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Article

Polarization and Dielectric Properties of BiFeO3-BaTiO3 Superlattice-Structured Ferroelectric Films

by 1,* and 2,*
1
Division of Information and Energy, Faculty of Advanced Science and Technology, Kumamoto University, 2-39-1, Kurokami, Chuo-ku, Kumamoto 860-8555, Japan
2
International Research Organization for Advanced Science & Technology (IROAST), Kumamoto University, 2-39-1, Kurokami, Chuo-ku, Kumamoto 860-8555, Japan
*
Authors to whom correspondence should be addressed.
Nanomaterials 2021, 11(7), 1857; https://doi.org/10.3390/nano11071857
Received: 21 June 2021 / Revised: 9 July 2021 / Accepted: 16 July 2021 / Published: 19 July 2021
(This article belongs to the Special Issue Pulsed Laser Deposited Nanostructures)

Abstract

:
Superlattice-structured epitaxial thin films composed of Mn(5%)-doped BiFeO3 and BaTiO3 with a total thickness of 600 perovskite (ABO3) unit cells were grown on single-crystal SrTiO3 substrates by pulsed laser deposition, and their polarization and dielectric properties were investigated. When the layers of Mn-BiFeO3 and BaTiO3 have over 25 ABO3 unit cells (N), the superlattice can be regarded as a simple series connection of their individual capacitors. The superlattices with an N of 5 or less behave as a unified ferroelectric, where the BaTiO3 and Mn-BiFeO3 layers are structurally and electronically coupled. Density functional theory calculations can explain the behavior of spontaneous polarization for the superlattices in this thin regime. We propose that a superlattice formation comprising two types of perovskite layers with different crystal symmetries opens a path to novel ferroelectrics that cannot be obtained in a solid solution system.

1. Introduction

Chemical tuning of the dielectric, ferroelectric, and piezoelectric properties of perovskite oxides (ABO3) is traditionally based on the formation of solid solutions. Lead zirconate titanate, Pb(Zr, Ti)O3, is representative, composed of ferroelectric PbTiO3 in tetragonal symmetry, and antiferroelectric PbZrO3 in rhombohedral symmetry [1,2]. In this system, the dielectric and piezoelectric properties are maximized near the composition-driven phase boundary [2], called the morphotropic phase boundary (MPB) [3], between the tetragonal and rhombohedral structures. The similar materials strategy has provided an extremely high piezoelectric response [4,5] in solid solutions such as Pb(Mg, Nb)O3–PbTiO3 and Pb(Zn, Nb)O3–PbTiO3, where an electric field (E) is considered to induce a rotation of spontaneous polarization (Ps) [6].
Recently, bismuth ferrite (BiFeO3) [7,8] has attracted considerable attention because of its multiferroic nature [9,10], i.e., the simultaneous presence of ferroelectric Ps and an incommensurate spin cycloid structure, even at room temperature. Bulk BiFeO3 has a rhombohedral structure in space group R3c and possesses a large Ps along the pseudo-cubic [111]c direction [11,12]. Moreover, BiFeO3 exhibits an extremely high Curie temperature (TC) of 830 ℃ [11,12], which can provide piezoelectric devices operating at high temperatures. In analogy to Pb(Zr, Ti)O3, considerable efforts have been made to investigate the solid solutions of rhombohedral BiFeO3 and other perovskites in tetragonal symmetry. The BiFeO3–BaTiO3 system [13,14,15,16,17] has been widely studied mainly in ceramic form because the MPB is expected to appear between rhombohedral R3c and tetragonal P4mm. Detailed structural analysis reveals that an increase in the BaTiO3 content causes a structural change from rhombohedral R3c to a pseudo-cubic structure [17], where the phase boundary is ambiguous at around 33% BaTiO3 content. Moreover, it has been reported that BiFeO3–BaTiO3 solid solutions do not have a ferroelectric nature in the BaTiO3 content range of 40–50% [18].
Another approach exploiting the interplay of two types of perovskite oxides is to build a superlattice by thin-film growth technology [19,20]. Epitaxially grown superlattices composed of BiFeO3 and BaTiO3 have been reported to show a high magnetoelectric coupling coefficient compared with pristine films or bulk ceramics of BiFeO3, where the interface plays a crucial role [21,22]. At present, ferroelectric and dielectric properties of BiFeO3–BaTiO3 superlattices have been reported in a few reports [23,24,25], and thereby the fundamental questions remain unanswered concerning how the layers of BiFeO3 and BaTiO3 are structurally and ferroelectrically coupled, and how the coupling of the two layers is activated.
In this paper, we report the crystal structure, polarization, and dielectric properties of superlattice-structured epitaxial thin films composed of BaTiO3 and BiFeO3 on single-crystal SrTiO3 substrates prepared by pulsed laser deposition (PLD) (Figure 1). Here, we adopted Mn(5%)-doped BiFeO3 instead of BiFeO3 to avoid a considerable influence of oxygen vacancies on the polarization and leakage current properties [23,26,27,28], because a trapping capability of oxygen vacancies by Mn3+ at the Fe3+ site, i.e., a strong attractive interaction between Mn3+ and oxygen vacancy, inhibits the formation of an oxygen vacancy-rich layer at the interfaces. The total number of ABO3 unit cells were fixed at 600, and that of the BaTiO3 and Mn-BiFeO3 layers (N) varied from 300 down to 1 (Figure 1b), while the average composition of the entire superlattices remained unchanged, i.e., 50% Mn-BiFeO3–50% BaTiO3. We found that the samples for an N greater than 25 can be regarded as a simple series connection of their individual capacitors, while those for an N of 5 or less behave as a unified ‘ferroelectric’, where the BaTiO3 and Mn-BiFeO3 layers are structurally and electronically coupled.

