Successive redox-mediated visible-light ferrophotovoltaics

Abstract

Titanium oxide materials have multiple functions such as photocatalytic and photovoltaic effects. Ferroelectrics provide access to light energy conversion that delivers above-bandgap voltages arising from spatial inversion symmetry breaking, whereas their wide bandgap leads to poor absorption of visible light. Bandgap narrowing offers a potential solution, but this material modification suppresses spontaneous polarization and, hence, sacrifices photovoltages. Here, we report successive-redox mediated ferrophotovoltaics that exhibit a robust visible-light response. Our single-crystal experiments and ab initio calculations, along with photo-luminescence analysis, demonstrate that divalent Fe²⁺ and trivalent Fe³⁺ coexisted in a prototypical ferroelectric barium titanate BaTiO₃ introduce donor and acceptor levels, respectively, and that two sequential Fe³⁺/Fe²⁺ redox reactions enhance the photogenerated power not only under visible light but also at photon energies greater than the bandgap. Our approach opens a promising route to the visible-light activation of photovoltaics and, potentially, of photocatalysts.

Introduction

Light-induced functions such as photocatalytic and photovoltaic (PV) effects rely on the formation of electron (e’)-hole (h^•) pairs under illumination. As a representative photocatalyst, titanium dioxide¹, absorbs only ultraviolet light owing to its large bandgap (E_g), several approaches for controlling the electronic structure have been used to activate a visible-light response, often with the aid of sacrificial reagents, dyes or precious metal co-catalysts: introducing donor levels into the bandgap via doping^2,3, raising the valence band to a more negative level than that arising from O-2p by a composition modification^4,5, and narrowing the bandgap by forming a solid solution⁶ or a two-dimensional structure⁷.

For strontium titanate, Reunchan et al.⁸ have demonstrated that the Fermi-level lifting by a co-doping promotes a photocatalytic response under visible-light, which is achieved by stabilizing Cr³⁺ in the presence of La³⁺. Defect levels inside the bandgap, called gap states, of Cr³⁺ are located above the valence band maximum (VBM), and the donor states play a crucial role in visible-light activation⁹. Wang et al.¹⁰ have shown that La- and Rh-codoped SrTiO₃ functions as a photocatalyst, where the occupied states of Rh³⁺ narrows the bandgap.

Ferrophotovoltaics have attracted considerable interest because their bulk PV effect^11,12,13 leads to high voltages that are beyond the bandgap limit of semiconductor p–n junctions^11,12,14,15. The ferroelectric PV effect has been extensively studied for wide-bandgap oxides such as LiNbO₃^11,16,17, BaTiO₃^{18,19,20,21,22}, PbTiO₃-based perovskites^23,24,25, and BiFeO₃^14,15,26. The poor absorption of visible-light is partially overcome by narrowing the bandgap^{27,28,29,30,31}. This is realized by incorporating non-polar components into the widegap ferroelectrics, which is, in principle, accompanied by a substantial decrease in spontaneous polarization (P_s). As the intense photoresponse originates from the large magnitude of P_s^13,32, these material modifications are inevitably associated with a marked suppression of photovoltage. Gap-state engineering that utilizes mid-gap states for BiFeO₃³³ can enhance photocurrents without sacrificing photovoltages, where the photon energy of at least half of E_g are required.

Here, we report successive-redox-mediated ferrophotovoltaics, where two gap states realize e’-h^• pair formation over a wide photon-energy (hv) range. Our approach is based on acceptor and donor states that act as scaffolds for generating photoinduced carriers. A single transition-metal dopant with two different valence states introduces these gap states, thereby providing successive redox cycles under illumination. In principle, it can induce PV currents at small hv without being restricted by the material bandgap. Our experimental and theoretical study on a prototypical ferroelectric BaTiO₃ demonstrates that the 3d orbitals of iron derive donor and acceptor levels in the Fe²⁺-Fe³⁺ coexisting state and that e’-h^• pairs injected by two sequential Fe³⁺/Fe²⁺ reactions deliver a robust PV response not only under visible-light but also at hv greater than E_g.

Results

Strategy for visible-light activation

Because of the wide E_g of BaTiO₃ (3.2 to 3.3 eV)^34,35, the PV effect occurs under ultraviolet light. To activate a visible-light response, we introduce electronic states derived from Fe²⁺ and Fe³⁺ into the bandgap and utilize these gap states as scaffolds for carrier generation. The most striking feature is that e’-h^• pairs are, in principle, formed at photon energies much smaller than that of the mid-gap-state engineering³³, as described later.

