Ferroelectrics with a controlled oxygen-vacancy distribution by design

Controlling and manipulating defects in materials provides an extra degree of freedom not only for enhancing physical properties but also for introducing additional functionalities. In ferroelectric oxides, an accumulation of point defects at specific boundaries often deteriorates a polarization-switching capability, but on the one hand, delivers interface-driven phenomena. At present, it remains challenging to control oxygen vacancies at will to achieve a desirable defect structure. Here, we report a practical route to designing oxygen-vacancy distributions by exploiting the interaction with transition-metal dopants. Our thin-film experiments combined with ab-initio theoretical calculations for BiFeO3 demonstrate that isovalent dopants such as Mn3+ with a partly or fully electron-occupied eg state can trap oxygen vacancies, leading to a robust polarization switching. Our approach to controlling oxygen vacancy distributions by harnessing the vacancy-trapping capability of isovalent transition-metal cations will realize the full potential of switchable polarization in ferroelectric perovskite oxides.


Interaction Between transition-Metal Cations and oxygen Vacancies
) in P1 symmetry (Fig. 1b), the total energy (E total ) is calculated and compared; O1 and O2 are the oxygen atoms in the TM-O 6 octahedron, and their distance with TMs is ~0.2 nm, while O3 is present in the next nearest FeO 6 octahedra, and the distance of O3-TMs is lengthened to ~0.4 nm. Figure 2 displays the E total of the defective cell with an oxygen vacancy (V On •• ) on the n th nearest-neighbor (NN) sites (n = 1−3) with respect to TMs, where the E total of n = 1 is set at zero. Figure 3a,b depicts the total and (selected) partial density of states (DOS) with V O1 •• (V O2 •• ) and V O3 •• along with the partial charge densities of the states indicated by arrows. The downward E total with increasing n shows that the system is lower in energy when V O •• is away from TMs, while the upward E total features an attractive interaction between TMs and V O •• . In an ionic picture, TM 3+ has the following electronic configuration: Ti 3+ with d 1 , V 3+ with d 2 , Cr 3+ with d 3 , Mn 3+ with d 4 , Co 3+ with d 6 , Ni 3+ with d 7 , Cu 3+ with d 8 . The valence states of TMs expect for Ti, Co, and Cu are confirmed by the partial magnetic moment analysis 38 : V 3+ with ~1.8 μ B , Cr 3+ with ~2.8 μ B , Mn 3+ with ~3.6 μ B , Ni 3+ with ~0.8 μ B , where μ B is the Bohr magneton. We note that the cells of TM = Ti, V, and Cr have a smaller E total of n = 3 than that of n = 1, whereas those of others exhibit the smallest E total with n = 1. These tendencies reflect the following spin  48 in P1 symmetry (Z = 1) for DFT calculations. As TM atoms are positioned on the three-fold axis, TMs form the shortest bonds with three O1 atoms and the nextshortest bonds with three O2. O3 is the third nearest-neighbor oxygen atom with respect to TMs. For creating the defective cells with an oxygen vacancy, we remove one oxygen atom from the primitive cell and then perform the calculations for the Bi 16   ) with respect to TM. As shown in Fig. 1, O1 and O2 are the 1 st -NN and 2 nd -NN oxygen atoms forming the TM-O polyhedron, respectively. The total energy of n = 1 is set at zero. A downward total energy with increasing n indicates that V O •• tends to keep away from TM atoms, whereas an upward total energy shows that V O •• is apt to be located close to the TM atoms.
configuration of TM 3+ : the e g state for the cells of Ti, V, and Cr is empty, while that for others is partly or fully electron-occupied. The detailes of the formation energies of TM dopants in the trivalent ionic state into BiFeO 3 have been reported by Gebhardt and Rappe 39 . The results described above can be intuitively explained by the electronic states formed by the orbital interaction between TM-3d and adjacent O-2p. For TM = Ti, the system has Ti 4+ (d 0 ) and Fe1 2+ (d 6 ) because of the higher energy states of Ti-3d, where the Fermi level (E F ) is located at the electron-occupied Fe1-3d state. These results are supported by the partial magnetic moments of 0.1 μ B for Ti-3d and 3.6 μ B for Fe1-3d (smaller than the other Fe-3d values of ~4.1 μ B ). This can be qualitatively understood by the charge transfer: the electron of Ti 3+ is transferred to Fe1 on the 1 st NN site with the oxygen vacancies. With respect to the valence band maximum (VBM; the lower dashed line), the Fe1-d xy state with V O3 •• is lower by ~0.1 eV than the Fe1-d z2 state with V O1 •• , which is the main reason why the n = 3 cell is lower in energy than the n = 1 cell. The V cells have two occupied states of V-3d (d 2 ) in the gap; comparing the higher gap states at the E F , the d yz state with V O3 •• is lower in energy by ~0.1 eV than the d yz state with V O2

••
, resulting in the lower E total of n = 3. For TM = Cr, the empty gap state with the d z2 character appears with V O1 •• , whereas there is no state in the gap with V O3 •• . Although the change in the coordinate from CrO 6 (n = 3) to CrO 5 (n = 1) splits the e g state into the low-lying d z2 and the high-lying d x2−y2 , this does not lead to a significant stabilization in the system, because both the states are empty. The CrO 6 structure (n = 3) maintains a regular octahedron, and the Cr-3d state is represented by t 2g 3 e g 0 , which contributes to a lower E total of n = 3. A stabilization of V •• away from Cr has also been reported for hexagonal BaTiO 3 40 . The details for TM = Mn are described later.
