An accurate estimate of the ferroelectric polarization in ferroelectric-dielectric stacks is important from a materials science perspective, and it is also crucial for the development of ferroelectric based electron devices. This paper revisits the theory and application of the PUND technique in Metal-Ferroelectric-Dielectric-Metal (MFDM) structures by using analytical derivations and numerical simulations. In an MFDM structure the results of the PUND technique may largely differ from the polarization actually switched in the stack, which in turn is different from the remnant polarization of the underlying ferroelectric. The main hindrances that prevent PUND measurements from providing a good estimate of the polarization switching in MFDM stacks are thus discussed. The inspection of the involved physical quantities, not always accessible in experiments, provides a useful insight about the main sources of the errors in the PUND technique, and clarifies the delicate interplay between the depolarization field and the charge injection and trapping in MFDM stacks with a thin dielectric layer.
Using the density functional theory calculations, we studied the ferroelectric, electrical and optical properties of series of bias-controllable endohedral fullerenes (TM@C28, TM= Ti-Ni). The important finding is that Cr@C28 has a large electric dipole moment and an appropriate bandgap (~1.2eV) as building blocks for ferroelectric-photovoltaic materials. By sandwiching Cr@C28 molecules between two van der Waals layers, e.g., graphene or transition metal dichalcogenides, the heterostructures may have exotic ferroelectric and photovoltaic properties with high tunability and performance.
We fabricated ultrathin ferroelectric/correlated electron oxide heterostructures composed of the ferroelectric Pb(Zr0.2Ti0.8)O3 and the correlated electron oxide (CEO) La0.8Sr0.2MnO3 on SrTiO3 substrates by pulsed laser epitaxy. The hole accumulation in the ultrathin CEO layer was substantially modified by heterostructuring with the ferroelectric layer, resulting in an insulator-metal transition. In particular, our thickness dependent study showed that drastic changes in transport and magnetic properties were strongly coupled to the modulation of charge carriers by ferroelectric field effect, …
A model for Metal-Ferroelectric-Metal structures with Schottky contacts is proposed. The model adapts the general theories of metal-semiconductor rectifying contacts for the particular case of metal-ferroelectric contact by introducing: the ferroelectric polarization as a sheet of surface charge located at a finite distance from the electrode interface; a deep trapping level of high concentration; the static and dynamic values of the dielectric constant. Consequences of the proposed model on relevant quantities of the Schottky contact such as built-in voltage, charge density and depletion widt…
We investigate magnetic domain wall (MDW) dynamics induced by applied electric fields in ferromagnetic-ferroelectric thin-film heterostructures. In contrast to conventional driving mechanisms where MDW motion is induced directly by magnetic fields or electric currents, MDW motion arises here as a result of strong pinning of MDWs onto ferroelectric domain walls (FDWs) via local strain coupling. By performing extensive micromagnetic simulations, we find several dynamical regimes, including instabilities such as spin wave emission and complex transformations of the MDW structure. In all cases, th…
Relaxor ferroelectrics are complex materials with distinct properties different from classic ferroelectrics. Probing frequency depended dielectric susceptibility is its trait. Other empirical laws build on classic ferroelectrics are still applicable to relaxor ferroelectrics. Here we report an abnormal improved dielectric in La doped relaxor ferroelectric 0.4PNN-0.6PHT, which deviated from the consistent variation relationship with piezoelectric coefficient. A mesoscale mechanism is proposed to reveal the origin of the improved dielectric response in 0.4PNN-0.6PHT, where the polar nanoregions …
We report on multiple fundamental qualitative improvements in the growth of improper ferroelectric hexagonal YMnO$_3$ (YMO) thin films and heterostructures by pulsed laser deposition (PLD). By a combination of pre-growth substrate annealing and low-energy-fluence PLD, we obtain a two-dimensional growth mode of the YMO films on yttria-stabilized zirconia (YSZ) with ultralow roughness and devoid of misoriented nanocrystalline inclusions. By inserting a sacrificial manganite layer capped with conducting indium-tin oxide between the substrate and the final film, the latter is grown in a fully latt…
A dielectric nonlinear response in model two-phase composites, prepared from a displacive ferroelectric material with a dominant dielectric response due to a single oscillator ferroelectric mode and a dielectric material, is characterized by the existence of new modes due to geometric resonances below the percolation threshold in the ferroelectric matrix. The geometric nature of oscilations depends on composition and geometric properties of the mixture. Generation of higher frequency modes is studied within our model and discussed for displacive ferroelectric materials of the $BaTiO_{3}$ type.…
We demonstrate that the magnetization of a ferromagnet in contact with an antiferromagnetic multiferroic (LuMnO3) can be speedily reversed by electric field pulsing, and the sign of the magnetic exchange bias can switch and recover isothermally. As LuMnO3 is not ferroelastic, our data conclusively show that this switching is not mediated by strain effects but is a unique electric-field driven decoupling of the ferroelectric and ferromagnetic domains walls. Their distinct dynamics are essential for the observed magnetic switching.
