  So far magnetic domain walls in one-dimensional structures have been
described theoretically only in the cases of flat strips, or cylindrical
structures with a compact cross-section, either square or disk. Here we
describe an extended phase diagram unifying the two pictures, extensively
covering the (width,thickness) space. It is derived on the basis of symmetry
and phase-transition arguments, and micromagnetic simulations. A simple
classification of all domain walls in two varieties is proposed on the basis of
their topology: either with a combined transverse/vortex character, or of the
Bloch-point type. The exact arrangement of magnetization within each variety
results mostly from the need to decrease dipolar energy, giving rise to
asymmetric and curling structures. Numerical evaluators are introduced to
quantify curling, and scaling laws are derived analytically for some of the
iso-energy lines of the phase diagram.
