Application of Conformal Mapping to the determination of Magnetic Moment   Distributions in typical Antidot Film Nanostructures
  There has been an increasing technological interest on magnetic thin films containing antidot arrays of hexagonal or square symmetry. Part of this interest is related to the possibility of domain formation and pinning at the antidots boundaries. In this paper, we develop a method for the calculation of the magnetic moment distribution for such arrays which concentrates on the immediate vicinity of each antidot. For each antidot distribution (square or hexagonal) a suitable system of coordinates is defined to exploit the shape of the unit-cells of the overall nanostructure. The Landau-Lifshitz-Gilbert-Brown equations that govern the distribution of moments are rewritten in terms of these coordinates. The equilibrium moments orientation is calculated for each position in a Cartesian grid defined for these new coordinate systems, and then a conformal transformation is applied to insert the moment vectors into the actual unit-cell. The resulting vector maps display quite clearly regions of different moment orientation around the antidots, which can be associated with nanoscale domains. These results are similar to the ones obtained by other authors[1-4] using the NIST oommf method. 
Osvaldo F. Schilling