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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={1/21/21/2}. Starting from a general microscopic Hamiltonian including anisotropic nearest-neighbor exchange, long-range dipolar interactions, and second- and third-nearest neighbor exchange, we use standard mean-field theory (SMFT) to identify an extended range of interaction parameters that support partially ordered phases. We demonstrate that thermal fluctuations ignored in SMFT 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 four-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.
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Spin ices, frustrated magnetic materials analogous to common water ice, have emerged over the past 15 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, diffuse neutron scattering, and specific-heat measurements on the paradigmatic Dy2Ti2O7 spin ice material. In this 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. © 2016 American Physical Society.
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- English (2)