Low dimensional structures comprised of ferroelectric (FE) PbTiO$_3$ (PTO) and quantum paraelectric SrTiO$_3$ (STO) are hosts to complex polarization textures such as polar waves, flux-closure domains and polar skyrmion phases. Density functional theory (DFT) simulations can provide insight into this order, but, are limited by the computational effort needed to simulate the thousands of required atoms. To relieve this issue, we use the novel multi-site support function (MSSF) method within DFT to reduce the solution time for the electronic groundstate whilst preserving high accuracy. Using MSSFs, we simulate thin PTO films on STO substrates with system sizes $>2000$ atoms. In the ultrathin limit, the polar wave texture with cylindrical chiral bubbles emerges as an intermediate phase between full flux closure domains and in-plane polarization. This is driven by an internal bias field born of the compositionally broken inversion symmetry in the [001] direction. Since the exact nature of this bias field depends sensitively on the film boundary conditions, this informs a new principle of design for manipulating chiral order on the nanoscale through the careful choice of substrate, surface termination or use of overlayers. Antiferrodistortive (AFD) order locally interacts with these polar textures giving rise to strong FE/AFD coupling at the PbO terminated surface driving a $p(2 \times Λ)$ surface reconstruction. This offers another pathway for the local control of ferroelectricity.
Artificial PbTiO$_{3}$/SrTiO$_{3}$ superlattices were constructed using off-axis RF magnetron sputtering. X-ray diffraction and piezoelectric atomic force microscopy were used to study the evolution of the ferroelectric polarization as the ratio of PbTiO$_{3}$ to SrTiO$_{3}$ was changed. For PbTiO$_{3}$ layer thicknesses larger than the 3-unit cells SrTiO$_{3}$ thickness used in the structure, the polarization is found to be reduced as the PbTiO$_{3}$ thickness is decreased. This observation confirms the primary role of the depolarization field in the polarization reduction in thin films. For …
We report first-principles calculations, within the density functional theory, on the structural and energetic properties of 180$^\circ$ stripe domains in (PbTiO$_{3}$)$_{n}$/(SrTiO$_{3}$)$_{n}$ superlattices. For the explored periodicities ($n$=3 and 6) we find that the polydomain structures compete in energy with the monodomain phases. Our results suggest the progressive transition, as a function of $n$, from a strong to a weak electrostatic coupling regime between the SrTiO$_{3}$ and PbTiO$_{3}$ layers. Structurally, they display continuous rotation of polarization connecting 180$^\circ$ do…
In this paper, an efficient computational material design approach (cluster expansion) is employed for the ferroelectric $PbTiO_3$/$SrTiO_3$ system. Via exploring a conguration space including over $3 \times 10^6$ candidates, two special cation ordered configurations: either perfect or mixed 1/1 (101) superlattice, are identified with the mostly enhanced ferroelectric polarization by up to about 100% in comparison with the (001) superlattice. Analyzing these two special configurations reveals the exotic couplings between the antiferrodistortive distortion (AFD) and ferroelectric polarization (…
We report first principles density functional perturbation theory calculations and inelastic neutron scattering measurements of the phonon density of states, dispersion relations and electromechanical response of PbTiO3, BaTiO3 and SrTiO3. The phonon density-of-states of the quantum paraelectric SrTiO3 is found to be fundamentally distinct from that of ferroelectric PbTiO3 and BaTiO3 with a large 70-90 meV phonon band-gap. The phonon dispersion and electromechanical response of PbTiO3 reveal giant anisotropies. The interplay of covalent bonding and ferroelectricity, strongly modulates the elec…
