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 limit to the strain-induced polarization enhancement.
We report the temperature dependent capacitance-voltage characteristics of Pt/SrTiO3 Schottky diodes fabricated using compressively strained SrTiO3 thin films grown on (LaAlO3)0.3(Sr2AlTaO6)0.7 (LSAT) substrates. The measurements reveal a divergence of the out of plane dielectric constant of SrTiO3 peaked at ~140K, implying a ferroelectric transition. A Curie-Weiss law fit to the zero-bias dielectric constant suggests a Curie temperature of ~56 K. This observation provides experimental confirmation of the theoretical prediction of out of plane ferroelectricity in compressively strained SrTiO3 …
Density functional calculations are performed to study the effect of epitaxial strain on PbZrO3. We find a remarkably small energy difference between the epitaxially strained polar R3c and nonpolar Pbam structures over the full range of experimentally accessible epitaxial strains -3% < η< 4%. While ferroelectricity is favored for all compressive strains, for tensile strains the small energy difference between the nonpolar ground state and the alternative polar phase yields a robust antiferroelectric ground state. The coexistence of ferroelectricity and antiferroelectricity observed in thin fil…
Epitaxial CaMnO3 films grown with 2.3% tensile strain on (001)-oriented LaAlO3 substrates are found to be incipiently ferroelectric below 25 K. Optical second harmonic generation (SHG) was used for the detection of the incipient polarization. The SHG analysis reveals that CaMnO3 crystallites with in-plane orientation of the orthorhombic b axis contribute to an electric polarization oriented along the orthorhombic a (resp.\ c) axis in agreement with the predictions from density functional calculations.
The influence of depolarizing field on the magnitude and stability of a uniform polarization in ferroelectric capacitors and tunnel junctions is studied using a nonlinear thermodynamic theory. It is predicted that, in heterostructures involving strained epitaxial films and metal electrodes, the homogeneous polarization state may remain stable against transformations into the paraelectric phase and into polydomain states down to the nanoscale. This result supports the possibility of depolarizing-field-related resistive switching in ferroelectric tunnel junctions with dissimilar electrodes. The …
The structure and polarization of the as-yet hypothetical Ruddlesden-Popper compound Pb$_2$TiO$_4$ are investigated within density-functional theory. Zone enter phonons of the high-symmetry K$_2$NiF$_4$-type reference structure, space group $I4/mmm$, were calculated. At the theoretical ground-state lattice constants, there is one unstable infrared-active phonon. This phonon freezes in to give the $I2mm$ ferroelectric state. As a function of epitaxial strain, two additional ferroelectric phases are found, with space groups $I4mm$ and $F2mm$ at compressive and tensile strains, respectively.
Ferroelectric (FE) metals have been attracting attention as they possess both metallicity and ferroelectricity, the two seemingly incompatible physical properties. An important problem for both fundamental research and potential applications is how to realize a strong FE metal. One strategy is to dope a strong FE insulator into an FE metal provided that the induced free electrons do not destroy FE distortion. Strained EuTiO$_{3}$ film is a strong FE ferromagnet and a promising candidate for such a strategy. Here, we calculate the structural, electronic, and polarization properties of Nb-doped …
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…
Very recently there was a report of the discovery using piezoelectric force microscopy (PFM) of a switchable ferroelectric polarization in 1.6 % tensile strained TiO2 thin film with anatase crystal structure (see N. Deepak et al. Adv. Funct. Mater. 2014, 24, 2844). The polarization disappeared only above 450 K, which was assigned as a Curie temperature, Tc. Here we have performed X-ray diffraction, second-harmonic generation (SHG) and infrared investigations of the same films. Phonon frequencies exhibit less than a 10 % shift down with the tensile strain and no anomaly near expected TC. SHG ex…
