Critical slowing down in the two-dimensional Ising model measured using ferromagnetic ultrathin films

Abstract

Power-law scaling of the relaxation time $\ensuremath{\tau}$ associated with critical slowing down has been experimentally measured in the dynamics of the magnetization of a bilayer of iron grown on top of a $W(110)$ substrate using the complex magnetic ac susceptibility $\ensuremath{\chi}(T)$. The observed value of the critical exponent for the slowing down above the Curie transition of this two-dimensional Ising ferromagnetic system is $z\ensuremath{\nu}=2.09\ifmmode\pm\else\textpm\fi{}0.06$ (95% confidence), in agreement with most contemporary theories and simulations. Further analysis reveals that dynamical effects cause $\ensuremath{\chi}(T)$ to deviate from power-law scaling as the temperature is decreased towards ${T}_{c}$, whereas the saturation of the correlation length due to finite-size effects (on the order of 500 lattice spaces) limits the divergence of $\ensuremath{\tau}$.