  We demonstrate experimentally that the presence of a single domain wall in an
underlying ferromagnetic BaFe_{12}O_{19} substrate can induce a considerable
asymmetry in the current (I) - voltage (V) characteristics of a superconducting
Al bridge. The observed diode-like effect, i.e. polarity-dependent critical
current, is associated with the formation of a vortex-free channel inside the
superconducting area which increases the total current flowing through the
superconducting bridge without dissipation. The vortex-free region appears only
for a certain sign of the injected current and for a limited range of the
external magnetic field.
