Structural, magnetic, and magnetocaloric properties of triangular-lattice transition-metal phosphates

The recent discovery of the spin supersolid candidate ${\mathrm{Na}}_2\mathrm{BaCo}({\mathrm{PO}}_4{)}_2$ has stimulated a great deal of research on triangular-lattice transition-metal phosphates. Here we report a comprehensive study on the structural, magnetic, and magnetocaloric properties of polycrystalline ${\mathrm{Na}}_{2}AT({\mathrm{PO}}_4{)}_2$ ($A$ = Ba,Sr; $T$ = Co,Ni,Mn). X-ray and neutron diffraction measurements confirm that ${\mathrm{Na}}_2\mathrm{Ba}T({\mathrm{PO}}_4{)}_2$ ($\mathrm{NB}T\mathrm{P}$) crystallizes in a trigonal structure, while ${\mathrm{Na}}_2\mathrm{Sr}T({\mathrm{PO}}_4{)}_2$ ($\mathrm{NS}T\mathrm{P}$) forms a monoclinic structure with a slight distortion of the triangular network of $T^{2+}$ ions. The dc magnetization data show that all six compounds order antiferromagnetically below 2 K, and the Néel temperatures of $\mathrm{NS}T\mathrm{P}$ are consistently higher than those of $\mathrm{NB}T\mathrm{P}$ for $T$ = Co, Ni, and Mn, due to the release of geometrical frustration by monoclinical distortions. Furthermore, magnetocaloric measurements show that trigonal $\mathrm{NB}T\mathrm{P}$ can reach a lower temperature in the quasiadiabatic demagnetization process and thus it demonstrates a better performance in the magnetic refrigeration, compared with monoclinic $\mathrm{NS}T\mathrm{P}$. Our findings highlight the outstanding magnetocaloric performances of the trigonal transition-metal phosphates and disclose two necessary ingredients for a superior magnetic coolant that can reach an ultralow temperature, including a perfect geometrically frustrated lattice and a small effective spin number associated with the magnetic ions.

Figure 1

Room-temperature XRD and NPD patterns of NBNP (a), (e), NBMP (b), (f), NSNP (c), (g), and NSMP (d), (h) and corresponding Rietveld refinements. The circles represent the observed intensities, and the solid lines are the calculated patterns. The differences between the observed and calculated intensities are shown at the bottom. The short vertical bars correspond to the expected nuclear Bragg reflections.

Figure 2

The monoclinic unit cell of $\mathrm{NS}T\mathrm{P}$ (a) with the in-plane structure viewed along the $c$ axis illustrated in (b), where the angle enclosed by the dashed line marks the in-plane $T\text{−}T\text{−}T$ bond angle in the isosceles triangular network of the $T^{2+}$ layers.

Figure 3

dc magnetic susceptibility ($\chi$, filled circles) and inverse susceptibility (1/$\chi$, empty squares) of the polycrystalline NBCP (a), NBNP (b), NBMP (c), NSCP (d), NSNP (e), and NSMP (f), respectively, measured in a magnetic field of 0.1 T. The black solid lines represent the CW fittings to 1/$\chi$ in the low-temperature paramagnetic state from 2 to 20 K. The insets are enlarged plots of $\chi \left(T\right)$ in the temperature range from 0.4 to 1.8 K, in which the arrows mark the AFM ordering temperatures.

Figure 4

Isothermal magnetization [$M\left(H\right)$, filled circles] of polycrystalline NBCP (a), NBNP (b), NBMP (c), NSCP (d), NSNP (e), and NSMP (f), respectively, measured at 0.4 K and their first derivatives ($dM/dH$, solid lines). Dashed lines in (a), (b), and (d) correspond to the contribution from the Van-Vleck paramagnetism. The shaded zones in (b) and (c) mark the region of the slope change of the $M\left(H\right)$ curve, for which a dip appears in $dM/dH$ for NBNP and NBMP. The green arrows in (a), (b), and (d) mark the critical field ($H_{\mathrm{s}}$) corresponding to the moment saturation for NBCP, NBNP, and NSCP, respectively.

Figure 5

The cooling curve of polycrystalline ${\mathrm{Na}}_{2}AT$(${\mathrm{PO}}_4{)}_2$ samples in the adiabatic demagnetization process starting from an initial temperature of $T_0$ = 2 K and an initial magnetic field of $H_0$ = 4 T (a) and 6 T (b), respectively. The cooling performances of the commercial sub-Kelvin magnetic coolant GGG in similar conditions are also shown, in dashed lines, for comparison.

Figure 6

The zero-field molar specific heat ($C$, filled circles) and magnetic entropy ($S$, solid lines) of NBCP and GGG single crystals, respectively, at low temperatures. The specific-heat data of single-crystal GGG are from Refs. [46, 47]. $S$ is obtained by integrating $C/T$. The horizontal dashed lines mark the maximal magnetic entropy of $R$ ln2 and $R$ ln8 as expected for the $J_{\mathrm{eff}}$ = 1/2 and $J$ = 7/2 systems, respectively.