Supersolid, an exotic quantum state of matter that consists of particles forming an incompressible solid structure while simultaneously showing superfluidity of zero viscosity¹, is one of the long-standing pursuits in fundamental research^2,3. Although the initial report of ⁴He supersolid turned out to be an artefact⁴, this intriguing quantum matter has inspired enthusiastic investigations into ultracold quantum gases^5,6,7,8. Nevertheless, the realization of supersolidity in condensed matter remains elusive. Here we find evidence for a quantum magnetic analogue of supersolid—the spin supersolid—in the recently synthesized triangular-lattice antiferromagnet Na₂BaCo(PO₄)₂ (ref. ⁹). Notably, a giant magnetocaloric effect related to the spin supersolidity is observed in the demagnetization cooling process, manifesting itself as two prominent valley-like regimes, with the lowest temperature attaining below 100 mK. Not only is there an experimentally determined series of critical fields but the demagnetization cooling profile also shows excellent agreement with the theoretical simulations with an easy-axis Heisenberg model. Neutron diffractions also successfully locate the proposed spin supersolid phases by revealing the coexistence of three-sublattice spin solid order and interlayer incommensurability indicative of the spin superfluidity. Thus, our results reveal a strong entropic effect of the spin supersolid phase in a frustrated quantum magnet and open up a viable and promising avenue for applications in sub-kelvin refrigeration, especially in the context of persistent concerns about helium shortages^10,11.

超固体是一种奇特的物质量子态，由形成不可压缩固体结构的粒子组成，同时表现出零粘度的超流动性¹ ，是基础研究中长期追求的目标之一^2,3 。尽管⁴ He 超固体的最初报道被证明是人工制品⁴ ，但这种有趣的量子物质激发了人们对超冷量子气体的热情研究^5,6,7,8 。然而，在凝聚态物质中实现超固体仍然难以实现。在这里，我们在最近合成的三角晶格反铁磁体 Na ₂ BaCo(PO ₄ ) ₂中找到了超固体（自旋超固体）的量子磁性类似物的证据（参考文献⁹ ）。值得注意的是，在退磁冷却过程中观察到与自旋超固体相关的巨磁热效应，表现为两个突出的谷状状态，最低温度达到100 mK以下。不仅存在通过实验确定的一系列临界场，而且退磁冷却曲线也显示出与易轴海森堡模型的理论模拟非常一致。中子衍射还通过揭示三亚晶格自旋固序和表明自旋超流性的层间不可通约性的共存，成功地定位了所提出的自旋超固相。因此，我们的结果揭示了受挫量子磁体中自旋超固相的强熵效应，并为亚开尔文制冷应用开辟了一条可行且有前途的途径，特别是在人们持续关注氦短缺的背景下^10,11 。