In O_h symmetry (Fig. 1a, b), the electronic configurations of iron in the high-spin state are expressed as Fe³⁺ (d⁵) with t_2g³(up) e_g²(up) t_2g⁰(down) e_g⁰(down) and Fe²⁺ (d⁶) with t_2g³(up) e_g²(up) t_2g¹(down) e_g⁰(down)³⁶. In the BaTiO₃ lattice, the states of t_2g³(up) e_g²(up) are located near the bottom of the valence band³⁷, while it is probable that the states of t_2g⁰(down) of Fe³⁺ (Fig. 1c) and t_2g¹(down) of Fe²⁺ (Fig. 1d) are present inside the bandgap by tuning their local structures. We, therefore, consider the following strategy for generating e’-h^• pairs under visible-light: Fe³⁺ plays the role of an electron acceptor that results in hole injection into the valence band^38,39, and Fe²⁺ acts as an electron donor that leads to electron injection into the conduction band^40,41,42. Provided that Fe³⁺ and Fe²⁺ coexist and also that their acceptor and donor states are present at moderate levels near the VBM (the top of the O-2p band) and the conduction band minimum (CBM: the bottom of the Ti-3d band), respectively, e’-h^• pairs can be created at hv much smaller than E_g. As displayed in Supplementary Fig. 1, the hybridization between Fe-3d and its adjacent orbitals provides the bonding states (t_2g and e_g) and the antibonding states (t_2g^* and e_g^*), as for the majority spin components. Hereafter, the Fe-3d derived states without an asterisk, such as t_2g and d_xy, are the bonding states, while those with asterisk (*), e.g., t_2g^* and d_xy^*, are the antibonding ones.

Fig. 1: Defects states in Fe-doped BaTiO₃.

a, b Electronic configurations in the high-spin state of Fe³⁺ and Fe²⁺ in O_h symmetry. c, d Gap states derived from Fe²⁺ and Fe³⁺ in the bandgap (E_g) between the conduction band (Ti-3d) and the valence band (O-2p) in the host BaTiO₃ lattice. e Defect concentrations at 25 °C as a function of oxygen partial pressure (Po₂^900 °C) at 900 °C (annealing temperature). In the region III, Fe²⁺ and Fe³⁺ coexist and their defect (gap) states can be utilized as scaffolds for visible-light absorption. In the Fe²⁺-Fe³⁺ coexisting state, photoinduced carriers are expected to be generated as follows: the unoccupied t_2g state of Fe³⁺ c is positioned above the valence band maximum (VBM, the top of the O-2p band) and then play the role of an electron acceptor, while the electron-occupying t_2g state of Fe²⁺ d is located below the conduction band minimum (CBM, the bottom of the Ti-3d band) and then acts as an electron donor.

Figure 1e plots the defect concentrations at 25 °C as a function of Po₂^900 °C in Fe (0.3%)-doped BaTiO₃. These calculations are based on the assumption that the oxygen vacancy concentration, [V_O^••], equilibrated in a high-temperature state at 900 °C remains unchanged at 25 °C (Po₂^900 °C is the oxygen partial pressure at 900 °C). The defect feature is divided into four regions. In the regions I and II, the majority of iron is trivalent, namely, the concentration of Fe³⁺, [Fe³⁺], is several orders of magnitude higher than others; the minority is Fe⁴⁺ at a higher Po₂ (I) and Fe²⁺ at a lower Po₂ (II). We note that the region III is regarded as the coexisting state of Fe³⁺ and Fe²⁺, the concentrations of which have the same order. At the higher Po₂^900 °C side (I, II, and III), the charge neutrality is approximated as 2[Fe²⁺] + [Fe³⁺] ≈ 2[V_O^••]. The region IV is semiconducting with a high-electron concentration (n), along with Fe²⁺ as the majority, where the charge neutrality is expressed as n ≈ 2[V_O^••] except near the transition Po₂^900 °C. According to the strategy described above, we expect that the coexisting state of Fe³⁺ and Fe²⁺ in the region III is capable of inducing a robust PV response under visible-light. We therefore adopt an Po₂^900 °C of 10⁻²³ atm as an annealing condition, where the concentrations are calculated to be [Fe³⁺] ≈ 3.5 × 10¹⁹ cm⁻³ and [Fe²⁺] ≈ 4.3 × 10¹⁹ cm⁻³.

Formation of defect associates

Figure 2 displays the DFT energy versus n of V_On^••, where V_On^•• denotes the oxygen vacancy on the n-th nearest-neighbor site with respect to Fe (Supplementary Fig. 2). The cells with n = 1 to 3 exhibit small energies compared with those with n > 4 regardless of the Fe valence. Considering the energy difference of 0.2 to 0.8 eV, we posit that an attractive interaction is formed between iron and V_O^••. If V_O^•• is mobile below the Curie temperature (T_C), we consider that V_O^•• is trapped by Fe and is eventually positioned on the nearest-neighbor O1 site (Fig. 3b, c) after a certain period of time. These results suggest that V_O^•• exists as a defect associate of Fe³⁺-V_O^•• and/or Fe²⁺-V_O^••.

Fig. 2: DFT energies of Fe-doped BaTiO₃.

