  Here we demonstrate a new monoclinic iron oxide phase
({\mu}-Fe$_{2}$O$_{3}$), epitaxially stabilized by growth on (010)
{\beta}-Ga$_{2}$O$_{3}$. Density functional theory (DFT) calculations find that
the lattice parameters of freestanding {\mu}-Fe$_{2}$O$_{3}$ are within ~1% of
those of {\beta}-Ga$_{2}$O$_{3}$ and that its energy of formation is comparable
to that of naturally abundant Fe$_{2}$O$_{3}$ polytypes. A superlattice of
{\mu}-Fe$_{2}$O$_{3}$/{\beta}-Ga$_{2}$O$_{3}$ is grown by plasma assisted
molecular beam epitaxy, with resulting high-resolution x-ray diffraction (XRD)
measurements indicating that the {\mu}-Fe$_{2}$O$_{3}$ layers are
lattice-matched to the substrate. The measured out-of-plane (b) lattice
parameter of 3.12 $\pm$ 0.4 {\AA} is in agreement with the predicted lattice
constants and atomic-resolution scanning transmission electron microscopy
(STEM) images confirm complete registry of the {\mu}-Fe$_{2}$O$_{3}$ layers
with {\beta}-Ga$_{2}$O$_{3}$. Finally, DFT modeling predicts that bulk
{\mu}-Fe$_{2}$O$_{3}$ is antiferromagnetic, while the interface region between
{\mu}-Fe$_{2}$O$_{3}$ and {\beta}-Ga$_{2}$O$_{3}$ leads to ferromagnetic
coupling between interface Fe$^{3+}$ cations selectively occupying tetrahedral
positions. Magnetic hysteresis persisting to room temperature is observed via
SQUID measurements, consistent with the computationally predicted interface
magnetism.
