Quadrupole Order in the Frustrated Pyrochlore Tb$_{2+x}$Ti$_{2-x}$O$_{7+y}$

TL;DR

This paper investigates a hidden quadrupole order in a frustrated pyrochlore material, revealing an electric quadrupole ordered state through experimental and theoretical analysis, and discusses its relation to the spin liquid state.

Contribution

It provides the first evidence of electric quadrupole order in Tb-based pyrochlore using combined experimental and theoretical methods.

Findings

Identification of quadrupole order in Tb$_{2+x}$Ti$_{2-x}$O$_{7+y}$

Evidence supporting a U(1) quantum spin-liquid state in Tb$_2$Ti$_2$O$_7$

Demonstration of electric quadrupole moments as the hidden order parameter

Abstract

A hidden order that emerges in the frustrated pyrochlore Tb$_{2+x}$Ti$_{2-x}$O$_{7+y}$ with $T_{\text{c}}=0.53$ K is studied using specific heat, magnetization, and neutron scattering experiments on a high-quality single crystal. Semi-quantitative analyses based on a pseudospin-1/2 Hamiltonian for ionic non-Kramers magnetic doublets demonstrate that it is an ordered state of electric quadrupole moments. The elusive spin liquid state of the nominal Tb$_2$Ti$_2$O$_7$ is most likely a U(1) quantum spin-liquid state.