Finite-temperature properties of Pb(Zr1-xTi(x))O3 alloys from first principles

Controlling double vortex states in low-dimensional dipolar systems

The reversal process of the chirality of each opposite vortex belonging to a double vortex state in ferromagnetic hysterons, via the application of in-plane magnetic fields, is reported. Simulations reveal that such a process involves the formation of four intermediate states, including original ones. Hysteresis loops can occur only in a counterclockwise fashion because of one of these intermediate states. Double vortex states can also be controlled by electric fields in ferroelectric nanostructures of different shapes, but with some key differences with respect to the ferromagnetic case.

Notes of the recent structural studies on lead zirconate titanate

Atomic scale structure has a central importance for the understanding of functional properties of ferroelectrics. The X-ray and neutron diffraction studies used for the average symmetry determination of lead zirconate titanate [Pb(ZrxTi(1- x))O3, PZT] ceramics and powders are reviewed. The results obtained through two frequently used local probes, transmission electron microscopy (TEM) combined with electron diffraction (ED) and Raman scattering measurements, are summarized. On the basis of these studies, structural trends as a function of composition x and temperature are outlined. There are two distinguished intrinsic structural features, (i) lead-ion shifts and (ii) local structural distortions related to different B cations and the spatial composition variation of x, which have a pronounced effect on the functional properties of PZT. Particular attention is paid to the morphotropic phase boundary (MPB) compositions for which a large number of different structural models have been proposed. Earlier symmetry considerations show that the monoclinic phase cannot serve as a continuous bridge between tetragonal and rhombohedral phases. This suggests that the two-phase coexistence has an important role for the piezoelectric properties. Near the MPB, the extrinsic contribution to piezoelectricity includes pressure (or electric-field)-induced changes in phase fractions and domain wall motion. It was recently shown that the domain contribution is crucial for the electromechanical properties of PZT in the vicinity of the MPB. The dependence of domain widths on crystal size and shape should also be properly accounted for when TEM/ED measurements complement X-ray and/or neutron diffraction experiments. The structure-piezoelectric property relations are summarized.

Control of vortices by homogeneous fields in asymmetric ferroelectric and ferromagnetic rings

Effective Hamiltonians have been used (i) to demonstrate that the shape asymmetry of ferromagnetic rings is essential to the recently discovered switching of the chirality of their vortices by homogeneous magnetic fields, via a transition into onion states; (ii) to reveal that an electric vortex can also be controlled by a homogeneous electric field in asymmetric ferroelectric nanorings, via the formation of antiferrotoroidic pair states rather than onion states; and (iii) to provide the fundamental reason that allows such control, namely, two new interaction energies involving a vector characterizing the asymmetry, the applied field, and the toroidal moment.

Stability of ferroic phases in the highly piezoelectric Pb(ZrxTi1−x)O3ceramics

The morphotropic phase boundary in the phase diagram of the technologically important Pb(ZrxTi1−x)O3(PZT) ceramics has been traditionally believed to separate ferroelectric tetragonal and rhombohedral phase regions. This old picture has come under close scrutiny during the last eight years following the discovery of new monoclinic phases in theCmandCcspace groups. This article presents a brief overview of these discoveries in which the use of multiple diffraction probes (X-ray, electron, neutron diffraction) in conjunction with physical property measurements has played a crucial role. A new phase diagram of PZT showing the stability fields of these structures below room temperature is also presented.

Dielectric anomalies in ferroelectric nanostructures

First-principles-based methods are used to determine the external dielectric susceptibility (i.e., the polarization response to the external electric field) and the internal susceptibility (i.e., the polarization response to the average internal field) in ferroelectric dots, wires, and films, as a function of the electrical boundary conditions. While the external susceptibility is obviously positive, we find that the internal one is negative over a wide range of boundary conditions for all kinds of nanostructures. A Landau-type phenomenological model provides a rationale for all of our findings.