The horizontal axis n denotes the V_On^•• (oxygen vacancy)-site number in the tetragonal Ba₂₇Ti₂₆FeO₈₁ structures (Supplementary Fig. 2), and the vertical axis is the density-functional-theory (DFT) energy with respect to that of n = 1 in the a Fe³⁺ and b Fe²⁺ cells. V_O^•• is adjacent to iron atoms in the n = 1 to 3 cells and is away from iron atoms in the n = 4 to 21 cells, as illustrated in the insets of the n = 1 (V_O1^••) and n = 4 (V_O4^••) cells. Regardless of the valence state of iron, the energies with n = 1 to 3 are 0.6 to 0.8 eV lower than those with n = 4 to 21. These results show that V_O^•• is attracted by iron and eventually stabilized on the O1 site (the nearest-neighbor site with Fe).

Fig. 3: Crystal structures of tetragonal (T) Fe-BaTiO₃ cells.

The crystal structures optimized by density-functional theory (DFT) calculations are displayed for a Ba₂₇Ti₂₆FeO₈₁ (Fe³⁺), b Ba₂₇Ti₂₆FeO₈₀ (Fe³⁺-V_O1^••), and c Ba₂₇Ti₂₆FeO₈₀ (Fe²⁺-V_O1^••). The valence states of Fe are controlled by the total number of electrons. The crystal symmetry was converged in tetragonal space group P4mm for all the cells, where the spontaneous polarization (P_s) is parallel to the c axis. O1 and O3 are defined as the first and third nearest-neighbor (NN) oxygen atoms with respect to Fe in the defect-free cell. Ti1 is the first-NN titanium atom with Fe. In the defective cells, an oxygen vacancy (V_O^••) is stabilized on the first NN O1 site (see Fig. 2), namely, is present as the associate of Fe³⁺-V_O^•• or Fe²⁺-V_O^••.

The formation of the defect associates can be explained in terms of the energy levels of the Fe-derived states. The orbital interactions provide bonding and antibonding states in both the majority (↑) and minority (↓) spin bands. In the ↑ band, the bonding states appear near the bottom of the valence band (Supplementary Fig. 3), and the antibonding states (marked with asterisk) arise near or inside the bandgap (Fig. 4 and Supplementary Fig. 4). For the Fe³⁺-V_O1^•• and Fe³⁺-V_O4^•• cells, the t_2g^* and e_g^* states are similar and their energy levels are close, while the t_2g and e_g states exhibit different features (Supplementary Fig. 3): these bonding states of the Fe³⁺-V_O1^•• cell are lower in energy by ≈0.5 eV than those of the Fe³⁺-V_O4^•• cell. The attractive interaction between Fe³⁺ and V_O^•• originates from these low-lying bonding states. As for Fe²⁺, the Fe²⁺-V_O4^•• cell (Supplementary Fig. 4c, d) has electron-occupying gap states: the Fe-3d_xz state (↓) and the Fe-3$d_{z^2}{\,\!}^*$, -3$d_{x^2 - y^2}{\,\!}^*$ and -3$d_{yz} {\,\!}^*$ states in the ↑ band. In contrast, the Fe²⁺-V_O1^•• cell (Fig. 4e, f,) exhibits only two gap states of Fe-3$d_{z^2}$ (↓) and -3$d_{x^2 - y^2} {\,\!}^*$ (↑). The remaining ↑ states, namely, Fe-3$d_{xz}$, -3$d_{yz} {\,\!}^*$, -3$d_{xy} {\,\!}^*$, and -3$d_{z^2}$, are lower in energy and are near the bottom of the valence band. The stabilization of V_O^•• on the O1 site, i.e., the formation of the Fe²-V_O^•• associate, results from these lower-lying Fe-3d states.

Fig. 4: Electronic structures of tetragonal (T) Fe-BaTiO₃.

Band structures and total (partial) density of states (DOS) for the a, b Fe³⁺, c, d Fe³⁺-V_O1^••, and e, f Fe²⁺-V_O1^•• cells, where V_O1^•• denotes the oxygen vacancy on the O1 site. The Fermi-level is indicated by E_F. In the band structure, the red and blue lines represent the majority (↑) and minority (↓) spin components, respectively. The valence band and the conduction band of the host BaTiO₃ lattice are colored light blue and light orange, respectively. The bandgap is denoted by E_g. The red and blue arrows in e represent electrons occupying in their corresponding spin bands. In the DOS, the right and left panels correspond to the ↑ and ↓ bands, respectively, as indicated in the total DOS. The Fe³⁺ cell has the empty gap state of t_2g (bonding) in the ↓ band. In the Fe³⁺-V_O^•• and Fe²⁺-V_O^•• cells, the degeneracy of the d orbitals is lifted owing to the presence of V_O^••. In the Fe³⁺-V_O^•• cell, four empty d (↓) states (bonding) appear near the middle of the bandgap. In the Fe²⁺-V_O^•• cell, the electron-occupied $d_{x^2 - y^2} {\,\!}^*$ (↑) state is above the valence band maximum (VBM) (asterisk denotes antibonding), and the E_F is formed near the middle of the bandgap by the occupied $d_{z^2}$ (↓) state (bonding).

