Effects of 6 MeV proton irradiation on the vortex ensemble in BaFe$_{2}$(As$_{0.67}$P$_{0.33}$)$_2$ revealed through magnetization measurements and real-space vortex imaging

Abstract

The change in vortex ensemble in BaFe$_{2}$(As$_{0.67}$P$_{0.33}$)$_2$, an isovalently doped iron-based superconductor (IBS), is studied through global magnetization measurements and single vortex imaging before and after 6 MeV proton irradiation. The field dependence of the critical current density ($J_\mathrm{c}$) is analyzed through the strong pinning model, with which the pristine sample is consistent. After the irradiation, the $J_\mathrm{c}$ aberrates from the strong pinning field dependence of $B^{-5/8}$, and evolves to a weaker $B^{-1/3}$ dependence with an anomalous two-step behavior creating a cusp like feature. The cusp coincides with the field of the local minima in the normalized relaxation rate ($S$), manifested by increased pinning due to increased intervortex interactions followed by fast vortex dynamics caused by flux activation at higher fields. Furthermore, single vortex imaging reveals that while long-range triangular correlation of the Abrikosov vortex lattice is observed in pristine samples, irradiated samples exhibit a highly disordered glassy vortex state which is more densely packed with increased pinning force. These artificial defects incorporated via proton irradiation have the same pinning effect as Co doping which not only shifts the pinning force to a higher degree but also broadens its distribution, in contrast to P doping which only broadens the pinning distribution without inducing a shift. All in all, through this investigation, we provide a systematic understanding of the pinning behavior in BaFe$_{2}$(As$_{0.67}$P$_{0.33}$)$_2$ through carefully controlling the defects in the system.