Antiferroelectric oxide thin-films: Fundamentals, properties, and applications

There is no direct observation of pure ferrielectric structure, only its fragments, such as abundant but irregular appearance at anti-phase domain walls and field-induced ferrielectric-like phase.

“Actually, there is no direct observation of pure ferrielectric structure, only its fragments, like abundant but irregular appearance at the anti-phase domain walls and field-induced ferrielectric-like phase, where it sets the lone-displacement motif of more complicated”

A long-range and periodic structure of the ferrielectric-like structure has not been observed in experiment so far.

“On the other hand, a long-range and periodic structure of such has not been observed in experiment so far.”

With increasing thickness, ECE strength ΔT/ΔE enhances significantly in AFE material systems.

“Fig. 12c-d summarize the ECE of different AFE material systems, which clearly indicate that with increasing thickness, ECE strength ΔT/ΔE enhances significantly [5,39,287,[362][363][364][365][366]367,369,.”

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For bulk systems, most studies observed negative ECE in AFE materials.

“From Fig. 12c-d, we can also see that for bulk systems, most studies observed the negative ECE in AFE materials.”

By controlling crystalline orientation, the giant electrostrain in PbZrO3 thin film is strongly anisotropic with respect to the electric field direction.

“By controlling the crystalline orientation, the giant electrostrain in PbZrO 3 thin film is reported, which is strongly anisotropic with respect to the electric field direction as shown in Fig. 13e-f.”

Recent research has unveiled new AFE systems in multiferroic BiFeO3-based, lead-based PbSnO3, fluorite-structure HfxZr1-xO2 thin films, and quasi-2D francisite Cu3Bi(SeO3)2O2Cl.

“In addition to the size effect, recent research has unveiled new AFE systems in multiferroic BiFeO 3 -based [40], lead-based PbSnO 3 [59], fluorite-structure Hf x Zr 1-x O 2 thin films [43], and quasi-2 dimensional francisite Cu 3 Bi(SeO 3 ) 2 O 2 Cl [29].”

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The AFE phase transition can be understood as an interruption of an imminent FE phase transition at or slightly above the FE critical temperature T0, by a structural phase transition at T_A (T_A ≥ T0).

“When considering cooling-induced phase transition under a field-free condition, the emerged AFE phase can be understood as an interruption of an imminent FE phase transition at or slightly above the FE critical temperature T 0 , by a structural phase transition at T A (T A ≥ T 0 ).”

During PE-AFE phase transition around T_A, a FE phase would emerge briefly under electric field or under the influence of defects and impurities.

“During PE-AFE phase transition around T A , a FE phase would emerge briefly under electric field or under the influence of defects and impurities [66,67].”

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In many well-established AFE samples, the suppressed FE soft mode and related high-temperature dielectric anomaly are a vital ingredient of antiferroelectricity, including classic perovskite AFE oxides PbZrO3, PbHfO3, NaNbO3, and AgNbO3.

“In many well-established AFE samples, the suppressed FE soft mode and related high-temperature dielectric anomaly credit as the vital ingredient of antiferroelectricity [30], this includes classic perovskite AFE oxides such as PbZrO 3 , PbHfO 3 , NaNbO 3 , and AgNbO 3 .”

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When an external electric field is applied, the interaction between polarization and external electric field lifts the degenerate states and one polar state becomes preferential, leading to the characteristic AFE-FE phase transition.

“When an external electric field is applied, the interaction between the polarization and external electric field can lift the otherwise degenerate states with different polarization directions and thus one polar state becomes preferential in energy, leading to the characteristic AFE-FE phase transition, as depicted in Fig. 2b.”

Size effect from bulk to thin film makes structural order parameters more complex in AFE, manifested by deviation of cationic displacement from antiparallel shifts in PbZrO3.

“One typical example is that associated with the miniaturization of the microelectronic devices, the tendency of size effect from bulk to thin film makes the structural order parameters even more complex in the AFE, which is manifested by the deviation of cationic displacement from the antiparallel shifts as documented in prototypical AFE PbZrO 3 [16].”

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This interruption can be modeled by a repulsive interaction between polarization P and structural order parameter ξ, that spontaneously emerges at T_A.

“This interruption can be modeled by a repulsive interaction between polarization P, and structural order parameter ξ, that spontaneously emerges at T A .”

Thin-film epitaxy provides additional strategies to effectively tune structural and physical properties in AFEs.

“In addition to this, thin-film epitaxy also provides additional strategies to effectively tune the structural and physical properties in AFEs [19,20].”

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In conventional FE systems, manipulating the energy barrier via orientation control is an effective approach to switch the electric dipoles.

“In conventional FE systems, it has been reported that manipulating the energy barrier via orientation control is an effective approach to switch the electric dipoles.”

For bulk PbZrO3, calculations have shown a small energy difference of only about 1 meV/f.u. between the AFE Pbam and FE R3c phases.

“For bulk PbZrO 3 , calculations have shown a small energy difference of only ~1 meV/f.u. between the AFE Pbam and FE R3c phases [133].”

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To achieve high-quality, coherently-strained epitaxial films, the key factor is to keep the film thickness thinner than the critical thickness.

“To achieve high-quality, coherently-strained epitaxial films, the key factor is to keep the film thickness thinner than the critical thickness [130].”

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Reducing the film thickness from 900 nm to 100 nm replaces AFE behavior with FE behavior in PbZrO3 thin films.

“By reducing the film thickness from 900 nm to 100 nm, the AFE behavior is replaced by FE behavior, and whether it is induced by residual strain or the self-biasing effect at the interface remains an open question [57,116].”

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By applying an electric field along different crystallographic orientations in AFEs, the critical electric field for AFE-FE phase transition and maximum polarization varies significantly.

“By applying an electric field along different crystallographic orientations in AFEs, the critical electric field for AFE-FE phase transition and maximum polarization varies significantly.”

Epitaxial strain is an effective tool to modify crystal and domain structures, tune physical properties, and even create new emergent functionalities in ferroic oxide thin films.

“Epitaxial strain has been recognized as an effective tool to modify the crystal and domain structures, to tune the physical properties, and even to create new emergent functionalities in ferroic oxide thin films [131,132].”

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Clamping due to mismatch in thermal expansion coefficient with the substrate suppresses the formation of the AFE phase by forming FE and PE phases.

“It is proposed that clamping due to mismatch in thermal expansion coefficient with the substrate suppresses the formation of AFE phase by forming FE and PE phases [140].”

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Most current understanding regarding the influence of epitaxial strain on the stability of different phases in AFEs has been derived from zero-Kelvin DFT calculations.

“It is important to emphasize that most of our current understanding regarding the influence of epitaxial strain on the stability of different phases in AFEs has been derived from zero-Kelvin density functional theory (DFT) calculations.”

Size scaling induced mixed FE/AFE feature can also be found in HfO2-based thin films.

“The size scaling induced mixed FE/AFE feature can also be found in HfO 2 -based thin films [124][125][126].”

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Epitaxial strain can disturb the balance of phase stability between the AFE and FE phases, thereby inducing the AFE-FE phase transition.

“Based on first principles calculations, it is anticipated that epitaxial strain can disturb the balance of phase stability between the AFE and FE phases, thereby inducing the AFE-FE phase transition.”

The surface of a FE can be regarded as a defect coupled to the order parameter, resulting in phase transition smearing in thin film.

“As Bratkovsky and Levanyuk suggested, the surface of a FE can be regarded as a defect coupled to the order parameter, resulting in the phase transition smearing in thin film [118].”

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The multilayers undergo a thickness-dependent transition from mixed AFE-FE behavior to purely FE behavior.

“The electric measurements have revealed that the multilayers undergo a thickness-dependent transition from a mixed AFE-FE behavior to a purely FE behavior.”

One cannot conclude whether the AFE transition is first order or not without considering the specific structures from both sides of the transition.

“Therefore, we could not conclude whether the AFE transition is first order or not without considering the specific structures from both sides of the transition.”