2. Materials and Methods

2.1. Experimental

Thin films of BaTiO3 [29] and Mn(5%)-doped BiFeO3 [28,30], a (Ba0.7Sr0.3)TiO3 buffer layer [29], and (Ba0.1Sr0.9)RuO3 electrodes [31] were fabricated on (100) SrTiO3 single-crystal substrates (5 × 5 × 1 mm3) by PLD (KrF excimer laser, λ = 248 nm) using ceramic targets. The details of the deposition conditions are summarized in Supplementary Tables S1 and S2. Figure 1 displays the schematic of the superlattice composed of Mn-BiFeO3 and BaTiO3. The total number of ABO3 unit cells was fixed at 600 (Figure 1a). The number (N) of those in each layer forming the superlattice varied: N = 300, 50, 25, 10, 5, 3, and 1. Figure 1b depicts the structure of N = 3 as an example, where the superlattice is constructed by an alternate stacking of the thin layers of BaTiO3 and Mn-BiFeO3 with three ABO3 unit cells (N = 3). For all the samples, the Mn-BiFeO3 layer was deposited on the bottom electrode because of its better in-plane lattice matching with it. As a result, the layer just beneath the top electrode was the BaTiO3 layer. During the deposition, the following condition was adopted: a substrate temperature Tsub of 640 °C, an oxygen pressure (Po2) of 2.6 Pa, and a laser repetition rate of 1 Hz for BaTiO3 and 7 Hz for Mn-BiFeO3. The diameter of the top electrode was 0.1 mm. The polarization electric field (P-E) hysteresis properties were measured at 25 °C (3 kHz); the direction from the bottom to the top electrode was defined as positive for E and P.
High-resolution X-ray diffraction (XRD) reciprocal space maps (RSMs) were observed by using a Cu-1 source. The data of the intensity profile Ii(qx, qz) of reflection i in the reciprocal space (qx, qz) were used for the detailed analysis of the lattice parameters of the in-plane (a) and the out-of-plane (c) directions, where the parameters a and c denote those of the pseudo-cubic ABO3 unit cell. Throughout this paper, we adopted the pseudo-cubic notation unless otherwise stated.

