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 ΨΓF(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 lawTc∝(Bc-B)2/3and a clear data collapse of the magnetic Gr"uneisen ratio with 3D Bose-gas scaling function ΨΓB(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.