Ferroelectric Distortion Research Articles

Structural Disorder and Coherence across the Phase Transitions of Lead-Free Piezoelectric Bi0.5K0.5TiO3

Relaxor ferroelectrics exhibit superior properties for converting mechanical energy into electrical energy, and vice versa, but the structural disorder hampers an understanding of structure–property relationships and impedes rational design of new, lead-free materials. Bi0.5K0.5TiO3 (BKT) is a prototypical lead-free relaxor ferroelectric, but the microscopic origins of polarization, nature of the ferroelectric transition (TC), and structural changes across the tetragonal to pseudocubic transition (T2) are poorly understood. Here the local and intermediate structure of BKT is studied from room temperature to above TC by pair distribution functions (PDFs) from synchrotron X-ray total scattering experiments and complemented by ab initio molecular dynamics (AIMD) simulations. The local structure varies smoothly across T2 as well as TC, in contrast to the abrupt changes at TC inferred from conventional diffraction. Ferroelectric distortions are larger on the local scale than in the average structure, with polar Ti4+ displacements prevailing above TC. We find that local polar regions partly cancel each other below TC, while completely averaging out above, implying that BKT goes through a transition from partial to complete disorder across TC.

High-throughput density functional calculations to optimize properties and interfacial chemistry of piezoelectric materials

High-throughput density functional theory calculations are conducted to search through 1572 $AB{\mathrm{O}}_{3}$ compounds to find a potential replacement material for lead zirconate titanate (PZT) that exhibits the same excellent piezoelectric properties as PZT and lacks both its use of the toxic element lead (Pb) and the formation of secondary alloy phases with platinum (Pt) electrodes. The first screening criterion employed a search through the Materials Project database to find $A\ensuremath{-}B$ combinations that do not form ternary compounds with Pt. The second screening criterion aimed to eliminate potential candidates through first-principles calculations of their electronic structure, in which compounds with a band gap of 0.25 eV or higher were retained. Third, thermodynamic stability calculations were used to compare the candidates in a Pt environment to compounds already calculated to be stable within the Materials Project. Formation energies below or equal to 100 meV/atom were considered to be thermodynamically stable. The fourth screening criterion employed lattice misfit to identify those candidate perovskites that have low misfit with the Pt electrode and high misfit of potential secondary phases that can be formed when Pt alloys with the different $A$ and $B$ components. To aid in the final analysis, dynamic stability calculations were used to determine those perovskites that have dynamic instabilities that favor the ferroelectric distortion. Analysis of the data finds three perovskites warranting further investigation: $\mathrm{CsNb}{\mathrm{O}}_{3}, \mathrm{RbNb}{\mathrm{O}}_{3}$, and $\mathrm{CsTa}{\mathrm{O}}_{3}$.

Stabilization of E -type magnetic order caused by epitaxial strain in perovskite manganites

The magnetism and spin-induced ferroelectricity of perovskite $R{\mathrm{MnO}}_{3}$ ($R=\text{La}$-Lu) epitaxial films grown on ${\mathrm{YAlO}}_{3}$ substrate have been investigated by means of first-principles density-functional-theory calculations. We show that the epitaxial strain leads to an $E$-type magnetic ground state for all of the rare-earth manganites, which explains the large ferroelectric polarization observed in ${R\mathrm{MnO}}_{3}$ ($R=\text{Gd}$-Lu) epitaxial films. The transition of the ground state from the $A$-type or spiral antiferromagnetic phase to the $E$-type phase can be attributed mainly to the significant weakening of ferromagnetism in the in-plane nearest-neighbor exchange interaction, which changes from ferromagnetic to antiferromagnetic with the increase of $R$ ionic radius. The enhancement of Jahn-Teller distortion caused by the epitaxial strain plays an important role in the change of exchange interactions. The predicted $E$-type phase in strained films for larger $R$ ions ($R=\text{La}$-Dy) can greatly improve the ferroelectric polarization. However, for the smaller $R$ ions ($R=\text{Ho}$-Lu) whose ground state of the bulk is the $E$-type phase, the ferroelectric polarization of strained films is slightly reduced compared to the bulks, resulting from the competition between the opposite trends of electronic and ion polarization. The ferroelectric distortion caused by the magnetostriction effect is enhanced by the epitaxial strain, while the polarization induced by the pure electronic mechanism is significantly suppressed. The introduction of Coulomb repulsion $U$ in the calculations overestimates the tendency of exchange interactions toward ferromagnetism, leading to the incorrect ground states.