2.2. DFT Calculations

Density functional theory (DFT) calculations were conducted using the generalized gradient approximation [32] with a plane wave basis set. We used the projector-augmented wave method [33] as implemented in the Vienna ab initio simulation package (VASP) [34]. We employed the Perdew–Burke–Ernzerhof gradient-corrected exchange correlation functional revised for solids (PBEsol) [35] and a plane wave cut-off energy of 520 eV. A Γ centered k-point mesh was used, and the details are provided later. Within the simplified generalized gradient approximation (GGA)+U approach [36], we added on-site Coulomb interaction parameters of U−J of 6 eV to Fe-3d throughout the calculations. As the spin configuration in BiFeO3 can be approximated as the G-type antiferromagnet [37], we set the spin arrangement in which the adjacent Fe ions have an antiparallel spin configuration as much as possible. The experimental results for Mn-doped BiFeO3 films reveal that the crystal symmetry and the spontaneous polarization (Ps) are not influenced by the doping of Mn up to 10%, and therefore we considered BiFeO3 instead of Mn-doped BiFeO3 for simplicity.
For building a superlattice cell, we took the following lattice constraint. Based on the experimental results of XRD for an N of 5 or less, the superlattice cell had a tetragonal structure with the lattice parameters of in-plane aDFT and out-of-plane cDFT in space group P4mm; its aDFT was fixed at the experimental a of 0.3985 nm, i.e., aDFT = a (experiment). The parameter cDFT is given by the following equation, c DFT = N c BiFeO 3 + N c BaTiO 3 , where c BiFeO 3 denotes the parameter c of the BiFeO3 unit cell, and c BaTiO 3 that of the BaTiO3 unit cell. The c BiFeO 3 and c BaTiO 3 were determined from the lattice volumes (V) derived from the geometrical optimizations of the BaTiO3 cell (5 × 5 × 5 k-point) and the BiFeO3 cell in P4mm symmetry. Considering the antiparallel spin configuration, we performed the optimization calculation of the BiFeO3 cell with 2 c BiFeO 3 (5 × 5 × 3 k-point) and regarded the half cell with c BiFeO 3 as the BiFeO3 unit cell. For imposing the antiparallel spin configuration for N = 1, the long lattice with 2 c super was taken as the superlattice cell, as depicted in Figure 2a. The structural optimizations were performed under a fixed aDFT and cDFT with 5 × 5 × 3 k-point mesh for all the supercells. From the structural parameters of the optimized cell, we obtained the atomic displacements (Δz) from the corresponding positions in the hypothetical non-polar paraelectric lattice. We also calculated the Born effective charges (Z*) [38] in the superlattice cells by density-functional perturbation theory. We estimated Ps, as expressed by the following equation:
P s = i m i · Δ z i · Z i * / V ,
where m i denotes the site multiplicity of the constituent atom i, and Δ z i · Z i * is its dipole moment. The summation in Equation (1) is taken over the superlattice cell with the cell volume (V).

