  Prototypical models and their material incarnations are cornerstones to the
understanding of quantum magnetism. Here we show theoretically that the
recently synthesized magnetic compound Na$_2$BaCo(PO$_4$)$_2$ (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 analogue 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.
