We study the magnetoresistance (MR) of a one-dimensional
electron gas in a ferromagnetic semiconducting nanocontact
containing an atomic-size domain wall, and in the presence of
the Rashba and the Dresselhaus spin–orbit interactions. The
MR is calculated in the ballistic regime, within the Landauer–
Bu¨ttiker formalism. It is shown that, the Dresselhaus spin–orbit
interaction which is the result of bulk-induced inversion
asymmetry makes a reduction in the domain wall MR. In
contrast, the Rashba coupling may lead to a negative or positive
change in the domain wall MR, depending on the Fermi energy
and the lateral confinement potentials which can be induced by
both parabolic lateral confinement and lateral gate potentials.