Theory of paramagnetic scattering in highly frustrated magnets with long-range dipole-dipole interactions: The case of the Tb2Ti2O7, pyrochlore antiferromagnet

TL;DR

This paper develops a mean-field theory for paramagnetic scattering in highly frustrated pyrochlore magnets with long-range dipole interactions, revealing the limitations of Ising models and supporting Heisenberg-like moments for Tb2Ti2O7.

Contribution

It introduces a mean-field theoretical framework for understanding paramagnetic neutron scattering in frustrated magnets with dipolar interactions, highlighting the inadequacy of Ising models for Tb2Ti2O7.

Findings

Ising models cannot reproduce observed correlations in Tb2Ti2O7

Heisenberg-like moments better explain experimental data

Single-ion anisotropy considerations are crucial for accurate modeling

Abstract

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 Tb2Ti207 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 Tb2Ti207 system. Modeling Tb2Ti207 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 Tb2Ti207 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+.