Ab-initio calculations yield very similar energies for the Pbam-symmetric AFE phase and R3c-symmetric FE phase.

“For these two phases, the ab-initio calculations yield very similar energies [74].”

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Otherwise, strain tends to relax with the assistance of interfacial misfit dislocations.

“Otherwise, the strain tends to relax with the assistance of interfacial misfit dislocations.”

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Size effects in ferroic materials have revealed a critical thickness necessary to stabilize the primary ferroic order parameter and thus device functionality.

“Size effects in ferroic materials have been extensively studied over the years, and these studies have revealed the presence of a critical thickness necessary to stabilize the primary ferroic order parameter and thus the device functionality [113,114].”

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The coercive field in 20 nm PbZr0.2Ti0.8O3 thin films can be reduced from about 350 kV/cm on SrTiO3(001) substrate to about 150 kV/cm on SrTiO3(111) substrate.

“For example, Xu et al. demonstrated that the coercive field in 20 nm PbZr 0.2 Ti 0.8 O 3 thin films can be reduced from ~ 350 kV/cm for films on SrTiO 3 (0 0 1) substrate to ~ 150 kV/cm on SrTiO 3 (1 1 1) substrate [143].”

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With decreasing thickness, the built-in electric field increases until it reaches a critical value and induces the AFE-FE phase transition.

“With decreasing thickness, the built-in electric field progressively increases until it reaches a critical value and induces the AFE-FE phase transition.”

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In Hf0.5Zr0.5O2 thin films, a giant in-plane tensile strain induced by coalescence of the nucleating grain is proposed to enhance ferroelectricity by transforming the nonpolar tetragonal phase to polar orthorhombic phase.

“In Hf 0.5 Zr 0.5 O 2 thin films, a giant in-plane tensile strain, induced by coalescence of the nucleating grain, are proposed to enhance the ferroelectricity by transforming the nonpolar tetragonal phase to polar orthorhombic phase [141].”

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Growth strain, originating from the coalescence of nucleating grains and densification during crystallization, is another important factor that influences structure stability.

“Growth strain, originating from the coalescence of the nucleating grains and densification during crystallization, is another important factor that influences the structure stability [139,141].”

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In polycrystalline AFE oxide thin films grown on semiconducting substrates, thermal and growth strain play a crucial role in determining the free energy of the AFE and FE phases, altering structure stability and consequent electrical behaviors.

“In polycrystalline AFE oxide thin films grown on semiconducting substrates (e.g., Si), the thermal and growth strain would play a crucial role in determining the free energy of AFE phase and FE phase, altering the structure stability and consequent electrical behaviors.”

ZrO2 thin films predominantly persist in the AFE tetragonal structure.

“In contrast with HfO 2 thin films, it is widely acknowledged that ZrO 2 thin films predominantly persist AFE tetragonal structure [128,129].”

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For the high temperature PE phase of bulk AFEs, the dielectric constant follows the Curie-Weiss law.

“For the high temperature PE phase of bulk AFEs, the dielectric constant follows the Curie-Weiss law [75]:”

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Below a critical thickness of about 6 nm, PbZrO3 films develop a FE tetragonal phase under short-circuit boundary condition even in the absence of epitaxial strain.

“Surprisingly, below a critical thickness (about 6 nm), the PbZrO 3 films would develop a FE tetragonal phase for films under short-circuit boundary condition even in the absence of epitaxial strain.”

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The theory for controlling the functional behavior of AFE films in terms of specific demands is still in its development stage.

“However, in contrast to the much more developed theory about FE films, the theory for controlling the functional behavior of AFE films in terms of specific demands is still in its development stage [112].”

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The physical properties in thin films usually show differences from bulk due to additional constraints on electrical and mechanical boundary conditions.

“The physical property in thin films usually show differences from that in bulks due to the additional constraints on electrical and mechanical boundary conditions.”

For lead-free AFE AgNbO3 thin films, two phase transitions (from Pm to Cm and from Cm to Amm2) occur at ranges of compressive strain and tensile strain, respectively.

“For lead-free AFE AgNbO 3 thin films, first-principles calculations revealed that two phase transitions (from Pm to Cm and from Cm to Amm2) would occur at the range of compressive strain and tensile strain, respectively.”

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These zero-Kelvin DFT findings may not accurately reflect the actual behavior at finite temperatures.

“However, these findings may not accurately reflect the actual behavior at finite temperatures.”

Substrate strain plays a crucial role in driving the AFE-to-FE transition of PbZrO3 layers.

“Further, X-ray diffraction studies suggest that the substrate strain plays a crucial role in driving the AFE-to-FE transition of the PbZrO 3 layers.”

The S mode maintains a mixed feature of the AFE and AFD modes.

“Instead, the S mode maintains a mixed feature of the AFE and AFD modes [73].”

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Strain can alter the critical electric fields E_FA and E_AF for the AFE-FE phase transition and thus tune the energy storage properties.

“In addition to the strain-induced structural phase transition, the strain can also alter the critical electric fields (E FA and E AF ) for AFE-FE phase transition and thus tune the energy storage properties [136].”

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The surface piezo-effect can break inversion symmetry near the surface and generate a built-in electric field inversely proportional to the film thickness in AFE thin films.

“In 2007, Eliseev and Glinchuk took the size effects into account in AFE thin films and reported that the surface piezo-effect can break the inversion symmetry near the surface and generate a built-in electric field that is inversely proportional to the film thickness [119].”

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For AFEs, taking PbZrO3 as an example, the AFE phase has an orthorhombic structure (Pbam, a-a-c0), which transforms into a FE rhombohedral (R3c, a-a-a-) phase with polarization along the [111] direction under a sufficiently strong electric field.

“For AFEs, taking PbZrO 3 as an example, it is widely accepted that the AFE phase has an orthorhombic structure (Pbam, a -a -c 0 ), which transforms into a FE rhombohedral (R3c, a -a -a -) phase with the polarization along the [1 1 1] direction under a sufficiently strong electric field [101].”

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Both antipolar structures transform to FE structure with decreasing thickness below 25 nm.

“Both antipolar structures transform to FE structure with decreasing thickness below 25 nm [121].”

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For epitaxial growth, the in-plane lattice constant of thin films is expected to be identical to that of the substrate when the film is thinner than a specific critical thickness.

“For epitaxial growth of thin films, the in-plane lattice constant of thin films is expected to be identical to that of the substrate when the film is thinner than a specific critical thickness value.”

Due to the impact of surface energy, the monoclinic, orthorhombic and tetragonal structures are energetically favorable in sequence as the thickness decreases.

“As suggested by DFT calculations, due to the impact of surface energy, the monoclinic, orthorhombic and tetragonal structure are energetically favorable in sequence as the thickness decreases [127].”

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In 2007, a thickness-driven AFE-FE phase transition was reported in PbZrO3/PbZr0.8Ti0.2O3 multilayers.

“Subsequently, in 2007, a thickness driven AFE-FE phase transition was reported in PbZrO 3 /PbZr 0.8 Ti 0.2 O 3 multilayers.”

The presence of a wide-range FE rhombohedral phase has been reported in PbZrO3 thin films grown on SrRuO3-buffered SrTiO3 substrates.

“On the other hand, the presence of wide-range FE rhombohedral phase has also been reported in PbZrO 3 thin films grown on SrRuO 3 -buffered SrTiO 3 substrates [123].”

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In NaNbO3 thin films, an energy-versus-misfit strain phase diagram has been constructed, revealing three phases corresponding to different strain regimes.

“In NaNbO 3 thin films, an energy-versus-misfit strain phase diagram has been constructed, revealing three phases (monoclinic Cc, orthorhombic Pca2 1 , and orthorhombic Pmc2 1 symmetries) corresponding to different strain regimes [135].”

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Ayyub et al. first reported the size effect in AFEs in polycrystalline PbZrO3 thin films grown on Si substrates.

“In 1998, Ayyub et al. first reported the size effect in AFEs in polycrystalline PbZrO 3 thin films grown on Si substrates.”

Thermal strain originates from the mismatch of the thermal expansion coefficients between the film and the underlying substrate during the cooling process after film deposition.