We report the ferroelectric property in Tb2Ti2O7 pyrochlore, prepared by a two-step solid-state reaction method. A concave P-E (polarisation vs electric field) loop observed from 382 K confirms ferroelectricity, below which the loop remains as pointed or banana-shaped. Dielectric plots clearly show an anomaly at 383 K and the magnetic data reveals a deviation from 380 K supporting the observed ferroelectric ordering. The origin of ferroelectricity in Tb2Ti2O7 is discussed which is due to the structural distortion in TiO6 octahedron.
We demonstrate a 2D ferroelectric heterostructure with monolayer MoSe$_2$ and CuInP$_2$S$_6$ (CIPS). In the heterostructure, the electric polarization of CIPS results in c electronic modulation in monolayer MoSe$_2$.
A new approach to all-optical detection and control of the coupling between electric and magnetic order on ultrafast timescales is achieved using time-resolved second harmonic generation (SHG) to study a ferroelectric (FE)/ferromagnet (FM) oxide heterostructure. We use femtosecond optical pulses to modify the spin alignment in a Ba$_{0.1}$Sr$_{0.9}$TiO$_{3}$(BSTO)/La$_{0.7}$Ca$_{0.3}$MnO$_{3}$ (LCMO) heterostructure and selectively probe the ferroelectric response using SHG. In this heterostructure, the pump pulses photoexcite non-equilibrium quasiparticles in LCMO, which rapidly interact with…
We calculate the pyrocoefficient, static dielectric susceptibility profiles and its thickness dependence of ferroelectric thin films. Also, the temperature dependences of above quantities have been calculated. For the calculations we use Landau phenomenological theory, leading to Lame equations. These equations subject to boundary conditions with different extrapolation length on the surfaces have been solved numerically. The divergency of pyroelectric coefficient and static dielectric susceptibility in the vicinity of thickness induced ferroelectric phase transition (i.e. at $l\approx l_c$ or…
An analysis of the dynamic dielectric and electro-optic relaxation response of thin film ferroelectrics is presented. The analysis is based upon the relaxation of ferroelectric domains with a continuous distribution of sizes given by percolation theory. The resulting temporal response is described by the expression (t^-m) exp(-(t/tau)^beta). The analysis was applied to KNbO3 thin films. Measurements of the polarization, birefringence and dielectric transients show qualitative agreement with the model over 11 orders of magnitude in time.
