Introduction

Spontaneous polarization (Ps) in ferroelectrics presents unique opportunities to develop sensors, actuators, medical imaging transducers, and non-volatile random access memories1,2,3,4. Recently, ferroelectric tunnel junctions have attracted much attention owing to their potential applications in non-destructive readout memories in high-density integration5,6,7,8,9. In all these applications, the control of domain structures and polarization states by applying external fields are crucial to achieve desirable properties. Even though ferroelectric bulk has the insulating nature, charged domain walls stabilized by point defects act as an electrically conductive interface10,11,12,13,14,15, which opens possibilities for nanoelectronics such as domain-wall memories16,17,18. Moreover, exploiting a high mobility of defects enables to create a p–n junction that can be erased and inverted by electric fields19.

Meanwhile, an accumulation of defects at specific interfaces deteriorates the overall behaviour of polarization-switching dynamics20,21. For the charged domain walls stabilized by oxygen vacancies, the defect kinetics determine the switching process that is accompanied by a vacancy redistribution22,23, and thereby the device operation speed is limited by vacancy transport times22. The strong interaction with the vacancies gives rise to the clamping of domain walls24,25,26,27 and eventually causes imprint, retention loss, and fatigue of polarization states, preventing the widespread use of ferroelectric-based memories1,21,28,29.

For piezoelectric devices made of PbTiO3-based ferroelectrics, the properties can be tailored by doping of lower-valent and/or higher valent cations, mainly on the Ti4+ site, by adjusting the concentration of oxygen vacancies30,31,32,33. The doping of, e.g., Fe3+ increases an oxygen-vacancy concentration, and then the mobility of domain walls is reduced, leading to electromechanically hard lattices32,34,35. By contrast, the introduction of Nb5+ decreases the concentration and then the interaction between the domain walls and the vacancies is suppressed, resulting in soft lattices32,36,37. Despite over fifty years of intense research, it remains difficult to control the oxygen-vacancy distribution without changing its overall concentration. It is desirable to establish a design principle that can control and manipulate the vacant positions in the vicinity of the specific sites or interfaces at will with its controlled concentration.

Interaction Between Transition-Metal Cations and Oxygen Vacancies

Figure 1 shows the crystal structures of transition-metal (TM)-doped cells for DFT calculations. For the primitive cell with an oxygen vacancy (VO••) in P1 symmetry (Fig. 1b), the total energy (Etotal) is calculated and compared; O1 and O2 are the oxygen atoms in the TM-O6 octahedron, and their distance with TMs is ~0.2 nm, while O3 is present in the next nearest FeO6 octahedra, and the distance of O3-TMs is lengthened to ~0.4 nm. Figure 2 displays the Etotal of the defective cell with an oxygen vacancy (VOn••) on the nth nearest-neighbor (NN) sites (n = 1−3) with respect to TMs, where the Etotal of n = 1 is set at zero. Figure 3a,b depicts the total and (selected) partial density of states (DOS) with VO1•• (VO2••) and VO3•• along with the partial charge densities of the states indicated by arrows. The downward Etotal with increasing n shows that the system is lower in energy when VO•• is away from TMs, while the upward Etotal features an attractive interaction between TMs and VO••. In an ionic picture, TM3+ has the following electronic configuration: Ti3+ with d1, V3+ with d2, Cr3+ with d3, Mn3+ with d4, Co3+ with d6, Ni3+ with d7, Cu3+ with d8. The valence states of TMs expect for Ti, Co, and Cu are confirmed by the partial magnetic moment analysis38: V3+ with ~1.8 μB, Cr3+ with ~2.8 μB, Mn3+ with ~3.6 μB, Ni3+ with ~0.8 μB, where μB is the Bohr magneton. We note that the cells of TM = Ti, V, and Cr have a smaller Etotal of n = 3 than that of n = 1, whereas those of others exhibit the smallest Etotal with n = 1. These tendencies reflect the following spin configuration of TM3+: the eg 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 BiFeO3 have been reported by Gebhardt and Rappe39.

Figure 1
figure 1

Crystal structures of transition-metal (TM)-doped BiFeO3. (a) Hexagonal Bi16(Fe15TM)O48 cell in space group R3 (Z = 3) and (b) primitive Bi16(Fe15TM)O48 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 next-shortest 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 Bi16(Fe15TM)O47 cell in P1 symmetry.

