## Main

Rechargeable Li-ion batteries offer great hopes for achieving higher energy density and meeting increasing future societal energy storage demands. The emergence of anionic redox opens a new direction towards the design of Li-rich positive electrodes (cathodes), Li1+xTM1−xO2 (TM denotes transition metal, 0 < x < 1), with high energy density, relying on cumulative cationic and anionic redox reactions1,2,3,4. The science underlying anionic redox has reached a great level of understanding owing to the wide family of Li-rich rock-salt structures that enlist either layered oxides (Li2RuO3, Li2IrO3 and so on)5,6,7,8 or isostructural Li2TiS3-based sulfides9,10. Despite these fruitful understandings, a remaining practical issue regards how to utilize anionic redox in real-world applications. The well-known anionic-redox-based archetypical cathode, Li-rich nickel–manganese–cobalt oxide (Li-rich NMC), can deliver capacity as high as 300 mA h g−1. However, its commercialization is plagued by important issues, such as sluggish kinetics, voltage hysteresis and voltage fade11,12. Thus, further studies are urgently needed to get deeper insights into these issues so as to provide a cure that could help in bridging the gap between fundamental research and real applications.

It is well accepted that the voltage-fade problem is linked to irreversible cation migration, but there are still many debates regarding the origin of voltage hysteresis. Numerous researchers have proposed that voltage hysteresis is deeply rooted in reversible cation migration, which perturbs the Li site energies on lithium removal/uptake12,13,14. However, this view is challenged by a recent study claiming that highly reversible cation migration favours the mitigation of the redox asymmetry/voltage hysteresis in the compound O2-Lix(Li0.2Ni0.2Mn0.6)O2 (ref. 15). Other proposed mechanisms either rely on the energy penalty caused by the (re)formation/breaking of O–O dimers16, redox inversion induced by a small charge-transfer bandgap17 or sluggish structural rearrangements through cycling as implied by micro-calorimetry study18. More recently, first-cycle hysteresis was elegantly linked to the formation of trapped molecular O2 favoured by irreversible cation migration in P2-type Na0.75[Li0.25Mn0.75]O2 and Li-rich NMC compounds19,20 although its persistence on cycling was not tackled. Obviously, further studies are thus desirable to clarify voltage hysteresis.

Interestingly, most of the aforementioned studies have overlooked the thermodynamic–kinetic aspects of anionic redox as a possible origin of voltage hysteresis. Ohmic resistance and Li-diffusion limitation are part of kinetic polarization that can be experimentally decoupled from other observables by slowing down the current rate, or investigated more elegantly using the galvanostatic intermittent titration technique (GITT). For classical insertion compounds, this polarization closes at zero current with the charge and discharge relaxed potentials nearly superimposing. By contrast, most anionic-redox electrodes show GITT profiles that hardly close the voltage gap11,21. This led researchers to propose ‘quasi-static hysteresis’ or even ‘thermodynamic’ originated hysteresis18,22. Another unexploited piece of information regarding voltage hysteresis is that its amplitude changes among various anionic-redox compounds, namely it increases from Li2RuO3- to Li2MnO3- and then to Li2TiO3-based phases.

In this Article, we investigate a Li-rich cation-disordered rock-salt compound, 0.4Li2TiO3–0.6LiFeO2 (Li1.17Ti0.33Fe0.5O2), denoted hereafter as LTFO, that combines anionic/cationic redox activity with a prominent voltage hysteresis of ~1.4 V. Although this compound shows a partially reversible Fe migration between octahedral and tetrahedral sites, we demonstrate that this specific feature is not the origin of voltage hysteresis. Instead, we prove that the sluggish reductive coupling mechanism involving a charge transfer from O(2p) to Fe(3d) states is responsible for the hysteresis. We also shed light on how the covalence/ionicity governs the charge-transfer kinetics in different compounds and discuss its role in voltage hysteresis.

## Results and discussion

### Structure and electrochemistry of LTFO

Electrochemically active well-crystallized LTFO powders containing particles with 30–50 nm diameters were obtained by a hydrothermal process, as detailed in the Methods section. The elemental nominal composition of the obtained powders was confirmed by inductively coupled plasma atomic emission spectroscopy (ICP-AES), while their homogeneity was verified by scanning transmission electron microscopy-energy dispersive X-ray spectroscopy (STEM-EDX) analysis (Supplementary Fig. 1) revealing the Ti/Fe = 0.40(2):0.60(2) atomic ratio. Rietveld refinement from a synchrotron powder X-ray diffraction (SXRD) pattern (Fig. 1a and Supplementary Table 1a) shows that LTFO adopts a cation-disordered rock-salt structure (Fm$$\bar 3$$m) while the [100] and [110] electron diffraction (ED) patterns (Fig. 2e and Supplementary Fig. 2a) indicate a structured diffuse scattering (labelled with arrows). This is evidence for cationic short-range ordering driven by the tendency for each O atom to be as homogeneously as possible surrounded by the TM and Li cations, like [Li3TM3] clusters in ordered layered compounds.

