Rare-earth Titanate Pyrochlores Research Articles

Structural Distortion-Modulated Magnetic and Dielectric Properties in Nonstoichiometric Yb2-xTi2O7-δ Pyrochlore.

Rare-earth titanate pyrochlores have attracted considerable attention for their unique magnetic frustration. Among those compounds, Yb2Ti2O7, a candidate for quantum spin ice, has been extensively studied in its magnetic ground state. However, works on its dielectric property and structure-property relationship lag far more behind. Here, by preparing and investigating nonstoichiometric Yb2-xTi2O7-δ (x = 0-0.15) ceramics, we demonstrate that the samples with x ≤ 0.05 maintain a single-pyrochlore phase, but the nonstoichiometry arouses significant structural distortion and increased oxygen vacancy. As a result, the ferromagnetism, indicated by a positive Curie-Weiss temperature, decreases almost linearly with increasing x value. Remarkably composition-dependent low-temperature dielectric relaxations have been observed. In addition, through introducing nonstoichiometry, the relaxor degree of dielectric behavior is enhanced, and the dielectric curve shows an altered shape. The origin of this dielectric relaxation is attributed to the increased structural distortion reflected by the changed bond length/angle, since there is no phase transition in 90-300 K. Our work gives a comprehensive view on the structural, magnetic, and dielectric properties of Yb2Ti2O7, which is instructive for further work on pyrochlores.

Thermal conductivity of rare-earth titanate pyrochlores

Pyrochlore oxides with the chemical formula ${R}_{2}{B}_{2}{\mathrm{O}}_{7}$ ($R=$ rare earth and $B=$ tetravalent metal) exhibit very low thermal conductivities (\ensuremath{\kappa}) and are considered as promising materials for thermal barrier coatings. To achieve better understanding of their intrinsic thermal properties, this study reports \ensuremath{\kappa} for single crystalline ${\mathrm{Gd}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$ and ${\mathrm{Dy}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$, and for a series of polycrystalline ${R}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$, in the temperature range from 300 to 773 K. For the single crystals, \ensuremath{\kappa} values are evaluated in comparison to spinel ${\mathrm{MgAl}}_{2}{\mathrm{O}}_{4}$ and garnet ${\mathrm{Y}}_{3}{\mathrm{Al}}_{5}{\mathrm{O}}_{12}$ using the Slack equation. It is more difficult to obtain satisfactory analysis for the pyrochlores, and this is attributed to the strong involvement of low-lying optic phonons and very low energies of zone-boundary acoustic phonons. For polycrystalline ${R}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$, \ensuremath{\kappa} values similar to single crystals are obtained. Comparison with published data shows a systematic trend of $\ensuremath{\kappa}({R}_{2}{\mathrm{Sn}}_{2}{\mathrm{O}}_{7})>\ensuremath{\kappa}({R}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7})>\ensuremath{\kappa}({R}_{2}{\mathrm{Zr}}_{2}{\mathrm{O}}_{7})$ at 300 K, which reflects the increasing ionicity from ${\mathrm{Sn}}^{4+}$ to ${\mathrm{Ti}}^{4+}$ to ${\mathrm{Zr}}^{4+}$. For the three ${R}_{2}{B}_{2}{\mathrm{O}}_{7}$ systems, \ensuremath{\kappa} appears to decrease with either decreasing ionic radius or increasing cation mass of $R$.

Dipolar-octupolar Ising antiferromagnetism in Sm2Ti2O7 : A moment fragmentation candidate

Over the past two decades, the magnetic ground states of all rare-earth titanate pyrochlores have been extensively studied, with the exception of ${\mathrm{Sm}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$. This is, in large part, due to the very high absorption cross section of naturally occurring samarium, which renders neutron scattering infeasible. To combat this, we have grown a large, isotopically enriched single crystal of ${\mathrm{Sm}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$. Using inelastic neutron scattering, we determine that the crystal field ground state for ${\mathrm{Sm}}^{3+}$ is a dipolar-octupolar doublet with Ising anisotropy. Neutron diffraction experiments reveal that ${\mathrm{Sm}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$ orders into the all-in, all-out magnetic structure with an ordered moment of $0.44(7){\ensuremath{\mu}}_{B}$ below ${T}_{N}=0.35$ K, consistent with expectations for antiferromagnetically coupled Ising spins on the pyrochlore lattice. Zero-field muon spin relaxation measurements reveal an absence of spontaneous oscillations and persistent spin fluctuations down to 0.03 K. The combination of the dipolar-octupolar nature of the ${\mathrm{Sm}}^{3+}$ moment, the all-in, all-out ordered state, and the low-temperature persistent spin dynamics make this material an intriguing candidate for moment fragmentation physics.