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Figure 2
figure 2

Total energies of transition-metal (TM)-doped BiFeO3. Total energy as a function of n, where n denotes the n-th nearest neighbor (NN) site of oxygen vacancy (VOn••) with respect to TM. As shown in Fig. 1, O1 and O2 are the 1st-NN and 2nd-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 VO•• tends to keep away from TM atoms, whereas an upward total energy shows that VO•• is apt to be located close to the TM atoms.

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Figure 3
figure 3

Electronic structures of transition-metal (TM)-doped BiFeO3. (a) Representative partial charge densities of the electronic states indicated by arrows in (b) total density of states (DOS) and partial DOS of TM atoms, where the states in the majority spin component (↑) are colored in blue while those in the minority spin component (↓) in yellow. In (b), the Fermi energy (EF) is set at zero, and upper and lower dashed lines are the conduction band minimum and the valence band maximum, respectively. For the TM = Ti cells, the DOS of the Fe1 adjacent to VOn•• is also shown. In each the DOS panel, the majority spin component (↑) is displayed in the right while the minority spin component (↓) in the left.

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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 Ti4+ (d0) and Fe12+ (d6) because of the higher energy states of Ti-3d, where the Fermi level (EF) is located at the electron-occupied Fe1-3d state. These results are supported by the partial magnetic moments of 0.1 μB for Ti-3d and 3.6 μB for Fe1-3d (smaller than the other Fe-3d values of ~4.1 μB). This can be qualitatively understood by the charge transfer: the electron of Ti3+ is transferred to Fe1 on the 1st NN site with the oxygen vacancies. With respect to the valence band maximum (VBM; the lower dashed line), the Fe1-dxy state with VO3•• is lower by ~0.1 eV than the Fe1-dz2 state with VO1••, 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 (d2) in the gap; comparing the higher gap states at the EF, the dyz state with VO3•• is lower in energy by ~0.1 eV than the dyz state with VO2••, resulting in the lower Etotal of n = 3. For TM = Cr, the empty gap state with the dz2 character appears with VO1••, whereas there is no state in the gap with VO3••. Although the change in the coordinate from CrO6 (n = 3) to CrO5 (n = 1) splits the eg state into the low-lying dz2 and the high-lying dx2−y2, this does not lead to a significant stabilization in the system, because both the states are empty. The CrO6 structure (n = 3) maintains a regular octahedron, and the Cr-3d state is represented by t2g3eg0, which contributes to a lower Etotal of n = 3. A stabilization of V•• away from Cr has also been reported for hexagonal BaTiO340. The details for TM = Mn are described later.

For TM = Co, the electronic configuration of Co3+ (d6) in Oh symmetry is expressed as t2g4eg2 in the high-spin state41,42. 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 eg(↑). In this case, the electronic state is regarded as t2g(↓)3eg(↓)2eg(↑)1 rather than as t2g(↓)3eg(↓)2t2g(↑)1, in which the strong hybridization of Co-eg with O-2p leads to a relatively small magnetic moment of Co3+ with ~3.0 μB. Comparing the energies of the dz2-derived state (↓), we found that the cell with VO1•• 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 VO1••), along with the orbital mixing with O-2p of two apical oxygen atoms. This marked stabilization of the dz2-derived bonding state is attributed to the lower Etotal of n = 1. The Ni cells exhibit relatively complex electronic features; the electronic configuration of Ni3+ (d7) in Oh symmetry is described as t2g6eg1. With VO1•• in the minority spin component (↓), the unoccupied dx2−y2 state is present in the gap, while the dz2-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 VO3••, its energy is higher by ~0.5 eV. The low-lying dz2-derived state with VO1•• is responsible for the lower Etotal of n = 1. For TM = Cu, the electronic configuration of Cu3+ (d8) is expressed as t2g6eg2, which is supported by the empty eg(↑) state present in the band gap. Nevertheless, the apparent orbital mixing of Cu-eg(↑) and O-2p is clearly seen in their partial charge density (Fig. 3a) and thus result in a relatively small magnetic moment of Cu3+ with 0.6–0.8 μB. The cell with VO3•• has the eg(↑) state whereas that with VO1•• features the low-lying dz2 and the high-lying dx2−y2 sates owing to the absence of O1. Also for the occupied states in the minority spin component (↓), the cell with VO1•• has the dz2-derived state at ~−6.1 eV, which is lower by ~0.3 eV than that with VO3••, leading to the lower Etotal of n = 1.

