  We present a theoretical study of the transport properties of magnetic point
contacts under bias. Our calculations are based on the Keldish's
non-equilibrium Green's function formalism combined with a self-consistent
empirical tight-binding Hamiltonian, which describes both strong ferromagnetism
and charging effects. We demonstrate that large magnetoresistance solely due to
electronic effects can be found when a sharp domain wall forms inside a
magnetic atomic-scale point contact. Moreover we show that the symmetry of the
$I$-$V$ characteristic depends on the position of the domain wall in the
constriction. In particular diode-like curves can arise when the domain wall is
placed off-center within the point contact, although the whole structure does
not present any structural asymmetry.
