  We consider interaction effects related to a nonuniform magnetization in
ferromagnetic nanowires and their possible generalization to nanorings. First
we show that the electric current in a ferromagnetic nanowire with more than
one domain wall induces an exchange coupling between the walls mediated by the
spin-dependent interference of scattered carriers. This interaction reveals a
complex behavior as a function of mutual orientations and separation of the
domain walls, thus affecting the domain wall dynamics. Then we consider how the
theory should be modified in the case of a magnetized quantum ring. In this
case the situation is more complicated because the vortex and onion
magnetization states in the ring are not truly ferromagnetic.
