Strong pinning in the hole-doped pnictide superconductor La$_{0.34}$Na$_{0.66}$Fe$_2$As$_2$

Abstract: We present magnetization studies as a function of time, temperature and magnetic field for $H$ $\parallel$ c-axis, in a hole-doped pnictide superconductor, La${0.34}$Na${0.66}$Fe$_2$As$_2$, with, $T_c$ $\approx$ 27 K. The obtained vortex phase-diagram shows that the magnetic irreversibility line is very close to the mean-field superconducting transition line, similar to the low $T_c$ superconductors, evidencing a strong pinning behavior. The irreversibility line does not follow a power law behavior with ($T_c$-$T$), however, it is well described using an expression developed in the literature considering the effect of disorder in the system. The critical current density estimated using the Bean's critical-state model is found to be of the order of 10$^5$ A/cm$^2$ below 12 K in the limit of zero magnetic field. A plot of the normalized pinning force density as a function of the reduced magnetic field at different temperatures shows a good scaling and the analysis suggests that the vortex pinning is due to normal point like pinning centers. The temperature dependence of the critical current density suggests that the pinning due to the variation in charge carrier mean free path alone is not sufficient to explain the experimental data. Magnetic relaxation rate as a function of temperature and magnetic field is also studied.