We present a density functional theory investigation of strained Ca$_{0.5}$Sr$_{0.5}$TiO$_3$. We have determined the structure and polarization for a number of arrangements of Ca and Sr in a 2$\times$2$\times$2 supercell. The a and b lattice vectors are strained to match the lattice constants of the rotated Si(001) face. To set the context for the CSTO study, we also include simulations of the Si(001) constrained structures for CaTiO$_3$ and SrTiO$_3$. Our primary findings are that all Ca$_{0.5}$Sr$_{0.5}$TiO$_3$ structures examined except one are ferroelectric, exhibiting polarizations rangin…
We report on theoretical and experimental investigation of A-site driven ferroelectricity in ferromagnetic La2NiMnO6 thin films grown on SrTiO3 substrates. Structural analysis and density functional theory calculations show that epitaxial strain stretches the rhombohedral La2NiMnO6 crystal lattice along the [111]cubic direction, triggering a displacement of the A-site La ions in the double perovskite lattice. The lattice distortion and the A-site displacements stabilize a ferroelectric polar state in ferromagnetic La2NiMnO6 crystals. The ferroelectric state only appears in the rhombohedral La2…
The direct magnetoelectric (ME) effect resulting from the polarization changes induced in a ferroelectric film by the application of a magnetic field to a ferromagnetic substrate is described using the nonlinear thermodynamic theory. It is shown that the ME response strongly depends on the initial strain state of the film. The ME polarization coefficient of the heterostructures involving Terfenol-D substrates and compressively strained lead zirconate titanate (PZT) films, which stabilize in the out-of-plane polarization state, is found to be comparable to that of bulk PZT/Terfenol-D laminate c…
We use first principles density functional theory calculations to investigate the effect of biaxial strain in the low-temperature structural and ferroelectric properties of [111]-oriented SrTiO$_3$. We find that [111] biaxial strain, achievable by coherent epitaxial growth along the [111] direction, induces structural distortions in SrTiO$_3$ that are not present in either bulk or [001]-oriented SrTiO$_3$. Under [111] biaxial strain, SrTiO$_3$ displays ferroelectricity at tensile strain, and paraelectricity at compressive strain. We compute the phonon spectrum and macroscopic polarization of S…
First-principles calculations of the epitaxial-strain phase diagram of perovskite SrCoO$_{3}$ are presented. Through combination of the large spin-phonon coupling with polarization-strain coupling and coupling of the band gap to the polar distortion, both tensile and compressive epitaxial strain are seen to drive the bulk ferromagnetic-metallic (FM-M) phase to antiferromagnetic-insulating-ferroelectric (AFM-I-FE) phases, the latter having unusually low elastic energy. At these coupled magnetic-ferroelectric metal-insulator phase boundaries, cross responses to applied electric and magnetic fiel…
Zirconia and hafnia based thin films have attracted tremendous attention in the last decade due to their unexpected ferroelectric behavior at the nanoscale, which facilitates the downscaling of ferroelectric devices. The present work reports a novel ferroelectric rhombohedral phase of ZrO2 that can be achieved in thin films grown on (111)- Nb:SrTiO3 substrates by ion-beam sputtering. Structural and ferroelectric characterizations reveal that the (111)-oriented ZrO2 films are under epitaxial compressive strain and display a switchable ferroelectric polarization of about 20.2 μC/cm2 with a coerc…
SrTiO3 is an incipient ferroelectric that is believed to exhibit a prototype displacive, soft mode ferroelectric transition when subjected to mechanical stress or alloying. We use high-angle annular dark-field imaging in scanning transmission electron microscopy to reveal local polar regions in the room-temperature, paraelectric phase of strained SrTiO3 films, which undergo a ferroelectric transition at low temperatures. These films contain nanometer-sized domains in which the Ti columns are displaced. In contrast, these nanodomains are absent in unstrained films, which do not become ferroelec…
PbZrxTi1-xO3 (PZT) is one of the technologically most important ferroelectric materials. Bulk single-domain single crystals of PZT have never been synthesized for a significant compositional range across the solid-solution phase diagram. This leaves the fundamental properties of PZT under debate. Synthesis of defect-free single crystalline films enables us to unambiguously determine the intrinsic quantities that describe ferroelectric materials, such as spontaneous polarization and dielectric constant. Defect-free single crystalline, strained PbZr0.2Ti0.8O3 thin films were grown by pulsed-lase…
