Demagnetizing fields in chiral magnetic structures

A method for calculating the magnetic dipole-dipole interaction in topological magnetic systems has been developed. It can be used to calculate stable states and minimum energy paths that determine the magnetic transition in chiral magnetic structures. Instead of directly summing the dipole interactions between magnetic moments/magnetic elements, we solve a local equation for demagnetizing fields. The states corresponding to the local energy minimum can be found using the Lagrange method for the conditional extrema. The efficiency of the algorithm has been demonstrated by calculating the dependence of the size and shape of magnetic skyrmions and anti-skyrmions on the magnitude of magnetization.