Oxygen-vacancy distributions

Figure 4 shows the VO•• distributions of the TM-doped cells. For TM = Ti, V, and Cr, VO•• does not find an energetically favourable site inside the lattice; the vacancies in the vicinity of the bottom electrode are pulled toward its interface owing to a strong depolarization field arising from the discontinuity of Ps, suggesting a formation of an VO••-rich layer (Fig. 4a). This defective layer has been reported for non-doped BiFeO3 films22,43,44,45,46. By contrast, the cells with TM = Mn, Co, Ni, and Cu provide a stable position of VO••, i.e., the 1st NN site adjacent to the TMs. Provided that the concentration of TMs is higher than that of VO•• and also that the attractive interaction between VO•• and TMs is sufficiently strong, VO•• is trapped by TMs in an equilibrium state, as displayed in Fig. 4b.

Figure 4
figure 4

Oxygen-vacancy distributions in capacitor form. (a) BiFeO3 and transition-metal (TM)-doped BiFeO3 [Bi(Fe,TM)O3, TM = V, Cr (Ti)] and (b) TM-doped BiFeO3 [Bi(Fe,TM)O3, TM = Mn, Co, Ni, Cu]. The TM atoms except for Ti have a valence state of TM3+. As the TM = Ti cell exhibits a valence state of Ti4+ because of the presence of Fe2+, Ti is indicated in parenthesis in (a). In (a), oxygen vacancy (VO••) does not find a stable site inside the lattice and thereby accumulates at the interface with the bottom electrode, forming a VO••-rich layer; this defective layer is formed by an attractive interaction with negative bound charges caused by a discontinuity of spontaneous polarization (Ps). In (b), VO•• is stabilized adjacent to TM3+; provided that the concentration of TM is higher than that of VO•• ([VO••]), all of VO•• are trapped by TM3+.

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For a robust switching of Ps by applying electric fields, in addition to the attractive interaction of VO••-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 TM3+; 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 range47, and the valence state is controllable to Mn3+ 48. Moreover, the empty dx2−y2 state of the Mn cell with VO1•• is far above the VBM49, and thereby a leakage current is expected to be relatively low.

Crystal structures and properties

As displayed in Fig. 5 of the X-ray diffraction reciprocal space maps (XRD-RSMs), we confirmed that the capacitors are hetero-epitaxially grown on the SrTiO3 substrate, i.e., the [001]pc directions of the films are normal to (001) of the substrate. For both the capacitors, we observed the superlattice reflections of 1/2 1/2 3/2 and 3/2 3/2 1/2 in addition to the fundamental ones. Figure 5c–f displays the high-resolution XRD-RSMs of the 103 pc and 113 pc reflections. The Ba0.3Sr0.7TiO3 film exhibits the reflection with a smaller qx value compared with the substrate. We note that the qx position of the reflection for the Ba0.1Sr0.9RuO3 electrode is almost the same as that of the Ba0.3Sr0.7TiO3 film. These results show that the Ba0.1Sr0.9RuO3 electrode along with the Ba0.3Sr0.7TiO3 film acts as a buffer layer for reducing the lattice mismatch between BiFeO3 (BFO) or Bi(Fe0.95Mn0.05)O3 (Mn-BFO) and SrTiO3.

Figure 5
figure 5

X-ray diffraction analysis. X-ray diffraction reciprocal space maps for (a,c,d) BiFeO3 and (b,e,f) Bi(Fe0.95Mn0.05)O3 capacitors with a Ba0.3Sr0.7TiO3 (300 nm)-buffered Ba0.1Sr0.9RuO3 electrodes. (a,b) Maps measured using the sources of Cu-Kα + Kβ while (c,d,e,f) those measured using Cu-Kα1. All the Mirror indices and crystallographic directions are described in the pseudo-cubic notation; ‘pc’ is omitted.

