  A phenomenological approach based on the principle of minimum heat generation
is proposed for understanding experiments for metallic wires with a
ferromagnetic domain wall controlled by a magnetic field. This approach
elucidates the origin of negative jump and of hysteresis in the
magnetoresistance experiments. To justify our approach, we computed the
transmission probability of a single electron through a wire. Under certain
conditions, the presence of a domain wall enhances the transmission through an
impurity potential. Combining this result with the principle of minimum heat
generation explains the counterintuitive negative resistance jump.