Ferroelectricity, nonlinear dynamics, and relaxation effects in monoclinic Sn2P2S6

An ab initio-based model of the temperature-induced ferroelectric phase transition in Sn2P2S6 (SPS) as a prototype of an unconventional ferroelectric is developed. The order parameter in SPS is found as the valley line on a total-energy surface of the zone-center fully symmetrical Ag and polar Bu distortions. Significant nonlinear coupling between order parameter and strain is observed. Monte Carlo simulations describe the additional low-temperature rearrangement in polar structure, which appears in domain boundaries, and describe the relaxation phenomena near the ferroelectric phase transition.

Low-temperature phase transformations of PbZr(1-x)Ti(x)O(3) in the morphotropic phase-boundary region

We present anelastic and dielectric spectroscopy measurements of PbZr(1-x)Ti(x)O(3) with 0.455 < or = x < or = 0.53, which provide new information on the low-temperature phase transitions. The tetragonal-to-monoclinic transformation is first order for x < 0.48 and causes a softening of the polycrystal Young's modulus whose amplitude may exceed the one at the cubic-to-tetragonal transformation; this is explainable in terms of linear coupling between shear strain components and tilting angle of polarization in the monoclinic phase. The transition involving rotations of the octahedra below 200 K is visible both in the dielectric and anelastic losses, and it extends within the tetragonal phase, as predicted by recent first-principle calculations.

Correlations between transition temperature, tolerance factor and cohesive energy in 2+:4+ perovskites

Cohesive energies were calculated ab initio for a range of simple 2+:4+ perovskites (A(2+)B(4+)O(3)). Correlations were sought between the sets of lattice parameters, cohesive energies, cubic transition temperatures and Goldschmidt tolerance factors for these compounds. There is a noticeable correlation (R = -0.60) between the transition temperatures and the tolerance factors, but only weak relationships between the cohesive energy and the other parameters. However, for more than half the set of compounds, there is a strong correlation (R = 0.989), in the form of a simple linear trend between the tolerance factor and the ratio of cubic transition temperature to cohesive energy density. The remaining compounds form two distinct clusters and either retain cubicity down to 0 K or undergo transitions to lower symmetry at substantially lower temperatures than might be expected from the trend.

Structure and polarization in the high Tc ferroelectric Bi(Zn,Ti)O3-PbTiO3 solid solutions

Theoretical ab initio and experimental methods are used to investigate the [Bi(Zn1/2Ti1/2)O3]x[PbTiO3]1-x solid solution. We find that hybridization between Zn 4s and 4p and O 2p orbitals allows the formation of short, covalent Zn-O bonds, enabling favorable coupling between A-site and B-site displacements. This leads to unusually large polarization, strong tetragonality, and an elevated ferroelectric to paraelectric phase transition temperature.

Vortex-to-polarization phase transformation path in ferroelectric Pb(ZrTi)O3 nanoparticles

Phase transformation in finite-size ferroelectrics is of fundamental relevance for understanding collective behaviors and balance of competing interactions in low-dimensional systems. We report a first-principles effective Hamiltonian study of vortex-to-polarization transformation in Pb(Zr0.5Ti0.5)O3 nanoparticles, caused by homogeneous electric fields normal to the vortex plane. The transformation is shown to (1) follow an unusual macroscopic path that is symmetry nonconforming and characterized by the occurrence of a previously unknown structure as the bridging phase, and (2) lead to the discovery of a striking collective phenomenon, revealing how ferroelectric vortex is annihilated microscopically. Interactions underlying these behaviors are discussed.

Nonmonotonic TC trends in bi-based ferroelectric perovskite solid solutions

We use first-principles density functional theory calculations to investigate the strongly nonlinear compositional trends in ferroelectric BiBO3-PbTiO3 solid solutions for a variety of cations on the perovskite B site. We demonstrate that previously tabulated crystal chemical parameters (extracted from other Pb-based perovskite alloys [Grinberg et al., J. Appl. Phys. 98, 094111 (2005)]) permit accurate prediction of cation displacements in these new Bi-Pb alloys. We find that observed transition temperatures in these materials are well correlated with computed polarization magnitudes. The presented model for coupling between compositional variation and cation displacements explains the highly nonlinear and often nonmonotonic dependence of the Curie temperature (T(C)) on composition observed in these solid solutions.