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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 nm3, which are almost the same as those of the bulk (a = 0.3964 nm, α = 89. 43 deg. and V = 6.23 × 10−2 nm3)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 nm3, 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 state44,51,52. 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 Pr value along [001]pc provides a Ps (// [111]pc) of 96.0 μC cm−2, which is close to the Ps observed for bulk crystals53 and calculated by first-principles calculations54. 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 VO••-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 process55.

Figure 6
figure 6

Polarization and leakage-current properties. (a,b) Polarization-electric field (P-E) hysteresis loops (3 kHz) and (c,d) leakage-current density as a function of E (J-E) properties along the [001]pc direction; (a,c) BiFeO3 and (b,d) Bi(Fe0.95Mn0.05)O3 capacitors with a Ba0.3Sr0.7TiO3 (300 nm)-buffered Ba0.1Sr0.9RuO3 electrodes. Data were measured at 25 °C.

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Electronic structures of Mn-doped BiFeO3

Figure 7 presents the results of the DFT calculations for the defective cells of TM = Mn. The relative value of Etotal as a function of n is plotted in Fig. 7a. We note that the cells of n greater than three exhibit a relatively large Etotal by 0.1–0.2 eV compared with n = 1 and 2, indicating that the cell has a lower energy provided that VO•• is located adjacent to Mn. Notably, the energy gain when VO•• is present on the O1 (n = 1) site is 250 meV, which is three times as large as that of the thermal energy kBT even at the deposition temperature (Tsub = 610 °C, kBTsub ~75 meV). Because the Curie temperature (830 °C for BiFeO3) is higher than Tsub, a crystallization during the film deposition occurs in the ferroelectric state. We assume that the majority of VO•• are trapped by Mn even in the deposition process at high temperatures through a trapping-detrapping dynamics56,57. Also, after the film is exposed to a subsequent annealing or a polarization switching, Mn provides the preferred site for VO•• in its immediate vicinity, and then almost all VO•• associates with Mn in an equilibrium state.

Figure 7
figure 7

Interaction between Mn and Oxygen vacancy. (a) Total energy as a function of n obtained by DFT calculations, where n denotes the n-th nearest neighbor (NN) site of oxygen vacancy (VOn••) with respect to Mn3+. O1 and O2 are the 1st-NN and 2nd-NN oxygen atoms (see in Fig. 1b). The total energy of n = 1 is set at zero. Total density of states (DOS) and partial DOS of the cells of (b) VO3•• and (c) VO1•• and their respective band structures are shown in (d,e). In DOS panels, the majority spin component (↑) is indicated in the right while the minority spin component (↓) in the left. The Fermi energy (EF) is set at zero, and upper and lower dashed lines are the conduction band minimum and the valence band maximum, respectively. In band structures, the majority spin component is colored in red and the minority spin component in blue. Partial charge densities of the gap states formed primarily by the orbital interaction between Mn-3d and O-2p for the (f) VO3•• and (g) VO1•• cells, where the majority spin components are colored in blue while those in the minority spin component in yellow. The lower panel of (g) is the Mn-3d derived state in the valence band indicated by an arrow in (c).

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Here, we address the mechanism of the attractive interaction between Mn and VO•• (Fig. 4b). Given that Mn is octahedrally coordinated with six oxygen atoms and is placed in Oh symmetry, Mn3+ (d4) has a configuration of t2g3eg1, and an electron occupies the half of the eg state. In the ferroelectric state with VO••, the degeneracy of eg is lifted, rendering either of the component dx2−y2 or dz2 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.

Figure 7b,c displays the density of states (DOS) of the VO3•• and VO1•• cells, and their respective band structures are presented in d and e. The fundamentals of the electronic structures are described in the literature44,49,54. For the VO1•• cell having the smallest Etotal, an empty state derived mainly from the Mn-3d state (dx2−y2) is left in the band gap, i.e., an unoccupied gap state is formed in the minority spin component above the EF. The relatively large DOS of Mn-3d around −5 eV indicates that the rest four occupied d states (dxy, dxz, dyz, and dz2) exist inside the valence band, which are hybridized with the neighboring O-2p (e.g., the dz2-derived partial charge density depicted in the lower panel of Fig. 7g). By contrast, the VO3•• cell has two gap states: one is an empty dx2−y2 state and the other is an occupied dz2 state. This result proves that the dz2-derived occupied state is much lower in the VO1•• cell than in the VO3•• one.

