Recent elastic and inelastic neutron scattering studies of the highly frustrated pyrochlore antiferromagnet Tb 2 Ti 2 O 7 have shown some very intriguing features that cannot be modeled by the local ͗111͘ classical Ising model, naively expected to describe this system at low temperatures. By including single-ion excitations from the ground state doublet to higher crystal field levels, we successfully describe the elastic neutron scattering pattern and dispersion relations in Tb 2 Ti 2 O 7 , quantitatively consistent with experimental observations.

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+ .

No abstract

Despite the availability of a spin Hamiltonian for the Gd3Ga5O12 garnet (GGG) for over twenty five years, there has so far been little theoretical insight regarding the many unusual low temperature properties of GGG. Here we investigate GGG in zero magnetic field using mean-field theory. We reproduce the spin liquid-like correlations and, most importantly, explain the positions of the sharp peaks seen in powder neutron diffraction experiments. We show that it is crucial to treat accurately the long-range nature of the magnetic dipolar interactions to allow for a determination of the small exchange energy scales involved in the selection of the experimental ordering wave vector. Our results show that the incommensurate order in GGG is classical in nature, intrinsic to the microscopic spin Hamiltonian and not caused by weak disorder.The diversity of empirical data collected over the past fifteen years has demonstrated that geometrically frustrated triangular and tetrahedral arrangements of antiferromagnetically coupled spins are highly partial towards the realization of exotic correlated phases in magnetic materials [1,2,3]. The reason for the rich and typically material specific properties of frustrated magnets is understood. It stems from their sensitivity to perturbations beyond the frustrating nearest-neighbor antiferromagnetic (AFM) exchange which, on its own, leads to a macroscopic number of exactly degenerate and competing, hence fragile, classical ground states. In this paper we show, through a careful theoretical analysis of neutron scattering experiments, that the extensively studied Gd 3 Ga 5 O 12 garnet (GGG) is precisely such a system, though evidence for this fact emerges from a perspective on the problem that has heretofore escaped scrutiny.GGG displays a gamut of complex and interesting low temperature magnetic phenomena. In zero magnetic field, the behavior of GGG is uniquely rich. The nonlinear magnetic susceptibility χ 3 peaks at T g ∼ 180 mK [4], indicating a spin glass transition [5]. However, muon spin relaxation [6,7] and Mössbauer spectroscopy [8] find persistent spin dynamics down to T ≪ T g . Meanwhile, powder neutron scattering data [9,10] indicate that GGG is on the verge of developing true incommensurate longrange magnetic order with a correlation length (ξ ≈ 100 A) extending over 8 cubic unit cells below 140 mK.A Hamiltonian H describing GGG, that we shall explicitly define below, has long been available [11]. It assumes classical Gd 3+ spins, is parameterized as a sum of empirical exchange contributions up to third nearestneighbors as well as a magnetic dipolar contribution, and ignores potentially important quantum fluctuations or disorder inherent to GGG [4]. Previous numerical studies based on H have been unable to provide a quantitative explanation for the bulk [4] and dynamical [6,7,8] properties of GGG or the incommensurate spin-spin correlations that develop below 200 mK [9,10]. This could be interpreted as evidence that exotic mechanisms involving either quantum fluctuations ...