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Advances in Condensed Matter Physics
Volume 2012 (2012), Article ID 714625, 10 pages
http://dx.doi.org/10.1155/2012/714625
Review Article

Ferroelectric Instability and Dimensionality in Bi-Layered Perovskites and Thin Films

Department of Physics, Hokkaido University, Sapporo 060-0810, Japan

Received 25 May 2012; Accepted 3 August 2012

Academic Editor: Biljana Stojanovic

Copyright © 2012 Akira Onodera et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The dielectric and thermal properties of Bi (bismuth)-layered perovskite SrBi2Ta2O9 (SBT) are discussed in comparison with ferroelectric thin BaTiO3 films. Although these two perovskites exhibit quite a different nature, the dielectric properties of BaTiO3 thin film are similar to those in bulk SBT. The dielectric properties and pseudo-two-dimensional structure between SBT and thin film suggest that the bulk layered ferroelectric SBT is a good model of ultra-thin ferroelectric film with two perovskite layers, free from any misfit lattice strain with substrate and surface charge at the interface with electrodes. Based on the mechanism of ferroelectric phase transition of SBT, it seems plausible that the ferroelectric interaction is still prominent but shows a crossover from ferroelectric to antiferroelectric interaction in perovskite ultra-thin films along the tetragonal axis.

1. Introduction

Barium titanate (BaTiO3) is a well-known ferroelectric with perovskite structure, which has been considered to be a prototype for many oxide ferroelectrics. The dielectric constant () follows a well-known Curie-Weiss law, , and shows a large dielectric anomaly at (409 K), which has been explained by the concept of soft mode by Cochran [1, 2]. Recently, however, it has been recognized that the dielectric constant begins to decrease with decreasing the sample thickness, and shows broad and non-Curie-Weiss behavior. This evidence indicates that the well-established soft mode may be modified in the treatment of lattice dynamics of thin films of BaTiO3, if the LST (Lyddane-Sachs-Teller) relation holds even in thin films as well as in bulk crystals. Furthermore, the anomalous part of specific heat () changes to a very broad and unclear one in thin BaTiO3 films, while it is sharp and large at in bulk crystals. This suggests that the temperature dependence of an order parameter (the spontaneous polarization in the case of ordinary ferroelectrics) plays somewhat in different manners as the usual mean-field behavior known in typical ferroelectrics, because is related to in the mean field theory as As pointed out by many researches, these novel ferroelectric properties are considered to be essentially due to the two-dimensionality in thin films.

On the other hand, the similar novel dielectric behavior has been found in layered perovskite compounds. SrBi2Ta2O9 (SBT) has been extensively studied as a candidate for ferroelectric nonvolatile memory devices [35]. SBT has a pseudo-two-dimensional crystal structure with two TaO6 perovskite groups sandwiched by Bi2O2 semiconducting layers along the pseudotetragonal axis within the unit cell. SBT undergoes a ferroelectric phase transition at 608 K, while the dielectric anomaly and anomalous specific heat are small in comparison with BaTiO3. This similarity of crystal structures and dielectric properties between BaTiO3 thin films and layered perovskite SBT shows that both materials have a common mechanism resulted in dielectric nature as discussed in the following section. Moreover, it suggests that SBT may be a good model for an ideal ferroelectric ultra-thin film with two perovskite unit cells, though SBT itself is a bulk crystal. In this paper, we will discuss the ferroelectric nature and stability in ultra-thin films on the basis of ferroelectric properties of Bi-layered perovskites.

2. Dielectric and Thermal Properties in BaTiO3 and SrBi2Ta2O9

The temperature dependence of of BaTiO3 and SBT is compared in Figure 1 as a function of for simplicity, where is a ferroelectric phase transition temperature of each perovskite, SBT, and BaTiO3. The large Curie-Weiss dielectric anomaly associated with ferroelectric phase transition was noticed in BaTiO3 at , while a broad non-Curie-Weiss behavior was observed in layered perovskite SBT [6, 814]. The half temperature widths of dielectric anomalies are 10 K for BaTiO3 and about 400 K for SBT, respectively. The spontaneous polarization () of SBT is relatively large (μC/cm2 along the axis at room temperature), while μC/cm2 in BaTiO3 along the tetragonal axis. As in SBT is the same order as those in order-disorder ferroelectrics, we expect that obeys the Curie-Weiss law and the peak value of is the order of several thousands. However, we could only observe a round peak of about 300 and weak temperature dependency around 608 K () in SBT.

fig1
Figure 1: Temperature dependence of dielectric constant of (a) BaTiO3 (black line) and SrBi2Ta2O9 (red line) and (b) that of an expanded figure in SrBi2Ta2O9 [6].

