Characteristic Bose-Einstein condensation scaling close to a quantum critical point inBaCuSi2O6

We report an experimental determination of the phase boundary approaching the quantum critical point separating a quantum paramagnetic state and the proposed spin Bose-Einstein condensate of triplons in the spin dimer compound ${\mathrm{BaCuSi}}_2{\mathrm{O}}_6$. The ordering temperature is related to the proximity to a quantum critical point at the lower critical magnetic field $H_{\mathrm{c}1}=23.52\pm 0.03\mathrm{T}$ by a power law parametrized by critical exponent $\nu$. We obtain an experimental estimate of $\nu =0.63\pm 0.03$ down to a temperature of 0.61 K, which is in good agreement with the mean-field prediction of $\nu =2∕3$ for the three-dimensional Bose-Einstein condensation universality class.