Doping-induced structural transformation in the spin-1/2 triangular-lattice antiferromagnet Na$_{2}$Ba$_{1-x}$Sr$_{x}$Co(PO$_{4}$)$_{2}$

The effects of Sr doping on the structural properties of Na$_{2}$BaCo(PO$_{4}$)$_{2}$, a spin-1/2 triangular-lattice antiferromagnet as a quantum spin liquid candidate, are investigated by complementary x-ray and neutron powder diffraction measurements. It is found that in Na$_{2}$Ba$_{1-x}$Sr$_{x}$Co(PO$_{4}$)$_{2}$ (NBSCPO), the trigonal phase (space group $\mathit{P}$$\bar{3}$$\mathit{m}$1) with a perfect triangular lattice of Co$^{2+}$ ions is structurally stable when the doping level of Sr is below 30% ($\mathit{x}$ $\le$ 0.3), while a pure monoclinic phase (space group $\mathit{P}$2$_{1}$/$\mathit{a}$) with slight rotations of CoO$_{6}$ octahedra and displacements of Ba$^{2+}$/Sr$^{2+}$ ions will be established when the Sr doping level is above 60% ($\mathit{x}$ $\ge$ 0.6). Such a doping-induced structural transformation in NBSCPO is supported by first-principles calculations and Raman spectroscopy. Na$_{2}$SrCo(PO$_{4}$)$_{2}$, a novel spin-1/2 triangular-lattice antiferromagnet with glaserite-type structure, although monoclinically distorted, exhibits no long-range magnetic order down to 2 K and a similar negative Curie-Weiss temperature as Na$_{2}$BaCo(PO$_{4}$)$_{2}$ with a perfect triangular lattice, suggesting the robustness of magnetic exchange interaction against the Ba/Sr substitutions.