Ligand-induced symmetry breaking, size and morphology in colloidal lead sulfide QDs: from classic to thiourea precursors

Colloidal lead chalcogenide quantum dots (CQDs) exhibit promising optoelectronic properties for applications in solar cell devices and as thermoelectrics. Herein, we report and discuss a ferroelectric structural distortion, at the picometer scale resolution, in PbS CQDs prepared using both classic and new synthetic pathways. The investigation was performed using synchrotron X-ray total scattering data and advanced methods of analysis that rely on a homo-core-shell model and evaluate the atomic arrangement, stoichiometry, size and morphology of nanocrystals. The CQDs show comparable size-dependent relative elongation, up to 0.7 % of one body diagonal of the cubic rock-salt structure, which corresponds to a rhombohedral lattice deformation. The findings suggest a joint role for the oleate ligands (which induce surface tensile strain) and the Pb(II) lone pair as the driving forces of the deformation. Pb displacements along the [111] direction, which provoke a ferrolectric distortion related to the lattice change, fall in the 0.0 – 0.1 Å. Overall, the findings suggest the local nature of the metal off-centering, leading to different average displacements which depend on the synthetic conditions.

Density functional theory based interfacial studies of ABO3/SrTiO3 (A = La, Y, Sc, B = Al, Ga) and its relation to polar catastrophe

We have studied the density functional theory of epitaxially strained ABO3 (A = La, Y, Sc, B = Al, Ga) films on SrTiO3 (001) crystals with SrO- and TiO-terminations to investigate polar catastrophe induced by the epitaxial thin film growth. Interfacial polar nature of the strained films depends on the type of cations. While lanthanum based perovskite films produces polarity based on the ionic nature of interfacial atoms, the smaller cations show rather opposite polarities arising from progressive ferroelectric structural distortion acting opposite to the polar nature of cation ions.

Unusual Metallic Multiferroic Transitions in Electron‐Doped PbTiO3

The coexistence of some materials which are normally in mutually exclusive states is attracting considerable attention as an intriguing means of obtaining nontrivial physical phenomena and unconventional multifunctional substances. Although single‐phase materials endowed with integrated ferroelectric, magnetic, and optical multifunctions hold promise for new technological paradigms, the mutually exclusive mechanisms within ferroelectricity, conductivity, and magnetism hinder the discovery of conducting multiferroics. Here, a new path toward metallic multiferroics is provided by theoretically demonstrating the possible compatible nature of ferroelectric distortion, free carriers, and magnetism in electron‐doped PbTiO3 using the hybrid Hartree–Fock density functional theories. Doping with electrons is found to induce metallic conductivity that coexists with and even enhances the ferroelectric distortion in PbTiO3, due to the unique lone‐pair ferroelectricity in this material. The injected excess electrons, in spin‐polarized states, interact with one another in the plane perpendicular to the polar direction, resulting in layer‐arranged ferromagnetism and multiferroics with nonlinear magnetoelectric coupling. These results indicate a means of circumventing conventional restrictions, leading to new types of multifunctional materials in which unusual multiferroic and conductive characteristics are simultaneously present.

