Several defect configurations including oxygen vacancies have been investigated as possible origins of the reported room-temperature ferroelectricity of strontium titanate (STO) thin films [Appl. Phys. Letts. 91, 042908 (2007)]. First-principles calculations revealed that the Sr-O-O vacancy complexes create deep localized states in the band gap of SrTiO3 without affecting its insulating property. These results are in agreement with electronic structural changes determined from optical transmission and X-ray absorption measurements. This work opens the way to exploiting oxygen vacancies and their complexes as a source of ferroelectricity in perovskite oxide thin films, including STO.
We present a study of the local strain effects associated with vacancy defects in strontium titanate and report the first calculations of elastic dipole tensors and chemical strains for point defects in perovskites. The combination of local and long-range results will enable determination of x-ray scattering signatures that can be compared with experiments. We find that the oxygen vacancy possesses a special property -- a highly anisotropic elastic dipole tensor which almost vanishes upon averaging over all possible defect orientations. Moreover, through direct comparison with experimental mea…
We have used energy filtered x-ray photoelectron emission microscopy (XPEEM) and synchrotron radiation to measure the grain orientation dependence of the work function of a sintered niobium doped strontium titanate ceramic. A significant spread in work function values is found. Grain orientation and surface reducing/oxidizing conditions are the main factors in determining the work function. Energy filtered XPEEM looks ideally suited for analysis of other technologically interesting polycrystalline samples.
We demonstrate an approach for calculating temperature-dependent quantum and anharmonic effects with beyond density-functional theory accuracy. By combining machine-learned potentials and the stochastic self-consistent harmonic approximation, we investigate the cubic to tetragonal transition in strontium titanate and show that the paraelectric phase is stabilized by anharmonic quantum fluctuations. We find that a quantitative understanding of the quantum paraelectric behavior requires a higher-level treatment of electronic correlation effects via the random phase approximation. This approach e…
We investigated the ferroelectric properties of strontium titanate (STO) thin films deposited on SrTiO3 (001) substrate with SrRuO3 electrodes. The STO layer was grown coherently on the SrTiO3 substrate without in-plane lattice relaxation, but its out-of-plane lattice constant increased with a decrease in the oxygen pressure during deposition. Using piezoresponse force microscopy and P-V measurements, we showed that our tetragonal STO films possess room-temperature ferroelectricity. We discuss the possible origins of the observed ferroelectricity.
The surface composition of polycrystalline niobium-doped strontium titanate (SrTiO3 : Nb) is studied using X-ray photoelectron emission microscopy (XPEEM) for many grain orientations in order to characterise the surface chemistry with high spatial resolution. The surface sensitivity is maximised by the use of soft X-ray synchrotron radiation (SR). The grain orientation is determined by electron backscattering diffraction (EBSD). Stereographic plots are used to show the correlation between surface composition and orientation for several grains. Predominant surface terminations are assigned to m…
Monodispersed strontium titanate nanoparticles were prepared and studied in detail. It is found that ~10 nm as-prepared stoichiometric nanoparticles are in a polar structural state (with possibly ferroelectric properties) over a broad temperature range. A tetragonal structure, with possible reduction of the electronic hybridization is found as the particle size is reduced. In the 10 nm particles, no change in the local Ti-off centering is seen between 20 and 300 K. The results indicate that nanoscale motifs of SrTiO3 may be utilized in data storage as assembled nano-particle arrays in applicat…
The results of positron annihilation lifetime spectroscopy measurements on undoped, electron irradiated, and Nb doped SrTiO3 single crystals are reported. Perfect lattice and vacancy defect positron lifetimes were calculated using two different first-principles schemes. The Sr vacancy defect related positron lifetime was obtained from measurements on Nb doped, electron irradiated, and vacuum annealed samples. Undoped crystals showed a defect lifetime component dominated by trapping to Ti vacancy related defects.
The Landau theory of phase transitions of Ba0.8Sr0.2TiO3 thin film under external electric field applied in the planar geometry is developed. The interfacial van-der-Waals field Ez=1.1x10^8 V/m oriented normal to the film-substrate interface was introduced in to the model calculation to explain experimentally observed behavior of the polarization as a function of planar electric field. The Ez - misfit strain phase diagram of the film is constructed and discussed.