“Thermal strain originates from the mismatch of the thermal expansion coefficients between the film and the underlying substrate during the cooling process after film deposition [138,139].”

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In 2011, Chaudhuri et al. reported that a FE rhombohedral structure could be stabilized by substrate-induced strain in ultrathin PbZrO3 epitaxial films grown on SrRuO3-buffered SrTiO3 substrates.

“In 2011, Chaudhuri et al. [18] reported that a FE rhombohedral structure could be stabilized by substrate-induced strain in ultrathin PbZrO 3 epitaxial films grown on (0 0 1) SrRuO 3 -buffered SrTiO 3 substrates.”

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The PbZrO3 sub-layer undergoes a structural transition from an orthorhombic AFE phase to a rhombohedral FE phase when its thickness decreases to about 10 nm.

“This indicates that the PbZrO 3 sub-layer undergoes a structural transition from an orthorhombic AFE phase to rhombohedral FE phase when the PbZrO 3 sub-layer thickness decreases to ~ 10 nm [117].”

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Emergent AFE behavior has been discovered in several artificial superlattice systems.

“Emergent AFE behavior has been discovered in several artificial superlattice systems.”

The starting layer with HfO2 can strengthen the field-induced ferroelectricity from AFE thin films.

“The starting layer with HfO 2 can strengthen the field-induced ferroelectricity from AFE thin films.”

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Antipolar phases have been identified in BiFeO3/La0.7Sr0.3MnO3, BiFeO3/La0.4Bi0.6FeO3, and BiFeO3/TbScO3 superlattices.

“This is evidenced by identification of antipolar phases in BiFeO 3 / La 0.7 Sr 0.3 MnO 3 , BiFeO 3 /La 0.4 Bi 0.6 FeO 3 , and BiFeO 3 /TbScO 3 superlattices [186][187][188][189].”

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Interfacial control offers an effective strategy for the design of new AFE materials for versatile applications.

“These studies demonstrate that interfacial control offers an effective strategy for the design of new AFE materials for versatile applications.”

The inherent AFE nature in ZrO2 thin films enables Hf1-xZrxO2 thin films to exhibit antiferroelectricity over a wide range of composition compared to other dopants.

“For the famous Hf 1-x Zr x O 2 solid solution, the inherent AFE nature in ZrO 2 thin films enables the Hf 1-x Zr x O 2 thin films to exhibit antiferroelectricity over a wide range of composition compared to other dopants [27,43,178].”

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Defect-controlled electrocaloric effect was reported in PbZrO3 thin films.

“Defectcontrolled electrocaloric effect (ECE) was also reported in PbZrO 3 thin films [164].”

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The field-induced phase transition into these new polar phases is predicted to generate extremely large strain of up to 3.6%.

“Moreover, the field-induced phase transition into these new polar phases is predicted to generate extremely large strain of up to 3.6 %, which holds significant technological significance [145].”

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The superlattices can be tailored to address specific needs by means of epitaxial strain, layer thicknesses, and dielectric stiffness.

“Moreover, the superlattices can be tailored to address specific needs by means of epitaxial strain, layer thicknesses, and dielectric stiffness.”

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In fluorite HfO2-based thin films, different dopants can result in either FE or AFE behavior depending on the dopant size and doping content.

“In fluorite HfO 2 -based thin films, different dopants can result in either FE or AFE behavior depending on the dopant size and doping content [43].”

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The B-site cation modulation imposed by the superlattice is considered as the origin of antiferroelectricity.

“The B-site cation modulation imposed by the superlattice is considered as the origin of antiferroelectricity [86].”

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The presence of oxygen vacancies, leading to deviation from ideal stoichiometry, can cause changes in vibrational frequency of the FE and AFE mode, resulting in the presence of an intermediate FE phase.

“One paradigm is that the presence of oxygen vacancies, leading to deviation from the ideal stoichiometry, can cause changes in vibrational frequency of the FE and AFE mode, resulting in the presence of intermediate FE phase [67].”

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By introducing point-defect via decreasing oxygen pressure, a FE-like switching can be obtained in PbZrO3 thin films at room temperature.

“In addition, by introducing point-defect via decreasing oxygen pressure, it has been revealed that a FE-like switching can be obtained in PbZrO 3 thin films at room temperature [162].”

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By mediating the interfacial compressive strain using a BaZrO3 buffer layer, polar domain walls can be abundantly formed near the interface.

“By mediating the interfacial compressive strain using BaZrO 3 buffer layer, the polar domain walls can be abundantly formed near the interface.”

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This occurs regardless of film thickness, in contrast to the Kittel law.

“This occurs regardless of film thickness, in contrast to the so-called Kittel law, i.e., a square root dependence of domain size on thickness which has been reported for diverse ferroic systems [159,160].”

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In bulks, translational domains pack themselves into superdomains, which are separated by curved 90° domain walls and more exotic junctions, such as cloverleaf patterns.

“In bulks, it has been shown that those translational domains pack themselves into superdomains, which are in turn separated by curved 90 • domain walls and more exotic junctions, such as cloverleaf patterns [147].”

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In Si-doped HfO2 thin films where Si has a smaller radius than Hf, the AFE behavior can be obtained with increasing the doping content of Si.

“In Si-doped HfO 2 thin films where Si has a smaller radius than Hf, the AFE behavior can be obtained with increasing the doping content of Si [126].”

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The AFE-FE phase transition can directly be stimulated in nonstoichiometric Pb1.2ZrO3+δ thin films.

“For instance, the AFE-FE phase transition can directly be stimulated in nonstoichiometric Pb 1.2 ZrO 3+δ thin films (Fig. 5d) [13].”

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This FE-like switching can be attributed to the pinning effect from point defect, which can effectively delay the AFE-FE phase transition.

“This FE-like switching can be attributed to the pinning effect from pointdefect, which can effectively delay the AFE-FE phase transition.”

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The estimated domain size of 13 nm can characterize the length scale of the densest kind of domain packing-the scale of translational domains.

“Therefore, it is likely that the estimated domain size of 13-nm can characterize the length scale of the densest kind of domain packingthe scale of translational domains.”

• cites [158]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Reducing hysteresis with slim hysteresis loops can be achieved by breaking the long-range ordered domains into nanometer scale, thereby introducing nanoscale heterogeneity in AFEs via chemical doping.

“Recent studies have also shown that reducing hysteresis with slim hysteresis loops can be achieved by breaking the long-range ordered domains into nanometer scale, thereby introducing nanoscale heterogeneity in AFEs via chemical doping [157], which is particularly important for their applications in energy storage devices.”

• cites [157]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

The properties of perovskite oxides are intricately linked to the average electronegativity.

“Apart from the tolerance factor that reflects the arrangements of ions in perovskite structures, the properties of perovskite oxides are intricately linked to the average electronegativity.”

In 2013, a polar translational antiphase boundary was initially discovered in PbZrO3.

“In 2013, polar translational antiphase boundary was initially discovered in PbZrO 3 [64].”

• cites [64]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

This can be attributed to the low monoclinic phase fraction in the starting layer of HfO2.

“This can be attributed to the low monoclinic phase fraction in the starting layer of HfO 2 .”

• cites [190]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites [191]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

The above results of effective Hamiltonian studies disagree with experimental observations by Fesenko et al. in PbZrO3 single crystals.

“It is interesting to note that the above results of pioneering effective Hamiltonian studies disagree with experimental observations by Fesenko et al. [55] in PbZrO 3 single crystals.”

• cites [55]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Interfacial control is also an effective engineering strategy to tune AFE properties in fluorite-structure Hf1-xZrxO2 thin films.

“The interfacial control is also an effective engineering strategy to tune AFE properties in fluorite-structure Hf 1-x Zr x O 2 thin films [190].”

• cites [190]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Increasing the single layer thickness of ZrO2 can stabilize the AFE behavior due to the energetically favorable tetragonal structure in pure ZrO2.