As a short-range V_O^•• motion with a distance of a few unit cells occurs even near room temperature^43,44, it is reasonable to assume that all oxygen vacancies are present as the defect associates of Fe³⁺-V_O^•• and/or Fe²⁺-V_O^•• in our samples, as reported for SrTiO₃^45,46 and PbTiO₃^47,48 and BaTiO₃^49,50. Considering the charge neutrality and the strong attractive interaction between iron and V_O^•• (Fig. 2), we can say that the Fe²⁺-V_O^•• associate⁵¹ is the majority, i.e., the concentration of [Fe²⁺-V_O^••] is several orders or magnitude higher than that of an isolated Fe²⁺ (Fig. 3c). Similarly, the Fe³⁺-V_O^•• associate^51,52 (Fig. 3b) and an isolated Fe³⁺⁵³ are present with approximately the same concentration (Fig. 3a).

Gap states derived from Fe-3d

Figure 4 displays the electronic structures of the Fe³⁺, Fe³⁺-V_O^••, and Fe²⁺-V_O^•• cells, the crystal structures of which are shown in Fig. 3. In Fig. 5, the defect levels for the Fe²⁺-V_O1^•• and Fe³⁺-V_O1^•• cells are illustrated along with the corresponding partial charges of the Fe-3d derived gaps states. As reported in the literature^54,55, the valence band is mainly formed by O-2p, while the conduction band is primarily composed of Ti-3d, where an orbital hybridization between them occurs.

Fig. 5: Mechanism of the visible-light PV effect.

The photoresponse of the reduced sample in the Fe²⁺-Fe³⁺ coexisting state is focused. Because of the charge neutrality and the attractive interaction, Fe²⁺ is associated with an oxygen vacancy (V_O1^••). Half of Fe³⁺ also forms an Fe³⁺-V_O1^•• associate and the other half is isolated. The defect (gap) states are schematized for the a Fe²⁺-V_O1^•• and b Fe³⁺-V_O1^•• cells. The k-weighted and averaged energy differences are indicated by black arrows. The right and left states are the majority (↑) and minority (↓) spin components, respectively, and electrons occupying in the gap states are denoted by red and blue arrows in their corresponding spin bands. The partial charge densities near Fe atoms at the Γ point are displayed: the Fe²⁺-V_O1^•• cell has the b $d_{z^2}$- (↓) and c $d_{x^2 - y^2} {\,\!}^*$ (↑) states, while the Fe³⁺-V_O^•• cell involves the e d_xz-d_yz (↓) (degenerate), f $d_{z^2}$ (↓), and g d_xy (↓) states. The partial charge densities in the ↑ and ↓ bands are colored light blue and yellow, respectively. The Fe²⁺-V_O^•• cell shows the electron-occupied $d_{x^2 - y^2} {\,\!}^*$ (↑) state at a depth of 2.3 eV from the conduction band minimum (CBM) and the occupied $d_{z^2}$ (↓) state at 1.5 eV from the CBM. The Fe³⁺-V_O^•• cell contains the empty d (↓) states at 1.8 to 1.9 eV from the valence band maximum (VBM). Light illumination induces electron (e’) injection from the Fe²⁺-$d_{z^2}$ (↓) donor state along with an oxidation to Fe³⁺ and hole (h^•) injection from the empty Fe³⁺-d (↓) acceptor states that are associated with a reduction to Fe²⁺. A sequential electron pumping from the valence band to the conduction band through the acceptor and donor states can, in principle, be realized at a photon energy (hv) much smaller than E_g. As e’-h^• pairs are created through two sequential redox reactions of Fe³⁺/Fe²⁺, the resultant PV response is termed the successive redox-mediated ferrophotovoltaics.

Here, we focus on the electronic configuration and the defect levels derived from Fe-3d. In the Fe³⁺ cell (Fig. 4a, b), the empty t_2g (↓) state appears in the bandgap at a depth of 1.9–2.3 eV from the VBM. For the Fe³⁺-V_O^•• cell (Fig. 4c, d), four empty bonding (↓) states arise near the middle of the bandgap; at the Γ point, two are low-lying degenerate states of Fe-3d_xz and -3d_yz (Fig. 5e), and the remaining two are higher-lying Fe-3$d_{z^2}$ (Fig. 5f) and -3d_xy (Fig. 5g) states. The energy difference between these gap states and the VBM is 1.8–2.1 eV. Both for the single isolated Fe³⁺ and the Fe³⁺-V_O^•• associate (Fig. 5d), we consider that visible-light at hv above 1.8 to 1.9 eV can pump electrons from the VBM to the empty states, namely, visible-light drives h^• injection from Fe³⁺ to the valence band. This is achieved by an electron transfer to Fe³⁺ from the adjacent atoms, which is accompanied by a reduction from Fe³⁺ to Fe²⁺.

