Flux dynamics and vortex phase diagram in $Ba(Fe_{1-x}Co_x)_2As_2$ single crystals revealed by magnetization and its relaxation

Magnetization and its relaxation have been measured in $Ba(Fe_{1-x}Co_x)_2As_2$ single crystals at various doping levels ranging fromvery underdoped to very overdoped regimes. Sizable magnetization relaxation rate has been observed in all samples, indicating a moderate vortex motion and relatively small characteristic pinning energy. Detailed analysis leads to the following conclusions: (1) A prominent second-peak (SP) effect was observed in the samples around the optimal doping level (x $\approx$ 0.08), but it becomes invisible or very weak in the very underdoped and overdoped samples; (2) The magnetization relaxation rate is inversely related to the transient superconducting current density revealing the non-monotonic field and temperature dependence through the SP region; (3) A very sharp magnetization peak was observed near zero field which corresponds to a much reduced relaxation rate; (4) A weak temperature dependence of relaxation rate or a plateau was found in the intermediate temperature region. Together with the treatment of the Generalized-Inversion-Scheme, we suggest that the vortex dynamics is describable by the collective pinning model. Finally, vortex phase diagrams were drawn for all the samples showing a systematic evolution of vortex dynamics.