Uncovering ferroelectric polarization in tetragonal (Bi1/2K1/2)TiO3–(Bi1/2Na1/2)TiO3 single crystals

We report the robust ferroelectric properties of (1 − x)(Bi1/2Na1/2)TiO3–x(Bi1/2K1/2)TiO3 (x = 33%) single crystals grown by a top-seeded solution growth process under a high oxygen-pressure (0.9 MPa) atmosphere. The sample exhibit a large remanent polarization of 48 μC/cm2 and a sizeable piezoelectric strain constant of 460 pm/V. Neutron powder diffraction structural analysis combined with first-principles calculations reveals that the large ferroelectric polarization comparable to PbTiO3 stems from the hybridization between Bi-6p and O-2p orbitals at a moderately negative chemical pressure.

By contrast, few studies on BKT-based single crystals have been performed to date because of the difficulty in growing high-quality samples. At a temperature above 1300 K, BKT undergoes a thermal decomposition 36 , which makes the crystal growth difficult; to the best of our knowledge, the preparation of BKT crystals has never been achieved. Although some studies have reported the crystal growth of BKT-based solid solutions [37][38][39] , these crystals suffer from the problems arising from point defects. Owing to a high vapor pressure, Bi is apt to evaporate from the lattice leaving a vacancy of Bi (V Bi "'), which is accompanied by the formation of oxygen vacancy 40 . In addition, an oxidation treatment is required for as-grown samples but increases leakage currents to some extent because of p-type conduction, which prevents us from applying an electric field (E) 41,42 tends to accumulate at ferroelastic domain walls, which are strongly pinned and eventually clamped even under high fields 43,44 . For revealing the ferroelectric nature, it is desirable to develop a high-quality single crystal with a low concentration of V Bi "' where external fields can switch spontaneous polarization (P s ).
In this study, we report a growth of high-quality BKT-based single crystals exhibiting a complete switching of P s , employing the top-seeded solution growth (TSSG) method under high-oxygen-pressure (high-Po 2 ) atmosphere 45,46 . We chose a BKT-rich tetragonal phase in the BKT-BNT system. Our process enables us to obtain relatively large and high-performance single crystals with a large P s of 48 μC/cm 2 and a high piezoelectric strain constant (d 33 ) of 460 pm/V. Structural analysis combined with first-principles calculations reveals that the robust ferroelectric polarization and resultant high d 33 stem from the orbital interaction between Bi-6p and O-2p at a moderate chemical pressure.

Results
Neutron diffraction data were collected 47 for (1 − x)BNT-xBKT powders (x = 30-35%) prepared by solid-state reaction, and the powders were found to have a tetragonal P4mm structure. Figure 1(a) shows the fitting result of the Rietveld analysis for x = 30% measured at 295 K along with the calculated profile, the difference in intensity, and the peak positions. Our analysis leads to a profile reliability (R p ) factor of 5.8% and a weighted R p (R wp ) factor of 9.9%. All reflections are indexed by a perovskite unit cell in tetragonal P4mm symmetry indicating a clear splitting of, e.g., 200 and 002 reflections, which is due to a tetragonal strain (c/a) of 1.016. The refined crystal structure with the atomic displacements is illustrated in Fig. 1(b) and the detailed structural parameters are summarized in Supplementary Information I. Figure 1(c) shows the displacements of the constituent atoms along the c (polar [001]) axis. The off-center displacements are estimated from the hypothetic paraelectric structure, whose origin is set to the center of mass of the oxygen octahedron. The displacement of the A-site atoms (Bi 0.50 Na 0.35 K 0.15 ) is as large as 0.034 nm, which is about twice that of the B-site atom (Ti). Figure 1 Our crystal-growth process provides a high-quality single crystal of x = 33% [ Fig. 2(a,b)]. The crystal is transparent in yellow color with dimensions of 6 × 6 × 5 mm 3 . X-ray diffraction analysis shows that the crystallographic orientation coincides with that of the seed crystal, indicating an epitaxial growth from the seed. Figure 2(c) shows the leakage current density (J) at 298 K as a function of electric field (E) applied along [001], where the data of the crystal grown in the air (Po 2 = 0.02 MPa) is also shown. The crystal grown at Po = 0.9 MPa exhibits a lower J by 1-2 orders of magnitude than that at Po 2 = 0.02 MPa. Figure 3 shows the polarization (P) and strain (S) properties at 298 K. The crystal (Po 2 = 0.02 MPa) [ Fig. 3(a)] exhibits a remanent polarization (P r ) of 32 μC/cm 2 and a coercive field (E c ) of 23 kV/cm; because this crystal displays a high J of the order of ~10 −6 A/cm 2 at high fields, the leakage currents are comparable to the polarization-switching currents in the P-E measurements, leading to a blunted response. By contrast, the crystal (Po 2 = 0.9 MPa) [ Fig. 3(b)] features a well-saturated loop with a large P r of 48 μC/cm 2 and a low E c of 18 kV/cm. The blue line in Fig. 3   , which is larger than that along [111]. A piezoelectric strain constant (d * ) estimated from the slope of the unipolar curve at E < 5 kV/cm is as high as 460 pm/V along [001], which is comparable to that 34 for commercial PZT ceramics. The bipolar curve along [001] exhibits a large negative S of ~−0.8% at E = E c (20 kV/cm), whereas that along [111] has a negative S that can be extrapolated from the slope. These results enable us to understand the mechanism of the polarization-switching dynamics under E. If the P s vector is reversed by the 180° switching and a 90° domain structure does not participate in the process, the negative S is attributed solely to the converse piezoelectric effect. In this case, the slope of S with decreasing E remains constant until the 180°-P s switching starts, and the negative S can be expected from d * . Provided that the polarization reversal proceeds through the 90°-P s switching, i.e., the successive rotation of P s by 90° mediated in a 90° domain state, this process is accompanied by a change in crystallographic configuration from E // c to E // a in each domain. Assuming that the state at E = E c has a 90° domain structure composed of the domains in the E // c and E // a configurations, we estimate an averaged S of -(c − a)/2a to be −0.8%, which accords with the experiment (−0.8%).

Discussion
Here we discuss the origin of the structural difference between BKT with tetragonal P4mm and BNT with rhombohedral R3c. We investigate the external pressure (p) dependence of the free energy G for the BKT and BNT cells by density functional theory (DFT) calculations, the details of which are described in Calculation Method and Supplementary Information II. For both the cells, the R3c structure is stabilized at a higher p while the P4mm one is at a lower p, because the R3c structure with octahedral rotations of a − a − a − (Glazer notation) prefers a smaller cell volume (V) in the higher-p region. The equilibrium state (p = 0) was found in the R3c phase for the BNT cell with the R3c-P4mm boundary p (p 1 ) at −2.21 GPa, while that appears in the P4mm phase with its p (p 2 ) of 3.20 GPa. A partial substitution of K having a larger ionic radius (r ion ) for Na increases the average r ion on the A site and V; a negative chemical pressure caused by the K substitution increases the phase-boundary p.
Although we did not find an anomaly in the bond valence sum (BVS) as a function of p ( Supplementary  Fig. SI), the cation-O bonds show prominent features; especially, the Bi-O bonds exhibit a reconstruction across www.nature.com/scientificreports www.nature.com/scientificreports/ the phase boundary. In the centrosymmetric structure, Bi is surrounded by twelve O atoms. In the R3c structure, Bi is displaced along [111], leading to four different lengths: the shortest Bi-O1 (×3), followed by Bi-O2 (×3), Bi-O2* (×3) and Bi-O1* (×3), where asterisk (*) denotes a longer bond. Essentially, Bi-O1 is independent of p at ~0.240 nm, whose length is in good agreement with the experiments 48 . By contrast, Bi-O2 is lengthened when p decreases, leading to a smaller BVS of Bi. In the P4mm structure, the displacement of Bi along [001] results in three different lengths: the shorter four, the intermediate four (Bi-O1) and the longer four. Moreover, the tetragonal P4mm accommodates the markedly short Bi-O2 of ~0.225 nm.