We study the emergence of Berezinskii-Kosterlitz-Thouless (BKT) phases in (PbTiO$_3$)$_3$/(SrTiO$_3$)$_3$ superlattices by means of second-principles simulations. Beyond a threshold tensile epitaxial strain of $ε= 0.25 \%$ the local dipole moments within the superlattices are confined to the film-plane, and thus the polarization can be effectively considered as two-dimensional. The analysis of the decay of the dipole-dipole correlation with the distance, together with the study of the density of defects and its distribution as function of temperature, supports the existence of a BKT phase in a…
We report first-principles calculations on the coupling between epitaxial strain, polarization, and oxygen octahedra rotations in monodomain (PbTiO$_{3}$)$_{n}$/(SrTiO$_{3}$)$_{n}$ superlattices. We show how the interplay between (i) the epitaxial strain and (ii) the electrostatic conditions, can be used to control the orientation of the main axis of the system. The electrostatic constrains at the interface facilitate the rotation of the polarization and, as a consequence, we predict large piezoelectric responses at epitaxial strains smaller than those that would be required considering only s…
The spontaneously formed striped polarization nanodomain configuration of a PbTiO${_3}$/SrTiO${_3}$ superlattice transforms to a uniform polarization state under above-bandgap illumination with a time dependence varying with the intensity of optical illumination and a well-defined threshold intensity. Recovery after the end of illumination occurs over a temperature-dependent period of tens of seconds at room temperature and shorter times at elevated temperatures. A model in which the screening of the depolarization field depends on the population of trapped electrons correctly predicts the obs…
We study Ti 1s near-edge spectroscopy in PbTiO$_3$ at various temperatures above and below its tetragonal-to-cubic phase transition, and in SrTiO$_3$ at room temperature. Ab initio molecular dynamics (AIMD) runs on 80-atom supercells are used to determine the average internal coordinates and their fluctuations. We determine that one vector local order parameter is the dominant contributor to changes in spectral features: the displacement of the Ti ion with respect to its axial O neighbors in each Cartesian direction, as these displacements enhance the cross section for transitions to E$_{\rm g…
Complex polar superstructure controlled thermal conductivity in ferroelectric PbTiO3/SrTiO3 superlattices
Universidade de Santiago de Compostela（圣地亚哥-德孔波斯特拉大学）；Universidad Rey Juan Carlos（胡安卡洛斯国王大学）；Universitat de Barcelona（巴塞罗那大学）；Catalan Institute of Nanoscience and Nanotechnology (ICN2)（加泰罗尼亚纳米科学与技术研究所）；ALBA Synchrotron Light Facility（阿尔巴同步辐射光源设施）
Specific forms of the exchange correlation energy functionals in first-principles density functional theory-based calculations, such as the local density approximation (LDA) and generalized-gradient approximations (GGA), give rise to structural lattice parameters with typical errors of -2% and 2%. Due to a strong coupling between structure and polarization, the order parameter of ferroelectric transitions, they result in large errors in estimation of temperature dependent ferroelectric structural transition properties. Here, we employ a recently developed GGA functional of Wu and Cohen [Phys. …
The defect stability in a prototypical perovskite oxide superlattice consisting of SrTiO$_3$ and PbTiO$_3$ (STO/PTO) is determined using first principles density functional theory calculations. Specifically, the oxygen vacancy formation energies E$_v$ in the paraelectric and ferroelectric phases of a superlattice with four atomic layers of STO and four layers of PTO (4STO/4PTO) are determined and compared. The effects of charge state, octahedral rotation, polarization, and interfaces on the E$_v$ are examined. The formation energies vary layer-by-layer in the superlattices, with E$_v$ being hi…
PbTiO$_3$ is a simple but very important ferroelectric oxide that has been extensively studied and widely used in various technological applications. However, most previous studies and applications were based on the bulk material or the conventional [$001$]-orientated films. There are few studies on PbTiO$_3$ films grown along other crystalline axes. In this study, a first-principles calculation was performed to compute the polarization of PbTiO$_3$ films strained by SrTiO$_3$ and LaAlO$_3$ substrates. Our results show that the polarization of PbTiO$_3$ films strongly depends on the growth ori…
