Strain-temperature Phase Diagram Research Articles

Strain-tuned quantum criticality in electronic Potts-nematic systems

Motivated by recent observations of threefold rotational symmetry breaking in twisted moir\'e systems, cold-atom optical lattices, quantum Hall systems, and triangular antiferromagnets, we phenomenologically investigate the strain-temperature phase diagram of the electronic 3-state Potts-nematic order. While in the absence of strain the quantum Potts-nematic transition is first order, quantum critical points (QCP) emerge when uniaxial strain is applied, whose nature depends on whether the strain is compressive or tensile. In one case, the nematic amplitude jumps between two nonzero values while the nematic director remains pinned, leading to a symmetry-preserving metanematic transition that terminates at a quantum critical end point. For the other type of strain, the nematic director unlocks from the strain direction and spontaneously breaks an in-plane twofold rotational symmetry, which in twisted moir\'e superlattices triggers an electric polarization. Such a piezoelectric transition changes from first to second order upon increasing strain, resulting in a quantum tricritical point. Using a Hertz-Millis approach, we show that these QCPs share interesting similarities with the widely studied Ising-nematic QCP. The existence of three minima in the nematic action also leaves fingerprints in the strain-nematic hysteresis curves, which display multiple loops. At nonzero temperatures, because the upper critical dimension of the 3-state Potts model is smaller than three, the Potts-nematic transition is expected to remain first order in three dimensions, but to change to second order in two dimensions (2D). As a result, the 2D strain-temperature phase diagram displays two first-order transition wings bounded by lines of critical end points or tricritical points, reminiscent of the phase diagram of metallic ferromagnets. We discuss how our results can be used to unambiguously identify spontaneous Potts-nematic order.

Quantitative spatial mapping of distorted state phases during the metal-insulator phase transition for nanoscale VO2 engineering

ABSTRACT Vanadium dioxide (VO2) material, known for changing physical properties due to metal-insulator transition (MIT) near room temperature, has been reported to undergo a phase change depending on the strain. This fact can be a significant problem for nanoscale devices in VO2, where the strain field covers a large area fraction, spatially non-uniform, and the amount of strain can vary during the MIT process. Direct measurement of the strain field distribution during MIT is expected to establish a methodology for material phase identification. We have demonstrated the effectiveness of geometric phase analysis (GPA), high-resolution transmission electron microscopy techniques, and transmission electron diffraction (TED). The GPA images show that the nanoregions of interest are under tensile strain conditions of less than 0.4% as well as a compressive strain of about 0.7% (Rutile phase VO2[100] direction), indicating that the origin of the newly emerged TED spots in MIT contains a triclinic phase. This study provides a substantial understanding of the strain-temperature phase diagram and strain engineering strategies for effective phase management of nanoscale VO2.

Misfit-Strain Phase Diagram, Electromechanical and Electrocaloric Responses in Epitaxial PIN-PMN-PT Thin Films.

xPb(In1/2Nb1/2)O3-(1-x-y)Pb(Mg1/3Nb2/3)O3-yPbTiO3 (PIN-PMN-PT) bulks possess excellent electromechanical coupling and dielectric properties, but the corresponding epitaxial PIN-PMN-PT thin films have not yet been explored. This paper adopts a nonlinear thermodynamics analysis to investigate the influences of misfit strains on the phase structures, electromechanical properties, and electrocaloric responses in epitaxial PIN-PMN-PT thin films. The misfit strain-temperature phase diagram was constructed. The results reveal that the PIN-PMN-PT thin films may exist in tetragonal c-, orthorhombic aa-, monoclinic M-, and paraelectric PE phases. It is also found that the c-M and aa-PE phase boundaries exhibit a superior dielectric constant ε11 which reached 1.979 × 106 with um = -0.494%, as well as the c-M phase boundary showing a large piezoelectric response d15 which reached 1.64 × 105 pm/V. In comparison, the c-PE and M-aa phase boundaries exhibit a superior dielectric constant ε33 over 1 × 105 around um = 0.316% and the piezoelectric response d33 reached 7235 pm/V. The large electrocaloric responses appear near the paraelectric- ferroelectric phase boundary. These insights offer a guidance for experiments in epitaxial PIN-PMN-PT thin films.