It is interesting to point out that similar diffuse and round dielectric anomalies were observed in ferroelectric thin films. In BaTiO3 epitaxial thin films, diffuse dielectric anomaly was reported by Yoneda et al. [7, 1518]. Thin films of BaTiO3 showed a small and broad dielectric anomaly as shown in Figure 2. The peak value of is 1400 for 4000 Å thick film, and only 370 for 1000 Å thick film. This similarity of dielectric properties suggests the existence of some common mechanism between SBT bulk crystal and BaTiO3 thin film. Recently, Tagantsev et al. discussed a two-dimensional strain effect on dielectric constant in perovskite ferroelectric thin films and reported a diffuse dielectric anomaly [19].

714625.fig.002
Figure 2: Temperature dependence of dielectric constant of SBT and BaTiO3 epitaxial thin films on SrTiO3 with 4000 Å and 1000 Å [7].

Thermal anomaly associated with the phase transition is also diffuse and widely spread in SBT as shown in Figure 3 [8, 10], while a sharp and large anomaly was found at in bulk BaTiO3 (Figure 4) [20]. However, the specific heat of BaTiO3 epitaxial films shows diffuse temperature dependence (Figure 5) just as those in SBT [21]. With decreasing thickness of epitaxial films of BaTiO3, the shape of anomalous part of specific heat becomes round and diffuse and exhibits thermal hysteresis in those with 2000 Å and 60 Å. In BaTiO3 polycrystalline thin films, a rather sharp anomaly was reported [22, 23]. The diffuse dielectric and thermal behavior observed around may be attributed to the two-dimensional effect in SBT and BaTiO3 epitaxial thin films.

714625.fig.003
Figure 3: Temperature dependence of specific heat of SrBi2Ta2O9 single crystal [8].
714625.fig.004
Figure 4: Temperature dependence of specific heat of BaTiO3 single crystal around the paraelectric-ferroelectric phase transition point [20].
fig5
Figure 5: Temperature dependence of specific heat of BaTiO3 epitaxial thin films on SrTiO3 substrate; (a) 2000 Å thick and (b) 60 Å thick. The arrows show the direction of heating and cooling. The sharp anomalous specific heat in the single crystal changes to diffuse one in thin films [21].

3. Structural Analogy: Pseudo-Two-Dimensionality

BaTiO3 has a prototype cubic crystal structure of perovskite in the paraelectric high-temperature phase (space group Pm3 m, with lattice parameter  Å at 393 K). It changes to tetragonal (space group P4 mm, ,  Å at r. t.) associated with the paraelectric-ferroelectric phase transition. The unit cell contains one TiO6 octahedron at the center and Ba ions locate at the corners. The TiO6 octahedron is tightly bonded with each other and generally considered as a hard unit, which has a regular octahedral form in the paraelectric phase. According to Slater, the correlation along the -O-Ti-O-Ti-O- chain is very strong along the tetragonal axis and the small octahedral distortion results in ferroelectricity below [26]. Epitaxial BaTiO3 films were grown by on SrTiO3 and MgO substrates using the activated reaction evaporation method, which were characterized by X-ray diffraction as shown in Figure 6 [24, 27]. Only the (0 0 l) reflections were observed. The submaximum peaks of the Laue function were observed around the fundamental peaks of the (0 0 1), (0 0 2), (0 0 3), and (0 0 4). The strong peaks denoted as “Sub” in Figure 6 mean the (0 0 l) reflections from the SrTiO3 substrate. This evidence indicates that this film is an epitaxial crystal with a perovskite structure. Two films with thickness of 2000 Å and 60 Å were used for the specific heat measurements. The heat capacity was measured using an a. c. calorimeter.

714625.fig.006
Figure 6: X-ray diffraction profiles along the [0 0 l] direction of the BaTiO3 thin films with 60 Å on SrTiO3 substrate (monochromatized CuKα). Subscript “Sub” means reflections from SrTiO3 substrate [24].

