A variational approach to exchange energy calculations in micromagnetics

This article presents a magnetization interpolation method for micromagnetic exchange energy calculations using a variational procedure to relax spins on a supplemental (refined) lattice. The approximations implicit in standard micromagnetic discretization schemes fail when angles between neighboring spins in the model become large, but the proposed approach effectively reduces the angle between neighboring spins, alleviating many of the associated problems. Moreover, this method does not introduce excessive discretization-induced vortex pinning observed with some large angle exchange energy formulations. This article includes details on proper post-interpolation exchange torque calculation, bounds on nearest-neighbor angles for interpolated lattices, a simple model predicting discretization-induced Néel wall collapse, and an example of a collapsed (1 cell wide) domain wall that can be restored by the proposed technique.