We report far-infrared dielectric properties of powder form ferroelectric SrTiO3. Terahertz time-domain spectroscopy (THz-TDS) measurement reveals that the low-frequency dielectric response of SrTiO3 is a consequence of the lowest transverse optical (TO) soft mode TO1 at 2.70 THz (90.0 1/cm), which is directly verified by Raman spectroscopy. This result provides a better understanding of the relation of low-frequency dielectric function with the optical phonon soft mode for ferroelectric materials. Combining THz-TDS with Raman spectra, the overall low-frequency optical phonon response of SrTiO…
Bulk photovoltaic (BPVE) effect in crystals lacking inversion symmetry offers great potential for optoelectronic applications due to its unique properties such as above bandgap photovoltage and switchable photocurrent. Because of their large spontaneous polarizations, ferroelectric materials are ideal platforms for studying BPVE. However, identifying the origin of experimentally observed photovoltaic response is often challenging due to the entanglement between bulk and interface effects, leading to much debate in the field. This issue is particularly pronounced in vertical heterostructures, w…
Quantum spin Hall (QSH) insulator materials feature topologically protected edge states that can drastically reduce dissipation and are useful for the next-generation electronics. However, the nonvolatile control of topological edge state is still a challenge. In this paper, based on first-principles calculations, the switchable topological states are found in the van der Waals (vdW) heterostructures consisting of two dimensional (2D) Bi(111) bilayer (BL) and α-In2Se3 by reversing the electric polarization of the ferroelectric α-In2Se3. The topological switching results from the different char…
Using Landau-Ginzburg-Devonshire approach we calculated the equilibrium distributions of electric field, polarization and space charge in the ferroelectric-semiconductor heterostructures containing proper or incipient ferroelectric thin films. The role of the polarization gradient and intrinsic surface energy, interface dipoles and free charges on polarization dynamics are specifically explored. The intrinsic field effects, which originated at the ferroelectric-semiconductor interface, lead to the surface band bending and result into the formation of depletion space-charge layer near the semic…
We have proposed the phenomenological description of dielectric hysteresis loops in ferroelectric semiconductors with charged defects and prevailing extrinsic conductivity. Exactly we have modified Landau-Ginsburg approach and shown that the macroscopic state of the aforementioned inhomogeneous system can be described by three coupled equations for three order parameters. Both the experimentally observed coercive field values well below the thermodynamic one and the various hysteresis loop deformations (constricted and double loops) have been obtained in the framework of our model. The obtaine…
Novel phenomena appear when two different oxide materials are combined together to form an interface. For example, at the interface of LaAlO3/SrTiO3, two dimensional conductive states form to avoid the polar discontinuity and magnetic properties are found at such interface. In this work, we propose a new type of interface between two nonmagnetic and nonpolar oxides that could host a conductive state with magnetic properties, where it is the ferroelectric polarization discontinuity instead of the polar discontinuity that leads to the charge transfer, forming the interfacial conductive or magnet…
Recently, based on the phase-field modeling, it was predicted that Hf1-xZrxO2 (HZO) exhibits the morphotropic phase boundary (MPB) in its compositional phase diagram. Here, we investigate the effect of structural changes between tetragonal (t) and orthorhombic (o) phases on the ferroelectric and dielectric properties of HZO films to probe the existence of MPB region. The structural analysis show that by adjusting the ozone dosage during the atomic layer deposition process and annealing conditions, different ratios of t- to o-phases (f_(t/o) ) were achieved which consequently affect the ferroel…
Ferroelectric domain structure evolution induced by an external electric field was investigated by means of nematic liquid crystal (NLC) method in two strontium-barium niobate single crystals of nominal composition: Sr_{0.70}Ba_{0.30}Nb_{2}O_{6} (SBN:70 - relaxor) and Sr_{0.26}Ba_{0.74}Nb_{2}O_{6} (SBN:26 - ferroelectric). Our results provide evidence that the broad phase transition and frequency dispersion that are exhibited in SBN:70 crystal have a strong link to the configuration of ferroelectric microdomains. The large leakage current revealed in SBN:26 may compensate internal charges acti…
Lead-free Ba0.85Ca0.15Zr0.10Ti0.90O3 (BCZT) ceramics have demonstrated excellent dielectric, ferroelectric and piezoelectric properties in comparison to lead-based materials. The synthesis of pure and crystalline BCZT nanopowders at low temperatures of 25, 80 and 160 C was reported previously by using a sol-gel method followed by a hydrothermal route. In this study, the structural, dielectric and ferroelectric properties of sintered BCZT ceramics at 1250 °C for 10h were investigated. XRD measurements revealed the presence of a single perovskite phase at room temperature with the coexistence of…
The origin of the functional properties of complex oxide superlattices can be resolved using time-resolved synchrotron x-ray diffraction into contributions from the component layers making up the repeating unit. The CaTiO3 layers of a CaTiO3/BaTiO3 superlattice have a piezoelectric response to an applied electric field, consistent with a large continuous polarization throughout the superlattice. The overall piezoelectric coefficient at large strains, 54 pm/V, agrees with first-principles predictions in which a tetragonal symmetry is imposed on the superlattice by the SrTiO3 substrate.
