Direct Measurement of the Bose-Einstein Condensation Universality Class in NiCl$_{2}$-4SC(NH$_{2})_{2}$ at Ultralow Temperatures*

In this work, we demonstrate field-induced Bose-Einstein condensation (BEC) in the organic compound NiCl$_{2}$-4SC(NH$_{2})_{2}$ using ac susceptibility measurements down to 1 mK. The Ni S=1 spins exhibit 3D XY antiferromagnetism between a lower critical field H$_{c1} \quad \sim $ 2 T and a upper critical field H$_{c2} \quad \sim $ 12 T. The results show a power-law temperature dependence of the phase transition line H$_{c1}$(T) -- H$_{c1}$(0) = aT$^{\alpha }$ with $\alpha $ = 1.47$\pm $ 0.10 and H$_{c1}$(0) = 2.053 T, consistent with the 3D BEC universality class. Near H$_{c2}$, a kink was found in the phase boundary at approximately 150 mK.