Crystal symmetry and magnetism in Ti substituted Bi0.8Ba0.2FeO3 ceramic

The effect of Ti4+ substitution on the crystal structure and magnetic properties of the Bi0.8Ba0.2FeO3 ceramic nanoparticles was investigated. Bi0.8Ba0.2Fe1−xTixO3 (x=0, 0.05, 0.10, 0.15 and 0.20) ceramics have been prepared by tartaric acid modified sol-gel method. Rietveld refinement of the XRD profile pattern of Bi0.8Ba0.2FeO3 ceramic revealed the formation of pseudo-cubic (Pm3m) phase and confirms structural distortion on incorporation of Ti4+ ions, which consequently transform pseudo-cubic (Pm3m) structure to tetragonal (P4mm) structure. The saturation magnetization increases appreciably on Ti4+ ions substitution in Bi0.8Ba0.2FeO3 and is found to be 0.57emu/g for Bi0.8Ba0.2Fe0.95Ti0.05O3 ceramic. The increase in the magnetization by the substitution of non-magnetic Ti4+ ions has been ascribed to crystal structure modification made by the Ti4+ ions. However, a sudden decrease in the magnetization has been observed for Bi0.8Ba0.2Fe0.8Ti0.2O3 ceramic nanoparticles. The prominent Ti (3d) – O (2p) hybridization would stabilize the ferroelectric distortion and consequently reduce the magnetization. Scanning Electron Microscope (SEM) image of Bi0.8Ba0.2Fe0.8Ti0.2O3 ceramic sample revealed the formation of dense microstructure with uniform grains size.

Accuracy of first-principles interatomic interactions and predictions of ferroelectric phase transitions in perovskite oxides: Energy functional and effective Hamiltonian

While first-principles density functional theory (DFT)-based models have been effective in capturing the physics of ferroelectric phase transitions in ${\mathrm{BaTiO}}_{3}, {\mathrm{PbTiO}}_{3}$, and ${\mathrm{KNbO}}_{3}$, quantitative estimates of the transition temperatures (${T}_{C}$) suffer from errors that are believed to originate from the errors in estimating lattice constants obtained within the local density approximation (LDA) and generalized gradient approximation (GGA) of DFT. The recently developed strongly constrained and appropriately normed (SCAN) meta-GGA functional has been shown to be quite accurate in the estimation of lattice constants. Here, we present a quantitative analysis of the estimates of ferroelectric ground-state properties of eight perovskite oxides and transition temperatures of ${\mathrm{BaTiO}}_{3}, {\mathrm{PbTiO}}_{3}$, and ${\mathrm{KNbO}}_{3}$ obtained with molecular dynamics simulations using an effective Hamiltonian derived from the SCAN meta-GGA-based DFT. Relative to LDA, we find an improvement in the estimates of ${T}_{C}$, which arises from the changes in the calculated strain-phonon, anharmonic coupling constants, and strength of ferroelectric instabilities, i.e., frequencies of the soft modes. We also assess the errors in ${T}_{C}$ originating from approximately integrating out the high-energy phonons during construction of the model Hamiltonian through estimates of the effects of fourth-order couplings between the soft mode and higher-energy modes of ${\mathrm{BaTiO}}_{3}, {\mathrm{PbTiO}}_{3}$, and ${\mathrm{KNbO}}_{3}$. We find that inclusion of these anharmonic couplings results in deeper double-well energy functions of ferroelectric distortions and further improvement in the estimates of transition temperatures. Consistently improved estimates of lattice constants and transition temperatures with the SCAN meta-GGA calculations augur well for their use in simulations of superlattices or heterostructures of perovskite oxides, in which the effects of lattice matching are critical.

First-principles reinvestigation of bulk WO3

Using first-principles calculations, we analyze the structural properties of tungsten trioxide WO3 . Our calculations rely on density functional theory and the use of the B1-WC hybrid functional, which provides very good agreement with experimental data. The hypothetical high-symmetry cubic reference structure combines several ferroelectric and antiferrodistortive (antipolar cation motions, rotations and tilts of oxygen octahedra) structural instabilities. The instability related to antipolar W motions combines with those associated to oxygen rotations and tilts to produce the biggest energy reduction, yielding a P21/c ground state. This non-polar P21/c phase is only different from the experimentally reported Pc ground state by the absence of a very tiny additional ferroelectric distortion. The calculations performed on a stoichiometric compound so suggest that the low temperature phase of WO3 is not intrinsically ferroelectric and that the reported ferroelectric character might arise from extrinsic defects such as oxygen vacancies. Independently, we also identify never observed R3m and R3c ferroelectric phases with large polarizations and low energies close to the P 21/c ground state, which makes WO3 a potential antiferroelectric material. The relative stability of various phases is discussed in terms of the couplings between different structural distortions, highlighting a very complex interplay involving improper-like couplings up to fourth order in the energy expansion in the cubic phase.