“In that work, the increasing single layer thickness of ZrO 2 can stabilize the AFE behavior due to the energetically favorable tetragonal structure in pure ZrO 2 .”

• cites [191]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

In this proposed model, superior energy storage performance is obtained.

“In this proposed model, superior energy storage performance is obtained [185].”

• cites [185]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

A similar AFE-type behavior has been demonstrated in SrTiO3/BaZrO3 superlattices, where both constituent phases are PE in bulk.

“Soon afterwards, a similar AFE-type behavior has been demonstrated in SrTiO 3 /BaZrO 3 superlattices, where both constituent phases are PE in bulk.”

• cites [87]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Chemical doping is an efficient way to modulate material properties.

“Chemical doping is an efficient way to modulate the material properties.”

None of these newly identified phases exhibit the commonly acknowledged rhombohedral structure with R3c symmetry.

“None of these newly identified phases exhibit the commonly acknowledged rhombohedral structure with the R3c symmetry.”

• cites [145]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

The gradual increase of lead volatilization results in asymmetric interface nucleation.

“The gradual increase of lead volatilization results in asymmetric interface nucleation.”

• cites [164]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Three new polar phases, Cc, Ima2 and I4cm, are obtained under electric field along the [111], [110] and [001] directions, respectively.

“Notably, they discovered the emergence of three new polar phases: Cc, Ima2 and I4cm are obtained under electric field along the [1 1 1], [1 1 0] and [0 0 1] directions, respectively.”

• cites [145]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

In PbZrO3/BaZrO3/SrTiO3 thin films, the polar domain walls (180° walls) correlated strongly with the interfacial strain.

“In PbZrO 3 /BaZrO 3 /SrTiO 3 thin films, it was found that the polar domain walls (180 • walls) correlated strongly with the interfacial strain [154].”

• cites [154]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

First principles study suggested that the dopant size can change the metal-oxygen bonding to cause energy differences.

“First principles study suggested that the dopant size can change the metal--oxygen bonding to cause energy differences [180].”

• cites [180]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

In PbZrO3/SrRuO3/SrTiO3(001) heterostructures, individual domains are usually not larger than about 13 nm.

“Using the Bragg peak shape analysis combined with X-ray nanoscopy where a nano-focused X-ray beam is used, it has been shown that individual domains are usually not larger than about 13 nm [158].”

• cites [158]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

AFE behavior can also be derived from multiferroic BiFeO3 nanolayers with delicate interface engineering.

“Apart from the emergent antiferroelectricity in para-and ferro-electric materials, the AFE behavior can also be derived from multiferroic BiFeO 3 nanolayers with delicate interface engineering.”

A B-site dopant with a smaller radius, such as Sn4+ and Ti4+, has been employed to decrease the E_AF and minimize the hysteresis loop area.

“On the one hand, Sr 2+ [111] and La 3+ [170] can stabilize the AFE phase and bring a higher E AF than undoped PbZrO 3 , on the other hand, the B-site dopant with a smaller radius, such as Sn 4+ and Ti 4+ [171], has been employed to decrease the E AF and minimize the hysteresis loop area.”

• cites [171]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

a-a-c0 octahedral tilts are attractive to incommensuration and antiferroelectricity in PbHfO3, at least at high temperatures.

“Single-crystal diffuse scattering experiments suggest that a -a -c 0 octahedral tilts are attractive to incommensuration and antiferroelectricity in PbHfO 3 , at least at high temperatures [201].”

• cites [201]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

According to first-principles calculations, the energy difference between the antiferroelectric and ferroelectric phases of NaNbO3 is remarkably small, about 1.4 meV/f.u.

“According to first-principles calculations, the energy difference between the AFE and FE phases is remarkably small (~1.4 meV/f.u.) [222,224].”

• cites [222]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites [224]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

The ferrielectric-like structure cannot be regarded as a pure phase but only as a local structure.

“Therefore, this cannot be regarded as a pure phase but only as a local structure.”

Increasing pressure can affect phase stability in PHO by altering Pb-ion displacements and oxygen octahedral distortion.

“The pressure increase can obviously affect the phase stability by altering the Pb-ion displacements and oxygen octahedral distortion.”

NaNbO3 undergoes a phase transition to another PE phase with a tetragonal structure and space group P4/mbm (T2 phase) at 639 °C.

“It undergoes a phase transition to another PE phase while with a tetragonal structure and space group of P4/mbm (T 2 phase) at a transition temperature of 639 • C.”

• cites [218]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites [219]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

When the coupling between octahedral tilts and antiferroelectricity is turned off, both types of distortions appear at much higher temperatures compared to the case when they are coupled.

“When the coupling is turned off, both types of distortions appear at much higher temperatures as compared to the case when they are coupled.”

• cites [69]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

In Pb0.97La0.02Zr0.95Ti0.05O3 epitaxial thin films, phase stability can be controlled by thickness-related strain effect, presenting a depth-dependent FE to incommensurate/commensurate AFE phase transition.

“For example, in Pb 0.97 La 0.02 Zr 0.95 Ti 0.05 O 3 epitaxial thin films, the phase stability can be controlled by thickness-related strain effect, presenting a depth dependent FE to incommensurate/commensurate AFE phase transition [210].”

• cites [210]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Model understanding of short-period phases belongs to a different realm than that of original incommensurate phases, despite both having transverse lead ion displacements as the main feature.

“Model understanding of these short-period phases belongs to a different realm than that of the original incommensurate phases, despite they both have transverse lead ion displacements as the main feature.”

Similar ↑↑↓ Pb displacement features have been observed at the R II-1-type translation boundary, characterized by displacement vector 1/4R[2 1n] with a π/2 phase shift for separated neighboring unit cells.

“similar Pb displacement of”

• cites [206]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Experimental progress in PbZrO3 structures goes far ahead of theoretical progress.

“From these recent works, one can see that that the experimental progress goes far ahead of the theoretical one.”

Temperature-dependent dielectric permittivity of a pure NaNbO3 ceramic shows that the largest dielectric anomaly occurs at the P-to-R phase transition.

“Temperature-dependent dielectric permittivity of a pure NaNbO 3 ceramic shows that the largest dielectric anomaly occurs at the P-to-R phase transition (Fig. 8a) [221].”

• cites [221]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

The substrate's octahedral tilt pattern can propagate into the film to a small but considerable depth.

“The essence is that the substrate's octahedral tilt pattern can propagate into the film to a small but considerable depth.”

With increasing temperature, two intermediate phases exist in two sequential temperature ranges below the transition temperature in PHO.

“With temperature increasing, two intermediate phases are found to exist in two sequential temperature ranges below the transition temperature.”

Analysis of phase transitions in PHO driven by temperature and hydrostatic pressure unveils a quite different story from PbZrO3.

“The analysis of phase transitions in PHO driven by temperature and hydrostatic pressure unveils a quite different story from PbZrO 3 [213].”

• cites [213]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Recent X-ray diffraction experiments on PbZrO3/SrRuO3/SrTiO3 (001) heterostructures indicate a curiously frustrated state of the AFE domains.

“For example, recent X-ray diffraction experiments on PbZrO 3 /SrRuO 3 /SrTiO 3 (0 0 1) heterostructures indicate a curiously frustrated state of the AFE domains there [17].”

• cites [17]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Epitaxial integration has a huge impact on the property of the materials.

“Obviously, epitaxial integration has a huge impact on property of the materials.”

The modulation period for the transverse polarization wave is fixed at a series of commensurate positions.

“Essentially, the modulation period for the transverse polarization wave is fixed at a series of [55].”

• cites [55]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

In FE thin films, epitaxial strain alone has shown great influence on the transition temperature.

“In FE thin films, epitaxial strain alone has shown great influence on the transition temperature [205].”

• cites [205]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

From a modern perspective, PHO is remarkable in demonstrating that the incommensurate phase can be formed by an antiferrodistortive soft mode.

“However, from a modern perspective, PHO is remarkable in demonstrating that the incommensurate phase can be formed by antiferrodistortive soft mode [201].”

