Antiferromagnetic ordering and glassy nature in NASICON type NaFe$_2$PO$_4$(SO$_4$)$_2$

We investigate crystal structure and magnetic properties including spin relaxation and magnetocaloric effect in NASICON type NaFe$_2$PO$_4$(SO$_4$)$_2$ sample. The Rietveld refinement of x-ray and neutron diffraction patterns show a rhombohedral crystal structure with the R$\bar{3}$c space group. The core-level spectra confirm the desired oxidation state of constituent elements. The {\it dc}--magnetic susceptibility ($\chi$) behavior in zero field-cooled (ZFC) and field-cooled (FC) modes show the ordering temperature $\approx$50~K. Interestingly, the analysis of temperature dependent neutron diffraction patterns reveal an A-type antiferromagnetic (AFM) structure with the ordered moment of 3.8 $\mu_{B}$/Fe$^{3+}$ at 5~K, and a magnetostriction below $T_{\rm N}=$ 50~K. Further, the peak position in the {\it ac}--$\chi$ is found to be invariant with the excitation frequency supporting the notion of dominating AFM transition. Also, the unsaturated isothermal magnetization curve supports the AFM ordering of the moments; however, the observed coercivity suggests the presence of weak ferromagnetic (FM) correlations at 5~K. On the other hand, a clear bifurcation between ZFC and FC curves of {\it dc}--$\chi$ and the observed decrease in peak height of {\it ac}--$\chi$ with frequency suggest for the complex magnetic interactions. The spin relaxation behavior in thermo-remanent magnetization and aging measurements indicate the glassy states at 5~K. Moreover, the Arrott plots and magnetocaloric analysis reveal the AFM--FM interactions in the sample at lower temperatures.