SrBi2Ta2O9 is a Bi-layered perovskite oxide with a highly anisotropic structure, where perovskite-type [SrTa2O7]2− groups and semiconducting [Bi2O2]2+ layers are stacked alternately along the pseudo-tetragonal axis as shown in Figure 7. The general chemical formula of Bi-layered perovskite oxides with stacking number () of octahedral BO6 perovskite groups is given as (Bi2O2)2+ ()2−, where , K+, Ba2+, Ca2+, Pb2+, Sr2+, Bi3+, , Ti4+, Nb5+, Ta5+, W6+, and to 6. Many of these compounds are ferroelectric with high transition temperatures. Ferroelectricity in SBT with was discovered below 608 K by Smolenskii et al. in 1961 [6]. The crystal structure of SBT is orthorhombic at r. t. with space group A21am (, ,  Å). The lattice is highly anisotropic and pseudo-two-dimensional, and the -O-Ta-O-Ta-O- linkage along the pseudo-tetragonal axis is interrupted by the existence of semiconducting Bi2O2 layers in SBT [11, 14, 25]. SBT undergoes two successive phase transitions at 608 K and 850 K. The high-temperature paraelectric phase is tetragonal with space group I4/mmm, , and  Å at 1000 K, where the TaO6 octahedra take antiparallel arrangements along the tetragonal axis. The crystal structures of the ferroelectric (300 K) and paraelectric phases (1000 K) were determined by X-ray diffraction as summarized in Tables 1 and 2. X-ray diffraction profile was given in Figure 8 [25].

tab1
Table 1: Positional and thermal parameters of ferroelectric phase (A21am) of SrBi2Ta2O9 at 300 K [25].
tab2
Table 2: Positional and thermal parameters of the paraelectric phase (I4/mmm) SrBi2Ta2O9 at 1000 K [25].
fig7
Figure 7: Crystal structure of (a) fundamental perovskite and (b) Bi-layered perovskite SrBi2Ta2O9 (upper half of the unit cell) [11, 25].
714625.fig.008
Figure 8: X-ray diffraction patterns of SrBi2Ta2O9 (CuKα) at 1000 K [25].

The shape of TaO6 octahedron is not perfect and is still distorted even in the paraelectric phase along the axis. The Ta-O bond length owned commonly by adjacent octahedra normal to the pseudo-tetragonal axis is a little bit short and that of O directed to Bi2O2 layer is long. In the ferroelectric phase, this crystal favors canted octahedral arrangements below , which results in the net spontaneous polarization along the -axis.

4. Ferroelectricity

Ferroelectricity in Bi-layered perovskite SrBi2Ta2O9 (SBT) does not appear along the pseudo-tetragonal axis but along the axis normal to the pseudo-tetragonal axis, while along the tetragonal axis in BaTiO3. The crystal structure is highly anisotropic along the pseudo-tetragonal axis and the single crystal of SBT has easily cleaved along the pseudo-tetragonal axis, as the semiconducting Bi2O2 layer connects weakly upper and lower perovskite groups by van der Waals interaction. Crystal structure analysis of SBT shows that TaO6 octahedra are still distorted along the pseudo-tetragonal axis, and locate in antiparallel way even in the high-temperature paraelectric phase above 850 K. Although the -O-Ta-O-Ta-O- chain along the pseudo-tetragonal axis is interrupted by the existence of semiconducting Bi2O2 layers, this evidence indicates the strong interaction to displace along the axis exists and the strongly correlated -O-Ta-O-Ta-O- chain should play an essential role for the appearance of ferroelectricity in SBT as those in BaTiO3 [26]. In the high-temperature paraelectric phase, total polarization cancels by the antiparallel arrangement of octahedra, since TaO6 is not perfect octahedron but elongates along the axis; this indicates SBT is antiferroelectric above 850 K. In the ferroelectric phase, this crystal favors canted octahedral arrangements below , which results in the net spontaneous polarization along the axis. As this situation is just the same as those reported in the case of weak ferromagnetism in magnetic materials, we suggest canted ferroelectricity (weak ferroelectricity) for SBT.

On the other hand, this pseudo-two-dimensional character of crystal structure is just suitable for fabrication of thin films. The spontaneous polarization () is relatively large (μC/cm2 along the axis at room temperature), while μC/cm2 in a representative perovskite ferroelectric BaTiO3 along the tetragonal axis.

It should be noticed that these two perovskite oxides exhibit quite different dielectric nature. However, it is very interesting to point out the similarity in dielectric properties between BaTiO3 thin films and SBT bulk crystals, since BaTiO3 thin ferroelectric films exhibit diffuse dielectric anomaly.

5. Size Effect in Ferroelectric Thin Films

Ferroelectricity appears due to a delicate balance between long-range dipole-dipole interaction along the polar axis and short-range interaction. The typical dipolar correlation lengths for many ferroelectrics are  Å along the polar axis and  Å normal to the polar axis [28]. The needle-shaped correlation region is sketched in Figure 9, where is several unit cells, of the same order as the thickness of a 180° domain wall, and is about  unit cells in the case of BaTiO3. Therefore, it should be reasonable to consider that the stability of the ferroelectricity may be suppressed by decreasing the thickness of the thin films.

