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Highly frustrated antiferromagnets composed of magnetic rare-earth moments are currently attracting much experimental and theoretical interest. Rare-earth ions generally have small exchange interactions and large magnetic moments. This makes it necessary to understand in detail the role of long-range magnetic dipole-dipole interactions in these systems, in particular, in the context of spin-spin correlations that develop in the paramagnetic phase, but are often unable to condense into a conventional long-range magnetic-ordered phase. This scenario is most dramatically emphasized in the frustrated pyrochlore antiferromagnet material Tb2Ti2O7, which does not order down to 50 mK despite an antiferromagnetic Curie-Weiss temperature TCW∼-20 K. In this paper we report results from mean-field theory calculations of the paramagnetic elastic neutron scattering in highly frustrated magnetic systems with long-range dipole-dipole interactions, focusing on the Tb2Ti2O7 system. Modeling Tb 2Ti2O7 as an antiferromagnetic 〈111〉 Ising pyrochlore, we find that the mean-field paramagnetic scattering is inconsistent with the experimentally observed results. Through simple symmetry arguments we demonstrate that the observed paramagnetic correlations in Tb 2Ti2O7 are precluded from being generated by any spin Hamiltonian that considers only Ising spins, but are qualitatively consistent with Heisenberg-like moments. Explicit calculations of the paramagnetic scattering pattern for both 〈111〉 Ising and Heisenberg models, which include finite single-ion anisotropy, support these claims. We offer suggestions for reconciling the need to restore spin isotropy with the Ising-like structure suggested by the single-ion properties of Tb3+.
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Dy2Ti2O7 has been advanced as an ideal spin ice material. We present a neutron scattering investigation of a single-crystal sample of 162Dy2Ti2O 7. The scattering intensity has been mapped in zero applied field in the h,h,l and h,k,0 planes of reciprocal space at temperatures between 0.05 and 20 K. The measured diffuse scattering has been compared with that predicted by the dipolar spin ice model. The comparison is good, except at the Brillouin-zone boundaries where extra scattering appears in the experimental data. It is concluded that the dipolar spin ice model provides a successful basis for understanding Dy2Ti2O7, but that there are issues which remain to be clarified.