For TM = Co, the electronic configuration of Co 3+ (d 6 ) in O h symmetry is expressed as t 2g 4 e g 2 in the high-spin state 41,42 . Regardless of the position of V •• 40 , the occupied DOS of Co-3d in the majority spin component (↑) is spread in the valence band (−5 to 0 eV), showing that one electron is present in the bonding state of e g (↑). In this case, the electronic state is regarded as t 2g (↓) 3 e g (↓) 2 e g (↑) 1 rather than as t 2g (↓) 3 e g (↓) 2 t 2g (↑) 1 , in which the strong hybridization of Co-e g with O-2p leads to a relatively small magnetic moment of Co 3+ with ~3.0 μ B . Comparing the energies of the d z2 -derived state (↓), we found that the cell with V O1 •• has the low-lying state at the valence band minimum of −7.1 eV, which is mainly due to the absence of O1 (the presence of V O1 •• ), along with the orbital mixing with O-2p of two apical oxygen atoms. This marked stabilization of the d z2 -derived bonding state is attributed to the lower E total of n = 1. The Ni cells exhibit relatively complex electronic features; the electronic configuration of Ni 3+ (d 7 ) in O h symmetry is described as t 2g •• in the minority spin component (↓), the unoccupied d x2−y2 state is present in the gap, while the d z2 -derived state is markedly stabilized and appears at the valence band minimum because of the strong hybridization with the adjacent O-2p. Although the similar feature was found in that with V O3 •• , its energy is higher by ~0.5 eV. The low-lying d z2 -derived state with V O1

••
is responsible for the lower E total of n = 1. For TM = Cu, the electronic configuration of Cu 3+ (d 8 ) is expressed as t 2g 6 e g 2 , which is supported by the empty e g (↑) state present in the band gap. Nevertheless, the apparent orbital mixing of Cu-e g (↑) and O-2p is clearly seen in their partial charge density (Fig. 3a) and thus result in a relatively small magnetic moment of Cu 3+ with 0.6-0.8 μ B . The cell with V O3 •• has the e g (↑) state whereas that with V O1  www.nature.com/scientificreports www.nature.com/scientificreports/ oxygen-vacancy distributions. Figure  and also that the attractive interaction between V O •• and TMs is sufficiently strong, V O •• is trapped by TMs in an equilibrium state, as displayed in Fig. 4b.
