#
Polarization and Dielectric Properties of BiFeO_{3}-BaTiO_{3} Superlattice-Structured Ferroelectric Films

^{1}

^{2}

^{*}

## Abstract

**:**

_{3}and BaTiO

_{3}with a total thickness of 600 perovskite (ABO

_{3}) unit cells were grown on single-crystal SrTiO

_{3}substrates by pulsed laser deposition, and their polarization and dielectric properties were investigated. When the layers of Mn-BiFeO

_{3}and BaTiO

_{3}have over 25 ABO

_{3}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 BaTiO

_{3}and Mn-BiFeO

_{3}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.

_{3}; BaTiO

_{3}; superlattice; film; epitaxial thin film

## 1. Introduction

_{3}) is traditionally based on the formation of solid solutions. Lead zirconate titanate, Pb(Zr, Ti)O

_{3}, is representative, composed of ferroelectric PbTiO

_{3}in tetragonal symmetry, and antiferroelectric PbZrO

_{3}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)O

_{3}–PbTiO

_{3}and Pb(Zn, Nb)O

_{3}–PbTiO

_{3}, where an electric field (E) is considered to induce a rotation of spontaneous polarization (P

_{s}) [6].

_{3}) [7,8] has attracted considerable attention because of its multiferroic nature [9,10], i.e., the simultaneous presence of ferroelectric P

_{s}and an incommensurate spin cycloid structure, even at room temperature. Bulk BiFeO

_{3}has a rhombohedral structure in space group R3c and possesses a large P

_{s}along the pseudo-cubic [111]

_{c}direction [11,12]. Moreover, BiFeO

_{3}exhibits an extremely high Curie temperature (T

_{C}) of 830 ℃ [11,12], which can provide piezoelectric devices operating at high temperatures. In analogy to Pb(Zr, Ti)O

_{3}, considerable efforts have been made to investigate the solid solutions of rhombohedral BiFeO

_{3}and other perovskites in tetragonal symmetry. The BiFeO

_{3}–BaTiO

_{3}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 BaTiO

_{3}content causes a structural change from rhombohedral R3c to a pseudo-cubic structure [17], where the phase boundary is ambiguous at around 33% BaTiO

_{3}content. Moreover, it has been reported that BiFeO

_{3}–BaTiO

_{3}solid solutions do not have a ferroelectric nature in the BaTiO

_{3}content range of 40–50% [18].

_{3}and BaTiO

_{3}have been reported to show a high magnetoelectric coupling coefficient compared with pristine films or bulk ceramics of BiFeO

_{3}, where the interface plays a crucial role [21,22]. At present, ferroelectric and dielectric properties of BiFeO

_{3}–BaTiO

_{3}superlattices have been reported in a few reports [23,24,25], and thereby the fundamental questions remain unanswered concerning how the layers of BiFeO

_{3}and BaTiO

_{3}are structurally and ferroelectrically coupled, and how the coupling of the two layers is activated.

_{3}and BiFeO

_{3}on single-crystal SrTiO

_{3}substrates prepared by pulsed laser deposition (PLD) (Figure 1). Here, we adopted Mn(5%)-doped BiFeO

_{3}instead of BiFeO

_{3}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 Mn

^{3+}at the Fe

^{3+}site, i.e., a strong attractive interaction between Mn

^{3+}and oxygen vacancy, inhibits the formation of an oxygen vacancy-rich layer at the interfaces. The total number of ABO

_{3}unit cells were fixed at 600, and that of the BaTiO

_{3}and Mn-BiFeO

_{3}layers (N) varied from 300 down to 1 (Figure 1b), while the average composition of the entire superlattices remained unchanged, i.e., 50% Mn-BiFeO

_{3}–50% BaTiO

_{3}. 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 BaTiO

_{3}and Mn-BiFeO

_{3}layers are structurally and electronically coupled.

