Resistivity due to a domain wall in ferromagnetic metal

The resistivity due to a domain wall in ferromagnetic metallic wire is calculated based on the linear response theory. The interaction between conduction electrons and the wall is expressed in terms of a classical gauge field which is introduced by the local gauge transformation in the electron spin space. It is shown that the wall contributes to the decoherence of electrons and that this quantum correction can dominate over the Boltzmann resistivity, leading to a decrease of resistivity by nucleation of a wall. Conductance fluctuations due to the motion of the wall are also investigated. The results are compared with recent experiments.