We report a detailed study of isofield magnetic relaxation and isothermal magnetization measurements with $H$$parallel$c on an underdoped Ba$_{0.75}$K$_{0.25}$Fe$_2$As$_2$ pnictide single crystal, with superconducting transition temperature $T_c$ = 28 K. The second magnetization peak (SMP) has been observed at temperatures below $T_c$/2 and vanished at higher temperatures. The observed behaviour of the SMP has been studied by measuring the magnetic field dependence of relaxation rate, $R(H)$ and by performing the Maleys analysis. The results suggest that the crossover from collective to plastic pinning observed in the SMP disappears above 12 K with plastic pinning replacing collective pinning. An interesting $H$-$T$ phase diagram is obtained. The critical current density ($J_c$) was estimated using Beans model and found to be $sim$ $3.4 times 10^9$ A/m$^2$ at 10 K in the SMP region, which is comparable to an optimally doped Ba-KFe$_2$As$_2$ superconductor and may be exploited for potential technological applications. The pinning mechanism is found to be unconventional and does not follow the usual $delta l$ and $delta T_c$ pinning models, which suggest the intrinsic nature of pinning in the compound.
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