Session K41: Focus Session:Dielectric, Ferroelectric, and Piezoelectric Oxides II

Ferroelectricity of Perovskites under Pressure

\textit{Ab-initio} simulations and experimental techniques are combined to reveal that, unlike commonly accepted for more than 30 years, perovskites and related materials \emph{enhance} their ferroelectricity as hydrostatic pressure increases above a critical value [1]. This unexpected high-pressure ferroelectricity is different in nature from conventional ferroelectricity because it is driven by an original electronic effect rather by long-range interactions. [1]. Igor A. Kornev, L. Bellaiche, P. Bouvier, P.-E. Janolin, B. Dkhil, and J. Kreisel, Phys. Rev. Lett. 95, 196804 (2005)   

NMR quadruopole spectra of PZT from first-principles

High performance piezoelectric materials are disordered alloys, so it can be difficult to determine the local atomic geometry. Recently, high field NMR measurements have shown great promise as a microscopic probe of $\mathrm{ABO_{3}}$ perovskite-based alloys \footnote{G. L. Hoatson, D. H. Zhou, F. Fayon, D. Massiot, and R. L. Vold, Phys. Rev. B, {\bf 66}, 224103 (2002).} by their ability to resolve line-splittings due to nuclear quadrupolar coupling with the electric field gradient (EFG) at the nucleus. We report first-principles LDA calculations of the EFG's in monoclinic and tetragonal Pb(Zr$_{0.5}$Ti$_{0.5}$)O$_3$ systems using the linear augmented planewave (LAPW) method, and we compute NMR static powder spectra for $^{91}$Zr, $^{47}$Ti, and $^{17}$O atoms as a function of applied strain. With decreasing $c/a$ ratio PZT converts from tetragonal to monoclinic symmetry. We observe that the calculated NMR spectra show dramatic deviations with decreasing $c/a$ from that in tetragonal $P4mm$ well before the electric polarization begins to rotate away from the [001] direction. This indicates that NMR measurements can be a very accurate probe of local structural changes in perovskite piezoelectrics.   

A First Principles Approach to Modelling Ba$_{(1-x)}$Ca$_{(x)}$ZrO$_{3}$

Dielectric properties are often optimized by varying material composition, so there is a need to understand the impact of doping on the local structure and properties of a material. One study showed that the dielectric constant of BaZrO$_{3}$ (BZ) can be increased by up to 50\% by doping with small amount of Ca [1]. This is interesting because CaZrO$_{3}$ (CZ) actually has a lower epsilon than BZ. We use first principles methods to characterize the local structure of Ba$_{(1-x)}$Ca$_{(x)}$ZrO$_{3}$ (BCZ) at various compositions and compute the contribution to the dielectric response of each normalized mode at 0~K. There arise low frequency phonon modes related to Ca-O motions and a transformation of Raman modes to IR modes caused by the introduction of Ca. [1]Levin, I. et al. J Sol. State Chem. 175 (2003) 170-181   

Pressure-Induced Ferroelectric-to-Relaxor Crossover in PSN and Isomorphs

We discuss the influences of pressure (P) and bias field on the dielectric properties and phase behavior of a single crystal of the chemically-disordered ABB'O$_{3}$ perovskite Pb(Sc$_{0.5}$Nb$_{0.5}$)O$_{3}$ or PSN. On cooling from high temperatures (T), PSN first enters a relaxor (R) state and then spontaneously transforms to a ferroelectric (FE) phase at a temperature T$_{c}$ substantially below the maximum in the dielectric susceptibility. The R state indicates the presence of polar nanoregions, arising from the B-site chemical disorder, that increase in size with decreasing T. At ambient P, these regions grow to macroscopic size, leading to a first-order FE transition at T$_{c}$. Hydrostatic P offers a unique method to systematically decrease the dielectric polarizability of PSN by reducing the unit cell volume and, hence, increasing the frequency of the soft transverse optic phonon modes. As P increases, the size of the polar regions decreases, enhancing the R state at the expense of the FE phase. It appears that the FE phase vanishes somewhat above the highest P reached in the experiments, making the R state the ground state of the crystal at reduced volume. This suggests a T-P phase diagram with a T$_{c}$(P) phase line that terminates between 10 and 15 kbar in a manner akin to a critical point; however, in the case of PSN this feature represents a FE-to-R crossover. In contrast, a biasing electric field favors the FE phase over the R state, and the data indicate that the R state vanishes above 5 kV/cm. Additional insight is provided by comparison to dielectric results on isomorphous Pb(Sc$_{0.5}$Ta$_{0.5}$)O$_{3}$ in both its compositionally ordered and disordered forms.   