## 2. Materials and Methods

#### 2.1. Experimental

_{3}[29] and Mn(5%)-doped BiFeO

_{3}[28,30], a (Ba

_{0.7}Sr

_{0.3})TiO

_{3}buffer layer [29], and (Ba

_{0.1}Sr

_{0.9})RuO

_{3}electrodes [31] were fabricated on (100) SrTiO

_{3}single-crystal substrates (5 × 5 × 1 mm

^{3}) 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-BiFeO

_{3}and BaTiO

_{3}. The total number of ABO

_{3}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 BaTiO

_{3}and Mn-BiFeO

_{3}with three ABO

_{3}unit cells (N = 3). For all the samples, the Mn-BiFeO

_{3}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 BaTiO

_{3}layer. During the deposition, the following condition was adopted: a substrate temperature T

_{sub}of 640 °C, an oxygen pressure (Po

_{2}) of 2.6 Pa, and a laser repetition rate of 1 Hz for BaTiO

_{3}and 7 Hz for Mn-BiFeO

_{3}. 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.

_{1}source. The data of the intensity profile I

_{i}(q

_{x}, q

_{z}) of reflection i in the reciprocal space (q

_{x}, q

_{z}) 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 ABO

_{3}unit cell. Throughout this paper, we adopted the pseudo-cubic notation unless otherwise stated.

#### 2.2. DFT Calculations

_{3}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 BiFeO

_{3}films reveal that the crystal symmetry and the spontaneous polarization (P

_{s}) are not influenced by the doping of Mn up to 10%, and therefore we considered BiFeO

_{3}instead of Mn-doped BiFeO

_{3}for simplicity.

_{DFT}and out-of-plane c

_{DFT}in space group P4mm; its a

_{DFT}was fixed at the experimental a of 0.3985 nm, i.e., a

_{DFT}= a (experiment). The parameter c

_{DFT}is given by the following equation, ${c}_{\mathrm{DFT}}$ = $N{c}_{{\mathrm{BiFeO}}_{3}}+N{c}_{{\mathrm{BaTiO}}_{3}}$, where ${c}_{{\mathrm{BiFeO}}_{3}}$ denotes the parameter c of the BiFeO

_{3}unit cell, and ${c}_{{\mathrm{BaTiO}}_{3}}$ that of the BaTiO

_{3}unit cell. The ${c}_{{\mathrm{BiFeO}}_{3}}$ and ${c}_{{\mathrm{BaTiO}}_{3}}$ were determined from the lattice volumes (V) derived from the geometrical optimizations of the BaTiO

_{3}cell (5 × 5 × 5 k-point) and the BiFeO

_{3}cell in P4mm symmetry. Considering the antiparallel spin configuration, we performed the optimization calculation of the BiFeO

_{3}cell with 2${c}_{{\mathrm{BiFeO}}_{3}}$ (5 × 5 × 3 k-point) and regarded the half cell with ${c}_{{\mathrm{BiFeO}}_{3}}$ as the BiFeO

_{3}unit cell. For imposing the antiparallel spin configuration for N = 1, the long lattice with 2${c}_{\mathrm{super}}$ was taken as the superlattice cell, as depicted in Figure 2a. The structural optimizations were performed under a fixed a

_{DFT}and c

_{DFT}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 P

_{s}, as expressed by the following equation:

## 3. Results

#### 3.1. Crystal Structure

_{3}substrate at 46.5°, the (Ba

_{0.1}Sr

_{0.9})RuO

_{3}electrodes at 46.4°, and the (Ba

_{0.7}Sr

_{0.3})TiO

_{3}buffer at 44.7°, the sample with N = 300 exhibits peaks individual to the layers of BaTiO

_{3}and Mn-BiFeO

_{3}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.

_{3}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-BiFeO

_{3}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.

