Session P24: Focus Session: Dielectric, Ferroelectric, and Piezoelectric Oxides -- Nanostructures

Equilibrium Polarization under Ionic Surface Compensation in Ultrathin PbTiO$_{3}$

The polarization structure of a ferroelectric film depends strongly on the charge compensation at its interfaces. When there is no electrode, ions from the environment can compensate a surface. We have previously shown that changing the chemistry of the environment can drive polarization switching in a ferroelectric film, and for the thinnest films the switching occurs continuously, without domain nucleation. In this talk we present results on the equilibrium polarization of a film as a function of the ionic compensation of its surface. Synchrotron x-ray scattering is used to determine the polarization structure of epitaxial PbTiO$_{3}$ films on conductive SrRuO$_{3}$ layers coherently strained to SrTiO$_{3}$ (001) substrates as a function of temperature, film thickness, and external oxygen partial pressure (pO$_{2})$. We observe a suppression of the Curie temperature (T$_{C})$ at intermediate values of pO$_{2}$, which becomes very large for films thinner than $\sim $5 nm. This suppression of T$_{C}$ is explained by a model for the equilibrium between the chemical environment and the surface of the ferroelectric. Work supported by the U. S. Department of Energy under Contract No. DE-AC02-06CH11357.   

Absence of Thermodynamic Critical Thickness in Ferroelectric Thin Films

We have constructed the external field versus temperature/thickness phase diagram for ferroelectric thin film with real electrodes, and considered the effect of inhomogeneous elastic strains. The main features of the diagram are: (i) The single domain state is at best metastable and is never thermodynamically stable [1]. Therefore, the ``critical thickness for single domain ferroelectricity'' does not exist in thermodynamic sense. The only ``critical thickness'' of a practical importance is the one corresponding to a desired retention time of a metastable single domain state. (ii) Upon lowering external electric field, there is a phase transition between homogeneous and inhomogeneous states. For a part of the interval, the phase transition is second order while for another one it is first order, i.e. there exists a tricritical point on the phase diagram. In the elastically anisotropic materials, the elastic coupling for the films on substrates may have either stabilizing or destabilizing effect, depending on specific material [2].\\[4pt] [1] A.M. Bratkovsky and A.P. Levanyuk, arXiv: 0801.1669.\\[0pt] [2] A.M. Bratkovsky and A.P. Levanyuk, Phys. Rev. Lett. 100, 149701 (2008).   

First-principles studies of ultrathin ferroelectric capacitors with Ru-based perovskite electrodes

First-principles calculations are used to investigate the electrostatics and polarization screening effects in ultrathin PbTiO$_{3}$ films capped with SrRuO$_{3}$ or CaRuO$_{3}$ electrodes under short-circuit boundary conditions. In accordance with previous results, we find that the SrRuO$_{3}$/PbTiO$_{3}$/SrRuO$_{3}$ system without antiferrodistortive octahedral rotations is ``non-pathological'' with respect to the metal/ferroelectric band alignment across the interface. Such rotations, however, have to be explicitly considered to correctly determine the band alignment and polarization screening in the SrRuO$_{3}$/PbTiO$_{3}$/SrRuO$_{3 }$nanocapacitor. (*) Present address: Vanderbilt University, Nashville, Tennessee 37235 and Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831   

Atomic-scale compensation phenomena at ferroelectric interfaces

The electrical polarization in ferroelectrics induces electrical charges at the surfaces or interfaces of ferroelectric films. The interfacial screening charge at the ferroelectric/electrode interface is now recognized as the most important factor in determining the stability of ferroelectricity in thin films. By combination of first-principles density-functional theory (DFT) calculations and electron microscopy imaging techniques, we investigate the atomic-scale compensation mechanism at the PbTiO$_3$/SrRuO$_3$ (PTO/SRO) and the PbTiO$_3$/SrTiO$_3$ (PTO/STO) interfaces. Two very different interfacial reactions to screen the depolarization field are identified. In the case of PTO/SRO, screening by ionic displacement is observed, in addition to electronic screening in the metallic SRO. In the case of PTO/STO, a compensation mechanism by oxygen vacancies is identified. This mechanism is an important option for the design and growth of ferroelectric thin films.\\ This research was sponsored by the DOE Office of Basic Energy Sciences, Division of Materials Sciences and Engineering. Computations were performed at the National Energy Research Scientific Computing Center.   

