Neutron scattering studies of the cooperative paramagnet pyrochlore Tb₂Ti₂O₇

We have carried out extensive neutron-scattering studies on the pyrochlore antiferromagnet Tb₂Ti₂O₇ in both polycrystalline and single-crystal form. This insulating material belongs to a family of rare-earth titanate pyrochlores, R₂Ti₂O₇, whose magnetic rare-earth ions reside on a network of comer sharing tetrahedra. Such a local geometry is known to give rise to geometrical frustration in the presence of antiferromagnetic interactions. Earlier studies have shown Tb₂Ti₂O₇ to be an Ising system with large moments constrained to point along local [1, 1, 1] directions; that is, into and out of the tetrahedra. It displays a cooperative paramagnetic spin liquid state at low temperatures, with neither long-range Néel order nor spin glass ordering at temperature as low as 0.07 K. Our elastic neutron-scattering measurements show that very short-range correlations develop below ∼ 100 K. At 4 K a checkerboard pattern of diffuse magnetic scattering within the [h, h, l] plane reciprocal space is observed, consistent with spin correlations over near neighbors only. Inelastic scattering measurements on both powder and single-crystal samples show three bands of magnetic excitations. At temperatures above ∼ 20 K, these bands are dispersionless, but at low temperature an appreciable softening in the lowest band of excitations occurs at those wave vectors which characterize the development of the very short-range magnetic order, qualitatively consistent with theoretical expectations derived from the single-mode approximation.