Finite-size effect on magnetic ordering temperatures in long-period antiferromagnets: Holmium thin films

The thickness dependence of the helical antiferromagnetic ordering temperature ${T}_{N}$ was studied for thin Ho metal films by resonant magnetic soft x-ray and neutron diffraction. In contrast with the Curie temperature of ferromagnets, ${T}_{N}$ was found to decrease with film thickness $d$ according to $[{T}_{N}(\ensuremath{\infty})\ensuremath{-}{T}_{N}(d)]/{T}_{N}(d)\ensuremath{\propto}(d\ensuremath{-}{d}_{0}{)}^{\ensuremath{-}{\ensuremath{\lambda}}^{\ensuremath{'}}}$, where ${\ensuremath{\lambda}}^{\ensuremath{'}}$ is a phenomenological exponent and ${d}_{0}$ is of the order of the bulk magnetic period ${L}_{b}$. These observations are reproduced by mean-field calculations that suggest a linear relationship between ${d}_{0}$ and ${L}_{b}$ in long-period antiferromagnets.