_{x}, q

_{z}) exhibit the following features: the (Ba

_{0.7}Sr

_{0.3})TiO

_{3}buffer and the (Ba

_{0.1}Sr

_{0.9})RuO

_{3}electrodes have an apparently small q

_{x}compared with the SrTiO

_{3}substrate, demonstrating that the parameter a of the (Ba

_{0.7}Sr

_{0.3})TiO

_{3}buffer is sufficiently expanded to the bulk value, and also that the (Ba

_{0.1}Sr

_{0.9})RuO

_{3}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-BiFeO

_{3}layer has a rhombohedral-like monoclinic M

_{A}structure. The splitting into two peaks of the 103 reflection of the Mn-BiFeO

_{3}layer stems from the ferroelastic domain variants. With further decreasing N, the splitting of the Mn-BiFeO

_{3}layer is smaller, and then the reflection can be regarded as a single peak for N = 25 and 10. At the same time, the q

_{z}of the Mn-BFO layer with N = 50, 25, and 10 becomes larger than that of N = 300, suggesting a structural change from the M

_{A}to monoclinic M

_{B}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 q

_{z}shift, and the apparent 1/2 1/2 3/2 reflection (Figure 3), indicate that the Mn-BiFeO

_{3}layer for N = 25 and 10 has a pseudo-tetragonal structure, with a small monoclinic (M

_{B}) distortion [39]. We note that for an N less than 5, the reflections from the Mn-BiFeO

_{3}and BaTiO

_{3}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

_{c}at 3 kHz), and Figure 6a,b display the resultant remanent polarization (P

_{r}) and the maximum polarization (P

_{max}) 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 P

_{r}, which is completely different from the solid solutions in the same composition (50% BaTiO

_{3}content) featuring a non-ferroelectric nature [18]. The N = 300 sample has a P

_{r}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 BaTiO

_{3}layer has the same a, whereas the Mn-BiFeO

_{3}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-BiFeO

_{3}layer adjacent to the boundary with the bottom electrode.

_{r}and P

_{max}are monotonically reduced (Figure 6a,b). We note that the relative dielectric permittivity (ε

_{r}) remains constant at ~120. This constant ε

_{r}can be understood in terms of a simple series connection of the capacitors of the Mn-BiFeO

_{3}and the BaTiO

_{3}layers. Considering an ε

_{r}of 399 for the Mn-BiFeO

_{3}capacitor, and that of 93 for the BaTiO

_{3}one (those were measured individually for their respective capacitors), we obtain ε

_{r}~150 (=2ε

_{r}(BaTiO

_{3})·ε

_{r(}Mn-BiFeO

_{3)}/[ε

_{r}(BaTiO

_{3})+ε

_{r}(Mn-BiFeO

_{3})]). This is qualitatively in good agreement with the experiment (ε

_{r}~120). In region III, with decreasing N, the P

_{r}is reduced, while the ε

_{r}is higher.

## 4. Discussion

_{s}component along the out-of-plane direction (P

_{s}//[001]

_{c}). In region I (N ≥ 25), the presence of the 1/2 1/2 3/2 reflection from the Mn-BiFeO

_{3}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 BaTiO

_{3}and Mn-BiFeO

_{3}. In the BaTiO

_{3}layer, the P

_{s}vector is present along [001]

_{c}; our DFT calculations reveal that the P

_{s}strength is 28.5 μC cm

^{−2}, which is close to the bulk value [42]. In contrast, the Mn-BiFeO

_{3}layer has a P

_{s}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 P

_{s}vector across it, as in ferroelastic domain walls [43,44,45,46,47,48,49,50]. As a result, a depolarization field (E

_{dep.}) is built up in the interface region, where the E

_{dep.}is present in a direction that prevents the change in the polarization component. Given that the P

_{s}vectors are switched by an E application, the P

_{r}is expected to be ~40 μC cm

^{−2}. The P

_{r}of 25 μC cm

^{−2}for N = 300 is smaller than this expected value, which is caused by a domain clamping by the E

_{dep}. In region I, the P

_{r}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 E

_{dep}.

_{3}layer is absent (Figure 3), and the polarization and dielectric properties (Figure 6) cannot be explained by the series connection of the capacitors of BaTiO

_{3}and Mn-BiFeO

_{3}. It is reasonable to consider that the superlattice has a unified unit cell, where electronic orbitals of the BaTiO

_{3}and the Mn-BiFeO

_{3}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 P

_{s}of 27.3 μC cm

^{−2}, which is close to the experimental P

_{r}(21.6 μC cm

^{−2}) of N = 1. Moreover, the enhancement in P

_{r}with increasing N (Figure 6a) can be qualitatively explained by the theoretical calculations (Figure 6d): P

_{s}is 31.4 μC cm

^{−2}for the N = 2 cell, and 43.7 μC cm

^{−2}for the N = 4 cell.

