Session D32: Focus Session: Dielectric, Ferroelectric, and Piezoelectric Oxides - Lattice Dynamics

Dynamical couplings in ferroelectrics and multiferroics

First-principle-based molecular dynamics simulations are developed and used to investigate dynamical phenomena in the $\textrm{Pb(Zr,Ti)}\textrm{O}_{3}$ (PZT) ferroelectric solid solutions and in the multiferroic BiFeO$_3$ system\footnote{D. Wang, J. Weerasinghe,and L. Bellaiche, Phys. Rev. B {\bf 83},020301(R) (2011).}$^,$\footnote{D. Wang, E. Buixaderas, J. \'I\~niguez, J. Weerasinghe,H. Wang, and L. Bellaiche,Phys. Rev. Lett. {\bf 107}, 175502 (2011). }. Several interesting effects are reported, including: (1) the existence of \emph{two} $E$ modes in PZT in the 50--75\quad cm$^{-1}$ range for temperatures smaller than $\simeq 200$\quad K when the system is in its $R3c$ phase. Such existence originates from a {\it linear} coupling between ferroelectric (FE) motions and tiltings of oxygen octahedra; (2) a Fermi resonance (FR) emerging from a {\it nonlinear} coupling between FE distortions and oxygen octahedra tilts. This FR manifests itself as the doubling of a nominally-single FE mode in a purely FE phase, when the resonant frequency of the FE mode is close to the first overtone of the oxygen octahedra tiltings; and (3) the prediction of an electromagnon peak, that results from specific interactions between magnetic dipoles, FE motions and oxygen octahedra tiltings, in BiFeO$_3$. Some of these results have been confirmed by recent Raman scattering experiments, and analytical models are also developed to better understand such effects.\footnote{This work is done in collaboration with L. Bellaiche (University of Arkansas), J. Hlinka (Institute of Physics, Czech Republic), E. Buxiaderas (Institute of Physics, Czech Republic), J. \'I\~niguez (Institut de Ci\`encia de Materials de Barcelona, Spain) and J. Weerasinghe (University of Arkansas)}   

A-site ion vibrational modes in ABO3 polar perovskites

It is well known that Pb(B'B'')O3 family of complex perovskites contains materials with very useful dielectric, piezoelectric and ferroelectric properties. The overall electromechanical response of these system is believed to be related to their characteristic micro- to nanoscale structural correlations (chemical clusters, polar nanoregions or nanotwins). At the level of the ABO3 unit cell, the remarkable polarizability of these materials originates from lead-ion displacements, and the anharmonic motion of these ions, loosely linked to the core oxygen octahedra network, largely dominates in the low-frequency phonon modes in the system. Therefore, the investigation of the low-frequency phonon modes in these systems is of a great importance. The aim of this contribution is to report recent experimental studies of such low-frequency vibrations by inelastic X-ray, neutron and light scattering techniques, in materials like lead zirconate titanate, lead magnesium niobium titanate or lead titanate. In particular, attention will be payed to our recent inelastic X-ray scattering studies of PZT lattice dynamics.   

Fully-atomistic first-princples approach to the temperature-dependent lattice-dynamical properties of perovskite oxides

We present a methodology for the parametrization of effective Hamiltonians for ferroelectric perovskites that provides a fully atomistic description of the materials. The parameters in our effective models are obtained from first-principles calculations; no experimental input is used. The potential energy surface is represented by a truncated Taylor expansion around the ideal cubic perovskite structure, and is, up to second order, exactly equivalent to the first-principles computed one. Higher order terms are determined by fitting to the first-principles energetics and phonon dispersion relations of the relevant low-symmetry phases. By treating all structural degrees of freedom explicitly, our models allow us to investigate the competition between the soft modes that drive the ferroelectric phase transitions in these materials and other, secondary modes. We will show that such an interaction is of significant importance in the prototypical ferroelectric compound PbTiO3; our method's ability to capture it constitutes a considerable improvement upon earlier approaches. We will also report on our current work to extend this methodology to treat inhomogeneous materials, as e.g. superlattices.   