Figure 4e, f displays the electronic structure of the Fe²⁺-V_O1^•• cell, and a schematic representation is shown in Fig. 5a. There are several Fe-3d derived states in the bandgap: the low-lying two states are electron-occupied, while three states near the CBM are empty. The filled Fe-3$d_{z^2}$ (↓) state (Fig. 5b) emerges in the middle of the bandgap, which is positioned at a depth of 1.5–1.9 eV from the CBM. This energy difference in the vicinity of the k-points of Z–A–R–Z remains unchanged at ≈1.5 eV. Therefore, this occupied state can deliver an onset of electron injection to the conduction band at this photon energy. As shown in Fig. 5c, the occupied Fe-3$d_{x^2 - y^2} {\,\!}^*$ (↓) state with significant dispersion is present. As this state is located at a depth of 2.3–2.6 eV from the CBM, an additional onset of electron injection appears at ≈2.3 eV. These electron pumping processes can be regarded as an electron transfer from Fe²⁺ to titanium along with an oxidation from Fe²⁺ to Fe³⁺.

In the Fe²⁺ and Fe³⁺ coexisting state under illumination, the first onset is at ≈1.5 eV, above which the electron in the Fe²⁺-3$d_{z^2}$ (↓) state is pumped to the conduction band (Fig. 5a). This serves as a PV response originating from electron conduction through a trapping-detrapping process^16,17,56. The second onset is at 1.8–1.9 eV, above which holes are injected into the valence band from the empty gap states (↓) of Fe³⁺ (Fig. 5d). At hv greater than the second onset energy, the photoinduced carrier is regarded as e’-h^• pair. The third onset is at 2.3 eV, above which the electron in the Fe²⁺-3$d_{x^2 - y^2} {\,\!}^*$ (↑) state is additionally injected into the conduction band (Fig. 5a). We note that e’-h^• pairs are effectively generated above the third onset, because visible-light can pump electrons from the valence band to the conduction band mediated through these occupied and empty gap states, namely, electrons are excited from the two occupied states of Fe²⁺ (resulting in an oxidation to Fe³⁺), and holes are injected into the valence band from the empty gap states of Fe³ (leading to a reduction to Fe²⁺). This sequential electron pumping is accompanied by two successive redox reactions of Fe³⁺/Fe²⁺. The PV response mediated through the occupied (donor) and empty (acceptor) states is termed the successive redox-mediated ferrophotovoltaics.

Visible-light PV properties

Figure 6 shows the current density normalized by optical intensity, J_sc I_opt⁻¹, as a function of hv. Both the samples exhibit a complicated PV response above E_g of 3.2 eV. While this behavior is assumed to be explained by the shift current theory¹³, we focus on the PV properties at hv below E_g.

Fig. 6: Photovoltaic currents versus photon energy.

The short-circuit current density (J_sc) normalized by optical intensity (I_opt) is plotted as a function of photon energy (hv) for the a, b oxidized and c, d reduced samples. The valence state of iron in the oxidized sample is Fe³⁺ as the majority, while that in the reduced sample is a mixture of Fe²⁺ and Fe³⁺. The first PV onset is determined as the threshold by considering the noise level and the strong emissions of Xe lamp (light source) in the near-infrared range. The oxidized sample displays the first PV onset at 1.9–2.0 eV. The reduced sample exhibits a multiple-PV process: the first PV onset appears at less than 1.6 eV followed by the second at 1.9 eV and the third at 2.4 eV.

The oxidized (Fig. 6a, b) and non-doped (Supplementary Fig. 5) samples exhibit a PV onset at 1.9–2.0 eV, which is in good agreement with the energy difference between the VBM and the empty states of the isolated Fe³⁺ and the Fe³⁺-V_O^•• associate (Fig. 4). As displayed in Fig. 6c, d, the reduced sample indicates a much higher J_sc I_opt⁻¹ in a wide hv range. Considering the strong emission lines of the light source (Xe lamp) in the near-infrared region of >820 nm (>1.5 eV, Supplementary Fig. 6) and the low-hv data (the inset of Fig. 6d), we posit that the first onset is below 1.6 eV. This agrees with the 1.5 eV difference of the CBM to Fe²⁺-3$d_{z^2}$ (↓) (Fig. 5a). The second onset was found at ≈1.9 eV, which is in quantitative agreement with the difference between the VBM and the empty Fe³⁺ (↓) states (Fig. 5b). The third onset was observed at ≈2.4 eV, which accords with the gap of the CBM to the filled Fe²⁺-3$d_{x^2 - y^2} {\,\!}^*$ (↑) state.