For a robust switching of P s by applying electric fields, in addition to the attractive interaction of V O •• -TM, the doped lattice should meet the following requirements: the first is a high solubility limit of TM; the second is the stable valence state of TM 3+ ; and the third is the electronic character of TM that does not lead to a significant increase in leakage current. Here, we choose Mn as a TM because of the following reasons: Mn can be introduced into the lattice in a wide composition range 47 , and the valence state is controllable to Mn 3+ 48 . Moreover, the empty d x2−y2 state of the Mn cell with V O1 •• is far above the VBM 49 , and thereby a leakage current is expected to be relatively low. Fig. 5 of the X-ray diffraction reciprocal space maps (XRD-RSMs), we confirmed that the capacitors are hetero-epitaxially grown on the SrTiO 3 substrate, i.e., the [001] pc directions of the films are normal to (001) of the substrate. For both the capacitors, we observed the The 103 and 113 reflections are split into two spots, which is the typical character of the rhombohedral structure in R3c space group. From the peak positions of these spots, we obtained the following rhombohedral lattice parameters for the BFO film: a = 0.3984 nm, α = 89.53 deg., and V (lattice volume) = 6.32 × 10 −2 nm 3 , which are almost the same as those of the bulk (a = 0.3964 nm, α = 89. 43 deg. and V = 6.23 × 10 −2 nm 3 ) 50 . Because a monoclinic distortion induced by compressive stress was not found from the XRD data and the difference in the parameter a is as small as 0.5%, we think that a strain-free bulk-like lattice is obtained for the BFO film. The Mn-BFO film has a = 0.3978 nm, α = 89.59 deg., and V = 6.29 × 10 −2 nm 3 , indicating that the 5% Mn doping does not lead to a significant change in crystal structure and that a bulk-like lattice is also attained for the Mn-BFO film. Figure 6a,b shows the polarization-electric field (P-E) hysteresis properties with the current profiles during the polarization switching. For the BFO capacitor, the P curve in a positive field exhibits a loop typical for normal ferroelectrics, whereas that in a negative field rounds. This feature is attributed to a markedly large leakage current at negative fields. The asymmetric hysteresis loop has been reported for as-prepared BFO films in a strained state 44,51,52 . We note that the Mn-BFO capacitor presents a well-saturated hysteresis loop with a remanent polarization of 55.4 μC cm −2 , where the P-E loop, as well as the current profile, is symmetric with respect to E. This P r value along [001] pc provides a P s (// [111] pc ) of 96.0 μC cm −2 , which is close to the P s observed for bulk crystals 53 and calculated by first-principles calculations 54 . Figure 6c,d displays the current density-electric field (J-E) properties in the low field region (−50 kV cm −1 to 50 kV cm −1 ). The BFO capacitor exhibits a rectification behavior, where the J becomes larger when the E direction is parallel to the macroscopic polarization. In particular, the negative P state (−P) at negative fields (−E) features a markedly large J, which is consistent with the P-E properties. Even though the Mn-BFO capacitor has a higher J by over an order of magnitude, it presents a symmetric J-E property. The rectified current behavior and the associated round P-E loop observed for the BFO capacitor can be explained by an V O •• -rich layer at the BFO/electrode interface (Fig. 4a) 22,[43][44][45][46] , which is probably formed during either the film deposition or the cooling process 55 . www.nature.com/scientificreports www.nature.com/scientificreports/ electronic structures of Mn-doped BiFeo 3 . Figure 7 presents the results of the DFT calculations for the defective cells of TM = Mn. The relative value of E total as a function of n is plotted in Fig. 7a. We note that the cells of n greater than three exhibit a relatively large E total by 0.1-0.2 eV compared with n = 1 and 2, indicating that the cell has a lower energy provided that V O •• is located adjacent to Mn. Notably, the energy gain when V O •• is present on the O1 (n = 1) site is 250 meV, which is three times as large as that of the thermal energy k B T even at the deposition temperature (T sub = 610 °C, k B T sub ~75 meV). Because the Curie temperature (830 °C for BiFeO 3 ) is higher than T sub , a crystallization during the film deposition occurs in the ferroelectric state. We assume that the majority of V O •• are trapped by Mn even in the deposition process at high temperatures through a trapping-detrapping dynamics 56,57 . Also, after the film is exposed to a subsequent annealing or a polarization switching, Mn provides the preferred site for V O •• in its immediate vicinity, and then almost all V O •• associates with Mn in an equilibrium state.

Crystal structures and properties. As displayed in
Here, we address the mechanism of the attractive interaction between Mn and V O •• (Fig. 4b). Given that Mn is octahedrally coordinated with six oxygen atoms and is placed in O h symmetry, Mn 3+ (d 4 ) has a configuration of t 2g 3 e g 1 , and an electron occupies the half of the e g state. In the ferroelectric state with V O •• , the degeneracy of e g is lifted, rendering either of the component d x2−y2 or d z2 filled with electron. Therefore, the total energy of the system is governed by an energy lowering of the highest-occupied d level as a result of the interaction with neighbors.  Fig. 7g), and thereby its level is lower in energy far below E F . Provided that V O •• is away from Mn, which involves a change from the MnO 5 pyramid to the MnO 6 octahedron, the d orbitals are affected by the adjacent six oxygens and then the d z2 orbital is shifted to higher energy, forming the occupied gap state above the VBM. As a result, the system is stabilized when V O •• resides adjacent to Mn. These results lead to the conclusion that Mn acts as an effective trap for V O We address the V O •• distribution in the capacitors. As reported in the literature 58 and shown in Fig. 6, the as-prepared BFO capacitor show the distinct characteristics such as the asymmetric P-E hysteresis loop and the www.nature.com/scientificreports www.nature.com/scientificreports/ rectified current behavior. All these properties can be explained by an V O •• -rich layer formed at the BFO/electrode interface (Fig. 3a). During the deposition process at high temperatures, BFO tends to have a Bi-poor composition because of a high vapor pressure of Bi 46,59,60 ; Bi vacancy (V Bi ″′) is formed and acts as an acceptor 13  is apt to accumulate at high-energy boundaries such as ferroelastic domain (twin) walls and ferroelectric/electrode interfaces 10-15,30-33 .
