Neutron Diffuse Scattering from Polar Nanoregions in the Relaxor Pb(Mg1/3Nb2/3)O3

We have studied the neutron diffuse scattering in the relaxor PMN. The diffuse scattering appears around the Burns temperature (~620K), indicating its origin from the polar nanoregions (PNR). While the relative diffuse intensities are consistent with previous reports, they are entirely different from those of the lowest-energy TO phonon. Because of that, it has been considered that this TO mode could not be the ferroelectric soft mode. Recently, a neutron scattering study has unambiguously shown that the TO mode does soften on cooling. If the diffuse scattering in PMN originates from the soft mode condensation, then the atomic displacements must satisfy the center of mass condition. But, the atomic displacements determined from diffuse scattering intensities do not fulfill this condition. To resolve this contradiction, we propose a simple model in which the total atomic displacement consists of two components: $\delta_{CM}$ is created by the soft mode condensation, satisfying the center of mass condition, and, $\delta_{shift}$ represents a uniform displacement of the PNR along their polar direction relative to the surrounding (unpolarized) cubic matrix. Within this framework, we can successfully describe the neutron diffuse scattering intensities observed in PMN.Comment: 7 pages, 7 figures (Revised: 11-16-2001

Dynamical effects of the nanometer-sized polarized domains in Pb(Zn1/3Nb2/3)O3

Recent neutron scattering measurements performed on the relaxor ferroelectric Pb[(Zn1/3Nb2/3)0.92Ti0.08]O3 (PZN-8%PT) in its cubic phase at 500 K, have revealed an anomalous ridge of inelastic scattering centered ~0.2 A-1 from the zone center (Gehring et al., Phys. Rev. Lett. 84, 5216 (2000)). This ridge of scattering resembles a waterfall when plotted as a phonon dispersion diagram, and extends vertically from the transverse acoustic (TA) branch near 4 meV to the transverse optic (TO) branch near 9 meV. No zone center optic mode was found. We report new results from an extensive neutron scattering study of pure PZN that exhibits the same waterfall feature. We are able to model the dynamics of the waterfall using a simple coupled-mode model that assumes a strongly q-dependent optic mode linewidth Gamma1(q) that increases sharply near 0.2 A-1 as one approaches the zone center. This model was motivated by the results of Burns and Dacol in 1983, who observed the formation of a randomly-oriented local polarization in PZN at temperatures far above its ferroelectric phase transition temperature. The dramatic increase in Gamma1 is believed to occur when the wavelength of the optic mode becomes comparable to the size of the small polarized micro-regions (PMR) associated with this randomly-oriented local polarization, with the consequence that longer wavelength optic modes cannot propagate and become overdamped. Below Tc=410 K, the intensity of the waterfall diminishes. At lowest temperatures ~30 K the waterfall is absent, and we observe the recovery of a zone center transverse optic mode near 10.5 meV.Comment: 8 pages, 9 figures (one color). Submitted to Physical Review

A Neutron Elastic Diffuse Scattering Study of PMN

We have performed elastic diffuse neutron scattering studies on the relaxor Pb(Mg$_{1/3}$Nb$_{2/3}$)O$_3$ (PMN). The measured intensity distribution near a (100) Bragg peak in the (hk0) scattering plane assumes the shape of a butterfly with extended intensity in the (110) and (1$\bar{1}$0) directions. The temperature dependence of the diffuse scattering shows that both the size of the polar nanoregions (PNR) and the integrated diffuse intensity increase with cooling even for temperatures below the Curie temperature $T_C \sim 213$ K.Comment: Submitted to PR

X-Ray Diffuse Scattering Study on Ionic-Pair Displacement Correlations in Relaxor Lead Magnesium Niobate

Ionic-pair equal-time displacement correlations in relaxor lead magnesium niobate, $Pb(Mg_{1/3}Nb_{2/3})O_{3}$, have been investigated at room temperature in terms of an x-ray diffuse scattering technique. Functions of the distinct correlations have been determined quantitatively. The results show the significantly strong rhombohedral-polar correlations regarding Pb-O, Mg/Nb-O, and O-O' pairs. Their spatial distribution forms an ellipse or a sphere with the radii of 30-80$\AA$. This observation of local structure in the system proves precursory presence of the polar microregions in the paraelectric state which leads to the dielectric dispersion.Comment: 11 pages, 3 figure

Diffuse Neutron Scattering Study of a Disordered Complex Perovskite Pb(Zn1/3Nb2/3)O3 Crystal

Diffuse scattering around the (110) reciprocal lattice point has been investigated by elastic neutron scattering in the paraelectric and the relaxor phases of the disordered complex perovskite crystal-Pb(Zn1/3Nb2/3)O3(PZN). The appearance of a diffuse intensity peak indicates the formation of polar nanoregions at temperature T*, approximately 40K above Tc=413K. The analysis of this diffuse scattering indicates that these regions are in the shape of ellipsoids, more extended in the direction than in the direction. The quantitative analysis provides an estimate of the correlation length, \xi, or size of the regions and shows that \xi ~1.2\xi , consistent with the primary or dominant displacement of Pb leading to the low temperature rhombohedral phase. Both the appearance of the polar regions at T*and the structural transition at Tc are marked by kinks in the \xi curve but not in the \xi one, also indicating that the primary changes take place in a direction at both temperatures.Comment: REVTeX file. 4 pages, 3 figures embedded, New version after referee cond-mat/010605