Properties of ferroelectric nanodots embedded in a polarizable medium: atomistic simulations

An atomistic approach is used to investigate finite-temperature properties of ferroelectric nanodots that are embedded in a polarizable medium. Different phases are predicted, depending on the ferroelectric strengths of the material constituting the dot and of the system forming the medium. In particular, novel states, exhibiting a coexistence between two kinds of order parameters or possessing a peculiar order between dipole vortices of adjacent dots, are discovered. We also discuss the origins of these phases, e.g., depolarizing fields and medium-driven interactions between dots.

Phase diagram of pb(Zr,Ti)O3 solid solutions from first principles

A first-principles-derived scheme that incorporates ferroelectric and antiferrodistortive degrees of freedom is developed to study finite-temperature properties of Pb(Zr1-xTix)O3 solid solution near its morphotropic phase boundary. The use of this numerical technique (i) resolves controversies about the monoclinic ground state for some Ti compositions, (ii) leads to the discovery of an overlooked phase, and (iii) yields three multiphase points that are each associated with four phases. Additional neutron diffraction measurements strongly support some of these predictions.

First-principles combinatorial design of transition temperatures in multicomponent systems: the case of Mn in GaAs

The transition temperature TC of multicomponent systems--ferromagnetic, superconducting, or ferroelectric--depends strongly on the atomic arrangement, but an exhaustive search of all configurations for those that optimize TC is difficult, due to the astronomically large number of possibilities. Here we address this problem by parametrizing the TC of a set of approximately 50 input configurations, calculated from first principles, in terms of configuration variables ("cluster expansion"). Once established, this expansion allows us to search almost effortlessly the transition temperature of arbitrary configurations. We apply this approach to search for the configuration of Mn dopants in GaAs having the highest ferromagnetic Curie temperature. Our general approach of cluster expanding physical properties opens the way to design based on exploring a large space of configurations.

Controlling toroidal moment by means of an inhomogeneous static field: an ab initio study

A first-principles-based approach is used to show (i) that stress-free ferroelectric nanodots under open-circuit-like electrical boundary conditions maintain a vortex structure for their local dipoles when subject to a transverse inhomogeneous static electric field, and, more importantly, (ii) that such a field leads to the solution of a fundamental and technological challenge: namely, the efficient control of the direction of the macroscopic toroidal moment. The effects responsible for such striking features are revealed and discussed.

Electric-field-induced domain evolution in ferroelectric ultrathin films

The electric-field-induced evolution of the recently discovered periodic 180 degree nanostripe domain structure is predicted in epitaxial Pb(Zr0.5Ti0.5)O3 ultrathin films from first principles. This evolution involves (1) the lateral growth of majority dipole domains at the expense of minority domains with the overall stripe periodicity remaining unchanged, (2) the creation of surface-avoiding nanobubbles, and (3) the formation of a single monodomain state. Analogies and differences (i) with ferroelectric thin films made of BaTiO3 and (ii) with ferromagnetic thin films under magnetic field are discussed.

Polar domains in lead titanate films under tensile strain

Thin films of PbTiO3, a classical ferroelectric, have been grown under tensile strain on single-crystal substrates of DyScO3. The films, of only 5 nm thickness, grow fully coherent with the substrate, as evidenced by synchrotron x-ray diffraction. A mapping of the reciprocal space reveals intensity modulations (satellites) due to regularly spaced polar domains in which the polarization appears rotated away from the substrate normal, characterizing a low-symmetry phase not observed in the bulk material. This could have important practical implications since these phases are known to be responsible for ultrahigh piezoelectric responses in complex systems.