Here, we address the photogenerated carriers under visible-light. The carrier for the oxidized sample is h^• above the first onset, while that for the reduced sample is e’ in the hv range from the first to the second onset. These single-carrier-type PV effects lead to a |J_sc I_opt⁻¹| of ≈1 × 10⁻⁹V⁻¹ at most. For the reduced sample above the second onset, h^• is generated in addition to e’. This yields e’-h^• pairs, thereby leading to an intense PV response. In the hv range from the second to the third onset, the concentration of h^• is higher than that of e’. This is because the two orbitals of Fe³⁺ and the three orbitals of Fe³⁺-V_O^•• act as an accepter state for h^• injection whereas the only one orbital of Fe²⁺-V_O^•• contributes to a donor state for e’ injection. We therefore consider that e’-h^• pairs and the surplus h^• contribute to the PV currents in this energy range. Above the third onset, e’ pumped from the Fe²⁺-3$d_{x^2 - y^2} {\,\!}^*$ (↑) state is superimposed; hence, the e’-h^• concentration increases markedly, thereby delivering the robust PV effect.

Figure 7a presents the current density (J) versus bias voltage (V) properties under light at hv = 3.1 eV. The oxidized sample exhibits a short-circuit J (J_sc) of −32 nA cm⁻² and an open-circuit voltage (V_oc) of 5.9 V. The reduced sample shows a large response: compared with the oxidized sample, the reduced sample has a J_sc of −520 nA cm⁻² that is more than one order of magnitude and an extrapolated V_oc of ≈35 V that is approximately six times.

Fig. 7: PV current density (J)-bias voltage (V) properties.

The measurements were performed under light at a wavelength of 405 nm (photon energy hv of 3.1 eV) and an intensity of 5.6 W cm⁻². The J–V properties at a light-polarization angle (Θ) of zero are presented in a, and the short-circuit current density (J_sc) versus Θ is plotted in b along with the measurement system. The inset in b schematizes the measurement system. The direction of I_opt is set at i = 1 and that of P_s at i = 3. The light-polarization (Θ) is defined as the angle between the polarization plane of light and the measured direction of J. In the configuration in the inset of b, the photocurrent is parallel to P_s, and the current density is J₃. The fitting analysis of the J_sc(Θ) data by the equation derived from the symmetry consideration provides the bulk PV tensor elements of β₃₁ and β₃₁, as listed in Supplementary Table 1.

The current density J_i arising from the bulk-PV effect is expressed by a third-rank tensor β_ijk. For the tetragonal crystal in 4 mm point group, the non-zero components of the bulk PV tensor are β₃₁, β_33, and β₁₅. Figure 7b indicates the data of J₃ (Θ) at hv = 3.1 eV and the results of the fitting analysis, where Θ denotes the light-polarization angle. As listed in Supplementary Table 1, the oxidized sample has β₃₃ = −1.77 × 10⁻⁹V⁻¹ and β₃₁ = −2.86 × 10⁻⁹V⁻¹, while the reduced sample features larger components by over an order of magnitude: β₃₃ = −3.25 × 10⁻⁸V⁻¹ and β₃₁ = −5.54 × 10⁻⁸ V⁻¹. We confirmed that β₁₅ is much smaller than β₃₁ and β₃₃ for both samples.

Photo-luminescence analysis

Figure 8 displays the photo-luminescence (PL) spectra of the single-crystal samples at 10 K, where the samples have a rhombohedral R3m structure. We confirmed that the electronic structures are essentially the same for the tetragonal (Fig. 4) and rhombohedral (Supplementary Fig. 7) cells. The data of the oxidized sample (Fig. 8a) could be traced by a single log-normal function, and the long-wavelength edge (LWE) is roughly estimated to be ≈660 nm (1.88 eV). This is in satisfactory agreement with the Fe³⁺-derived PV onsets (1.9–2.0 eV; see Fig. 6a, b). The PL spectra of the reduced sample (Fig. 8b) could not be reproduced by a single function but are are well fitted by a superposition of two log-normal functions. The LWEs are evaluated to be ≈660 nm (1.88 eV) and ≈570 nm (2.18 eV), which agree quantitatively with the Fe³⁺-derived second onset (1.9 eV) and the Fe²⁺-derived third onset (2.3 eV), respectively (Fig. 6d). The cathode-luminescence (CL) analysis of Fe (1%)-doped BaTiO₃ ceramics (Supplementary Fig. 8) gave consistent results: LWEs of ≈680 nm (1.82 eV) for the oxidized ceramic and those of ≈630 nm (1.97 eV) and ≈530 nm (2.34 eV) for the reduced ceramic. Moreover, the integrated data of the reduced ceramic indicate a CL peak with a LWE of ≈860 nm (1.44 eV), which agrees with the Fe²⁺-derived first onset (<1.6 eV).

Fig. 8: Photo-luminescence (PL) spectra.

The PL data (gray crossbar) were collected at 10 K for the single-crystal samples. The profile of the oxidized sample can be traced by a single log-normal function (red curve with H = 23,548, λ₀ = 341.5 nm, w = 369.1 nm, and ρ = 1.50). In contrast, that of the reduced sample could not be fitted by a single function and is well reproduced by a superposition (red curve) of two log-normal functions (black lines): the parameters of the large peak are H = 21,720, λ₀ = 341.5 nm, w = 369.1 nm, and ρ = 1.50, and those of the small peak are H = 4,502, λ₀ = 148.0 nm, w = 263.4 nm, and ρ = 1.16. The oxidized sample displays a long-wavelength edge (LWE) of ≈660 nm (1.88 eV), while the reduced sample exhibits LWEs of ≈660 nm (1.88 eV) and ≈570 nm (2.18 eV).