Interface effects on the ferroelectric behavior of PbTiO$_3$ ultrathin films deposited on SrTiO$_3$ substrate are investigated using an interatomic potential approach with parameters fitted to first-principles calculations. We find that the correlation of atomic displacements across the film/substrate interface is crucial for the stabilization of the ferroelectric state in films a few unit-cells thick. We show that the minimum film thickness for the appearance of a spontaneous polarized domain state is not an intrinsic property of the ferroelectric film but depends on the polarizability of the…
The lattice thermal conductivity ($κ_{\rm L}$) of PbTiO$_3$ (PTO) is estimated using a combination of {\em ab initio} calculations and semiclassical Boltzmann transport equation. The computed $κ_{\rm L}$ is remarkably low, nearly comparable with the $κ_{\rm L}$ of good thermoelectric materials such as PbTe. In addition, a semiclassical analysis of the electronic transport quantities is presented, which suggests excellent thermoelectric properties, with a figure of merit $zT$ well over 1 for a wide range of temperature. For thermoelectric applications, the $κ_{\rm L}$ could be further reduced b…
Depth-Resolved Evolution of Buried Polar Topologies in a PbTiO3/SrTiO3 Superlattice
Catalan Institute of Nanoscience and Nanotechnology - ICN2 (CSIC & BIST)（加泰罗尼亚纳米科学和技术研究所）；Ernst Ruska-Centre for Microscopy and Spectroscopy with Electrons, Forschungszentrum Jülich（于利希研究中心恩斯特·鲁卡电子显微与谱学中心）；CiQUS, Centro Singular de Investigacion en Quimica Bioloxica e Materiais Moleculares, Departamento de Quimica-Fisica, Universidade de Santiago de Compostela（圣地亚哥-德孔波斯特拉大学生物化学与分子材料 singular 研究中心）；Department of Materials Science and Engineering, University of Wisconsin-Madison（威斯康星大学麦迪逊分校材料科学与工程系）；Chinese Academy of Sciences Fujian Institute of Research on the Structure of Matter（中国科学院福建物质结构研究所）；School of Aerospace Engineering, Beijing Institute of Technology（北京理工大学航天工程学院）；Institució Catalana de Recerca i Estudis Avançats (ICREA)（加泰罗尼亚研究高级学院）
In the first-principles bulk-layer model the superlattice structure and polarization are determined by first-principles computation of the bulk responses of the constituents to the electrical and mechanical boundary conditions in an insulating superlattice. In this work the model is extended to predict functional properties, specifically dielectric permittivity and piezoelectric response. A detailed comparison between the bulk-layer model and full first-principles calculations for three sets of perovskite oxide superlattices, PbTiO$_3$/BaTiO$_3$, BaTiO$_3$/SrTiO$_3$ and PbTiO$_3$/SrTiO$_3$, is…
We develop a general and unified first-principles theory of piezoelectric and flexoelectric tensor, formulated in such a way that the tensor elements can be computed directly in the context of density-functional calculations, including electronic and lattice contributions. We introduce a practical supercell-based methods for calculating the flexoelectric coefficients from first principles, and demonstrate them by computing the coefficients for a variety of cubic insulating materials, including C, Si, MgO, NaCl, CsCl, BaZrO3, BaTiO3, PbTiO3 and SrTiO3.
A reduction of polarization in ultra-thin ferroelectric films appears to be fundamental to ferroelectricity at the nanoscale. For the model system PbTiO3 on SrTiO3, we report observation of the polarization vs. thickness relation. Distinct periodicity changes of ferroelectric domains obtained from x-ray diffraction and total energy calculations reveal a linear lowering of the polarization below a critical thickness of ~12 nm. Independent polarization and tetragonality measurements provide insight into the fundamental relation between polarization and tetragonality in nanoscale ferroelectrics.