Spontaneous polarization in one-dimensional Pb(ZrTi)O3 nanowires

Formation of spontaneous polarization in one-dimensional (1D) structures is a key phenomenon that reveals collective behaviors in systems of reduced dimensions, but has remained unsolved for decades. Here we report ab initio studies on finite-temperature structural properties of infinite-length nanowires of Pb(Zr0.5Ti0.5)O3 solid solution. Whereas existing studies have ruled out the possibility of phase transition in 1D chains, our atomistic simulations demonstrate a different conclusion, characterized by the occurrence of a ferroelectric polarization and critical behaviors of dielectric and piezoelectric responses. The difference is accounted for by the use of depolarizing effects associated with finite thickness of wires. Our results suggest no fundamental constraint that limits the use of ferroelectric nanowires and nanotubes arising from the absence of spontaneous ordering.

Pressure-induced anomalous phase transitions and colossal enhancement of piezoelectricity in PbTiO3

We find an unexpected tetragonal-to-monoclinic-to-rhombohedral-to-cubic phase transition sequence induced by pressure, and a morphotropic phase boundary in a pure compound using first-principles calculations. Huge dielectric and piezoelectric coupling constants occur in the transition regions, comparable to those observed in the new complex single-crystal solid-solution piezoelectrics such as Pb(Mg(1/3)Nb(2/3))O3-PbTiO3, which are expected to revolutionize electromechanical applications. Our results show that morphotropic phase boundaries and giant piezoelectric effects do not require intrinsic disorder, and open the possibility of studying this effect in simple systems.

Ab initio design of high-k dielectrics: La(x)Y1-xAlO3

We use calculations based on density-functional theory in the virtual crystal approximation for the design of high-k dielectrics, which could offer an alternative to silicon dioxide in complementary metal-oxide semiconductor devices. We show that aluminates LaxY1-xAlO3 alloys derived by mixing aluminum oxide with lanthanum and yttrium oxides have unique physical attributes for a possible application as gate dielectrics when stabilized in the rhombohedral perovskite structure, and which are lost in the orthorhombic modification. Stability arguments locate this interesting composition range as 0.2<x<0.4. Phase separation in microdomains is shown to have the tendency to further enhance the dielectric constant. We propose this as a novel family of high-k dielectrics deserving experimental exploration.

Unusual phase transitions in ferroelectric nanodisks and nanorods

Bulk ferroelectrics undergo structural phase transformations at low temperatures, giving multi-stable (that is, multiple-minimum) degenerate states with spontaneous polarization. Accessing these states by applying, and varying the direction of, an external electric field is a key principle for the operation of devices such as non-volatile ferroelectric random access memories (NFERAMs). Compared with bulk ferroelectrics, low-dimensional finite ferroelectric structures promise to increase the storage density of NFERAMs 10,000-fold. But this anticipated benefit hinges on whether phase transitions and multi-stable states still exist in low-dimensional structures. Previous studies have suggested that phase transitions are impossible in one-dimensional systems, and become increasingly less likely as dimensionality further decreases. Here we perform ab initio studies of ferroelectric nanoscale disks and rods of technologically important Pb(Zr,Ti)O3 solid solutions, and demonstrate the existence of previously unknown phase transitions in zero-dimensional ferroelectric nanoparticles. The minimum diameter of the disks that display low-temperature structural bistability is determined to be 3.2 nm, enabling an ultimate NFERAM density of 60 x 10(12) bits per square inch-that is, five orders of magnitude larger than those currently available. Our results suggest an innovative use of ferroelectric nanostructures for data storage, and are of fundamental value for the theory of phase transition in systems of low dimensionality.

Ultrathin films of ferroelectric solid solutions under a residual depolarizing field

A first-principles-derived approach is developed to study the effects of depolarizing electric fields on the properties of Pb(Zr,Ti)O3 ultrathin films for different mechanical boundary conditions. A rich variety of ferroelectric phases and polarization patterns is found, depending on the interplay between strain and the amount of screening of surface charges. Examples include triclinic phases, monoclinic states with in-plane and/or out-of-plane components of the polarization, homogeneous and inhomogeneous tetragonal states, as well as peculiar laminar nanodomains.

