  We report on the structural and electronic properties of the interface
between the multiferoic oxide YMnO$_3$ and wide band-gap semiconductor GaN
studied with the Hubbard-corrected local spin density approximation (LSDA+U) to
density-functional theory (DFT). We find that the band offsets at the interface
between antiferromagnetically ordered YMnO$_3$ and GaN are different for
spin-up and spin-down states. This behavior is due to the spin splitting of the
valence band induced by the interface. The energy barrier depends on the
relative orientation of the electric polarization with respect to the
polarization direction of the GaN substrate suggesting an opportunity to create
magnetic tunnel junctions in this materials system.