Long-wavelength correlations in ferromagnetic titanate pyrochlores as revealed by small-angle neutron scattering

We have carried out small angle neutron scattering measurements on single crystals of two members of the family of cubic rare-earth titanate pyrochlores that display ferromagnetic Curie-Weiss susceptibilities,Yb$_2$Ti$_2$O$_7$ and Ho$_2$Ti$_2$O$_7$. Ho$_2$Ti$_2$O$_7$ is established as displaying a prototypical classical dipolar spin ice ground state, while Yb$_2$Ti$_2$O$_7$ has been purported as a candidate for a quantum spin ice ground state. While both materials have been well studied with neutron scattering techniques, neither has been previously explored in single crystal form with small angle neutron scattering (SANS). Our results for Yb$_2$Ti$_2$O$_7$ show distinct SANS features below its $\Theta_{CW}$$\sim$ 0.50 K, with rods of diffuse scattering extending along $\langle 111 \rangle$ directions in reciprocal space, off-rod scattering which peaks in temperature near $\Theta_{CW}$, and quasi-Bragg scattering at very small angles which correlates well with T$_C$ $\sim$ 0.26 K. The quasi-Bragg scattering corresponds to finite extent ferromagnetic domains $\sim$ 140 \AA$~$ across, at the lowest temperatures. We interpret the $\langle 111\rangle$ rods of diffuse scattering as arising from domain boundaries between the finite-extent ferromagnetic domains. In contrast the SANS signal in Ho$_2$Ti$_2$O$_7$ is isotropic within the (HHL) plane around $\textbf{Q}$=0. However the strength of this overall SANS signal has a temperature dependence resembling that of the magnetic heat capacity, with a peak near 3 K. Below the break between the field-cooled and the zero-field cooled susceptibility in Ho$_2$Ti$_2$O$_7$ at $\sim$ 0.60 K, the SANS signal is very low, approaching zero.

Elastic properties of rare earth pyrochlores R2Ti2O7 (R = Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu): Ab initio calculations

The experimental elastic constants of R2Ti2O7 (R = Gd–Lu), in particular for R = Tb, Dy, Ho published in scientific literature up to now are slightly different, so this makes an ab initio investigation of the current elastic constants for the whole rare-earth row R2Ti2O7 (R = Gd-Lu). The aim of this paper is to give the ab initio calculations of the structural and elastic properties for a whole row of rare-earth titanate pyrochlores in terms of the MO LCAO approximation, using hybrid DFT Hamiltonian PBE0, with periodic code CRYSTAL14. First, the geometry optimization was performed using the analytical energy gradients, with respect to atomic coordinates and unit cell parameters. All-electron Gaussian basis sets were adopted for Titanium and Oxygen and for Rare-Earth atoms internal shells up to 4f are replaced by the pseudopotentials. The results obtained are discussed and the agreement between the calculated values and experimental data are quite satisfactory.

First-principles calculation and experimental investigation of lattice dynamics in the rare-earth pyrochloresR2Ti2O7(R=Tb,Dy,Ho)

We present a model of the lattice dynamics of the rare earth titanate pyrochlores R2Ti2O7 (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. The 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.

Changes in structure and electrical conductivity of rare-earth titanate pyrochlores under highly reducing atmosphere

M2Ti2O7 (M=Y, Gd, Sm) pyrochlore materials are synthesized by a Pechini method. The pyrochlore phase evolution with temperature under air and under highly reducing conditions (2% H2 in Ar) is investigated using high-temperature X-ray diffraction. The decomposition of pyrochlore oxides into their component single oxides is evidenced when they are exposed to a hydrogen atmosphere. Sm2Ti2O7 pyrochlore is the most stable compound, while Gd2Ti2O7 undergoes a strong reduction even at RT. The bulk electrical conductivity of the samples is evaluated by electrochemical impedance spectroscopy. The greatest increase in conductivity is evidenced for Gd2Ti2O7, while Sm2Ti2O7 is the most stable among the investigated compounds. Besides oxygen ions and electrons, the contribution of hydrogen defects to the bulk conductivity must be considered in such reducing atmosphere.

Crystal field states ofTb3+in the pyrochlore spin liquidTb2Ti2O7from neutron spectroscopy

We report time-of-flight neutron scattering measurements of the magnetic spectrum of ${\mathrm{Tb}}^{3+}$ in ${\mathrm{Tb}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$. The data, which extend up to 120 meV and have calibrated intensity, enable us to consolidate and extend previous studies of the single-ion crystal field spectrum. We successfully refine a model for the crystal field potential in ${\mathrm{Tb}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$ without relying on data from other rare-earth titanate pyrochlores, and we confirm that the ground state is a non-Kramers doublet with predominantly $|\ifmmode\pm\else\textpm\fi{}4\ensuremath{\rangle}$ components. We compare the model critically with earlier models.