Dielectric Behavior of Compositionally Graded Ferroelectrics

Graded ferroelectric thin films offer the possibility of engineering the dielectric response by spatial variations in composition. While a homogenous ferroelectric material achieves very high dielectric constants near the phase transition, heterogeneous compositions can result in high dielectric responses over a wide range of temperatures. This can be understood as an ``aggregate'' response of the graded film, and has been experimentally observed. It is a promising candidate for tunable microwave applications that benefit from temperature-insensitivity. We examine this issue through a continuum model that accounts for the spatial variation in properties and the long-range electrostatic interaction. This model is applied to graded Barium Strontium Titanate and Lead Barium Titanate films in a single-domain system where the polarization gradient is normal to the film surface. We examine the effect of grading and the geometry of electrode/ferroelectric layers on the dielectric behavior with temperature and provide results that are useful as design tools for functionally graded devices.   

Origin of Curie temperature non-linearity in ferroelectric BiBO$_3$-PbTiO$_3$ solid solutions

We use first-principles density functional theory calculations to investigate compositional trends in ferroelectric BiBO$_3$-PbTiO$_3$ solid solutions. We find that cation displacements which give rise to ferroelectricity in these materials follow a linear relationship with the average displacive characteristics of the B-site. The transition temperatures in these materials are well correlated with polarization magnitudes computed from our calculations. The coupling between composition of the B-site and A- and B-site displacements explains the highly nonlinear and sometimes non-monotonic dependence of the Curie temperature ($T_c$) on composition observed in these materials.   

Atomistic simulation of strained BaTiO$_3$/SrTiO$_3$ superlattices

The BaTiO$_3$(BT)/SrTiO$_3$(ST) superlattice is one of the most intensively studied because of the possibility of polarization enhancement by manipulating strain and layer thicknesses. In this work, we apply an atomistic-level description to explore the structural, polar and dielectric properties of epitaxial 001-oriented BT/ST superlattices. The shell-model potentials used here have previously described well the phase diagram and properties of BT perfect crystals and ST in the high-temperature limit, and in combination, these potentials reproduced the FE properties of Ba$_x$Sr$_{1-x}$TiO$_3$~random solid solutions. Here, we focus on asymmetric BT/ST superlattices with in-plane lattice parameter matched to a ST substrate, and periods ranging from 6 to 18 unit cells. These structures have strain induced tetragonal symmetry at low temperature with polarization along the modulation direction and transform to a paraelectric phase at high temperature. Ferroelectric transition temperatures and static dielectric constant are reported as functions of the BT/ST ratio. Also, we show values for local strain and local spontaneous polarization.   

Effects of Pressure and Electric Field on the Relaxational Dielectric Properties of K$_{0.97}$Li$_{0.03}$O$_{3}$ (KLT-3)

The temperature dependence of the dielectric response of KLT-3 shows no evidence of a thermodynamic phase transition, but reveals two prominent relaxational features associated with the off-center Li$^{+}$ ion, one attributed to the hopping of the Li$^{+}$ dipole and the other with the reorientation of Li$^{+}$ - Li$^{+}$ ion pair. Both relaxations are Debye-like and follow Arrhenius kinetics, the energy barriers decreasing with pressure. While pressure favors the relaxational behavior, a biasing \textit{dc} electric field favors long-range order of the dipolar system. The interplay between pressure and field provides additional insight. Pressure suppresses the magnitude of the $\varepsilon \prime $(T) response over the whole temperature range The results allow evaluation of the contributions of the soft mode and of the Li$^{+}$ dipoles to the measured $\varepsilon \prime $(T) response.   

Ferroelectricity in PbTiO$_3$ and BaTiO$_3$ under Pressure

First-principles total energy and linear response calculations reveal a complicated pressure-induced phase transition sequence for PbTiO$_3$ (PT) under pressure. The previously proposed $P4mm$-to-$Cm$-to-$R3m$-to-$Pm\bar{3}m$ transition sequence [1] is not complete because only zone-center ($\Gamma$) instabilities and pressures $P$ less than 30 GPa were considered. Recently Kornev {\it et al.} reported an unexpected enhancement of ferroelectric instability at high pressures [2]. Our computations confirm this result, and in addition, the zone-boundary R-point rotational instability is enhanced with pressure. Preliminary results show $R3m$-to-$R3c$-to-$R\bar{3}c$-to-$R3c$ phase transitions in PT for 18 GPa $< P <$ 120 GPa due to the competition and interaction of zone-center and zone-boundary instabilities. On the other hand, there is no instability in cubic BaTiO$_3$ for $P > $ 10 GPa up to 120 GPa, resulting in a single $R3m$-to-$Pm\bar{3}m$ transition at 0 K. We are investigating whether the covalency of Pb is responsible for the unusual enhancement of ferroelectricity under high pressure. The electromechanical coupling constants become enormous in the transition regions from the tetragonal to high pressure phases for PT, suggesting that the large coupling in PT solid solutions such as PZT, PMN-PT, and PZN-PT, simply tune this transition to zero pressure[1]. Supported by ONR. [1] Z. Wu and R. E. Cohen, Phys. Rev. Lett. {\bf 95}, 037601 (2005). [2] Kornev {\it et al.}, Phys. Rev. Lett. {\bf 95}, 196804 (2005).   

