Thermodynamic and Magnetostriction Measuremetns of the Bose-Einstein Condensate NiCl$_{2}$-4SC(NH$_{2})_{2}$

We investigate Bose-Einstein condensation (BEC) of magnons in the organic magnet NiCl$_{2}$-4SC(NH$_{2})_{2}$ (DTN). For magnetic fields applied along the tetragonal c-axis, the antiferromagnetically (AFM) ordered Ni spins can be recharacterized as a system of effective bosons with a hard-core repulsive interaction where the AFM transition corresponds to BEC. New, detailed data of the field-temperature phase diagram of DTN have been taken by means of thermodynamic measurements to dilution fridge temperatures. The magnetic field-temperature quantum phase transition line H$_{c}$-H$_{c1} \quad \sim $ T$^{\alpha }$ approaches a power law at low temperatures, with an exponent $\alpha $ at the quantum critical point that is consistent with the BEC theory prediction of $\alpha $ = 3/2. In addition, new magnetostriction data at dilution refrigerator temperatures will be presented. In the AFM ordering regime, field-induced 2$^{nd}$ order changes in the lattice parameters create field-dependent AFM and spin-orbit coupling parameters, which can in turn distort the phase diagram at high fields.