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 an accurate method for the simulation of the magnetic moments distribution for such arrays. The method concentrates the calculations 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 moments orientation is calculated as a function of time until equilibrium is reached, in a Cartesian grid defined for these new coordinate systems. 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. The results are similar to the ones obtained by other authors C.C. Wang, A.O. Adeyeye, N. Singh, Nanotechnology 17, 1629 (2006); C.C. Wang, A.O. Adeyeye, N. Singh, Y.S. Huang, Y.H. Hu, Phys. Rev. B 72, 174426 (2005); C.T. Yu, H. Jiang, L. Shen, P. Flanders, G. Mankey, J. Appl. Phys. 87, 6322 (2000); E. Mengotti, L.J. Heyderman, F. Nolting, B.R. Craig, J.N. Chapman, L.L. Diaz, R.J. Matelon, U.G. Volkman, M. Klaui, U. Rudiger, C. Vaz, J. Bland, J. Appl. Phys. 103, 07D509 (2008)] using the NIST oommf method, but obtained in a much simpler and direct way.