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

In this work we present the results of the bulk magnetization measurements in a superconducting state of single crystals of Ba$_{0.65}$Na$_{0.35}$Fe$_2$As$_2$. The isothermal magnetic field ($H||c$ axis) dependent magnetization ($M$) loops exhibit a second peak (SP) or `fishtail effect', as well as remarkable flux jumps at low temperatures. The critical current density $J_c$ obtained from the $M(H)$ loops is rather high, of the order 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 of vortices by dense microscopic point defects with some contribution from a strong pinning mechanism. Pronounced magnetic instabilities in terms of flux jumps depend strongly on temperature as well on the field sweep rate. The field for first flux jump as calculated from an adiabatic model, however, is much lower than the experimentally observed values, and this enhanced stability is attributed to a flux creep phenomenon. The analysis of field dependent magnetic relaxation data additionally supports a collective pinning model. The data further suggests that SP in M(H) is likely related to crossover in creep dynamics from elastic to plastic mechanism. We have constructed the vortex phase diagram on field-temperature plane.