Coexistence of the phonon and relaxation soft modes in the terahertz dielectric response of tetragonal BaTiO3

Crossover from Linear to Quadratic Electro-optic Behavior in BaTiO_{3} and (Ba, Sr)TiO_{3} Solid Solution

We derive a numerical method based on coupled density functional theory and effective Hamiltonian schemes to calculate the linear and quadratic electro-optic response of ferroelectrics at finite temperature and in different frequency ranges. By applying the developed method to BaTiO_{3}, we successfully resolve apparent discrepancies in the experimental literature that reported a linear or quadratic electro-optic response when visible or terahertz radiation was employed to measure the optical index, respectively. We further demonstrate that (and explain why), in the case of the Ba_{1-x}Sr_{x}TiO_{3} disordered solid solutions, structural phase transitions not only lead to larger linear electro-optic constants, as previously demonstrated in the literature, but also significantly enhance the quadratic electro-optic constants.

Discovery of enhanced lattice dynamics in a single-layered hybrid perovskite

Layered hybrid perovskites exhibit emergent physical properties and exceptional functional performances, but the coexistence of lattice order and structural disorder severely hinders our understanding of these materials. One unsolved problem regards how the lattice dynamics are affected by the dimensional engineering of the inorganic frameworks and their interaction with the molecular moieties. Here, we address this question by using a combination of spontaneous Raman scattering, terahertz spectroscopy, and molecular dynamics simulations. This approach reveals the structural dynamics in and out of equilibrium and provides unexpected observables that differentiate single- and double-layered perovskites. While no distinct vibrational coherence is observed in double-layered perovskites, an off-resonant terahertz pulse can drive a long-lived coherent phonon mode in the single-layered system. This difference highlights the dramatic change in the lattice environment as the dimension is reduced, and the findings pave the way for ultrafast structural engineering and high-speed optical modulators based on layered perovskites.

Self-oscillatory instability of the driven phase front propagation induced by liberation of latent heat

We theoretically address crystals exhibiting first-order phase transformations subjected to a steadily propagating temperature gradient. The latter drives a nonisothermal propagation of a phase front. We theoretically demonstrate that for the phase transformations of the displacive type, the phase front always steadily follows the isotherm. In contrast, in the case of the order-disorder or hybrid phase transformations in a crystal containing pinning defects, one finds a velocity of the isotherm, the first critical velocity, at which the steady front motion becomes unstable, and a stick-slip front propagation starts. Upon reaching the second critical velocity, the stick-slip behavior vanishes, and the motion becomes steady again. Our results enable one to determine the activation energy of the leading order-disorder process from the measurements of the driven motion of the phase front. In light of these results, we discuss experimental findings for PbTiO_{3} and NaNbO_{3}.

Towards two-dimensional van der Waals ferroelectrics

The discovery of ferroelectricity in two-dimensional (2D) van der Waals (vdW) materials has brought important functionalities to the 2D materials family, and may trigger a revolution in next-generation nanoelectronics and spintronics. In this Perspective, we briefly review recent progress in the field of 2D vdW ferroelectrics, focusing on the mechanisms that drive spontaneous polarization in 2D systems, unique properties brought about by the reduced lattice dimensionality and promising applications of 2D vdW ferroelectrics. We finish with an outlook for challenges that need to be addressed and our view on possible future research directions.

Photovoltaic effect by soft phonon excitation

SignificanceThe quantum-mechanical geometric phase of electrons provides various phenomena such as the dissipationless photocurrent generation through the shift current mechanism. So far, the photocurrent generations are limited to above or near the band-gap photon energy, which contradicts the increasing demand of the low-energy photonic functionality. We demonstrate the photocurrent through the optical phonon excitations in ferroelectric BaTiO3 by using the terahertz light with photon energy far below the band gap. This photocurrent without electron-hole pair generation is never explained by the semiclassical treatment of electrons and only arises from the quantum-mechanical geometric phase. The observed photon-to-current conversion efficiency is as large as that for electronic excitation, which can be well accounted for by newly developed theoretical formulation of shift current.

Sub-THz Raman response in BaTiO3 and link with structural phase transition

The THz and sub-THz polarized Raman response was measured in tetragonal and cubic phases of single domain BaTiO₃ crystal. A large peak was detected at very low wavenumber, within a scattering geometry in which all phonon lines are Raman inactive. It lies below 700 GHz in the whole temperature range of the tetragonal phase, and is clearly distinct from the soft phonon band. This peak has relaxational behavior with a slowing down on approaching the phase transition from above and from below.