3. Results

3.1. Crystal Structure

Supplementary Figure S1 shows the θ-2θ XRD patterns around the 002 reflection. In addition to the peaks of the SrTiO3 substrate at 46.5°, the (Ba0.1Sr0.9)RuO3 electrodes at 46.4°, and the (Ba0.7Sr0.3)TiO3 buffer at 44.7°, the sample with N = 300 exhibits peaks individual to the layers of BaTiO3 and Mn-BiFeO3 because their layers are sufficiently thick for providing their corresponding reflections. With decreasing N, the integrated intensities of these peaks are weakened and eventually vanish for an N less than 5.
Supplementary Figure S2 shows the wide-area XRD-RSMs for N = 300 and 5. For N = 300 (Figure S2b), the apparent reflections of 3/2 3/2 1/2 and 1/2 1/2 3/2 of Mn-BiFeO3 in monoclinic symmetry appear, whereas those were not observed for an N of 5 (Figure S2d) or less. Figure 3 shows the integrated intensity of the 1/2 1/2 3/2 reflection as a function of N. With decreasing N, the intensity is weakened and then zero for N = 1–5. These results indicate that the monoclinic distortion, similar to the bulk (rhombohedral), is maintained in the Mn-BiFeO3 layer for the superlattice with N ≥ 10, while that is lost with N ≤ 5. The details of the structural analysis are described in Supplementary Note 2.
Figure 4 shows the high-resolution XRD-RSMs around the 103 reflections. For all the samples, the peak positions (qx, qz) exhibit the following features: the (Ba0.7Sr0.3)TiO3 buffer and the (Ba0.1Sr0.9)RuO3 electrodes have an apparently small qx compared with the SrTiO3 substrate, demonstrating that the parameter a of the (Ba0.7Sr0.3)TiO3 buffer is sufficiently expanded to the bulk value, and also that the (Ba0.1Sr0.9)RuO3 bottom electrode is coherently grown on the buffer. The detailed structural analysis for N = 300 (Figure 4a along with the 113 reflection; see Supplementary Note 2) indicates that the Mn-BiFeO3 layer has a rhombohedral-like monoclinic MA structure. The splitting into two peaks of the 103 reflection of the Mn-BiFeO3 layer stems from the ferroelastic domain variants. With further decreasing N, the splitting of the Mn-BiFeO3 layer is smaller, and then the reflection can be regarded as a single peak for N = 25 and 10. At the same time, the qz of the Mn-BFO layer with N = 50, 25, and 10 becomes larger than that of N = 300, suggesting a structural change from the MA to monoclinic MB phases owing to an in-plane tensile strain (see Supplementary Note 2). The experimental results, i.e., the single peak of the 103 reflection, the qz shift, and the apparent 1/2 1/2 3/2 reflection (Figure 3), indicate that the Mn-BiFeO3 layer for N = 25 and 10 has a pseudo-tetragonal structure, with a small monoclinic (MB) distortion [39]. We note that for an N less than 5, the reflections from the Mn-BiFeO3 and BaTiO3 layers cannot be distinguished. These results enable us to consider that the superlattice has a unified tetragonal cell with a c/a of 1.01–1.02 as an average structure.

3.2. Polarization and Dielectric Properteis

Figure 5 shows the P-E loops (E//[001]c at 3 kHz), and Figure 6a,b display the resultant remanent polarization (Pr) and the maximum polarization (Pmax) at the highest positive E as a function of N, respectively. It is interesting to note that the superlattice samples exhibit an apparent ferroelectric polarization with an apparent Pr, which is completely different from the solid solutions in the same composition (50% BaTiO3 content) featuring a non-ferroelectric nature [18]. The N = 300 sample has a Pr of 22 μC cm−2. The P-E loop exhibits an imprint, i.e., a shift in the negative E direction. This behavior is assumed to stem from a flexoelectric effect [29,40,41], where a strain gradient in the out-of-plane direction in the ferroelectric layer stabilizes the upward polarization compared with the downward one. Compared with the buffered electrode with a = 0.3986 nm, the BaTiO3 layer has the same a, whereas the Mn-BiFeO3 layer possesses a slightly small a = 0.3965 nm. This result indicates that a strain gradient driving the flexoelectric effect is present in the Mn-BiFeO3 layer adjacent to the boundary with the bottom electrode.
From the data shown in Figure 6a–c, we think that the polarization and dielectric behavior can be divided into three regions: I. the simple series connection of the capacitors (N ≥ 25, see Figure 7a), II. the transition region (10 ≤ N < 25), and III. the unified ferroelectric regime (N < 10, see Figure 7b). In region I, with decreasing N, the hysteresis is slanted, and the resultant Pr and Pmax are monotonically reduced (Figure 6a,b). We note that the relative dielectric permittivity (εr) remains constant at ~120. This constant εr can be understood in terms of a simple series connection of the capacitors of the Mn-BiFeO3 and the BaTiO3 layers. Considering an εr of 399 for the Mn-BiFeO3 capacitor, and that of 93 for the BaTiO3 one (those were measured individually for their respective capacitors), we obtain εr~150 (=2εr(BaTiO3εr(Mn-BiFeO3)/[εr(BaTiO3)+εr(Mn-BiFeO3)]). This is qualitatively in good agreement with the experiment (εr~120). In region III, with decreasing N, the Pr is reduced, while the εr is higher.

