Strain-temperature Phase Diagram Research Articles

Phase transitions associated with competing order parameters in compressively strainedSrTiO3thin films

(100)-epitaxial ${\mathrm{SrTiO}}_{3}$ thin films having biaxial compressive strains up to $\ensuremath{-}1.60%$ were grown on lattice mismatched substrates. Two phase transitions induced by the coupled instabilities (antiferrodistortive and ferroelectric) in ${\mathrm{SrTiO}}_{3}$ were revealed in a common set of samples investigated at temperatures from 8 to 600 K by $\mathrm{CuK}\ensuremath{\alpha}$ and synchrotron x-ray diffractions and by UV-Raman spectroscopy. It is shown that the in-plane compressive strain in ${\mathrm{SrTiO}}_{3}$ significantly increases the transition temperature between cubic and tetragonal-antiferrodistortive phases and furthermore precipitates a ferroelectric polar phase at lower temperatures. The strain-temperature phase diagram based on the measurements shows a cubic-to-antiferrodistortive transition temperature that is substantially higher than predicted within a phenomenological Landau-Ginsburg-Devonshire treatment. In contrast the transition to the ferroelectric polar phase is found to be close to the temperature predicted, with the consequence that there is no crossing of the two phase transitions for temperatures up to 600 K.

Misfit strain phase diagrams of epitaxial PMN–PT films

Misfit strain–temperature phase diagrams of three compositions of (001) pseudocubic (1 − x)·Pb (Mgl/3Nb2/3)O3 − x·PbTiO3 (PMN–PT) thin films are computed using a phenomenological model. Two (x = 0.30, 0.42) are located near the morphotropic phase boundary (MPB) of bulk PMN–PT at room temperature (RT) and one (x = 0.70) is located far from the MPB. The results show that it is possible to stabilize an adaptive monoclinic phase over a wide range of misfit strains. At RT, the stability region of this phase is much larger for PMN–PT compared to barium strontium titanate and lead zirconate titanate films.

Impact of thermal expansion of substrates on phase transition temperature of VO2 films

Non-epitaxial, (010)M1-oriented VO2 thin films were grown on various substrates [amorphous SiO2, Si (001), Al2O3 (0001), and CaF2 (001)] with Pt (111)/SiO2 buffer layers. Phase transition from MoO2-type monoclinic to rutile-type tetragonal structures of these VO2 layers was investigated with temperature-controlled micro-Raman spectroscopy. It was confirmed that substrates with larger thermal expansion coefficient cause larger out-of-plane lattice spacings of both Pt and VO2, and thus lower transition temperatures of VO2 films, as a result of higher in-plane shrinkage during cooling from the deposition temperature. The transition temperatures and aM1/2 lengths, estimated from bM1 lengths, of present samples were compared with previous reports in a strain—temperature phase diagram. The present results fit with previous reports better by assuming that in-plane lattice aspect ratio of VO2 films is not clamped by the substrates but is flexible during the temperature change. Thermal expansion of substrates is an essential parameter to be taken into account when one considers device application of the phase transition properties of VO2 films, especially thick or non-epitaxial.

Longitudinal and Transversal Polarization Switching in Strained Ferroelectrics

Using the multicomponent Landau-Devonshire functional we study the field-induced polarization switching in c-oriented ferroelectric phase of epitaxial perovskite film and found that two different regimes are possible: (i) longitudinal switching with change of the polarization modulus and (ii) transversal switching with virtual admixing of the a-component of polarization. The results are specified for the case of barium titanate oxide BaTiO3where the crossover line between two types of switching is found at strain-temperature phase diagram.

