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Prototypical models and their material incarnations are cornerstones to the understanding of quantum magnetism. Here we show theoretically that the recently synthesized magnetic compound Na2BaCo(PO4)2 (NBCP) is a rare, nearly ideal material realization of the S = 1/2 triangular-lattice antiferromagnet with significant easy-axis spin exchange anisotropy. By combining the automatic parameter searching and tensor-network simulations, we establish a microscopic model description of this material with realistic model parameters, which can not only fit well the experimental thermodynamic data but also reproduce the measured magnetization curves without further adjustment of parameters. According to the established model, the NBCP hosts a spin supersolid state that breaks both the lattice translation symmetry and the spin rotational symmetry. Such a state is a spin analog of the long-sought supersolid state, thought to exist in solid Helium and optical lattice systems, and share similar traits. The NBCP therefore represents an ideal material-based platform to explore the physics of supersolidity as well as its quantum and thermal melting. [ABSTRACT FROM AUTHOR]

• A doping-induced structural transformation from trigonal to monoclinic symmetry is evidenced in the spin-1/2 triangular-lattice antiferromagnet Na 2 Ba 1−x Sr x Co(PO 4) 2 by complementary x-ray diffraction, neutron diffraction and first-principles calculations. • Na 2 SrCo(PO 4) 2 , a compound with imperfect triangular-lattice network of Co2+ ions and a monoclinic symmetry, is synthesized and characterized for the first time, providing a new playground to tune the intriguing quantum magnetism in this family. • Na 2 SrCo(PO 4) 2 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. 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 P 3 ̅ m 1) with a perfect triangular lattice of Co2+ ions is structurally stable when the doping level of Sr is below 30% (x ≤ 0.3), while a pure monoclinic phase (space group P 2 1 / a) with slight rotations of CoO 6 octahedra and displacements of Ba2+/Sr2+ ions will be established when the Sr doping level is above 60% (x ≥ 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 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. [ABSTRACT FROM AUTHOR]