Low-field vortex dynamics over seven time decades in a ${\mathrm{Bi}}_2{\mathrm{Sr}}_2\mathrm{Ca}{\mathrm{Cu}}_2{\mathrm{O}}_{8+\delta }$ single crystal for temperatures $13<~T<~83$ K

Using a custom-made dc superconducting quantum interference device (dc-SQUID) magnetometer, we have measured the time relaxation of the remanent magnetization $M_{\mathrm{rem}}$ of a ${\mathrm{Bi}}_2{\mathrm{Sr}}_2\mathrm{Ca}{\mathrm{Cu}}_2{\mathrm{O}}_{8+\delta }$ single crystal from the fully critical state for temperatures $13 \mathrm{K}<~T<~83 \mathrm{K}$. The measurements cover a time window of seven decades ${10}^{-2\mathrm{}} \mathrm{s}\lesssim t\lesssim {10}^5 \mathrm{s}$, so that the current density $j$ can be studied from values very close to $j_c$ down to values considerably smaller than $j_c$. From the data we have obtained (i) the flux-creep activation barriers $U$ as a function of current density $j$, (ii) the current-voltage characteristics $E\left(j\right)\mathrm{}$ in a typical range of ${10}^{-7\mathrm{}}$-${10}^{-15\mathrm{}}$ V/cm, and (iii) the critical current density $j_c\mathrm{}\left(0\right)\mathrm{}$ at $T=0\mathrm{}$. Three different regimes of vortex dynamics are observed: For temperatures $T\lesssim 20$ K the activation barrier $U\left(j\right)\mathrm{}$ is logarithmic, no unique functional dependence $U\left(j\right)\mathrm{}$ could be found for the intermediate-temperature interval $20 \mathrm{K}\lesssim T\lesssim 40 \mathrm{K}$, and finally for $T\gtrsim 40$ K the activation barrier $U\left(j\right)\mathrm{}$ follows a power-law behavior with an exponent $\mu \simeq 0.6$. From the analysis of the data within the weak collective pinning theory for strongly layered superconductors, it is argued that for temperatures $T\lesssim 20$ K pancake vortices are pinned individually, while for temperatures $T\gtrsim 40$ K pinning involves large collectively pinned vortex bundles. A description of the vortex dynamics in the intermediate-temperature interval $20 \mathrm{K}\lesssim T\lesssim 40 \mathrm{K}$ is given on the basis of a qualitative low-field phase diagram of the vortex state in ${\mathrm{Bi}}_2{\mathrm{Sr}}_2\mathrm{Ca}{\mathrm{Cu}}_2{\mathrm{O}}_{8+\delta }$. Within this description a second peak in the magnetization loop should occur for temperatures between 20 and 40 K, as has been observed in several magnetization measurements in the literature.