_{3}and the Mn-BiFeO

_{3}layers, where material properties can be tuned by different N(BaTiO

_{3}) and N(Mn-BiFeO

_{3}). For example, we can expect that N(BaTiO

_{3}) < N(Mn-BiFeO

_{3}) delivers an enhanced P

_{s}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

_{3}and BaTiO

_{3}with a total thickness of 600 perovskite (ABO

_{3}) unit cells. The number of ABO

_{3}unit cell (N) in the layers of Mn-BiFeO

_{3}and BaTiO

_{3}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 BaTiO

_{3}and Mn-BiFeO

_{3}layers are structurally and electronically coupled. With decreasing N from five to one, the εr is markedly enhanced, whereas the P

_{r}is reduced. DFT calculations show that the P

_{s}is suppressed with decreasing N, which is in good agreement with the experimental P

_{r}. 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

_{z}//[001] and the horizontal axis is q

_{x}//[110]. Schematics of (b) ferroelastic domain structure, (c) the crystal structure of the monoclinic M

_{A}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-BiFeO

_{3}layer and the tetragonal BaTiO

_{3}layer, Table S1: Deposition conditions of substrate temperature (T

_{sub}), oxygen partial pressure (Po

_{2}), laser repetition frequency, and laser fluence, Table S2: Number of laser shots to deposit one layers of Mn-BiFeO

_{3}and BaTiO

_{3}comprising the superlattice samples. Supplementary Note 1: Deposition conditions of PLD, Supplementary Note 2: Crystal structural analyses for the Mn (5%)-BiFeO

_{3}layer, Supplementary Note 3: Crystallographic relation between the monoclinic Mn-BiFeO

