Utilizing ferrorestorable polarization in energy-storage ceramic capacitors

A self-powered system with a long lifetime would represent an opportunity in the development of a next-generation, standalone Internet of Things. Ceramic capacitors are promising candidates for energy storage components because of their stability and fast charge/discharge capabilities. However, even the energy density of state-of-the-art capacitors needs to be increased markedly for this application. Improving the breakdown electric field represents a potential solution, but operations at such high fields relying on unchanged dielectric permittivity sacrifice the lifetime of the capacitor to some degree. Here, we report ferrorestorable polarization engineering capable of more than doubling the effective permittivity. Our experiments and ab initio calculations demonstrate that a defect dipole composed of Cu3+ and oxygen vacancy in a prototypical ferroelectric BaTiO3 ceramic is coupled with spontaneous polarization. The resultant ferrorestorable polarization delivers an extraordinarily large effective relative permittivity, beyond 7000, with a high energy efficiency up to 89%. Our work paves the way to realizing efficient ceramic capacitors for self-powered applications. Our experiments and ab initio calculations demonstrate that a defect dipole (μdef) composed of Cu3+ and oxygen vacancy in a ferroelectric BaTiO3 ceramic is coupled with spontaneous polarization (Ps). By designing an arrangement μdef, a shifted polarization (P)-electric field (E) loop is obtained because of the strong interaction between μdef and Ps. The resultant ferrorestorable polarization delivers an extraordinarily large effective relative permittivity, beyond 7,000, with a high recoverable energy density (Urec) and efficiency. This work paves the way to realizing efficient energy storage ceramic capacitors for self-powered applications.