The magnetic and electronic properties of strontium titanate with different carbon dopant configurations are explored using first-principles calculations with a generalized gradient approximation (GGA) and the GGA+U approach. Our results show that the structural stability, electronic properties and magnetic properties of C-doped SrTiO3 strongly depend on the distance between carbon dopants. In both GGA and GGA+U calculations, the doping structure is mostly stable with a nonmagnetic feature when the carbon dopants are nearest neighbors, which can be ascribed to the formation of a C-C dimer pair…
Multiferroicity can be induced in strontium titanate by applying biaxial strain, resulting in the coexistence of both ferroelectric and antiferrodistortive domains. The magnitude and sign of the strain imposed on the lattice by design can be used to tune the phase transitions and interactions between these two phenomena. Using optical second harmonic generation, we report a transition from centrosymmetric 4/mmm phase to ferroelectric mm2, followed by an antiferrodistortive transition to a coupled ferroelastic-ferroelectric mm2 phase in a strontium titanate thin film strained in biaxial tension…
For many applications, it is important to measure the local work function of a surface with high lateral resolution. Low-energy electron microscopy is regularly employed to this end since it is, in principle, very well suited as it combines high-resolution imaging with high sensitivity to local electrostatic potentials. For surfaces with areas of different work function, however, lateral electrostatic fields inevitably associated with work function discontinuities deflect the low-energy electrons and thereby cause artifacts near these discontinuities. We use ray-tracing simulations to show tha…
Density functional theory calculations of twin-domain walls in strontium titanate are presented. The two possible domain walls are characterized. The domain wall type is set by the relative phase of the octahedral rotations in the body-centered-tetragonal SrTiO$_3$ on either side of the domain wall. The width of the domain walls is estimated to be approximately 3 nm.
Emphasizing the contribution of Professor Roger A Cowley, FRS to the Theory of Raman Scattering from crystals, the development of the Theory of Raman cattering since 1928 has been briefly discussed. Some experimental studies of Strontium Titanate using Inelastic Neutron Scattering, Raman Scattering, Electro- paramagnetic resonance measurement and X-ray & Gamma Ray techniques has been briefly discussed. Using Schwabl's semi-phenomenological theory for the soft mode and central peak, we have developed (a) a one-phonon Green's function exhibiting the three peaked structure and (b) a two phonon Gr…
We report an experimental demonstration of thermal tuning of resonance frequency in a planar terahertz metamaterial consisting of a gold split-ring resonator array fabricated on a bulk single crystal strontium titanate (SrTiO3) substrate. Cooling the metamaterial starting from 409 K down to 150 K causes about 50% shift in resonance frequency as compare to its room temperature resonance, and there is very little variation in resonance strength. The resonance shift is due to the temperature-dependent refractive index (or the dielectric constant) of the strontium titanate. The experiment opens up…
We present the first systematic {\em ab initio} study of anti-ferrodistortive (AFD) order in Ruddlesden-Popper (RP) phases of strontium titanate, Sr$_{1+n}$Ti$_n$O$_{3n+1}$, as a function of both compressive epitaxial strain and phase number $n$. We find all RP phases to exhibit AFD order under a significant range of strains, recovering the bulk AFD order as $\sim 1/n^2$. A Ginzburg-Landau Hamiltonian generalized to include inter-octahedral interactions reproduces our {\em ab initio} results well, opening a pathway to understanding other nanostructured perovskite systems.
