Localized Wannier functions provide an efficient and intuitive framework to compute electric polarization from first-principles. They can also be used to represent the electronic systems at fixed electric field and to determine dielectric properties of insulating materials. Here we develop a Wannier-function-based formalism to perform first-principles calculations at fixed polarization. Such an approach allows to extract the polarization-energy landscape of a crystal and thus supports the theoretical investigation of polar materials. To facilitate the calculations, we implement a quasi-Newton method that simultaneously relaxes the internal coordinates and adjusts the electric field in crystals at fixed polarization. The method is applied to study the ferroelectric behavior of $\mathrm{BaTiO_3}$ and $\mathrm{PbTiO_3}$ in tetragonal phases. The physical processes driving the ferroelectricity of both compounds are examined thanks to the localized orbital picture offered by Wannier functions. Hence, changes in chemical bonding under ferroelectric distortion can be accurately visualized. The difference in the ferroelectric properties of $\mathrm{BaTiO_3}$ and $\mathrm{PbTiO_3}$ is highlighted. It can be traced back to the peculiarities of their electronic structures.
We report on the implementation of the Wannier Functions (WFs) formalism within the full-potential linearized augmented plane wave method (FLAPW), suitable for bulk, film and one-dimensional geometries. The details of the implementation, as well as results for the metallic SrVO3, ferroelectric BaTiO3 grown on SrTiO3, covalently bonded graphene and a one-dimensional Pt-chain are given. We discuss the effect of spin-orbit coupling on the Wannier Functions for the cases of SrVO3 and platinum. The dependency of the WFs on the choice of the localized trial orbitals as well as the difference between…
In insulators, the method of Marzari and Vanderbilt [Phys. Rev. B {\bf 56}, 12847 (1997)] can be used to generate maximally localized Wannier functions whose centers are related to the electronic polarization. In the case of layered insulators, this approach can be adapted to provide a natural definition of the local polarization associated with each layer, based on the locations of the nuclear charges and one-dimensional Wannier centers comprising each layer. Here, we use this approach to compute and analyze layer polarizations of ferroelectric perovskite superlattices, including changes in l…
We present an alternative formalism for calculating the maximally localized Wannier functions in crystalline solids, obtaining an expression which is extremely simple and general. In particular, our scheme is exactly invariant under Brillouin zone folding, and therefore it extends trivially to the Gamma-point case. We study the convergence properties of the Wannier functions, their quadratic spread and centers as obtained by our simplified technique. We show how this convergence can be drastically improved by a simple and inexpensive ``refinement'' step, which allows for very efficient and acc…
We have constructed maximally-localized Wannier functions for prototype structures of solid molecular hydrogen under pressure, starting from LDA and tight-binding Bloch wave functions. Each occupied Wannier function can be associated with two paired protons, defining a ``Wannier molecule''. The sum of the dipole moments of these ``molecules'' always gives the correct macroscopic polarization, even under strong compression, when the overlap between nearby Wannier functions becomes significant. We find that at megabar pressures the contributions to the dipoles arising from the overlapping tails …
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.
The polarization and the susceptibility of a ferroelectric multilayer with a non-ferroelectric slab are investigated within the framework of transverse Ising model with a four-spin interaction term. The effect of the thickness and the position of the non-ferroelectric slab are investigated in this paper. We find that the increase of the thickness of the non-ferroelectric will decrease the polarization and the susceptibility of the film. If the position of the non-ferroelcetric slab shifts from the center of the film to the surface, the number of the peaks of the susceptibility will change. And…
We investigate the origin of the coplanar helicoidal magnetic structure and the ferroelectric polarization in Cu3Nb2O8 by combining first-principles calculations and our spin-induced ferroelectric polarization model. The coplanar helicoidal spin state comes from the competition between the isotropic exchange interactions, and the ferroelectric polarization from the symmetric exchange striction with slight spin canting. However, the direction of the polarization is not determined by the orientation of the spin rotation plane.
