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

The recent discovery of the spin supersolid candidate Na$_2$BaCo(PO$_4$)$_2$ stimulates numerous research interest on the triangular-lattice transition-metal phosphates. Here we report a comprehensive study on the structural, magnetic and magnetocaloric properties of polycrystalline Na$_2$$A$$T$(PO$_4$)$_2$ ($A$ = Ba, Sr; $T$ = Co, Ni, Mn). X-ray and neutron diffraction measurements confirm that Na$_2$Ba$T$(PO$_4$)$_2$ (NB$T$P) crystallizes in a trigonal structure, while Na$_2$Sr$T$(PO$_4$)$_2$ (NS$T$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 N\'{e}el temperatures of NS$T$P are consistently higher than those of NB$T$P for $T$ = Co, Ni, and Mn, due to the release of geometrical frustration by monoclinic distortions. Further magnetocaloric measurements show that trigonal NB$T$P can reach a lower temperature in the quasi-adiabatic demagnetization process and thus shows a better performance in the magnetic refrigeration, compared with monoclinic NS$T$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 ultra-low temperature, including a perfect geometrically frustrated lattice and a small effective spin number associated with the magnetic ions.