Measuring universal magnetocaloric scaling functions near quantum critical point

Near a quantum critical point (QCP), the low-temperature thermodynamics follow universal scaling laws. Using copper sulfate pentahydrate --- a canonical spin-1/2 antiferromagnetic Heisenberg chain compound--- we report the observation of a universal magnetocaloric effect (MCE) near a field-driven QCP. Remarkably, in the 1D quantum critical regime, we measure the universal magnetocaloric scaling function via adiabatic demagnetization process, which agrees with the analytical solution Ψ_Γ^F(x) of critical 1D Fermi gas. This establishes copper sulfate crystal as an ideal platform for studying quantum criticality and universal phenomena. Upon further cooling, our MCE and NMR measurements reveal a dimensional crossover to a 3D quantum critical regime of the Bose-Einstein condensation (BEC) universality class, characterized by the scaling lawT_c∝(B_c-B)^2/3and a clear data collapse of the magnetic Gr"uneisen ratio with 3D Bose-gas scaling function Ψ_Γ^B(x). Practically, this quantum-critical MCE enables cooling to 68.7 mK near the QCP and achieves a lowest temperature of 12.8 mK at zero field without the need for helium-3. Our work identifies a universal MCE in a common compound, establishing this magnon BEC system as a prototypical quantum critical coolant and a platform for next-generation millikelvin refrigeration.