An effective Hamiltonian for the ferroelectric transition in PbTiO3 is constructed from first-principles density-functional-theory total-energy and linear-response calculations through the use of a localized, symmetrized basis set of ``lattice Wannier functions.'' Explicit parametrization of the polar lattice Wannier functions is used for subspace projection, addressing the issues of LO-TO splitting and coupling to the complementary subspace. In contrast with ferroelectric BaTiO3 and KNbO3, we find significant involvement of the Pb atom in the lattice instability. Monte Carlo simulations for t…
The ferroelectric trends of rutile (TiO$_2$) in bulk and at the (110) surface are investigated by means of ab initio density functional theory. We discuss the underlying mechanism of the incipient ferroelectric behavior of rutile in terms of Born effective charges, which we decompose in individual contributions by means of maximally localized Wannier functions. We show that a ferroelectric phase can be stabilized for a variety of different lattice distortions which all enlarge the shortest Ti-O distance, even if the longer apical Ti-O bond is simultaneously shortened. At the (110) surface, the…
We present a self-consistent, real-space calculation of the Wannier functions of Si and GaAs within density functional theory. We minimize the total energy functional with respect to orbitals which behave as Wannier functions under crystal translations and, at the minimum, are orthogonal. The Wannier functions are used to calculate the total energy, lattice constant, bulk modulus, and the frequency of the zone-center TO phonon of the two semiconductors with the accuracy required nowadays in ab-initio calculations. Furthermore, the centers of the Wannier functions are used to compute the macros…
Here we demonstrate a method to tune ferroelectric imprint, which is stable in time, based on the coupling between the non-switchable polarization of ZnO and switchable polarization of PbZrxTi(1-x)O3. SrRuO3/PbZrxTi(1-x)O3 /ZnO/SrRuO3 heterostructures were grown with different ZnO thicknesses. It is shown that the coercive voltages and ferroelectric imprint varies linearly with the thickness of ZnO. It is also demonstrated that the ferroelectric imprint remains stable with electric field cycling and electric field stress assisted aging.
We present a first-principles calculation of the electronic properties of crystalline silicon and gallium arsenide in a uniform electric field. Polarized Wannier-like functions which are confined in a finite region are obtained by minimizing a total-energy functional which depends explicitly on the macroscopic polarization of the solid. The polarization charge density and the electronic dielectric constant are computed via finite differences. The results coincide with those of the linear response approach in the limit of vanishing electric field and infinite localization region.
The ability to manipulate ferroelectrics at ultrafast speeds has long been an elusive target for materials research. Coherently exciting the ferroelectric mode with ultrashort optical pulses holds the promise to switch the ferroelectric polarization on femtosecond timescale, two orders of magnitude faster compared to what is possible today with pulsed electric fields. Here, we report on the demonstration of ultrafast optical reversal of the ferroelectric polarization in LiNbO3. Rather than driving the ferroelectric mode directly, we couple to it indirectly by resonant excitation of an auxiliar…
Short period ferroelectric/ferroelectric BaTiO3 (BTO)/PbTiO3 (PTO) superlattices are studied using density functional theory. Contrary to the trends in paraelectric/ferroelectric superlattices the polarization remains nearly constant for PTO concentrations below 50%. In addition, a significant decrease in the c/a ratio below the PTO values were observed. Using a superlattice effective Hamiltonian we predict an enhancement in the d33 piezoelectric coefficient peaking at ~75% PTO concentration due to the different polarization-strain coupling in PTO and BTO layers. Further analysis reveals that …
Ferroelectrics that are also ionic conductors offer possibilities for novel applications with high tunability, especially if the same atomic species causes both phenomena. In particular, at temperatures just below the Curie temperature, polarized states may be sustainable as the mobile species is driven in a controlled way over the energy barrier that governs ionic conduction, resulting in unique control of the polarization. This possibility was recently demonstrated in CuInP2S6, a layered ferroelectric ionic conductor in which Cu ions cause both ferroelectricity and ionic conduction. Here, we…
An accurate estimate of the ferroelectric polarization in ferroelectric-dielectric stacks is important from a materials science perspective, and it is also crucial for the development of ferroelectric based electron devices. This paper revisits the theory and application of the PUND technique in Metal-Ferroelectric-Dielectric-Metal (MFDM) structures by using analytical derivations and numerical simulations. In an MFDM structure the results of the PUND technique may largely differ from the polarization actually switched in the stack, which in turn is different from the remnant polarization of t…
Berry phase polarization calculations have been investigated for several ferroelectric materials from the point of view of practical calculations. It was shown that interpretation of the results is particular to each case due to the multivalued aspect of polarization in the modern theory. Almost all of the studied examples show ambiguous polarization results which can be difficult to solve especially for super-cells containing large number of atoms. For this reason, a procedure has been proposed to minimize the number of calculations required to produce an unambiguous polarization result from …
Time-dependent polarization relaxation behaviors induced by a depolarization field $E_{d}$ were investigated on high-quality ultrathin SrRuO$_{3}$/BaTiO$_{3}$/SrRuO$_{3}$ capacitors. The $E_d$ values were determined experimentally from an applied external field to stop the net polarization relaxation. These values agree with those from the electrostatic calculations, demonstrating that a large $E_{d}$ inside the ultrathin ferroelectric layer could cause severe polarization relaxation. For numerous ferroelectric devices of capacitor configuration, this effect will set a stricter size limit than…
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 present experimental evidence for hexagonal domain faceting in the ferroelectric polymer PVDF-TrFE films having the lower orthorhombic crystallographic symmetry. This effect can arise from purely electrostatic depolarizing forces. We show that in contrast to magnetic bubble shape domains where such type of deformation instability has a predominantly elliptical character, the emergence of more symmetrical circular harmonics is favored in ferroelectrics with high dielectric constant.
