Quasi-Elastic Scattering, Random Fields and phonon-coupling effects in PbMg1/3Nb2/3O3

The low-energy part of the vibration spectrum in PbMg$_{1/3}$Nb$_{2/3}$O$_3$ (PMN) relaxor ferroelectric has been studied by neutron scattering above and below the Burns temperature, T$_d$. The transverse acoustic and the lowest transverse optic phonons are strongly coupled and we have obtained a model for this coupling. We observe that the lowest optic branch is always underdamped. A resolution-limited central peak and quasi-elastic scattering appear in the vicinity of the Burns temperature. It is shown that it is unlikely that the quasi-elastic scattering originates from the combined effects of coupling between TA and TO phonons with an increase of the damping of the TO phonon below T$_d$. The quasi-elastic scattering has a peak as a function of temperature close to the peak in the dielectric constant while the intensity of the central peak scattering increases strongly below this temperature. These results are discussed in terms of a random field model for relaxors

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

Coexistence of the Critical Slowing Down and Glassy Freezing in Relaxor Ferroelectrics

We have developed a dynamical model for the dielectric response in relaxor ferroelectrics which explicitly takes into account the coexistence of the critical slowing down and glassy freezing. The application of the model to the experiment in PMN allowed for the reconstruction of the nonequilibrium spin glass state order parameter and its comparison with the results of recent NMR experiment (Blinc et al., Phys. Rev. Lett. 83, No. 2 (1999)). It is shown that the degree of the local freezing is rather small even at temperatures where the field-cooled permittivity exceeds the frequency dependent permittivity by an order of magnitude. This observation indicates the significant role of the critical slowing down (accompanying the glass freezing) in the system dynamics. Also the theory predicts an important interrelationship between the frequency dependent permittivity and the zero-field-cooled permittivity, which proved to be consistent with the experiment in PMN (A. Levstik et. al., Phys. Rev. B 57, 11204 (1998))

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

Soft Phonon Anomalies in the Relaxor Ferroelectric Pb(Zn_1/3Nb_2/3)_0.92Ti_0.08O_3

Neutron inelastic scattering measurements of the polar TO phonon mode dispersion in the cubic relaxor Pb(Zn_1/3Nb_2/3)_0.92Ti_0.08O_3 at 500K reveal anomalous behavior in which the optic branch appears to drop precipitously into the acoustic branch at a finite value of the momentum transfer q=0.2 inverse Angstroms, measured from the zone center. We speculate this behavior is the result of nanometer-sized polar regions in the crystal.Comment: 4 pages, 4 figure

Strong Influence of the diffuse component on the lattice dynamics in Pb(Mg1/3_{1/3}Nb2/3_{2/3})O3_{3}

The temperature and zone dependence of the lattice dynamics in Pb(Mg$_{1/3}$Nb$_{2/3}$)O$_{3}$ is characterized using neutron inelastic scattering. A strong correlation between the diffuse and phonon scattering is measured. The lattice dynamics in Brillouin zones where the diffuse scattering is strong is observed to display qualitatively different behavior than those zones where the diffuse scattering is weak. In the (220) and (200) zones, where there is a weak diffuse component, the dynamics are well described by coupled harmonic oscillators. Compared with SrTiO$_{3}$, the coupling is weak and isotropic, resulting in only a small transfer of spectral weight from one mode to another. A comparison of the scattering in these zones to the (110) zone, where a strong diffuse component is present, reveals a strong coupling of the diffuse (or central) component to the acoustic mode. We speculate that the coupling to the central peak is the reason for several recent conflicting interpretations of the lattice dynamics based on data from zones with a strong diffuse component.Comment: 7 pages, 7 figure

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 Structural Phase Transition of the Relaxor Ferroelectric 68%PbMg1/3Nb2/3O3-32%PbTiO3

Neutron scattering techniques have been used to study the relaxor ferroelectric 0.68PbMg1/3Nb2/3O3-0.32PbTiO3 denoted in this paper as 0.68PMN-0.32PT. On cooling, these relaxor ferroelectrics have a long-range ordered ferroelectric phase and the composition is close to that at which the ferroelectric structure changes from rhombohedral to tetragonal. It was found that above the Burns temperature of about 600K, the transverse optic mode and the transverse acoustic mode are strongly coupled and a model was used to describe this coupling that gave similar parameters to those obtained for the coupling in PMN. Below the Burns temperature additional quasi-elastic scattering was found which increased in intensity as the sample was cooled down to the ferroelectric transition temperature but then decreased in intensity. This behaviour is similar to that found in PMN. This scattering is associated with the dynamic polar nano-regions that occur below the Burns temperature. In addition to this scattering a strictly elastic resolution limited peak was observed that was much weaker than the corresponding peak in pure PMN and which decreased in intensity on cooling below the ferroelectric phase whereas for PMN, which does not have a long-range ordered ferroelectric phase, the intensity of this component increased monotonically as the sample was cooled. The results of our study are compared with the recent measurements of Stock et al. [PRB 73 064107] who studied 0.4PMN-0.6PT. The results are qualitatively consistent with the random field model developed to describe the scattering from PMN

A Universal Phase Diagram for PMN-xPT and PZN-xPT

The phase diagram of the Pb(Mg1/3Nb2/3)O3 and PbTiO3 solid solution (PMN-xPT) indicates a rhombohedral ground state for x < 0.32. X-ray powder measurements by Dkhil et al. show a rhombohedrally split (222) Bragg peak for PMN-10%PT at 80 K. Remarkably, neutron data taken on a single crystal of the same compound with comparable q-resolution reveal a single resolution-limited (111) peak down to 50 K, and thus no rhombohedral distortion. Our results suggest that the structure of the outer layer of these relaxors differs from that of the bulk, which is nearly cubic, as observed in PZN by Xu et al.Comment: Replaced Fig. 3 with better versio

Development of Ferroelectric Order in Relaxor (1-x)Pb(Mg1/3Nb2/3)O3 - xPbTiO3

The microstructure and phase transition in relaxor ferroelectric Pb(Mg1/3Nb2/3)O3 (PMN) and its solid solution with PbTiO3 (PT), PMN-xPT, remain to be one of the most puzzling issues of solid state science. In the present work we have investigated the evolution of the phase symmetry in PMN-xPT ceramics as a function of temperature (20 K < T < 500 K) and composition (0 <= x <= 0.15) by means of high-resolution synchrotron x-ray diffraction. Structural analysis based on the experimental data reveals that the substitution of Ti^4+ for the complex B-site (Mg1/3Nb2/3)^4+ ions results in the development of a clean rhombohedral phase at a PT-concentration as low as 5%. The results provide some new insight into the development of the ferroelectric order in PMN-PT, which has been discussed in light of the kinetics of polar nanoregions and the physical models of the relaxor ferroelectrics to illustrate the structural evolution from a relaxor to a ferroelectric state.Comment: Revised version with updated references; 9 pages, 4 figures embedde