Boundary Vortices in Micromagnetics

We study the asymptotic behavior of boundary vortices and their interaction energy in a certain regime of thin-film micromagnetics. The key tool relies on the notion of “boundary Jacobian" which detects the topological defects at the boundary. The concentration of the energy around boundary vortices is proven via a Gamma-convergence result and we determine the renormalized energy that represents the interaction between the boundary vortices leading to their optimal position. The major difficulty consists in estimating the nonlocal part of the micromagnetic energy generated by the static Maxwell equation in order to detect the exact terms corresponding to the topological defects.

This is a joint work with Matthias Kurzke (Nottingham).