The resistivity due to a domain wall in a ferromagnetic metal is calculated based on a linear response theory. The scattering by impurities is taken into account. The electron-wall interaction is derived from the exchange interaction between the conduction electron and the magnetization by use of a local gauge transformation in the spin space. This interaction is treated perturbatively to the second order. The classical (Boltzmann) contribution from the wall scattering turns out to be negligiblly small if the wall is thick compared with the fermi wavelength. In small contacts a large classical domain wall resistance is expected due to a thin wall trapped in the constriction. In the dirty case, where quantum coherence among electrons becomes important at low temperature, spin flip scattering caused by the wall results in dephasing and hence suppresses weak localization. Thus the quantum correction due to the wall can lead to a decrease of resistivity. This effect grows rapidly at low temperature where the wall becomes the dominant source of dephasing. Conductance change in the quantum region caused by the motion of the wall is also calculated.
Domain-wall-assisted giant magnetoimpedance of thin-wall ferromagnetic nanotubes
