Origin of the "waterfall" effect in phonon dispersion of relaxor perovskites

We have undertaken an inelastic neutron scattering study of the perovskite relaxor ferroelectric Pb(Zn(1/3)Nb(2/3))O3 with 8% PbTiO3 (PZN-8%PT) in order to elucidate the origin of the previously reported unusual kink on the low frequency transverse phonon dispersion curve (known as the "waterfall effect"). We show that its position (q(wf)) depends on the choice of the Brillouin zone and that the relation of q(wf) to the size of the polar nanoregions is highly improbable. The waterfall phenomenon is explained in the framework of a simple model of coupled damped harmonic oscillators representing the acoustic and optic phonon branches.     

Crossover between a displacive and an order-disorder phase transition

The phase transition in a three-dimensional array of classical anharmonic oscillators with harmonic nearest-neighbor coupling (discrete straight phi(4) model) is studied by Monte Carlo (MC) simulations and by analytical methods. The model allows us to choose a single dimensionless parameter a determining completely the behavior of the system. Changing a from 0 to +infinity allows to go continuously from the displacive to the order-disorder limit. We calculate the transition temperature T(c) and the temperature dependence of the order parameter down to T=0 for a wide range of the parameter a. The T(c) from MC calculations shows an excellent agreement with the known asymptotic values for small and large a. The obtained MC results are further compared with predictions of the mean-field and independent-mode approximations as well as with predictions of our own approximation scheme. In this approximation, we introduce an auxiliary system, which yields approximately the same temperature behavior of the order parameter, but allows the decoupling of the phonon modes. Our approximation gives the value of T(c) within an error of 5% and satisfactorily describes the temperature dependence of the order parameter for all values of a.     

Theoretical modelling of infrared spectra of the twinned lead zirconate

The THz-frequency range dispersion of the complex dielectric permittivity tensor of antiferroelectric lead zirconate, associated with its multiple weak infrared active phonon modes, is modelled by the oscillator formula with parameters fully determined from the recently developed atomistic shell model. The resulting realistic dielectric function is used to estimate the far-infrared reflectivity spectra of a twinned lead zirconate crystal in the limit of narrow and wide domains. It is shown that in case of the sufficiently narrow domain widths, the effective-medium average permittivity shows additional modes identified as geometric resonances (i.e. extraneous excitations created by material interfaces), possibly distinguishable in suitable experiments.     

Causality in Reversed Time Series: Reversed or Conserved?

The inference of causal relations between observable phenomena is paramount across scientific disciplines; however, the means for such enterprise without experimental manipulation are limited. A commonly applied principle is that of the cause preceding and predicting the effect, taking into account other circumstances. Intuitively, when the temporal order of events is reverted, one would expect the cause and effect to apparently switch roles. This was previously demonstrated in bivariate linear systems and used in design of improved causal inference scores, while such behaviour in linear systems has been put in contrast with nonlinear chaotic systems where the inferred causal direction appears unchanged under time reversal. The presented work explores the conditions under which the causal reversal happens—either perfectly, approximately, or not at all—using theoretical analysis, low-dimensional examples, and network simulations, focusing on the simplified yet illustrative linear vector autoregressive process of order one. We start with a theoretical analysis that demonstrates that a perfect coupling reversal under time reversal occurs only under very specific conditions, followed up by constructing low-dimensional examples where indeed the dominant causal direction is even conserved rather than reversed. Finally, simulations of random as well as realistically motivated network coupling patterns from brain and climate show that level of coupling reversal and conservation can be well predicted by asymmetry and anormality indices introduced based on the theoretical analysis of the problem. The consequences for causal inference are discussed.     

Coexistence of the phonon and relaxation soft modes in the terahertz dielectric response of tetragonal BaTiO3

The dielectric response to infrared waves polarized along the tetragonal axis of a ferroelectric single-domain crystal of BaTiO3 was determined by time-domain THz spectroscopy and Fourier-transform infrared reflectivity techniques. In addition to the three well-known polar lattice modes, the experiment shows an additional mode of the relaxation type in the THz spectral region, which accounts for the Curie-Weiss behavior of the c-axis dielectric constant. A comparison of experimental results with ab initio based effective-Hamiltonian simulations allows us to elucidate its relation to the order-disorder model of Comes, Lambert, and Guinier [Solid State Commun. 6, 715 (1968)10.1016/0038-1098(68)90571-1].