Spin glass dynamics at the mesoscale

The mesoscale allows a new probe of spin glass dynamics. Because the spin glass lower critical dimension d(l)> 2, the growth of the correlation length xi(t,T) can change the nature of the spin glass state at a crossover time t(co) when xi(t(co),T)=l, a minimum characteristic sample length (e.g., film thickness for thin films and crystallite size for bulk samples). For thin films, and times t < t(co) such that xi(t,T) < l, conventional three-dimensional dynamics is observed. When t > t(co), a crossover to d = 2 behavior takes place. The parallel correlation length, associated with a T-g = 0 transition, increases in time from the saturated value of the perpendicular correlation length l to an equilibrium value of the parallel correlation length proportional to T-nu. This results in a pancakelike correlated state, with a thickness l and a temperature-dependent in-plane radius that increases with decreasing temperature. Activated dynamics is associated with these states. Measurements on Cu:Mn thin films are analyzed quantitatively within this framework. We extract a temperature-dependent activation energy from a fit to the frequency dependence of the dynamic susceptibility. The extrapolated temperature at which the activation energy would become large is close to the extrapolated glass transition temperature from ac susceptibility measurements. All known relevant experimental data are consistent with this approach. For polycrystalline materials, there is a distribution of length scales P(l). For sufficiently broad distributions, a logarithmic time dependence is derived for the time decay of the thermoremanent magnetization M-TRM(t,T) using an approach originally derived by Ma. Properties dependent upon an effective waiting time t(w)(eff) are derived that are consistent with experiment, and further measurements are suggested.