The Curie temperature $T_C\mathrm{}\left(l\right)\mathrm{}$for Ising spin films calculated analytically as a function of $l,$ the number of monolayers in the film, is compared with available data. When the exchange coupling between nearest neighboring pairs is assumed to be uniform, the normalized $T_C\mathrm{}\left(l\right)\mathrm{}$ is generally higher than what is observed, especially in the dimensionality crossover region in which $T_C\mathrm{}\left(l\right)\mathrm{}$ increases with $l$ much too fast. To reproduce the experimental data measured by various groups on ultrathin Ni films in (001) orientation, we calculate the normalized transition temperature $T_C{\mathrm{}\left(l\right)/T}_C$(bulk) to fourth order in the variational cumulant expansion for a face-centered-cubic lattice with variable anisotropic exchange coupling $J_{\mathrm{ij}}.$ It is shown that the data can be very well described by adjusting $J_{\mathrm{ij}}$ for a few monolayers near the surfaces. The results are consistent with the finite-size scaling law outside the region of dimensionality crossover, providing a clue to the number of monolayers influenced by the presence of surfaces.

• Received 9 May 1996

DOI:https://doi.org/10.1103/PhysRevE.56.2805