Crossover from Ferroelectric to Relaxor Behavior in Ba1-xCaxTiO3 (x = 0.17) System

The dielectric properties of Ba_1−xCa_xTiO₃ (x = 0.17) ceramics were studied in a wide frequency range of 20 Hz–53 GHz. Diffused ferroelectric phase transition was revealed close to 339 K in the dielectric properties of ceramics. The behaviour of distributions of relaxation times in vicinity of the ferroelectric phase transition temperature is also typical for order-disorder ferroelectric phase transition. However, at lower temperatures (below 200 K), the most probable relaxation increased according to the Arrhenius law. At lower temperatures the maximum of the imaginary part of dielectric permittivity versus temperature strongly shifted to higher temperatures when the frequency increased (from 125 K at 1.21 kHz to 300 K at 33 GHz). This behaviour was attributed to the dynamics of Ti ions. The origin of the crossover from ferroelectric to relaxor behaviour of Ba_1−xCa_xTiO₃ (x = 0.17) ceramics is discussed in the paper.

Terahertz refractive index matching solution

We report on the fabrication and characterisation of a terahertz (THz) refractive index matching solution (TeraSol) based on barium titanate (BaTiO₃) particles and benzocyclobutene (BCB). The high refractive index of BaTiO₃ in the THz range makes this material ideal for tuning the effective refractive index of the solution over a wide range. Exploiting the effective medium approximation, we are able to determine the concentration of BaTiO₃ particles necessary to obtain target refractive index values between n = 1.8 and n = 5, optimised to match those of substrates widely used in the THz. TeraSol can dramatically reduce the reflections from the substrate during measurements with THz time domain spectroscopy at cryogenic and room temperature. These properties make TeraSol an appealing material for anti-reflective coatings.

Ultrafast Structural Dynamics along the β-γ Phase Transition Path in MnAs

We investigate the orthorhombic distortion and the structural dynamics of epitaxial MnAs layers on GaAs(001) using static and time-resolved x-ray diffraction. Laser-induced intensity oscillations of Bragg reflections allow us to identify the optical phonon associated with orthorhombic distortion and to follow its softening along the path towards an undistorted phase of hexagonal symmetry. The frequency of this mode falls in the THz range, in agreement with recent calculations. Incomplete softening suggests that the β-γ transformation deviates from a purely second-order displacive transition.

Precursor Phenomena of Barium Titanate Single Crystals Grown Using a Solid-State Single Crystal Growth Method Studied with Inelastic Brillouin Light Scattering and Birefringence Measurements

The nature of precursor phenomena in the paraelectric phase of ferroelectrics is one of the main questions to be resolved from a fundamental point of view. Barium titanate (BaTiO₃) is one of the most representative perovskite-structured ferroelectrics intensively studied until now. The pretransitional behavior of BaTiO₃ single crystal grown using a solid-state crystal growth (SSCG) method was investigated for the first time and compared to previous results. There is no melting process in the SSCG method, thus the crystal grown using a SSCG method have inherent higher levels of impurity and defect concentrations, which is a good candidate for investigating the effect of crystal quality on the precursor phenomena. The acoustic, dielectric, and piezoelectric properties, as well as birefringence, of the SSCG-grown BaTiO₃ were examined over a wide temperature range. Especially, the acoustic phonon behavior was investigated in terms of Brillouin spectroscopy, which is a complementary technique to Raman spectroscopy. The obtained precursor anomalies of the SSCG-grown BaTiO₃ in the cubic phase were similar to those of other single crystals, in particular, of high-quality single crystal grown by top-seeded solution growth method. These results clearly indicate that the observed precursor phenomena are common and intrinsic effect irrespective of the crystal quality.

Stabilization of Polar Nanoregions in Pb-free Ferroelectrics

The formation of polar nanoregions through solid-solution additions is known to enhance significantly the functional properties of ferroelectric materials. Despite considerable progress in characterizing the microscopic behavior of polar nanoregions (PNR), understanding their real-space atomic structure and dynamics of their formation remains a considerable challenge. Here, using the method of dynamic pair distribution function, we provide direct insights into the role of solid-solution additions towards the stabilization of polar nanoregions in the Pb-free ferroelectric of Ba(Zr,Ti)O_{3}. It is shown that for an optimum level of substitution of Ti by larger Zr ions, the dynamics of atomic displacements for ferroelectric polarization are slowed sufficiently below THz frequencies, which leads to increased local correlation among dipoles within PNRs. The dynamic pair distribution function technique demonstrates a unique capability to obtain insights into locally correlated atomic dynamics in disordered materials, including new Pb-free ferroelectrics, which is necessary to understand and control their functional properties.

Dynamic Displacement Disorder of Cubic BaTiO_{3}

The three-dimensional distribution of the x-ray diffuse scattering intensity of BaTiO_{3} has been recorded in a synchrotron experiment and simultaneously computed using molecular dynamics simulations of a shell model. Together, these have allowed the details of the disorder in paraelectric BaTiO_{3} to be clarified. The narrow sheets of diffuse scattering, related to the famous anisotropic longitudinal correlations of Ti ions, are shown to be caused by the overdamped anharmonic soft phonon branch. This finding demonstrates that the occurrence of narrow sheets of diffuse scattering agrees with a displacive picture of the cubic phase of this textbook ferroelectric material. The presented methodology allows one to go beyond the harmonic approximation in the analysis of phonons and phonon-related scattering.

