  A domain wall in a ferromagnetic one-dimensional nanowire experiences current
induced motion due to its coupling with the conduction electrons. When the
current is not sufficient to drive the domain wall through the wire, or it is
confined to a perpendicular layer, it nonetheless experiences oscillatory
motion. In turn, this oscillatory motion of the domain wall can couple
resonantly with the electrons in the system affecting the transport properties
further. We investigate the effect of the coupling between these domain wall
modes and the current electrons on the transport properties of the system and
show that such a system demonstrates negative differential magnetoresistance
due to the resonant coupling with the low-lying modes of the domain wall
motion.
