Cooperative Paramagnetism in the Geometrically Frustrated Pyrochlore Antiferromagnet ${\mathrm{Tb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$

Neutron scattering, muon spin relaxation, and dc susceptibility studies have been carried out on polycrystalline ${\mathrm{Tb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$, a pyrochlore antiferromagnet in which the ${\mathrm{Tb}}^{3+}$ moments reside on a network of corner-sharing tetrahedra. Unlike other geometrically frustrated systems, ${\mathrm{Tb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ remains paramagnetic down to $\sim 0.07\mathrm{K}$, rather than ordering into a conventional Néel or spin-glass-like state, despite the fact that short-range antiferromagnetic correlations (AFC) develop at $\sim 50\mathrm{K}$. At the first AFC wave vector, its low-lying, relatively flat magnetic excitation spectrum softens partially below 30 K.