• cites [201]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

There is a mixed feature of ferroelectricity and antiferroelectricity of Pb2+ displacement in PbZrO3 thin films, resulting in the fluctuation of uncompensated polarization.

“This indicates there is a mixed feature of ferroelectricity and antiferroelectricity of Pb 2+ displacement in PbZrO 3 thin films, resulting in the fluctuation of uncompensated polarization as shown in Fig. 7b and 7c.”

• cites [15]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

The modulation wave in these incommensurate phases is accompanied by a longitudinal component.

“More surprisingly, the structure is accompanied with a longitudinal component in the modulation wave.”

Due to the low energy barrier between AFE and FE phases in PbZrO3, the polarization/phase structure can be easily tuned by external stimuli such as electric field, temperature, pressure, and chemical doping.

“In fact, due to the low energy barrier between the AFE and FE phases, e.g., in the PbZrO 3 system [208], the polarization/phase structure can be easily tuned by external stimuli, such as electric field, temperature, pressure, chemical doping, etc.”

• cites [208]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

The third group of exotic structures is primarily manifested by a FE cycloidal phase activated by electron beam irradiation.

“The third group consists of exotic structures, primarily manifested by FE cycloidal phase, which is activated by electron beam irradiation [103].”

• cites [103]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Similar ferrielectric structures have been experimentally discovered in PbZrO3 thin films.

“Similar structures have been also experimentally discovered in PbZrO 3 thin films.”

• cites [121]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

A TiN capping layer is commonly used as a mechanical confinement to engineer the FE/AFE behavior in Hf1-xZrxO2 films.

“TiN capping layer is commonly used as a mechanical confinement to engineer the FE/AFE behavior in Hf 1-x Zr x O 2 films [43,139].”

• cites [43]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites [139]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

During the PE-AFE phase transition, an unusually high transition temperature is observed in epitaxial PbZrO3 thin films.

“During the PE-AFE phase transition, which is essentially related to the origin of antiferroelectricity, an unusually high transition temperature is observed in epitaxial PbZrO 3 thin films.”

• cites [15]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Control of domain states at nanometer scale (~10 nm) has been realized in ferroelectrics.

“The control of domain states at nanometer scale (~10 nm) has been realized in FEs [207]”

• cites [207]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

The abrupt change in modulation period can be attributed to synergistic effects of combined variables such as strain gradient and boundary conditions, which act as additional stimuli for the commensurate structure.

“This can be attributed to the synergistic effect of combined variables, e.g., strain gradient and boundary conditions, which play as additional stimulus for flourish of the commensurate structure.”

Theoretical modeling of PbZrO3 films commonly considered them as only homogeneously strained or not strained at all.

“Obviously, that is a huge complication to the theoretical modeling, where the PbZrO 3 films were commonly considered as only homogeneously strained [133] or not strained at all [212].”

• cites [133]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites [212]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Additional elements are usually introduced to stabilize the AFE structure of NaNbO3, e.g., SrZrO3-NaNbO3 solid solutions, to verify its AFE characteristics.

“To successfully verify its AFE characteristics, additional elements are usually introduced to stabilize the AFE structure, e.g., SrZrO 3 -NaNbO 3 solid solutions [217].”

• cites [217]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

These different orthorhombic phases of NaNbO3 are distinguished by atomic displacement of Nb5+ and oxygen octahedral rotation patterns.

“These different orthorhombic phases are distinguished by two factors, i.e., the atomic displacement of Nb 5+ and the oxygen octahedral rotation patterns.”

The coupling between octahedral tilts and antiferroelectricity has a collaborative nature.

“This, again, suggests a collaborative nature of the coupling between octahedral tilts and antiferroelectricity.”

• cites [202]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Raman studies show that the presence of mechanical stress may lead to the presence of FE phase in PbZrO3/SrRuO3/SrTiO3 heterostructures.

“Indications on the importance of such an effect in PbZrO 3 films are reported by earlier studies performed at Max Planck Institute, where Raman studies show that the presence of mechanical stress may lead to the presence of FE phase in PbZrO 3 /SrRuO 3 /SrTiO 3 heterostructures [123].”

• cites [123]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

The large lattice mismatch of ~6% between PbZrO3 and SrRuO3 is relaxed almost completely by forming dislocations near the PbZrO3/SrRuO3 interface.

“from being simply strained because of the large lattice mismatch of ~ 6 %, which is relaxed almost completely by forming dislocations near the PbZrO 3 /SrRuO 3 interface.”

It is very difficult to grow high-quality and stoichiometric NaNbO3 samples because Na volatilizes easily at high temperature during sample preparation.

“Because of the easy volatilization of Na at high temperature during sample preparation, it is very difficult to grow high-quality and stoichiometric NaNbO 3 samples [216].”

• cites [216]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

The higher T_A for dielectric anomaly and annihilation of 1/4 superstructure diffractions as the PbZrO3 film is grown on SrTiO3 substrate increases by 40 K in comparison with bulk PbZrO3.

“This is manifested by the higher T A for dielectric anomaly and annihilation of 1/ 4 superstructure diffractions as the PbZrO 3 film is grown on SrTiO 3 substrate, which increases by 40 K in comparison with bulk PbZrO 3 [15].”

• cites [15]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

At high temperature, NaNbO3 is PE with a cubic structure and space group Pm3m (C phase).

“At high temperature, NaNbO 3 is PE with a cubic structure and space group of Pm3m (C phase).”

• cites [218]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites [219]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Many new structures discovered recently in PbZrO3-based crystals and thin films share intrinsic unit-cell-scale heterogeneity.

“Owing to the structure sensitivity, many new structures have been discovered recently in PbZrO 3 -based crystals and thin films, all of which share intrinsic unit-cell-scale heterogeneity.”

Commonly used substrates and electrode layers, such as SrTiO3 and SrRuO3, differ by near -3% from Pb-based AFEs.

“The commonly used substrates and electrode layers, such as SrTiO 3 and SrRuO 3 , differs by near -3% from Pb-based AFEs.”

Incommensurate phases in PbZrO3-based materials appear as modulated structures with some degree of uncompensated polarization, contrary to originally conceived transverse modulation waves.

“Contrary to the originally conceived transverse modulation waves, those phases appear now as modulated structures with certain degree uncompensated polarization.”

To shift the antiferroelectric transition of BNT to room temperature, a second perovskite such as BNT-BaTiO3, BNT-NaNbO3, or BNT-SrTiO3 has been extensively incorporated into the BNT matrix.

“In order to shift the AFE transition to room temperature, a second perovskite has been extensively incorporated into the BNT matrix, such as BNT-BaTiO 3 (BNT-BT) [249], BNT-NaNbO 3 [250], BNT-SrTiO 3 [36], etc.”

• cites [249]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites [250]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites [36]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Doped HfO2 films exhibit another AFE-like behavior manifested by typical double-hysteresis curves.

“there is another AFE-like behavior in the doped HfO 2 films, manifested by typical double-hysteresis curves.”

• cites [276]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

The BNT-BT solid solution greatly improves piezoelectric, pyroelectric and energy storage performances due to inherently rich phase boundaries.

“Among them, BNT-BT solid solution is particularly interesting, which not only broadens the temperature region of AFE phase, but also greatly improves the piezoelectric, pyroelectric and energy storage performances due to the inherently rich phase boundaries (Fig. 8d) [237].”

• cites [237]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Because the energy difference between competing phases of NaNbO3 is small, its structure can be easily tuned by chemical composition, defects, electric field, temperature, epitaxial strain, film thickness and grain size.

“Due to the small energy difference between the competing phases, the structure of NaNbO 3 can be easily tuned by chemical composition, defects, electric field, temperature, epitaxial strain, film thickness and grain size.”

HfO2 thin films undergo monoclinic (M) to orthorhombic (O) to tetragonal (T) to cubic (C) phase transition with increasing formation energy.

“As shown in Fig. 10a, HfO 2 thin films undergo monoclinic (M) → orthorhombic (O) → tetragonal (T) → cubic (C) phase transition with increasing formation energy [266].”

