A direct measurement of the Bose-Einstein Condensation universality class in NiCl$_2$-4SC(NH$_2$)$_2$ at ultra-low 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 $\textsl{S}$=1 spins exhibit 3D $\mathit{XY}$ antiferromagnetism between a lower critical field $H_{c1} \sim$ 2 T and a upper critical field $H_{c2} \sim$ 12 T. The results show a power-law temperature dependence of the phase transition line $H_{c1} (T) -H_{c1} (0) = aT^α$ with $α=$ 1.47$\pm$0.10 and $H_{c1} (0) = 2.053$ T, consistent with the 3D Bose-Einstein Condensation universality class. An abnormal change was found in the phase boundary near $H_{c2}$ at approximately 150 mK.