As described above, we think that the ferroelectric films are crystallized in the polar state in their deposition process; the films have ferroelectric polarization once the BFO lattice is constructed. In capacitor form, the discontinuity of the P s vector is inevitable at interfaces with electrodes and results in a depolarization field 22,[43][44][45][46] . As the P s of BFO is markedly large, the depolarization field becomes strong. We note that the tail of P s vector has negative bound charges that attract positively charged V O   We expect that the application of the design principle of defect structures to other (multi)ferroic materials can provide a practical route to controlling and manipulating oxygen-vacancy distributions by harnessing the vacancy-trapping capability of isovalent transition-metal cations in ferroelectric perovskite oxides. atmosphere with a laser repetition rate of 1 Hz. For the ferroelectric layers, T sub , oxygen pressure and a laser repetition rate were set at 640 °C, 2.6 Pa, and 7 Hz, respectively. Then, the Ba 0.1 Sr 0.9 RuO 3 top electrode was prepared in the same manner as the bottom one. After the deposition process, the capacitors were annealed in air at 450 °C for one hour.
We characterized the capacitors in the as-prepared state and did not employ any treatment such as an electrical training 43,44 to control the distribution of oxygen vacancy (V O •• ). Crystal structure analysis was performed by X-ray diffraction (XRD) reciprocal space mapping (RSM), where the sources of Cu-Kα + Kβ and Cu-Kα 1 were used for wide-area and small-area (high-resolution) RSMs, respectively. The polarization-electric field (P-E) properties were measured at 25 °C, where the upward (downward) electric field and polarization are expressed as + E (−E) and +P (−P). For example, the vector of +E or +P is directed from the bottom to the top electrodes. We adopted the pseudo-cubic notation (denoted by 'pc') throughout this paper. DFt Calculations. First-principles calculations based on DFT 65 were performed within the generalized gradient approximation (GGA) 66 in the projector-augmented-wave (PAW) method 67 , as implemented in the Vienna ab initio simulation package (VASP) 68 . We employed the gradient corrected exchange-correlation functional of the Perdew-Burke-Ernzerhof revised for solids (PBEsol) 69 . Within the simplified GGA + U approach 70 , we added on-site Coulomb interaction parameters of U−J = 4 eV to all the d orbitals of transition metal (TM) atoms. Because the magnetic structure of BFO can be approximated to a G-type antiferromagnetism, we considered an antiferromagnetic spin configuration formed by the d electrons. Before geometry optimizations of BFO, we put a magnetic moment of +5 μ B (μ B denotes the Bohr magneton) or −5 μ B to the Fe atoms, which is accompanied by a symmetry lowering: the space group changes from R3c to R3.
For TM-substituted cells (TM = Ti, V, Cr, Mn, Co, Ni, Cu), we transformed the optimized BiFeO 3 cell with R3 symmetry (Z = 6) to the primitive rhombohedral lattice (Bi 2 Fe 2 O 6 , Z = 1) and then created the supercell of 2 × 2 × 2, leading to the Bi 16 Fig. 1a]. This supercell was geometrically optimized with a Monkhorst-Pack Γ-centred k-point mesh of 3 × 3 × 3. All results were obtained by treating the following valence electrons: 5d, 6s, and 6p for Bi, 3p, 3d, and 4s for Ti, V, Cr, and Mn, 3d and 4s for Fe, Co, Ni, and Cu, and 2s and 2p for O. The plane-wave cut-off energy was set at 520 eV in all calculations.
In the TM-BiFeO 3 cells, TM is positioned on the three-fold axis in R3 symmetry, and seventeen kinds of oxygen atom having different bond lengths with TM exist. After we created the primitive lattice of the TM-BiFeO 3 cell [Bi 16 47 , in P1 symmetry and then relaxed the fractional coordinates of all the atoms in the fixed cell size, where the Γ-centred 3 × 3 × 3 k-point mesh was also used. For these calculations, the valence state of TM remained to be +3 by controlling the total number of electrons. It has been reported that oxygen vacancies in zinc ferrites change the iron-iron coupling from the antiferromagnetic to the ferromagnetic spin configuration 38 . We confirmed that the antiferromagnetic configuration of Fe atoms is established in the defective cells after the structural optimizations