Phase diagrams and electromechanical properties of polydomain epitaxial (1−x)Pb(Mg1/3Nb2/3)O3–xPbTiO3 thin films

Ferroelectric thin films usually exhibit polydomain structures, while current thermodynamics analysis on (1−x)Pb(Mg1/3Nb2/3)–xPbTiO3 [(1−x)PMN–xPT] thin films assumed films only possessing single domain. Thus we predict misfit strain–temperature phase diagrams and electromechanical properties of epitaxial (1−x)PMN–xPT thin films via thermodynamics analysis with polydomain structures taken into account. The results show that polydomain structures are more stable than single domain in most areas, consistent well with experimental observations. Phase diagram for 0.7PMN-0.3PT thin films obviously differs from those for 0.58PMN-0.42PT and 0.3PMN-0.7PT thin films. Excellent electromechanical properties are observed near the phase boundary between c and r 1/r 2 phases in 0.7PMN-0.3PT thin films.

Phase Diagram of a Strained Ferroelectric Nanowire

Ferroelectric materials manifest unique dielectric, ferroelastic, and piezoelectric properties. A targeted design of ferroelectrics at the nanoscale is not only of fundamental appeal but holds the highest potential for applications. Compared to two-dimensional nanostructures such as thin films and superlattices, one-dimensional ferroelectric nanowires are investigated to a much lesser extent. Here, we reveal a variety of the topological polarization states, particularly the vortex and helical chiral phases, in loaded ferroelectric nanowires, which enable us to complete the strain–temperature phase diagram of the one-dimensional ferroelectrics. These phases are of prime importance for optoelectronics and quantum communication technologies.

Structural phase transitions in SrTiO3 from deep potential molecular dynamics

Strontium titanate ($\mathrm{SrTi}{\mathrm{O}}_{3}$) is regarded as an essential material for oxide electronics. One of its many remarkable features is the subtle structural phase transition, driven by the antiferrodistortive lattice mode, from a high-temperature cubic phase to a low-temperature tetragonal phase. Classical molecular dynamics (MD) simulation is an efficient technique to reveal atomistic features of phase transition, but its application is often limited by the accuracy of empirical interatomic potentials. Here, we develop an accurate deep potential (DP) model of $\mathrm{SrTi}{\mathrm{O}}_{3}$ based on a machine learning method using data from first-principles density functional theory (DFT) calculations. The DP model has DFT-level accuracy, capable of performing efficient MD simulations and accurate property predictions. Using the DP model, we investigate the temperature-driven cubic-to-tetragonal phase transition and construct the in-plane biaxial strain-temperature phase diagram of $\mathrm{SrTi}{\mathrm{O}}_{3}$. The simulations demonstrate that the strain-induced ferroelectric (FE) phase is characterized by two order parameters, FE distortion and antiferrodistortion, and the FE phase transition has both displacive and order-disorder characters. In this paper, we lay the foundation for the development of accurate DP models of other complex perovskite materials.

Q-POP-Thermo: A general-purpose thermodynamics solver for ferroelectric materials