We demonstrate that the frozen-ion contribution to the flexoelectric coefficient is given solely in terms of the sum of third moments of the charge density distortions induced by atomic displacements, even for ferroelectric or piezoelectric materials. We introduce several practical supercell-based methods for calculating these coefficients from first principles, and demonstrate them by computing the coefficients for C, Si, MgO, NaCl, SrTiO$_3$, BaTiO$_3$, and PbTiO$_3$. Three important subtleties associated with pseudopotentials, the treatment of surfaces, and the calculation of transverse com…
The effect of intermixing at the interface of short period PbTiO$_3$/SrTiO$_3$ superlattices is studied using first-principles density functional theory. The results indicate that interfacial intermixing significantly enhances the polarization within the superlattice. This enhancement is directly related to the off-centering of Pb and Sr cations and can be explained through a discussion of interacting dipoles. This picture should be general for a wide range of multicomponent superlattices and may have important consequences for the design of ferroelectric devices.
Using an extension of a first-principles method developed by King-Smith and Vanderbilt [Phys. Rev. B {\bf 49}, 5828 (1994)], we investigate the effects of in-plane epitaxial strain on the ground-state structure and polarization of eight perovskite oxides: BaTiO$_3$, SrTiO$_3$, CaTiO$_3$, KNbO$_3$, NaNbO$_3$, PbTiO$_3$, PbZrO$_3$, and BaZrO$_3$. In addition, we investigate the effects of a nonzero normal stress. The results are shown to be useful in predicting the structure and polarization of perovskite oxide thin films and superlattices.
We present the results of first-principles calculations on two possible terminations of the (001) surfaces of SrTiO3 (STO), BaTiO3 (BTO), and PbTiO3 (PTO) perovskite crystals. Atomic structure and the electronic configurations were calculated for different 2D slabs, both stoichiometric and non-stoichiometric, using hybrid (B3PW) exchange-correlation technique and reoptimized basis sets of atomic (Gaussian) orbitals. Results are compared with previous calculations and available experimental data. The electronic density distribution near the surface and covalency effects are discussed in details…
In the development of first-principles high-throughput searches for materials with desirable functional properties, there is a clear need for an efficient method to determine the ground state and low-energy alternative structures of superlattices. A method based on a simple strategy -- to generate starting structures based on low-energy structures of the constituent compounds, which are then optimized via structural relaxation calculations -- is proposed. This "stacking method" is demonstrated on the 2:2 PbTiO$_3$/SrTiO$_3$ superlattice, which has been the subject of recent experimental and th…
The interface between graphene and the ferroelectric superlattice $\mathrm{PbTiO_3/SrTiO_3}$ (PTO/STO) is studied. Tuning the transition temperature through the PTO/STO volume fraction minimizes the adsorbates at the graphene-ferroelectric interface, allowing robust ferroelectric hysteresis to be demonstrated. Intrinsic charge traps from the ferroelectric surface defects can adversely affect the graphene channel hysteresis, and can be controlled by careful sample processing, enabling systematic study of the charge trapping mechanism.
