Dipolar field and energy anisotropy in magnetic thin films

The formalism for dipolar field calculations in thin films is addressed. It is shown that in the limit of very thin films the separation of the dipolar field contribution perpendicular to the film plane cannot be split into a shape contribution and a lattice contribution. The failure in recognizing this leads to the wrong interpretation of magnetic-susceptibility measurements. It is shown that lattice summation can be carried out generalizing the Ewald-Born procedure to the case when the magnetization and the point where the field is being calculated are not constrained to the dipolar planes. This procedure avoids the direct summation of lattice dipoles and the split of the summation into a discrete part and a continuum integration. The formalism is applied to the $2H$ and $3R$ close-packed stacking arrangements.