  Interactions between pairs of magnetic domain walls (DW) and pinning by
radial constrictions were studied in cylindrical nanowires with surface
roughness. It was found that a radial constriction creates a symmetric pinning
potential well, with a change of slope when the DW is situated outside the
notch. Surface deformation induces an asymmetry in the pinning potential as
well as dynamical pinning. The depinning fields of the domain walls were found
generally to decrease with increasing surface roughness. A DW pinned at a
radial constriction creates a pinning potential well for a free DW in a
parallel wire. We determined that trapped bound DW states appear above the
depinning threshold and that the surface roughness facilitates the trapped
bound DW states in parallel wires.