In a ferroelectric field effect transistor (FeFET), it is generally assumed that the ferroelectric gate plays a purely electrostatic role. Recently it has been shown that in some cases, which could be called 'active FeFETs', electronic states in the ferroelectric contribute to the device conductance as the result of a modulation doping effect in which carriers are transferred from the channel into the ferroelectric layers near the interface. Here we report first-principles calculations and model analysis to elucidate the various aspects of this mechanism and to provide guidance in materials ch…
The release process for the fabrication of freestanding oxide microstructures relies on appropriate, controllable and repeatable wet etching procedures. SrTiO3 is among the most employed substrates for oxide thin films growth and can be decomposed in HF:water solution. Such process is strongly anisotropic and is affected by local defects and substrate cut-plane. We analyze the etching behavior of SrTiO3 substrates having (100), (110), and (111) cut-planes during immersion in a 5% HF:water solution. The etching process over the three substrates is compared in terms of pitting, anisotropy, macro…
We study the interplay of structural and polar distortions in hexagonal YMnO3 and short-period PbTiO3/SrTiO3 superlattices by means of first-principles calculations at constrained electric displacement field D. We find that in YMnO3 the tilts of the oxygen polyhedra produce a robustly polar ground state, which persists at any choice of the electrical boundary conditions. Conversely, in PTO/STO the antiferrodistortive instabilities alone do not break inversion symmetry, and open-circuit bundary conditions restore a non-polar state. We suggest that this qualitative difference naturally provides …
The mean-field Landau-type theory is used to analyze the polarization properties of epitaxial ferroelectric thin films grown on dissimilar cubic substrates, which induce biaxial compressive stress in the film plane. The intrinsic effect of the film surfaces on the spontaneous polarization is taken into account via the concept of the extrapolation length. The theory simultaneously allows for the influence of the misfit strain imposed on the film lattice by a thick substrate. Numerical calculations are performed for PbTiO3 and BaTiO3 films under an assumption of the polarization reduction in sur…
Weakly coupled ferroelectric/dielectric superlattice thin film heterostructures exhibit complex nanoscale polarization configurations that arise from a balance of competing electrostatic, elastic, and domain-wall contributions to the free energy. A key feature of these configurations is that the polarization can locally have a significant component that is not along the thin-film surface normal direction, while maintaining zero net in-plane polarization. PbTiO3/SrTiO3 thin-film superlattice heterostructures on a conducting SrRuO3 bottom electrode on SrTiO3 have a room-temperature stripe nanodo…
Thermodynamic theory is developed for the ferroelectric phase transition of an ultrathin film in equilibrium with a chemical environment that supplies ionic species to compensate its surface. Equations of state and free energy expressions are developed based on Landau-Ginzburg-Devonshire theory, using electrochemical equilibria to provide ionic compensation boundary conditions. Calculations are presented for a monodomain PbTiO$_3$ (001) film coherently strained to SrTiO$_3$ with its exposed surface and its electronically conducting bottom electrode in equilibrium with a controlled oxygen parti…
Ferroelectric and dielectric properties of polydomain (twinned) single-crystal Pb(Zr1-xTix)O3 thin films are described with the aid of a nonlinear thermodynamic theory, which has been developed recently for epitaxial ferroelectric films with dense laminar domain structures. For Pb(Zr1-xTix)O3 (PZT) films with compositions x = 0.9, 0.8, 0.7, 0.6, 0.5, and 0.4, the "misfit strain-temperature" phase diagrams are calculated and compared with each other. It is found that the equilibrium diagrams of PZT films with x > 0.7 are similar to the diagram of PbTiO3 films. They consist of only four differen…
A first principles embedded cluster approach is used to calculate O chemical shielding tensors, sigma, in prototypical transition metal oxide ABO_3 perovskite crystals. Our principal findings are 1) a large anisotropy of sigma between deshielded sigma_x ~ sigma_y and shielded sigma_z components (z along the Ti-O bond); 2) a nearly linear variation, across all the systems studied, of the isotropic sigma_iso and uniaxial sigma_ax components, as a function of the B-O-B bond asymmetry. We show that the anisotropy and linear variation arise from large paramagnetic contributions to sigma_x and sigma…
We present a scheme to construct model potentials, with parameters computed from first principles, for large-scale lattice-dynamical simulations of materials. Our method mimics the traditional solid-state approach to the investigation of vibrational spectra, i.e., we start from a suitably chosen reference configuration of the material and describe its energy as a function of arbitrary atomic distortions by means of a Taylor series. Such a form of the potential-energy surface is completely general, trivial to formulate for any compound, and physically transparent. Further, the approximations in…
Exploiting the emerging nanoscale periodicities in epitaxial, single-crystal thin films is an exciting direction in quantum materials science: confinement and periodic distortions induce novel properties. The structural motifs of interest are ferroelastic, ferroelectric, multiferroic, and, more recently, topologically protected magnetization and polarization textures. A critical step towards heterostructure engineering is understanding their nanoscale structure, best achieved through real-space imaging. X-ray Bragg coherent diffractive imaging visualizes sub-picometer crystalline displacements…