Q-POP-Thermo is a program designed to compute thermodynamic monodomain equilibrium states and their properties for ferroelectric single crystals and thin films based on the Landau-Ginzburg-Devonshire (LGD) Theory. Utilizing symbolic manipulation with the SymPy Library, the governing equations along with appropriate boundary conditions are solved for speedy minimization of the free energy of a crystal. Utilizing the popular Differential Evolution algorithm, with appropriate hybridization, multiple phase diagrams, such as the pressure-temperature phase diagram for bulk single crystals and the common strain-temperature phase diagram for monodomain thin-film systems can be readily generated. Furthermore, a variety of material properties of stable ferroelectric phases, including dielectric, piezoelectric, and electrocaloric properties, can simultaneously be calculated. Validation studies are presented for both thin-film and single crystal systems to test the effectiveness and capability of the open-source program. Program summaryProgram title: Q-POP-ThermoCPC Library link to program files:https://doi.org/10.17632/wd6228g9ww.1Code Ocean capsule:https://codeocean.com/capsule/1245708Licensing provisions: MITProgramming language: PythonExternal routines/libraries: numpy (Version 1.20.3), sympy (Version 1.8), numerical optimization (available with Q-POP-Thermo), pandas (Version 1.1.3), scipy (Version 1.6.3)Nature of program: Python-based program to perform energy minimization to determine the stable states and thermodynamic properties of ferroelectric systems.Solution method: Algebraic manipulation of boundary conditions and governing equations followed by a hybridized and improved a priori Differential Evolution solver to calculate equilibrium polar states and material properties.

Strain-temperature phase diagram of BaZrO3 with antiferrodistortive distortions

Barium zirconate ($\mathrm{BaZr}{\mathrm{O}}_{3}$) has attracted increasing attention due to its distinguished dielectric property and high chemical stability. As one kind of perovskite oxide, $\mathrm{BaZr}{\mathrm{O}}_{3}$ often exhibits a delicate interplay of lattice distortions and strain. In this work, the effect of strain on the ferroelectric and antiferrodistortive distortions in $\mathrm{BaZr}{\mathrm{O}}_{3}$ thin films is investigated at finite temperature by using density functional theory calculations and the first-principles based effective Hamiltonian method. It is found that due to the delicate balance between antiferrodistortive and ferroelectric distortions, polarization in $\mathrm{BaZr}{\mathrm{O}}_{3}$ thin films at absolute zero kelvin can be activated only under an in-plane tensile strain larger than 3.0%. The rotation of oxygen octahedra (antiferrodistortive distortion) is along the out-of-plane direction under the compressive strain and small tensile strain, whereas it changes to the in-plane direction when the tensile strain is larger than 0.3%. When the tensile strain increases to 4.1%, both rotation of oxygen octahedra and polarization are along the [110] direction. Furthermore, the temperature dependence of ferroelectric and antiferrodistortive distortions under different strains is investigated by using an effective Hamiltonian model. The strain-temperature phase diagram is calculated to identify the different distortions under different strains and temperatures.

Phase diagram and pyroelectric response of polydomain epitaxial Ba0.6Sr0.4TiO3 thin films

A nonlinear thermodynamic theory is used to investigate the phase structures, polarization and pyroelectric properties of polydomain epitaxial Ba0.6Sr0.4TiO3 thin films. Polydomain a1/a2/a1/a2, ca1/ca2/ca1/ca2, aa1/aa2/aa1/aa2, r1/r2/r1/r2 phases and single domain tetragonal c, paraelectric PE phases have been found in the misfit strain-temperature phase diagram. Note that the polydomain phases are found to be more complicated than single domain phases, which also leads to the variability of pyroelectric properties. The results of pyroelectric coefficients reveal that a distinguished in-plane and out-of-plane pyroelectric response appears near the phase boundaries of a1/a2/a1/a2-PE and ca1/ca2/ca1/ca2-c, c-PE, respectively, in which the pyroelectric coefficients |pi| are larger than 0.6 μC/cm2 K, exceeding most experimental and theoretical values. It is found that the maximum in-plane and out-of-plane pyroelectric coefficients occur under the strain of 0.23% and −0.225% at room temperature, respectively. The giant pyroelectric performance of polydomain Ba0.6Sr0.4TiO3 thin films may provide potential to highly sensitive infrared detectors.