Lattice dynamics of cubic PbTiO$_3$

The lattice dynamics of cubic PbTiO$_3$ has been investigated using inelastic neutron scattering. We found four kinds of soft modes in cubic PbTiO$_3$: (1) the TO modes toward the $\Gamma$ point, (2) the TA $\Lambda_3$ mode toward the $R$ point, (3) the TA $\Lambda_3$ mode around the midpoint (1/4,1/4,1/4), and (4) the TA branches in the entire range. Moreover, the TO $\Sigma_4$ branch becomes flat away from the zone center. The steep dispersion of the TO modes toward $\Gamma$ is isotropic and confined to the region $\xi<0.2$. The temperature dependence of the $\Gamma_{15}$ mode up to 1173 K is explained by a combination of the Lydanne-Sachs-Taller relation and the Curie-Weiss law. In contrast, the TA $\Lambda_3$ modes at the midpoint and $R$ point are weakly temperature dependent. The coexistence of the soft $\Gamma_{15}$ and $R_{25}$ modes is in agreement with the predicted phonon instability. The midpoint softening suggests the tendency toward forming a fourfold periodicity along the [1,1,1] direction. The energy of the TO $\Delta_5$ branch for cubic PbTiO$_3$ is considerably higher than that for Pb(Zn$_{1/3}$Nb$_{2/3}$)O$_3$. This indicates that the TO modes are dominated by the B-site atom motion.   

BaTiO$_{3}$ nanocrystals studied by Raman spectroscopy

Variable-temperature Raman spectroscopy study of BaTiO$_{3}$ nanocrystals of varied sizes (from 8 to 20 nm) will be presented. Highly uniform cube-shaped BaTiO$_{3}$ nanocrystals have been prepared by solvothermal synthesis at temperatures below 140\r{ }C and characterized by x-ray diffraction and transmission electron microscopy. Raman spectra (measured with ultraviolet and visible excitation) show that all nanocrystals studied are ferroelectric; nanocrystal size effect on the Curie temperature has been investigated. Temperature evolution of Raman spectra (10--600K) demonstrates that the ferroelectric phase of the nanocrystals is different from the bulk BaTiO$_{3}$. The transitions from tetragonal to orthorhombic and from orthorhombic to rhombohedral phases, which are characteristic for bulk BaTiO$_{3}$, have not been observed in the nanocrystals; the ferroelectric phase in the nanocrystals is the same in the entire temperature range below $T_{c}$, and is different from any of the bulk phases. The observed behavior may be explained by complex polarization patterns theoretically predicted for zero-dimensional ferroelectrics.   

Raman spectra and lattice dynamics of disordered complex perovskite BaMg$_{1/3}$Ta$_{2/3}$O$_3$

In relaxor ferroelectrics the chemical and the displacive ionic disorders coexist and may cause a relaxation of the selection rules for Raman scattering. We performed a Raman scattering study of BaMg$_{1/3}$Ta$_{2/3}$O$_3$ (BMT), which is chemically disordered cubic perovskite showing no evidences for displacive disorder. Polarized Raman spectra from a single crystal of BMT were collected in the temperature range of 5 $-$ 550 K. We are going to discuss the symmetry assignments of the observed modes and their temperature evolution. Simplified shell-model for the lattice dynamics of BMT will be presented. The results for BMT will be compared to the well-known observations for the Raman spectra from related relaxor ferroelectrics PbMg$_{1/3}$Ta$_{2/3}$O$_3$ and PbMg$_{1/3}$Nb$_{2/3}$O$_3$. In particular, the lowest Raman line observed in BMT is at $\sim$110 cm$^{-1}$, whereas the doublet line in PbMg$_{1/3}$Ta$_{2/3}$O$_3$ is observed around 50 cm$^{-1}$. Also, we found out that the width of well-isolated A$_{1g}$ line of BMT is approximately two times narrower than that observed in relaxors.   

