Magnetostriction in the Bose-Einstein Condensate quantum magnet NiCl2-4SC(NH2)2

The quantum magnet NiCl$_2$-4SC(NH$_2$)$_2$ is a candidate for observing Bose-Einstein Condensation of spin degrees of freedom in applied magnetic fields. An XY antiferromagnetic ordered state occurs in a dome-shaped region of the temperature-field phase diagram between H$_{c1}$ = 2.1 T and H$_{c2}$ = 12.6 T and below 1.2 K. BEC corresponds to the field-induced quantum phase transition into the ordered state. We investigate magnetostriction in single crystals of this compound at dilution refrigerator temperatures in magnetic fields up to 18 T, and as a function of magnetic field angle. We show that significant changes in the lattice parameters are induced by magnetic fields, and argue that these result from antiferromagnetic couplings between the Ni spins along the tetragonal c-axis. The magnetic phase diagram as a function of temperature, field, and field angle can be extracted from these data. We discuss the implications of these results to Bose-Einstein Condensation in this system.