4. Discussion

Figure 7 shows the schematics of the superlattice structures along with the Ps component along the out-of-plane direction (Ps//[001]c). In region I (N ≥ 25), the presence of the 1/2 1/2 3/2 reflection from the Mn-BiFeO3 layer (Figure 3) and the polarization and dielectric properties (Figure 6) indicate that the superlattice can be regarded as the simple series connection of the capacitors of BaTiO3 and Mn-BiFeO3. In the BaTiO3 layer, the Ps vector is present along [001]c; our DFT calculations reveal that the Ps strength is 28.5 μC cm−2, which is close to the bulk value [42]. In contrast, the Mn-BiFeO3 layer has a Ps nearly along [111]c, and the value is reported to be 90–100 μC cm−2 [37]. As the polarization components along [001]c in these layers are markedly different, the interface effect plays an important role. It is assumed that the interface region of several to several tens of unit cells in width needs to accommodate the difference in the direction and strength of the Ps vector across it, as in ferroelastic domain walls [43,44,45,46,47,48,49,50]. As a result, a depolarization field (Edep.) is built up in the interface region, where the Edep. is present in a direction that prevents the change in the polarization component. Given that the Ps vectors are switched by an E application, the Pr is expected to be ~40 μC cm−2. The Pr of 25 μC cm−2 for N = 300 is smaller than this expected value, which is caused by a domain clamping by the Edep. In region I, the Pr is reduced when the N is smaller, which is because the volume fraction of the clamped domains is raised by a denser interface with the Edep.
In region III, the 1/2 1/2 3/2 reflection of the Mn-BiFeO3 layer is absent (Figure 3), and the polarization and dielectric properties (Figure 6) cannot be explained by the series connection of the capacitors of BaTiO3 and Mn-BiFeO3. It is reasonable to consider that the superlattice has a unified unit cell, where electronic orbitals of the BaTiO3 and the Mn-BiFeO3 layers are hybridized. In other words, these two layers are no longer distinguished, but the structural and electronic features are completely different from the solid solutions [18]. On the assumption that the superlattice has a unified unit cell (Figure 2), our DFT calculations show that the N = 1 cell has a Ps of 27.3 μC cm−2, which is close to the experimental Pr (21.6 μC cm−2) of N = 1. Moreover, the enhancement in Pr with increasing N (Figure 6a) can be qualitatively explained by the theoretical calculations (Figure 6d): Ps is 31.4 μC cm−2 for the N = 2 cell, and 43.7 μC cm−2 for the N = 4 cell.
Finally, we comment on an additional degree of freedom in superlattice design by adopting an unequal N in the BaTiO3 and the Mn-BiFeO3 layers, where material properties can be tuned by different N(BaTiO3) and N(Mn-BiFeO3). For example, we can expect that N(BaTiO3) < N(Mn-BiFeO3) delivers an enhanced Ps in a unified cell in the superlattice. Moreover, superlattice design based on different unit cell numbers is anticipated to provide a means to control the strain effect at will.

5. Conclusions

We investigated the crystal structure and dielectric and polarization properties of superlattice-structured epitaxial thin films composed of Mn(5%)-doped BiFeO3 and BaTiO3 with a total thickness of 600 perovskite (ABO3) unit cells. The number of ABO3 unit cell (N) in the layers of Mn-BiFeO3 and BaTiO3 varied from 300 down to 1. It was revealed that the superlattices for an N greater than 25 can be regarded as a simple series connection of their individual capacitors. In the thin regime of an N of five or less, the superlattice behaves as a unified ferroelectric, where the BaTiO3 and Mn-BiFeO3 layers are structurally and electronically coupled. With decreasing N from five to one, the εr is markedly enhanced, whereas the Pr is reduced. DFT calculations show that the Ps is suppressed with decreasing N, which is in good agreement with the experimental Pr. We conclude that superlattices formed by two types of perovskite layers with different crystal symmetries represent a path to novel ferroelectrics that cannot be obtained in a solid solution system.