714625.fig.009
Figure 9: Ferroelectric correlation region in dipolar materials [28].

Measurements of thickness dependence of ferroelectricity are generally not so easy, because of difficulties in preparation of good quality of thin films, and additional surface effects such as depolarization fields, space-charge effects, and misfit strain between film and substrate. These effects essentially influence the ferroelectric behavior in thin films. Many attempts have been reported to study the thickness dependence of ferroelectric properties of ferroelectric thin films prepared by vacuum evaporation, sputtering techniques, chemical vapor deposition, and so on.

Tybell, Ahn, and Triscone have examined the possibility of the existence of a critical thickness and showed the detection of the ferroelectricity in perovskite Pb(Zr0.2Ti0.8)3 films down to a thickness of 10 unit cells (40 Å) [37]. Bune et al. reported ferroelectric activity in ferroelectric polymer films with thickness of two layers (10 Å) and the near absence of finite-size effects in these two-dimensional ferroelectrics which may be generated by coupling only within the plane of the film [38]. Recent Ab initio studies have confirmed the possibility of retaining the ferroelectricity in ultra-thin films, and suggested the absence of the critical size effect [39, 40].

On the other hand, Junquera and Ghosez reported first-principle calculations on a realistic model of perovskite thin films with metallic electrodes. They showed that BaTiO3 films with SrRuO3 electrodes have the critical thickness of 6 unit cells (~24 Å) and lose the ferroelectricity below this thickness, due to the depolarization field effect at the ferroelectric-metal interfaces (Figure 10) [29].

714625.fig.0010
Figure 10: First-principles calculations of the energy of BaTiO3 ferroelectric films with unit cells as a function of the soft-mode distortion [29].

Recent Raman scattering studies showed that ultra-thin BaTiO3 films grown commensurately on SrTiO3 substrates have a spontaneous polarization as thin as 4 unit cells (16 Å) [30]. The ferroelectric phase transition temperature are shown as a function of BaTiO3 film thickness in Figure 11. Recent experimental and theoretical works showed the critical thickness is much smaller than those previously reported.

714625.fig.0011
Figure 11: The plot of the ferroelectric phase transition temperature versus film thickness of BaTiO3 films grown on SrTiO3 substrates, observed by Raman scattering [30].

6. Mechanism of Phase Transition in SBT

It should be pointed out the close analogy of ferroelectric behavior between Bi-layered perovskite SrBi2Ta2O9 (SBT) and thin film of the so-called typical ferroelectric perovskite BaTiO3. The crystal structures of the high-temperature paraelectric phase at 1000 K and the ferroelectric phase at r. t. are schematically shown in Figure 10 [25]. The TaO6 octahedra are distorted in both phases. Even in the high-temperature paraelectric phase, the octahedra are elongated along the pseudo-tetragonal axis and locate in an antiparallel way. The distortion parameter of one TaO6 octahedron, , defined as is estimated to be 1.365 debye along the axis as shown in Table 3, where and are charge and position of each constituent ion, and is the gravity center of TaO6. The parameter is obtained as (0, 0, 1.365) in debye unit in the high-temperature paraelectric phase. In the ferroelectric phase, the absolute value is 1.682 debye, which is almost the same as that of the high-temperature paraelectric phase within errors. If the distortion of octahedron corresponds to a dipole moment, it should be probable that SBT prefers an antiferroelectric structure along the -axis, when the distorted octahedra are mainly responsible for the ferroelectric activity. Furthermore, these distorted octahedra have a canted arrangement in the ferroelectric phase as shown in Figure 12.

tab3
Table 3: Estimated dipole moment of TaO6 octahedron of the ferroelectric phase at 300 K (A21am) and the high-temperature paraelectric phase (I4/mmm) at 1000 K [25].
fig12
Figure 12: Crystal structures of (a) the paraelectric and (b) the ferroelectric phases of layered perovskite SrBi2Ta2O9. Arrows show estimated dipole arrangements of TaO6 octahedra [25].