Strain-tunable ferroelectricity and its control of Rashba effect in KTaO3

The effects of epitaxial strain on the ferroelectric, structural properties of KTaO3 are studied by means of first-principles calculations. We show that the ferroelectric polarization magnitude as well as the orientation can be tuned by an in-plane strain: the c-phase is energetically more stable than the aa-phase at a large compressive strain while a phase transition from c- to aa-phase is observed at a large tensile strain, owing to the significant polarization-strain coupling. More importantly, based on relativistic first-principles calculations, we demonstrate a large Rashba spin splitting in the strained KTaO3. Interestingly, the spin textures in momentum space can be controlled and switched via polarization switching. Our tight-binding analysis indicates that the combination of spin-orbit coupling and ferroelectric distortion plays a key role for the observed Rashba spin splitting. Our results present some fundamental understanding of the interplay between Rashba effect and ferroelectricity in oxides and open avenues for nonvolatile spintronic device applications.

Chemistry, growth kinetics, and epitaxial stabilization of Sn2+ in Sn-doped SrTiO3 using (CH3)6Sn2 tin precursor

PbTiO3-based ferroelectrics have impressive electroactive properties, originating from the Pb2+ 6s2 electron lone-pair, which cause large elastic distortion and electric polarization due to cooperative pseudo Jahn-Teller effect. Recently, tin-based perovskite oxide (SnTiO3) containing Sn2+ and a chemistry similar to that of the 6s2 lone-pair has been identified as a thermally stable, environmentally friendly substitute for PbTiO3-based ferroelectrics. However experimental attempts to stabilize Sn2+ on the A-site of perovskite ATiO3 have so far failed. In this work, we report on the growth of atomically smooth, epitaxial, and coherent Sn-alloyed SrTiO3 films on SrTiO3 (001) substrates using a hybrid molecular beam epitaxy approach. With increasing Sn concentration, the out-of-plane lattice parameter first increases in accordance with the Vegard’s law and then decreases for Sn(Sr+Ti+Sn) at. % ratio > 0.1 due to the incorporation of Sn2+ at the A-site. Using a combination of high-resolution X-ray photoelectron spectroscopy and density functional calculations, we show that while majority of Sn is on the B-site, there is a quantitatively unknown fraction of Sn being consistent with the A-site occupancy making SrTiO3 polar. A relaxor-like ferroelectric local distortion with monoclinic symmetry, induced by A-site Sn2+, was observed in Sn-doped SrTiO3 with Sn(Sr+Ti+Sn) at. % ratio = 0.1 using optical second harmonic generation measurements. The role of growth kinetics on the stability of Sn2+ in SrTiO3 is discussed.

Ferroelectric phase transition in multiferroic Ge1-x Mn x Te driven by local lattice distortions.

The evolution of local ferroelectric lattice distortions in multiferroic Ge1-x Mn x Te is studied by x-ray diffraction, x-ray absorption spectroscopy and density functional theory. We show that the anion/cation displacements smoothly decrease with increasing Mn content, thereby reducing the ferroelectric transition from 700 to 100 K at x = 0.5, where the ferromagnetic Curie temperature reaches its maximum. First principles calculations explain this quenching by different local bond contributions of the Mn 3d shell compared to the Ge 4s shell in excellent quantitative agreement with the experiments.

Atomistic simulation of trivalent ions doped in the hexagonal LuMnO3 ferroelectric phase

The interatomic potentials for multiferroic hexagonal LuMnO3 (h-LMO) in its ferroelectric (FE) phase was obtained for empirical fitting procedure and applied to study the effects of a series of trivalent metal and rare-earth dopants on its structural and ferroelectric distortions. The potential parameters found accurately reproduce lattice parameters (error below 0.3%), interatomic distances, pressure effect on the lattice parameters, and tilting angles of the MnO5 polyhedron. We investigated doping at Mn, Lu1 and Lu2 atom sites. It was found that the doped Mn atom site is the most energetically advantageous site for both the metal (Al, Ga, Fe and Cr) and rare-earth (La, Nb, Sm, Eu, Gd, Ho, Er, Yb, Y and Sc) atoms studied. The M-O3/O4 distances decrease when the Mn3+ ion site is doped by trivalent metal ions. The effects on the FE distortion of the material under doping and changes in the tilting angle of the M/MnO5 polyhedron were analyzed.