CuCrS2, a Heisenberg antiferromagnet with layered edge sharing triangular lattice, exhibits a spiral magnetic order. Dielectric (E) and polarization studies show magnetoelectric (ME) coupling at Neel temperature (T_N=38 K) where simultaneous dielectric and magnetic long range order occur. The compound shows a diffused ferroelectric (FE) transition and slow relaxation dynamics above T_N, indicative of relaxor FE behavior. Interestingly, memory effect and magnetic field induced rejuvenation are also observed in E, establishing cooperative glassy dynamics and ME coupling even above T_N. We discus…
The direct magnetoelectric (ME) effect resulting from the polarization changes induced in a ferroelectric film by the application of a magnetic field to a ferromagnetic substrate is described using the nonlinear thermodynamic theory. It is shown that the ME response strongly depends on the initial strain state of the film. The ME polarization coefficient of the heterostructures involving Terfenol-D substrates and compressively strained lead zirconate titanate (PZT) films, which stabilize in the out-of-plane polarization state, is found to be comparable to that of bulk PZT/Terfenol-D laminate c…
New relaxor ferroelectric system has been synthesized. BLTN exhibits a smeared maximum of permittivity, characteristic of classic relaxor behaviour, with a peak shift from 185 K at 100 Hz to 300 K at 1 GHz. BNTN undergoes a first order ferroelectric phase transition at 389 K and BLNTN exhibits both a ferroelectric phase transition at 274 K and relaxor behaviour at higher temperatures.
The effective barrier height between an electrode and a ferroelectric (FE) depends on both macroscopic electrical properties and microscopic chemical and electronic structure. The behavior of a prototypical electrode/FE/electrode structure, Pt/BaTiO3/Nb-doped SrTiO3, under in-situ bias voltage is investigated using X-Ray Photoelectron Spectroscopy. The full band alignment is measured and is supported by transport measurements. Barrier heights depend on interface chemistry and on the FE polarization. A differential response of the core levels to applied bias as a function of the polarization st…
Phase transition between ferroelectricity and quantum paraelectricity via non-thermal tuning parameters can lead to quantum critical behavior and associated emergent phenomena. Ferroelectric quantum critical systems are, however, rare despite the abundance of ferroelectric materials. Here, we show theoretically that in ferroelectric-paraelectric heterostructures, it is plausible to induce quantum paraelectricity where the quantum temperature (i.e., the temperature below with the onset of ferroelectricity is suppressed by quantum fluctuations) can be tuned by the thickness ratio. This, in turn,…
By performing density functional theory (DFT) and Green's functions calculations, complemented by X-ray Photoemission Spectroscopy, we investigate the electronic structure of Fe/GeTe(111), a prototypical ferromagnetic/Rashba-ferroelectric interface. We reveal that such system exhibits several intriguing properties resulting from the complex interplay of exchange interaction, electric polarization and spin-orbit coupling. Despite a rather strong interfacial hybridization between Fe and GeTe bands, resulting in a complete suppression of the surface states of the latter, the bulk Rashba bands are…
We have studied ferroelectricity and photovoltaic effects in atomic layer deposited (ALD) 40-nm thick SnTiO$_{x}$ films deposited directly onto p-type (001)Si substrate. These films showed well-saturated, square and repeatable hysteresis loops with remnant polarization of 1.5 $μ$C/cm$^{2}$ at room temperature, as detected by out-of-plane polarization versus electric field (P-E) and field cycling measurements. A photo-induced enhancement in ferroelectricity was also observed as the spontaneous polarization increased under white-light illumination. The ferroelectricity exhibits relaxor character…
The nanodomain pattern in ferroelectric/dielectric superlattices transforms to a uniform polarization state under above-bandgap optical excitation. X-ray scattering reveals a disappearance of domain diffuse scattering and an expansion of the lattice. The reappearance of the domain pattern occurs over a period of seconds at room temperature, suggesting a transformation mechanism in which charge carriers in long-lived trap states screen the depolarization field. A Landau-Ginzburg-Devonshire model predicts changes in lattice parameter and a critical carrier concentration for the transformation.
