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 corner 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 or spin liquid state at low temperatures, with neither long-range Néel order nor spin glass ordering at temperatures 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 in 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.