We report self-consistent ab-initio electronic, structural, elastic, and optical properties of cubic SrTiO$_{3}$ perovskite. Our non-relativistic calculations employed a generalized gradient approximation (GGA) potential and the linear combination of atomic orbitals (LCAO) formalism. The distinctive feature of our computations stem from solving self-consistently the system of equations describing the GGA, using the Bagayoko-Zhao-Williams (BZW) method. Our results are in agreement with experimental ones where the later are available. In particular, our theoretical, indirect band gap of 3.24 eV,…
The surfaces of metal oxides often are reconstructed with a geometry and composition that is considerably different from a simple termination of the bulk. Such structures can also be viewed as ultrathin films, epitaxed on a substrate. Here, the reconstructions of the SrTiO3 (110) surface are studied combining scanning tunneling microscopy, transmission electron diffraction, and X-ray absorption spectroscopy, and analyzed with density functional theory calculations. While SrTiO3 (110) invariably terminates with an overlayer of titania, with increasing density its structure switches from nx1 and…
The dielectric properties of strontium titanate (SrTiO$_3$) have previously been reported from room temperature to low temperatures with conflicting results. In this work, precision measurement of the permittivity is undertaken by simultaneously measuring transverse electric and transverse magnetic resonant modes within a single crystal. It is unequivocally shown that the permittivity is isotropic at room temperature with a permittivity of order $316.3\pm2.2$ by measuring multiple modes of different electric field polarisations. As the crystal is cooled to 5 K and undergoes well known phase tr…
The local structure and oxidation state of the cobalt impurity in SrTiO$_3$ is studied by X-ray absorption fine structure (XAFS) spectroscopy. The synthesis conditions, under which cobalt predominantly (up to 76%) substitutes the atoms at the $A$ site of the perovskite structure, is found for SrTiO$_3$(Co) samples. By varying the synthesis conditions, it is possible to appreciably change the ratio between the concentrations of cobalt atoms incorporated into the $A$ and $B$ sites. It is established that the oxidation state of cobalt is +2 at the $A$ site and +3 at the $B$ site. It is revealed t…
Strontium titanate is a wide-gap semiconductor avoiding a ferroelectric instability thanks to quantum fluctuations. This proximity leads to strong screening of static Coulomb interaction and paves the way for the emergence of a very dilute metal with extremely mobile carriers at liquid-helium temperature. Upon warming, mobility decreases by several orders of magnitude. Yet, metallicity persists above room temperature even when the apparent mean-free-path falls below the electron wavelength. The superconducting instability survives at exceptionally low concentrations and beyond the boundaries o…
In the present study, structural changes due to gradual doping of Sr in BaTiO3 were investigated by both x-ray and neutron powder diffraction techniques. Ba1-xSrxTiO3 (x=0.0, 0.5 and 1.0) samples were synthesized by PVA evaporation method and purity was confirmed by x-ray diffraction experiment. After that, neutron diffraction experiments were carried out and diffraction data were analyzed by Rietveld least-square data refinement method using the computer program RIETAN-2000 and FullProf to determine various crystallographic structural parameters. The cation and anion position coordinates were…
Stoichiometric Epitaxial Strontium Titanate Thin Films on Silicon by High-Temperature Sr Segregation
Imec；Department of Materials Engineering (MTM), KU Leuven（荷语鲁汶大学材料工程系）；Physics Department, Jean Monnet University（圣艾蒂安让·穆内大学物理系）；Department of Information Technology (INTEC), Photonics Research Group, Ghent University（根特大学信息与科技学院光子学研究组）
We report a systematic first-principles study based on density functional theory (DFT) of the structural and ferroelectric properties of the $R_2$Ti$_2$O$_{7}$ perovskite-related oxides with $R=$ La, Ce, Pr, and Nd. We show that, in all cases, the ferroelectric distortion to the ground-state polar $P2_1$ structure from its parent centrosymmetric $P2_1/m$ phase is driven by a single polar soft mode consisting of rotations and tilts of the TiO$_6$ octahedra combined with displacements of the $R$ ions. A secondary centrosymmetric distortion, which is stable in the parent structure, contributes su…
We investigate the effects of strain on superconductivity with particular reference to SrTiO$_3$. Assuming that a ferroelectric mode that softens under tensile strain is responsible for the coupling, an increase in the critical temperature and range of carrier densities for superconductivity is predicted, while the peak of the superconducting dome shifts towards lower carrier densities. Using a Ginzburg-Landau approach in 2D, we find a linear dependence of the critical temperature on strain: if the couplings between the order parameter and strains in different directions differ while their sum…
Ground-state structure is found and pressure-induced phase transitions up to 210 kbar are studied in mercury titanate from first principles within the density functional theory. It is established that the $R3c$ structure experimentally observed in HgTiO$_3$ is metastable at ambient pressure. With increasing the hydrostatic pressure, the ground-state structure changes following the $R{\bar 3} \to R3c \to Pbnm$ sequence. It is shown that the appearance of ferroelectricity in HgTiO$_3$ at $P = 0$ is associated with an unstable phonon mode. Optical and elastic properties of different phases of mer…
We investigated the nanosecond-scale time decay of the blue-green light emitted by nominally pure SrTiO$_3$ following the absorption of an intense picosecond laser pulse generating a high density of electron-hole pairs. Two independent components are identified in the fluorescence signal that show a different dynamics with varying excitation intensity, and which can be respectively modeled as a bimolecular and unimolecolar process. An interpretation of the observed recombination kinetics in terms of interacting electron and hole polarons is proposed.