The electrochemical behaviour of LTFO was tested versus Li between 2.0 and 4.8 V at a C/10 rate (Fig. 1b). On oxidation, the removal of Li occurs via a single-step plateau located at ~4.25 V as opposed to two different (pseudo)plateaus on the subsequent discharge, with the higher one showing a huge voltage hysteresis of ~1.4 V. The large irreversibility of ~0.3 Li during the first cycle (Fig. 1b) arises not only from electrochemical decomposition of Li2CO3 surface species and oxygen release but also from kinetic limitations, as deduced by online electrochemical mass spectrometry (OEMS) and constant-current-constant-voltage (CCCV) experiments, respectively (Supplementary Fig. 3).

The huge voltage hysteresis of ~1.4 V persists on further cycles, even when slowing down charge–discharge rates (Fig. 1c), indicating that this hysteretic behaviour is not simply nested in conventional kinetic polarizations caused by poor electronic/ionic conductivity. The hysteresis is shown to be path-independent by open-voltage-window experiments (Supplementary Fig. 4). This contrasts with the previously reported path-dependent voltage hysteresis in Li-rich NMC which led researchers to propose a ‘thermodynamic’ origin indirectly linked to cation migration13. Here we believe that our finding of path-independence in LTFO stems from the absence of interplay between cationic and anionic redox events, as will be shown later.

### Partially reversible Fe migration

The LTFO long-range structural evolution on cycling was checked using an in situ X-ray diffraction (XRD) cell cycled at a C/10 rate and XRD patterns were collected for every change in lithium stoichiometry of ~0.03 (Supplementary Fig. 5). On charging, both (002) and (220) peaks initially shift to high angles and then shift back while their amplitudes progressively decrease. Such a two-stage feature in XRD is also consistent with the GITT curve at first charge unravelling two open-circuit-voltage (OCV) processes (Supplementary Fig. 6). The subsequent discharge and second charge show similar peak shifting and intensity evolution with high reversibility, as highlighted by the contour plots in Supplementary Fig. 5c. Overall, from the 2nd cycle and onwards the in situ XRD reveals a single-phase (solid-solution) behaviour, with the average structure maintaining the rock-salt disordered cubic structure during cycling. However, our first trials to fit the ex situ SXRD pattern of the sample charged to 4.8 V based on a regular disordered rock-salt structure could not take into account the (002)/(220) relative intensity mismatch (Supplementary Fig. 7a). The refinement could be successfully improved by moving some TM ions from the octahedral 4a site to the interstitial tetrahedral 8c site of the rock-salt structure (Supplementary Fig. 7b), implying cation migration on charging. Neutron powder diffraction (NPD) confirms this cation migration and indicates that only Fe migrates (Fig. 2a,b and Supplementary Table 2), as schematically shown by the structural change from Fig. 2c (pristine) to Fig. 2d (migrated). The migration of Fe to the tetrahedral site was also visualized by high angle annular dark-field scanning transmission electron microscopy (HAADF-STEM). As shown in Fig. 2e, the HAADF-STEM image along the [100] direction of the pristine LTFO demonstrates no TM cations occupying the tetrahedral voids, as no HAADF intensity is found at the centres of the squared bright dots which mark the octahedrally coordinated TM cationic positions (denoted as TMoct.). After charging (Fig. 2f), corresponding faint contrast can be recognized in the HAADF-STEM image (marked by white triangles), indicating the existence of tetrahedral Fe (Fetet.). Also, the appearance of the Fetet is accompanied by an extra ordering violating the parent face-centered unit cell as evidenced by sharp spots in the [100] ED pattern of the charged material (Fig. 2f).