Misfit strain-temperature phase diagram of multi-domain structures in (111)-oriented ferroelectric PbTiO3 films

High-index-oriented epitaxial ferroelectric films have recently attracted great attention due to their emergent functional properties related to the multi-domain structures. Here, the equilibrium phases and domain structures in (111)-oriented ferroelectric PbTiO3 films were investigated via phase-field simulations and the misfit strain-temperature equilibrium phase diagram was constructed. It was found that the epitaxial strain can effectively control the orientations of polarization vectors, which uniquely determine the domain variant patterns, domain wall orientations and densities. In particular, two types of tetragonal-like domain patterns can form under different strains with their distinct structural characteristics, ferroelectric properties and thermal conductivities. These results provide guidance for interpreting and understanding experimental data as well as designing of (111)-oriented ferroelectric films with specified domain structures and properties.

Multicaloric effect in multiferroic EuTiO3 thin films

A modified Landau–Ginzburg–Devonshire phenomenological thermodynamic theory is used to investigate both the influence of biaxial compressive misfit strain between film and the substrate and the mechanical stress on the multicaloric response in epitaxial EuTiO3 thin films. The complicated compressive misfit strain–temperature phase diagram in the low-temperature region is developed. The excellent electrocaloric and elastocaloric effect can be achieved: $$ \Delta T(T_{\text{C}} ) = 3.66\,{\text{K}} $$, while $$ \Delta E = 100\,{\text{kV/cm}},u_{\text{m}} = - \,4.0{\%} $$; $$ \Delta T $$ = 5.31 K at 200 MPa. Besides, the maximal adiabatic temperature change $$ \Delta T(T_{\text{M}} ) = 17.3\,{\text{K}} $$, while $$ \Delta H = 5\,{\text{T}},u_{\text{m}} = - \,4.0{\%} $$, in the low-temperature region, which is comparable with the experimental result. Both the misfit strain and the external mechanical stress play a crucial role in the multicaloric response in EuTiO3 films. It may open more opportunities for practical application in refrigeration devices, especially for low-temperature solid-state multicaloric cooling.

Crystallographic orientation-dependent piezoelectric response in BaTiO3 thin films and the domain evolution under different temperatures

The effects of crystallographic orientation on the domain structures and piezoelectric response of BaTiO3 (BTO) thin films were investigated by piezoresponse force microscopy (PFM) systematically. It is found that the domain structures of BTO films are obviously orientation dependent, and the (111) oriented BTO film shows the best piezoelectric properties. Therefore, the nanoscale polydomain switchings within valid single grains of the BTO(111) thin film were observed by PFM under different temperatures. According to the switching process, the a1/a2c, r/a2c, and a1c/r polydomain states were specially introduced into the theoretical model to describe the temperature-induced polydomain switchings of the BTO(111) thin film. The misfit strain-temperature phase diagram was simulated to present the a1/a2c-r/a2c-a1c/r-p domain switching, which corresponds with the threshold temperature of domain switchings obtained from the experimental results of the BTO(111) thin film.

Ferroelectric domain structures and temperature-misfit strain phase diagrams of K1-xNaxNbO3 thin films: A phase-field study

Potassium-sodium niobate K1-xNaxNbO3 (KNN) is one of the most promising lead-free piezoelectric materials. While there have been many studies on the microstructures and properties of KNN ceramics, the phase transitions and ferroelectric domain structures of KNN thin films are not well understood. In this work, we employ three-dimensional (3D) phase-field simulations to obtain the ferroelectric domain structures of KNN (0 ≤ x ≤ 0.5) thin films under a range of temperatures (0 K to 1300 K) and equiaxial misfit strains (–1.5% to 1.5%), based on which we establish the misfit strain-temperature phase diagrams of KNbO3 and K0.5Na0.5NbO3 thin films. We identify a wide variety of complex domain structures with coexisting ferroelectric phases, implying enhanced dielectric and piezoelectric properties. We expect this work to provide guidance for the strain engineering of domain structures and properties of KNN thin films.