• cites [266]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

The energy between the antipolar phase and the ferroelectric phase in (Hf0.5Zr0.5)O2 is slightly different, which makes the reversible phase transition possible.

“The energy between this antipolar phase and the FE phase is slightly different, which makes the reversible phase transition possible [127].”

• cites [127]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

An electric field can induce a monoclinic (Cc) to rhombohedral (R3c) phase transformation in BNT.

“Further study reveals that the electric field can induce monoclinic (Cc) to rhombohedral (R3c) phase transformation”

• cites [245]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites [246]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Chemical substitution can stabilize the antiferroelectric phase of BFO at room temperature.

“Besides interfacial engineering, chemical substitution can also stabilize the AFE phase of BFO at room temperature [255], as illustrated by the P-E hysteresis curves of Nd doped BiFeO 3 solid solutions (Fig. 9e).”

• cites [255]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

The tetragonal phase of BNT exhibits an unusual combination of in-phase (a0a0c+) tilts and antiparallel cation displacements along the polar c axis, indicating an antiferroelectric feature.

“and the tetragonal phase exhibits an unusual combination of in-phase (a 0 a 0 c + ) tilts and antiparallel cation displacements along the polar c axis, indicating the AFE feature [241,242].”

• cites [241]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites [242]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Rhombohedral (R3c) and monoclinic (Cc) phases may coexist in the equilibrium state of BNT at room temperature.

“and rhombohedral (R3c) and monoclinic (Cc) phases may coexist in its equilibrium state at room temperature [245,246]”

• cites [245]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites [246]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

The antipolar phase in HfO2-based structures is equivalent to 8-fold 180° domain walls, a typical sub-lattice property.

“this antipolar phase is equivalent to 8-fold 180 • domain walls, which can be seen as a typical sub-lattice property of HfO 2 -based structure [275].”

• cites [275]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

The antipolar orthorhombic phase is fundamentally distinguished from the non-polar tetragonal AFE phase.

“Therefore, the antipolar orthorhombic phase is fundamentally distinguished from the non-polar tetragonal AFE phase.”

In 2009, Levin et al. reported that the M1 phase of AgNbO3 exhibits an orthorhombic structure with centrosymmetric Pbcm space group.

“In 2009, using a combination of high-resolution X-ray diffraction, neutron total scattering, electron diffraction, and X-ray absorption fine-structure measurements, Levin et al. reported that the M 1 phase exhibits orthorhombic structure with centrosymmetric Pbcm space group [230].”

• cites [230]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Recent atomic-resolution Cs-corrected scanning TEM study revealed that an antipolar orthorhombic Pbca phase with antiparallel oxygen-atom shifts coexists with the ferroelectric orthorhombic Pbc21 phase in (Hf0.5Zr0.5)O2 polycrystalline film.

“Recent atomic-resolution Cs-corrected scanning TEM study revealed that antipolar orthorhombic Pbca phase with antiparallel oxygen-atom shifts coexist with the FE orthorhombic Pbc2 1 phase in (Hf 0.5 Zr 0.5 )O 2 polycrystalline film (Fig. 10c) [274].”

• cites [274]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Evidence of a small remnant polarization from hysteresis loops and the pyroelectric effect indicates the presence of weak ferroelectricity in AgNbO3.

“However, the evidence of a small remnant polarization, obtained from hysteresis loops and the pyroelectric effect, indicated the presence of weak ferroelectricity [51,226], which was further confirmed in subsequent experiments [227].”

• cites [51]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites [226]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

The electric-field-induced nonpolar tetragonal to polar orthorhombic phase transition is widely accepted as the origin of antiferroelectric behaviors in fluorite-type materials.

“To achieve an AFE behavior, extra ZrO 2 are usually introduced to stabilize the metastable state, and the electric field induced nonpolar tetragonal → polar orthorhombic phase transition is widely accepted as the origin of AFE behaviors in the fluorite-type material [273].”

• cites [273]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

The centrosymmetric structure of the AgNbO3 M1 phase is not consistent with the presence of remnant polarization.

“However, the centrosymmetric structure is not consistent with the presence of remnant polarization.”

The composition of the morphotropic phase boundary in rare-earth substituted BiFeO3 can be tuned by systematically adjusting the average A-site ionic radius.

“Fig. 9f shows the phase diagram for rare-earth element substituted BiFeO 3 , and composition of the MPB can be tuned by systematically adjusting the average A-site ionic radius.”

Tensile-strained NaNbO3 epitaxial films with thickness of 250 nm are a ferroelectric Q phase rather than antiferroelectric at room temperature.

“For instance, it was found that tensile-strained NaNbO 3 epitaxial films with thickness of 250 nm are a FE Q phase rather than AFE at room temperature [222,225].”

• cites [222]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites [225]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

To achieve antiferroelectric behavior, extra ZrO2 is usually introduced to stabilize the metastable state.

“To achieve an AFE behavior, extra ZrO 2 are usually introduced to stabilize the metastable state, and the electric field induced nonpolar tetragonal → polar orthorhombic phase transition is widely accepted as the origin of AFE behaviors in the fluorite-type material [273].”

• cites [273]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Decreasing the A-site ion size introduces chemical pressure that enhances tilting of the oxygen octahedra and favors the antipolar structure in BFO.

“By decreasing the A-site ion size, the introduced chemical pressure enhances tilting of the oxygen octahedra and favors the antipolar structure [256].”

• cites [256]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Antiferroelectric behaviors were obtained in other doped HfO2 and pure ZrO2 thin films.

“Then, the AFE behaviors were obtained in other doped HfO 2 and pure ZrO 2 thin films [262,263].”

• cites [262]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites [263]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Compared with perovskite-type antiferroelectric materials, fluorite-type antiferroelectric materials show more compelling advantages in CMOS compatibility and integration.

“Compared with perovskite-type AFE materials, these fluorite-type AFE materials show more compelling advantages in CMOS compatibility and integration [264,265].”

• cites [264]Not matched

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• cites [265]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

A slim ferroelectric hysteresis loop with a small remnant polarization was observed in AgNbO3 under a weak electric field of 80 kV/cm.

“However, a slim FE hysteresis loop with a small remnant polarization was also observed under a weak electric field of 80 kV/cm [229]”

• cites [229]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

BNT undergoes rhombohedral (R3c, a-a-a-) to tetragonal (P4bm, a0a0c+) to cubic phase transitions with increasing temperature.

“Later, it is reported that BNT undergoes rhombohedral (R3c, a -a -a -) → tetragonal (P4bm, a 0 a 0 c + ) → cubic phase transitions with increasing temperature”

• cites [241]Not matched

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• cites [242]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Compared with bulk, AgNbO3 thin films are poorly studied mainly because of the difficulty in synthesizing high-quality and phase-pure samples.

“Compared with bulk, AgNbO 3 thin films are poorly studied mainly because of the difficulty in synthesizing high-quality and phase-pure samples [233,234].”

• cites [233]Not matched

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• cites [234]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Subsequent studies confirmed universal behavior in structural and electric properties in BFO doped with various rare-earth elements, including La3+, Dy3+, and Nd3+.

“Furthermore, subsequent studies confirmed the universal behavior in structural and electric properties in BFO doped with various rare-earth elements, including La 3+ [258], Dy 3+ [259], Nd 3+ [255,260].”

• cites [258]Not matched

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• cites [259]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites [255]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites [260]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Hf1-xZrxO2-based antiferroelectric materials are among the most promising for future microelectronic systems because of CMOS compatibility and excellent fatigue resistance in nonvolatile random access memory, energy storage, and negative capacitance.

“it indeed becomes one of the most promising materials for future utilization in microelectronic system, not only because of its compatibility with the CMOS technique, but also because of its excellent fatigue resistance in nonvolatile random access memory, energy storage, and negative capacitance [61,280].”

• cites [61]Not matched

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• cites [280]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• AssumptionRests on an assumption: The origin of Hf1-xZrxO2-based antiferroelectricity and its structure details are still obscure.

