Continuum Excitation and Pseudospin Wave in Quantum Spin-Liquid and Quadrupole Ordered States of Tb2+xTi2−xO7+y

The ground states of the frustrated pyrochlore oxide Tb2+xTi2−xO7+y have been studied by inelastic neutron scattering experiments. Three single-crystal samples are investigated; one shows no phase transition (x = −0.007 < xc ∼ −0.0025), being a putative quantum spin-liquid (QSL), and the other two (\(x = 0.000,0.003\)) show electric quadrupole ordering (QO) below Tc ∼ 0.5 K. The QSL sample shows continuum excitation spectra with an energy scale 0.1 meV as well as energy-resolution-limited (nominally) elastic scattering. As x is increased, pseudospin wave of the QO state emerges from this continuum excitation, which agrees with that of powder samples and consequently verifies good x control for the present single crystal samples.