The reversibility of this migration behaviour was checked at various states of charge (SoC) through combined SXRD/NPD refinements (Supplementary Fig. 8 and Supplementary Tables 1 and 2). The evolution of the Fetet content along with the cycling state is plotted as a histogram in Fig. 2h. The results show that 37.5% of Fe moves to the tetrahedral sites on first charge and ~21% moves back to the octahedral sites on the subsequent discharge, as further evidenced by the HAADF-STEM image (Fig. 2g). Regardless of the first charge, a ~21% highly reversible Feoct ↔ Fetet migration can be clearly observed from the 1st discharge to the 2nd charge process. This is supported by density functional theory (DFT) calculations (Supplementary Note 1) showing low kinetic barriers for Fe migration with Fetet sites that become as more thermodynamically favoured as the number of Li vacancies around the tetrahedral sites increases. Other than the reversible Fe migration, an irreversible local Li–TM ordering was also spotted in the HAADF-STEM images and this is discussed in Supplementary Fig. 2.

Although tempting, the scenario that Fe migration is linked to the large voltage hysteresis observed in LTFO is very unlikely. First, much less hysteresis is observed for the low-voltage pseudo-plateau below 2.7 V where reversible Fe migration also appears. Second, the path independence referred to above in LTFO suggests the hysteresis is independent of voltage window, that is, the amount of Fe migration. Therefore, an alternative explanation is needed.

### Redox mechanism

Ex situ X-ray adsorption spectroscopy (XAS) and hard X-ray photoelectron spectroscopy (HAXPES) demonstrate the redox inactivity of Ti, that is, it always stays as Ti4+ (Supplementary Fig. 9). In addition, in situ 57Fe Mössbauer spectroscopy was performed with the pure 57Fe LTFO sample and this was interpreted using three components from principal component analysis (PCA) associated with several Fe species, as indicated in Fig. 3a–c. Accessing accurately the Fe state is complex since, for instance, the Fe4+_B signal, corresponding to Fe4+ in octahedral sites (Fig. 3b), can equivalently be considered as Fe3+ in tetrahedral sites due to their similar isomer shifts23. However, we confidently assign this Fe signal to be Fe4+ in octahedral sites, combining the results of an in situ relaxation test as discussed in detail in Supplementary Fig. 10.

The evolution of these three components together with the different-valence Fe species along cycling is shown in Fig. 3d–g. The first charge demonstrates two distinct Fe redox processes, corresponding to the Fe3+/Fe4+ oxidation and the reduction of Fe4+ back to Fe3+ (see Fe4+ species in Fig. 3f), consistent with the two-stage process identified by in situ XRD and GITT data (Supplementary Fig. 6). The Fe valence change on first charge (from 3 to 3.4, Fig. 3g) accounts for only ~0.2Li+ (that is 0.5 × 0.4) of the overall charge capacity (~1Li+). This implies a predominance of the O redox process that is validated by ex situ O 1s HAXPES (#1→#3 Fig. 3i). Lastly, the reduction of Fe4+ (Fig. 3f, Fe4+ species) towards the end of the charge is consistent with a reductive coupling mechanism5,24, similar to previous findings in Li4FeSbO6 (ref. 25). Turning to the first discharge plateau at ~2.8 V (#3→#4), the remaining amount of Fe4+ is reduced back to Fe3+ (Fig. 3g) while O is largely reduced, indicative of a partially reversible O2−/O(2−n)− redox chemistry (#3→#4 in Fig. 3i). On further reduction Fe3+ partially converts to Fe2+ (Fig. 3f, Fe2+ species) with little oxygen contribution (#4→#5 in Fig. 3i). In the second charge, Fe2+ is reversibly oxidized to Fe3+ below 4 V and Fe4+ species appear again but in a lesser amount at the high voltage plateau above 4 V, accompanied by a highly reversible contribution of oxygen redox (#6→#7 in Fig. 3i). It is worth mentioning that no trace of Fe4+ could be detected by ex situ Fe 2p HAXPES (Fig. 3h) or ex situ Fe K-edge XAS (Supplementary Fig. 9c) recorded on the first 1.5 cycles, suggesting that Fe4+ might be a long-living non-equilibrium state.