_{3}layer and the tetragonal BaTiO

_{3}layer, Supplementary Note 4: Superlattice structures and their ambiguity.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Sawaguchi, E. Ferroelectricity versus Antiferroelectricity in the Solid Solutions of PbZrO
_{3}and PbTiO_{3}. J. Phys. Soc. Jpn.**1953**, 8, 615–629. [Google Scholar] [CrossRef] - Jaffe, B.; Roth, R.S.; Marzullo, S. Piezoelectric properties of Lead zirconate-Lead titanate solid-solution ceramics. J. Appl. Phys.
**1954**, 25, 809–810. [Google Scholar] [CrossRef] - Noheda, B.; Gonzalo, J.; Cross, L.; Guo, R.; Park, S. Tetragonal-to-monoclinic phase transition in a ferroelectric perovskite: The structure of PbZr
_{0.52}Ti_{0.48}O_{3}. Phys. Rev. B**2000**, 61, 8687–8695. [Google Scholar] [CrossRef] [Green Version] - Park, S.-E.; Shrout, T.R. Ultrahigh strain and piezoelectric behavior in relaxor based ferroelectric single crystals. J. Appl. Phys.
**1997**, 82, 1804. [Google Scholar] [CrossRef] - Sun, E.; Cao, W. Relaxor-based ferroelectric single crystals: Growth, domain engineering, characterization and applications. Prog. Mater. Sci.
**2014**, 65, 124–210. [Google Scholar] [CrossRef] [Green Version] - Fu, H.; Cohen, R.E. Polarization rotation mechanism for ultrahigh electromechanical response in single-crystal piezoelectrics. Nature
**2000**, 403, 281–283. [Google Scholar] [CrossRef] - Wang, J.; Neaton, J.B.; Zheng, H.; Nagarajan, V.; Ogale, S.B.; Liu, B.; Viehland, D.; Vaithyanathan, V.; Schlom, D.G.; Waghmare, U.V.; et al. Epitaxial BiFeO
_{3}Multiferroic Thin Film Heterostructures. Science**2003**, 299, 1719–1722. [Google Scholar] [CrossRef] - Fiebig, M. Revival of the magnetoelectric effect. J. Phys. D Appl. Phys.
**2005**, 38, R123. [Google Scholar] [CrossRef] - Ramesh, R.; Spaldin, N.A. Multiferroics: Progress and prospects in thin films. Nat. Mater.
**2007**, 6, 21–29. [Google Scholar] [CrossRef] - Ederer, C.; Spaldin, N.A. Weak ferromagnetism and magnetoelectric coupling in bismuth ferrite. Phys. Rev. B Condens. Matter Mater. Phys.
**2005**, 71, 060401(R). [Google Scholar] [CrossRef] [Green Version] - Michel, C.; Moreau, J.M.; Achenbach, G.D.; Gerson, R.; James, W.J. The atomic structure of BiFeO
_{3}. Solid State Commun.**1969**, 7, 701–704. [Google Scholar] [CrossRef] - Kubel, F.; Schmid, H. Structure of a ferroelectric and ferroelastic monodomain crystal of the perovskite BiFeO
_{3}. Acta Crystallogr. Sect. B Struct. Sci.**1990**, 46, 698–702. [Google Scholar] [CrossRef] [Green Version] - Kumar, M.M.; Srinivas, A.; Suryanarayana, S.V. Structure property relations in BiFeO
_{3}/BaTiO_{3}solid solutions. J. Appl. Phys.**2000**, 87, 855–862. [Google Scholar] [CrossRef] - Kitagawa, S.; Ozaki, T.; Horibe, Y.; Yoshii, K.; Mori, S. Ferroelectric domain structures in BiFeO
_{3}-BaTiO_{3}. Ferroelectrics**2008**, 376, 122–128. [Google Scholar] [CrossRef] - Wang, T.H.; Ding, Y.; Tu, C.S.; Yao, Y.D.; Wu, K.T.; Lin, T.C.; Yu, H.H.; Ku, C.S.; Lee, H.Y. Structure, magnetic, and dielectric properties of (1−x)BiFeO
_{3}-xBaTiO_{3}ceramics. J. Appl. Phys.**2011**, 109, 07D907. [Google Scholar] [CrossRef] - Wei, Y.; Jin, C.; Zeng, Y.; Wang, X.; Xu, G.; Wang, X. Polar Order Evolutions near the Rhombohedral to Pseudocubic and Tetragonal to Pseudocubic Phase Boundaries of the BiFeO
_{3}-BaTiO_{3}System. Materials**2015**, 8, 8355–8365. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Kim, S.; Khanal, G.P.; Nam, H.W.; Fujii, I.; Ueno, S.; Moriyoshi, C.; Kuroiwa, Y.; Wada, S. Structural and electrical characteristics of potential candidate lead-free BiFeO
_{3}-BaTiO_{3}piezoelectric ceramics. J. Appl. Phys.**2017**, 122, 164105. [Google Scholar] [CrossRef] - Leontsev, S.O.; Eitel, R.E. Dielectric and Piezoelectric Properties in Mn-Modified (1−x)BiFeO