Ultrafast Electric Field Pulse Control of Giant Temperature Change in Ferroelectrics

There is a surge of interest in developing environmentally friendly solid-state-based cooling technology. Here, we point out that a fast cooling rate (≈10^{11}  K/s) can be achieved by driving solid crystals to a high-temperature phase with a properly designed electric field pulse. Specifically, we predict that an ultrafast electric field pulse can cause a giant temperature decrease up to 32 K in PbTiO_{3} occurring on few picosecond time scales. We explain the underlying physics of this giant electric field pulse-induced temperature change with the concept of internal energy redistribution: the electric field does work on a ferroelectric crystal and redistributes its internal energy, and the way the kinetic energy is redistributed determines the temperature change and strongly depends on the electric field temporal profile. This concept is supported by our all-atom molecular dynamics simulations of PbTiO_{3} and BaTiO_{3}. Moreover, this internal energy redistribution concept can also be applied to understand electrocaloric effect. We further propose new strategies for inducing giant cooling effect with ultrafast electric field pulse. This Letter offers a general framework to understand electric-field-induced temperature change and highlights the opportunities of electric field engineering for controlled design of fast and efficient cooling technology.

Emergent Berezinskii-Kosterlitz-Thouless Phase in Low-Dimensional Ferroelectrics

Using first-principles-based simulations merging an effective Hamiltonian scheme with scaling, symmetry, and topological arguments, we find that an overlooked Berezinskii-Kosterlitz-Thouless (BKT) phase sustained by quasicontinuous symmetry emerges between the ferroelectric phase and the paraelectric one of BaTiO_{3} ultrathin film, being under tensile strain. Not only do these results provide an extension of BKT physics to the field of ferroelectrics, but they also unveil their nontrivial critical behavior in low dimensions.

Microscopic origins of the large piezoelectricity of leadfree (Ba,Ca)(Zr,Ti)O3

In light of directives around the world to eliminate toxic materials in various technologies, finding lead-free materials with high piezoelectric responses constitutes an important current scientific goal. As such, the recent discovery of a large electromechanical conversion near room temperature in (1-x)Ba(Zr_0.2Ti_0.8)O₃-x(Ba_0.7Ca_0.3)TiO₃ compounds has directed attention to understanding its origin. Here, we report the development of a large-scale atomistic scheme providing a microscopic insight into this technologically promising material. We find that its high piezoelectricity originates from the existence of large fluctuations of polarization in the orthorhombic state arising from the combination of a flat free-energy landscape, a fragmented local structure, and the narrow temperature window around room temperature at which this orthorhombic phase is the equilibrium state. In addition to deepening the current knowledge on piezoelectricity, these findings have the potential to guide the design of other lead-free materials with large electromechanical responses.

Fluctuations and Topological Defects in Proper Ferroelectric Crystals

Homotopy theory and first-principles-based effective Hamiltonian simulations are combined to investigate the stability of topological defects in proper ferroelectric crystals. We show that, despite a nearly trivial topology of the order parameter space, these materials can exhibit stable topological point defects in their tetragonal polar phase and stable topological line defects in their orthorhombic polar phase. The stability of such defects originates from a novel mechanism of topological protection related to finite-temperature fluctuations of local dipoles.

Application of emitter-sample hybrid terahertz time-domain spectroscopy to investigate temperature-dependent optical constants of doped InAs

We investigate temperature-dependent carrier dynamics of InAs crystal by using reflection-type terahertz time-domain spectroscopy, particularly with a recently developed emitter-sample hybrid structure. We successfully obtain the optical conductivity in a terahertz frequency of bulk InAs whose dc conductivity is in the range of 100-150  Ω^-1 cm^-1. We find that both real and imaginary parts of the optical conductivity can be fit well with the simple Drude model, and the free-carrier density and the scattering rate obtained from the fit are in good agreement with corresponding values obtained by using other techniques, such as the Hall measurement and the dc-resistivity measurement. These results clearly demonstrate that the proposed technique of adopting the emitter-sample hybrid structure can be exploited to determine temperature-dependent optical constants in a reflection geometry and hence to investigate electrodynamics of bulk metallic systems.

