Effect of a Domain Wall on the Conductance Quantization in a Ferromagnetic Nanowire

The effect of the domain wall (DW) on the conductance in a ballistic ferromagnetic nanowire (FMNW) is revisited by exploiting a specific perturbation theory which is effective for a thin DW; the thinness is often the case in currently interested conductance measurements on FMNWs. Including the Hund coupling between carrier spins and local spins in a DW, the conductance of a FMNW in the presence of a very thin DW is calculated within the Landauer-B\"{u}ttiker formalism. It is revealed that the conductance plateaus are modified significantly, and the switching of the quantization unit from $e^2/h$ to ``about $2e^2/h$'' is produced in a FMNW by the introduction of a thin DW. This accounts well for recent observations in a FMNW.