GdN and GaN are both insulators, the former being also a ferromagnet. Despite a lattice mismatch of 10.1% and different crystal structures, lattice-matched interfaces where GdN adopts the smaller lattice parameter of GaN can be formed. We study isotropically and epitaxially strained GdN, as well as the nonpolar (011) GdN=GaN interface by first-principles calculation. We show that upon compressive strain (isotropic or biaxial) corresponding to the strain imposed by the GaN lattice, GdN becomes a half-metallic ferromagnet. In the interface calculation, however, no magnetization of GaN at or away from the interface is observed. The interface exhibits a Schottky connection with the GdN Fermi energy 1.19 eV above the GaN valence band (close to midgap); i.e., the system can be used as a rectifier and possibly also for spintronic applications.