_{3}-xBaTiO_{3}Ceramics. J. Am. Ceram. Soc.**2009**, 92, 2957–2961. [Google Scholar] [CrossRef] - Ohtomo, A.; Muller, D.A.; Grazul, J.L.; Hwang, H.Y. Artificial charge-modulation in atomic-scale perovskite titanate superlattices. Nature
**2002**, 419, 378–380. [Google Scholar] [CrossRef] - Lee, H.N.; Christen, H.M.; Chisholm, M.F.; Rouleau, C.M.; Lowndes, D.H. Strong polarization enhancement in asymmetric three-component ferroelectric superlattices. Nature
**2005**, 433, 395–399. [Google Scholar] [CrossRef] [PubMed] - Lorenz, M.; Wagner, G.; Lazenka, V.; Schwinkendorf, P.; Modarresi, H.; Van Bael, M.J.; Vantomme, A.; Temst, K.; Oeckler, O.; Grundmann, M. Correlation of magnetoelectric coupling in multiferroic BaTiO
_{3}-BiFeO_{3}superlattices with oxygen vacancies and antiphase octahedral rotations. Appl. Phys. Lett.**2015**, 106, 012905. [Google Scholar] [CrossRef] [Green Version] - Lorenz, M.; Lazenka, V.; Schwinkendorf, P.; Van Bael, M.J.; Vantomme, A.; Temst, K.; Grundmann, M.; Höche, T. Epitaxial Coherence at Interfaces as Origin of High Magnetoelectric Coupling in Multiferroic BaTiO
_{3}–BiFeO_{3}Superlattices. Adv. Mater. Interfaces**2016**, 3, 1500822. [Google Scholar] [CrossRef] - Matsuo, H.; Noguchi, Y.; Miyayama, M.; Kiguchi, T.; Konno, T.J. Enhanced photovoltaic effects in ferroelectric solid solution thin films with nanodomains. Appl. Phys. Lett.
**2020**, 116, 132901. [Google Scholar] [CrossRef] - Hohenberger, S.; Jochum, J.K.; Van Bael, M.J.; Temst, K.; Patzig, C.; Höche, T.; Grundmann, M.; Lorenz, M. Enhanced magnetoelectric coupling in BaTiO
_{3}-BiFeO_{3}multilayers-an interface effect. Materials**2020**, 13, 197. [Google Scholar] [CrossRef] [Green Version] - Hohenberger, S.; Lazenka, V.; Selle, S.; Patzig, C.; Temst, K.; Lorenz, M. Magnetoelectric Coupling in Epitaxial Multiferroic BiFeO
_{3}–BaTiO_{3}Composite Thin Films. Phys. Status Solidi Basic Res.**2020**, 257, 1900613. [Google Scholar] [CrossRef] - Matsuo, H.; Kitanaka, Y.; Inoue, R.; Noguchi, Y.; Miyayama, M. Cooperative effect of oxygen-vacancy-rich layer and ferroelectric polarization on photovoltaic properties in BiFeO
_{3}thin film capacitors. Appl. Phys. Lett.**2016**, 108, 032901. [Google Scholar] [CrossRef] - Matsuo, H.; Kitanaka, Y.; Noguchi, Y.; Miyayama, M. Electrical conduction mechanism in BiFeO
_{3}-based ferroelectric thin-film capacitors: Impact of Mn doping. J. Asian Ceram. Soc.**2015**, 3, 426–431. [Google Scholar] [CrossRef] [Green Version] - Noguchi, Y.; Matsuo, H.; Kitanaka, Y.; Miyayama, M. Ferroelectrics with a controlled oxygen-vacancy distribution by design. Sci. Rep.
**2019**, 9, 4225. [Google Scholar] [CrossRef] - Noguchi, Y.; Maki, H.; Kitanaka, Y.; Matsuo, H.; Miyayama, M. Control of misfit strain in ferroelectric BaTiO
_{3}thin-film capacitors with SrRuO_{3}-based electrodes on (Ba, Sr)TiO_{3}-buffered SrTiO_{3}substrates. Appl. Phys. Lett.**2018**, 113, 012903. [Google Scholar] [CrossRef] - Matsuo, H.; Noguchi, Y.; Miyayama, M. Gap-state engineering of visible-light-active ferroelectrics for photovoltaic applications. Nat. Commun.
**2017**, 8, 207. [Google Scholar] [CrossRef] [Green Version] - Noguchi, Y.; Tada, M.; Kitanaka, Y.; Miyayama, M. Fabrication and characterization of (Ba, Sr)RuO
_{3}ceramic targets and thin films for ferroelectric BaTiO_{3}thin-film capacitors. AIP Adv.**2018**, 8, 115135. [Google Scholar] [CrossRef] [Green Version] - Langreth, D.C.; Perdew, J.P. Theory of nonuniform electronic systems. I. Analysis of the gradient approximation and a generalization that works. Phys. Rev. B