In 2007, Fu et al. obtained the first complete double hysteresis loop with a large polarization of 52 μC/cm2 in AgNbO3 ceramics under an electric field up to 220 kV/cm.

“In 2007, the first complete double hysteresis loop with a large polarization of 52 μC/cm 2 was obtained by Fu et al. in AgNbO 3 ceramics, where electric field is applied up to 220 kV/cm [229].”

• cites [229]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

The fatigue in pristine FE thin films is attributed to the polar-antipolar phase transition, not to oxygen loss or domain wall pinning.

“this kind of fatigue is attributed to the polar-antipolar phase transition, but not to oxygen loss or domain wall pinning”

• cites [274]Not matched

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Partial ordering of Nb displacements induced by coupling between (a-b-c-)/(a-b-c+) octahedral-tilting and local polar Nb displacements dominates the structural behavior of the M-phase polymorphs of AgNbO3.

“They further demonstrated that partial ordering of Nb displacements induced by coupling between (a -b -c -)/(a -b -c + ) octahedral-tilting and local polar Nb displacements dominate the structural behavior of the M-phase polymorphs [230].”

• cites [230]Not matched

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Recent high-resolution X-ray diffraction experiments suggest that the room-temperature ferroelectric structure of BNT is monoclinic (Cc, a-a-c-).

“For the room temperature FE structure, recent high resolution X-ray diffraction experiment suggests that the structure of BNT is monoclinic (Cc, a -a -c -) [243,244].”

• cites [243]Not matched

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• cites [244]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Impurity phases, mainly arising from decomposition of AgNbO3, are prone to appear during film deposition.

“An important reason lies in the fact that impurity phases, mainly arising from decomposition of AgNbO 3 , are prone to appear during the film deposition 236]”

• cites [236]Not matched

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Weak ferroelectricity in AgNbO3 was further confirmed in subsequent experiments.

“which was further confirmed in subsequent experiments [227].”

• cites [227]Not matched

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BNT has a sequence of several structural phase transitions upon heating: R(R3c, FE) → 200°C R+O(Pnma+R3c, AFE) → 280°C O(Pnma, AFE) → 320°C T(P4/mbm + P42/mnm, PE) → 520°C C(Pm3m).

“reinvestigation of phase transition and proposed that BNT has a sequence of several structural phase transitions upon heating [247,248], as given below: R(R3c, FE) ̅̅̅ ̅→ 200 o C R + O(Pnma + R3c, AFE) ̅̅̅ ̅→ 280 o C O(Pnma, AFE) ̅̅̅ ̅→ 320 o C T(P4/mbm + P 4 2 /mnm, PE) ̅̅̅ ̅→ 520 o C C(Pm 3m)”

• cites [247]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites [248]Not matched

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A fatigued sample can be rejuvenated by applying a slightly higher voltage.

“the fatigued sample can be rejuvenated by applying a slightly higher voltage.”

• cites [274]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

The BNT-BT solid solution broadens the temperature region of the antiferroelectric phase.

“Among them, BNT-BT solid solution is particularly interesting, which not only broadens the temperature region of AFE phase, but also greatly improves the piezoelectric, pyroelectric and energy storage performances due to the inherently rich phase boundaries (Fig. 8d) [237].”

• cites [237]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Interfacial electrostatic engineering can liberate the otherwise metastable antiferroelectric state of BFO.

“The interfacial electrostatic engineering can liberate the otherwise metastable AFE state of BFO (Fig. 9d), and the stability of the AFE phase can be further enhanced by tuning the dielectric constant of the neighboring layers [187].”

• cites [187]Not matched

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AgNbO3 undergoes a series of at least five reversible structural phase transitions.

“it is generally believed that AgNbO 3 undergoes a series of at least five reversible structural phase transitions (Fig. 8b) [228]”

• cites [228]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

The stability of the antiferroelectric phase in BFO can be further enhanced by tuning the dielectric constant of the neighboring layers.

“The interfacial electrostatic engineering can liberate the otherwise metastable AFE state of BFO (Fig. 9d), and the stability of the AFE phase can be further enhanced by tuning the dielectric constant of the neighboring layers [187].”

• cites [187]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

HfO2 thin films can be dominated by the metastable state at ambient conditions thermodynamically and kinetically by doping, stress, defects, thickness, and electric field.

“HfO 2 thin films can be dominated by the metastable state at ambient conditions thermodynamically and kinetically by doping [267], stress [268], defects [269], thickness [270], and electric field [271].”

• cites [267]Not matched

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• cites [268]Not matched

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• cites [269]Not matched

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The chemical pressure of A-site substituted cations can drive the formation of the morphotropic phase boundary in BFO.

“This proves that the chemical pressure of the A-site substituted cations can drive the formation of MPB.”

Imprint has been utilized to improve energy storage density in RFE thin films.

“This has been utilized to improve the energy storage density in RFE thin films [289,354].”

• cites [289]Not matched

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• cites [354]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

The hysteresis loop shift by imprint effect can effectively enhance EBDS and thus Pmax.

“Besides, the hysteresis loop shift by imprint effect can effectively enhance the E BDS and thus the P max .”

The overall polarization of AFEs can be modulated by introducing high-polarization phase, interface engineering, strain engineering, and orientation control.

“The overall polarization can be modulated by introducing high-polarization phase [295], interface engineering [296], strain engineering [205], and orientation control [19].”

• cites [295]Not matched

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• cites [296]Not matched

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• cites [205]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

In 2017, Li et al. reported excellent FE and AFE performances in (3-pyrrolinium)CdBr3.

“In 2017, Li et al. [77], reported excellent FE and AFE performances in (3-pyrrolinium) CdBr 3 .”

• cites [77]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

EBDS is inversely proportional to the square root of thickness, d (EBDS ∝ d^-1/2).

“Besides, E BDS is inversely proportional to the square root of thickness, d [304]:”

• cites [304]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

In (3-pyrrolinium)CdBr3, the AFE phase is an intermediate phase between the FE phase (<235.2 K) and PE phase (>244.2 K).

“In this organic-inorganic hybrid perovskite, the AFE phase can be seen as an intermediate phase between the FE phase (<235.2K) and PE phase(>244.2K).”

• cites [77]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Large strain level of ~0.3-1% can be obtained in AFE PbZrO3 thin films, several times larger than traditional FE and electrostrictive materials.

“Recent studies have demonstrated that large strain level of ~ 0.3-1 % can be obtained in AFE PbZrO 3 thin films, as shown in Fig. 13a, which is several times larger than traditional FE and electrostrictive materials [400][401][402].”

• cites [400]Not matched

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• cites [401]Not matched

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• cites [402]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Introducing nanoscale structural heterogeneity into AFEs generally via chemical doping is an effective approach to lower the energy barrier between the AFE and field-driven FE phases and thus reduce electric hysteresis.

“Previous studies have demonstrated that introducing nanoscale structural heterogeneity into AFEs generally via chemical doping is an effective approach to lower the energy barrier between the AFE and field-driven FE phases and thus reduce the electric hysteresis [157,[292][293][294].”

• cites [157,[292][293][294]Not matched

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The combination of structure heterogeneity and orientation control in relaxor AFE (Pb0.97La0.02)(Zr0.55Sn0.45)O3 thin films can simultaneously achieve high energy storage efficiency (~98.5%) and energy storage density (~84.45 J/cm3).

“For instance, Zhang et al. [294] demonstrated that the combination of structure heterogeneity and orientation control in relaxor AFE (Pb 0.97 La 0.02 )(Zr 0.55 Sn 0.45 )O 3 thin films can simultaneously achieve high energy storage efficiency (~98.5 %) and energy storage density (~84.45J/cm 3 ).”

• cites [294]Not matched

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AFEs lack piezoelectricity due to the presence of a center of symmetry.

“Although AFEs lack piezoelectricity due to the presence of the center of symmetry”

Disrupting long-range ordered antiferroelectric domains in relaxor antiferroelectrics reduces hysteresis upon applying and removing electric fields because of the fast response of nano-domains.

