Soft Acoustic Modes in the Two-Dimensional Spin SystemSrCu2(BO3)2

${\mathrm{SrCu}}_2({\mathrm{BO}}_3{)}_2$ is a two-dimensional dimerized quantum spin system which is close to a quantum critical point. The sound velocity for the longitudinal and transverse acoustic modes shows strong spin-lattice effects. The shear $c_{66}$ mode exhibits a pronounced softening of $4.5\%$ as a function of temperature and softens more than $25\%$ in fields up to 50 T. This huge effect occurs in the vicinity of the magnetization plateaus ${m/m}_0=1/4\mathrm{}$ and $1/3$. We can analyze quantitatively the temperature dependence of all measured elastic modes $c_{11}$, $c_{44}$, and $c_{66}$ with an exchange striction mechanism. The soft $c_{66}$ mode with $B_{2g}$ symmetry enables us to predict the possible symmetry of the condensed triplets in some plateaus.