### GITT analysis

GITT measurements from 1st discharge to 2nd charge performed at both room temperature (25 °C) and 55 °C confirm this hypothesis (Fig. 4). The GITT profile at 55 °C shows nearly no gap between charge and discharge for both the cationic and anionic redox processes (Fig. 4b), while at room temperature solely the Fe3+/Fe2+ redox reaches equilibrium (Fig. 4a). Similar results were also obtained for the 8th cycle (Supplementary Fig. 11) except for some capacity fading. Long-time relaxations within the oxygen redox range at 25 °C show a prompt recovery of the voltage in discharge (lower inset in Fig. 4c), while it takes more than 60 hours for the potential to reach equilibrium in charge (upper inset in Fig. 4c). Moreover, this relaxation proceeds by a two-stage behaviour (upper inset in Fig. 4c), which could result from two different relaxation processes that are coupled together. At 55 °C (Fig. 4d inset) the relaxation nearly replicated the 25 °C voltage-drop profile but over a threefold shorter time. Additionally, we also measured the capacity of two cells cycled with (red solid curves) and without (black dashed curves) relaxations and found that they are roughly identical at both 25 and 55 °C, as shown in Fig. 4c,d, respectively. This provides confidence that the measured voltage decay as a function of resting time is not due to self-discharge phenomena that are usually enhanced at high voltages and increased temperature.

Altogether, GITT analysis shows that the thermodynamic pathway between charge and discharge is a temperature-activated process. This calls for reconsidering the whole picture regarding the thermodynamics and kinetics of voltage hysteresis. The overpotential of any specific electrode enlists several components associated with various electronic/atomic motions having different time scales that are related to different kinetic barriers, such as Ohmic resistance (IR drop) and Li diffusion (Supplementary Fig. 12). From GITT (Fig. 4a) the cumulated IR drop and Li diffusion account for a ~0.3 V polarization for the Fe3+/Fe2+ redox process at ~2.5 V. By contrast, through the oxygen redox region at higher potential, once the cumulated IR drop and Li diffusion overpotential are subtracted, there is still a ~1 V OCV hysteresis, mainly nested in the charge process, that cannot be readily eliminated by short-period GITT at 25 °C (Fig. 4a). The origin of this hysteresis will be revealed later.

### In situ characterizations of relaxation

The electronic and structural evolution of the material along the relaxation process was examined by in situ techniques, starting at the mid-point of the second charge (O-redox plateau), as shown in Fig. 5. To avoid the self-discharge problem, Mössbauer spectra were collected on relaxing a dried electrode in a dry cell. The electrode was rapidly recovered from a cell charged to the targeted voltage, and then washed with dimethyl carbonate (DMC) and dried at reduced pressure. The data reveal the progressive reduction of Fe4+ as a function of relaxation time (Fig. 5a), which is even faster when relaxation is started from the middle of the first charge (Supplementary Figs. 10 and 13). In the absence of self-discharge the most feasible explanation to account for this reduction of Fe4+ is a charge redistribution between Fe4+ and O2− through an internal redox process, leading to the thermodynamic equilibrium state Fe3+–O(2−n)−/O2 (molecule). This confirms our ex situ HAXPES and Mössbauer spectroscopy data.

To interrogate how such an internal redox process could affect local structure during relaxation we resorted to in situ XAS and XRD experiments. In situ extended X-ray absorption fine structure (EXAFS) data show little change around Ti (Fig. 5b) during relaxation. By contrast, in situ Fe K-edge EXAFS data reveal a noticeable intensity damping of the Fe–M (M = Fe/Ti) coordination shell (Fig. 5c), probably due to the Fe4+–O2− charge redistribution. EXAFS fittings demonstrate that this change could be interpreted as a local structural variation of the Fe–M shell as supported by the change of Debye–Waller factors and bond length of different scattering paths (Fig. 5d and Supplementary Table 3). Moreover, in situ XRD collected on relaxation highlights a robust tiny shift of the (002) peak accompanied by its narrowing ( Fig. 5e,f) that is more pronounced during the first relaxation plateau (from pattern #1 to pattern #2). This experimentally observed XRD peak sharpening indicates a micro-strain release which can be triggered by lithium diffusion during the internal redox process. Eventually, the relative constancy of (002) and (022) peak intensities (Supplementary Fig. 14) during relaxation implies the absence of 3d-metal cation migration, consistent with the barely changeable Fe–O shell peak of Fe K-edge EXAFS. This suggests that Fe migration is so fast that it cannot be captured by any in situ characterizations during relaxation, in line with the small activation energies computed with DFT (Supplementary Note 1). Therefore, we believe that Fe migration is not responsible for driving the relaxation that eliminates voltage hysteresis.

### Correlating O 2p–Fe 3d charge transfer with voltage hysteresis

The charge redistribution of Fe4+–O2− along with relaxation is consistent with our inability to detect Fe4+ species by ex situ XAS and HAXPES, as the high-energy and high-flux X-ray beam may facilitate a rapid relaxation. This is an indication in favour of Fe4+ as a non-equilibrium state and consequently a supplementary argument for ascribing its return to Fe3+ via a sluggish process that is likely to be associated with significant reorganization energy that could be at the origin of the large voltage hysteresis.