Oxygen-vacancy trapping

When VO•• associates with Mn in the immediate vicinity, a MnO5 pyramid is formed, and Mn-3d interacts strongly with O-2p of the adjacent five oxygen atoms. Because a repulsive Coulomb interaction between electrons is markedly reduced along the Mn-VO•• direction, the MnO5 pyramid can accommodate the dz2 orbital affordably (see the partial charge density in Fig. 7g), and thereby its level is lower in energy far below EF. Provided that VO•• is away from Mn, which involves a change from the MnO5 pyramid to the MnO6 octahedron, the d orbitals are affected by the adjacent six oxygens and then the dz2 orbital is shifted to higher energy, forming the occupied gap state above the VBM. As a result, the system is stabilized when VO•• resides adjacent to Mn. These results lead to the conclusion that Mn acts as an effective trap for VO••.

We address the VO•• distribution in the capacitors. As reported in the literature58 and shown in Fig. 6, the as-prepared BFO capacitor show the distinct characteristics such as the asymmetric P-E hysteresis loop and the rectified current behavior. All these properties can be explained by an VO••-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 Bi46,59,60; Bi vacancy (VBi″′) is formed and acts as an acceptor13,44, which is accompanied by VO•• for charge compensation61,62. Atomic-scale chemical and structural analyses show that Fe4+ (FeFe•) is abundant in the domain wall region in BiFeO313. DFT calculations reveal that the iron atom adjacent to VO•• tends to a valence state of Fe4+ stabilized by a FeO5 pyramid13, which can explain a high concentration of Fe4+ owing to an accumulation of VO•• at the domain walls. We therefore think the charge neutrality of [VBi″′] ~ [VO••] ~ [FeFe•] and express the overall defect formation by

$${{{\rm{Bi}}}_{{\rm{Bi}}}}^{\times }+{{{\rm{Fe}}}_{{\rm{Fe}}}}^{\times }+{{{\rm{O}}}_{{\rm{o}}}}^{\times }\to {V\prime\prime\prime }_{{\rm{Bi}}}+{{{\rm{Fe}}}_{{\rm{Fe}}}}^{\cdot }+{{V}_{{\rm{o}}}}^{\cdot \cdot }+{\rm{Bi}}({\rm{g}})+1/2({\rm{g}}),$$
(1)

where BiBi×, FeFe×, and OO× are Bi3+ on the Bi site, Fe3+ on the Fe site, and O2− on the O site, respectively. Provided that VO•• hops to the other O site, the 1st NN Fe atom adjacent to the newly created VO•• is oxidized from Fe3+ to Fe4+ as a result of an electron transfer. Therefore, FeFe• always associates with VO•• regardless of its position and is present as the defect complex of VO••-FeFe•, which leads us to propose that the charge neutrality is expressed by [VBi″′] ~ [VO••-FeFe•]44. Because the mobility of VO•• is several orders of magnitude higher than that of cation defects such as VBi″′25, we can consider that VBi″′ is frozen, except at high temperatures during the film deposition, and thus has a random distribution at low temperatures. By contrast, VO•• is mobile even at room temperatures19 and then accumulates if its preferred site exists. Although the negatively charged VBi″′ is supposed to attract VO•• owing to an electrostatic interaction, DFT calculations44 show that VBi″′ does not act as a trap of VO•• and predict that VO•• is randomly distributed in bulk form. It has been reported that VO•• is apt to accumulate at high-energy boundaries such as ferroelastic domain (twin) walls and ferroelectric/electrode interfaces10,11,12,13,14,15,30,31,32,33.

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 Ps vector is inevitable at interfaces with electrodes and results in a depolarization field22,43,44,45,46. As the Ps of BFO is markedly large, the depolarization field becomes strong. We note that the tail of Ps vector has negative bound charges that attract positively charged VO••. DFT calculations51 predict that the VO•• near the electrodes moves to the interface and forms an VO••-rich layer to reduce an electrostatic energy. The concentration of VBi″′ ([VBi″′]) is likely to be less than 3%63, and leads to a comparable [VO••] at most because of [VBi″′] ~ [VO••-FeFe•]. In the Mn-BFO capacitor, VO•• can associate exclusively with Mn because of its higher content (5% Mn), as depicted in Fig. 3b. We conclude that Mn acts as an effective trap of VO•• and thereby inhibits the formation of an VO••-rich layer at the interface.