It has recently been shown that the polarization of a ferroelectric can be strongly affected by light pumping or even transiently reversed by mid-IR pumping within a record short subpicosecond timescale. It was then suggested that the reversal of polarization is most likely prevented by the depolarizing field that appears during the process. To minimize the effect of the depolarizing field, I propose to create an elongated domain by choosing a corresponding pump spot shape. I calculate the polarization dynamics for a particular experimental setup with mid-IR pumping and show that the polarizat…
Ferroelectric polar displacements have recently been observed in conducting electron-doped BaTiO3. The co-existence of a ferroelectric phase and conductivity opens the door to new functionalities which may provide a unique route for novel device applications. Using first-principles methods and electrostatic modeling we explore the effect that the switchable polarization of electron-doped BaTiO3 (n-BaTiO3) has on the electronic properties of the SrRuO3/n-BaTiO3 (001) interface. Ferroelectric polarization controls the accumulation or depletion of electron charge at the interface, and the associa…
The effect of polarization rotation on the performance of metal oxide semiconductor field-effect transistors was investigated with a Landau-Ginzburg-Devonshire theory based model. In this analytical model, depolarization field, polarization rotations and the electrostatic properties of the doped silicon substrate are considered to illustrate the size effect of ferroelectric oxides and the stability of polarization in each direction. Based on this model, we demonstrate that MOSFET operation could be achieved by polarization reorientation with a low operating voltage, if the thickness of ferroel…
The switching of electric polarization induced by electric fields -a fundamental functionality of ferroelectrics- is closely associated with the motions of the domain walls that separate regions with distinct polarization directions. Therefore, understanding domain-walls dynamics is of essential importance for advancing ferroelectric applications. In this Letter, we show that the topology of the multidomain structure can have an intrinsic impact on the degree of switchable polarization. Using a combination of polarization hysteresis measurements and piezoresponse force microscopy on a uniaxial…
Mobile charges and lattice polarization interact in ferroelectric materials because of the Coulomb interaction between the mobile free charges and the fixed lattice dipoles. We have investigated this mutual screening in KTiOPO4, a ferroelectric/superionic single crystal in which the mobile charges are K+ ions. The ionic accumulation close to the crystal surfaces leads to orders of magnitude increase of the Second Harmonic Generation. This ionic space charge model is supported by the absence of such an effect in non-ionic conductor but ferroelectric BaTiO3, by its temperature dependence in KTiO…
A stochastic model of electric field-driven polarization reversal in orthorhombic ferroelectrics is advanced, providing a description of their temporal electromechanical response. The theory accounts for all possible parallel and sequential switching events. Application of the model to the simultaneous measurements of polarization and strain kinetics in a lead-free orthorhombic (K,Na)NbO3-based ferroelectric ceramic over a wide timescale of 7 orders of magnitude allowed identification of preferable polarization switching paths, fractions of individual switching processes, and their activation …
Ferroelectric field-effect transistors (FE-FETs) consisting of tunable dielectric layers are utilized to investigate interfacial transport processes. Large changes in the dielectric constant as a function of temperature are observed in FE-FETs in conjunction with the ferroelectric to paraelectric transition. The devices offer a test bed to evaluate specific effects of polarization on the electrical processes. FE-FETs have dominant contributions from polarization-fluctuation rather than static dipolar disorder prevalent in high k paraelectric dielectric-based FETs. Additionally, photo-excitatio…
Polycrystals of CaxBa1-xNb2O6(CBN) tungsten bronze type oxides have been prepared and their structural, dielectric, and thermal properties have been investigated. It was found that CBN alloys with ferroelectric tetragonal tungsten bronze structure were only available in a composition range of 0.19 <= x <= 0.32. It was also showed that CBN can be classified as a ferroelectric with a first-order thermal phase transition showing polarization precursor dynamics before transition into the ferroelectric phase, in sharp contrast to an isostructural alloy SrxBa1-xNb2O6(SBN) that shows typical relaxor …