Band-alignment issues in the \emph{ab initio} simulation of ferroelectric nanocapacitors

Recent advances in growing and characterization techniques of complex oxides thin films have lead to the development of many novel interface-based devices with a great number of new functionalities, such as the formation of 2D electron gases or spin-polarized tunnel junctions. These experimental developments have been accompanied by a great explosion of theoretical works aiming to understand the origin of such phenomena. DFT simulations, both within LDA or GGA aproximations, have been shown to be an extremely powerful tool to study these systems. However, it is important to identify, in adition to the virtues, also the limitations of DFT which are specific to metal/perovskite interfaces, and that when overlooked might lead to erroneous physical conclusions. In this work we study the consecuences of the band-gap underestimation by usual DFT functionals. We show how this underestimation might lead to wrong band alignments both in nonpolar and in polar complex oxides heterostructures, and how they give rise to unphysical charge transfers across the interfaces. We also provide analysis tools to detect the fingerprints of such pathological behaviour.   

Vortex polarization instabilities in PbTiO$_{3}$ nanowires

The possibility of circular, toroidal or vortex-like ordering (closure domains) of magnetic spin vectors have been considered, and their existence versified, in the past. Recent experimental and computational (based on effective Hamiltonian simulations) work have contributed to the mounting evidence for the presence of such vortex-like domains of electric polarization vectors in ferroelectric nanostructures. Here, for the first time using parameter-free ab initio density functional theory (DFT) based computations, we show the existence of such a vortex polarization state in PbTiO$_{3}$ [001] nanowires. Our computations involved relaxed and axially strained free-standing PbTiO$_{3}$ [001] nanowires with varying sidewall terminations and diameters. While stress-free nanowires with their sidewalls terminated by PbO surfaces displayed purely axial rectilinear polarization at all sizes, the TiO$_{2}$-terminated nanowires, at a critical diameter of 16 {\AA}, display a vortex polarization transverse to the nanowire axis. Moreover, we predict the existence of novel stress-induced phase transitions between the vortex and the rectilinear polarization states in both the PbO- and TiO$_{2}$-terminated nanowires. Normal mode vibrational frequency analysis of these nanowires further confirms these results.   

Domains in Ferroelectric Nanostructures

Ferroelectric materials have great potential in influencing the future of small scale electronics. At a basic level, this is because ferroelectric surfaces are charged, and so interact strongly with charge-carrying metals and semiconductors - the building blocks for all electronic systems. Since the electrical polarity of the ferroelectric can be reversed, surfaces can both attract and repel charges in nearby materials, and can thereby exert complete control over both charge distribution and movement. It should be no surprise, therefore, that microelectronics industries have already looked very seriously at harnessing ferroelectric materials in a variety of applications, from solid state memory chips (FeRAMs) to field effect transistors (FeFETs). In all such applications, switching the direction of the polarity of the ferroelectric is a key aspect of functional behavior. The mechanism for switching involves the field-induced nucleation and growth of domains. Domain coarsening, through domain wall propagation, eventually causes the entire ferroelectric to switch its polar direction. It is thus the existence and behavior of domains that determine the switching response, and ultimately the performance of the ferroelectric device. A major issue, associated with the integration of ferroelectrics into microelectronic devices, has been that the fundamental properties associated with ferroelectrics, when in bulk form, appear to change quite dramatically and unpredictably when at the nanoscale: new modes of behaviour, and different functional characteristics from those seen in bulk appear. For domains, in particular, the proximity of surfaces and boundaries have a dramatic effect: surface tension and depolarizing fields both serve to increase the equilibrium density of domains, such that minor changes in scale or morphology can have major ramifications for domain redistribution. Given the importance of domains in dictating the overall switching characteristics of a device, the need to fully understand how size and morphology affect domain behaviour in small scale ferroelectrics is obvious. In this talk, observations from a programme of study examining domains in meso and nano-scale BaTiO$_{3}$ shapes, that have been cut directly from bulk single crystal using focused ion beam milling, will be presented. In general, the equilibrium static domain configurations that occur appear to be the result of a simultaneous desire to minimize both the macroscopic strain and depolarizing fields developed on cooling through the Curie Temperature. While such governing factors might be obvious, the specific patterns that result as a function of morphology are often non-intuitive, and a series of images of domains in nanodots, rods and wires will be presented and rationalised. In addition, the nature in which morphological factors influence domain dynamics during switching will be discussed, with particular focus on axial switching in nanowires, and the manner in which local surface perturbations (such as notches and antinotches) affect domain wall propagation. In collaboration with Alina Schilling, Li-Wu Chang, Mark McMillen, Raymond McQuaid, and Leo McGilly, Queen's University Belfast; Gustau Catalan, Universitat Autonoma de Barcelona; and James Scott, University of Cambridge.   

