Thermodynamic and single-ion properties of Tb³⁺ within the collective paramagnetic-spin liquid state of the frustrated pyrochlore antiferromagnet Tb₂Ti₂O₇

In a recent paper [J. S. Gardner et al., Phys. Rev. Lett. 82, 1012 (1999)] it was found that the Tb³⁺ magnetic moments in the Tb₂Ti₂O₇ antiferromagnetic pyrochlore lattice of corner-sharing tetrahedra remain in a collective paramagnetic state down to 70 mK. In this paper we present results from dc magnetic susceptibility, specific-heat data, inelastic neutron-scattering measurements, and crystal-field calculations that strongly suggest that (i) the Tb³⁺ ions in Tb₂Ti₂O₇ possess a moment of approximatively 5 μ_B, and (ii) the ground state g-tensor is extremely anisotropic below a temperature of O(10⁰) K, with Ising-like Tb³⁺ magnetic moments confined to point along a local cubic 〈111〉 diagonal (e.g., towards the middle of the tetrahedron). Such a very large easy-axis Ising-like anisotropy along a 〈111〉 direction dramatically reduces the frustration otherwise present in a Heisenberg pyrochlore antiferromagnet. The results presented herein underpin the conceptual difficulty in understanding the microscopic mechanism(s) responsible for Tb₂Ti₂O₇ failing to develop long-range order at a temperature of the order of the paramagnetic Curie-Weiss temperature θ_cw≅ - 10¹ K. We suggest that dipolar interactions and extra perturbative exchange coupling(s) beyond nearest neighbors may be responsible for the lack of ordering of Tb₂Ti₂O₇.