Theory of paramagnetic scattering in highly frustrated magnets with long-range dipole-dipole interactions: The case of theTb2Ti2O7pyrochlore antiferromagnet

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 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 Tb2Ti2O7 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 Tb2Ti2O7 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 Tb 3+ .

Fluctuation-Driven Selection at Criticality in a Frustrated Magnetic System: The Case of Multiple-kPartial Order on the Pyrochlore Lattice

“…In what follows, first, we consider only a nearest-neighbor Hamiltonian, H lc 0 . We identify the critical modes at T c [54]. These modes specify the ordering wave vector that first become soft (critical) as the temperature is decreased.…”

“…We begin by studying H 0 using s-MFT [9,23,53,54]. For a large region of parameter space, a degenerate line of modes with momenta {hhh} first becomes critical at T c [21,[23][24][25].…”

Magnetic correlations in HoxTb2−xTiChang1, Schweika2, Kao3 et al. 2011Phys. Rev. B174140View full textAdd to dashboardCite

“…11 When T MF is close to the largest λ α (q), the computed intensity shows low-temperature behavior of the spin system. The fitting parameter T MF is 4.92(3) K, and a constant intensity is added as a free parameter in the calculations to account for the background of nonmagnetic origins.…”

“…It is clear that this model described the data well, with small remaining discrepancies at Q ∼ 1.2 and 2.2Å −1 in the calculations that we cautiously attribute to spin-liquid correlations similar to those seen in Tb 2 Ti 2 O 7 . 11,12 The coexistences of Ho 2 Ti 2 O 7 and Tb 2 Ti 2 O 7 correlations in HoTbTi 2 O 7 indicate weak correlations between Ho 3+ and Tb 3+ . The system mainly consists of dipolar stabilized spin-ice correlation and a small number of correlated spin-liquid ions.…”

“…[6][7][8][9] Among the pyrochlore oxide family, Ho 2 Ti 2 O 7 , Ho 2 Sn 2 O 7 , Dy 2 Ti 2 O 7 , and Dy 2 Sn 2 O 7 have been identified as spin-ice materials and they can be modeled by a spin model with an 111 Ising-type anisotropy and a net ferromagnetic interaction. [6][7][8][9][10] Tb 2 Ti 2 O 7 is a fluctuating spin-liquid state at low temperature 5,[11][12][13][14] and, to date, there exists no model that can adequately describe all the physical properties observed in Tb 2 Ti 2 O 7 .…”