Relaxor Ferroelectrics: Back to the Single-Soft-Mode Picture

The fluctuations of electric polarization in a disordered ferroelectric substance, relaxor crystal PbMg_{1/3}Nb_{2/3}O_{3} (PMN), were studied using a nonlinear inelastic light-scattering technique, hyper-Raman scattering, within a 5-100  cm^{-1} spectral interval and in a broad temperature range from 20 to 900 K. The split ferroelectric mode reveals a local anisotropy of up to about 400 K. Spectral anomalies observed at higher temperatures are explained as due to avoided crossing of the single primary polar soft mode with a temperature-independent, nonpolar spectral feature near 45  cm^{-1}, known from Raman scattering. The temperature changes of the vibrational modes involved in the measured fluctuation spectra of PMN were captured in a simple model that accounts for the temperature dependence of the dielectric permittivity as well. The observed slowing down of the relaxational dynamics directly correlates with the huge increase of the dielectric permittivity.

Subterahertz dielectric relaxation in lead-free Ba(Zr,Ti)O3 relaxor ferroelectrics

Relaxors are complex materials with unusual properties that have been puzzling the scientific community since their discovery. The main characteristic of relaxors, that is, their dielectric relaxation, remains unclear and is still under debate. The difficulty to conduct measurements at frequencies ranging from ≃1 GHz to ≃1 THz and the challenge of developing models to capture their complex dynamical responses are among the reasons for such a situation. Here, we report first-principles-based molecular dynamic simulations of lead-free Ba(Zr0.5Ti0.5)O3, which allows us to obtain its subterahertz dynamics. This approach reproduces the striking characteristics of relaxors including the dielectric relaxation, the constant-loss behaviour, the diffuse maximum in the temperature dependence of susceptibility, the substantial widening of dielectric spectrum on cooling and the resulting Vogel-Fulcher law. The simulations further relate such features to the decomposed dielectric responses, each associated with its own polarization mechanism, therefore, enhancing the current understanding of relaxor behaviour.

Frustration and Self-Ordering of Topological Defects in Ferroelectrics

A first-principles-based effective Hamiltonian technique is used to investigate the interplay between geometrical frustration and the ordering of topological defects in a ferroelectric nanocomposite consisting of a square array of BaTiO_{3} nanowires embedded in a Ba_{0.15}Sr_{0.85}TiO_{3} matrix. Different arrangements of the wires' chiralities geometrically frustrate the matrix, which in response exhibits point topological defects featuring self-assembled ordered structures spatially fluctuating down to the lowest temperatures. These fluctuations thereby endow the system with residual configurational entropy from which many properties characteristic of geometric frustration, such as the ground state degeneracy and the broadness of the dielectric response, are further found to originate.

Two-Dimensional Disorder in Black Phosphorus and Monochalcogenide Monolayers

Ridged, orthorhombic two-dimensional atomic crystals with a bulk Pnma structure such as black phosphorus and monochalcogenide monolayers are an exciting and novel material platform for a host of applications. Key to their crystallinity, monolayers of these materials have a 4-fold degenerate structural ground state, and a single energy scale EC (representing the elastic energy required to switch the longer lattice vector along the x- or y-direction) determines how disordered these monolayers are at finite temperature. Disorder arises when nearest neighboring atoms become gently reassigned as the system is thermally excited beyond a critical temperature Tc that is proportional to EC/kB. EC is tunable by chemical composition and it leads to a classification of these materials into two categories: (i) Those for which EC ≥ kBTm, and (ii) those having kBTm > EC ≥ 0, where Tm is a given material's melting temperature. Black phosphorus and SiS monolayers belong to category (i): these materials do not display an intermediate order-disorder transition and melt directly. All other monochalcogenide monolayers with EC > 0 belonging to class (ii) will undergo a two-dimensional transition prior to melting. EC/kB is slightly larger than room temperature for GeS and GeSe, and smaller than 300 K for SnS and SnSe monolayers, so that these materials transition near room temperature. The onset of this generic atomistic phenomena is captured by a planar Potts model up to the order-disorder transition. The order-disorder phase transition in two dimensions described here is at the origin of the Cmcm phase being discussed within the context of bulk layered SnSe.

Discovery of stable skyrmionic state in ferroelectric nanocomposites

Non-coplanar swirling field textures, or skyrmions, are now widely recognized as objects of both fundamental interest and technological relevance. So far, skyrmions were amply investigated in magnets, where due to the presence of chiral interactions, these topological objects were found to be intrinsically stabilized. Ferroelectrics on the other hand, lacking such chiral interactions, were somewhat left aside in this quest. Here we demonstrate, via the use of a first-principles-based framework, that skyrmionic configuration of polarization can be extrinsically stabilized in ferroelectric nanocomposites. The interplay between the considered confined geometry and the dipolar interaction underlying the ferroelectric phase instability induces skyrmionic configurations. The topological structure of the obtained electrical skyrmion can be mapped onto the topology of domain-wall junctions. Furthermore, the stabilized electrical skyrmion can be as small as a few nanometers, thus revealing prospective skyrmion-based applications of ferroelectric nanocomposites.