Introduction
Miniaturized energy storage has played an important role in the development of high-performance electronic devices, including those associated with the Internet of Things (IoTs) 1,2 . Capacitors with a high power density are expected to provide innovative advances for energy management systems 3,4 , safety technologies 5,6 , and health care applications 7,8 . A key challenge is the creation of a standalone energy storage system with a long lifetime. A system equipped with a harvester or a wireless power transfer enables the semipermanent operation of IoT products beyond the constraints of energy supply 9 . Ceramic capacitors are considered the leading storage components because of their robustness and extremely long lifetimes 9,10 .
To design self-powered systems, the energy density of ceramic capacitors must be markedly improved. Various polar materials, including paraelectrics [11][12][13] , ferroelectrics [14][15][16] , antiferroelectrics 17,18 , and relaxors 19,20 , have been investigated. The following two indices obtained from polarization (P)-electric field (E) properties have been widely used to assess the energy storage performance: the recoverable energy density U rec ¼ R P max P r EdP and the energy efficiency η ¼ U rec = R P max P 0 EdP, where P max is the maximum P induced by the maximum field (E max ), P r is the remnant polarization, and P 0 is the initial P in the charge-discharge process 10 .
The U rec of typical ferroelectrics corresponds to the shaded area in the P-E loop shown in Fig. 1a. A large polarization change ΔP ¼ P max À P r results in a large U rec . A common approach is to form relaxors or solid solutions 21,22 that lead to a suppressed P r and a higher η, whereas the P max is reduced 23 ; a tradeoff exists between U rec and η. Moreover, the performance is often evaluated from the polarization curves around a breakdown field (E BD ), i.e., E max~EBD , because the resultant U rec becomes large 24 . Such operations relying on an unchanged dielectric permittivity, however, result in lifetime degradation to some extent. We therefore think that an appropriate indicator should be taken into account, that is, an effective relative permittivity (ε r, eff ) expressed as ε 0 ε r, eff = 2U rec /E max 2 , where ε 0 is the dielectric permittivity of vacuum. This is because ceramic capacitors need to be operated at fields much lower than E BD to exploit their long lifetimes.
We report that ferrorestorable polarization arising from an internal field (E i ) enhances ε r, eff . In principle, E i originates from an interaction between P s (spontaneous polarization vector) and μ def (defect dipole vector) [hereafter, Λ (bold) denotes the vector of its scalar Λ, i.e., Λ = |Λ|], which has been recognized as symmetryconforming short-range ordering 25 . Compared with the pristine material (Fig. 1a), a controlled sample with E i exhibits a shifted P-E loop with a markedly large ΔP, which is termed ferrorestorable polarization (Fig. 1b).
We selected a prototypical ferroelectric BaTiO 3 ceramic as a model material and chose μ def composed of Cu 3+ and oxygen vacancies (V O •• ). Our density functional theory (DFT) calculations reveal that V O •• is stabilized on the first nearest neighbor of Cu 3+ on the Ti 4+ site (forming μ def ) and that the ground-state configuration of μ def || P s leads to E i . We found that our controlled sample, with a strong E i , displays an extraordinarily large ε r, eff of approximately 7,000 and an unexpectedly high η of 89%. indicates the n th nearest-neighbor oxygen with respect to TM and V On •• denotes an oxygen vacancy in site On (n = 1-21). Figure 2a exhibits the dependence of the total energy (E total ) on n, where the vertical axis is the E total relative to that of n = 1. For the Cu cells, the E total of n =1-3 is smaller than that of n = 4-21 irrespective of the valence states of Cu [except for n = 6 of V On •• -Cu + (Supplementary Fig. 1)]. This upward tendency indicates that the system is stabilized by V O •• trapping by Cu owing to an attractive interaction. Provided that V O •• has a certain mobility at a moderate temperature (e.g., 80°C) and the system is equilibrated (so-called 'aging'), which is followed by cooling to room temperature, we can assume that Cu is associated with V O •• ; in other words, a CuO 5 pyramid is formed with μ def (Fig. 2b-d).
For the V 2+ cells, the relative E total decreases with increasing n, showing that a VO 6 octahedron is preserved; i.e., V O •• is distanced from V 2+ due to a repulsive interaction. The results of Fig The Cu cells with n = 1-3 have different μ def configurations, μ def || P s (μ def, 1 ), μ def ⊥ P s (μ def, 2 ), and μ def || −P s (μ def, 3 ), as displayed in Fig. 2b-d. μ def, 1 is the most stable for Cu 3+ because its E total is 0.15-0.36 eV lower than those of μ def, 2 and μ def, 3 . For Cu 2+ , μ def, 1 and μ def, 2 have almost the same E total, which is lower than that of μ def, 3 by 0.10 eV. Because the multiplicity of the O1 site is one while that of the O2 site is four in the Cu-doped BaTiO 3 supercell, μ def, 2 becomes the majority configuration. For Cu + , μ def 1 and μ def, 3 coexist because the difference in E total is quite small and E total of μ def, 2 is higher than that of the other two by approximately 0.16 eV. These results indicate that the highest probability of the formation of μ def, 1 is expected for Cu 3+ .
To explore the origin of μ def formation, we focused on the variation in the electronic structure of the Cu 3+ cells. As shown in Supplementary Fig. 1, V On •• -Cu 3+ with n = 1-3 has a lower energy in the low spin (LS) state, while V On •• -Cu 3+ with n ≥ 4 is stabilized in the high spin (HS) state. This is because the Cu 3+ with n = 1-3 is positioned in a weaker ligand field of the CuO 5 pyramid, whereas the Cu 3+ with n ≥ 4 is located in a stronger ligand field of the CuO 6 octahedron.  The controlled sample has a large U rec as a result of ΔP, which is termed ferrorestorable polarization. The interaction between μ def and P s stabilizes the downward polarization (P down ) at zero field, i.e., P 0 = P down , because the P-E loop shifts to a positive field by the magnitude of E i . E i is defined as the average of E c+ and E c− , that is, where E c+ and E c− are the electric fields at the extreme polarization switching currents in the positive and negative field sweeps, respectively. pO 2 900°C dependence of the Cu valence Figure 3 shows the pO 2 900°C dependence of the effective magnetic moment (μ eff ) for the Cu (1.5%) samples estimated from the temperature dependence of the inverse magnetic susceptibility (1/χ) ( Supplementary Fig. 2). The following four pO 2 900°C regions appear: Region I, pO 2 900°C ≤ 10 −25 atm, where μ eff is negligibly small; Region II, 10 −25 atm < pO 2 900°C ≤ 10 −10 atm, where μ eff sharply increases from zero to 1.7; Region III, 10 −10 atm < pO 2 900°C < 10 −2 atm, where μ eff is almost constant; and Region IV, pO 2 900°C ≥ 10 −2 atm, where μ eff further increases. In Region I, the negligible μ eff indicates that the dominant species is Cu + (d 10 electron configuration) with a spin-only magnetic moment (μ spin eff ) of zero. The increase in μ eff to approximately 1.7 in Region II is associated with the oxidation of Cu + to Cu 2+ (d 9 , μ spin eff ¼ 1:73), which is accompanied by a color change from black to dark brown.  Fig. 3). In Region IV, an increase in pO 2 900°C causes a steep rise in μ eff because of ½Cu 0 Ti;oc ) ½Cu 0 Ti;py , which is accompanied by a color change from light yellow to gray. We confirmed that impurity phases are not formed even after annealing under reducing atmospheres ( Supplementary  Fig. 4).

