Elastic study of electric quadrupolar correlation in the paramagnetic state of a frustrated quantum magnet $\rm Tb_{2+\it \delta}Ti_{2-\it \delta}O_7$.

Electric quadrupolar state in a frustrated quantum magnet $\rm Tb_{2+\it \delta}Ti_{2-\it \delta}O_7$ has been studied by means of ultrasonic and magnetostriction measurements. A single crystal showed elastic anomaly at about 0.4 K, manifesting a long-range quadrupole ordering. By investigating anisotropy of the magnetoelastic responses, we found a crossover temperature for the strongly correlated quadrupole state, below which the experimental data of elastic constant and magnetostriction become qualitatively different from their calculations based on a single-ion model. We suppose that relatively high onset temperature of the quadrupole correlation compared with the transition temperature is ascribed to the geometrical frustration effect, and this correlated state seems to be responsible for the unusual properties in the paramagentic state of $\rm Tb_2Ti_2O_7$.