We have studied flux-depinning phenomena in the ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{2}$${\mathrm{CaCu}}_{2}$${\mathrm{O}}_{8}$ (Bi 2:2:1:2) and Pb-doped ${\mathrm{Pb}}_{0.7}$${\mathrm{Bi}}_{1.3}$${\mathrm{Sr}}_{2}$${\mathrm{CaCu}}_{2}$${\mathrm{O}}_{8}$ (Pb-Bi 2:2:1:2) systems using the transverse-field muon-spin-relaxation (\ensuremath{\mu}SR) technique. Comparison of field-cooled (FC) and zero-field-cooled (ZFC) results with external fields applied along the c axis of single-crystal specimens defines an irreversibility temperature (depinning temperature) ${\mathit{T}}_{\mathrm{irr}}$: the FC and ZFC relaxation rates are essentially identical above ${\mathit{T}}_{\mathrm{irr}}$, while the relaxation rate in the ZFC measurements is larger than that in the FC measurements below ${\mathit{T}}_{\mathrm{irr}}$, reflecting the increased inhomogeneity of the local fields in the ZFC measurements due to flux pinning. The irreversibility line ${\mathit{T}}_{\mathrm{irr}}$(H) in the H-T phase diagram for Bi 2:2:1:2, obtained by \ensuremath{\mu}SR measurements for several fields, is compared with previous results from ac-susceptibility and mechanical-oscillator measurements. Using a superconducting-quantum-interference-device (SQUID) magnetometer, the time-dependent diamagnetic magnetization has been measured in the same Bi 2:2:1:2 crystals. We show that the results from \ensuremath{\mu}SR and these other techniques can be explained consistently within a framework of the flux-creep model. The irreversibility temperature in Pb-Bi 2:2:1:2, determined by \ensuremath{\mu}SR measurements, is significantly higher than that in the pure Bi 2:2:1:2 system. This result, together with the larger critical current and the higher activation energy ${\mathit{U}}_{0}$ in the Pb-Bi 2:2:1:2 crystals as found by the SQUID magnetization measurements, suggests an enhancement of flux pinning by the Pb doping. We also compare the \ensuremath{\mu}SR results in sintered ceramic, oriented film, and single-crystal specimens in the pure Bi 2:2:1:2 system, and discuss possible effects of sample morphology on \ensuremath{\mu}SR measurements.
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