Study of the second magnetization peak and the pinning behaviour in Ba(Fe$_{0.935}$Co$_{0.065}$)$_2$As$_2

Abstract: Isothermal magnetic field dependence of magnetization and the magnetic relaxation measurements were performed for $H$$\parallel$c axis on single crystal of Ba(Fe${0.935}$Co${0.065}$)$2$As$_2$ pnictide superconductor having $T_c$ = 21.7 K. The second magnetization peak (SMP) for each isothermal $M(H)$ was observed in a wide temperature range from $T_c$ to the lowest temperature of measurement (2 K). Magnetic field dependence of relaxation rate $R(H)$, shows a peak (H${spt}$) between H${on}$ (onset of SMP in $M(H)$) and H$_p$ (peak field of SMP in $M(H)$), which is likely to be related with a vortex-lattice structural phase transition, as suggested in literature for similar sample. In addition, the magnetic relaxation measured for magnetic fields near H${spt}$ show some noise which might be the signature of the structural phase transition of the vortex lattice. Analysis of the magnetic relaxation data using Maley's criterion and the collective pinning theory suggests that the second magnetization peak (SMP) in the sample is due to the collective (elastic) to plastic creep crossover, which is also accompanied with a rhombic to square vortex lattice phase transition. Analysis of the pinning force density suggests single dominating pinning mechanism in the sample and is not showing the usual $\delta$l and $\delta T_c$ nature of pinning. The critical current density ($J_c$) estimated using the Bean's critical state model is found to be 5 $\times$ 10$^5$ A/cm$^2$ at 2 K in the zero magnetic field limit. Surprisingly, the maximum in the pinning force density is not responsible for the maximum value of the critical current density in the sample.