Supplementary Materials

The following are available online at https://www.mdpi.com/article/10.3390/nano11071857/s1, Figure S1: θ-2θ XRD patters around 002 reflection, Figure S2: Wide-area XRD-RSMs, Figure S3: Lattice parameters estimated from the peak positions of 103 reflection in the high-resolution XRD-RSMs as a function of N, Figure S4: (a) High-resolution XRD-RSM around 113 reflection for N = 300 where the vertical axis is qz//[001] and the horizontal axis is qx//[110]. Schematics of (b) ferroelastic domain structure, (c) the crystal structure of the monoclinic MA phase, and reciprocal lattice vectors of two domains comprising the ferroelastic domain structure projected onto (d) [100]c vs [001]c plane and (e) [110]c vs [001]c plane, Figure S5: Relationships between the rhombohedral-like monoclinic Mn-BiFeO3 layer and the tetragonal BaTiO3 layer, Table S1: Deposition conditions of substrate temperature (Tsub), oxygen partial pressure (Po2), laser repetition frequency, and laser fluence, Table S2: Number of laser shots to deposit one layers of Mn-BiFeO3 and BaTiO3 comprising the superlattice samples. Supplementary Note 1: Deposition conditions of PLD, Supplementary Note 2: Crystal structural analyses for the Mn (5%)-BiFeO3 layer, Supplementary Note 3: Crystallographic relation between the monoclinic Mn-BiFeO3 layer and the tetragonal BaTiO3 layer, Supplementary Note 4: Superlattice structures and their ambiguity.

Author Contributions

Y.N. and H.M. conceived and initiated the project. Y.N. carried out theoretical calculations and wrote the manuscript. H.M. supervised experiments. All authors have read and agreed to the published version of the manuscript.

Funding

This research is supported by JSPS through Grant-in-Aid for JSPS Fellows (26-4693). This research is partly supported by JSPS KAKENHI Grant Numbers 26249094 and 17H06239.

Data Availability Statement

The data that support the findings of this study are available upon reasonable request from the corresponding author.

Acknowledgments

We thank H. Maki for thin-film deposition and experiments.

Conflicts of Interest

The authors declare no competing interests.

