  We study the effect of a domain wall on the electronic transport in
ferromagnetic quantum wires. Due to the transverse confinement, conduction
channels arise. In the presence of a domain wall, spin up and spin down
electrons in these channels become coupled. For very short domain walls or at
high longitudinal kinetic energy, this coupling is weak, leads to very few spin
flips, and a perturbative treatment is possible. For very long domain wall
structures, the spin follows adiabatically the local magnetization orientation,
suppressing the effect of the domain wall on the total transmission, but
reversing the spin of the electrons. In the intermediate regime, we numerically
investigate the spin-dependent transport behavior for different shapes of the
domain wall. We find that the knowledge of the precise shape of the domain wall
is not crucial for determining the qualitative behavior. For parameters
appropriate for experiments, electrons with low longitudinal energy are
transmitted adiabatically while the electrons at high longitudinal energy are
essentially unaffected by the domain wall. Taking this co-existence of
different regimes into account is important for the understanding of recent
experiments.
