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We present magnetization studies as a function of time, temperature andmagnetic field for $H$ $\parallel$ c-axis, in a hole-doped pnictidesuperconductor, 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 lineis very close to the mean-field superconducting transition line, similar to thelow $T_c$ superconductors, evidencing a strong pinning behavior. Theirreversibility line does not follow a power law behavior with ($T_c$-$T$),however, it is well described using an expression developed in the literatureconsidering the effect of disorder in the system. The critical current densityestimated using the Bean's critical-state model is found to be of the order of10$^5$ A/cm$^2$ below 12 K in the limit of zero magnetic field. A plot of thenormalized pinning force density as a function of the reduced magnetic field atdifferent temperatures shows a good scaling and the analysis suggests that thevortex pinning is due to normal point like pinning centers. The temperaturedependence of the critical current density suggests that the pinning due to thevariation in charge carrier mean free path alone is not sufficient to explainthe experimental data. Magnetic relaxation rate as a function of temperatureand magnetic field is also studied.

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