We calculate the ferroelectric polarization dynamics induced by a femtosecond midinfrared pulse as measured in the recent experiment by R. Mankowsky et al., Phys. Rev. Lett. 118, 197601 (2017). It is due to the nonlinear coupling of the excited infrared-active phonon with the ferroelectric mode or to the excitation of the ferroelectric mode itself depending on the pulse frequency. To begin with, we write the LiNbO$_3$ crystal symmetry invariant thermodynamic potential including electric field and nonlinear phonon coupling terms. We solve the equations of motion determined by this potential for…
Ferroelectrics are multifunctional smart materials finding applications in sensor technology, micromechanical actuation, digital information storage etc. Their most fundamental property is the ability of polarization switching under applied electric field. In particular, understanding of switching kinetics is essential for digital information storage. In this regard, scaling properties of the temporal polarization response are well-known for 180°-switching processes in ferroelectrics characterized by a unique field-dependent local switching time. Unexpectedly, these properties were now observe…
We have constructed the surface phase diagram of the BaTiO$_{3}$(001) surface by employing an evolutionary algorithm for surface structure prediction, where the ferroelectric polarization is included as a degree of freedom. Among over 1000 candidate structures explored, a surface reconstruction of (2$\times$1)-TiO is discovered to be thermodynamically stable and have the \emph{p2mm} plane group symmetry as observed experimentally. We find that the influence of ferroelectric polarization on the surface free energy can be either negligibly small or sizably large (over 1 eV per ($2 \times 1$) sup…
We have proposed the phenomenological description of polarization switching peculiarities in ferroelectric semiconductors with charged defects and prevailing extrinsic conductivity. Exactly we have modified Landau-Ginsburg approach shown that the macroscopic state of the aforementioned inhomogeneous system can be described by three coupled equations for three order parameters. Both the experimentally observed coercive field values well below the thermodynamic one and the various hysteresis loop deformations (minor, constricted and double loops) have been obtained in the framework of our model.…
Ultrafast optical control of ferroelectricity using intense terahertz fields has attracted significant interest. Here we show that the nonlinear interactions between two optical phonons in SnTe, a two-dimensional in-plane ferroelectric material, enables a dynamical amplification of the electric polarization within subpicoseconds time domain. Our first principles time dependent simulations show that the infrared-active out-of-plane phonon mode, pumped to nonlinear regimes, spontaneously generates in-plane motions, leading to rectified oscillations in the in-plane electric polarization. We sugge…
Polarization transfer force on ferroelectric domain walls
WPI-AIMR, Tohoku University（东北大学 WPI-AIMR）；Center for Spintronics Research Network, Tohoku University（东北大学自旋电子学研究中心）；School of Physics and State Key Laboratory of Electronic Thin Films and Integrated Devices, University of Electronic Science and Technology of China（电子科技大学物理学院电子薄膜与集成器件国家重点实验室）；Institute for Materials Research, Tohoku University（东北大学材料科学研究所）
Strain engineering of perovskite oxide thin films has proven to be an extremely powerful method for enhancing and inducing ferroelectric behavior. In ferroelectric thin films and superlattices, the polarization is intricately linked to crystal structure, but we show here that it can also play an important role in the growth process, influencing growth rates, relaxation mechanisms, electrical properties and domain structures. We have studied this effect in detail by focusing on the properties of BaTiO$_{3}$ thin films grown on very thin layers of PbTiO$_{3}$ using a combination of x-ray diffrac…
First-principles calculations are presented for the layered perovskite Ca$_3$Mn$_2$O$_7$. The results reveal a rich set of coupled structural, magnetic and polar domains in which oxygen octahedron rotations induce ferroelectricity, magnetoelectricity and weak-ferromagnetism. The key point is that the rotation distortion is a combination of two non-polar modes with different symmetries. We use the term "hybrid" improper ferroelectricity to describe this phenomenon and discuss how control over magnetism is achieved through these functional antiferrodistortive octahedron rotations.
