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We have conducted extensive investigations on the magnetization and itsdynamical 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 withthat in the cuprate superconductors, indicating a higher collective vortexpinning potential (or activation energy), although the intrinsic pinningpotential $U_\mathrm{c}$ is weaker. Detailed analysis leads to the followingdiscoveries: (1) A second-peak effect on the magnetization-hysteresis-loop wasobserved in a very wide temperature region, ranging from 2K to 24K. Its generalbehavior looks like that in YBa$_2$Cu$_3$O$_7$; (2) Associated with the secondpeak effect, the magnetization relaxation rate is inversely related to thetransient superconducting current density $J_\mathrm{s}$ revealing a quitegeneral and similar mechanism for the second peak effect in many hightemperature superconductors; (3) A detailed analysis based on the collectivecreep model reveals a large glassy exponent $\mu$ and a small intrinsic pinningpotential $U_\mathrm{c}$; (4) Investigation on the volume pinning force densityshows 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 theirreversible magnetic field. The maximum normalized pinning force densityappears near $b\approx0.47$. Finally, a vortex phase diagram is drawn forshowing the phase transitions or crossovers between different vortex phases.

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