Vibronic collapse of ordered quadrupolar ice in the pyrochore magnet Tb$_{2+x}$Ti$_{2-x}$O$_{7+y}$

TL;DR

This study uncovers how vibronic coupling involving quadrupolar degrees of freedom influences the magnetic state in Tb$_{2+x}$Ti$_{2-x}$O$_{7+y}$, linking lattice vibrations and quadrupolar order, and showing its dependence on stoichiometry.

Contribution

It reveals the role of magneto-elastic vibronic processes in destabilizing quadrupolar ice in a frustrated pyrochlore magnet, combining spectroscopy and simulations.

Findings

Vibronic coupling depends on off-stoichiometry x.

This coupling favors all-in all-out quadrupolar correlations.

It can destabilize the long-range quadrupolar ice order.

Abstract

While the spin liquid state in the frustrated pyrochlore Tb$_{2+x}$Ti$_{2-x}$O$_{7+y}$ has been studied both experimentally and theoretically for more than two decades, no definite description of this unconventional state has been achieved. Using synchrotron based THz spectroscopy in combination with quantum numerical simulations, we highlight a significant link between two previously unrelated features: the existence of a quadrupolar order following an ice rule and the presence of strong magneto-elastic coupling in the form of hybridized 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.