Discussion

Our study demonstrates that the donor and acceptor states derived from iron ions activate the visible-light PV effect that is mediated through the successive Fe³⁺/Fe²⁺ redox cycles. Another promising dopant is Mn that has the valence states of 2 +, 3 +, and 4+ ^57,58. As shown in Supplementary Figs. 9 and 10, the mixed valence state of Mn²⁺ and Mn³⁺ can activate sequential redox reactions that yield e’-h^• pairs. The Mn²⁺-V_O^•• associate creates a donor state at a depth of 1.3 eV from the CBM, thereby giving rise to the first PV onset. Considering the isolated Mn³⁺ having a acceptor state at 1.9 eV from the VBM, we expect that e’-h^• pairs can be generated at ≈1.9 eV, thereby leading to an intense PV response. The multiple gap states arising from Mn could produce the visible-light PV effect.

In summary, it is expected that our approach can be applied for photocatalysts of TiO₂ and SrTiO₃, as displayed in Supplementary Figs. 11 and 12, respectively. In these titanate systems, rigid TiO₆ octahedra govern the electronic structure near the bandgap, and the overall features of the iron-derived gap states are essentially the same. Moreover, the multivalent cations are not the unique dopants for e’-h^• pair generation. We can adopt a co-doping strategy: donor and acceptor states arise from cations of different elements, where their defect concentrations are easily controllable. Our work offers a starting point for further investigation of successive redox-mediated functions and opens an unprecedented route to robust photoinduced effects based on gap-state engineering.

Methods

Sample preparation and measurements

An Fe (0.3%)-doped BaTiO₃ bulk single-crystal was grown by a top-seeded solution growth method. After cutting the crystals, we annealed them in air at 1250 °C for 12 h in air for recovery from mechanical damage. To control the valence state of iron, the reduced sample was annealed at an oxygen partial pressure at 900 °C (Po₂^900 °C) of 10⁻²³ atm for 100 h, which was followed by quenching to 150 °C, and was slowly cooled to room temperature. The oxidized sample was also prepared by annealing at 1200 °C at an Po₂^1200 °C of 0.2 atm in a similar manner. A commercial single-crystal of BaTiO₃ (NEOTRON CO., LTD.) was used as a reference. Platinum electrodes were fabricated on the sample surface by sputtering. As a poling treatment, we applied an electric field of 2 kV cm⁻¹ during a slow cooling from 150 °C to room temperature through the Curie temperature (T_C ≈ 130 °C). This process enables us to obtain the single-domain sample with P_s//[001]. Ceramics of Fe (1.0%)-doped BaTiO₃ were prepared by solid-state reaction for luminescence measurements.

Photo- and cathode-luminescence measurements

Photo-luminescence (PL) spectra of the single-crystal samples were measured at 10 K with a spectrometer (Horiba LabRam-HR PL) through a long-wavelength-pass filter (>325 nm). Data were collected with a He-Cd laser excitation at 325 nm (a spot size of ≈100 μm and a laser power of ≈1.7 mW). As the data at a wavelength (λ) above 800 nm were strongly influenced by an inherent optical property of the filter, we analyzed the PL intensity (I_PL) in the λ range of 375–800 nm using the following log-normal function:

$$I_{{\mathrm{PL}}} = H \cdot {\mathrm{exp}}\left[ {\frac{{ - \ln 2}}{{\left( {\ln \rho } \right)^2}}\left\{ {\ln \left( {\frac{{\left( {\lambda - \lambda _0} \right)\left( {\rho ^2 - 1} \right)}}{{w\rho }}} \right) + 1} \right\}^2} \right]$$

(1)

where H denotes the peak height, λ₀ the shift parameter, w the full-width at half maximum, and ρ the half-width ratio. Cathode-luminescence (CL) spectra were also collected at 298 K with a scanning electron microscopy system (JEOL JSM-7800F Prime). Unfortunately, the CL intensities of the single-crystal samples were below the detection limit. Instead, we measured CL data of Fe (1.0%)-doped BaTiO₃ ceramics so that the output signal-to-noise ratio should be as high as possible. We analyzed the CL intensity (I_CL) data using the log-normal function in the similar manner.

We consider that luminescence profiles depend not only on the energy levels of defect states but also on the density-of-states of the relevant bands^59,60. It is reasonable to estimate the energy levels of gap states with respect to the valence band maximum (VBM) or the conduction band minimum (CBM) from the long-wavelength edge (LWE) rather than the peak wavelength of the PL/CL luminescence profiles. However, the spectra exhibit an inherent tail on the long-wavelength side, which prevents us from determining the edge unambiguously. Instead, we evaluate the LWE from the linear slope (dashed lines in Fig. 8 and Supplementary Fig. 8) of the log-normal distribution.

