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In this work we present the results of the bulk magnetization measurements ina superconducting state of single crystals ofBa$_{0.65}$Na$_{0.35}$Fe$_2$As$_2$. The isothermal magnetic field ($H||c$ axis)dependent magnetization ($M$) loops exhibit a second peak (SP) or `fishtaileffect', as well as remarkable flux jumps at low temperatures. The criticalcurrent density $J_c$ obtained from the $M(H)$ loops is rather high, of theorder of 10$^6$ A/cm$^2$. The analysis of the temperature and field dependent$J_c$ implies that high $J_c$ is mainly due to collective (weak) pinning ofvortices by dense microscopic point defects with some contribution from astrong pinning mechanism. Pronounced magnetic instabilities in terms of fluxjumps depend strongly on temperature as well on the field sweep rate. The fieldfor first flux jump as calculated from an adiabatic model, however, is muchlower than the experimentally observed values, and this enhanced stability isattributed to a flux creep phenomenon. The analysis of field dependent magneticrelaxation data additionally supports a collective pinning model. The datafurther suggests that SP in M(H) is likely related to crossover in creepdynamics from elastic to plastic mechanism. We have constructed the vortexphase diagram on field-temperature plane.

Flux jumps and vortex pinning in Ba$_{0.65}$Na$_{0.35}$Fe$_2$As$_2$ single crystals