Frequency shift of Raman modes due to an applied electric field and domain inversion in LiNbO3

We report changes in the frequency of several Raman modes in congruent and near-stoichiometric lithium niobate that are observed under the application of external applied electric fields parallel to the ferroelectric axis and after domain inversion. A comparison of the direction of the frequency shifts due to an applied electric field and domain inversion reveals that after forward poling there is a reduction of the internal field that is dependent on the intrinsic defect concentration present in the crystal. Upon back poling, the internal field returns to its original state. A further inspection of the Raman peaks reveals that the magnitude of the frequency shift is not consistent between an applied electric field and domain inversion. This indicates that the change in the local internal field introduced by domain inversion is not limited to the ferroelectric axis, but the fields orthogonal to the ferroelectric axis change. Work supported by the grants: NSF-DMR 0602986 and 1008075   

Infrared phonon anomaly and magnetic excitations in single-crystal Cu$_{3}$Bi(SeO$_{3})_{2}$O$_{2}$Cl

Infrared reflection as a function of temperature has been measured on the anisotropic single-crystal Cu$_{3}$Bi(SeO$_{3})_{2}$O$_{2}$Cl. The complex dielectric function and optical properties along all three crystal axes of the orthorhombic cell were obtained via Kramers-Kronig analysis and by fits to a Drude-Lorentz model. Below 110 K drastic anomalies in the phonon spectrum (e.g., new modes and splitting of existing modes) are observed along all three crystal axes. Transmission in the terahertz region as a function of temperature has revealed magnetic excitations originating below the ferromagnetic ordering temperature, T$_{c}$=24 K. The origin of the excitations in the magnetic state will be discussed in terms of their polarization and externally-applied magnetic field dependence.   

Hydrogen diffusion and tunneling in KTaO$_{3}$ from first principles

The high proton conductivity in many perovskites has attracted interest for potential applications, such as in fuel cells. A promising approach to increase their conductivity at lower temperatures involves enhancing quantum-mechanical tunneling. In order to determine the role of tunneling for H in KTaO$_{3}$ we employ first principles calculations for H interstitial atoms. We identify H binding sites and diffusion channels and calculate the associated activation energies. In addition, we analyze the effect of lattice relaxations on the diffusion barriers. Through calculating the 3D potential energy surface of H, we determine accurate H tunneling rates by numerically solving Schr\"{o}dinger's equation for H in the 3D potential energy surface. Finally, we examine lattice vibrations and analyze their role in assisting proton tunneling.   

Scaling of Flat Band Potential and Dielectric Constant as a Function of Ta Concentration in Ta-TiO2 Epitaxial Films

Electrochemical impedance spectroscopy measurements of pulsed laser deposited single crystal anatase TiO2 thin films with various concentrations of Ta substituting for Ti were carried out. UV-visible measurements show a systematic increase of the bandgap with Ta incorporation. Corresponding Mott-Schottky plot was applied to obtain a continuous shift of the flat band potential with increasing free charge carrier concentration. This was verified theoretically by ab initio calculation which shows that extra Ta d-electrons occupy Ti t2g orbital with increasing Ta concentration, thereby pushing up the Fermi level. The Mott-Schottky results were consistent when compared with Hall effect and temperature dependent resistivity measurements. From the measured deviation of carrier densities from Hall and Mott-Schottky measurements we have estimated the static dielectric constant of the TiO2 as a function of Ta incorporation. We are able to estimate the shifts of both the conduction and valence bands from these measurements.   

Raman spectroscopic studies of Ti$_{1-x}$Ta$_{x}$O$_{2}$ alloy thin films

Anatase Ti$_{1-x}$Ta$_{x}$O$_{2}$ thin films have been of interest not only because of the recently found defect originated room temperature ferromagnetism, but also because of the wide possibilities of its application as transparent conducting oxide in flat panel displays, light emitting diodes and solar cells. The incorporation of a foreign element in a host oxide crystal has conventionally been referred to as doping. However, recently we have experimentally shown that even with as less as 1{\%} Ta incorporation in TiO$_{2}$, a totally new alloy system is formed. Here we present a Raman and x-ray diffraction study of anatase Ti$_{1-x}$Ta$_{x}$O$_{2}$ thin films grown on (100) LaAlO$_{3}$ substrate by PLD to understand the crystal structure and defects in the Ta-incorporated TiO$_{2}$ thin films. We find that as Ta is incorporated in the TiO$_{2}$ lattice the out-of-plane phonons undergo red-shift while the in-plane phonon undergoes a blue-shift, suggesting an expansion of the TiO$_{2}$ lattice along the out-of-plane direction with a concomitant in-plane contraction.