Elastic properties of the rare-earth dititanates R2Ti2O7 (R = Tb, Dy, and Ho)

We have performed ultrasonic measurements on the a-pyrochlore spin compounds R2Ti2O7, R = Tb, Dy, and Ho. A distinct dip appears around 80 K, especially in transverse modes (C-11 - C-12)/2 and C-44 as a function of temperature in Dy2Ti2O7 and Ho2Ti2O7 compounds. This anomaly may correspond to a structural change detected by the temperature dependence of the permittivity and of the loss-angle tangent. No distinct anomaly was observed at lower temperatures in Dy2Ti2O7 and Ho2Ti2O7 compounds. On the other hand, a pronounced elastic softening toward low temperatures was observed in the temperature dependence of the principal elastic constants C-11, (C-11 - C-12)/2, and C-44 in Tb2Ti2O7. A detailed discussion of the highly distinct behavior among three compounds is given in terms of the magnitude of a splitting energy between the ground state and the excited one formed by the crystal-field effect. It seems that geometrically structural frustration prohibits the formation of a long-range quadrupolar ordering as well as a magnetic one, even if the coupling constant between quadrupolar moments is rather large enough in Tb2Ti2O7 at low temperatures.