  We show that an applied charge current in a magnetic nanowire containing
domain walls (DWs) results in an interaction between DWs mediated by
spin-dependent interferences of the scattered carriers. The energy and torque
associated with this interaction show an oscillatory behaviour as a function of
the mutual DWs orientations and separations, thus affecting the DWs'
arrangements and shapes. Based on the derived DWs interaction energy and torque
we calculate DW dynamics and uncover potential applications of interacting DWs
as a tunable nano-mechanical oscillator. We also discuss the effect of
impurities on the DW interaction.
