the form of nanometer sized single crystalline films on GaN(0001) surface. The epitaxial growth of as many as four distinctly different iron oxide phases is demonstrated within the same single-target Laser MBE technological process on a GaN semiconductor substrate widely used for electronic device fabrication. The discussed iron oxides belong to a family of simple formula magnetic materials exhibiting a rich variety of outstanding physical properties including peculiar Verwey and Morin phase transitions in Fe3O4 and {\alpha}-Fe2O3 and multiferroic behavior in metastable magnetically hard {\epsilon}-Fe2O3 ferrite. The physical reasons standing behind the nucleation of a particular phase in an epitaxial growth process deserve interest from the fundamental point of view. The practical side of the presented study is to exploit the tunable polymorphism of iron oxides for creation of ferroic-on-semiconductor heterostructures usable in novel spintronic devices. By application of a wide range of experimental techniques the surface morphology, crystalline structure, electronic and magnetic properties of the single phase iron oxide epitaxial films on GaN have been studied. A comprehensive comparison has been made to the properties of the same ferrite materials in the bulk and nanostructured form reported by other research groups., Comment: 25 pages, 12 figures