Antiferromagnetic ordering and glassy nature in the sodium superionic conductor ${\mathrm{NaFe}}_2{\mathrm{PO}}_4({\mathrm{SO}}_4{)}_2$

We investigate the crystal structure and magnetic properties, including spin relaxation and magnetocaloric effect, in a NASICON-type ${\mathrm{NaFe}}_2{\mathrm{PO}}_4{\left({\mathrm{SO}}_4\right)}_2$ sample. The Rietveld refinement of x-ray and neutron diffraction patterns shows a rhombohedral crystal structure with the $R\overline{3}c$ space group. The core-level spectra confirm the desired oxidation state of constituent elements. The dc-magnetic susceptibility $\left(\chi \right)$ behavior in zero field-cooled (ZFC) and field-cooled (FC) modes shows 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 ${\mu }_B/{\mathrm{Fe}}^{3+}$ at 5 K, and a magnetostriction below $T_{\mathrm{N}}=50$ K. Further, the peak position in the ac-$\chi$ is found to be invariant with the excitation frequency, supporting the notion of a 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 dc-$\chi$ and the observed decrease in a peak height of ac-$\chi$ with frequency suggests complex magnetic interactions. The spin relaxation behavior in thermoremanent 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.

Figure 1

(a) The experimentally observed (circles) and calculated (solid line) ND pattern for the ${\mathrm{NaFe}}_2{\mathrm{PO}}_4{\left({\mathrm{SO}}_4\right)}_2$ at 300 K. The solid line at the bottom represents the difference between observed and calculated patterns. The vertical bars indicate the positions of allowed nuclear Bragg peaks. (b) The Raman spectrum measured between 150–1500 ${\mathrm{cm}}^{-1}$ and fitted with the Lorentzian profile. The room temperature core-level photoemission spectra of (c) Fe $2p$, (d) P $2p$, (e) Na $1s$, (f) O $1s$, and (g) S $2p$.

Figure 2

The dc magnetic susceptibility of ${\mathrm{NaFe}}_2{\mathrm{PO}}_4{\left({\mathrm{SO}}_4\right)}_2$ sample in ZFC and FC modes from 2 to 300 K measured at (a) 500 Oe and (b) 10 kOe. (c) The inverse magnetic susceptibility of the FC curve where the black solid lines represent the Curie-Weiss fitting from 60–300 K. (d) The M–H curve in ZFC mode measured at 5 K where the inset shows the enlarged view in the low field region.

Figure 3

(a) The ND patterns measured in the temperature range of 5–300 K. (b) The magnetic diffraction pattern at 5 K after subtraction of the nuclear background at 60 K.

Figure 4

The experimentally observed (circles) and calculated (solid line) ND patterns for ${\mathrm{NaFe}}_2{\mathrm{PO}}_4{\left({\mathrm{SO}}_4\right)}_2$ at (a) 60 K and (b) 5 K. The solid lines at the bottom of each panel represent the difference between observed and calculated patterns. The vertical bars indicate the positions of allowed nuclear and magnetic Bragg peaks. (c) A schematic of the magnetic structure of ${\mathrm{NaFe}}_2{\mathrm{PO}}_4{\left({\mathrm{SO}}_4\right)}_2$ sample. (d) The ordered magnetic moment (order parameter) of ${\mathrm{Fe}}^{3+}$ ion as a function of temperature. (e) The temperature-dependent lattice parameters $a$ and $c$, and the unit cell volume $V$, and (f) the lattice parameters $a$ and $c$, and the unit cell volume $V$ normalized with their respective values at 300 K.

Figure 5

(a) The real and (b) imaginary parts of ac magnetic susceptibility, recorded at various frequencies in the temperature range of 30–51.5 K with 2.5 Oe excitation magnetic field. (c) The FC thermoremanent magnetization (TRM) data recorded at 5 K for various waiting times ($t_w$ = ${10}^2$ s, ${10}^3$ s, and ${10}^4$ s) with a magnetic field of 1000 Oe. The solid lines depict the best data fitting using stretched exponential behavior. The semilogarithmic plot of the data for $t_w$=1000 sec is shown in the inset of (c), and the solid black line indicates the fit using the logarithmic relaxation model. (d) The ZFC time-dependent isothermal magnetization of ${\mathrm{NaFe}}_2{\mathrm{PO}}_4{\left({\mathrm{SO}}_4\right)}_2$ sample measured at 5 K for different waiting times ($t_w$ = ${10}^2$ s, ${10}^3$ s, and ${10}^4$ s) with a magnetic field of 1000 Oe, and the black line is depicting the best-fit curve using a stretched exponential function.

Figure 6

(a) The virgin magnetization isotherms recorded from 2–100 K. (b) The magnetic susceptibility at different external magnetic fields extracted from the virgin isotherms.

Figure 7

(a) The Arrott plots extracted from the virgin data measured between 2–100 K, and the change in the magnetic entropy ($\mathrm{\Delta }\mathrm{S}$) versus temperature at different magnetic fields from (b) 70 kOe to 45 kOe, (c) 45 kOe to 10 kOe, (d) 10 kOe to 1 kOe, and (e) 1 kOe to 300 Oe.