Ferroelectric-like metallic state in electron doped BaTiO3

We report that a ferroelectric-like metallic state with reduced anisotropy of polarization is created by the doping of conduction electrons into BaTiO3, on the bases of x-ray/electron diffraction and infrared spectroscopic experiments. The crystal structure is heterogeneous in nanometer-scale, as enabled by the reduced polarization anisotropy. The enhanced infrared intensity of soft phonon along with the resistivity reduction suggests the presence of unusual electron-phonon coupling, which may be responsible for the emergent ferroelectric structure compatible with metallic state.

Electronic properties of electrical vortices in ferroelectric nanocomposites from large-scale ab initio computations

An original ab initio procedure is developed and applied to a ferroelectric nanocomposite, in order to reveal the effect of electrical vortices on electronic properties. Such procedure involves the combination of two large-scale numerical schemes, namely, the effective Hamiltonian (to incorporate ionic degrees of freedom) and the linear-scaling three-dimensional fragment method (to treat electronic degrees of freedom). The use of such procedure sheds some light into the origin of the recently observed current that is activated at rather low voltages in systems possessing electrical vortices. It also reveals a novel electronic phenomena that is a systematic control of the type of the band-alignment (i.e., type I versus type II) within the same material via the temperature-driven annihilation/formation of electrical topological defects.

The role of mechanical boundary conditions in the soft mode dynamics of PbTiO3

The role of different mechanical boundary conditions in the soft mode dynamics of ferroelectric PbTiO3 is systematically investigated using first-principles-based simulations and analytical model. The change in the soft mode dynamics due to hydrostatic pressure, uniaxial and biaxial stresses and biaxial strains is studied in a wide temperature range. Our computations predict: (i) the existence of Curie-Weiss laws that relate the soft mode frequency to the stress or strain; (ii) a non-trivial temperature evolution of the associated Curie-Weiss constants; (iii) a qualitative difference between the soft mode response to stresses/strains and hydrostatic pressure. The latter finding implies that the Curie-Weiss pressure law commonly used for residual stress estimation may not apply for the cases of uniaxial and biaxial stresses and strains. On the other hand, our systematic study offers a way to eliminate this difficulty through the establishment of Curie-Weiss stress and strain laws. Implications of our predictions for some available experimental data are discussed.

Multiple soft-mode vibrations of lead zirconate

Polarized Raman, IR, and time-domain THz spectroscopy of orthorhombic lead zirconate single crystals have yielded a comprehensive picture of temperature-dependent quasiharmonic frequencies of its low-frequency phonon modes. It is argued that these modes primarily involve vibrations of Pb ions and librations of oxygen octahedra. Their relation to phonon modes of the parent cubic phase is proposed. Counts of the observed IR and Raman active modes belonging to distinct irreducible representations agree quite well with group-theory predictions. Analysis of the results yields insight into the phase transition mechanism, involving a soft ferroelectric branch coupled by a trilinear term to another two oxygen octahedra tilt modes.

Diffuse Scattering from Lead-Containing Ferroelectric Perovskite Oxides

Ferroelectric materials rely on some type of non-centrosymmetric displacement correlations to give rise to a macroscopic polarisation. These displacements can show short-range order (SRO) that is reflective of the local chemistry, and so studying it reveals important information about how the structure gives rise to the technologically useful properties. A key means of exploring this SRO is diffuse scattering. Conventional structural studies use Bragg peak intensitiesto determine the average structure. In a single crystal diffuse scattering (SCDS) experiment, the coherent scattered intensity is measured at non-integer Miller indices, and can be used to examine the population of local configurations. This is because the diffuse scattering is sensitive to two-body averages, whereas the Bragg intensity gives single-body averages. This review outlines key results of SCDS studies on several materials and explores the similarities and differences in their diffuse scattering. Random strains are considered, as are models based on a phonon-like picture or a more local-chemistry oriented picture. Limitations of the technique are discussed.

Effect of central mode on the dielectric tunability of ferroelectrics near room temperature: a first-principle-based study

First-principles-based effective Hamiltonian molecular dynamics simulations are performed to investigate GHz-THz dynamical properties of bulk and epitaxially strained film made of SrTiO3 near room temperature. Our simulations confirm the huge dielectric tunability recently observed in films. Moreover, universal phenomenological laws, with bulk-like parameters, are found to describe reasonably well the dielectric tunability-versus-dc electric field curves in both systems at low and high electric fields, except for the sole case of the STO film in the low-field regime. Such deviation originates from the presence of a central mode in this low-dimensional system. A revised equation, arising from an original analysis of the simulations, is proposed for modeling this latter situation.

Terahertz sensing using ferroelectric nanowires

Molecular dynamics simulations are used to study the interaction of ferroelectric nanowires with terahertz (THz) Gaussian-shaped pulses of electric field. The computational data indicate the existence of two interaction scenarios that are associated with 'lossless' and dissipative, or 'lossy', interaction mechanisms. A thermodynamical approach is used to analyze the computational data for a wide range of THz pulses. The analysis establishes the foundation for understanding the nanowires' response to the THz pulses and reveals the potential of ferroelectric nanowires to function as nanoscale sensors of THz radiation. Various aspects of this THz nanosensing are analyzed and discussed.