These structural arrangements of TaO6 octahedra in SBT remind us of a canted-ferromagnet (or weak ferromagnet) discussed by Moriya [41] and in layered canted-ferromagnets by de Gennes [42]. The free energy is given in terms of sublattice polarizations , , and an angle between them as where the third symmetrical term is a well-known exchange interaction and the last term is an antisymmetric Dzialoshinski-Moriya interaction. If and , the above expression is just the same as that for antiferroelectrics proposed by Kittel [43]. The last term favors the canted arrangement of dipoles rather than antiferroelectric one. From the condition, , we get the following relation: As the observed value of is 154°, the coefficient of the antisymmetric term is about half of the symmetric one . From the relations we have the expression for the dielectric susceptibility as where when we assume . It is evident that the dielectric susceptibility shows small anomaly just like antiferroelectric one, which may be smeared by two-dimensional surface strain as pointed out by Tagantsev et al. [19]. Because of the term of the Dzialoshinski-Moriya interaction, the ferroelectric phase transition will be realized in SBT, and the characteristic weak dielectric properties may be explained. The asymmetric interaction may be attributed to the two-dimensional effect in SBT and BaTiO3 epitaxial thin films.

The decrease and nonclear behavior of dielectric constant were also observed around with decreasing film thickness in (Ba, Sr)TiO3 thin films. In this case, Hwang analyzed this decrease by considering the effects of a finite charge-screening length of metal electrodes and an intrinsic dead layer of the surface [44]. The layered ferroelectric SBT is a bulk crystal itself, and is considered to be an example of ultra-thin ferroelectric model with two perovskite layers, free from any misfit lattice strain and interface charge layer with electrodes.

It should be pointed out that the ferroelectricity of perovskite thin films with two unit cells may be stable even in those with , although its polarization does not appear along the tetragonal axis but along the axis normal to the tetragonal axis (within layer). Therefore, there is a crossover of ferroelectric to antiferroelectric interaction along the tetragonal axis, with decreasing the stacking number of perovskite units. Furthermore, the ultra-thin films prefer an antiferroelectric structure rather than a ferroelectric structure in thin films.

7. Soft Mode in Bi-Layered Perovskite

Measurements of the soft mode of SBT have been reported by Raman scattering as shown in Figure 13 [31, 32, 45]. The square of soft mode frequency decreases toward the highest phase transition temperature (850 K) and shows a clear anomaly at 610 K (). The soft mode exists in the ferroelectric phase and shows highly overdamped behavior near , although dielectric constant does not diverse at . Another anomaly was detected in the share strain c44 at 850 K [46], which corresponds to the high-temperature phase transition at 850 K.

714625.fig.0013
Figure 13: Temperature dependence of soft mode frequency (square of Raman frequency shift) and a normalized damping factor Γ(T)/Γ() in SrBi2Ta2O9 [3133].

A series of Bi-layered perovskites compounds Bi2mAnmBnO3(n+m) were synthesized by Aurivillius in 1949 [47]. As Sr2Bi4Ti5O18 is a compound with five perovskite layers with Bi2O2 semiconducting layers as shown in Figure 14, it is considered as a model of perovskite thin film with five unit cells. This crystal undergoes a ferroelectric phase transition at 558 K, although it has been reported that the ferroelectricity of thin films may be suppressed below six unit cells after Junquera and Ghosez [29]. In this compound, similar dielectric properties as those observed in SBT have been reported. The spontaneous polarization appears along the axis and the dielectric constant shows rather weak temperature dependence. In Sr2Bi4Ti5O18, similar temperature dependence of soft mode was observed by Raman scattering [33]. Raman spectra showed two anomalies at 551 K and at 730 K. The soft mode frequency decreases toward 730 K, although it shows overdamped behavior over 450 K. Furthermore, two additional relaxation modes have been observed, which show an anomaly at 551 K. Even in the case of SBT () and Sr2Bi4Ti5O18 (), the soft mode still exists, although it becomes highly overdamped near .

714625.fig.0014
Figure 14: Crystal structure of Bi-layered perovskite A2Bi4Ti5O18 with .

8. Summary and Discussion

Bi-layered perovskites have been much attracted as a promising material for ferroelectric integrated devices. According to the calculations of local field by Luttinger and Tisza [48], the strong ferroelectric interaction between Ti (or Ta) ion and O ions appears along the tetragonal axis. Although the strongly correlated -O-Ti-O-Ti-O- chain plays an important role for the appearance of ferroelectricity in bulk BaTiO3 [26], the -O-Ta-O-Ta-O- chain along the pseudo-tetragonal axis is interrupted by the existence of semiconductor Bi2O2 layers in SBT. The strength of interaction between Ti ion and adjacent O ions is half, but antiferroelectric in the - plane. However, the configuration of distortion parameter in Figure 12 suggests us that the interaction is strong but antiferroelectric along the pseudotetragonal axis, and ferroelectric along the axis in SBT. It is expected that a crossover of ferroelectric to antiferroelectric interaction will be realized even in thin films of BaTiO3, considering the similarity of dielectric properties between SBT bulk crystal and thin BaTiO3 films mentioned above. In this sense, SBT bulk crystals may be considered as a model of ferroelectric thin films. It might be expected that the cant of dipole moments may be induced even in thin BaTiO3 films by the two-dimensionality.