Novel interface effect in CaTiO$_3$/BaTiO$_3$ superlattices

Interfaces are a key focus for tuning the functionality of short-period superlattices. Previous work has shown that an increased density of interfaces normally tends to suppress the ferroelectricity in ferroelectric superlattices, but this is not always the case. Here, we show how suppression of rotational distortions at interfaces can enhance ferroelectricity. We carry out first-principles calculations for CaTiO$_3$/BaTiO$_3$ superlattices with epitaxial strain favoring the development of a spontaneous polarization along the [001] (out-of-plane) direction, and consider octahedral rotations as well as ferroelectric distortions. The calculations are done as a function of electric displacement field, and both a macroscopic and a local electrostatic analysis is carried out. We find that strong octahedral rotations occur for TiO$_6$ octahedra sandwiched between CaO layers on both sides, but are strongly suppressed if either neighboring layer is a BaO layer. Due to the resulting enhancement of the ferroelectric instability in these layers, we find that overall the ferroelectric instability of the superlattice is enhanced by the interface. Thus, short-period superlattices in this system have a higher polarization ferroelectricity than longer-period ones of the same average composition, contrary to the general expectation.   

First-Principles Study of Lattice Instabilities in the Ca-Ti-O Layered Perovskites

Advances in complex oxide thin-film growth techniques have allowed researchers to grow materials under a wide range of epitaxial strains. It is now possible to tune the properties of oxides (the paraelectric-to-ferroelectric transition temperature, for example) simply by choosing an appropriate substrate. Another path towards tailoring properties at the atomic scale is the controlled alteration of a material's structure via two-dimensional layering. We use first-principles Density Functional Theory (DFT) to study lattice instabilities in a family of Ca-Ti-O layered perovskites. We use symmetry arguments, in combination with DFT results, to analyze the interaction between polar and non-polar lattice modes in a homologous series of Ca-Ti-O layered materials. Our results may lead to an understanding of the emergence of a novel polar state in the more general family of ferroelectric heterostructures.   

Novel ferroelectrics in AA$\prime $BB$\prime $O$_{6}$ perovskites with double rock-salt order

In recent years, the effect of strain and symmetry on the properties of epitaxial ferroelectric perovskites (ABO$_{3})$ has been studied by many groups. However in most cases the studied systems were grown on (001) oriented substrates. Growing ferroelectrics in the $<$111$>$ direction allows us to apply strain in a different way and, furthermore, if [1:1] superlattices are grown of two different materials it would result in films where the neighboring atoms on both A-site and B-site are always different. The symmetry in such double perovskites will be altered and interesting and unique ferroelectric properties are expected. We fabricated such double perovskite superlattices in the $<$111$>$ direction. Using strain matching (that is selecting materials with equal, but opposite strain), we managed to keep the surface of the superlattice atomically smooth even after the growth of 100 monolayers. We will show this for the growth of a CaTiO$_{3}$ - SrMnO$_{3}$ as well as CaTiO$_{3}$ - BiFeO$_{3}$ superlattices on a (111) LaAlO$_{3}$ and SrTiO$_{3}$ substrate. We have used X-ray diffraction to show that the superlattice is fully strained to the substrates. In this contribution we will focus on the growth and structural properties of the superlattices, as well as the resulting properties.   

