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Here, we present results of ultrasound investigations of the frustrated Tb$_2$Ti$_2$O$_7$. This cubic material features a Curie-Weiss temperature of $\theta_{\text{CW}} = - 19$ K, but no magnetic ordering has been detected down to 50 mK, indicating a large frustration factor.
Our ultrasound results evidence a strong spin-lattice coupling in Tb$_2$Ti$_2$O$_7$. We observed pronounced minima in the sound velocity of different acoustic modes at 0.5 K and an additional anomaly at approximately 0.15 K. Below 0.5 K, the acoustic properties show a pronounced thermal hysteresis. Moreover, some anomalies have been detected in magnetic fields applied along the [110] direction.
Possible quadrupolar ordering and a spin-liquid state are discussed for Tb$_2$Ti$_2$O$_7$ in relation to our experimental observations.