Finite-size scaling in ${\mathrm{FeF}}_2$/${\mathrm{ZnF}}_2$ superlattices

Thermal-expansion measurements of (${\mathrm{FeF}}_2$${)}_{\mathit{n}}$(${\mathrm{ZnF}}_2$${)}_{\mathit{m}}$ magnetic/nonmagnetic superlattices via high-resolution x-ray diffraction have been made throughout the antiferromagnetic phase-transition region. Using the proportionality of the magnetically induced thermal expansion to the magnetic specific heat, the experimental results are compared with detailed Monte Carlo simulations. Both the experimental and Monte Carlo data are analyzed in terms of finite-size scaling theory. From this combined analysis, we are able to show that the observed shifts in the phase-transition temperature with respect to bulk ${\mathrm{FeF}}_2$ arise from three-dimensional to two-dimensional Ising-model crossover behavior. To our knowledge, this is the first time that dimensional crossover in a real Ising-like magnetic system has been experimentally observed.