Photovoltaic analysis

The current density J_i is the component along the i direction arising from the bulk-PV effect and is expressed by the following equation using a third-rank bulk PV tensor β_ijk:^11,12,13

$$J_i = I_{{\mathrm{opt}}}\beta _{ijk}{\mathrm{e}}_j{\mathrm{e}}_k$$

(2)

where I_opt denotes the light intensity and e_j and e_k are the components of the unit vectors along the j and k directions, respectively. We adopt the standard 3 × 6 matrix notation: β_ijk →β_iλ with λ = 1, 2, …, 6, as used in the representation of the piezoelectric tensor. As the direction of I_opt is i = 1, that of P_s is i = 3, and the light-polarization (Θ) is defined as the angle between the polarization plane of light and the measurement direction of J (Fig. 7b), the photocurrent densities in 4 mm point group²² are expressed by

$$ J_{1} = 0\left( {//I_{{\mathrm{opt}}}} \right) \,\qquad \qquad \quad$$

(3)

$$J_{2} = I_{{\mathrm{opt}}}\beta _{15}{\mathrm{sin2}}\varTheta ( \bot P_{\mathrm{s}}) \, \,\, \, \quad$$

(4)

$$J_{3} = I_{{\mathrm{opt}}}\left[ {\left( {\beta _{33} + \beta _{31}} \right){\mathrm{/}}2 + \left( {\beta _{33} - \beta _{31}} \right){\mathrm{/}}\left.{2 {\mathrm{cos2}}{\mathrm{\varTheta }}} \right)} \right]\left( {{\mathrm{//}}P_{\mathrm{s}}} \right)\,$$

(5)

We measured the current density (J)–bias voltage (V) characteristics under light with an intensity of 5.6 W cm⁻² using a laser module with a wavelength of 405 nm (a photon energy hv of 3.1 eV). The light-polarization was controlled by a half-wavelength plate and a polarizer. The details are described in the preceding paper²². We investigated the normalized short-circuit current density J_sc I_opt⁻¹ as a function of hv. Monochromatic light from a Xe lamp passing through a MgF₂-coated diffraction grating was irradiated to the sample using an optical fiber. The wavelength resolution of our optical system was estimated to be 20 nm. Through the PV measurements, we excluded a transient current due to the capacitance and resistance of the samples together with a pyroelectric current caused by the photothermal⁶¹ effect. In determining the open-circuit voltage (V_oc), we extrapolated the linear J–V characteristics in a limited range owing to our current amplifier. All the PV measurements were performed at 25 °C.

Defect concentration calculations

The defect concentrations in an equilibrium state were calculated on the basis of the thermodynamic data set for BaTiO₃, the details of which are described in Supplementary Information. The calculations were conducted by a generalized-reduced-gradient non-linear least-squares method. We made the following assumptions: the lattice is equilibrated at 900 °C or 1200 °C (the annealing temperature) at a specific Po₂, and then the concentration of oxygen vacancy (V_O^••) is quenched (fixed) at room temperature. We take into account the electronic reactions, such as the redox of Fe³⁺/Fe²⁺ and the thermally activated electron-hole pair generation of null ↔ e’ + h^• in the whole temperature range.

Density-functional theory (DFT) calculations

DFT calculations were conducted using the generalized gradient approximation⁶² with a plane-wave basis set. We used the projector-augmented wave method⁶³ as implemented in the Vienna ab initio simulation package (VASP)⁶⁴. We employed the Perdew–Burke–Ernzerhof gradient-corrected exchange-correlation functional revised for solids (PBEsol)⁶⁵ and a plane-wave cut-off energy of 520 eV. Within the simplified generalized gradient approximation (GGA) + U approach⁶⁶, we added on-site Coulomb interaction parameters of U−J of 2 eV to Fe-3d and Mn-3d throughout our calculations. We created TM-substituted cells (TM = Fe and Mn) with 3 × 3 × 3 from the optimized BaTiO₃ cell with tetragonal P4mm symmetry, leading to the tetragonal (T) Ba₂₇Ti₂₇O₈₁ structure. As displayed in Supplementary Fig. 2, there exists twenty-one types of oxygen atoms with different site symmetry. We therefore performed calculations for all the supercells with V_On^••, where V_On^•• denotes the oxygen vacancy on the n-th nearest-neighbor site with respect to Fe ions. Structural relaxation was performed for the atoms with less than 0.6 nm distance from the original position of V_On^••. The valence states of Fe atoms were controlled by adjusting the total number of electrons. We employed the Γ-centered 3 × 3 × 3 k-point mesh for the structural relaxations and the 5 × 5 × 5 k-point mesh for density-of-states and band structure calculations. We added U−J of 8 eV to Ti-3d in addition to U−J of 2 eV for Fe-3d and Mn-3d for the electronic structure calculations.