SPIN-GLASS DYNAMICS - RELATION BETWEEN THEORY AND EXPERIMENT - A BEGINNING

The configuration space of spin-glasses is characterized by the existence of quasi-degenerate equilibrium states separated by barriers, DELTA(T). A temperature cycling protocol enables us to extract the temperature dependence of a specific barrier. We determine partial derivative DELTA(T) /partial derivative T vs T, and partial derivative DELTA(T)/partial derivative T vs DELTA for barriers between 25T(g) and 35T(g) at temperatures 8, 9, 9.5 and 10 K (T(g) = 10.4 K) for Ag: Mn (2.6 at%). We find, in the range of temperature investigated and within experimental accuracy, that partial-derivative DELTA(T)/partial derivative T depends only on the particular value of DELTA(T) and not on the temperature. d-DELTA(T)/dT(r) can be fitted using all the data points to either a power law (a-DELTA-6) or an exponential [alpha exp(beta-DELTA)], where T(r) = T/T(g). Integration leads to a divergence of DELTA(T) at temperature T* (integration constant) as the temperature decreases, characteristic of the particular barrier considered. The existence of aging effects at all temperatures below T(g) in the whole range of accessible times implies a continuous distribution of barrier heights at any temperature. Hence, at any temperature below T(g) there are diverging barriers, associated with a distribution of T* with an upper cutoff value of T(g). Said another way, as the temperature is lowered to T(g), the first divergence of a barrier occurs, separating phase space into two (or more) regimes. States separated by divergent barriers are the "pure states". As the temperature is lowered, a continuous series of barrier divergences breaks up phase space into ever smaller regions, creating an ever increasing number of pure states. Between these divergent barriers, barriers of finite height exist. Those between 25T(g) and 35T(g) are responsible for the dynamics accessible to us in our experiments. We interpret the time decay of the thermoremanent magnetization, M(TRM)(t), at times t much larger than the waiting time, t(w), as a measure of the correlation of the spin-glass state at t with the field cooled state. Using the concept of ultrametricity, this enables us to "tract the branching ratio of the "tree" into which the spin-glass states are organized from a plot of log M(TRM)(t) vs log t, for t much greater than t(w). Experiments on the insulating spin-glass CdCr1.7In0.3S4 for a waiting time of 10.2 min and measurement times t up to 5 540 min (4 days!) exhibit a linear relationship between log M(TRM)(t) and log t. Within the approximations made, this implies a constant branching ratio for the ultrametric tree, at least within the (small) range of overlaps q accessible to us because of our experimental time window. These conclusions suggest that our dynamical measurements can be interpreted within the mean-field picture for spin-glasses.