Multiferroicity can be induced in strontium titanate by applying biaxial strain, resulting in the coexistence of both ferroelectric and antiferrodistortive domains. The magnitude and sign of the strain imposed on the lattice by design can be used to tune the phase transitions and interactions between these two phenomena. Using optical second harmonic generation, we report a transition from centrosymmetric 4/mmm phase to ferroelectric mm2, followed by an antiferrodistortive transition to a coupled ferroelastic-ferroelectric mm2 phase in a strontium titanate thin film strained in biaxial tension…
The phase transition behaviour of PbTiO3 and BaTiO3 under (111) epitaxial strain is investigated using density-functional theory calculations. From tensile strains of +0.015 to compressive strains of -0.015, PbTiO3 undergoes phase transitions from C2 through two Cm phases and then to R3m. The total polarisation is found to be almost independent of strain. For the same range of strains BaTiO3 undergoes phase transitions from a single Cm phase, through R3m and then to R-3m. In this case the application of compressive strain inhibits and then completely suppresses the polarisation on transition t…
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…
After decades of searching for robust nanoscale ferroelectricity that could enable integration into the next generation memory and logic devices, hafnia-based thin films have appeared as the ultimate candidate because their ferroelectric (FE) polarization becomes more robust as the size is reduced. This exposes a new kind of ferroelectricity, whose mechanism still needs to be understood. Towards this end, thin films with increased crystal quality are needed. We report the epitaxial growth of Hf0.5Zr0.5O2 (HZO) thin films on (001)-oriented La0.7Sr0.3MnO3/SrTiO3 (STO) substrates. The films, whic…
We present a theoretical description of the influence of misfit strain on mobile defects dynamics in thin strained ferroelectric films. Self-consistent solutions obtained by coupling the Poissons equation for electric potential with continuity equations for mobile donor and electron concentrations and time-dependent Landau-Ginzburg-Devonshire equations reveal that the Vegard mechanism (chemical pressure) leads to the redistribution of both charged and electro-neutral defects in order to decrease the effective stress in the film. Internal electric fields, both built-in and depolarization ones, …
The field-induced polarization reversal in $c$-oriented ferroelectric phase of strained perovskite film has been studied. We show that in additional to the conventional longitudinal switching mechanism, when c-oriented polarization vector changes its modulus, the longitudinal-transversal and transversal mechanisms when the perpendicular component of polarization is dynamically admixed are possible. The later process can occurs either via the straight-abrupt or initially-continues polarization turnover scenario. We specified the obtained results for the case of PbTiO$_{3}$ and BaTiO$_{3}$ ferro…
The ideal intrinsic barriers to domain switching in c-phase PbTiO_3 (PTO), PbZrO_3 (PZO), and PbZr_{1-x}Ti_xO_3 (PZT) are investigated via first-principles computational methods. The effects of epitaxial strain on the atomic structure, ferroelectric response, barrier to coherent domain reversal, domain-wall energy, and barrier to domain-wall translation are studied. It is found that PTO has a larger polarization, but smaller energy barrier to domain reversal, than PZO. Consequentially the idealized coercive field is over two times smaller in PTO than PZO. The Ti--O bond length is more sensitiv…
Design of novel artificial materials based on ferroelectric perovskites relies on the basic principles of electrostatic coupling and in-plane lattice matching. These rules state that the out-of-plane component of the electric displacement field and the in-plane components of the strain are preserved across a layered superlattice, provided that certain growth conditions are respected. Intense research is currently directed at optimizing materials functionalities based on these guidelines, often with remarkable success. Such principles, however, are of limited practical use unless one disposes o…