Universal Static and Dynamic Properties of the Structural Transition in Pb(Zn1/3Nb2/3)O3

The relaxors Pb(Zn$_{1/3}$Nb$_{2/3}$)O$_{3}$ (PZN) and Pb(Mg$_{1/3}$Nb$_{2/3}$)O$_{3}$ (PMN) have very similar properties based on the dielectric response around the critical temperature $T_{c}$ (defined by the structural transition under the application of an electric field). It has been widely believed that these materials are quite different below $T_{c}$ with the unit cell of PMN remaining cubic while in PZN the low temperature unit cell is rhombohedral in shape. However, this has been clarified by recent high-energy x-ray studies which have shown that PZN is rhombohedral only in the skin while the shape of the unit cell in the bulk is nearly cubic. In this study we have performed both neutron elastic and inelastic scattering to show that the temperature dependence of both the diffuse and phonon scattering in PZN and PMN is very similar. Both compounds show a nearly identical recovery of the soft optic mode and a broadening of the acoustic mode below $T_{c}$. The diffuse scattering in PZN is suggestive of an onset at the high temperature Burns temperature similar to that in PMN. In contrast to PMN, we observe a broadening of the Bragg peaks in both the longitudinal and transverse directions below $T_{c}$. We reconcile this additional broadening, not observed in PMN, in terms of structural inhomogeneity in PZN. Based on the strong similarities between PMN and PZN, we suggest that both materials belong to the same universality class and discuss the relaxor transition in terms of the three-dimensional Heisenberg model with cubic anisotropy in a random field.Comment: 11 pages, 10 figures. Updated version after helpful referee comment

Disorder and relaxation mode in the lattice dynamics of PbMg1/3_{1/3}Nb2/3_{2/3}O3_3 relaxor ferroelectric

The low-energy part of vibration spectrum in PbMg$_{1/3}$Nb$_{2/3}$O$_3$ relaxor ferroelectric was studied by inelastic neutron scattering. We observed the coexistence of a resolution-limited central peak with strong quasielastic scattering. The line-width of the quasielastic component follows a $\Gamma_0+Dq^2$ dependence. We find that $\Gamma_0$ is temperature-dependent. The relaxation time follows the Arrhenius law well. The presence of a relaxation mode associated with quasi-elastic scattering in PMN indicates that order-disorder behaviour plays an important r\^ole in the dynamics of diffuse phase transitions

Universality Class of Thermally Diluted Ising Systems at Criticality

The universality class of thermally diluted Ising systems, in which the realization of the disposition of magnetic atoms and vacancies is taken from the local distribution of spins in the pure original Ising model at criticality, is investigated by finite size scaling techniques using the Monte Carlo method. We find that the critical temperature, the critical exponents and therefore the universality class of these thermally diluted Ising systems depart markedly from the ones of short range correlated disordered systems. Our results agree fairly well with theoretical predictions previously made by Weinrib and Halperin for systems with long range correlated disorder.Comment: 7 pages, 6 figures, RevTe

Direct evidence of soft mode behavior near the Burns' temperature in PbMg1/3_{1 / 3}Nb2/3_{2 / 3}O3_{3} (PMN) relaxor ferroectric

Inelastic neutron scattering measurements of the relaxor ferroelectric PbMg$_{1 / 3}$Nb$_{2 / 3}$O$_{3}$ (PMN) in the temperature range 490~K$<$T$<$880~K directly observe the soft mode (SM) associated with the Curie-Weiss behavior of the dielectric constant $\varepsilon$(T). The results are treated within the framework of the coupled SM and transverse optic (TO1) mode and the temperature dependence of the SM frequency at q=0.075 a* is determined. The parameters of the SM are consistent with the earlier estimates and the frequency exhibits a minimum near the Burns temperature ($\approx$ 650K)Comment: 6 figure

The Energetics of Li Off-Centering in K1−x_{1-x}Lix_xTaO3_3; First Principles Calculations

K$_{1-x}$Li$_{x}$TaO$_3$ (KLT) solid solutions exhibit a variety of interesting physical phenomena related to large displacements of Li-ions from ideal perovskite A-site positions. First-principles calculations for KLT supercells were used to investigate these phenomena. Lattice dynamics calculations for KLT exhibit a Li off-centering instability. The energetics of Li-displacements for isolated Li-ions and for Li-Li pairs up to 4th neighbors were calculated. Interactions between nearest neighbor Li-ions, in a Li-Li pair, strongly favor ferroelectric alignment along the pair axis. Such Li-Li pairs can be considered "seeds" for polar nanoclusters in KLT. Electrostriction, local oxygen relaxation, coupling to the KT soft-mode, and interactions with neighboring Li-ions all enhance the polarization from Li off-centering. Calculated hopping barriers for isolated Li-ions and for nearest neighbor Li-Li pairs are in good agreement with Arrhenius fits to experimental dielectric data.Comment: 14 pages including 10 figures. To Physical Review B. Replaced after corrections due to referees' remark