**1980**, 21, 5469–5493. [Google Scholar] [CrossRef] - Blöchl, P.E. Projector augmented-wave method. Phys. Rev. B
**1994**, 50, 17953–17979. [Google Scholar] [CrossRef] [Green Version] - Kresse, G.; Hafner, J. Ab initio molecular-dynamics simulation of the liquid-metal–amorphous-semiconductor transition in germanium. Phys. Rev. B
**1994**, 49, 14251–14269. [Google Scholar] [CrossRef] - Perdew, J.P.; Ruzsinszky, A.; Csonka, G.I.; Vydrov, O.A.; Scuseria, G.E.; Constantin, L.A.; Zhou, X.; Burke, K. Restoring the Density-Gradient Expansion for Exchange in Solids and Surfaces. Phys. Rev. Lett.
**2008**, 100, 136406. [Google Scholar] [CrossRef] [Green Version] - Anisimov, V.I.; Zaanen, J.; Andersen, O.K. Band theory and Mott insulators: Hubbard U instead of Stoner I. Phys. Rev. B
**1991**, 44, 943–954. [Google Scholar] [CrossRef] [Green Version] - Neaton, J.B.; Ederer, C.; Waghmare, U.V.; Spaldin, N.A.; Rabe, K.M. First-principles study of spontaneous polarization in multiferroic BiFeO
_{3}. Phys. Rev. B**2005**, 71, 014113. [Google Scholar] [CrossRef] [Green Version] - Gonze, X.; Lee, C. Dynamical matrices, Born effective charges, dielectric permittivity tensors, and interatomic force constants from density-functional perturbation theory. Phys. Rev. B Condens. Matter Mater. Phys.
**1997**, 55, 10355–10368. [Google Scholar] [CrossRef] - Chen, Z.; Qi, Y.; You, L.; Yang, P.; Huang, C.W.; Wang, J.; Sritharan, T.; Chen, L. Large tensile-strain-induced monoclinic M
_{B}phase in BiFeO_{3}epitaxial thin films on a PrScO_{3}substrate. Phys. Rev. B Condens. Matter Mater. Phys.**2013**, 88, 054114. [Google Scholar] [CrossRef] [Green Version] - Zubko, P.; Catalan, G.; Tagantsev, A.K. Flexoelectric effect in solids. Annu. Rev. Mater. Res.
**2013**, 43, 387–421. [Google Scholar] [CrossRef] [Green Version] - Maki, H.; Noguchi, Y.; Kutsuna, K.; Matsuo, H.; Kitanaka, Y.; Miyayama, M. Crystal structure and polarization hysteresis properties of ferroelectric BaTiO 3 thin-film capacitors on (Ba,Sr)TiO
_{3}-buffered substrates. Jpn. J. Appl. Phys.**2016**, 55, 10TA03. [Google Scholar] [CrossRef] [Green Version] - Imura, R.; Kitanaka, Y.; Oguchi, T.; Noguchi, Y.; Miyayama, M. Polarization properties and crystal structures of ferroelectric (Ba,Ca)TiO
_{3}single crystals. J. Adv. Dielectr.**2014**, 04, 1450003. [Google Scholar] [CrossRef] [Green Version] - Meyer, B.; Vanderbilt, D. Ab initio study of ferroelectric domain walls in PbTiO
_{3}. Phys. Rev. B**2002**, 65, 104111. [Google Scholar] [CrossRef] [Green Version] - Catalan, G.; Seidel, J.; Ramesh, R.; Scott, J.F. Domain wall nanoelectronics. Rev. Mod. Phys.
**2012**, 84, 119–156. [Google Scholar] [CrossRef] [Green Version] - Farokhipoor, S.; Noheda, B. Conduction through 71° Domain Walls in BiFeO
_{3}Thin Films. Phys. Rev. Lett.**2011**, 107, 127601. [Google Scholar] [CrossRef] [Green Version] - Dennis, M.D.; Bradt, R.C. Thickness of 90° ferroelectric domain walls in (Ba,Pb)TiO
_{3}single crystals. J. Appl. Phys.**1974**, 45, 1931–1933. [Google Scholar] [CrossRef] - Yang, S.Y.; Seidel, J.; Byrnes, S.J.; Shafer, P.; Yang, C.-H.; Rossell, M.D.; Yu, P.; Chu, Y.-H.; Scott, J.F.; Ager, J.W.; et al. Above-bandgap voltages from ferroelectric photovoltaic devices. Nat. Nanotechnol.
**2010**, 5, 143–147. [Google Scholar] [CrossRef] [Green Version] - Inoue, R.; Ishikawa, S.; Imura, R.; Kitanaka, Y.; Oguchi, T.; Noguchi, Y.; Miyayama, M. Giant photovoltaic effect of ferroelectric domain walls in perovskite single crystals. Sci. Rep.
**2015**, 5, 14741. [Google Scholar] [CrossRef] - Matsuo, H.; Kitanaka, Y.; Inoue, R.; Noguchi, Y.; Miyayama, M.; Kiguchi, T.; Konno, T.J.T.J. Bulk and domain-wall effects in ferroelectric photovoltaics. Phys. Rev. B
**2016**, 94, 214111. [Google Scholar] [CrossRef] - Noguchi, Y.; Inoue, R.; Matsuo, H. Domain-wall photovoltaic effect in Fe-doped BaTiO
_{3}single crystals. J. Appl. Phys.**2021**, 129, 084101. [Google Scholar] [CrossRef]

