Topological defects in flat nanomagnets: the magnetostatic limit
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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.