  We investigate the effect of curvature on the energy and stability of domain
wall configurations in curved cylindrical nanotubes and nanowires. We use
micromagnetic simulations to calculate the phase diagram for the transverse
wall (TW) and vortex wall (VW) states in tubes, finding the ground state
configuration and the metastability region where both types of walls can exist.
The introduction of curvature shifts the range for which the TW is the ground
state domain wall to higher diameters, and increases the range of
metastability. We interpret this behavior to be primarily due to the
curvature-induced effective Dzyaloshinskii-Moriya term in the exchange energy.
Furthermore, we demonstrate qualitatively the same behavior in solid
cylindrical nanowires. Comparing both tubes and wires, we observe how while in
tubes curvature tends to suppress the transformation from the TW to VW, in
wires it promotes the transformation of the VW containing the Bloch point into
the TW. These findings have important implications in the fundamental
understanding of domain walls in 3D geometries, and the design of future domain
wall devices.
