Session V24: Focus Session: Dielectric, Ferroelectric, and Piezoelectric Oxides -- Bulk Ferroelectrics I

\emph{Ab initio} polarization calculations for large systems using a Wannier center method

The ionic (${\bf P}_{\rm ion}$) and electronic (${\bf P}_{e}$) terms in the electric polarization in solids are defined only modulo a quantum that connects different polarization branches and depends on the unit-cell dimensions. As the system cell size increases (especially perpendicular to ${\bf P}$) the quantum shrinks, becoming comparable to the expected polarization values, thus making the identification of the physically relevant branch unclear. To overcome this indeterminacy, a common approach involves multiple calculations of ${\bf P}$ along an adiabatic insulating path, so that $\Delta {\bf P}$ $\ll$ the quantum at every step. We remove the need for these multiple evaluations by using a representation of ${\bf P}_{e}$ in terms of the centers of Wannier functions. In this intuitive picture, the arbitrariness in ${\bf P}_{e}$ is removed by the implicit requirement that the position of the Wannier center move on a continuous path along with its corresponding ion or bond as the system is deformed from the initial to the final state. Our procedure for computing ${\bf P}$ consists of associating each Wannier center with a particular atom or bond in the unit cell, and then obtaining ${\bf P}_{\rm ion}$ and ${\bf P}_{e}$ through simple summations. We compare the results from this method to the Berry-phase technique using multiple evaluations for the case of supercell calculations of $V_{\rm Pb}$-$V_{\rm O}$ divacancies in PbTiO$_3$. The same polarization values are obtained, with differences below 0.75 $\mu$C/cm$^2$ associated with different $k$-point samplings.   

Goldstone-like states in a layered perovskite with frustrated polarization

With the help of first-principles-based computational techniques, we demonstrate that Goldstone-like states can be artificially induced in a layered-perovskite ferroelectric compound with frustrated polarization, resulting in emergence of a variety of interesting physical properties that include large, tunable dielectric constants and an ability to easily form vortex polar states in a nanodot geometry. In a similar fashion to the well-known perovskite materials with morphotropic phase boundaries (MPBs), these states manifest themselves as polarization rotations with almost no energy penalty, suggesting that the existence of an MPB is actually yet another manifestation of the Goldstone theorem in solids.   

Flexoelectricity as a bulk property

Piezoelectric composites can be created using nonpiezoelectric materials, by exploiting flexoelectricity. This is by definition the linear response of polarization to strain gradient, and is symmetry-allowed even in elemental crystals. However, the basic issue whether flexoelectricity is a bulk or a surface material property is open. We mention that the analogous issue about piezoelectricity is nontrivial either.$^1$ In this first attempt towards a full theory of flexoelectricity we prove that, for a simple class of strain and strain gradients, flexoelectricity is indeed a bulk effect. The key ingredients of the present theory are the long-range perturbations linearly induced by a unit displacement of a single nucleus in an otherwise perfect crystal: to leading order these are dipolar, quadrupolar, and octupolar. The corresponding tensors have rank 2, 3, and 4, respectively. Whereas dipoles and quadrupoles provide the piezoelectric response,$^1$ we show that dipoles and octupoles provide the flexoelectric response in nonpiezoelectric crystals. We conjecture that the full dipole and octupole tensors provide the flexoelectric response to the most general form of strain gradient. Our problem has a close relationship to the one of the ``absolute'' deformation potentials, which is based on a similar kind of dipolar and octupolar tensors.$^2$ \bigskip\par\noindent $^1$ R. M. Martin, Phys. Rev. B {\bf 5}, 1607 (1972). \par\noindent $^2$ R. Resta, L. Colombo and S. Baroni, Phys. Rev. B {\bf 41}, 12538 (1990).   

Effect of disorder on the piezoelectric properties of ferroelectrics

We develop a Ginzburg-Landau model for ferroelectrics which includes the polarization-strain coupling, the electrostatic interaction, and a quenched random compressional stress field generated by point defects. The strain field and its associated elastic energy are obtained in terms of the stress field and the electric polarization by energy minimization subjected to elastic compatibility. The model is applied to the computation of the piezoelectric response of BaTiO$_3$ in the vicinity of the cubic to tetragonal phase transition, as a function of temperature and the applied electric field in the polar direction. In the clean limit we obtain the divergence of the piezoelectric tensor at the critical point. Similar results are obtained in the presence of a small amount of disorder, the effect of which is a translation of the critical point in the temperature-electric field phase diagram. For large values of the disorder the piezoelectric response loses its critical properties.   