The suppression of ferroelectricity has been reported for nano-particles of BaTiO3 and PbTiO3, where the critical size is  unit cells [49]. However, the dipole-dipole interactions within plane are retained and contribute to ferroelectric activity in the case of thin films.

The dielectric and structural analogy between SrBi2Ta2O9 and thin film suggests that this bulk layered ferroelectric is a good model of ultra-thin ferroelectric films with two layers of TaO6 perovskite units, free from any misfit lattice strain with substrate and surface charge at the interface with electrodes. In perovskite ultra-thin films, ferroelectric interactions are still prominent and the octahedra prefer an antiferroelectric arrangement rather than ferroelectric one along the tetragonal axis (normal to the plane) in the case of two layers. The soft mode exists but changes to be highly over damped near the ferroelectric phase transition temperature. Moreover, the mechanism mentioned above might be applicable for Sr2Bi4Ti5O18 with five perovskite groups (), because the almost same dielectric behavior has been observed in Sr2Bi4Ti5O18 which has perovskite units less than six unit cells. Further experiments will be necessary both in layered oxide ferroelectrics and perovskite thin films.

References

  1. W. Cochran, “Crystal stability and the theory of ferroelectricity,” Advances in Physics, vol. 9, pp. 387–423, 1960. View at Publisher · View at Google Scholar
  2. W. Cochran, “Crystal stability and the theory of ferroelectricity part II. Piezoelectric crystals,” Advances in Physics, vol. 10, pp. 401–420, 1961.
  3. C. A.-P. de Marajo, J. D. Cushier, L. D. McMillan, et al., “Fatigue-free ferroelectric capacitors with platinum electrodes,” Nature, vol. 374, pp. 627–629, 1995.
  4. J. F. Scott, “NANO-phase SBT-family ferroelectric memories,” Ferroelectrics Review, vol. 1, pp. 1–14, 1998.
  5. M. Dauber, K. M. Raba, and J. F. Scott, “Physics of thin-film ferroelectric oxides,” Reviews of Modern Physics, vol. 77, pp. 1083–1130, 2005. View at Publisher · View at Google Scholar
  6. G. A. Smolenskii, V. A. Isupov, and A. I. Agranovskaya, “Ferroelectrics of the oxygen-octahedral type with layered structure,” Soviet Physics, vol. 3, no. 3, pp. 651–655, 1961.
  7. Y. Yoneda, H. Kasatani, H. Terauchi, Y. Yano, T. Terashima, and Y. Bando, “Ferroelectric phase transition in BaTiO3 films,” Journal of the Physical Society of Japan, vol. 62, no. 6, pp. 1840–1843, 1993. View at Scopus
  8. K. Yoshio, A. Onodera, and H. Yamashita, “Ferroelectric phase transition and new intermediate phase in Bi-layered perovskite SrBi2Ta2O9,” Ferroelectrics, vol. 284, no. 1, pp. 65–74, 2003. View at Publisher · View at Google Scholar
  9. E. C. Subbarao, “A family of ferroelectric bismuth compounds,” Journal of Physics and Chemistry of Solids, vol. 23, no. 6, pp. 665–676, 1962. View at Scopus
  10. A. Onodera, K. Yoshio, C. C. Myint, S. Kojima, H. Yamashita, and T. Takama, “Thermal and structural studies of phase transitions in layered perovskite SrBi2Ta2O9,” Japanese Journal of Applied Physics B, vol. 38, no. 9, pp. 5683–5685, 1999. View at Scopus
  11. A. Onodera, T. Kubo, K. Yoshio, S. Kojima, H. Yamashita, and T. Takama, “Crystal structure of high-temperature paraelectric phase in Bi-layered perovskite Sr0.85Bi2.1Ta2O9,” Japanese Journal of Applied Physics B, vol. 39, no. 9, pp. 5711–5715, 2000. View at Scopus
  12. A. Onodera, K. Yoshio, C. C. Myint, et al., “Thermal behavior in ferroelectric SrBi2Ta2O9 thin films,” Ferroelectrics, vol. 241, pp. 159–166, 2000. View at Publisher · View at Google Scholar
  13. W. Murata, A. Onodera, K. Yoshio, et al., “Ferroelectric phase transition in layered perovskite SrBi2Ta2O9,” Ferroelectrics, vol. 270, no. 1, pp. 303–308, 2002. View at Publisher · View at Google Scholar