Ferroelectricity in barium titanate quantum dots and wires

Properties of BaTiO3 colloidal quantum dots and wires are simulated using a first-principles-based approach. Large atomic off-center displacements (that are robust against capping matrix materials) are found to exist in very small (<5 nm) dots. We further determine the size dependences of electrical and electromechanical responses in the studied nanostructures, as well as provide microscopic understanding of these responses.

Conformal miniaturization of domains with low domain-wall energy: monoclinic ferroelectric states near the morphotropic phase boundaries

A theory is developed for intermediate monoclinic (FE(m)) phases near morphotropic phase boundaries in ferroelectrics of complex oxides. It is based on the conformal miniaturization of stress-accommodating tetragonal domains under the condition of low domain-wall energy density. The microdomain-averaged lattice parameters are determined and attributed to the parameters of an adaptive monoclinic phase. The theory is applied to the temperature, electric field, and compositional dependent FE(m) lattice parameters. The predictions of the theory are rigidly obeyed over the entire FE(m) stability range.

Unusual thermodynamic properties and nonergodicity in ferroelectric superlattices

The properties of [Pb(Zr(1-x(1))Ti(x(1)))O(3)](n)/[Pb(Zr(1-x(2))Ti(x(2)))O(3)](n) superlattices, with a 2n period, are simulated using an ab initio based approach. The x(1) and x(2) compositions are chosen to be located across the morphotropic phase boundary of the corresponding disordered alloys, while the (x(1)+x(2))/2 average composition lies inside this boundary. These superlattices exhibit an unusual thermodynamic phase transition sequence, including a triclinic ground state. They also have the kind of peculiar free-energy landscape yielding nonergodicity. The effects responsible for these anomalies are discussed.

Huge enhancement of electromechanical responses in compositionally modulated Pb(Zr(1-x )Tix)O3

Monte Carlo simulations based on a first-principles-derived Hamiltonian are conducted to study the properties of Pb(Zr1-xTix)O3 alloys compositionally modulated along the [100] pseudocubic direction near the morphotropic phase boundary. It is shown that compositional modulation causes the polarization to continuously rotate away from the modulation direction, resulting in the unexpected triclinic and C-type monoclinic ground states and huge enhancement of electromechanical responses (the peak of piezoelectric coefficient is as high as 30,000 pC/N). The orientation dependence of dipole-dipole interaction in modulated structure is revealed as the microscopic mechanism to be responsible for these anomalies.

Effects of atomic short-range order on the properties of perovskite alloys in their morphotropic phase boundary

The effects of atomic short-range order on the properties of Pb(Zr(1-x)Ti(x))O3 alloy in its morphotropic phase boundary (MPB) are predicted by combining first-principles-based methods and annealing techniques. Clustering is found to lead to a compositional expansion of this boundary, while the association of unlike atoms yields a contraction of this region. Atomic short-range order can thus drastically affect properties of perovskite alloys in their MPB, by inducing phase transitions. Microscopic mechanisms responsible for these effects are revealed and discussed.

Relationship between local structure and phase transitions of a disordered solid solution

The Pb(Zr,Ti)O3 (PZT) disordered solid solution is widely used in piezoelectric applications owing to its excellent electromechanical properties. Six different structural phases have been observed for PZT at ambient pressure, each with different lattice parameters and average electric polarization. It is of significant interest to understand the microscopic origin of the complicated phase diagram and local structure of PZT. Here, using density functional theory calculations, we show that the distortions of the material away from the parent perovskite structure can be predicted from the local arrangement of the Zr and Ti cations. We use the chemical rules obtained from density functional theory to create a phenomenological model to simulate PZT structures. We demonstrate how changes in the Zr/Ti composition give rise to phase transitions in PZT through changes in the populations of various local Pb atom environments.