Novel complex phenomena in ferroelectric nanocomposites

A first-principles-based effective Hamiltonian is used to investigate finite-temperature properties of ferroelectric nanocomposites made of periodic arrays of ferroelectric nanowires embedded in a matrix formed by another ferroelectric material. Novel transitions and features related to flux-closure configurations are found. Examples include (i) a vortex core transition, that is characterized by the change of the vortex cores from being axisymmetric to exhibiting a 'broken symmetry'; (ii) translational mode of the vortex cores; (iii) striking zigzag dipolar chains along the vortex core axis; and (iv) phase-locking of ferroelectric vortices accompanied by ferroelectric antivortices. These complex phenomena are all found to coexist with a spontaneous electrical polarization aligned along the normal of the plane containing the vortices.

Atomistic molecular dynamic simulations of multiferroics

A first-principles-based approach is developed to simulate dynamical properties, including complex permittivity and permeability in the GHz-THz range, of multiferroics at finite temperatures. It includes both structural degrees of freedom and magnetic moments as dynamic variables in Newtonian and Landau-Lifshitz-Gilbert (LLG) equations within molecular dynamics, respectively, with the couplings between these variables being incorporated. The use of a damping coefficient and of the fluctuation field in the LLG equations is required to obtain equilibrated magnetic properties at any temperature. No electromagnon is found in the spin-canted structure of BiFeO3. On the other hand, two magnons with very different frequencies are predicted via the use of this method. The smallest-in-frequency magnon corresponds to oscillations of the weak ferromagnetic vector in the basal plane being perpendicular to the polarization while the second magnon corresponds to magnetic dipoles going in and out of this basal plane. The large value of the frequency of this second magnon is caused by static couplings between magnetic dipoles with electric dipoles and oxygen octahedra tiltings.

Finite-temperature properties of Ba(Zr,Ti)O3 relaxors from first principles

A first-principles-based technique is developed to investigate the properties of Ba(Zr,Ti)O(3) relaxor ferroelectrics as a function of temperature. The use of this scheme provides answers to important, unresolved and/or controversial questions such as the following. What do the different critical temperatures usually found in relaxors correspond to? Do polar nanoregions really exist in relaxors? If yes, do they only form inside chemically ordered regions? Is it necessary that antiferroelectricity develop in order for the relaxor behavior to occur? Are random fields and random strains really the mechanisms responsible for relaxor behavior? If not, what are these mechanisms? These ab initio based calculations also lead to deep microscopic insight into relaxors.

Broken local symmetry in paraelectric BaTiO3 proved by second harmonic generation

Precursor dynamics of a cubic to tetragonal ferroelectric phase transition in BaTiO3 is studied by the accurate measurement of the second harmonic generation (SHG) integral intensities. A finite signal holds for the SHG integrated intensity above the ferroelectric Curie temperature T(c)=403  K. Above the Burn's temperature T(d)≈580  K, the power law with the exponent γ=1 shows normal SHG nature originating from the hyper-Raman scattering by dynamical polar excitations, while, below T(d), a SHG signal from polar nanoregions becomes dominant with the larger exponent γ=2. Such a crossover of the power law exponent near T(d) is discussed on the basis of the effective Hamiltonian method and Monte Carlo simulation.

4-(cyanomethyl)anilinium perchlorate: a new displacive-type molecular ferroelectric

A new organic ferroelectric compound, 4-(cyanomethyl)anilinium perchlorate, proceeds a second-order phase transition from a paraelectric phase (P2(1)/m) to a ferroelectric phase (P2(1)) at 184 K. A perfect ferroelectric hysteresis loop was observed even at 10 KHz. It is the first example of a molecule-based organic ferroelectric whose polarization can be switched at such a high frequency. The temperature dependent second harmonic generation effect shows that the second-order nonlinear coefficient is nearly zero above T(c) and proportional to the spontaneous polarization below T(c), suggesting the occurrence of symmetry breaking, in good agreement with crystal structural determination. The origin of ferroelectricity was ascribed to the displacements of -NH(3)(+) cations and ClO(4)(-) anions from the symmetric positions including a small part of the order-disorder behaviors of the ClO(4)(-) anions.

