Abstract

Numerous materials feature unexplained phases with invisible or hidden order of electronic origin. A particularly mysterious case is that of ${\mathrm{Tb}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$, which avoids magnetic order to the lowest temperatures, but nevertheless has an unexplained second-order phase transition near $T=0.5$ K. Our ultrasound measurements of ${\mathrm{Tb}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$ provide direct evidence of a huge softening followed by strong hardening of the structural lattice below $T=0.5$ K. In the absence of magnetic order at this temperature, our results provide conclusive evidence for the proposed quadrupolar order and emphasize the importance of higher-order multipolar interactions in rare-earth frustrated magnets.

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