At low temperatures, Tb2Ti2O7 enters a spin liquid state, despite expectations of magnetic order and/or a structural distortion. Using neutron scattering, we have discovered that in this spin liquid state an excited crystal field level is coupled to a transverse acoustic phonon, forming a hybrid excitation. Magnetic and phononlike branches with identical dispersion relations can be identified, and the hybridization vanishes in the paramagnetic state. We suggest that Tb2Ti2O7 is aptly named a "magnetoelastic spin liquid" and that the hybridization of the excitations suppresses both magnetic ordering and the structural distortion. The spin liquid phase of Tb2Ti2O7 can now be regarded as a Coulomb phase with propagating bosonic spin excitations.
In this work we present inelastic neutron scattering experiments which probe the single ion ground states of the rare earth pyrochlores R2Ti2O7 (R = Tb, Dy, Ho). Dy2Ti2O7 and Ho2Ti2O7 are dipolar spin ices, now often described as hosts of emergent magnetic monopole excitations; the low temperature state of Tb2Ti2O7 has features of both spin liquids and spin glasses, and strong magnetoelastic coupling. We measured the crystal field excitations of all three compounds and obtained a unified set of crystal field parameters. Additional measurements of a single crystal of Tb2Ti2O7 clarified the assignment of the crystal field levels in this material and also revealed a new example of a bound state between a crystal field level and an optical phonon mode.
We present a model of the lattice dynamics of the rare-earth titanate pyrochlores R 2 Ti 2 O 7 (R = Tb, Dy, Ho), which are important materials in the study of frustrated magnetism. The phonon modes are obtained by density functional calculations, and these predictions are verified by comparison with scattering experiments. Single crystal inelastic neutron scattering is used to measure acoustic phonons along high symmetry directions for R = Tb, Ho; single crystal inelastic x-ray scattering is used to measure numerous optical modes throughout the Brillouin zone for R = Ho; and powder inelastic neutron scattering is used to estimate the phonon density of states for R = Tb, Dy, Ho. Good agreement between the calculations and all measurements is obtained, allowing confident assignment of the energies and symmetries of the phonons in these materials under ambient conditions. Knowledge of the phonon spectrum is important for understanding spin-lattice interactions, and can be expected to be transferred readily to other members of the series to guide the search for unconventional magnetic excitations.
Recent experimental results have emphasized two aspects of Tb2Ti2O7 which have not been taken into account in previous attempts to construct theories of Tb2Ti2O7: the role of small levels of structural disorder, which appears to control the formation of a long-range ordered state of as yet unknown nature; and the importance of strong coupling between spin and lattice degrees of freedom, which results in the hybridization of crystal field excitons and transverse acoustic phonons. In this work we examine the juncture of these two phenomena and show that samples with strongly contrasting behavior vis-a-vis the structural disorder (i.e. with and without the transition to the ordered state), develop identical magnetoelastic coupling. We also show that the comparison between single crystal and powder samples is more complicated than previously thought -the correlation between lattice parameter (as a measure of superstoichiometric Tb 3+ ) and the existence of a specific heat peak, as observed in powder samples, does not hold for single crystals. arXiv:1510.07572v2 [cond-mat.str-el]
Determining the fate of the Pauling entropy in the classical spin ice material Dy 2 Ti 2 O 7 with respect to the third law of thermodynamics has become an important test case for understanding the existence and stability of ice-rule states in general. The standard model of spin ice-the dipolar spin ice model-predicts an ordering transition at T ≈ 0.15 K, but recent experiments by Pomaranski et al. suggest an entropy recovery over long timescales at temperatures as high as 0.5 K, much too high to be compatible with the theory. Using neutron scattering and specific heat measurements at low temperatures and with long timescales (0.35 K=10 6 s and 0.5 K=10 5 s, respectively) on several isotopically enriched samples, we find no evidence of a reduction of ice-rule correlations or spin entropy. High-resolution simulations of the neutron structure factor show that the spin correlations remain well described by the dipolar spin ice model at all temperatures. Furthermore, by careful consideration of hyperfine contributions, we conclude that the original entropy measurements of Ramirez et al. are, after all, essentially correct: The short-time relaxation method used in that study gives a reasonably accurate estimate of the equilibrium spin ice entropy due to a cancellation of contributions. DOI: 10.1103/PhysRevLett.121.067202 The properties of ice-rule states, such as water ice [1,2] and spin ice [3][4][5], provide a strong contrast with the conventional paradigm of condensed matter. Instead of broken symmetry, entropy that vanishes in accord with the third law, exponentially decaying correlations, and wavelike excitations, one finds Coulomb phase correlations [6], finite entropy [1,5], and pointlike fractional excitations (monopoles) [7,8]. The mapping between the hydrogen bonding network and spin configurations [4,9] and the resultant identical residual (Pauling) entropy [5] are cornerstones of spin ice physics, posing fundamental questions including how a realistic Hamiltonian can lead to practical evasion of the third law, and whether the entropic state is metastable. Because the low-temperature dynamics of spin ice depends on a vanishing number of thermally excited monopoles, relaxation becomes slow at low temperatures [2,10], and sensitivity to sample variations is enhanced [11,12]; both effects may mask the true equilibrium state. While the third law ground state of water ice can be accessed by doping that increases dynamics [9], the fate of the residual entropy in the spin ice Dy 2 Ti 2 O 7 [5] is unknown. Because of these experimental challenges, the problem of third law ordering in ice-type systems may best be addressed by a careful collaboration of experiment and theory, designed to accurately model the system and extrapolate properties beyond the experimental range.The spin ice state of Dy 2 Ti 2 O 7 [3-5] is a consequence of frustration arising from the competition between the Isinglike crystal field anisotropy [13,14], exchange, and dipolar interactions [15,16]. These ingredients can be described by a clas...
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