Polarization properties
Figure 4a-c shows the P-E loops of the undoped samples (pO 2 900°C = 0.2 atm). The P r of the as-prepared sample with neither poling pretreatment nor aging is 13.1 μC/cm 2 (Fig. 4a). The coercive field (E c ) is 0.4 kV/cm for E c+ and −0.5 kV/cm for E c− . The subsequent aging does not influence the properties with or without the poling pretreatment (Fig. 4b, c).
The Cu (1.5%) samples display diverse properties depending not only on the aging and poling pretreatment but also on the Cu valence (dependent on pO 2 900°C ). and high-spin (HS) states were adopted for V On

••
-Cu 3+ with n = 1-3 and n ≥ 4, respectively, according to the ground-state arrangements ( Supplementary Fig. 1a, b). b-d Schematics of possible configurations of P s with μ def in Cu 3+ . μ def, 1 is the most stable for Cu 3+ because its E total is 0.15-0.36 eV lower than those of μ def, 2 and μ def, 3 . For Cu 2+ , μ def, 2 is the majority configuration because μ def, 1 and μ def, 2 have almost the same E total . For Cu + , μ def 1 and μ def, 3 coexist because the difference in E total is quite small. e-g Total and partial density of states of V O1  stabilizes a multidomain (MD) state with zero net polarization at E = 0 and that an application of E transforms to a quasi-single domain (SD) state followed by recovery of the original MD state after the field is turned off (Supplementary Fig. 10). This polarization behavior has been observed in single crystals 25 and Mn-doped ceramics 27 . Moreover, the sample (pO 2 900°C = 3 × 10 −6 atm) with poling pretreatment followed by aging (hereafter denoted 'controlled') has a P-E loop shifted in the positive direction. It has an extraordinarily large E i of 47.5 kV/cm, which is defined by the average of E c+ = 50.1 kV/cm and E c− = 45.0 kV/cm (Fig. 4f). Namely, a negative polarization state is stabilized at E = 0. As a result, polarization switching cannot be observed in the range of E < 0. Note that the resultant ΔP (ferrorestorable polarization) is as high as 43.8 μC/cm 2 at 76 kV/cm. The aged samples (pO 2 900°C ≥ 4.0 × 10 −11 atm) without poling display an antiferroelectric-like pinched curve (Supplementary Fig.  5a, c, e), whereas those at pO 2 900°C = 2.0 × 10 −20 atm present a typical loop (Supplementary Fig. 5g). Figure 5a shows the E i as a function of pO 2 900°C for the controlled samples (their P-E loops are displayed in Supplementary Fig. 5b, d, f, h). The E i becomes stronger with increasing pO 2 900°C ; the E i starts to rise at approximately pO 2 900°C = 1 × 10 −10 atm and reaches 47.5 kV/cm at pO 2 900°C = 3 × 10 −6 atm. The pO 2

