The Time Dependency of the Remanent Magnetization of Spin Glasses.

The time dependence of the remanent magnetization, M(t), of the dilute metallic spin glasses Ag{: }Mn_{2.6at.%}, Cu{: }Mn_{6at.%} and Ag {:}Mn_{4at.%} + Sb_ {0.1at.%} have been measured in various experiments. We found that M(t) can be well characterized by a stretched exponential: M(t) = M_0exp (-(t/tau_{p})^{1 -n}] (0 < n < 1), for small applied field ({<}10^{-2 } T) and times up to the observation time at which the maximum of the response rate, R(t) (= -dM(t)/d {rm ln} t), occurs. The three parameters are the initial magnetization, M_0, the apparent relaxation rate, 1/tau_{p}, and the stretched exponential exponent, n. We show that these parameters are rather simply related to experimentally controllable quantities such as temperature, waiting time, etc. We propose a conceptual framework that allows us to develop a model of the spin glass state. The model incorporates both the main results of the Parisi theory and most of published and our experimental results of static and dynamic magnetization measurements on spin glasses. Our model assumes that the spin glass state is characterized by a complex free energy surface of which the (local) minima correspond to (metastable) thermodynamic states. The states with equilibrium magnetization are organized hierarchically (ultrametrically). Furthermore, we assume that a macroscopic sample consists of a large ensemble of individual spin glasses. At each instance a spin glass is in one of its available states and the distribution of state occupancies is postulated to describe the ensemble of individual spin glasses. The time evolution of the state occupancies corresponds then to the observed spin glass dynamics upon a change in applied fields such as external magnetic field and temperature. Another fundamental assumption is that a (temperature dependent) percentage of the individual spin glasses relaxes reversibly upon a small change in applied field whereas the others exhibit irreversible dynamics. These assumptions together with some results of the Parisi theory allow us to calculate the time evolution of the (irreversible) magnetization upon a field change. We find that this time evolution is a stretched exponential in a well defined time window and that the parameters that characterize this decay are in excellent agreement with our experimental results. Finally, we propose a new interpretation of the "snapshot" assumption: i.e. the assumption that within a certain time window the dynamic response of a spin glass sample represents a snapshot of the dynamic response at a specific thermalization stage ("age") of the sample.