Magnetic dipolar interaction in ultrathin films: Structural and size effects

A previously introduced formalism for calculating magnetic dipolar anisotropy energy Δ U in atomic layered structures is further developed. Numerical results are presented for ultrathin films with different close-packed (face centered cubic (FCC) [1 1 1]) and non-close-packed (FCC [0 0 1] and body centered cubic (BCC) [0 0 1]) structures. Structural effects become apparent in the magnetocrystalline dipolar anisotropy energy Δ U L when the ratio between the interlayer separation c and the 2D lattice constant a is changed. Despite the long-range character of the dipolar interaction, it is shown that the number of significantly interacting layers, conventially called coupled layers, is limited and depends on the structural aspect ratio c / a . The slope in the observed linear dependence between Δ U L and the inverse of the film thickness t is explained by the number of the so-called coupled layers, and not by a surface contribution to volume values. Size effects appearing in Δ U are unambiguously distinguished from structural effects. Effective anisotropy energy Δ U eff and Δ U are presented for Co [0 0 0 1] and Ni [0 0 1] ultrathin films. It is verified that the dipolar interaction makes an important contribution to Δ U eff , but the spin reorientation transition is determined by non-dipolar interactions. The former favors the magnetization switching only when the size aspect ratio d / t , with d the characteristic lateral dimension of the film, is sufficiently small. Applications to other layered arrays of magnetic dipoles are straightforward.