900°C
region where E i rises coincides with Region III (Fig. 3), where the oxidation of Cu 2+ to Cu 3+ proceeds. These results indicate that controlling the Cu valence to Cu 3+ is important for strengthening E i . Considering that the E i saturates at pO 2 900°C = 0.2 atm in Region IV, we think that [Cu 0 Ti;py ] is more crucial than [Cu 0 Ti;oc ] in achieving a high E i . We consider that the optimal pO 2 900°C for enhancing E i exists at approximately 0.2 atm because annealing at a higher pO 2 900°C results in a low probability of μ def, 1 because of ½Cu 0 Ti;oc ) ½Cu 0 Ti;py . It is also notable that a ½V ÁÁ O difference can be excluded from the major origin of the dependence of E i on pO 2 900°C because the samples annealed at a higher pO 2 900°C exhibit a higher E i despite a lower concentration of V ÁÁ O required to form μ def . A similar ferrorestorable polarization appears for the controlled samples with Cu (0.3%) ( Supplementary Fig. 6), whereas this is not observed for the samples with V (0.3%), irrespective of pO 2 900°C , as shown in Fig. 4g-i and Supplementary Fig. 7.

Energy storage performance
By analogy with the relative permittivity ε r for linear dielectrics with U rec = ε 0 ε r E 2 max =2, we define the effective relative permittivity ε r, eff for nonlinear dielectrics with U rec = ε 0 ε r;eff E 2 max =2. Figure 5b shows the pO 2 900°C dependence of ε r, eff and η for the controlled samples with Cu (1.5%). The corresponding U rec is shown in Supplementary Fig. 8. With increasing pO 2 900°C , ε r, eff rises and is as high as 7,000. Moreover, η reaches 89% in the same pO 2 900°C region. Here, we discuss why an extraordinarily large ε r, eff is achieved in the relatively high pO 2 900°C region. Compared dependence of E i and effective relative permittivity (ε r, eff ) and energy efficiency (η) of the controlled samples with Cu (1.5%). c, d Unipolar polarization curves of the as-prepared and the control samples at pO 2 900°C = 3 × 10 −6 atm. Schematics of the polarization and μ def configurations of the sample subjected to the poling pretreatment (e) and the controlled sample (f) at zero field. g Configuration of the controlled sample with E = E max . State 1 of (f) and State 2 of (g) correspond to those in (d).
with the as-prepared material (Fig. 5c), the controlled sample has a strong E i (μ def, 1 as the majority), providing a marked shift in the P-E loop (Fig. 5d). Our DFT calculations indicate that μ def, 1 is preferable for Cu 3+ because its E total is 0.15-0.36 eV lower than those of μ def, 2 and μ def, 3 . Given that an [V O •• ] and its random distribution equilibrated at pO 2 900°C > 10 −10 atm are frozen by successive quenching to room temperature, the charge neutrality is expressed as 2 Cu 00 3+ and Cu 2+ coexist. During the thermal treatment at 200°C (>T C ), V ÁÁ O migrates toward Cu 3+ owing to an attractive interaction, and eventually, μ def (Cu 3+ O 5 pyramid) is formed in the paraelectric cubic lattice (Supplementary Fig. 9a); i.e., ½Cu 0 Ti ¼ ½Cu 0 Ti;py þ ½Cu 0 Ti;oc . In the cooling process, a phase transition from the paraelectric phase to the ferroelectric phase occurs. In this asprepared sample, an MD structure with zero net polarization is formed (Supplementary Fig. 9b). Because the V ÁÁ O distribution above T C is frozen at room temperature, the probabilities of μ def, 1 , μ def, 2 , and μ def, 3 seem to be 1/6, 2/3, and 1/6, respectively; no correlation between the configurations of μ def -P s exists in each ferroelectric domain.
In the sample with Cu 3+ as the majority, the poling pretreatment by applying negative fields results in a transformation from the MD state with P = 0 to a quasi-SD state with P down (Fig. 5e). Successive aging at 80°C (<T C ) promotes a rearrangement of V ÁÁ O to attain the ground-state defect structure (Fig. 2a); V ÁÁ O is stabilized on the O1 site, which increases μ def, 1 and decreases μ def, 2 and μ def, 3 . As aging proceeds, μ def, 1 becomes the majority, which corresponds to State 1 in Fig. 5d, f. In other words, the SD structure with P down is stabilized by μ def, 1 , which leads to a certain E i .
When an upward E max is applied to the controlled sample, the polarization is switched from P down to P max , which is accompanied by a change from μ def, 1 to μ def, 3 . During the subsequent field decrease, the polarization returns to the initial P down in the SD state, where ΔP (= P max − P down ) corresponds to ferrorestorable polarization. Given that a negative field is applied to the sample with P down , the P down state remains unchanged regardless of the field strength, and thereby, the linear polarization appears in the negative field region, as shown in Fig. 4f.