Comparative study of exchange-correlation functionals for accurate predictions of structural and magnetic properties of multiferroic oxides

We systematically compare predictions of various exchange correlation functionals for the structural and magnetic properties of perovskite ${\mathrm{Sr}}_{1\ensuremath{-}x}{\mathrm{Ba}}_{x}{\mathrm{MnO}}_{3} (0\ensuremath{\le}x\ensuremath{\le}1)$---a representative class of multiferroic oxides. The local spin density approximation (LSDA) and spin-dependent generalized gradient approximation with Perdew-Burke-Ernzerhof parametrization (sPBE) make substantial different predictions for ferroelectric atomic distortions, tetragonality, and ground state magnetic ordering. Neither approximation quantitatively reproduces all the measured structural and magnetic properties of perovskite ${\mathrm{Sr}}_{0.5}{\mathrm{Ba}}_{0.5}{\mathrm{MnO}}_{3}$. The spin-dependent generalized gradient approximation with Perdew-Burke-Ernzerhof revised for solids parametrization (sPBEsol) and the charge-only Perdew-Burke-Ernzerhof parametrized generalized gradient approximation with Hubbard $U$ and Hund's $J$ extensions both provide overall better agreement with measured structural and magnetic properties of ${\mathrm{Sr}}_{0.5}{\mathrm{Ba}}_{0.5}{\mathrm{MnO}}_{3}$, compared to LSDA and sPBE. Using these two methods, we find that different from previous predictions, perovskite ${\mathrm{BaMnO}}_{3}$ has large Mn off-center displacements and is close to a ferromagnetic-to-antiferromagnetic phase boundary, making it a promising candidate to induce effective giant magnetoelectric effects and to achieve cross-field control of polarization and magnetism.

Multiferroic crossover in perovskite oxides

Recently, the perovskite BiCoO$_3$ has been shown experimentally to be isostructural with PbTiO$_3$, while simultaneously the $d^6$ Co$^{3+}$ ion has a high spin ground state with $C$-type antiferromagnetic ordering. Using hybrid density functional calculations, we investigate the atomic, electronic and magnetic structure of BiCoO$_3$ to elucidate the origin of the multiferroic state. To begin with, we perform a qualitative trend sudy of the role of $d$ electrons in affecting the tendency for perovskite materials to exhibit a ferroelectric distortion; this work initially explores a qualitative trend study in artificial cubic and tetragonal LaBO$_3$ perovskites. We choose La as the A-cation so as to remove the effects of Bi $6s$ hybridization. Through first-principles calculations of the LaBO$_3$ series, where B is a $d^0 - d^8$ cation from the $3d$-block, the trend study reveals that increasing the $d$ orbital occupation initially removes the tendency for a polar distortion, as expected. However, for high spin $d^5-d^7$ and $d^8$ cations a strong ferroelectric instability is recovered. We explained this effect in terms of the pseudo Jahn-Teller theory for ferroelectricity. It is shown that, in some cases, unpaired electron spins actually drive ferroelectricity, rather than inhibit it, which represents a shift in the understanding of how ferroelectricity and magnetism interact in perovskite oxides. It follows, that for the case of BiCoO$_3$, the Co$^{3+}$ ion plays a major role in the ferroelectric lattice instability. Importantly, the ferroelectric polarization is greatly enhanced when the Co$^{3+}$ ion is in the high spin state, when compared to the nonmagnetic, low spin state, and a large coupling of the electrical and magnetic polarization is present. Importantly, it is demonstrated that the ground spin state is switched by reducing the internal ferroelectric polarization.

