  We discuss elementary topological defects in soft magnetic nanoparticles in
the thin-film geometry. In the limit dominated by magnetostatic forces the
low-energy defects are vortices (winding number n = +1), cross ties (n = -1),
and edge defects with n = -1/2. We obtain topological constraints on the
possible composition of domain walls. The simplest domain wall in this regime
is composed of two -1/2 edge defects and a vortex, in accordance with
observations and numerics.
