Atomic and electronic structure of Fe$_2$O$_3$(0001) films on polar and non-polar substrates

To address the role of polarity on the growth and stability of heterointerfaces, we present a first-principles study of the structural, electronic, and magnetic properties of the layer-by-layer growth of Fe$_2$O$_3$(0001) thin films on polar MgO(111) and metallic Ti(0001) substrates. The films show thickness-dependent properties, including metallic interface states even at the polar ``oxide-like'' interface between Fe$_2$O$_3$ and MgO. Drastic structural relaxations are, especially at thicknesses of three Fe-bilayers on both the polar and metallic substrates. The stability of the Fe and O surface terminations as a function of the chemical potential will also be discussed.