Discussion
The ε r, eff of our controlled samples along with those of the previously reported capacitors are plotted in Fig. 6. In principle, a tradeoff exists between ε r, eff and η except for a few examples of antiferroelectrics. In contrast, our controlled sample (pO 2 900°C = 3 × 10 −6 atm), denoted "b", possesses both a large ε r, eff (7,000) and a high η (89%). This ε r, eff is over twice as large as that of typical BaTiO 3based ceramics [28][29][30] This excellent performance is due to the large ferrorestorable polarization (ΔP) and the small hysteresis loop of the P-E curve that arises from the strong E i introduced without sacrificing the polar nature. We consider that the ferrorestorable polarization can be utilized in BaTiO 3 doped with other TM acceptors, such as Mn 27 and Fe 31 , that can trap V O •• . Our approach using the interaction between μ def and P s is effective in breaking the tradeoff between U rec and η. Since a fabrication process of BaTiO 3 -based multilayered ceramic capacitors (MLCCs) has been established, we can readily adapt our material design to energy-storage MLCCs. Moreover, it is expected that employing Bi-based ferroelectrics with a larger P s can further enhance ε r, eff .
Our experimental and theoretical investigations demonstrate that a built-in internal field arising from defect-polarization interactions delivers excellent energy storage performance in ferroelectrics. This method is applicable to relaxor ferroelectrics 32,33 , antiferroelectrics 17,34 , and ferrielectrics 35,36 . Our findings will pave the way for energy storage capacitors utilizing ferrorestorable polarization in self-powered systems.

Preparation of Cu-doped and V-doped BaTiO 3 ceramics
Cu-doped and V-doped BaTiO 3 powders were prepared by a solid-state reaction. BaCO 3 (99.99%), TiO 2 (99.99%), CuO (99.9%) and V 2 O 5 (>99%) powders were mixed by ball milling. The mixtures of the raw materials were calcined at 850-1000°C for 5-10 h. The calcined powders were crushed by ball milling again and pelletized into disks (10 mm diameter) at 120 MPa by uniaxial pressing. The disks were pressed isostatically at 150 MPa for 1 h and then sintered at 1200-1400°C for 5-10 h. The sintered ceramics were cut and polished; the resulting sample size was 8 mm × 4 mm × 0.3 mm. The samples were annealed again at 1200°C for 24 h to heal the microcracks introduced during the preparation process. The oxygen vacancy concentration ([V O •• ]) and valence state of Cu were controlled by annealing at 900°C for 12 h at an oxygen partial pressure (pO 2 900°C ) ranging from 4 × 10 −20 atm to 0.2 atm followed by quenching to room temperature (25°C) in a short time (1-3 s). A sample annealed at a pO 2 900°C of 1 × 10 2 atm was also prepared by hot isostatic pressing.