Single phase barium titanate-bismuth ferrite ((1-x)BaTi$_3$-(x)BiFe$_3$, BTO-BFO) solid solutions were prepared using citric acid and ethylene glycol assisted sol-gel synthesis method. Depending on the dopant content the samples are characterized by tetragonal, tetragonal-pseudocubic, pseudocubic and rhombohedral structure as confirmed by Raman spectroscopy and XRD measurements. An increase of the BFO content leads to a reduction in the cell parameters accompanied by a decrease in polar distortion of the unit cell wherein an average particle size increases from 60 up to 350 nm. Non zero piezor…
We report measurements of the thermal Hall effect in single crystals of both pristine and isotopically substituted strontium titanate. We discovered a two orders of magnitude difference in the thermal Hall conductivity between $SrTi^{16}O_3$ and $^{18}O$-enriched $SrTi^{18}O_3$ samples. In most temperature ranges, the magnitude of thermal Hall conductivity ($κ_{xy}$) in $SrTi^{18}O_3$ is proportional to the magnitude of the longitudinal thermal conductivity ($κ_{xx}$), which suggests a phonon-mediated thermal Hall effect. However, they deviate in the temperature of their maxima, and the therma…
We show that the Bloch states in the conduction band of SrTiO$_3$ arise from the interplay between highly anisotropic hopping in sub-bands derived from the Ti $t_{2g}$ orbitals and spin-orbit coupling that mixes these orbitals. Because of the nearly flat-band characteristics for one of the principal axes, at sufficiently high doping these Bloch states become unstable with respect to electron interactions, resulting in Mott-like singlet correlations. These findings may be relevant to the anomalous electronic properties of SrTiO$_3$, including its unusual superconductivity.
We report torque magnetometry measurements of an oxide heterostructure consisting of an amorphous Al$_2$O$_3$ thin film grown on a crystalline SrTiO$_3$ substrate ($a$-AO/STO) by atomic layer deposition. We find a torque response that resembles previous studies of crystalline LaAlO$_3$/SrTiO$_3$ (LAO/STO) heterointerfaces, consistent with strongly anisotropic magnetic ordering in the plane of the interface. Unlike crystalline LAO, amorphous Al$_2$O$_3$ is nonpolar, indicating that planar magnetism at an oxide interface is possible without the strong internal electric fields generated within th…
Cooling oxygen-deficient strontium titanate to liquid-helium temperature leads to a decrease in its electrical resistivity by several orders of magnitude. The temperature dependence of resistivity follows a rough T$^{3}$ behavior before becoming T$^{2}$ in the low-temperature limit, as expected in a Fermi liquid. Here, we show that the roughly cubic resistivity above 100K corresponds to a regime where the quasi-particle mean-free-path is shorter than the electron wave-length and the interatomic distance. These criteria define the Mott-Ioffe-Regel limit. Exceeding this limit is the hallmark of …
Strontium titanate (SrTiO$_3$) is a foundational material in the emerging field of complex oxide electronics. While its electronic and optical properties have been studied for decades, SrTiO$_3$ has recently become a renewed materials research focus catalyzed in part by the discovery of magnetism and superconductivity at interfaces between SrTiO$_3$ and other oxides. The formation and distribution of oxygen vacancies may play an essential but as-yet-incompletely understood role in these effects. Moreover, recent signatures of magnetization in gated SrTiO$_3$ have further galvanized interest in…
Oxygen Vacancies at Dislocation Core Modulate Plasticity in Strontium Titanate
Ames National Laboratory（艾姆斯国家实验室）；North Carolina State University（北卡罗来纳州立大学）；Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）；Iowa State University（爱荷华州立大学）；University of Virginia（弗吉尼亚大学）
Electric double layer transistor configurations have been employed to electrostatically dope single crystals of insulating SrTiO_{3}. Here we report on the results of such doping over broad ranges of temperature and carrier concentration employing an ionic liquid as the gate dielectric. The surprising results are, with increasing carrier concentration, an apparent carrier-density dependent conductor-insulator transition, a regime of anomalous Hall effect, suggesting magnetic ordering, and finally the appearance of superconductivity. The possible appearance of magnetic order near the boundary b…
Extended Mean-Field Theory for the 2D Hubbard Model in Degenerate Dilute Electron Gases: Fluctuations, Superconducting Dome, and Interaction Mechanisms in Strontium Titanate
School of Materials Science and Engineering, Guilin University of Electronic Technology（桂林电子科技大学材料科学与工程学院）
