Magnetization relaxation, critical current density and vortex dynamics in a Ba$_{0.66}$K$_{0.32}$BiO$_{3+\delta}$ single crystal

We have conducted extensive investigations on the magnetization and its dynamical relaxation on a Ba$_{0.66}$K$_{0.32}$BiO$_{3+\delta}$ single crystal. It is found that the magnetization relaxation rate is rather weak compared with that in the cuprate superconductors, indicating a higher collective vortex pinning potential (or activation energy), although the intrinsic pinning potential $U_\mathrm{c}$ is weaker. Detailed analysis leads to the following discoveries: (1) A second-peak effect on the magnetization-hysteresis-loop was observed in a very wide temperature region, ranging from 2K to 24K. Its general behavior looks like that in YBa$_2$Cu$_3$O$_7$; (2) Associated with the second peak effect, the magnetization relaxation rate is inversely related to the transient superconducting current density $J_\mathrm{s}$ revealing a quite general and similar mechanism for the second peak effect in many high temperature superconductors; (3) A detailed analysis based on the collective creep model reveals a large glassy exponent $\mu$ and a small intrinsic pinning potential $U_\mathrm{c}$; (4) Investigation on the volume pinning force density shows that the data can be scaled to the formula $F_{p}\propto b^p(1-b)^q$ with $p=2.79$ and $q=3.14$, here $b$ is the reduced magnetic field to the irreversible magnetic field. The maximum normalized pinning force density appears near $b\approx0.47$. Finally, a vortex phase diagram is drawn for showing the phase transitions or crossovers between different vortex phases.