Spin Glass Dynamics: Finite Size Effects

Because the spin glass lower critical dimension $2t_{co}$, spin glass dynamics cross over to two-dimensional behavior. However, even for $t>t_{co}$, there remain correlated spin glass states for which $\xi(t,T)<\ell$, but with a maximum barrier height $\Delta_{max}$. Furthermore, because of ultrametricity, the number of states separated by $\Delta_{max}$ is exponentially large. This leads to activated dynamics controlling the time dependence of the zero field cooled and thermoremanent magnetization near the glass transition temperature. We have measured these phenomena in films of a-Ge:Mn, and obtained quantitative results for (the related) $t_{co}$ and $\Delta_{max}$. These states are also responsible for the frequency dependence of the dynamic susceptibility $\chi(t)$ of Cu:Mn thin film sandwiches previously measured by Sandlung {\it et al}. We show that the spin glass temperature remains at the bulk $T_g$, and that the temperature dependence of $\chi(t)$ is a consequence of $\Delta_{max}$.