Discussion

We show that isovalent dopants with partly or fully electron-filled eg state, such as Mn3+ (MnFe×), act as an effective trap for oxygen vacancies, which enables us to provide a design principle to tailor the defect structures in a wide range of [VO••]. The isovalent dopants do not influence [VO••], and the intrinsic defect of VBi″′ dictates [VO••], where [VBi″′] is not easily controllable. Introducing higher valent cations such as Ti4+ (TiFe•) reduce [VO••]64; the doping of a small amount of MnFe× together with [TiFe•] ( > 3[VBi″′]) can lower [VO••] by several orders of magnitude, and all the vacancies are present only in the adjacent vicinity of Mn3+. This defect structure leads to a high mobility of domain walls, which is suitable not only for reliable high-speed non-volatile memories but also for piezoelectric applications utilizing high strain constants. For the applications based on conducting domain walls stabilized by VO••, a finely tuned [VO••] should considerably improve the device performance, which is accomplished by the balanced co-doping of MnFe× and TiFe•; free, mobile VO•• with an adjusted concentration accumulates the domain walls and leads to a desirable interaction strength, delivering domain-wall memories exhibiting a high-speed switching.

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.

Methods

Experiments

Thin films of ferroelectric BiFeO3 (BFO) and Mn(5%)-substituted BiFeO3 [Mn-BFO, Bi(Fe0.95Mn0.05)O3] were fabricated on (100) SrTiO3 single-crystal substrates. To reduce a lattice mismatch between the substrate and the ferroelectric films as much as possible, we adopted Ba0.3Sr0.7TiO3 as a buffer layer and Ba0.1Sr0.9RuO3 as an electrode. We prepared the capacitors of Ba0.1Sr0.9RuO3 (30 nm)/BiFeO3 or Bi(Fe0.95Mn0.05)O3 (125 nm)/Ba0.1Sr0.9RuO3 (30 nm)/ Ba0.3Sr0.7TiO3 (300 nm)/SrTiO3, where their thickness is indicated in parenthesis. All the films were deposited hetero-epitaxially by pulsed-laser deposition (PLD). The Ba0.3Sr0.7TiO3 buffer layer was grown at a substrate temperature (Tsub) of 740 °C under 0.26 Pa O2 atmosphere with a laser repetition rate of 1 Hz. The Ba0.1Sr0.9RuO3 electrodes were prepared at a Tsub of 610 °C under 13 Pa O2 atmosphere with a laser repetition rate of 1 Hz. For the ferroelectric layers, Tsub, oxygen pressure and a laser repetition rate were set at 640 °C, 2.6 Pa, and 7 Hz, respectively. Then, the Ba0.1Sr0.9RuO3 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 training43,44 to control the distribution of oxygen vacancy (VO••). Crystal structure analysis was performed by X-ray diffraction (XRD) reciprocal space mapping (RSM), where the sources of Cu-Kα + Kβ and Cu-Kα1 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 DFT65 were performed within the generalized gradient approximation (GGA)66 in the projector-augmented-wave (PAW) method67, 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 approach70, 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 μB (μB denotes the Bohr magneton) or −5 μB 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 BiFeO3 cell with R3 symmetry (Z = 6) to the primitive rhombohedral lattice (Bi2Fe2O6, Z = 1) and then created the supercell of 2 × 2 × 2, leading to the Bi16Fe16O48 structure. We replaced one Fe atom with a negative magnetic moment by TM [Bi16(Fe15TM)O48] and lifted the symmetry to the hexagonal R3 [TM-BiFeO3 cell (Z = 3), see 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-BiFeO3 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-BiFeO3 cell [Bi16(Fe15TM)O48 (Z = 1), Fig. 1b], we constructed 17 defective TM-BiFeO3 cells with one VO••, Bi16(Fe15TM)O47, 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 configuration38. We confirmed that the antiferromagnetic configuration of Fe atoms is established in the defective cells after the structural optimizations under no constraint regarding the total magnetic moment, even though the initial spin state around VO•• is set to the ferromagnetic order.