Origins of Asymmetries in Ferroelectricity

In this talk, we will discuss possible origins of asymmetries in ferroelectricity, i.e., two opposite polarizations are not exactly equivalent. We found that both extrinsic and intrinsic mechanism could result in asymmetric ferroelectricity. This asymmetry in ferroelectricity plays an important role in the design and fabrication of ferroelectric or multiferroic tunnel junctions, which could be the building blocks of next-generation information storage and processing devices.   

Dipole-glass behavior in substances with coexisting ferroelectric and antiferroelectric phases

Using the substances with small difference in free energies of ferroelectric and antiferroelectric phases as example we will demonstrate that these compounds possess the set of properties characteristic for the so-called ``dipole glasses''. We will discuss possible phase diagrams of substances that can be misguidedly attributed as glasses. By no means have we wanted to cast doubt on the existence of ``dipole glasses'' in the nature. Main attention will be paid to the long-time relaxation process of physical characteristics of these compounds after their state of thermodynamic equilibrium was disturbed by external influences. The long-time relaxation along with the pronounced frequency dependence of parameters (for example, dependence of dielectric or magnetic characteristics on the frequency of measuring field) is considered as main features to consider these systems as ``glasses''. Our main purpose is only to call attention to the fact that one has to be really careful during the interpretation of experimental results in substances in which the inhomogeneous states with coexisting domains of ferroelectric and antiferroelectric phases can take place.   

First-principles Raman Spectra of Lead Titanate with Pressure

PbTiO$_{3}$ displays[1,2] a morphotropic phase boundary (MPB) under pressure at which electromechanical properties are maximal. Previously only complex solid-solutions were thought to exhibit such a boundary. To aid in the experimental study of the MPB region, we compute Raman scattering spectra of different phases of PbTiO$_{3}$ with pressure using a DFT based first-principles approach and Density Functional Perturbation Theory (DFPT) [3]. The computed intensities and shifts with pressure agree very well with the experimental data measured on powder samples. Computations further allow comparison of Raman spectra and shifts in energetically competing phases raising the possibility of using calculations for experimental calibration of Raman spectra at any pressure. The results substantiate previous claims of a low-temperature monoclinic phase at the MPB at approximately 10 GPa in PbTiO$_{3}$ as well as refute the possibility of an I4cm phase at higher pressures as suggested by other groups [4]. [1] Z. Wu and R. E. Cohen, Phys. Rev. Lett. 95, 037601 (2005), [2] M. Ahart et.al., Nature 451, 545 (2008), [3] P. Hermet et.al., J. Phys.:Condens. Matter 21, 215901 (2009) [4] P.E. Janolin et.al., Phys. Rev. Lett. 101, 237601 (2008).   

Second harmonic generation and high pressure ferroelectricity in PbTiO$_{3}$

We performed measurements of second harmonic generation (SHG) in single-crystal PbTiO$_{3 }$under hydrostatic pressure up to 60 GPa and polycrystalline samples up to 100 GPa at room temperature. The SHG effect is a nonlinear optical effect resulting from a nonlinear dependence of the polarization on the electric field and it strongly couples to ferroelectric order parameters. The integral intensity of SHG in the material is remarkably sensitive to pressure and its intensity decreases monotonically with pressure below 12 GPa. The SHG shows weak intensity with no obvious dependence on pressure above 12 GPa. The integral intensity of the SHG can serve as an order parameter that is responsible for the pressure induced phase transition in PbTiO$_{3}$ crystals. To understand the experiment results, we also performed first-principles density functional calculations using both plane-wave and tight-binding methods and phonon band-structure calculations. We find the ground state to have zone-boundary distortions, with a small polarization. The energy differences between the competing phases are within $\sim $ 1-6 meV/at. suggesting a low Tc at higher pressures, which would be consistent with observed room temperature SHG measurements. This work is supported by the ONR (N000140210506) and the Carnegie/DOE Alliance Center (CDAC) (DF-FC03N00144).   

