Ising Supercriticality and Universal Magnetocalorics in Spiral Antiferromagnet Nd${}_3$BWO${}_9$

The celebrated analogy between the pressure-temperature phase diagram of a liquid-gas system and the field-temperature phase diagram of ferromagnet has long been a cornerstone for understanding universality of phase transitions and critical phenomena. Here we extend this analogy to a highly frustrated antiferromagnet, the spiral Ising compound Nd${}_3$BWO${}_9$ with kagome layers. In its phase diagram, we identify a metamagnetic transition line with a critical endpoint (CEP) located at ${\mu }_0{H}_{\mathrm{c}}\simeq 1.04$ T and $T_{\mathrm{c}}\simeq 0.3$ K. Above the CEP, an Ising supercritical regime} emerges with supercritical crossover lines that adhere to a universal scaling law, as evidenced by the specific heat, magnetic susceptibility, and magnetocaloric measurements. Remarkably, we observe a highly sensitive field dependence in the magnetic cooling near the emergent CEP, characterized by a divergent magnetic Grüneisen ratio ${\mathrm{\Gamma }}_H\propto 1\mathrm{/}{t}^{\beta +\gamma -1}$, with $\beta +\gamma \simeq 1.563$ the critical exponents of 3D Ising universality class and $t\equiv (T-T_{\mathrm{c}})\mathrm{/}{T}_{\mathrm{c}}$ the reduced temperature. Our adiabatic demagnetization measurements on Nd${}_3$BWO${}_9$ reveal a lowest temperature of 195~mK, achieved from the initial condition of 2 K and 4 T. Our findings open a new avenue for studying supercritical phenomena and magnetic cooling in rare-earth RE${}_3$BWO${}_9$ family and, more broadly, in Ising-anisotropic magnets such as spin ices.