Thermodynamic properties of quadrupolar states in the frustrated pyrochlore magnet Tb₂Ti₂O₇

The low-temperature thermodynamic properties of the frustrated pyrochlore Tb_2+x Ti_2−x O_7+y have been studied using the single crystal of x = 0.005 sitting in a long range ordered phase in the x – T phase diagram. We observed that the specific heat exhibits a minimum around 2 K and slightly increases on cooling, similar to a Schottky-like anomaly for canonical spin ices. A clear specific-heat peak observed at T _c = 0.53 K is ascribable to the phase transition to a quadrupolar state, which contributes to a relatively large change in entropy, S ≃ 2.7 J K⁻¹mol⁻¹. However, it is still smaller than R ln 2 for the ground state doublet of the Tb ions. The entropy release persists to higher temperatures, suggesting strong fluctuations associated with spin ice correlations above T_c. We discuss the field dependence of the entropy change for H ‖ [111] and H ‖ [001]. (paper)