Neutron scattering, muon spin relaxation, and dc susceptibility studies have been carried out on polycrystalline Tb 2 Ti 2 O 7 , a pyrochlore antiferromagnet in which the Tb 31 moments reside on a network of corner-sharing tetrahedra. Unlike other geometrically frustrated systems, Tb 2 Ti 2 O 7 remains paramagnetic down to ϳ0.07 K, rather than ordering into a conventional Néel or spin-glass-like state, despite the fact that short-range antiferromagnetic correlations (AFC) develop at ϳ50 K. At the first AFC wave vector, its low-lying, relatively flat magnetic excitation spectrum softens partially below 30 K.

We describe the relation between spin fluctuations and superconductivity in a highly-ordered sample of YBa2Cu3O6.5 using both polarized and unpolarized neutron inelastic scattering. The spin susceptibility in the superconducting phase exhibits one-dimensional incommensurate modulations at low-energies, consistent with hydrodynamic stripes. With increasing energy the susceptibility curves upward to a commensurate, intense, well-defined and asymmetric resonance at 33 meV with a precipitous high-energy cutoff. In the normal phase, which we show is gapless, the resonance remains surprisingly strong and persists clearly in Q scans and energy scans. Its similar asymmetric spectral form above Tc=59 K suggests that incoherent superconducting pairing fluctuations are present in the normal state. On cooling, the resonance and the stripe modulations grow in well above Tc below a temperature that is comparable to the pseudogap temperature where suppression occurs in local and low-momentum properties. The spectral weight that accrues to the resonance is largely acquired by transfer from suppressed low-energy fluctuations. We find the resonance to be isotropically polarized, consistent with a triplet carrying ∼ 2.6 % of the total spectral weight of the Cu spins in the planes.

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The magnetic metal ions in the cubic pyrochlore Tb2M02O7 form an infinite three-dimensional network of corner-sharing tetrahedra with a very high potential for frustration in the presence of antiferromagnetism. We have performed neutron scattering measurements which show short-range spatial correlations that develop continuously with decreasing temperature, while the characteristic time scale for the fluctuating moments decreases dramatically below 77 -25 K. Therefore, this pure material, which possesses frustration that is purely geometrical in origin, displays a spin-glass state at low temperatures.