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Figure 1. Schematics of the superlattice-structured thin film composed of layers of Mn(5%)-doped BiFeO3 and BaTiO3. The total thickness of the superlattice is fixed at 600 ABO3 unit cells (a), and the number (N) of ABO3 in the two layers varies from 300 to 1, see (b) for N = 3.
Figure 1. Schematics of the superlattice-structured thin film composed of layers of Mn(5%)-doped BiFeO3 and BaTiO3. The total thickness of the superlattice is fixed at 600 ABO3 unit cells (a), and the number (N) of ABO3 in the two layers varies from 300 to 1, see (b) for N = 3.
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Figure 2. Crystal structures of the superlattice cells with (a) N = 1, (b) N = 2, and (c) N = 4 obtained from the structural optimizations by DFT calculations, where BiFeO3 is employed instead of Mn-BiFeO3 for simplicity. The in-plane lattice parameter aDFT of the superlattice cell was fixed at the experiment: a (experiment) = 0.3985 nm. The out-of-plane lattice parameter cDFT of the superlattice cell was determined from the cell volume obtained by geometrical optimizations in our preceding calculations of BiFeO3 and BaTiO3 in tetragonal P4mm symmetry.
Figure 2. Crystal structures of the superlattice cells with (a) N = 1, (b) N = 2, and (c) N = 4 obtained from the structural optimizations by DFT calculations, where BiFeO3 is employed instead of Mn-BiFeO3 for simplicity. The in-plane lattice parameter aDFT of the superlattice cell was fixed at the experiment: a (experiment) = 0.3985 nm. The out-of-plane lattice parameter cDFT of the superlattice cell was determined from the cell volume obtained by geometrical optimizations in our preceding calculations of BiFeO3 and BaTiO3 in tetragonal P4mm symmetry.
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Figure 3. Integrated intensity of 1/2 1/2 3/2 reflection in the XRD-RSMs as a function of N, where N denotes the number of ABO3 unit cells in the two layers of Mn-BiFeO3 and BaTiO3 comprising the superlattice. We confirmed that the integrated intensity of 1/2 1/2 3/2 reflection of the pristine Mn-BiFeO3 film (300 unit cell thickness) is almost the same as that for N = 300.
Figure 3. Integrated intensity of 1/2 1/2 3/2 reflection in the XRD-RSMs as a function of N, where N denotes the number of ABO3 unit cells in the two layers of Mn-BiFeO3 and BaTiO3 comprising the superlattice. We confirmed that the integrated intensity of 1/2 1/2 3/2 reflection of the pristine Mn-BiFeO3 film (300 unit cell thickness) is almost the same as that for N = 300.
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Figure 4. High-resolution XRD-RSMs around 103 reflection for (a) N = 300, (b) N = 50, (c) N = 25, (d) N = 10, (e) N = 5, (f) N = 3 and (g) N = 1, where the vertical axis is qz//[001] and the horizontal axis is qx//[100], where N denotes the number of ABO3 unit cells in the two layers of Mn-BiFeO3 and BaTiO3 comprising the superlattice. Here, [001] and [100] are the crystallographic directions of the (100) SrTiO3 substrate.
Figure 4. High-resolution XRD-RSMs around 103 reflection for (a) N = 300, (b) N = 50, (c) N = 25, (d) N = 10, (e) N = 5, (f) N = 3 and (g) N = 1, where the vertical axis is qz//[001] and the horizontal axis is qx//[100], where N denotes the number of ABO3 unit cells in the two layers of Mn-BiFeO3 and BaTiO3 comprising the superlattice. Here, [001] and [100] are the crystallographic directions of the (100) SrTiO3 substrate.
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Figure 5. Polarization (P) electric field (E) hysteresis loops at 25 ℃, for (a) N = 300, (b) N = 50, (c) N = 10, (d) N = 5, (e) N = 3 and (f) N = 1, where an E of 3 kHz is applied along [001], where N denotes the number of ABO3 unit cells in the two layers of Mn-BiFeO3 and BaTiO3 comprising the superlattice.
Figure 5. Polarization (P) electric field (E) hysteresis loops at 25 ℃, for (a) N = 300, (b) N = 50, (c) N = 10, (d) N = 5, (e) N = 3 and (f) N = 1, where an E of 3 kHz is applied along [001], where N denotes the number of ABO3 unit cells in the two layers of Mn-BiFeO3 and BaTiO3 comprising the superlattice.
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Figure 6. (a) Remanent polarization (Pr), (b) relative dielectric permittivity (εr), (c) polarization maximum at the maximum E (Pmax), and (d) spontaneous polarization (Ps) from DFT calculations of the unified unit cells in Figure 2.
Figure 6. (a) Remanent polarization (Pr), (b) relative dielectric permittivity (εr), (c) polarization maximum at the maximum E (Pmax), and (d) spontaneous polarization (Ps) from DFT calculations of the unified unit cells in Figure 2.
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Figure 7. Schematics of the crystal structures of the supercells with (a) N ≥ 25, and (b) N ≤ 5, along with the [001]c component of Ps. In (a), the thickness of the layers of Mn-BiFeO3 and BaTiO3 is sufficiently thin, and thereby their polarization features are maintained inside them. In (b), the structural and electronic coupling of Mn-BiFeO3 and BaTiO3 is activated, and the two layers can no longer be distinguished, leading to a unified ferroelectric unit cell.
Figure 7. Schematics of the crystal structures of the supercells with (a) N ≥ 25, and (b) N ≤ 5, along with the [001]c component of Ps. In (a), the thickness of the layers of Mn-BiFeO3 and BaTiO3 is sufficiently thin, and thereby their polarization features are maintained inside them. In (b), the structural and electronic coupling of Mn-BiFeO3 and BaTiO3 is activated, and the two layers can no longer be distinguished, leading to a unified ferroelectric unit cell.
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Noguchi, Y.; Matsuo, H. Polarization and Dielectric Properties of BiFeO3-BaTiO3 Superlattice-Structured Ferroelectric Films. Nanomaterials 2021, 11, 1857. https://doi.org/10.3390/nano11071857

AMA Style

Noguchi Y, Matsuo H. Polarization and Dielectric Properties of BiFeO3-BaTiO3 Superlattice-Structured Ferroelectric Films. Nanomaterials. 2021; 11(7):1857. https://doi.org/10.3390/nano11071857

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Noguchi, Yuji, and Hiroki Matsuo. 2021. "Polarization and Dielectric Properties of BiFeO3-BaTiO3 Superlattice-Structured Ferroelectric Films" Nanomaterials 11, no. 7: 1857. https://doi.org/10.3390/nano11071857

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