Domain wall scattering in an interacting one-dimensional electron gas

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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.