Misfit strain-temperature phase diagrams and domain stability of asymmetric ferroelectric capacitors: Thermodynamic calculation and phase-field simulation

Thermodynamic calculation and phase-field simulation have been conducted to investigate the misfit strain-temperature phase diagrams, dielectric property, and domain stability of asymmetric ferroelectric capacitors (FCs), with considering the effects of dissimilar screening properties and work function steps at the two interfaces. The distinct features of asymmetric FCs from their symmetric counterparts have been revealed and discussed. Polar states with nonzero out-of-plane polarization in parallel with the built-in field are found preferential to form in asymmetric FCs. Meanwhile, the built-in field breaks the degeneracy of states with out-of-plane polarization in anti-directions. This leads to the necessity of redefining phases according to the bistability of out-of-plane polarization. Moreover, the phase stability as well as the dielectric behavior can be significantly controlled by the properties of electrodes, misfit strain, and temperature. The phase-field simulation result also shows that polydomain instability would happen in asymmetric FCs as the equivalence of domain stability in anti-directions is destroyed.

A complete strain–temperature phase diagram for BiFeO3 films on SrTiO3 and LaAlO3 (0 0 1) substrates

BiFeO3 has a complex phase diagram as function of both strain and temperature, undergoing a morphotropic phase transformation under large compressive strain. Epitaxial films, grown by pulsed laser deposition, are ideal for the study of the intricate phase coexistence between multiple polymporphs. Three polymorphs have been identified in the literature. They are carefully described in this paper (labelled R′, T′, and S′). As both ferroelectric and magnetic properties are typically strongly linked to structural distortions, the structural, ferroelectric and magnetic transition temperatures are expected to differ between the R′, T′ and S′ polymorphs. In this paper we present a complete strain–temperature phase diagram for each of the polymorphs.

Ferroelectric domains and diffuse transitions in ultrathin films of PbTiO3: Effects of strain and electrodes

We determine strain-temperature phase diagrams that map the stability of ferroelectric ordering and domains in nanothin (1.6-20 nm) films of PbTiO${}_{3}$ using molecular dynamics based on a first-principles model Hamiltonian. The ferroelectric domain structure is shown to depend sensitively on the epitaxial strain and the nature of the electrodes that screen the surface charges of a ferroelectric. We show that a broad peak in the dielectric response as a function of temperature marks a diffuse transition to a flux closure stripe-domain structure in the ultrathin films with incomplete screening of charges at their interface with the electrode. We demonstrate that the strain-phonon coupling is fundamental to the stability and topology of such a domain structure, which can be engineered at the nanoscale with a suitable choice of electrodes and substrate, and used in ultrahigh-density memory chips.

Free-standing ferroelectric multilayers: Crossover from thin-film to bulk behavior

Ferroelectric films usually have phase states and physical properties very different from those of bulk ferroelectrics. Here we propose free-standing ferroelectric-elastic multilayers as a bridge between these two material systems. Using a nonlinear thermodynamic theory, we determine phase states of such multilayers as a function of temperature, misfit strain, and volume fraction φp of passive elastic material. The numerical calculations performed for two classical ferroelectrics—PbTiO3 and BaTiO3—demonstrate that polarization states of multilayers in the limiting cases φp→1 and φp→0 coincide with those of thin films and bulk crystals. At intermediate volume fractions, however, the misfit strain-temperature phase diagrams of multilayers differ greatly from those of epitaxial films. Remarkably, a ferroelectric phase not existing in thin films and bulk crystals can be stabilized in BaTiO3 multilayers. Owing to additional tunable parameter and reduced clamping, ferroelectric multilayers may be superior for a wide range of device applications.

Strain effect on phase transitions of BaTiO3 nanowires

The effects of strain on the phase transitions of BaTiO3 nanowires taking into account three components of polarization are studied by thermodynamic analysis based on the Landau theory. Similar to the strain effect on phase transitions in thin films, the mismatch strain between the nanowire and substrate governs the Curie temperature. The complete misfit strain–temperature phase diagram shows six stable ferroelectric phases for BaTiO3 nanowires under different strain and temperature conditions.