Low dimensional ferroelectrics are highly desired for applications and full of exotic physics. Here a functionalized MXene Hf$_2$CF$_2$ monolayer is theoretically studied, which manifests a nonpolar to polar transition upon moderate biaxial compressive strain. Accompanying this structural transition, a metal-semiconductor transition occurs. The in-plane shift of unilateral fluorine layer leads to a polarization pointing out-of-plane. Such ferroelectricity is unconventional, similar to the recently-proposed interlayer-sliding ferroelectricity but not identical. Due to its specific hexapetalous …
SrTiO$_3$ is an incipient ferroelectric on the verge of a polar instability, which is avoided at low temperatures by quantum fluctuations. Within this unusual quantum paraelectric phase, superconductivity persists despite extremely dilute carrier densities. Ferroelectric fluctuations have been suspected to play a role in the origin of superconductivity by contributing to electron pairing. To investigate this possibility, we used optical second harmonic generation to measure the doping and temperature dependence of the ferroelectric order parameter in compressively strained SrTiO$_3$ thin films…
The emergent behaviors in thin films of a multiaxial ferroelectric due to an electrochemical coupling between the rotating polarization and surface ions are explored within the framework of the 2-4 Landau-Ginzburg-Devonshire (LGD) thermodynamic potential combined with the Stephenson-Highland (SH) approach. The combined LGD-SH approach allows to describe the electrochemical switching and rotation of polarization vector in the multiaxial ferroelectric film covered by surface ions with a charge density dependent to the relative partial oxygen pressure. We calculate the phase diagrams and analyze …
The structural evolution of the strain-driven morphotropic phase boundary (MPB) in BiFeO3 films has been investigated using synchrotron x-ray diffractometry in conjunction with scanning probe microscopy. Our results demonstrate the existence of mixed-phase regions that are mainly made up of two heavily tilted ferroelectric triclinic phases. Analysis of first-principles computations suggests that these two triclinic phases originate from a phase separation of a single monoclinic state accompanied by elastic matching between the phase-separated states. These first-principle calculations further …
Combining effective Hamiltonian and direct $ab$ $initio$ computation, we obtain the phase diagram of SnTiO$_{3}$ with respect to epitaxial strain and temperature, demonstrating the complex features of the phase diagram and providing insight into the epitaxially strained SnTiO$_{3}$, a presumably simple perovskite. In the phase diagram, two triple points are found, which may be exploited to to achieve high-performance piezoelectric effects. On the other hand, despite the inclusion of the degree of freedoms related to oxygen octahedron tilting, it is found that ferroelectric displacements domina…
By performing first-principles calculations, we systematically explore the effect of epitaxial strain on the structure and properties of multiferroic TbMnO3. We show that, although the unstrained bulk TbMnO3 displays a non-collinear antiferromagnetic spin order, TbMnO3 can be ferromagnetic under compressive strain, in agreement with the experimental results on TbMnO3 grown on SrTiO3. By increasing the tensile strain up to 5%, we predict that TbMnO3 transforms into a new multiferroic state with a large ferroelectric polarization,two orders of magnitude larger than that in the unstrained bulk, a…
The direct magnetoelectric (ME) effect mediated by lattice strains induced in a ferroelectric film by a ferromagnetic substrate is evaluated using first-principles-based calculations. To that end, the strain sensitivity of ferroelectric polarization and the film permittivity are calculated as a function of the in-plane biaxial strain for Pb(Zr0.52Ti0.48)O3 films under various depolarizing fields. It is found that the ME voltage coefficient varies nonmonotonically with this strain and may reach giant values exceeding 100 Vcm-1 Oe-1 over a strain range that can be controlled through the electric…
We performed first principles calculations for epitaxially strained orthorhombic CaTiO$_3$. The computational results reveal the existence of a metastable ferroelectric phase at compressive strain with unexpected in-plane polarization. Symmetry analysis indicates that two distortion modes at the X point combine to induce the polarization, leading to characterization as a hybrid improper ferroelectric. Our work demonstrates a mechanism for improper ferroelectricity in simple perovskites without the need for symmetry lowering by layering or cation ordering.
