Elastic properties of the titanate pyrochlore Tb$_{2}$Ti$_{2}$O$_{7}$*

The presence of geometric frustration inhibits the formation of long-range spin ordering in Tb$_{2}$Ti$_{2}$O$_{7}$ even at very low temperatures, making this compound the prototype of a ``spin liquid.'' We have initiated a study of the elastic properties of Tb$_{2}$Ti$_{2}$O$_{7}$ as a function of temperature (0.5-300 K) and magnetic field (0-15T) using Resonant Ultrasound Spectroscopy (RUS). All three elastic constants show a pronounced softening below 50 K, indicative of a possible structural transition at very low temperatures. Application of a magnetic field partially suppresses the elastic softening in this compound, suggesting that the magnetoelastic coupling plays a significant role in the spin liquid physics of Tb$_{2}$Ti$_{2}$O$_{7}$ at low temperatures.