Evidence for Strain-Induced Ferroelectric Order in Epitaxial Thin-FilmKTaO3

In perovskite-structure epitaxial films, it has been theoretically predicted that the polarization and the coherence of polar order can increase with increasing crystallographic strain. Experimental evidence of strain-induced long-range ferroelectric order has not been obtained thus far, posing the fundamental question of whether or not strain can induce the long-range polar order. Here we demonstrate the existence of strain-induced ferroelectric order in quantum paraelectric KTaO3 by combining experimental investigations of epitaxial KTaO3 films and density-functional-theory calculations. The long-range ferroelectric order does exist under a large enough epitaxial strain. We suggest that a region of short-range polar order might appear between paraelectric and ferroelectric states in the strain-temperature phase diagrams.

Phenomenological analysis of phase transitions in epitaxial perovskite ferroelectric thin films

A phenomenological Landau–Ginzburg–Devonshire theory is employed to investigate the effect of biaxial misfit strains and in-plane shear strain on thermodynamic equilibrium states and dielectric properties of single domain KNbO 3, BaTiO 3, and PbTiO 3 thin films. For KNbO 3 thin films grown on cubic substrates, the constructed isotropic misfit strain–temperature phase diagram is in qualitative agreement with the result from first-principle calculations. For BaTiO 3 and PbTiO 3, misfit strain–temperature phase diagrams at constant in-plane shear strains are constructed. In-plane shear strain is shown to restrain formation of a phase (polarization along [1 0 0]). The anisotropic misfit strain–temperature and misfit strain–misfit strain phase diagrams are also developed for KNbO 3 thin films grown on orthorhombic substrates. The anisotropic biaxial misfit strains lead to appearance of orthorhombic phases (a 1, a 2) and monoclinic phases (a 1c, a 2c).

Dielectric response and structure of in-plane tensile strained BaTiO3 thin films grown on the LaNiO3 buffered Si substrate

Highly (001)-textured BaTiO3 films were grown epitaxially on the LaNiO3 buffered Si substrate. A strong in-plane tensile strain has been revealed by using x-ray diffraction and high resolution transmission electron microscopy. The BaTiO3 film has exhibited a small remnant polarization, indicating the presence of ca1∕ca2∕ca1∕ca2 polydomain state in the film. Temperature dependent dielectric permittivity has demonstrated that two phase transitions occurred at respective temperatures of 170 and 30°C. The result was discussed in detail based on the misfit strain-temperature phase diagrams theory.

Ferroelectric Phase Transitions in Ultrathin Films ofBaTiO3

We present molecular dynamics simulations of a realistic model of an ultrathin film of BaTiO3 sandwiched between short-circuited electrodes to determine and understand effects of film thickness, epitaxial strain, and the nature of electrodes on its ferroelectric phase transitions as a function of temperature. We determine a full epitaxial strain-temperature phase diagram in the presence of perfect electrodes. Even with the vanishing depolarization field, we find that ferroelectric phase transitions to states with in-plane and out-of-plane components of polarization exhibit dependence on thickness; it arises from the interactions of local dipoles with their electrostatic images in the presence of electrodes. Secondly, in the presence of relatively bad metal electrodes which only partly compensate the surface charges and depolarization field, a qualitatively different phase with stripelike domains is stabilized at low temperature.

Phase diagrams of single-domain ferroelectric-dielectric superlattices

Using the thermodynamic theory, the authors developed misfit strain-temperature phase diagrams of single-domain ferroelectric-dielectric superlattices grown on cubic substrates. Owing to internal electric fields appearing in such multilayers, the superlattice diagrams are expected to be very different from phase maps of homogeneous ferroelectric films. The calculations show, however, that this electrostatic effect does not change relative positions of phase transition lines. It only shifts the diagram as a whole along the line separating stability ranges of paraelectric phase and in-plane polarization state. The magnitude of this shift is governed by the capacitance of dielectric layer and the thickness of ferroelectric one.