High sensitivity of $^{17}$O NMR to p-d hybridization in transition metal perovskites: first principles calculations of large anisotropic chemical shielding

First principles calculations are used to show that O chemical shielding tensors, $\hat{\sigma}$, are a sensitive indicator of local structure in transition metal ABO$_3$ perovskites, due to their strong dependence on covalent O(2p)-B($n$d) interactions.\footnote{Pechkis et al., JCP {\bf 131}, 184511 (2009); references therein.} This indicates that $^{17}$O NMR spectroscopy, coupled with first principles calculations, can be an especially useful tool to study the local structure in complex perovskite alloys. Our principal findings are 1) a large anisotropy between deshielded $\sigma_{x}\simeq\sigma_{y}$ and shielded $\sigma_{z}$ components; 2) a nearly linear variation of isotropic $\sigma_{\mathrm{iso}}$ and uniaxial $\sigma_{\mathrm{ax}}$ components, as a function of the B-O-B bond asymmetry, across all the systems studied; 3) the demonstration that the anisotropy and linear variation arise from large paramagnetic contributions to $\sigma_{x}$ and $\sigma_{y}$, due to virtual transitions between O(2p) and unoccupied B($n$d) states. 4) Very good agreement with recent BaTiO$_3$ and SrTiO$_3$ single crystal $^{17}$O NMR measurements of isotropic $\delta_{\mathrm{iso}}$ and uniaxial $\delta_{\rm ax}$ chemical shifts, and good agreement with PbTiO$_3$ and PbZrO$_3$ powder spectrum $\delta_{\mathrm{iso}}$ measurements.\footnotemark[2]   

On the origin of the polymorphic phase transition in KNN

The discovery of outstanding piezoelectric performance in perovkiste niobates alloys has pointed to these materials as viable lead-free substitutes for enviromentally sound transducers and actuators. Similarly to PZT (the solid solution between PbTiO$_3$ and PbZrO$_3$) the large electromechanical coupling in niobates has been originally linked to a morphotropic phase boundary (MPB) that involves a tetragonal phase formed at room temperature when 1-7\% of Li is inserted in K$_x$Na$_{1-x}$NbO$_3$ (KNN) with $x \simeq 0.5$. More recently an alternative explanation based on polymorphic phase transition (PPT) was proposed that equally justifies the enhanced piezoelectric constants and points to lack of stability of the electromechanical response as a function of temperature. We have performed first principles density functional calculations to characterize the role of the different chemical components and the local structure near Li atoms. We will discuss Li-Na interaction as the key mechanism that lead to PPT and we will point to specific consequences of the local structure in KNN on the temperature dependence.   

Polar Behavior of Double Perovskites BiPbZnNbO$_6$ and BiSrZnNbO$_6$: A First Principles Study

Perovskites are classed in two groups, $A$- and $B$-site driven materials, according to the tolerance factor $t$. In the majority of $A$-site driven materials, which have $t<1$, $B$O$_6$ octahedra are tilted and they are not ferroelectrics except for perovskite with lone-pair $A$-sites such as Pb and Bi. However, if the octahedra are prevented from tilting by mixing large and small $A$-site ions, they may become strong ferroelectrics. Here we report the polar behavior of BiPbZnNbO$_6$ and BiSrZnNbO$_6$ based on first principles supercell calculation. The motivation of these choices come from the ion size differences of Pb and Sr as compared with Bi. Additionally, while Pb and Sr ions have approximately the same size, Pb has a low lying $6p$ state. An anomalously large $Z^*$ are found on the Pb compared with one on Sr. It implies there is stronger covalency of Pb-O than one of Sr-O reflecting the absence of $6p$ state on Sr. The polarizations were $\sim$40$\mu$C/cm$^2$. These perovskites, especially Pb, will be good candidates for new ferroelectric materials.   

