  We present a circuit model to describe the electron transport through a
domain wall in a ferromagnetic nanowire. The domain wall is treated as a
coherent 4-terminal device with incoming and outgoing channels of spin up and
down and the spin-dependent scattering in the vicinity of the wall is modelled
using classical resistances. We derive the conductance of the circuit in terms
of general conductance parameters for a domain wall. We then calculate these
conductance parameters for the case of ballistic transport through the domain
wall, and obtain a simple formula for the domain wall magnetoresistance which
gives a result consistent with recent experiments. The spin transfer torque
exerted on a domain wall by a spin-polarized current is calculated using the
circuit model and an estimate of the speed of the resulting wall motion is
made.
