Elastic study of electric quadrupolar correlation in the paramagnetic state of the frustrated quantum magnet Tb2+delta Ti2-delta O7

The electric quadrupolar state in the frustrated quantum magnet Tb2+delta Ti2-delta O7 has been studied by means of ultrasonic and magnetostriction measurements. A single crystal showed an elastic anomaly around 0.4 K, manifesting a long-range quadrupole ordering. By investigating the anisotropy of the magnetoelastic responses, we found a crossover temperature for the strongly correlated quadrupole state, below which the experimental data of the 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 paramagnetic state of Tb2Ti2O7.