Artificially layered PbTiO$_{3}$/BaTiO$_{3}$ superlattices

Artificially layered superlattices of ferroelectric oxides provide an appealing route for the tailoring of materials to particular applications [1] by taking advantage of electrostatics, strain and more exotic interactions between different materials at interfaces [2]. First principles calculations [3] suggest that the piezoelectric properties can be enhanced at certain ratios of layer thicknesses in the PbTiO$_{3}$/BaTiO$_{3}$ superlattice system. We have fabricated high quality artificially layered PbTiO$_{3}$/BaTiO$_{3}$ superlattices on SrTiO$_{3}$ substrates (with SrRuO$_{3}$ electrodes) using an off-axis RF magnetron sputtering technique, allowing us to perform a range of experiments, including x-diffraction, electrical measurements and atomic force microscopy. We will discuss our experimental results and their relationship with the theoretical expectations for this system and highlight the potential of using a superlattice approach to create enhanced materials for piezoelectric applications. \textbf{References} [1] M. Dawber, N. Stucki, C. Lichtensteiger, S. Gariglio, P. Ghosez and J.-M. Triscone, Advanced Materials, 19, 4153 (2007). [2] E. Bousquet, M. Dawber, N. Stucki, C. Lichtensteiger, P. Hermet, S.Gariglio, J.-M. Triscone, and P. Ghosez, Nature, 452, 732 (2008). [3] V. R. Cooper and K. M. Rabe, Phys. Rev. B 79, 180101 (R) (2009)   

Piezoelectric response of epitaxial ferroelectric heterostructures

The electromechanical response of epitaxial oxide heterostructures can be used to probe novel properties arising from nanoscale structural confinement. To resolve the layer-by-layer origin of piezoelectric responses of ferroelectric/dielectric superlattices, we performed time-resolved x-ray microdiffraction studies of a 2(BaTiO$_{3})$/4(CaTiO$_{3})$ superlattice in an applied electric field. The contributions of individual components to the overall piezoelectric response are deduced using kinematic x-ray diffraction calculations. We found that the dielectric CaTiO$_{3}$ component has an equal piezoelectric response and remnant polarization to the ferroelectric BaTiO$_{3}$ component, in good agreement with predictions of piezoelectric coefficient ($\sim $50 pm/V) and local polarization distribution based on density functional theory calculations.   

Structural, Electrical and Optical Properties of BaTiO$_{3}$(BT)/Ba$_{(1-x)}$Sr$_{x}$TiO$_{3}$(BST) and SrTiO$_{3}$(ST)/BST Superlattices

Superlattices (SL) have attracted interests due to the possibility of producing superior and new properties compared to the parent constituents. We have fabricated SL of BT/BST and ST/BST with x= 0 - 1 by pulse laser deposition. The films modulation period ($\Lambda )$ in all SL were $\Lambda $= 80 {\AA}, that is, BT$_{\Lambda /2 }$or ST$_{\Lambda /2 }$/BST$_{\Lambda /2 }$and the total thickness of each SL film was $\sim $600 nm. XRD revealed (00l) perovskite structure and the so-called satellite peaks typical of modulated structures. The angular distance ($\theta _{n})$ between the satellite peaks for BT/BST (ST/BST) increases (decrease) with increase (decrease) of x concentration. The polarized Raman spectra of BT/BST SL at room temperature are very close to those of BT; however the activation of folded acoustic phonons in SL was observed when the $\theta _{n}$ increase (BT/ST, BT/BST$_{x=0.7})$. The BT/BST$_{x=0.7 }$showed well defined ferroelectric loop ($\sim $10 $\mu $C/cm$^{2})$, and the dielectric constant and loss values at 10 kHz was 350 and 0.05 respectively. Temperature dependent Raman studies will be discussed.