We present a study of thermal conductivity, $κ$, in undoped and doped strontium titanate in a wide temperature range (2-400 K) and detecting different regimes of heat flow. In undoped SrTiO$_{3}$, $κ$ evolves faster than cubic with temperature below its peak and in a narrow temperature window. Such a behavior, previously observed in a handful of solids, has been attributed to a Poiseuille flow of phonons, expected to arise when momentum-conserving scattering events outweigh momentum-degrading ones. The effect disappears in presence of dopants. In SrTi$_{1-x}$Nb$_{x}$O$_{3}$, a significant redu…
SrTiO3 plays a central role in oxide electronics. It is the substrate of choice for functional oxide heterostructures based on perovskite-structure thin-film stacks, and its surface or interface with a polar oxide such as LaAlO3 can become a two-dimensional conductor because of electronic reconstruction or the presence of oxygen defects. Inconsistent reports of magnetic order in SrTiO3 abound in the literature. Here we report a systematic experimental study aimed at establishing how and when SrTiO3 can develop a magnetic moment at room temperature. Polished 100, 110 or 111 crystal slices from …
The photoluminescence (PL) spectra of Ar-ion irradiated single crystals of SrTiO3 (STO) excited by the 325 nm line of a He-Cd laser are compared with those of pristine crystals, epitaxial films, and amorphous layers of STO at several temperatures down to 20 K. The 550 eV Ar-beam irradiation activates three distinctly visible PL peaks: blue (~430 nm), green (~550 nm), and infrared (~820 nm) at room temperature, making the photoluminescence multicolored. The abrupt changes in PL properties below ~100 K are discussed in relation with the antiferrodistortive structural phase transition in SrTiO3 f…
Spatial correlation between atoms can generate a depletion in the energy dispersion of acoustic phonons. Two well known examples are rotons in superfluid helium and the Kohn anomaly in metals. Here we report on the observation of a large softening of the transverse acoustic mode in quantum paraelectric SrTiO$_3$ by means of inelastic neutron scattering. In contrast to other known cases, this softening occurs at a tiny wave vector implying spatial correlation extending over a distance as long as 40 lattice parameters. We attribute this to the formation of mesoscopic fluctuating domains due to t…
Titanates with the perovskite structure, including ferroelectrics (e.g., BaTiO$_3$) and ferromagnetic ones (e.g., YTiO$_3$), are important functional materials. Recent theoretical studies predicted multiferroic states in strained EuTiO$_3$ and titanate superlattices, the former of which has already been experimental confirmed. Here, a first-principles calculation is performed to investigate the structural, magnetic, and electronic properties of Y half-substituted LaTiO3. Our results reveal that the magnetism of Y$_{0.5}$La$_{0.5}$TiO$_3$ sensitively depends on its structural details because of…
SrTiO$_3$, although a wide gap insulator, has long been known to become metallic and superconducting at extremely low doping levels. This has given rise to questions concerning the coexistence or interdependence of metallicity, superconductivity, and the material's polar properties. This issue becomes especially intriguing in conjunction with the observation that filamentary metallicity can be induced by means of resistive switching at conditions well below relevant doping levels for homogeneous metallicity. In this study, we demonstrate that resistive switching can also be employed to generat…
When an electronic system is subjected to a sufficiently strong magnetic field that the cyclotron energy is much larger than the Fermi energy, the system enters the "extreme quantum limit" (EQL) and becomes susceptible to a number of instabilities. Bringing a three-dimensional electronic system deeply into the EQL can be difficult, however, since it requires a small Fermi energy, large magnetic field, and low disorder. Here we present an experimental study of the EQL in lightly-doped single crystals of strontium titanate, which remain good bulk conductors down to very low temperatures and high…
The properties of quantum materials are commonly tuned using experimental variables such as pressure, magnetic field and doping. Here we explore a different approach: irreversible, plastic deformation of single crystals. We show for the superconductor SrTiO$_3$ that compressive plastic deformation induces low-dimensional superconductivity significantly above the superconducting transition temperature ($T_c$) of undeformed samples, with evidence of superconducting correlations at temperatures two orders of magnitude above the bulk $T_c$. The superconductivity enhancement is correlated with the …
X-ray photoelectron diffraction is used to directly probe the intra-cell polar atomic distortion and tetragonality associated with ferroelectricity in ultrathin epitaxial PbTiO3 films. Our measurements, combined with ab-initio calculations, unambiguously demonstrate non-centro-symmetry in films a few unit cells thick, imply that films as thin as 3 unit cells still preserve a ferroelectric polar distortion, and also show that there is no thick paraelectric dead layer at the surface.
