  The magnetization reversal in ordered arrays of iron oxide nanotubes of 50 nm
outer diameter grown by atomic layer deposition is investigated theoretically
as a function of the tube wall thickness, $d_{w}$. In thin tubes ($d_{w}<13$
nm) the reversal of magnetization is achieved by the propagation of a vortex
domain boundary, while in thick tubes ($d_{w}>13$ nm) the reversal is driven by
the propagation of a transverse domain boundary. Magnetostatic interactions
between the tubes are responsible for a decrease of the coercive field in the
array. Our calculations are in agreement with recently reported experimental
results. We predict that the crossover between the vortex and transverse modes
of magnetization reversal is a general phenomenon on the length scale
considered.
