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(n)0ex0ex=0ex0ex1-Tc(n)/Tc(∞) follows the usual power law t(n)~n^-λ in thin films crossing over to linear behavior t(n)~n in the ultrathin film thickness limit. Experimental results for ferromagnetic thin films are compared, and shown to follow curves of $t(n)$ with λ values dependent on the nature of the spin-spin interactions.