The ferroelectric properties of Cd2Nb2O7: a Monte Carlo simulation study

The order–disorder contributions to the ferroelectric properties of Cd2Nb2O7(CNO) have been studied by Monte Carlo simulation of a 12-state modified Potts model on the pyrochlore lattice. Spin configurations obtained by these simulations are mapped to local Nb displacements. Secondary Cd displacements normal to the Nb displacement directions are considered as well. The model correctly reproduces diffuse scattering experimentally observed in CNO. A first-order phase transition is observed forkTp/J= 0.3891 (kis the Boltzmann constant,Tpis the model phase transition temperature andJis the interaction energy). To further adapt the model to the properties of CNO, coupling of local Nb displacements to theT2usoft mode is simulatedviathe addition of an appropriate field term in the model Hamiltonian. The critical temperatureTcof the soft mode is scaled tokTc/J= 0.3704. Similarities to experimental observations,i.e.the occurrence of stable domains with {100} boundaries, as well as spontaneous polarization along the cubic 〈100〉 and 〈110〉 directions, indicate thatTpcan be associated with the transition temperatureT1= 205 K in CNO. Frequency dispersion of the dielectric permittivity of CNO can be attributed to the low-frequency switching of correlated chains of Nb displacement that remain partially disordered in the temperature range between 195 and ∼100 K.

Correlations and local order parameter in the paraelectric phase of barium titanate

General features of the order parameter distribution in barium titanate in its paraelectric phase and in its ferroelectric phases (tetragonal and orthorhombic) are presented. The density of probability of the polarization [Formula: see text], defined by an average of the local order parameters over regions of various sizes and shapes (L(x) × L(y) × L(z)), is examined by molecular dynamics simulations using a first-principles derived effective Hamiltonian. The free energies [Formula: see text] associated with these probabilities are computed by thermodynamic integration. The evolution of these quantities are explained through the computation of pair correlations, which are found, as stated in several previous works, very anisotropic, 'needle-like', with longitudinal correlations ([Formula: see text]) having much longer range than transverse ones ([Formula: see text]). The correlations explain why the density of probability of the order parameter evolves from a multiple-peaked distribution with maxima along [111] (in the single cell), along [100] for small needle-like regions, towards a single-peaked distribution for larger regions. A useful expression in which the shape-dependence of the free energy is manifest is provided.

Dielectric, magnetic and structural properties of novel multiferroic Eu(0.5)Ba(0.5)TiO(3) ceramics

Dielectric properties of Eu(0.5)Ba(0.5)TiO(3) ceramics were investigated between 10 and 300 K in the frequency range of 1 MHz-100 THz. Permittivity exhibits a strong peak near the ferroelectric phase transition at 215 K. This is mainly due to softening of the lowest frequency polar phonon revealed in THz and infrared spectra. Dielectric relaxation was observed also below the ferroelectric soft mode frequency in the whole investigated temperature region, but it is probably caused by some defects such as Eu(3 + ) cations or oxygen vacancies. This implies that the ferroelectric phase transition has predominantly a displacive character. Raman scattering spectra revealed a lowering of crystal symmetry in the ferroelectric phase and XRD analysis indicated orthorhombic A2mm symmetry below 215 K. The magnetic measurements performed at various frequencies in the field cooled and field heating regime after cooling in zero magnetic fields excluded spin glass behavior and proved an antiferromagnetic order below 1.9 K in Eu(0.5)Ba(0.5)TiO(3).

Millimeter-wave dielectric properties of single-crystal ferroelectric and dielectric materials

Transmittance measurements on various single crystal ferroelectric and dielectric materials, BaTiO(3), SrTiO(3), LiNbO(3), LiTaO(3), (PbMg(1/3)Nb(2/3)O(3))0.73-(PbTiO(3))0.27, LaAlO(3), and Bi(4)Ge(3)O(12), over a broad millimeter-wave (MMW) frequency range have been performed. Frequency dependence of the complex dielectric permittivity has been measured in the MMW region using high-power sources for the first time, using a free-space, quasi-optical MMW spectrometer equipped with high-power backward wave oscillators (BWOs) as sources of coherent radiation, tunable in the range from 30 to 120 and 180 to 260 GHz. These results are compared with MMW permittivity of these materials obtained by other methods as well as to RF, microwave, and optical frequency permittivities for all the materials tested. The effects of both crystallographic orientation and quality of the surface polishing of the crystals have been examined. Uncertainties and possible sources of instrumentation and measurement errors related to the freespace MMW technique are discussed. This work demonstrates that precise MMW permittivity data can be obtained even on relatively small and thin crystals of different surface conditions and orientations using the high-power BWO-based quasioptical approach.

Microscopic insight into temperature-graded ferroelectrics

A microscopic approach based on the first-principles effective Hamiltonian is developed to study the polarization response in temperature-graded ferroelectrics. This approach has been applied to the case of (Ba(0.75)Sr(0.25))TiO₃ alloy. A comparison of the computational results with available experimental data attests to the remarkable accuracy of the present approach. Our computations reveal a strong anisotropy in the response of polarization to the temperature gradient (TG). In particular, the polarization offset along the direction of TG is an order of magnitude lower than in the perpendicular direction. The large as well as the small TGs are considered and found to yield qualitatively different polarization field responses. Among other striking findings are (i) the coexistence of different phases in chemically homogeneous regions, (ii) formation of low-symmetry phases, and (iii) thermally controlled polarization rotation.