Structure–Curie temperature relationships inBaTiO3-based ferroelectric perovskites: Anomalous behavior of(Ba,Cd)TiO3from DFT, statistical inference, and experiments

One of the key impediments to the development of ${\mathrm{BaTiO}}_{3}$-based materials as candidates to replace toxic-Pb-based solid solutions is their relatively low ferroelectric Curie temperature (${T}_{C}$). Among many potential routes that are available to modify ${T}_{C}$, ionic substitutions at the Ba and Ti sites remain the most common approach. Here, we perform density functional theory (DFT) calculations on a series of $A{\mathrm{TiO}}_{3}$ and $\mathrm{Ba}B{\mathrm{O}}_{3}$ perovskites, where $A=\mathrm{Ba}$, Ca, Sr, Pb, Cd, Sn, and Mg and $B=\mathrm{Ti}$, Zr, Hf, and Sn. Our objective is to study the relative role of $A$ and $B$ cations in impacting the ${T}_{C}$ of the tetragonal ($P4mm$) and rhombohedral ($R3m$) ferroelectric phases in ${\mathrm{BaTiO}}_{3}$-based solid solutions, respectively. Using symmetry-mode analysis, we obtain a quantitative description of the relative contributions of various divalent ($A$) and tetravalent ($B$) cations to the ferroelectric distortions. Our results show that Ca, Pb, Cd, Sn, and Mg have large mode amplitudes for ferroelectric distortion in the tetragonal phase relative to Ba, whereas Sr suppresses the distortions. On the other hand, Zr, Hf, and Sn tetravalent cations severely suppress the ferroelectric distortion in the rhombohedral phase relative to Ti. In addition to symmetry modes, our calculated unit-cell volume also agrees with the experimental trends. We subsequently utilize the symmetry modes and unit-cell volumes as features within a machine learning approach to learn ${T}_{C}$ via an inference model and uncover trends that provide insights into the design of new high-${T}_{C}\phantom{\rule{4pt}{0ex}}{\mathrm{BaTiO}}_{3}$-based ferroelectrics. The inference model predicts ${\mathrm{CdTiO}}_{3}\ensuremath{-}{\mathrm{BaTiO}}_{3}$ solid solutions to have a higher ${T}_{C}$ and, therefore, we experimentally synthesized these solid solutions and measured their ${T}_{C}$. Although the calculated mode strength for ${\mathrm{CdTiO}}_{3}$ in the tetragonal phase is even larger than that for ${\mathrm{PbTiO}}_{3}$, the ${T}_{C}$ of ${\mathrm{CdTiO}}_{3}\ensuremath{-}{\mathrm{BaTiO}}_{3}$ solid solutions in the tetragonal phase does not show any appreciable enhancement. Thus, ${\mathrm{CdTiO}}_{3}\ensuremath{-}{\mathrm{BaTiO}}_{3}$ does not follow the inference model, which is based on established data and trends for $A{\mathrm{TiO}}_{3}$. Rather, our experimental phase diagram for ${\mathrm{CdTiO}}_{3}\ensuremath{-}{\mathrm{BaTiO}}_{3}$ suggests that it behaves markedly differently from any other ${\mathrm{BaTiO}}_{3}$-based systems studied so far.

First-principles approach to the dynamic magnetoelectric couplings for the non-reciprocal directional dichroism in BiFeO3**This manuscript has been written by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725 with the US Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish

Due to the complicated magnetic and crystallographic structures of BiFeO3, its magnetoelectric (ME) couplings and microscopic model Hamiltonian remain poorly understood. By employing a first-principles approach, we uncover all possible ME couplings associated with the spin-current (SC) and exchange-striction (ES) polarizations, and construct an appropriate Hamiltonian for the long-range spin-cycloid in BiFeO3. First-principles calculations are used to understand the microscopic origins of the ME couplings. We find that inversion symmetries broken by ferroelectric and antiferroelectric distortions induce the SC and the ES polarizations, which cooperatively produce the dynamic ME effects in BiFeO3. A model motivated by first principles reproduces the absorption difference of counter-propagating light beams called non-reciprocal directional dichroism. The current paper focuses on the spin-driven (SD) polarizations produced by a dynamic electric field, i.e. the dynamic ME couplings. Due to the inertial properties of Fe, the dynamic SD polarizations differ significantly from the static SD polarizations. Our systematic approach can be generally applied to any multiferroic material, laying the foundation for revealing hidden ME couplings on the atomic scale and for exploiting optical ME effects in the next generation of technological devices such as optical diodes.

