Effects of proton irradiation on flux-pinning properties of underdoped Ba(Fe$_{0.96}$Co$_{0.04}$)$_2$As$_2$ pnictide superconductor

We study the effect of proton irradiation on Ba(Fe$_{0.96}$Co$_{0.04}$)$_2$As$_2$ superconducting single crystals from combined magnetisation and magnetoresistivity measurements. The study allows the extraction of the values of the apparent pinning energy $U_0$ of the samples prior to and after irradiation, as well as comparison of the values of $U_0$ obtained from the flux-flow reversible region with those from the flux-creep irreversible region. Irradiation reduces $T_c$ modestly, but significantly reduces $U_0$ in both regimes: the critical current density $J_c$ is modified, most strikingly by the disappearance of the second magnetisation peak after irradiation. Analysis of the functional form of the pinning force and of the temperature dependence of $J_c$ for zero field, indicates that proton irradiation in this case has not changed the pinning regime, but has introduced a high density of shallow point-like defects. By consideration of a model that takes into account the effect of disorder on the irreversibility line, the data suggests that irradiation produced a considerable reduction in the average effective disorder overall, consistent with the changes observed in $U_0$ and $J_c$.