**Figure 1.**Schematics of the superlattice-structured thin film composed of layers of Mn(5%)-doped BiFeO

_{3}and BaTiO

_{3}. The total thickness of the superlattice is fixed at 600 ABO

_{3}unit cells (

**a**), and the number (N) of ABO

_{3}in the two layers varies from 300 to 1, see (

**b**) for N = 3.

**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 BiFeO

_{3}is employed instead of Mn-BiFeO

_{3}for simplicity. The in-plane lattice parameter a

_{DFT}of the superlattice cell was fixed at the experiment: a (experiment) = 0.3985 nm. The out-of-plane lattice parameter c

_{DFT}of the superlattice cell was determined from the cell volume obtained by geometrical optimizations in our preceding calculations of BiFeO

_{3}and BaTiO

_{3}in tetragonal P4mm symmetry.

**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 ABO

_{3}unit cells in the two layers of Mn-BiFeO

_{3}and BaTiO

_{3}comprising the superlattice. We confirmed that the integrated intensity of 1/2 1/2 3/2 reflection of the pristine Mn-BiFeO

_{3}film (300 unit cell thickness) is almost the same as that for N = 300.

**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 q

_{z}//[001] and the horizontal axis is q

_{x}//[100], where N denotes the number of ABO

_{3}unit cells in the two layers of Mn-BiFeO

_{3}and BaTiO

_{3}comprising the superlattice. Here, [001] and [100] are the crystallographic directions of the (100) SrTiO

_{3}substrate.

**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 ABO

_{3}unit cells in the two layers of Mn-BiFeO

_{3}and BaTiO

_{3}comprising the superlattice.

**Figure 6.**(

**a**) Remanent polarization (P

_{r}), (

**b**) relative dielectric permittivity (ε

_{r}), (

**c**) polarization maximum at the maximum E (P

_{max}), and (

**d**) spontaneous polarization (P

_{s}) from DFT calculations of the unified unit cells in Figure 2.

**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 P

_{s}. In (

**a**), the thickness of the layers of Mn-BiFeO

_{3}and BaTiO

_{3}is sufficiently thin, and thereby their polarization features are maintained inside them. In (

**b**), the structural and electronic coupling of Mn-BiFeO

_{3}and BaTiO

_{3}is activated, and the two layers can no longer be distinguished, leading to a unified ferroelectric unit cell.

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**MDPI and ACS Style**

Noguchi, Y.; Matsuo, H.
Polarization and Dielectric Properties of BiFeO_{3}-BaTiO_{3} 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 BiFeO_{3}-BaTiO_{3} Superlattice-Structured Ferroelectric Films. *Nanomaterials*. 2021; 11(7):1857.
https://doi.org/10.3390/nano11071857

**Chicago/Turabian Style**

Noguchi, Yuji, and Hiroki Matsuo.
2021. "Polarization and Dielectric Properties of BiFeO_{3}-BaTiO_{3} Superlattice-Structured Ferroelectric Films" *Nanomaterials* 11, no. 7: 1857.
https://doi.org/10.3390/nano11071857