To elucidate the origin of the phase stability, we investigate the electronic structures at p~13.4 GPa and −2.3 GPa; the high p stabilizes the R3c structure (Fig. 4a-c) while the low p does the P4mm phase (Fig. 4d-f). The conduction band is formed primality by Ti-3d, and the valence band has a dominant contribution of O-2p. We note that the marked density of states (DOS) of not only Ti-3d but also Bi-6p appears in the valence band; especially the hybridized states of Bi-6p and O-2p determine the bottom of the valence band. At p~13.4 GPa in the BNT cell, the R3c phase features a dominant contribution of the Bi-6p (p x + p y ) derived states around the bottom with a minimum at −5.79 eV in the vicinity of the Γ point (the wavefunction is seen in Fig. 4c), which is lower by ~0.1 eV than the P4mm [ Supplementary Fig. S2(a,b)]. We found that the stabilization of the R3c phase for BNT stems from the low-lying valence states arising from the Bi-6p and O-2p hybridization.
The similar feature is also seen in the BKT cell at p~−2.3 GPa; the mixed states of Bi-6p and O-2p dominate the bottom of the valence band. The maximal DOS of Bi-6p lies at ~−4.3 eV for the P4mm phase, which is higher than that (~−4.5 eV) for the R3c phase [ Supplementary Fig. S2(c,d)]. However, the P4mm phase exhibits a markedly large DOS arising from the Bi-6p (p x + p y ) and O-2p in-plane hybridization (see the wavefunction shown in Fig. 4f), which is due to a small band dispersion in the entire Brillouin zone. Indeed, the atomic partial charge of Bi-6p is 0.89 for the P4mm phase, which is larger than 0.85 for the R3c phase. We found that the P4mm phase of BKT is stabilized by a large DOS of the Bi-6p (p x + p y ) states derived from the orbital interaction with O-2p.
In summary, we uncover the ferroelectric polarization and piezoelectric strain constant in the BKT-based single crystals grown by the high-P O2 TSSG process. These properties originate from a P s of ~56 μC/cm 2 with a c/a of ~1.6%; this P s rivals that of PbTiO 3 (70 μC/cm 2 ). Our theoretical calculations show that the Bi-6p and O-2p hybridization at a moderately negative chemical pressure stabilizes the ferroelectric distortion in tetragonal www.nature.com/scientificreports www.nature.com/scientificreports/ symmetry. We could apply the high-P O2 process to other functional materials including Bi and/or K in bulk and film forms, here that we have developed high-quality BKT-based crystals by suppressing a defect formation reaction.

Methods
Experimental procedure. We prepared powders of (1 − x)BNT-xBKT (x = 30-35%) via solid-state reaction of the raw materials of Bi 2 O 3 (99.99%), TiO 2 (99.99%), Na 2 CO 3 (99.99%), and K 2 CO 3 (99.99%). These starting materials were mixed using ball milling with 100-μm beads and then calcined at 1,223 K for 4 h. The calcined powders were crushed by the ball milling and then calcined again at 1,423 K for 4 h to achieve a homogeneous solid solution.
For crystal structural anlyises, we performed time-of-flight (TOF) NPD measurements using a neutron powder diffractometer iMateria (BL20) 47 at Japan Proton Accelerator Research Complex (J-PARC). NPD data in the d range of 0.05 < d/nm < 0.25 were collected with a high resolution Δd/d = 0.16%. The crystal structure was refined by the Rietveld method with a computer software Z-Rietveld 49 .