Phase diagram of ultrathin Pb(Zr0.5Ti0.5)O3 films under strain

Using a first-principles-based approach, we investigate the strain–temperature phase diagram of Pb(Zr0.5Ti0.5)O3 ultrathin film without surface charge screening. We find that the compressive strain dramatically affects the sequence of phase transitions, and observe a rich variety of ferroelectric phases, including a monoclinic phase and a stripe domain forbidden in the bulk crystal. The vortex stripe structure leads to an unusual characteristic of the phase diagram.

Strain Phase Diagram and Domain Orientation inSrTiO3Thin Films

SrTiO3 thin films were used as a model system to study the effects of strain and epitaxial constraint on structural phase transitions of perovskite films. The basic phenomena revealed will apply to a variety of important structural transitions including the ferroelectric transition. Highly strained SrTiO3 films were grown on different substrates, providing both compressive and tensile strain. The measured strain-temperature phase diagram is qualitatively consistent with theory; however, the increase in the phase transition temperature is much larger than predicted. Because of the epitaxial strain and substrate clamping, the SrTiO3 lattice is tetragonal at all temperatures. The phase transitions involve only changes in internal symmetry. The low temperature phase under tensile strain has a unique structure with orthorhombic Cmcm space group but a tetragonal lattice, an interesting consequence of epitaxial constraint.

In-plane polarization states and their instabilities in polydomain epitaxial ferroelectric thin films

A Landau–Ginsburg–Devonshire-type thermodynamic theory is used to describe epitaxial ferroelectric films with dense laminar domain structures, where spontaneous polarizations in both domains are oriented in the film plane. For PbTiO3 films, it is found that, at positive misfit strains, the domain patterning transforms the orthorhombic aa phase, which is stable in single-domain films, into a pseudotetragonal a1/a2/a1/a2 polydomain state. In BaTiO3 films, the latter is further replaced at low temperatures by a polydomain aa1/aa2/aa1/aa2 state. With decreasing misfit strain, both a1/a2/a1/a2 and aa1/aa2/aa1/aa2 patterns become unstable with respect to the appearance of polarization component orthogonal to film surfaces. This results in the formation of polydomain states in BaTiO3 films, which do not exist in bulk crystals. The stability ranges of various states in the misfit strain-temperature phase diagram are determined.

Effects of domain formation on the dielectric properties of ferroelectric thin films

A Landau-Ginsburg-Devonshire-type thermodynamic theory is used to describe dense laminar domain structures in epitaxial ferroelectric thin films grown on “tensile” substrates and to compute their small-signal dielectric responses. For PbTiO3 and BaTiO3 films, it is found that the ferroelectric phase transition results in the formation of a pseudo-tetragonal polydomain a 1/a 2/a 1/a 2 state. The stability range of the a 1/a 2/a 1/a 2 structure in the misfit strain-temperature phase diagram is determined. Effects of domain formation on the dielectric properties of ferroelectric films are analyzed by comparing permittivities of polydomain and single-domain films. Theoretical results are compared with the experimental data on (Ba1−xSrx)TiO3 films grown on platinum coated silicon substrates.

Phase transitions and strain-induced ferroelectricity inSrTiO3epitaxial thin films

A Landau-Ginsburg-Devonshire-type theory is used to describe the mechanical substrate effect on equilibrium states and phase transitions in ${\mathrm{SrTiO}}_{3}$ epitaxial thin films. The misfit strain-temperature phase diagram of ${\mathrm{SrTiO}}_{3}$ films is developed taking into account the existence of two coupled instabilities (antiferrodistortive and ferroelectric) in this crystal. It is shown that ${\mathrm{SrTiO}}_{3}$ films remain paraelectric down to 0 K only in a narrow range of small negative misfit strains between $\ensuremath{-}2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ and $\ensuremath{-}2.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}.$ Outside this ``paraelectric gap,'' the 2D clamping and straining of the film by the substrate leads to the appearance of ferroelectricity in ${\mathrm{SrTiO}}_{3}$ films. The temperature of the ferroelectric transition increases rapidly outside the aforementioned misfit strain range.