Local ferroelectricity in SrTiO3 thin films

The temperature-dependent polarization of SrTiO3 thin films is investigated using confocal scanning optical microscopy. A homogeneous out-of-plane and an inhomogeneous in-plane ferroelectric phase are identified from images of the linear electro-optic response. Both hysteretic and nonhysteretic behavior are observed under a dc bias field. Unlike classical transitions in bulk ferroelectrics, local ferroelectricity is observed at temperatures far above the dielectric permittivity maximum. The results demonstrate the utility of local probe experiments in understanding inhomogeneous ferroelectrics.

First-principles study of the temperature-pressure phase diagram of BaTiO3

We investigate the temperature-pressure phase diagram of BaTiO3 using a first-principles effective-Hamiltonian approach. We find that the zero-point motion of the ions affects the form of the phase diagram dramatically. Specifically, when the zero-point fluctuations are included in the calculations, all the polar (tetragonal, orthorhombic, and rhombohedral) phases of BaTiO3 survive down to 0 K, while only the rhombohedral phase does otherwise. This behavior results from a practical equivalence between thermal and quantum fluctuations. Our work confirms the essential correctness of the phase diagram proposed by Ishidate et al. [Phys. Rev. Lett. 78, 2397 (1997)]].

Planar defects and incommensurate phases in highly ordered perovskite solid solutions

A first-principles-derived approach is used to study the effects of planar defects on structural properties of a rocksalt-ordered Pb(Sc0.5Nb0.5)O3 alloy. These defects lead to unusual features, including a less symmetrical ground state with respect to the perfectly ordered material. We also propose that a simple and original mechanism, involving these defects, may be responsible for the existence and anomalous characteristics of the incommensurate phases observed in insulating perovskites.

Anomalous properties in ferroelectrics induced by atomic ordering

Complex insulating perovskite alloys are of considerable technological interest because of their large dielectric and piezoelectric responses. Examples of such alloys include (Ba1-xSrx)TiO3, which has emerged as a leading candidate dielectric material for the memory-cell capacitors in dynamic random access memories; and Pb(Zr1-xTix)O3 (PZT), which is widely used in transducers and actuators. The rich variety of structural phases that these alloys can exhibit, and the challenge of relating their anomalous properties to the microscopic structure, make them attractive from a fundamental point of view. Theoretical investigations of modifications to the atomic ordering of these alloys suggest the existence of further unexpected structural properties and hold promise for the development of new functional materials with improved electromechanical properties. Here we report ab initio calculations that show that a certain class of atomic rearrangement should lead simultaneously to large electromechanical responses and to unusual structural phases in a given class of perovskite alloys. Our simulations also reveal the microscopic mechanism responsible for these anomalies.

Ab initio design of perovskite alloys with predetermined properties: the case of Pb(Sc(0.5)Nb(0.5))O(3)

A first-principles derived approach is combined with the inverse Monte Carlo technique to determine the atomic orderings leading to prefixed properties in Pb(Sc(0.5)Nb(0.5))O(3) perovskite alloy. We find that some arrangements between Sc and Nb atoms result in drastic changes with respect to the disordered material, including ground states of new symmetries, large enhancement of electromechanical responses, and considerable shift of the Curie temperature. We discuss the microscopic mechanisms responsible for these unusual effects.

Polarization rotation via a monoclinic phase in the piezoelectric 92% PbZn(1/3)Nb(2/3)O3-8% PbTiO3

The origin of ultrahigh piezoelectricity in the relaxor ferroelectric PbZn(1/3)Nb(2/3)O3-PbTiO3 was studied with an electric field applied along the [001] direction. The zero-field rhombohedral R phase starts to follow the direct polarization path to tetragonal symmetry via an intermediate monoclinic M phase, but then jumps irreversibly to an alternate path involving a different type of monoclinic distortion. Details of the structure and domain configuration of this novel phase are described. This result suggests that there is a nearby R-M phase boundary as found in the Pb(Ti,Zr)O3 system.