Vibronic collapse of ordered quadrupolar ice in the pyrochlore magnet Tb2+xTi2−xO7+y

While the spin-liquid state in the frustrated pyrochlore ${\mathrm{Tb}}_{2+x}{\mathrm{Ti}}_{2\ensuremath{-}x}{\mathrm{O}}_{7+y}$ has been studied both experimentally and theoretically for more than two decades, a definite description of this unconventional state still needs to be achieved. Using synchrotron-based THz spectroscopy in combination with quantum numerical simulations, we highlight a significant link between two features: the existence of a quadrupolar order following an ice rule and the presence of strong magnetoelastic coupling in the form of hybridized ${\mathrm{Tb}}^{3+}$ crystal-field and phonon modes. The magnitude of this so-called vibronic process, which involves quadrupolar degrees of freedom, is significantly dependent on small off-stoichiometry $x$ and favors all-in--all-out-like correlations between quadrupoles. This mechanism competes with the long-range ordered quadrupolar ice, and for slightly different stoichiometry, is able to destabilize it.