Flux Pinning and Quasi-particle Scattering in Charge- Doped Iron-Based Superconductors

Whereas isovalently doped iron-based superconductors, such as BaFe$_2$(As$_{1-x}$P$_x$)$_2$ and Ba(Fe$_{1-x}$Ru$_x$)$_2$As$_2$ show only strong, ''individual-defect'' vortex pinning due to nanometer-sized defects, charge-doped iron-pnictide superconductors show a low-field, field-independent contribution to the critical current density $j_c$ that is well described by the collective pinning theory. Quantitative analysis of the magnitude, temperature, and field-dependence of $j_c$ in the PrFeAsO$_{1-y}$ compound shows that the behavior of $j_c$ can be fully explained, if one assumes the oxygen vacancies in this material to be responsible for quasi-particle scattering in the vortex cores. Analysis of $j_c$ of this and other charge-doped compounds such as NdFeAs(O,F), (Ba,K)Fe$_2$As$_2$, and Ba(Fe,Co)$_2$As$_2$ yields estimates for the transport scattering cross-section of the dopant impurities in all these materials. We find scattering to be in the Born limit, with a scattering phase angle $\delta_0$ such that $\sin \delta_0 \sim 0.2 - 0.3$.