A series of Pb-free ferroelectric materials Ba0.9Sr0.1Ti1-xSnxO3 (BSTS-x) with 0 < x < 0.15 was successfully prepared via solid-state reaction method. The effect of Sn substitution on the crystal structure, microstructure, dielectric behavior, ferroelectric and tunable features of BSTS-x ceramics were systematically investigated. Room temperature (RT) x-ray diffraction (XRD) analysis using the Rietveld refinement method reveals that all the synthesized BSTS-x ceramics were well crystallized into single perovskite structure. The results show a tetragonal phase for 0.00 < x < 0.02, which evolves…
Heterostructures consisting of PbZr0.2Ti0.8O3 and PbZr0.4Ti0.6O3 films grown on a SrTiO3 (100) substrate with a SrRuO3 bottom electrode were prepared by pulsed laser deposition. Using the additional interface provided by the ferroelectric bilayer structure and changing the sequence of the layers, the dislocation content and domain patterns were varied. The resulting microstructure was investigated by transmission electron microscopy. Macroscopic ferroelectric measurements have shown a large impact of the formation of dislocations and the a/c domain structure on the ferroelectric polarization a…
Within the modified model of proton ordering of one-dimensional ferroelectric having hydrogen bonds of PbHPO$_4$-type, their thermodynamic and dynamic characteristics are studied and calculated taking into account the linear (by crystal deformations $\varepsilon_i$ ($i=1,3$) and $\varepsilon_4$) contributions into the energy of a proton system but without taking into account the tunneling in the two-particle cluster approximation. There has been obtained a good quantitative description of the temperature dependence of polarization, static dielectric permittivity, heat capacity and frequency de…
A method for the calculation of the temperature dependence of dielectric and piezoelectric responses, based on the use of a first-principles effective Hamiltonian, is described. Results are presented for the ferroelectric perovskite PbTiO3. While the method includes only the soft-mode contributions to the responses, it is argued to give a good description of the divergences or near-divergences of the response functions near the cubic-tetragonal transition. The expression of the response functions in terms of correlation functions is used to provide a real-space interpretation of the responses …
The radiofrequency dielectric response of the lead-free Ba(Zr$_{0.5}$Ti$_{0.5}$)O$_3$ relaxor ferroelectric is simulated using a coarse-grained Hamiltonian. This concept, taken from Real-Space Renormalization Group theories, allows depicting the collective behavior of correlated local modes gathered in blocks. Free-energy barriers for their thermally activated collective hopping are deduced from this {\it ab-initio}-based approach, and used as input data of Kinetic Monte Carlo simulations. The resulting numerical scheme allows to simulate the dielectric response for external field frequencies …
Large Rashba effect efficiently tuned by an external electric field is highly desired for spintronic devices. Using first-principles calculations, we demonstrate that large Rashba splitting is locked at conduction band minimum in ferroelectric Bi(Sc/Y/La/Al/Ga/In)O3/PbTiO3 heterostructures where the position of Fermi level is precisely controlled via its stoichiometry. Fully reversible Rashba spin texture and drastic change of Rashba splitting strength with ferroelectric polarization switching are realized in the symmetric and asymmetric heterostructures, respectively. By artificially tuning t…
The structural, dielectric and ferroelectric properties of lead-free (Na0.5-xKxBi0.5-xLax)TiO3 powders synthesized by sol-gel self-combustion method were investigated. Rietveld refinement of Synchrotron x-ray diffraction data confirms pure single phase rhombohedral crystal structure with R3c space group for all the compositions and anti-phase octahedral tilting angle decreased with increase in composition x. Homogeneity and elemental proportions were confirmed by Energy dispersive x-ray spectrometry. The temperature-dependent dielectric study has shown two diffuse type of dielectric anomaly fo…
It has been considered that polar nanoregions in relaxors form at Burns temperature Td approx 600 K. High-temperature dielectric investigations of Pb(Mg1/3Nb2/3)O3 (PMN) and 0.7PMN-0.3PbTiO3 reveal, however, that the dielectric dispersion around 600 K appears due to the surface-layer contributions. The intrinsic response, analyzed in terms of the universal scaling, imply much higher Td or formation of polar nanoregions in a broad temperature range, while high dielectric constants manifest that polar order exists already at the highest measured temperatures of 800 K. The obtained critical expon…
In thin film ferroelectric capacitor the chemical and electronic structure of the electrode/FE interface can play a crucial role in determining the kinetics of polarization switching. We investigate the electronic structure of a Pt/BaTiO3/SrTiO3:Nb capacitor using time-resolved photoemission spectroscopy. The chemical, electronic and depth sensitivity of core level photoemission is used to probe the transient response of different parts of the upper electrode/ferroelectric interface to voltage pulse induced polarization reversal. The linear response of the electronic structure agrees quantitat…
