Bose-Einstein Condensation of Triplons in Ba$_3$Cr$_2$O$_8$*

By performing heat capacity, magnetocaloric effect, torque magnetometry and force magnetometry measurements up to 33 T, we have mapped out the T-H phase diagram of the S = 1/2 spin dimer compound Ba$_3$Cr$_2$O$_8$. We found evidence for field-induced magnetic order between Hc1 = 12.52(2) T and Hc2 $\sim$ 23.6 T, with the maximum transition temperature Tc $\sim$ 2.7 K at H $\sim$ 18 T. There are many qualitative features of the data suggesting that the transition at Hc1 corresponds to a Bose-Einstein condensation of triplons universality class. These include the apparent preservation of U(1) symmetry for applied fields below Hc1, a highly symmetric phase diagram, and an absence of any magnetization plateaus in the magnetic torque and force measurements.