Structural and crystal chemical properties of rare-earth titanate pyrochlores

Rare-earth titanates, RE2Ti2O7 (where RE=a rare-earth) with the pyrochlore structure continue to be investigated for use as potential stable host materials for nuclear and actinide-rich wastes. Accordingly, the present work is directed towards the elucidation of the fundamental structural, physical, and thermochemical properties of this class of compounds. Single-crystals of the rare earth pyrochlores were synthesized using a high-temperature flux technique and were subsequently characterized using single-crystal X-ray diffraction. The cubic lattice parameters display an approximately linear correlation with the RE-site cation radius. Theoretical calculations of the lattice constants and bond lengths of the subject materials were carried out using density functional theory, and the results are compared to the experimental values. The Sm and Eu titanates exhibit a covalency increase between the REO8 and TiO6 polyhedral resulting in a deviation from the increasing linear lattice parameter through the transition series. Gd2Ti2O7 with the 4f7 half-filled f-orbital Gd3+ sub-shell exhibits the lowest 48f oxygen positional parameter. The coefficient of thermal expansion for the rare-earth titanate series is approximately linear, and it has a range of 10.1–11.2×10−6°C−1. Raman spectroscopy indicated that the ∼530cm−1 peak associated with the Ti–O stretching mode follows a general trend of decreasing frequency with increasing RE reduced mass.

Static magnetic susceptibility, crystal field and exchange interactions in rare earth titanatepyrochlores

The experimental temperature dependence (T = 2–300 K) of single crystal bulk and site susceptibilities of rare earth titanate pyrochloresR2Ti2O7 (R = Sm, Eu, Gd, Tb, Dy, Ho, Er, Yb) is analyzed in the framework of crystal field theory and amean field approximation. Analytical expressions for the site and bulk susceptibilities ofthe pyrochlore lattice are derived taking into account long range dipole–dipole interactionsand anisotropic exchange interactions between the nearest neighbor rare earth ions. Thesets of crystal field parameters and anisotropic exchange coupling constants havebeen determined and their variations along the lanthanide series are discussed.

Phonon and crystal field excitations in geometrically frustrated rare earth titanates

The phonon and crystal field excitations in several rare earth titanate pyrochlores are investigated. Magnetic measurements on single crystals of ${\text{Gd}}_{2}{\text{Ti}}_{2}{\text{O}}_{7}$, ${\text{Tb}}_{2}{\text{Ti}}_{2}{\text{O}}_{7}$, ${\text{Dy}}_{2}{\text{Ti}}_{2}{\text{O}}_{7}$, and ${\text{Ho}}_{2}{\text{Ti}}_{2}{\text{O}}_{7}$ are used for characterization, while Raman spectroscopy and terahertz time domain spectroscopy are employed to probe the excitations in the materials. The lattice excitations are found to be analogous across the compounds over the whole temperature range investigated (295--4 K). The resulting full phononic characterization of the ${R}_{2}{\text{Ti}}_{2}{\text{O}}_{7}$ pyrochlore structure is then used to identify crystal field excitations observed in the materials. Several crystal field excitations have been observed in ${\text{Tb}}_{2}{\text{Ti}}_{2}{\text{O}}_{7}$ in Raman spectroscopy, among which all of the previously reported excitations. The presence of additional crystal field excitations, however, suggests the presence of two inequivalent ${\text{Tb}}^{3+}$ sites in the low-temperature structure. Furthermore, the crystal field level at approximately $13\text{ }{\text{cm}}^{\ensuremath{-}1}$ is found to be both Raman and dipole active, indicating broken inversion symmetry in the system and thus undermining its current symmetry interpretation. In addition, evidence is found for a significant crystal field--phonon coupling in ${\text{Tb}}_{2}{\text{Ti}}_{2}{\text{O}}_{7}$. The additional crystal field information on ${\text{Tb}}_{2}{\text{Ti}}_{2}{\text{O}}_{7}$ adds to the recent discussion on the low temperature symmetry of this system and may serve to improve its theoretical understanding.

Stuffed rare earth pyrochlore solid solutions

Synthesis and crystal structures are described for the compounds Ln 2(Ti 2− xLn x )O 7− x /2, where Ln=Tb, Dy, Ho, Er, Tm, Yb, Lu, and x ranges from 0 to 0.67. Rietveld refinements of X-ray powder diffraction data indicate that in the Tb and Dy titanate pyrochlores, the extra Ln 3+ cations mix mainly on the Ti 4+ site with little disorder on the original Ln 3+ site. For the smaller rare earths (Ho–Lu), stuffing additional lanthanide ions results in a pyrochlore to defect fluorite transition, where the Ln 3+ and Ti 4+ ions become completely randomized at the maximum ( x=0.67). Initial magnetic characterization for the fully stuffed x=0.67 samples for Ln=Tb–Yb shows no long range ordering down to 2 K, and only partial saturation of the full expected magnetic moment under applied fields up to 5 T. In all of these Ln–Ti–O pyrochlores, the addition of magnetic Ln 3+ in place of non-magnetic Ti 4+ adds edge sharing tetrahedral spin interactions to a normally corner sharing tetrahedral network of spins. The increase in spin connectivity in this family of solid solutions represents a new avenue for investigating geometrical magnetic frustration in the rare earth titanate pyrochlores.