Multiferroics with the coexistence of ferroelectric and ferromagnetic orders are ideal candidates for magnetoelectric applications. Unfortunately, only very few ferroelectric-ferromagnetic multiferroics (with low magnetic critical temperature) were discovered. Here we perform first principles calculations to investigate the effects of the epitaxial strain on the properties of BiMnO3 films grown along the pseudocubic [001] direction. Unlike the ground state with the centrosymmetric C2/c space group in bulk, we reveal that the tensile epitaxial strain stabilizes the ferromagnetic and ferroelectr…
Strontium titanate is an incipient ferroelectric in which superconductivity emerges at exceptionally low doping levels. Remarkably, stabilizing the polar phase through strain or chemical substitution has been shown to significantly enhance the superconducting critical temperature, and the polar instability plays a pivotal role in the majority of proposed superconducting pairing mechanisms. A rigorous understanding of ferroelectricity is therefore essential to elucidate the electron pairing mechanism in this material. To investigate the nature of the polar order in strontium titanate, we develo…
We report the relationship between epitaxial strain and the crystallographic orientation of the in-phase rotation axis and A-site displacements in Pbnm-type perovskite films. Synchrotron diffraction measurements of EuFeO3 films under strain states ranging from 2% compressive to 0.9% tensile on cubic or rhombohedral substrates exhibit a combination of a-a+c- and a+a-c- rotational patterns. We compare the EuFeO3 behavior with previously reported experimental and theoretical work on strained Pbnm-type films on non-orthorhombic substrates, as well as additional measurements from LaGaO3, LaFeO3, an…
We use density-functional theory with the local-density approximation to study the structural and ferroelectric properties of SrTiO$_3$ under misfit strains. Both the antiferrodistortive (AFD) and ferroelectric (FE) instabilities are considered. The rotation of the oxygen octahedra and the movement of the atoms are fully relaxed within the constraint of a fixed in-plane lattice constant. We find a rich misfit strain-induced phase transition sequence and is obtained only when the AFD distortion is taken into account. We also find that compressive misfit strains induce ferroelectricity in the te…
Nonlinear evolution of three-dimensional strained islands or quantum dots in heteroepitaxial thin films is studied via a continuum elasticity model and the development of a nonlinear dynamic equation governing the film morphological profile. All three regimes of island array evolution are identified and examined, including a film instability regime at early stage, a nonlinear coarsening regime at intermediate times, and the crossover to a saturated asymptotic state, with detailed behavior depending on film-substrate misfit strains but not qualitatively on finite system sizes. The phenomenon of…
We report on the dielectric properties of epitaxial [001] and [100]-textured thin films of antiferromagnetic orthorhombic YMnO3 and their variation under compressive epitaxial strain. It is found that weakly strained YMnO3 films are ferroelectric with a polarization along c-axis switchable by 90 degrees by an external magnetic field. When reducing film thickness and increasing epitaxial strain, the ferroelectric order is progressively suppressed. Analysis of structural, dielectric and magnetic data indicates that suppression of ferroelectricity when reducing thickness is accompanied by an enla…
We report a synthesis route to grow iron nitride thin films with giant saturation magnetization (Ms) through an N inter-diffusion process. By post annealing Fe/Fe-N structured films grown on GaAs(001) substrates, nitrogen diffuses from the over-doped amorphous-like Fe-N layer into strained crystalline Fe layer and facilitates the development of metastable Fe16N2 phase. As explored by polarized neutron reflectometry, the depth-dependent Ms profile can be well described by a model with the presence of a giant Ms up to 2360 emu/cm3 at near-substrate interface, corresponding to the strained region…
