Ferrielectric-mediated morphotropic phase boundaries in Bi-based polar perovskites

Spontaneous polarization (Ps) in ferroelectrics has provided the impetus to develop piezoelectric devices such as sensors, actuators and diagnostic imaging transducers. Widely used lead-based perovskites exhibit a composition-driven phase diagram involving a transition region, known as a morphotropic phase boundary, where the ferroelectric structure changes dramatically and the piezoelectric activity is maximal. In some perovskites, ferroic polarization coexists with nonpolar rotations of octahedra, suggesting an unprecedented phase diagram. Here, we show morphotropic phase boundaries, where ‘ferrielectric’ appears as a bridging phase between ferroelectrics with rhombohedral and tetragonal symmetries in Bi1/2Na1/2TiO3-based perovskites. Neutron diffraction analysis demonstrates that the intermediate ferrielectric displays a small Ps resulting from up and down polarizations coupled with an in-phase TiO6 rotation. Our ab initio calculations indicate that a staggered Bi-O conformation at an appropriate chemical pressure delivers the ferrielectric-mediated phase boundaries, which provides a promising platform for (multi)ferroic materials with enhanced physical properties.


Supplementary Fig. 4 | Bi1/2Na1/2TiO3 cells. For investigating the first MPB by the DFT calculations,
we adopt the Bi1/2Na1/2TiO3 cells with a rock-salt-like A-site ordering. The arrangement of Bi and Na on the A site lowers rhombohedral symmetry from R3c to R3 and tetragonal symmetry from P4bm to P42nm.
We use the higher symmetry to denote these cells along with their DFT results throughout this paper. Owing representatives; for the rhombohedral R3c, a the total and partial density of states (DOS) and b the electronic band structure are shown, where the vertical energy level is the same; for the tetragonal P4bm, c the total and partial DOS and d the electronic band structure are exhibited in a similar manner. EF is the Fermi energy, which is defined as that of the valence band maximum (VBM). The VBM is formed mainly by O-2p while the conduction band minimum (CBM) is constructed by Bi-6p and Ti-3d. The hybridization of Ti-3d and O-2p leads to a DOS in the valence band, which contributes to the off-centring of Ti (ref. 5 ).
Note that Bi-6p is mixed with O-2p and thereby has a marked DOS in the valence band. In the rhombohedral (the opposite to the c axis). The octahedra sandwiched between the Bi-Ba and Bi-Na layers (Ti1-O6 and Ti4-O6) exhibit an apparent rotation whereas those between the Bi-Na and Ba-Na layers (Ti2-O6 and Ti3-O6) have an almost zero . The hypothetical paraelectric structure possesses the mirror plane normal to the c axis, and then Ti1-O6 and Ti4-O6 between the Bi-Na and Bi-Ba layers have the same structural environment. In the polar lattice, where the small but significant Ps is present along [001], the dipole moment derived from the Bi-Na and Bi-Ba layers adjacent to Ti1-O6 is parallel to the Ps vector, while that to Ti4-O6 is opposite to it. This parallel configuration is ascribed to the large  of the Ti1-O6 octahedron.

Supplementary Fig. 11 | Bond Valence Sum (BVS) across the second phase boundary. The
BVSs as a function of p are estimated from the optimized structures obtained by the DFT calculations for the Ba2/8Bi3/8Na3/8TiO3 cells. All the atoms have a downward tendency of BVS with decreasing p. Near the second phase-boundary p (p2nd), the BVSs of Na and Ti are in good agreement with their respective formal valences (Na + and Ti 4+ ), while that of Ba is larger than the formal valence (Ba 2+ ) but is comparable to 2.73 for tetragonal BaTiO3 (ref. 6 ). The BVS of Bi2 is close to the formal valence (Bi 3+ ), whereas those of Bi1 and Bi3 are smaller and exhibit a reconstruction of their bonds with O atoms across p2nd (see Fig. 3).

Supplementary Fig. 14 | Density of states (DOS) of Ba for the P4bm and P4mm phases.
Compared with other atoms (see Supplementary Fig. 12), the partial DOS of Ba are much small in the valence band in the energy range of 6 eV to 0 eV. These results clearly show that the electronic interaction between Ba and neighbors itself does not provide a major contribution to the phase stability and also that the influence of partial Ba occupation on the A site can be regarded as an expansion of unit cell volume (V), as shown in Fig. 1. We can think that a change in V depending on the Ba composition (x) in a restricted x range, where a morphotropic phase boundary (MPB) exists, can be regarded as that on the pressure (p) for a specific model cell. In our experimental results, the two distinct MPBs; the 1 st MPB and 2 nd MPB are present at x ~ 5% and x ~ 7.5%, respectively. It is reasonable to consider that the 1 st MPB and 2 nd MPB are treated in Ba-poor and the Ba-rich structural models in DFT calculations. We, therefore, investigate the 1 st MPB and 2 nd MPB for the Bi1/2Na1/2TiO3 cell and the Ba2/8Bi3/8Na3/8TiO3 cells, respectively.
While some of the papers report an irreversible phase transition after applying external stimuli, such as electric field or stress, the phases in as-prepared samples are listed. *1 Our analysis does not provide a better fitting in the structural model with monoclinic Cc. We regard the room-temperature phase with x ≤ 4 % as rhombohedra R3c for simplicity to investigate the MPB. *2 Cubic symmetry with rhombohedral R3c and tetragonal P4bm polar nanoregions. *3 Two phase mixture of a monoclinic Cc phase and a minor fraction of a metrically cubic Pm3 ̅ m phase. *4 Pseudocubic with long ranged modulated complex octahedral tilt. *5 Rhombohedral (R3c) with local monoclinic phase.