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

Kadowaki, Hiroaki*; Wakita, Mika*; F${aa}$k, B.*; Ollivier, J.*; Kawamura, Seiko; Nakajima, Kenji ; Lynn, J. W.*

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-range correlations around $$Gamma$$ points, tiny antiferromagnetic Bragg scattering at L and $$Gamma$$ points, and pinch-point-type structures around $$Gamma$$ points. The short-range 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 tenth-neighbor site pairs. This suggests that no symmetry breaking occurs in the QSL sample and that a quantum treatment beyond the semiclassical RPA approach is required. Implications of the experimental data and the RPA analyses are discussed.

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