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Critical current and vortex dynamics in single crystals of Ca(Fe$_{1-x}$Co$_{x}$)$_2$As$_2$

We investigate the critical current density and vortex dynamics in single crystals of Ca(Fe$_{1-x}$Co$_{x}$)$_2$As$_2$ ($x$ = 0.051, 0.056, 0.065, and 0.073). The samples exhibit different critical temperatures and superconducting phase fractions. We show that in contrast to their Ba-based counterpart, the crystals do not exhibit a second peak in the field dependence of magnetization. The calculated composition-dependent critical current density ($j_{\rm c}$) increases initially with Co doping, maximizing at $x$ = 0.065, and then decreases. This variation in $j_{\rm c}$ follows the superconducting phase fractions in this series. The calculated $j_{\rm c}$ shows strong temperature dependence, decreasing rapidly upon heating. Magnetic relaxation measurements imply a nonlogarithmic dependence on time. We find that the relaxation rate is large, reflecting weak characteristic pinning energy. The analysis of temperature- and field-dependent magnetic relaxation data suggests that vortex dynamics in these compounds is consistent with plastic creeping rather than the collective creep model, unlike other 122 pnictide superconductors. This difference may cause the absence of the second peak in the field dependent magnetization of Ca(Fe$_{1-x}$Co$_{x}$)$_2$As$_2$.