Analysis of polarization behavior in relaxation of BaTiO₃-based ferroelectrics using wideband dielectric spectroscopy

Wideband dielectric spectra from the kilohertz to terahertz range are discussed for BaTiO₃-based ferroelectrics. Ceramics of BaTiO₃ (BT), Ba(0.6)Sr(0.4)TiO₃ (BST-0.6), and BaZr(0.25)Ti(0.75)O₃ (BZT-0.25) were selected as normal ferroelectrics, ferroelectrics with diffuse phase transition (DPT ferroelectrics), and relaxor ferroelectrics, respectively. The variation of ionic polarization in both BT and BST-0.6 ceramics with temperature could be explained by the softening of the soft phonon mode. In BZT-0.25, a permittivity anomaly at the dielectric maximum temperature (T(m)) at low frequencies is not attributed to the softening of the soft phonon mode, but originates from the permittivity derived from the dipole polarization (ϵ(dipole)). Relaxor behavior in BZT-0.25 is derived from the increase in the depression of ϵ(dipole) on cooling across the T(m) with increasing frequency. In dipole polarization, BT, BST- 0.6, and BZT-0.25 all exhibited a similar tendency of ϵ(dipole) above the Curie temperature (T(c)) and T(m). However, behavior of ϵ(dipole) below the T(c) can be explained by the ferroelectric domains in BT, whereas the variation of ϵ(dipole) below the Tm could be explained by growth process of polar nanoregions (PNRs) in BST-0.6 and BZT-0.25. Regarding this, BT can be distinguished from BST-0.6 and BZT-0.25. Relaxation in BT could be interpreted as successive change in polarization mechanism from normal ferroelectrics to relaxor ferroelectrics via DPT ferroelectrics.

A multiferroic material to search for the permanent electric dipole moment of the electron

We describe the first-principles design and subsequent synthesis of a new material with the specific functionalities required for a solid-state-based search for the permanent electric dipole moment of the electron. We show computationally that perovskite-structure europium barium titanate should exhibit the required large and pressure-dependent ferroelectric polarization, local magnetic moments and absence of magnetic ordering at liquid-helium temperature. Subsequent synthesis and characterization of Eu(0.5)Ba(0.5)TiO(3) ceramics confirm the predicted desirable properties.

Precursor polar clusters in the paraelectric phase of ferroelectric Ba₀.₈₀Ca₀.₂₀TiO₃ single crystals studied by Brillouin light scattering

A strong relaxation mode was observed in the gigahertz frequency window in the paraelectric phase of Ba₀.₈₀Ca₀.₂₀TiO₃ single crystals by using Brillouin light scattering. The appearance and growth of this relaxation mode were accompanied by substantial softening of the longitudinal acoustic mode as well as a remarkable increase in the hypersonic damping. Similar to BaTiO₃, the temperature dependence of the relaxation time of Ba₀.₈₀Ca₀.₂₀TiO₃ displayed a slowing-down behavior near the Curie temperature, indicating the order-disorder nature of the paraelectric-ferroelectric phase transition in this substance. The dynamics of precursor polar clusters observed in this work was discussed in relation with recent theoretical studies and found to be consistent with their predictions.

Evidence for strain-induced ferroelectric order in epitaxial thin-film KTaO3

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.

Broad-band dielectric spectroscopy and ferroelectric soft-mode response in the Ba(0.6)Sr(0.4)TiO(3) solid solution

Ceramic Ba(0.6)Sr(0.4)TiO(3) (BST-0.6) samples were studied in the broad spectral range of 10(6)-10(14) Hz by using several dielectric techniques in between 20 and 800 K. The dominant dielectric dispersion mechanism in the paraelectric phase was shown to be of strongly anharmonic soft-phonon origin. The whole soft-mode response in the vicinity of the ferroelectric transition was shown to consist of two coupled overdamped THz excitations, which show classical features of a coupled soft and central mode, known from many ferroelectric crystals with a dynamics near the displacive and order-disorder crossover. Similar behaviour has been recently revealed and theoretically simulated in pure BaTiO(3) (see Ponomareva et al 2008 Phys. Rev. B 77 012102 and Hlinka et al 2008 Phys. Rev. Lett. 101 167402). Also for the BST system, this feature was confirmed by the theory based on molecular dynamics simulations with an effective first-principles Hamiltonian. In all the ferroelectric phases, additional relaxation dispersion appeared in the GHz range, assigned to ferroelectric domain-wall dynamics. The microwave losses were analysed from the point of view of applications. The paraelectric losses above 1 GHz are comparable with those in single crystals and appear to be of intrinsic multi-phonon origin. The ceramic BST system is therefore well suited for applications in the whole microwave range.