Radiation-induced amorphization of rare-earth titanate pyrochlores

Single crystals of the entire series of ${A}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$ $(A=\mathrm{Sm}$ to Lu, and Y) pyrochlore compounds were irradiated by 1-MeV ${\mathrm{Kr}}^{+}$ ions at temperatures from 293 to 1073 K, and the microstructure evolution, as a function of increasing radiation fluence, was characterized using in situ transmission electron microscopy (TEM). The critical amorphization temperature, ${T}_{c},$ generally increases from \ensuremath{\sim}480 to \ensuremath{\sim}1120 K with increasing A-site cation size (e.g., 0.977 \AA{} for ${\mathrm{Lu}}^{3+}$ to 1.079 \AA{} for ${\mathrm{Sm}}^{3+}).$ An abnormally high susceptibility to ion beam damage was found for ${\mathrm{Gd}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$ (with the highest ${T}_{c}$ of \ensuremath{\sim}1120 K). Factors influencing the response of titanate pyrochlores to ion irradiation-induced amorphization are discussed in terms of cation radius ratio, defect formation, and the tendency to undergo an order-disorder transition to the defect-fluorite structure. The resistance of the pyrochlore structure to ion beam-induced amorphization is not only affected by the relative sizes of the A- and B-site cations, but also the cation electronic configuration and the structural disorder. Pyrochlore compositions that have larger structural deviations from the ideal fluorite structure, as evidenced by the smaller $48f$ oxygen positional parameter, x, are more sensitive to ion beam-induced amorphization.

Neutron scattering studies of the cooperative paramagnet pyrochloreTb2Ti2O7

We have carried out extensive neutron-scattering studies on the pyrochlore antiferromagnet ${\mathrm{Tb}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$ in both polycrystalline and single-crystal form. This insulating material belongs to a family of rare-earth titanate pyrochlores, ${R}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7},$ whose magnetic rare-earth ions reside on a network of corner sharing tetrahedra. Such a local geometry is known to give rise to geometrical frustration in the presence of antiferromagnetic interactions. Earlier studies have shown ${\mathrm{Tb}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$ to be an Ising system with large moments constrained to point along local [1, 1, 1] directions; that is, into and out of the tetrahedra. It displays a cooperative paramagnetic or spin liquid state at low temperatures, with neither long-range N\'eel order nor spin glass ordering at temperatures as low as 0.07 K. Our elastic neutron-scattering measurements show that very short-range correlations develop below \ensuremath{\sim}100 K. At 4 K a checkerboard pattern of diffuse magnetic scattering within the [h,h,l] plane in reciprocal space is observed, consistent with spin correlations over near neighbors only. Inelastic scattering measurements on both powder and single-crystal samples show three bands of magnetic excitations. At temperatures above \ensuremath{\sim}20 K, these bands are dispersionless, but at low temperature an appreciable softening in the lowest band of excitations occurs at those wave vectors which characterize the development of the very short-range magnetic order, qualitatively consistent with theoretical expectations derived from the single-mode approximation.

Bulk magnetization of the heavy rare earth titanate pyrochlores - a series of model frustrated magnets

We describe magnetization measurements on the heavy rare earth titanate pyrochlores R2Ti2O7, where R = Gd, Dy, Ho, Er, Yb, in the temperature range 1.8-300 K, and the field range 0-70 000 Oe. In these materials magnetism arises from the rare earth ions, while Ti is non-magnetic. Analysis of the low field susceptibility versus temperature curves shows that Gd2Ti2O7 has antiferromagnetic coupling (-9 K), which suggests that it is an example of a frustrated antiferromagnet on the pyrochlore lattice. Er2Ti2O7 is likewise found to have a large negative Curie-Weiss temperature, -22 K, which we argue is indicative of antiferromagnetic coupling. Ho2Ti2O7, Dy2Ti2O7 and Yb2Ti2O7 are found to have weak ferromagnetic coupling (2 K, 1 K and 1 K respectively) which may be largely dipolar in origin. Fitting of the high field magnetization versus field curves suggests a strong 1,1,1 single ion anisotropy that identifies these three materials as possible realizations of the ferromagnetic `spin ice' model.