Landau–Devonshire thermodynamic potentials for displacive perovskite ferroelectrics from first principles

A general approach for fitting Landau–Devonshire thermodynamic potentials directly from first principles is developed for simple displacive ferroelectric perovskite materials. As the first step, a $$\hbox {PbTiO}_3$$ potential is parameterized completely from density functional theory calculations as a test case, under the only assumption that the transition between the non-polar and polar phases is of first order. The utility of this approach is assessed by comparing quantities characterizing the phase transition, dielectric and piezoelectric properties and equibiaxial strain–temperature phase diagrams with the predictions of several thermodynamic potentials parameterized from experimental data. In the second step, a similar parameterization is generated for a fictitious polar perovskite $$\hbox {SnTiO}_{3}$$ , enabling us to predictively evaluate an approximate ‘equibiaxial strain–temperature–spontaneous polarization’ phase diagram for its thin films.

Giant electrocaloric effect in ferroelectric ultrathin films at room temperature mediated by flexoelectric effect and work function

In ferroelectric ultrathin films, built-in electric fields are often present due to the flexoelectric effect and the difference of work functions at asymmetric electrodes, which may change the properties of the materials. In this paper, the influence of build-in electric fields induced by flexoelectric effect and/or work function difference on the misfit strain-temperature phase diagrams, and the electrocaloric properties of epitaxial BaTiO3 ultrathin films are investigated by using an extended nonlinear thermodynamic theory. It is found that the flexoelectric effect, i.e., the coupling of polarization and strain gradient, changes the misfit strain-temperature phase diagrams notably, in which the phases with out-of-plane polarizations increase due to the presence of a built-in field. The electrocaloric properties are remarkably enhanced when the built-in fields induced by both the flexoelectric effect and work function difference are considered. In particular, a giant adiabatic temperature change of 7.89 K in ultrathin Pt/BaTiO3/SrRuO3 capacitors at 460 K is predicted. Moreover, it is demonstrated that the peak of adiabatic temperature change versus working temperature is shifted from a high temperature to room temperature, suggesting that ferroelectric ultrathin films with asymmetric electrodes and strain gradient are promising candidates for room temperature refrigeration.

Theory of strain phase separation and strain spinodal: Applications to ferroelastic and ferroelectric systems

In the well-known phase decomposition process, a phase with a homogeneous composition separates into two phases with different local compositions that can be geometrically determined by the common tangent construction on the molar free energy versus composition curves. Here we consider an analogous phase destrain process in which a phase with a homogeneous strain separates into two phases with different local strains that can be geometrically determined by the common tangent construction on the volume free energy density versus strain curves. There is also a complete analogy between compositional and strain spinodals. Within the phase destrain model, we provide a general thermodynamic formulation for the phase rule, lever rule, equilibrium conditions of chemical potential, and coherent/incoherent strain spinodals. Using the cubic to tetragonal ferroelastic/ferroelectric transition as an example, we study the possible strain phase separation and spinodal phenomena, and calculate the strain-strain and strain-temperature phase diagrams for the first-order proper, first-order improper, and second-order improper ferroelastic transitions. The proposed phase destrain theory complements the existing compositional phase separation theory and can serve as guidance for the analysis and design of multi-domain/multi-phase structures during any phase transitions associated with structural changes.

Engineering of the Curie temperature of epitaxial Sr1−xBaxTiO3 films via strain

The impact of strain on the structural and electrical properties of epitaxial Sr1−xBaxTiO3 films grown on single crystalline DyScO3 (110), TbScO3 (110), and GdScO3 (110) substrates is presented. X-ray diffraction measurements demonstrate that all films are grown epitaxially. The tensile in-plane strain is only partially compensated by a contraction of the out-of-plane lattice parameter. As a result, the volume of the unit cell of the Sr1−xBaxTiO3 film increases due to the tensile strain, and the resulting Poisson ratio of the film is ν ≈ 0.33, which is larger than but still close to the literature values of ν ≈ 0.23 for unstrained defect-free SrTiO3. The Curie temperature derived from the temperature dependence of the in-plane dielectric response leads to a strain-temperature phase diagram for the epitaxial Sr1−xBaxTiO3 films. The experimental data show a deviation from the linear dependence predicted by the Landau thermodynamic theory for large strain (>1.2%). However, using the equilibrium thermodynamic analysis, we can demonstrate that this deviation arises from the relaxation of the strain due to defect formation in the film. The result reveals that in addition to the nominal misfit strain, the defect formation strongly affects the effective strain and, thus, the dielectric response of epitaxially grown ferroelectric films.