  14. A. Onodera, K. Yoshio, and H. Yamashita, “Structural study of intermediate phase in layered perovskite SrBi2Ta2O9 single crystal,” Japanese Journal of Applied Physics, vol. 42, pp. 6218–6221, 2003. View at Publisher · View at Google Scholar
  15. H. Terauchi, Y. Yoneda, Y. Watanabe et al., “Epitaxial BaTiO3 crystals,” Ferroelectrics, vol. 151, no. 1, pp. 21–26, 1994. View at Scopus
  16. Y. Yoneda, H. Kasatani, H. Terauchi, Y. Yano, T. Terashima, and Y. Bando, “Ferroelectric phase transition in BaTiO3 films,” Journal of Crystal Growth, vol. 150, no. 1, pp. 1090–1093, 1995. View at Scopus
  17. K. Iijima, T. Terashima, Y. Bando, K. Kamigaki, and H. Terauchi, “Atomic layer growth of oxide thin films with perovskite-type structure by reactive evaporation,” Journal of Applied Physics, vol. 72, no. 7, pp. 2840–2845, 1992. View at Publisher · View at Google Scholar · View at Scopus
  18. Y. Yano, K. Iijima, Y. Daitoh et al., “Epitaxial growth and dielectric properties of BaTiO3 films on Pt electrodes by reactive evaporation,” Journal of Applied Physics, vol. 76, no. 12, pp. 7833–7838, 1994. View at Publisher · View at Google Scholar · View at Scopus
  19. A. K. Tagantsev, N. A. Pertsev, P. Muralt, et al., “Strain-induced diffuse dielectric anomaly and critical point in perovskite ferroelectric thin films,” Physical Review B, vol. 65, Article ID 012104, 4 pages, 2001. View at Publisher · View at Google Scholar
  20. S. Grabovsky, M. Takesada, A. Onodera, et al., “Specific heat and light scattering data of barium titanate crystals near ferroelectric phase transition,” in Abstract of Annual Meeting of Physical Society of Japan, Kansei-Gakuin University, March 2012.
  21. A. Onodera, Y. Kawamura, T. Okabe, and H. Terauchi, “Specific heat in ferroelectric BaTiO3 epitaxial thin films,” Journal of the European Ceramic Society, vol. 19, no. 6-7, pp. 1477–1480, 1999. View at Scopus
  22. B. A. Strukov, S. T. Davitadze, S. A. Taraskin, et al., “Thermodynamical properties of the thin polycrystalline BaTiO3 films on substrates,” Ferroelectrics, vol. 286, pp. 245–250, 2003. View at Publisher · View at Google Scholar
  23. S. T. Davitadze, S. N. Kravchun, B. A. Strukov, B. M. Goltzman, V. V. Lemanov, and S. G. Shulman, “Specific heat and thermal conductivity of BaTiO3 polycrystalline thin films,” Applied Physics Letters, vol. 80, no. 9, pp. 1631–1633, 2002. View at Publisher · View at Google Scholar · View at Scopus
  24. H. Terauchi, Y. Watanabe, H. Kasatani et al., “Structural study of epitaxial BaTiO3 crystals,” Journal of the Physical Society of Japan, vol. 61, no. 7, pp. 2194–2197, 1992. View at Scopus
  25. H. Yamashita, K. Yoshio, W. Murata, et al., “Structural changes and ferroelectricity in bi-layered SrBi2Ta2O9,” Japanese Journal of Applied Physics, vol. 41, pp. 7076–7079, 2002.
  26. J. C. Slater, “The lorentz correction in barium titanate,” Physical Review, vol. 78, pp. 748–761, 1950. View at Publisher · View at Google Scholar
  27. H. Terauchi, Y. Watanabe, H. Kasatani, et al., “X-Ray studies on single crystal films of BaTiO3,” Ferroelectrics, vol. 137, pp. 33–38, 1992. View at Publisher · View at Google Scholar
  28. M. E. Lines and A. M. Glass, Principles and Applications of Ferroelectrics and Related Materials, Clarendon Press, Oxford, UK, 1977.
  29. J. Junquera and P. Ghosez, “Critical thickness for ferroelectricity in perovskite ultrathin films,” Nature, vol. 422, no. 6931, pp. 506–509, 2003. View at Publisher · View at Google Scholar · View at Scopus
  30. D. A. Tenne, P. Turner, J. D. Schmidt et al., “Ferroelectricity in ultrathin BaTiO3 films: probing the size effect by ultraviolet raman spectroscopy,” Physical Review Letters, vol. 103, no. 17, Article ID 177601, 2009. View at Publisher · View at Google Scholar · View at Scopus