We adopted the high-oxygen-pressure top-seeded solution growth (high-Po 2 TSSG) method to obtain high-quality BNT-BKT single crystals, the details of which are described in refs. 45,46,50 . 70%BNT-30%BKT (x = 30%) powders were mixed with a Bi 2 O 3 -KF flux at a weight ratio of BNT-BKT: Bi 2 O 3 (99.99%): KF (99%) = 10: 10: 2. The mixture was soaked at over 1,430 K for 4 h in a Pt crucible rotated at 10 rpm, and then slowly cooled to approximately 1,400 K to form the solution. We used a BNT seed crystal obtained by a conventional flux method, which was set with a {001} plane normal to the melt surface. The seed rotated at 20 rpm counter to the crucible rotation was dipped into the solution, held at the same height for 1-4 h, and then slowly pulled out at a rate of 0.1-0.2 mm h −1 for over 20 h during cooling (<0.5 °C h −1 ). Eventually, a grown bulk crystal was detached from the solution and then slowly cooled to room temperature. The chemical composition of the grown crystal was analysed by inductively coupled plasma-atomic emission-spectrometry, indicating that the chemical composition is BNT-33%BKT with a composition deviation less than 1%. www.nature.com/scientificreports www.nature.com/scientificreports/ The single crystals obtained were annealed at 1173 K for 10 h in air to remove mechanical stress induced during the crystal growth. The annealed crystals were cut along the {001} and {111} plane into plates with a thickness of 0.2 mm, and then gold electrodes were sputtered onto the cut surfaces. We measured polarization and leakage current of the crystal at 298 K using a ferroelectric test system (Toyo Corporation; Model 6252 Rev. B), and strain properties using a laser Doppler displacement meter.
Calculation methods. DFT calculations were performed via the generalized gradient approximation 51 with a plane wave basis set. The projector-augmented wave method 52 was applied by the Vienna ab initio simulation package (VASP) 53 . We employed the gradient-corrected exchange-correlation functional of the Perdew-Burke-Ernzerhof revised for solids (PBEsol) 54 and a plane-wave cut-off energy of 520 eV. The adopted mesh size of the k-point sampling grid was less than 5 nm -1 for structural optimizations, 2.5 nm −1 for density-functional perturbation theory (DFPT) calculations. A rock-salt-like A-site ordering were adopted for constructing the Bi 1/2 Na 1/2 TiO 3 and Bi 1/2 K 1/2 TiO 3 cells 55,56 .
To obtain the Born effective charges, all the atomic positions were optimized in the Bi 1/2 Na 1/2 TiO 3 and Bi 1/2 K 1/2 TiO 3 cells under the constraints of the fixed lattice constants determined by the NPD analysis. Adopting a weighted average (mol %) of the Born effective charges (Z eff *) of the constituent atoms obtained in their respective Bi 1/2 Na 1/2 TiO 3 and Bi 1/2 K 1/2 TiO 3 cells, we estimated the averaged Z eff * of each atom in the BNT-BKT solid solutions. The calculations for the Bi 1/2 Na 1/2 TiO 3 cell result in the following Z eff * values: 3.9 e for Bi, 1.1 e for Na To evaluate phase stability, we calculated the total energy (U) per ABO 3 unit cell as a function of the cell volume (V) for the Bi 1/2 Na 1/2 TiO 3 and Bi 1/2 K 1/2 TiO 3 cells in R3c and P4mm symmetries, and then analyzed by the Murnaghan equation of state 57 : where U 0 , B 0 , B 0 ′, and V 0 are the total energy, the bulk modulus and its first derivative with respect to the hydrostatic pressure (p) and V at p = 0. Since the free energy (G) is expressed as G = U + pV, we can obtain the relation between G and p using the fitting parameters in Eq. 1. The arrangement of the A-site atoms in the cells lowers the symmetry, i.e., the space group of the rhombohedral changes from R3c to R3 and that of the tetragonal from P4mm to I4mm. For simplicity, the higher symmetry is used to denote the space group throughout this paper.