Spectroscopic studies of the ferroelectric and magnetic phase transitions in multiferroic Sr1−xBaxMnO3

Dielectric response of perovskite Sr1−xBaxMnO3 (x = 0.43 and 0.45) ceramics was investigated using microwave, THz and infrared spectroscopic techniques in order to study the ferroelectric and antiferromagnetic phase transitions with critical temperatures TC ≈ 350 K and TN ≈ 200 K, respectively. The two lowest-frequency polar phonons are overdamped above TN and they exhibit pronounced softening on heating towards TC. Nevertheless, permittivity ε′ in the THz range shows only a small anomaly at TC because the phonon contribution to ε′ is rather small. The phonons are coupled with a central mode which provides the main contribution to the dielectric anomaly at TC. Thus, the ferroelectric phase transition has characteristics of a crossover from displacive to order–disorder type. At the same time, the intrinsic THz central peak is partially screened by conductivity and related Maxwell–Wagner relaxation, which dominates the microwave and lower-frequency spectra. Below TN, the ferroelectric distortion markedly decreases, which has an influence on the frequencies of both the central and soft modes. Therefore, ε′ in the THz range increases at TN on cooling. In spite of the strong spin–phonon coupling near TN, surprisingly no magnetodielectric effect was observed in the THz spectra upon applying magnetic field of up to 7 T, which is in contradiction with the theoretically expected huge magnetoelectric coupling. We explain this fact as due to the insensitivity of TN to magnetic field.

Analysis of polarization offsets observed for temperature-graded ferroelectric materials

A transverse Ising model in the framework of the mean field approximation is developed to analyze the polarization offsets phenomena in temperature-graded ferroelectric materials. A function of two-spin exchange interaction strength has been introduced to describe the ferroelectric distortion due to the distribution of temperature gradients in materials. Comparisons of the computational results with the experimental data reveal some fundamental factors in the formation of polarization offsets. It is shown that ferroelectric distortion has influenced much on polarization offsets in temperature-graded ferroelectric materials. When quantum fluctuation effect as well as ferroelectric distortion is considered, we have successfully reproduced the experimental observations qualitatively, especially for the indistinguishable polarization offsets from the background at small temperature gradients, which were not successfully reproduced in prior theoretical studies.

Bi deficiency-tuned functionality in multiferroic Bi1-δFe0.95Mn0.05O3 films.

Structural evolution and ferroelectric (FE)-to-antiferroelectric (AFE) transition behaviors were observed in Bi1-δFe0.95Mn0.05O3 (100)-textured films with a carefully controlled Bi deficiency concentration δ. Raman spectra revealed an orthorhombic structural transition induced by Mn substitution. The polarization-electric field hysteresis loops and capacitance-voltage loops of Bi1-δFe0.95Mn0.05O3 films clearly demonstrated antiferroelectric behavior with increasing δ. The responses of the domain structure of the Bi1-δFe0.95Mn0.05O3 film under positive and negative applied voltages directly suggested the coexistence of FE and AFE phases. The existence of (100) superstructure reflections and antiparallel displacements of the Bi atoms along the [100] direction observed by transmission electron microscopy unambiguously reveal the AFE phase. The chemical substitution-induced orthorhombic structural transition in BiFe0.95Mn0.05O3 film implies that as the δ concentration increases, the changes in Bi-O bonding and the stereochemical activity of Bi 6s lone pair affect both the ferroelectric distortion and the antiferrodistortive rotation and therefore drive the Bi1-δFe0.95Mn0.05O3 crystal lattice to form a PbZrO3-type orthorhombic phase with an AFE order. A continuing increase in Bi deficiency creates defect dipole complexes which produce an internal field leading to a preferred direction of the ferroelectric domain. The Bi deficiency in multiferroic BiFeO3 provides a new route by which to tune functionality.