Magnetoelastic and magnetoelectric coupling in the artificial multiferroic heterostructures facilitate valuable features for device applications such as magnetic field sensors and electric write magnetic-read memory devices. In a ferromagnetic/ferroelectric heterostructures, the strain mediated coupling exploits piezoelectricity/electrostriction in ferroelectric phase and magnetostriction/piezomagnetism in ferromagnetic phase. Such verity of these combined effect can be manipulated by an external perturbation, such as electric field, temperature or magnetic field. Here, we demonstrate the remo…
We investigate the low temperature behaviour of Pb(In$_{1/2}$Nb$_{1/2}$)O$_{3}$-Pb(Mg$_{1/3}$Nb$_{2/3}$)O$_{3}$-PbTiO$_{3}$ using dielectric permittivity measurements. We compare single crystal plates measured in the [001] and [111] directions with a polycrystalline ceramic of the same composition. Poled crystals behave very differently to unpoled crystals, whereas the dielectric spectrum of the ceramic changes very little on poling. A large, frequency dependent dielectric relaxation seen in the poled [001] crystal around 100 K is much less prominent in the [111] crystal, and doesn't occur in …
The authors of paper commented claim that trimethylammonium tetrachlorozincate crystal shows at 282 K the ferroelectric-paraelectric phase transition. But no ferroelectric hysteresis loop was observed below this temperature. Moreover, in the low-temperature phase the ferroelectric domain walls should exist giving dielectric relaxation in a low frequency electric field. The authors conclude that the phase transition is of the second order. This conclusion is contrary to the DSC data where the phase transition has a strong first order character. In the whole measured temperature range the dielec…
Ferroelectric relaxors are complex materials with distinct properties. The understanding of their dielectric susceptibility, which strongly depends on both temperature and probing frequency, have interested researchers for many years. Here we report a macroscopic and phenomenological approach based on statistical modeling to investigate and better understand how the dielectric response of a relaxor depends on temperature. Employing the Maxwell-Boltzmann distribution and considering temperature dependent dipolar orientational polarizability, we propose a minimum statistical model and specific e…
Dielectric response as a function of frequency for high-permittivity dielectric and ferroelectric materials is discussed emphasizing the dynamic behaviour in the microwave and infrared range. After introducing the usual modelling of the polar phonon response and anharmonic hopping in locally dynamically disordered solids, including discussion of displacive and order-disorder ferroelectric phase transitions, we summarised the experimental data for selected ferroelectric, incipient ferroelectric and antiferroelectric perovskite ceramics (STO, BTO, BST, PZO), discussing the dielectric grain size …
In this paper, an efficient computational material design approach (cluster expansion) is employed for the ferroelectric $PbTiO_3$/$SrTiO_3$ system. Via exploring a conguration space including over $3 \times 10^6$ candidates, two special cation ordered configurations: either perfect or mixed 1/1 (101) superlattice, are identified with the mostly enhanced ferroelectric polarization by up to about 100% in comparison with the (001) superlattice. Analyzing these two special configurations reveals the exotic couplings between the antiferrodistortive distortion (AFD) and ferroelectric polarization (…
Dielectric, anelastic and ^139La NMR relaxation measurements have been made on the relaxor ferroelectric Pb(1-3x/2)La(x)Zr(0.2)Ti(0.8)O(3) (PLZT) with x = 0.22. The dielectric susceptibility exihibits the frequency dispersive maximum due to the freezing of the polar degrees of freedom around T ~250 K. The anelastic and especially NMR relaxation, besides this maximum, indicate an intense and broad component at lower temperatures, attributed to rotational modes of the O octahedra, weakly coupled to the polar modes. It is discussed why such short range rotational instabilities, known to occur in …
The polarization and strain response of ferroelectric materials at fields below the macroscopic coercive field is of a paramount importance for the operation of many electronic devices. The response of real ferroelectric and related materials is in general complex and difficult to interpret. The reason for this is that many processes in a ferroelectric material contribute to its properties, often concurrently. Examples include motion of ferroelectric and ferroelastic domains, presence of domains within domains, dynamics of different types of polar nano-entities, interaction of polar nano-entit…
We present here the results of frequency dependent dielectric, polarization and powder X-ray powder diffraction studies in the 300 to 100K temperature range for Ba_0.55Sr_0.45TiO_3. The dielectric results indicate a succession of three relaxor ferroelectric transitions accompanying the cubic to tetragonal to orthorhombic to rhombohedral phase transitions confirmed by XRD studies. Our results confirm the coexistence of the relaxor ferroelectric and ferroelectric behaviours.