“Eventually, by disrupting long-range ordered AFE domains, relaxor antiferroelectrics (RAFEs) can reduce hysteresis upon applying and removing electric fields due to the fast response of nano-domains [293]”

• cites [293]Not matched

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A synergistic approach with engineered structural heterogeneity and meticulous orientation control can improve energy storage density.

“Therefore, a synergistic approach with engineered structural heterogeneity and meticulous orientation control can be applied to improve the energy storage density Fig. 11b.”

In addition to frequency, doping and stress are methods applied to modulate the ECE.

“In addition to frequency, many other methods have been applied to modulate the ECE such as doping [5,367] and stress [378].”

• cites [5]Not matched

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• cites [367]Not matched

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• cites [378]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

In relaxor antiferroelectrics, large E_BDS, small P_r and small hysteresis enable simultaneous enhancement of large J_reco and efficiency.

“That is to say, accompanied with large E BDS , small P r and small hysteresis enable the simultaneous enhancement of large J reco and η [293].”

• cites [293]Not matched

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The frequency of the external electric field significantly influences the ECE.

“As stated in Section 3.5, the frequency of the external electric field significantly influences the ECE.”

In 2019, Wu et al. reported an above-room-temperature AFE in the organic-inorganic Ruddlesden-Popper hybrid perovskite (i-BA)2CsPb2Br7.

“In 2019, Wu et al. [286], reported an above-room-temperature AFE in organic-inorganic Ruddlesden-Popper hybrid perovskite, (i-BA) 2 CsPb 2 Br 7 (i-BA is isobutylammonium).”

• cites [286]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

For practical applications of electrocaloric cooling, large ΔT and ΔS are needed to guarantee the cooling energy density Q.

“For practical applications of the electrocaloric cooling technology, large ΔT and ΔS are needed to guarantee the cooling energy density Q.”

Many factors can affect EBDS, including band gap, porosity/cavity, grain size, thickness, and sample geometry.

“There are many factors that can affect E BDS , such as band gap (E g ) [297], porosity/cavity [298], grain size [299], thickness [300], sample geometry [301], and etc.”

• cites [297]Not matched

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• cites [298]Not matched

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• cites [299]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Since 2011, the ECE of AFEs has attracted broad attention due to the large negative ΔT.

“Since then, the ECE of AFEs has attracted broad attention due to the large negative ΔT [5,[363][364][365].”

• cites [5]Not matched

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• cites [363]Not matched

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• cites [364]Not matched

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A sharp deformation can be induced by phase transitions from AFE to FE and AFE to PE under electric field or heating, especially along the field direction.

“a sharp deformation can also be induced by phase transitions from AFE to FE phase and AFE to PE phase under electric field or heating, especially in the direction along the field [399].”

• cites [399]Not matched

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La substitution in M-type hexaferrites can divide the lattice into different pieces, generating nano-domains with opposite polarization.

“La substitution can divide the lattice into different pieces, leading to the generation of nano-domains with opposite polarization [283].”

• cites [283]Not matched

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Introducing La3+ and Sn4+ dopants into AFE PbZrO3 can engineer structural heterogeneity and disrupt long-range ordered AFE domains, effectively decreasing polarization hysteresis (EAF-EFA).

“In that work, introducing La 3+ and Sn 4+ dopants into AFE PbZrO 3 can engineer the structural heterogeneity and disrupt the long-range ordered AFE domains, which can effectively decrease the polarization hysteresis (E AF -E FA ) [294].”

• cites [294]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Bandgap engineering is an effective method to improve energy storage properties.

“Thus, bandgap engineering is an effective method to improve energy storage properties [303].”

• cites [303]Not matched

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Imprint is related to the presence of an internal (built-in) electric field within FE/AFE films, which causes a shift of the P-E loop along the field axis.

“Imprint is related to the presence of an internal (built-in) electric field within the FE/AFE films, which causes a shift of the P-E loop along the field axis [131,353].”

• cites [131]Not matched

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• cites [353]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Among dielectric materials, AFE materials afford advantages for high recoverable energy storage density Jreco by steeply increasing polarization at a relatively high electric field EAF and fully releasing stored charge at another high electric field EFA.

“Among dielectric materials, including linear dielectrics (LDs), FEs, and relaxor FEs (RFEs), AFEs, AFE materials afford advantages for high J reco by steeply increasing the polarization at a relatively high electric field E AF and fully releasing the stored charge at another high electric field E FA , as shown in Fig. 11a.”

• AssumptionRests on an assumption: Capacitors generally have low energy densities (typically less than 10 J/cm3) relative to other energy storage systems.

Thin films show much higher energy density than bulk materials due to larger EBDS.

“As a result, thin films [305] show much higher energy density than bulk materials due to the larger E BDS”

• cites [305]Not matched

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For AFEs, the electric-field-driven ECE also evolves from negative to positive.

“From the right panel of Fig. 12a, similar to the temperature induced ECE evolution, the electric field driven ECE also evolves from negative to positive for AFEs.”

Hybrid organic-inorganic perovskite AFEs are expected to show significant potential in energy storage and electrocaloric cooling applications because of their chemical diversity and structural tunability.

“the hybrid organic-inorganic perovskite AFEs are expected to show significant potential in energy storage and electrocaloric cooling applications [286,287].”

• cites [286]Not matched

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• cites [287]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

The negative and positive ECE in AFEs can be combined to increase the value of Q.

“The negative and positive ECE in AFEs can be combined to increase the value of Q [367][368][369][370].”

• cites [367]Not matched

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• cites [368]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites [369]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

AFE phase in perovskite oxides can be stabilized by decreasing the tolerance factor t within the range of perovskite structural stability.

“AFE phase in perovskite oxides can be stabilized by decreasing t within the range of perovskite structural stability [355].”

• cites [355]Not matched

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• AssumptionRests on an assumption: The tolerance factor t is a critical indicator for the phase stability of perovskite structure.

In Ruddlesden-Popper structures, A3B2O7-type compounds such as high-temperature antipolar Pnab Sr3Zr2O7 are proposed as hybrid improper AFEs.

“In Ruddlesden-Popper structure, a series of A 3 B 2 O 7 type compounds are proposed as a hybrid improper AFE, such as high-temperature antipolar Pnab structure Sr 3 Zr 2 O 7 [284].”

• cites [284]Not matched

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Formation of defect dipoles by ion bombardment can induce imprint and delay low-field polarization saturation in RFE Pb(Mg1/3Nb2/3)O3-PbTiO3 thin films.

“It has been reported that the formation of defect dipoles by ion bombardment can induce the imprint and delay low-field polarization saturation in RFE Pb(Mg 1/3 Nb 2/3 )O 3 -PbTiO 3 thin films [289].”

• cites [289]Not matched

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Switching dynamics analysis based on the nucleation-limited-switching model revealed a characteristic switching time as short as 3 ns in AFE films, indicating ultrafast charging.

“The switching dynamics analysis based on the nucleation-limited-switching model has reveal a characteristic switching time as short as 3 ns [90], indicating an ultrafast charging time in AFE films.”

• cites [90]Not matched

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The volume change accompanied with field-driven phase transition is regarded as the main reason for electric-field-induced strain in AFE materials, other than domain reorientation, inverse piezoelectric effect, or electrostriction.

“The volume change accompanied with field-driven phase transition is regarded as the main reason for the electric field induced strain in AFE materials other than domain reorientation, inverse piezoelectric effect, or electrostriction [88].”

• cites [88]Not matched

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The antiferroelectricity in (i-BA)2CsPb2Br7 is attributed to the synergistic dynamic motion of organic i-BA cations and inorganic Cs atoms.

“The antiferroelectricity can be attributed to the synergistic dynamic motion of organic i-BA cations and inorganic Cs atoms.”

• cites [286]Not matched

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Antiferroelectricity exists in a wide range of unconventional structures, broadening the AFE family and understanding of antiferroelectricity.

“antiferroelectricity was reported to exist in a wide range of unconventional structures as well, which highly broadened the AFE family and understanding of antiferroelectricity.”