Phenomenological thermodynamic potentials for bulk and thin-film Ba(Zr0.08Ti0.92)O3 single crystals

Phenomenological thermodynamic analysis is an important theoretical investigation method for ferroelectric materials, however, it cannot be implemented for Ba(ZrxTi1−x)O3 due to the lack of thermodynamic potential coefficients. In this paper, we have constructed a phenomenological thermodynamic potential for bulk Ba(Zr0.08Ti0.92)O3 single crystals, which reproduces the three phase transition temperatures, dielectric and piezoelectric constants of bulk Ba(Zr0.08Ti0.92)O3 single crystals well, suggesting that the constructed thermodynamic potential is reliable. Then the thermodynamic potential with appropriate modification is applied to predict misfit strain-temperature phase diagram and electromechanical properties of Ba(Zr0.08Ti0.92)O3 thin films. It is found that compressive strain favors the tetragonal c phase with an out-of-plane polarization component, while tensile misfit strain favors orthorhombic aa phase with an in-plane polarization component. It also reveals that Ba(Zr0.08Ti0.92)O3 thin films under appropriate compressive strain show higher piezoelectric coefficient d15 than that of their bulk counterpart. The constructed thermodynamic potential opens a new avenue to theoretical analysis on Ba(Zr0.08Ti0.92)O3.

Fluctuation and strain effects in a chiralp-wave superconductor

For a tetragonal material, order parameters of $p_x$ and $p_y$ symmetry are related by rotation and hence have the same $T_{\rm c}$ at a mean-field level. This degeneracy can be lifted by a symmetry-breaking field, like (uniaxial) in-plane strain, such that at $T_{\rm c}$, the order parameter is only of $p_x$ or $p_y$ symmetry. Only at a lower temperature also the respective other order parameter condenses to form a chiral $p$-wave state. At the mean-field level, the derivative of $T_{\rm c}$ with strain is discontinuous at zero strain. We analyze consequences of (thermal) fluctuations on the strain-temperature phase diagram within a Ginzburg-Landau approach. We find that the order-parameter fluctuations can drive the transition to be weakly first order, rounding off this discontinuity. We discuss the possibility of a second-order transition into a non-superconducting time-reversal-symmetry-breaking phase and consequences for the spin-triplet superconductor Sr$_2$RuO$_4$.

Effect of crystal orientation on the phase diagrams, dielectric and piezoelectric properties of epitaxial BaTiO3 thin films

The influence of crystal orientations on the phase diagrams, dielectric and piezoelectric properties of epitaxial BaTiO3 thin films has been investigated using an expanded nonlinear thermodynamic theory. The calculations reveal that crystal orientation has significant influence on the phase stability and phase transitions in the misfit strain-temperature phase diagrams. In particular, the (110) orientation leads to a lower symmetry and more complicated phase transition than the (111) orientation in BaTiO3 films. The increase of compressive strain will dramatically enhance the Curie temperature TC of (110)-oriented BaTiO3 films, which matches well with previous experimental data. The polarization components experience a great change across the boundaries of different phases at room temperature in both (110)- and (111)-oriented films, which leads to the huge dielectric and piezoelectric responses. A good agreement is found between the present thermodynamics calculation and previous first-principles calculations. Our work provides an insight into how to use crystal orientation, epitaxial strain and temperature to tune the structure and properties of ferroelectrics.