Room-temperature metallicity of lightly doped SrTiO$_3$ is puzzling, because the combination of mobility and the effective mass would imply a mean-free-path (mfp) below the Mott Ioffe Regel (MIR) limit and a scattering time shorter than the Planckian time ($τ_P=\hbar/k_BT$). We present a study of electric resistivity, Seebeck coefficient and inelastic neutron scattering extended to very high temperatures, which deepens the puzzle. Metallic resistivity persists up to 900 K and is accompanied by a large Seebeck coefficient whose magnitude (as well as its temperature and doping dependence) indica…
It has been known for more than a decade that phonons can produce an off-diagonal thermal conductivity in presence of magnetic field. Recent studies of thermal Hall conductivity, $κ_{xy}$, in a variety of contexts, however, have assumed a negligibly small phonon contribution. We present a study of $κ_{xy}$ in quantum paraelectric SrTiO$_3$, which is a non-magnetic insulator and find that its peak value exceeds what has been reported in any other insulator, including those in which the signal has been qualified as 'giant'. Remarkably, $κ_{xy}(T)$ and $κ(T)$ peak at the same temperature and the …
SrTiO$_3$, a quantum paralectric, displays a detectable phonon thermal Hall effect (THE). Here we show that the amplitude of THE is extremely sensitive to stoichiometry. It drastically decreases upon substitution of a tiny fraction of Sr atoms with Ca, which stabilizes the ferroelectric order. It drastically increases by an even lower density of oxygen vacancies, which turn the system to a dilute metal. The enhancement in the metallic state exceeds by far the sum of the electronic and the phononic contributions. We explain this observation as an outcome of three features: i) heat is mostly tra…
Room temperature ferromagnetism was characterized for thin films of SrTi$_{0.6}$Fe$_{0.4}$O$_{3-δ}$ grown by pulsed laser deposition on SrTiO$_{3}$ and Si substrates under different oxygen pressures and after annealing under oxygen and vacuum conditions. X-ray magnetic circular dichroism demonstrated that the magnetization originated from Fe$^{2+}$ cations, whereas Fe$^{3+}$ and Ti$^{4+}$ did not contribute. Films with the highest magnetic moment (0.8 μB per Fe) had the highest measured Fe$^{2+}$:Fe${^3+}$ ratio of 0.1 corresponding to the largest concentration of oxygen vacancies (δ = 0.19). …
We have investigated the size effect in lead zirconate titanate (PZT) thin films with a range of manganese (Mn) doping concentrations. We found that the size effect in the conventional Pt/PZT/Pt thin-film capacitors could be systematically reduced and almost completely eliminated by increasing Mn doping concentration. The interfacial layer at the electrode-film interface appears to disappear almost entirely for the PZT films with 2% Mn doping levels, confirmed by the fits using the conventional in-series capacitor model. Our work indicates that the size effect in ferroelectrics is extrinsic in…
We review all the published literature and show that there is no experimental evidence for homogeneous tin titanate SnTiO3 in bulk or thin-film form. Instead a combination of unrelated artefacts are easily misinterpreted. The X-ray Bragg data are contaminated by double scattering from the Si substrate, giving a strong line at the 2-theta angle exactly where perovskite SnTiO3 should appear. The strong dielectric divergence near 560K is irreversible and arises from oxygen site detrapping, accompanied by Warburg/Randles interfacial anomalies. The small (4 uC/cm2) apparent ferroelectric hysteresis…
