Spin correlations of quantum-spin-liquid and quadrupole-ordered states of Tb$_{2+x}$Ti$_{2-x}$O$_{7+y}$

TL;DR

This study investigates spin correlations in the frustrated pyrochlore oxide Tb$_{2+x}$Ti$_{2-x}$O$_{7+y}$ using neutron scattering, revealing short-range correlations and the limitations of semi-classical models in describing its quantum-spin-liquid state.

Contribution

It provides detailed experimental data on spin correlations in Tb$_{2+x}$Ti$_{2-x}$O$_{7+y}$ and demonstrates the effectiveness and limitations of RPA analysis for this quantum-spin-liquid candidate.

Findings

Short-range correlations around L points observed

RPA reproduces experimental scattering with temperature-dependent couplings

No symmetry breaking detected in the quantum-spin-liquid state

Abstract

Spin correlations of the frustrated pyrochlore oxide Tb$_{2+x}$Ti$_{2-x}$O$_{7+y}$ have been investigated by using inelastic neutron scattering on single crystalline samples ($x=-0.007, 0.000,$ and $0.003$), which have the putative quantum-spin-liquid (QSL) or electric-quadrupolar ground states. Spin correlations, which are notably observed in nominally elastic scattering, show short-ranged correlations around $L$ points [$q = (\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2})$], tiny antiferromagnetic Bragg scattering at $L$ and $\Gamma$ points, and pinch-point type structures around $\Gamma$ points. The short-ranged spin correlations were analyzed using a random phase approximation (RPA) assuming the paramagnetic state and two-spin interactions among Ising spins. These analyses have shown that the RPA scattering intensity well reproduces the experimental data using temperature and $x$ dependent coupling constants of up to 10-th neighbor site pairs. This suggests that no symmetry breaking occurs in the QSL sample, and that a quantum treatment beyond the semi-classical RPA approach is required. Implications of the experimental data and the RPA analyses are discussed.