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+ .

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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 ...

Spin ices, frustrated magnetic materials analogous to common water ice, have emerged over the past fifteen years as exemplars of high frustration in three dimensions. Recent experimental developments aimed at interrogating anew the low-temperature properties of these systems, in particular whether the predicted transition to long-range order occurs, behoove researchers to scrutinize our current dipolar spin ice model description of these materials. In this work we do so by combining extensive Monte Carlo simulations and mean-field theory calculations to analyze data from previous magnetization, elastic neutron scattering and specific heat measurements on the paradigmatic Dy2Ti2O7 spin ice material. In the present work, we also reconsider the possible importance of the nuclear specific heat, Cnuc, in Dy2Ti2O7. We find that Cnuc is not entirely negligible below a temperature ∼ 0.5 K and must therefore be taken into account in a quantitative analysis of the calorimetric data of this compound below that temperature. We find that in this material, small effective spin-spin exchange interactions compete with the magnetostatic dipolar interaction responsible for the main spin ice phenomenology. This causes an unexpected "refrustration" of the long-range order that would be expected from the incompletely self-screened dipolar interaction and which positions the material at the boundary between two competing classical long-range ordered ground states. This allows for the manifestation of new physical low-temperature phenomena in Dy2Ti2O7, as exposed by recent specific heat measurements. We show that among the four most likely causes for the observed upturn of the specific heat at low temperature -an exchange-induced transition to long-range order, quantum non-Ising (transverse) terms in the effective spin Hamiltonian, the nuclear hyperfine contribution and random disorder -only the last appears to be reasonably able to explain the calorimetric data.

The pyrochlore antiferromagnet Tb 2 Ti 2 O 7 has proven to be an enigma to experimentalists and theorists working on frustrated magnetic systems. The experimentally determined energy level structure suggests a local 111 Ising antiferromagnet at low temperatures, T 10 K. An appropriate model then predicts a long-range ordered Q = 0 state below approximately 2 K. However, muon spin resonance (µSR) experiments reveal a paramagnetic structure down to tens of millikelvins. The importance of fluctuations out of the ground state effective Ising doublet has been recently understood, for the measured paramagnetic correlations cannot be described without including the higher crystal field states. However, these fluctuations treated within the random phase approximation (RPA) fail to account for the lack of ordering in this system below 2 K. In this work, we briefly review the experimental evidence for the collective paramagnetic state of Tb 2 Ti 2 O 7 . The basic theoretical picture for this system is discussed, where results from classical spin models are used to motivate the investigation of quantum effects to lowest order via the RPA. Avenues for future experimental and theoretical work on Tb 2 Ti 2 O 7 are presented.

Previous studies have found that calculations which consider longrange magnetic dipolar interactions truncated at a finite cut-off distance R c predict spurious (unphysical) long-range ordered phases for Ising and Heisenberg systems on the pyrochlore lattice. In this paper we show that, similar to these two cases, calculations that use truncated dipolar interactions to model the Gd 3 Ga 5 O 12 garnet antiferromagnet also predict unphysical phases with incommensurate ordering wave vector q ord that is very sensitive to the dipolar cut-off distance R c .

We study the problem of partially ordered phases with periodically arranged disordered (paramagnetic) sites on the pyrochlore lattice, a network of corner-sharing tetrahedra. The periodicity of these phases is characterized by one or more wave vectors k = { 1 2 1 2 1 2 }. Starting from a general microscopic Hamiltonian including anisotropic nearest-neighbor exchange, long-range dipolar interactions and second-and third-nearest neighbor exchange, we identify using standard mean-field theory (s-MFT) an extended range of interaction parameters that support partially ordered phases. We demonstrate that thermal fluctuations ignored in s-MFT are responsible for the selection of one particular partially ordered phase, e.g. the "4-k" phase over the "1-k" phase. We suggest that the transition into the 4-k phase is continuous with its critical properties controlled by the cubic fixed point of a Ginzburg-Landau theory with a 4-component vector order-parameter. By combining an extension of the Thouless-Anderson-Palmer method originally used to study fluctuations in spin glasses with parallel-tempering Monte-Carlo simulations, we establish the phase diagram for different types of partially ordered phases. Our results elucidate the long-standing puzzle concerning the origin of the 4-k partially ordered phase observed in the Gd2Ti2O7 dipolar pyrochlore antiferromagnet below its paramagnetic phase transition temperature. Highly frustrated magnetism is one of the paradigms of modern condensed matter physics [1]. In frustrated magnets, the combination of lattice geometry and competing interactions often leads to degenerate classical states. The degeneracies are generally accidental as they are not protected by the symmetries of the spin Hamiltonian. Yet, the degenerate states may be related by transformations that form an emergent symmetry group. Near a continuous phase transition, these approximate symmetries provide "organizing principles" in determining the critical properties by distinguishing relevant perturbations from irrelevant ones. In the most interesting case, the leading degeneracy-lifting perturbations, which may be relevant or irrelevant in the renormalization group sense, are thermal or quantum fluctuations -a phenomenon called order-by-disorder (ObD) [2][3][4][5]. The competition among diverse degeneracy-lifting effects can result in a modulated long-range ordered state at nonzero wave vector k, which may or may not be commensurate with the lattice [6][7][8][9][10][11][12]. In some cases, a number of superposed symmetryrelated k modes within the first Brillouin zone form a socalled multiple-k order [6,7,13,14]. A particular interesting form of such modulated magnetism is a partially ordered state (POS) with periodically arranged "paramagnetic" sites [15][16][17][18]. These fluctuating magnetic moments decimate a fraction of the energy-costly frustrated bonds while retaining an extensive entropy, hence lowering the free energy.In this Letter, we study the convergence of the aforementioned phenomena (emergent symmet...