  We study the transport in a Luttinger liquid coupled to a magnetic chain
containing a Bloch domain wall. We compute the leading correction to the
adiabatic limit of a long domain wall, which causes no scattering. We show that
the problem is reminiscent of an impurity in a Luttinger liquid, but with a
different dependence on the interaction parameters due to spin-flip scattering.
For repulsive interactions, we find that the domain wall resistance diverges
with decreasing temperature. This may be relevant for the design of
one-dimensional systems with large magnetoresistance at low temperatures.