  31. K. Yoshio, I. Matsubara, A. Yamada, et al., “Phase transition in ferroelectric SrBi2Ta2O9 single crystal,” Journal of Korean Physics Society, vol. 43, p. S1034, 2003.
  32. A. Almeida, M. R. Chaves, H. Amorin, M. E. V. Costa, and A. L. Kholkin, “Lattice dynamics study of high-quality strontium bismuth tantalate single crystals,” Journal of Physics Condensed Matter, vol. 17, no. 48, pp. 7605–7612, 2005. View at Publisher · View at Google Scholar · View at Scopus
  33. M. Fukunaga, “Soft mode and relaxation behavior in two-dimensional ferroelectric Bi-layered perovskites,” [Ph.D. thesis], HokkaidoUniversity, 2009.
  34. K. Miura, “Electronic properties of ferroelectric SrBi2Ta2O9, SrBi2Nb2O9, and PbBi2Nb2O9 with optimized structures,” Applied Physics Letters, vol. 80, p. 2967, 2002. View at Publisher · View at Google Scholar
  35. Y. Shimakawa, Y. Kubo, Y. Nakagawa, et al., “Crystal structures and ferroelectric properties of SrBi2Ta2O9 and Sr0.8Bi2.2Ta2O9,” Applied Physics Letters, vol. 74, p. 1904, 1998. View at Publisher · View at Google Scholar
  36. A. D. Rae, J. G. Thompson, and R. L. Withers, “Structure refinement of commensurately modulated bismuth strontium tantalate, Bi2SrTa2O9,” Acta Crystallographica B, vol. 48, pp. 418–428, 1992.
  37. T. Tybell, C. H. Ahn, and J. M. Triscone, “Ferroelectricity in thin perovskite films,” Applied Physics Letters, vol. 75, no. 6, pp. 856–858, 1999. View at Scopus
  38. A. V. Bune, V. M. Fridkin, S. Ducharme et al., “Two-dimensional ferroelectric films,” Nature, vol. 391, no. 6670, pp. 874–877, 1998. View at Publisher · View at Google Scholar · View at Scopus
  39. B. Meyer and D. Vanderbilt, “Ab initio study of BaTiO3 and PbTiO3 surfaces in external electric fields,” Physical Review B, vol. 63, Article ID 205426, 2001.
  40. Ph. Ghosez and K. M. Rabe, “Microscopic model of ferroelectricity in stress-free PbTiO3 ultrathin films,” Applied Physics Letters, vol. 76, p. 2767, 2000. View at Publisher · View at Google Scholar
  41. T. Moriya, “Weak ferromagnetism,” in Magnetism, G. T. Rado and H. Suhl, Eds., vol. 1, p. 85, Academic Press, New York, NY, USA, 1963.
  42. P.-G. de Gennes, “Effects of double exchange in magnetic crystals,” Physical Review B, vol. 118, pp. 141–154, 1960. View at Publisher · View at Google Scholar
  43. C. Kittel, “Theory of antiferroelectric crystals,” Physical Review, vol. 82, pp. 729–732, 1951. View at Publisher · View at Google Scholar
  44. C. S. Hwang, “Thickness-dependent dielectric constants of (Ba,Sr)TiO3 thin films with Pt or conducting oxide electrodes,” Applied Physics, vol. 92, p. 432, 2002.
  45. J.-H. Ko, A. Hushur, S. Kojima, et al., “Acoustic anomalies and central peak in SrBi2Ta2O9 single crystals studied by micro-Brillouin scattering,” Applied Physics Letters, vol. 81, p. 4043, 2002. View at Publisher · View at Google Scholar
  46. M. Takesada, K. Sutoh, M. Fukunaga, and A. Onodera, “Light scattering study of bismuth layered ferroelectric SrBi2Ta2O9,” Ferroelectrics, vol. 355, no. 1, pp. 149–153, 2007. View at Publisher · View at Google Scholar · View at Scopus
  47. B. Aurivillius, “Mixed bismuth oxides with layer lattices I. The structure type of CaNb2Bi2O9,” Arkkitehtuuritoimisto, vol. 1, p. 893, 1949.
  48. J. M. Luttinger and L. Tisza, “Theory of dipole interaction in crystals,” Physical Review, vol. 72, no. 3, p. 257, 1947. View at Publisher · View at Google Scholar · View at Scopus
  49. K. Ishikawa, T. Nomura, N. Okada, et al., “Size effect on the phase transition in PbTiO3 fine particles,” Japanese Journal of Applied Physics, vol. 35, pp. 5196–5198, 1996. View at Publisher · View at Google Scholar