Quantum Criticality in Ferroelectrics

Materials tuned to the neighbourhood of a zero temperature phase transition often show the emergence of novel quantum phenomena. Ferroelectric crystals provide a type of quantum criticality that arises purely from the crystalline lattice. In many cases the ferroelectric phase can be tuned to absolute zero using hydrostatic pressure or chemical or isotopic substitution. Close to such a zero temperature phase transition, the dielectric constant and other quantities change into radically unconventional forms due to the quantum fluctuations of the electrical polarization. We present low temperature high precision data demonstrating these effects in pure single crystals of SrTiO3 and KTaO3. We outline a self-consistent field theory enabling quantitative predictions to be made without any free adjustable parameters and compare this to experiment. Near to the quantum critical point we observe the emergence of a peak in the dielectric constant at approximately 2 K in SrTiO3 and 3 K in KTaO3. The results are compared to quantum criticality in ferromagnetic d-metals and we indicate how the effective interactions between critical fluctuation modes often appear to become attractive as the ordering temperatures tend to absolute zero in both cases.   

Energy-polarization behaviors of AA$'$BB$'$O$_6$ perovskites with double rock-salt order

Using first-principles methods, we study the energy-polarization relation of double perovskites AA$'$BB$'$O$_6$ where atoms in both A and B sites are arranged in rock-salt order. The high-symmetry structure in this case is the {\it tetrahedral} $F\bar{4}3m$ space group. If a ferroelectric instability occurs, the energy-vs.-polarization landscape $E({\bf P})$ will tend to have minima for {$\bf P$} along tetrahedral directions leading to a rhombohedral space group $R3m$, with two different values of spontaneous polarization and associated energy along opposite body-diagonal directions; or along Cartesian directions, leading to orthorhombic space group $Imm2$. We search for polar {\it soft modes} at the $\Gamma$ point of the high-symmetry $F\bar{4}3m$ structure and analyze its eigenvectors to identify ferroelectric instabilities, which we find in CaBaTiZrO$_6$, KCaZrNbO$_6$ and PbSnTiZrO$_6$. The results of the first-principle calculations are modeled with a Landau-Devonshire expansion that is truncated at either 4th or 5th order in $\bf P$, and its predictions are found to agree favorably with our calculation. The 5th-order calculation improves the agreement further except in PSTZ. Recently, synthesis of SrCaTiMnO$_6$ in rock-salt order has been reported.\footnote{J.L Blok, G. Rijnders and D.H.A. Blank, private communication.} Unfortunately, preliminary results do not seem to indicate any polarized structure.   

First-principles determination of free energies of ferroelectric phase transitions and domains in BaTiO$_{3}$ and PbTiO$_3 $

We present a powerful method based on a combination of (a) constrained polarization molecular dynamics and (b) thermodynamic integration to determine the free energy landscape relevant to structural phase transitions and related phenomena in ferroelectric materials, bridging the gap between first-principles calculations and phenomenological Landau-like theories. We illustrate it using first-principles effective Hamiltonians of $ BaTiO_3 $ and $ PbTiO_3 $ to (a) uncover the quantitative features of the free energy function that are responsible for its first-order ferroelectric transitions, and (b) calculate the minimum free energy pathway for the polarization switching and (c) evaluate temperature dependent domain wall free energy and pathways of the formation of domains. Our method can be readily generalized to any classical microscopic Hamiltonian and ensembles characterized with a given constraint. We show that certain terms have to be added to the phenomenological Landau-Devonshire free energy functions to capture the physics of ferroelectric materials.   

Many-body large polaron optical conductivity in SrTi$_{1-x}$Nb$_{x}$O$_{3}$

Recent experimental data on the optical conductivity of niobium doped SrTiO$_{3}$ are interpreted in terms of a gas of large polarons. The theoretical approach takes into account many-body effects, the electron-phonon interaction with multiple LO-phonon branches, and the degeneracy and the anisotropy of the Ti t$_{2g}$ conduction band. The many-body large-polaron model based on the Fr\"{o}hlich interaction provides a fair agreement between the theoretical large-polaron optical conductivity band and the experimental mid-infrared optical conductivity band without any adjustment of material parameters. The large-polaron model gives then a convincing interpretation of the experimentally observed optical conductivity spectra of SrTi$_{1-x}$Nb$_{x}$O$_{3}$.