Poling and aging treatments
Some samples were heated at 200°C (>Curie temperature T C of 120-135°C) for 10 min in air to homogenize the distribution of V O

••
. After cooling to 25°C, an external electric field of −40 kV/cm was applied for 5 s to achieve a negatively poled state, which is termed 'poling pretreatment'. The poled sample was aged at 80°C (<T C ) for 24 h (aging) to accelerate the diffusion of V O •• in the presence of P s and then cooled to 25°C. Before and after aging, polarization measurements were performed at 25°C and 1 Hz (or 100 Hz) for the samples with and without the poling pretreatment.

Magnetic susceptibility measurements
To determine the valence state of Cu, the magnetic susceptibility χ of the 1.5% Cu-doped samples equilibrated at various pO 2 900°C s followed by quenching to room temperature was measured with a superconducting quantum interference device (Quantum Design Ltd., MPMS-XL). The size of the sample was 3 × 4 × 5 mm 3 , and the measurements were performed at a magnetic field of 1 T in the temperature range of 50-300 K.

Ab initio calculations
Density functional theory (DFT) calculations for tetragonal BaTiO 3 with V O •• (TM = Cu + , Cu 2+ , Cu 3+ , and V 2+ ) were performed to find a stable site of V O

••
according to the literature 35 . DFT calculations were carried out with the generalized gradient approximation (GGA+U) 37 using a plane wave basis set as implemented in the Vienna ab initio simulation package (VASP) 38 . We used projector-augmented wave potentials 39 with valenceelectron configurations of 5s 2 5p 6 6s 2 for Ba, 3p 6 3d 2 4s 2 for Ti, 3d 10 4s 1 for Cu, 3d 3 4s 2 for V, and 2s 2 2p 4 for O. A plane-wave cutoff energy of 520 eV was adopted, and all calculations were conducted until the total energy converged to less than 10 −6 eV. To investigate the electronic states, a supercell of BaTiO 3 was constructed by the following procedure. First, a BaTiO 3 lattice in space group P4mm was structurally optimized until the Hellmann-Feynman force on each atom was smaller than 0.1 eV/nm. A Monkhorst-Pack k-mesh of 5 × 5 × 5 centered at the Γ point was used for structural optimization for lattice parameters and fractional coordinates. Next, a supercell of 3 × 3 × 3 (Ba 27 Ti 27 O 81 ) was constructed using the optimized unit cell. One Ti atom in the supercell was replaced by one TM to obtain the supercell (Ba 27 Ti 26 TMO 81 ). The valence state of the dopants was controlled by changing the total number of electrons. For geometry optimization of the supercell, a simplified local spin density approximation +U approach 40 was adopted as a correction for localized and strongly correlated electrons within on-site Coulomb terms of U -J of 2 eV for both Cu-3d and V-3d and 0 eV for Ti-3d. Structural optimization of the supercell was performed using a k-mesh of 3 × 3 × 3 centered at the Γ point.
In the next step, calculations of the V O . From the optimized Ba 27 Ti 26 TMO 81 supercell, one O atom was removed from a specific O site. Structural optimization of the fractional coordinates was performed for all atoms and a fixed cell size in the same manner as that for the defect-free supercell. The oxygen atom on the n th nearest-neighbor O site with respect to TM is defined as "On", and the oxygen vacancy created by removing On is expressed as "V On •• ". The V On •• -containing cell is expressed as "Vo n •• -TM". For the calculations of DOS and band structures, the U -J of Ti-3d is set to 8 eV in a manner similar to that in the literature 31 .
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