Thickness-Dependent Curie Temperatures of Ultrathin Magnetic Films: Effect of the Range of Spin-Spin Interactions

We present a simple model of spin-spin coupling which provides insight into the nature of the rapid decrease in the Curie temperature with decreasing thin film thickness $n$ (number of monolayers). The shift of Curie temperature $t\left(n\right){=1-T}_c\left(n\right){/T}_c\left(\infty \right)$ follows the usual power law $t\left(n\right)\sim n^{-\lambda }$ in thin films crossing over to linear behavior $t\left(n\right)\sim n$ in the ultrathin film thickness limit. Experimental results for ferromagnetic thin films are compared, and shown to follow curves of $t\left(n\right)$ with $\lambda$ values dependent on the nature of the spin-spin interactions.