Anomalous Slow Relaxation of the Magnetization in Y$_{1-x}$Pr$_{x}$Ba$_2$Cu$_3$0$_{7-\delta}$

We have investigated the time $t$ evolution of the irreversible magnetization $M_{irr}$ in a series of single crystals of Y$_{1-x}$Pr$_{x}$Ba$_2$Cu$_3$0$_{7-\delta}$, $x=0.13$ ($T_{c}=82$ K), $x=0.34$ (($T_{c}=50$ K), and $x=0.47$ (($T_{c}=34$ K), all displaying a second peak in magnetization. In all cases, $M_{irr}(t)$ follows the well known law of relaxation, $M_{irr}(t)\propto[\mu k_{B}T/U_{o}ln(t/t_{0})]^{-1/\mu}$. For fields/temperatures lower than the corresponding values of the second magnetization peak, $\mu$ is anomalously large, $2.5\leq\mu\leq4$, in contrast with theoretical predictions which gives a maximum value of 2.5, and with data reported for other cuprates. These large $\mu$ values in the vortex glass state, which give rise to a low relaxation rate, occur for all Pr doping and could be due to the presence of Pr ions. In contrast, at fields/temperatures above the second magnetization peak, $\mu$ decreases to values expected from theories of plastic vortex liquid and validated by most experimental reports.