Topological defects in flat nanomagnets: The magnetostatic limit

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.