Field distributions of arbitrary-shaped magnetic domains calculated by two-dimensional discrete Fourier series

A two-dimensional discrete Fourier series method has been used to calculate the field distributions of arbitrary cylindrical-shaped magnetic domain arrays. In the present method there is generated a scalar magnetostatic potential φ(r), in discrete Fourier series form, which is related to the specified distribution of magnetic dipole densities by Poisson´s equation. The magnetic field strength is then derived from the gradient of the scalar magnetostatic potential, using the orthogonal properties of Fourier series to determine the unknown coefficients. A program has been prepared and numerical results are presented. Calculated results comparewell with known results for a specific lattice of magnetic bubble domains, a 24 μm × 41.57 μm hexagonal array.