A-site driven ferroelectricity in K$_{0.5}$Li$_{0.5}$NbO$_3$

Mixed A-site ferroelectric materials have gained recent attention. Here we report density functional calculations of K$_x$Li$_{1-x}$NbO$_3$ perovskite supercells in order to understand the interplay between various lattice instabilities with size mismatch on the A-site and the role of the A and B site ions in this case. The calculations were done using the general potential LAPW method. For x=0.5, we find a ferroelectric ground state, even though the average tolerance factor is significantly smaller than unity and there is no stereochemically active A site ion. This is due to frustration due to the very different ionic radii of K and Li. We find very large off-centering of the Li ions, which distinguishes this compound. Relative to this the Nb off-centering is quite small. This is in contrast to most perovskite ferroelectrics where there is significant off-centering of all ions, and resulting cooperativity. Also because of the large Li off-centering it contributes strongly to the anisotropy between tetragonal and rhombohedral ground states, yielding a tetragonal ground state. Normally the anisotropy is determined by the interplay of B site off-centering and strain coupling. This work was supported by the Office of Naval Research and the Department of Energy.   

Effective Hamiltonian study of PbSc$_{1/2}$Nb$_{1/2}$O$_3$ under pressure

In general, increasing pressure depresses the transition temperature $T_{FE}$ of ferroelectric transitions, and sufficient pressure yields a FE ~$\rightarrow$~ paraelectric (PE) transition. A more complicated behavior is observed for disordered PbSc$_{1/2}$Nb$_{1/2}$O$_3$ (PSN). At atmospheric pressure, PSN exhibits relaxor ferroelectric (RFE) properties within a small temperature range before transforming to a FE phase at low temperatures. Pressure of approximately 1.5 to 2.5 GPa induces a low-temperature RFE state without a RFE/FE phase boundary.[E. L. Venturini et al.] To investigate the effects of pressure on phase transitions in PSN, we used a first-principles based effective Hamiltonian. Our effective Hamiltonian includes a local field term arising from the charge difference between the Sc$^{3+}$ and Nb$^{5+}$ ions. Under pressure, the local field term changes little, while the FE well depths decrease, increasing the relative importance of the local fields. Molecular dynamics simulations show that $T_{FE}$ decreases with temperature and that the phase transition broadens.   

Pressure-induced phase transitions in PbTiO$_{3}$

We have investigated PbTiO$_{3}$ under pressure in a diamond anvil cell for temperatures of 20K to 300K using micro-Raman spectroscopy and x-ray diffraction. The Raman spectra show large changes: three peaks, centered at 200, 240 and 250 cm$^{-1}$ disappeared above 20, 19 and 17 GPa at 20, 47 and 77 K, respectively. Furthermore, a new peak centered at 300 cm$^{-1}$ appears above transition points. The disappearance of peaks and the appearance of new peaks are consistent with theoretical calculations of Z. Wu \textit{et al}., \textit{Phys. Rev. Lett}. 95, 37601, 2005, and suggest a zone boundary instability at high pressures. The experimental results also indicate that pressure induced phase transitions at low temperature are reversible. At room temperature the first order Raman spectrum disappears above 12 GPa consistent with a transition to the cubic phase, but x-ray diffraction data suggests a rhombohedral or monoclinic phase between the tetragonal and cubic phases, consistent with the predictions of Z. Wu et al. The experimental results provide a new phase diagram for PbTiO$_{3}$.   

Electronic structure and lattice distortion in PbMg$_{1/3}$Nb$_{2/3}$O$_3$

We investigated the local structural distortions of PMN(PbMg$_{1/3}$Nb$_{2/3}$O$_3$) within the density functional theory using the linearized augmented plane-wave method. Structural relaxations were performed on 30 atom unit cells with B-cations arranged in 1:1 chemical ordering along [111]. The direction and magnitude of Mg and Nb off-centering within O$_6$ octahedral cages and Pb within its cage as well as electronic structures were examined. The results are discussed in terms of the Nb 4d - O 2p and Pb 6p - O 2p hybridizations and their interplay. A significant role is found for the on-site Ewald potential of different Nb sublattices, which is correlated with the off-centering. \\ \\ $\dag$This work was supported by ONR and DOE.