We investigate the impact of uniaxial strain on atomic shifts, dipolar interactions, polarization and electric permittivity in TiO$_2$ (rutile) by using two different implementations of density functional theory. It is shown that calculations using the Vienna ab inito simulation package (VASP) and the plane-wave self-consistent field method (PWscf) yield qualitatively the same atomic relaxations and ferroelectric trends under strain. The phonon dispersion curves of unstrained and strained TiO$_2$ (rutile) obtained by employing the linear response method confirm previous calculations of the gia…
We report on growth and ferroelectric (FE) properties of superlattices (SLs) composed of the FE BaTiO3 and the paraelectric (PE) CaTiO3. Previous theories have predicted that the polarization in (BaTiO3)n/(CaTiO3)n SLs increases as the sublayer thickness (n) increases when the same strain state is maintained. However, our BaTiO3/CaTiO3 SLs show a varying lattice-strain state and systematic reduction in polarization with increasing n while coherently-strained SLs with n=1, 2 show a FE polarization of ca. 8.5 uC/cm^2. We suggest that the strain coupling plays more important role in FE properties…
Using Landau-Ginzburg-Devonshire theory and phase field modeling, we explore the complex interplay between the long-range structural order parameter (oxygen octahedron rotations) and polarization in EuxSr1-xTiO3 thin epitaxial films. In biaxially tensile strained films, we discover the presence of a low symmetry monoclinic phase with in-plane ferroelectric polarization that is stabilized by antiferrodistortive oxygen octahedra tilts. The monoclinic phase is stable in a wide temperature range, and is characterized by the large number of energetically equivalent polar and structural twin domains…
In epitaxially strained ferroelectric thin films and superlattices, the ferroelectric transition temperature can lie above the growth temperature. Ferroelectric polarization and domains should then evolve during the growth of a sample, and electrostatic boundary conditions may play an important role. In this work, ferroelectric domains, surface termination, average lattice parameter and bilayer thickness are simultaneously monitored using in-situ synchrotron x-ray diffraction during the growth of BaTiO$_3$/SrTiO$_3$ superlattices on SrTiO$_3$ substrates by off-axis RF magnetron sputtering. The…
The alkaline earth binary oxides adopt a simple rocksalt structure and form an important family of compounds because of their large presence in the earth's mantle and their potential use in microelectronic devices. In comparison to the class of multifunctional ferroelectric perovskite oxides, however, their practical applications remain limited and the emergence of ferroelectricity and related functional properties in simple binary oxides seems so unlikely that it was never previously considered. Here, we show using first-principles density functional calculations that ferroelectricity can be …
A combined experimental and computational investigation of coupling between polarization and epitaxial strain in highly polar ferroelectric PbZr_0.2Ti_0.8O_3 (PZT) thin films is reported. A comparison of the properties of relaxed (tetragonality c/a = 1.05) and highly-strained (c/a = 1.09) epitaxial films shows that polarization, while being amongst the highest reported for PZT or PbTiO_3 in either film or bulk forms (P_r = 82 microC/cm^2), is almost independent of the epitaxial strain. We attribute this behavior to a suppressed sensitivity of the A-site cations to epitaxial strain in these Pb-…
We use symmetry analysis to show that the G, C and A-type antiferromagnetic Pnma perovskites can exhibit magnetoelectric (ME) responses when a ferroelectric instability is induced with epitaxial strain. Using first-principles calculations we compute the values of the allowed ME response in strained CaMnO3 as a model system. Our results show that large linear and non-linear ME responses are present and can diverge when close to the ferroelectric phase transition. By decomposing the electronic and ionic contributions, we explore the detailed mechanism of the ME response.
We measure the remnant polarization of ferroelectric domains in BiFeO3 films down to 3.6 nm using low energy electron and photoelectron emission microscopy. The measured polarization decays strongly below a critical thickness of 5-7 nm predicted by continuous medium theory whereas the tetragonal distortion does not change. We resolve this apparent contradiction using first-principles-based effective Hamiltonian calculations. In ultra thin films the energetics of near open circuit electrical boundary conditions, i.e. unscreened depolarizing field, drive the system through a phase transition fro…