Using density-functional calculations we study the structure and polarization response of tetragonal PbTiO3, BaTiO3 and SrTiO3 in a strain regime that is previously overlooked. Different from common expectations, we find that the polarizations in all three substances saturate at large strains, demonstrating a universal phenomenon. The saturation is shown to originate from an unusual and strong electron-ion correlation that leads to cancellation between electronic and ionic polarizations. Our results shed new insight on the polarization properties, and reveal the existence of a fundamental limi…
Nonlinear electrostatic interaction between the surface ions of electrochemical nature and ferroelectric dipoles gives rise to the coupled ferroionic states in nanoscale ferroelectrics. Here, we investigated the role of the surface ions formation energy value on the polarization states and polarization reversal mechanisms, domain structure and corresponding phase diagrams of ferroelectric thin films. Using 3D finite elements modeling we analyze the distribution and hysteresis loops of ferroelectric polarization and ionic charge, and dynamics of the domain states. These calculations performed o…
A systematic method is presented for constructing effective Hamiltonians for general phonon-related structural transitions. The key feature is the application of group theoretical methods to identify the subspace in which the effective Hamiltonian acts and construct for it localized basis vectors, which are the analogue of electronic Wannier functions. The results of the symmetry analysis for the perovskite, rocksalt, fluorite and A15 structures and the forms of effective Hamiltonians for the ferroelectric transition in $PbTiO_3$ and $BaTiO_3$, the oxygen-octahedron rotation transition in $SrT…
Bent band structures have been empirically described in ferroelectric materials to explain the functioning of recently developed ferroelectric tunneling junction and photovoltaic devices. This report presents experimental evidence for ferroelectric band bending, which was observed in the depth profiles of atomic orbitals of angle-resolved hard x-ray photoemission spectra of ferroelectric BaTiO3 thin films. The ferroelectric bent band structure is separated into three depth regions; the shallowest and deepest regions are slightly modulated by the screening effect at surface and interface, respe…
All known proper ferroelectrics are unable to polarize normal to a surface or interface if the resulting depolarization field is unscreened, but there is no fundamental principle that enforces this behavior. In this work, we introduce hyperferroelectrics, a new class of proper ferroelectrics which polarize even when the depolarization field is unscreened, this condition being equivalent to instability of a longitudinal optic mode in addition to the transverse-optic-mode instability characteristic of proper ferroelectrics. We use first principles calculations to show that several recently disco…
Electric-field control of spin-dependent properties has become one of the most attractive phenomena in modern materials research due the promise of new device functionalities. One of the paradigms in this approach is to electrically toggle the spin polarization of carriers injected into a semiconductor using ferroelectric polarization as a control parameter. Using first-principles density functional calculations, we explore the effect of ferroelectric polarization of electron-doped BaTiO3 (n-BaTiO3) on the spin-polarized transmission across the SrRuO3/n-BaTiO3 (001) interface. Our study reveal…
Ferroelectric BaTiO3 films with large polarization have been integrated with Si(001) by pulsed laser deposition. High quality c-oriented epitaxial films are obtained in a substrate temperature range of about 300 deg C wide. The deposition temperature critically affects the growth kinetics and thermodynamics balance, resulting on a high impact in the strain of the BaTiO3 polar axis, which can exceed 2% in films thicker than 100 nm. The ferroelectric polarization scales with the strain and therefore deposition temperature can be used as an efficient tool to tailor ferroelectric polarization. The…
Here, we report a combined experimental-theoretical study showing that collective application of rare earth doping on A-site and epitaxial strain to ferroelectric bismuth titanate does not lead to a very large c-axis polarization as reported previously. Further first principles calculations based on the examination of polarization tensor suggest that simultaneous Bi and Ti site doping could result in moderate polarization along c-axis of bismuth titanate which is typically a preferential axis of film growth and thus enabling c axis oriented films to have appreciable polarization. This approach…
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 carry out first-principles density-functional-theory calculations to elucidate the polarization switching mechanism in charge-ordering-induced ferroelectrics based on the prototypical case of the (SrVO$_3$)$_1$(LaVO$_3$)$_1$ superlattice. We find that lattice relaxation for a specific charge ordering state can "lock" that state in, making non-adiabatic switching to a different CO variant energetically prohibitive, and in some cases, even making the energy barrier for adiabatic switching prohibitively large. We classify charge-ordering materials into two types, polyhedral breathing and off-c…
