We have carried out extensive neutron-scattering studies on the pyrochlore antiferromagnet ${\mathrm{Tb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ in both polycrystalline and single-crystal form. This insulating material belongs to a family of rare-earth titanate pyrochlores, $R_2{\mathrm{Ti}}_2{\mathrm{O}}_7,$ 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 ${\mathrm{Tb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ 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.

• Received 21 February 2001

DOI:https://doi.org/10.1103/PhysRevB.64.224416