In line with Marcus theory26,27,28 (a brief introduction can be found in Supplementary Note 2), the anionic redox process taking place during charging in the LTFO electrode is a typical non-adiabatic process due to the lack of orbital overlapping between O(2p) lone-pair states and TM(nd) states. As pictured in Fig. 6a, the oxidation of the Fe3+/O2− pristine state (grey parabola) to the charged Fe3+/O state (red parabola) does not follow a stepwise adiabatic reaction mechanism along one unique reaction coordinate. Instead, it undergoes a concerted mechanism involving an intermediate metastable state (Fe4+/O2−, blue parabola), the potential energy surface (PES) of which is coupled with the pristine and Fe3+/O equilibrium states through a different reaction coordinate associated with reasonable kinetic barriers. In simple terms, to overcome the large kinetic barrier associated with the reorganization of the oxygen network required to directly transform the Fe3+/O2− pristine state into the charged Fe3+/O equilibrium state, the system follows an adiabatic pathway through the Fe4+/O2− intermediate state. Then, it evolves along a new reaction coordinate (Fig. 6a) which is levered by the Fe4+ Jahn–Teller distortion and whose rotation with respect to the initial coordinate enables the system to easily de-excite into the Fe3+/O ground state (equilibrium) to lower its energy with the appropriate local geometry (distortion of the O network).

Such a concerted mechanism is fully inferred from DFT calculations. As depicted in Fig. 7a the Fukui function computed for the pristine material shows that the early stage of charge involves σ-type Fe(3d)–O(2p) hybridized states, rather than the localized oxygen lone-pair states lying just below the Fermi level in the density of states (DOS) (Fig. 7b and Supplementary Fig. 16). The facile contraction of the Fe–O bond (Supplementary Fig. 17) associated with this Fe oxidation process sets the reaction coordinate along which the system dynamically evolves. Increasing the number of holes in the σ-type Fe(3d)–O(2p) states triggers the Fe4+ Jahn–Teller distortion which lowers the system symmetry, therefore allowing the system to evolve through a novel reaction coordinate which is compatible with the typical O-network distortion of anionic redox (Supplementary Fig. 17). Due to the new hybridization between the metal d orbitals and the oxygen 2p orbitals (originally the lone-pair states), an internal redox reaction occurs to lower the system energy and reach the thermodynamically stable Fe3+–O state through sluggish structural reorganization. This equilibrium anion-oxidized state is experimentally confirmed by ex situ measurements evidencing only Fe3+ and theoretically proved by Bader charge (Fig. 7c) and DOS analysis as well as the calculated equilibrium potentials showing the sole oxidation of the anions (Supplementary Fig. 18). The charge redistribution of Fe4+ and O2− also leads to another possible adiabatic reaction involving O2 molecules, in addition to reversible O redox, based on the calculated oxygen-release enthalpy as discussed in Supplementary Fig. 18d.

In light of these results, we propose the scenario pictured in Fig. 6b to account for voltage hysteresis in LTFO. Within the O redox region, the charge/discharge follows a non-equilibrium path (blue curve) involving a ‘Fe4+–O2−’ intermediate state as a result of bypassing the direct electron removal from the localized O(2p) lone-pair states. The system is then dynamically trapped in this ‘Fe4+–O2−’ intermediate until the rotation of the reaction coordinate allows its relaxation to the equilibrium Fe3+/O(2−n)− ground state (red curve) via an internal O 2p to Fe 3d electron transfer. Moreover, in situ electrochemical impedance spectroscopy (EIS) study during relaxation (Supplementary Fig. 19) proves that the non-equilibrium Fe4+–O2− state possesses better charge-transfer kinetics than the equilibrium Fe3+–O state as deduced by the hugely increased charge-transfer resistance after relaxation. This explains why the non-equilibrium path with Fe4+ is kinetically favoured. The sluggish kinetics of O redox are further supported by sluggish Li diffusion kinetics quantified from GITT (Supplementary Fig. 20) and the electrochemical quantitative analysis based on the phenomenological Butler–Volmer model (Supplementary Note 3). The analysis gives a much lower exchange current density of (9.62 ± 1.64) × 10−7 mA cm−2 for the O redox reaction than normal cationic reactions (for example, Fe3+/2+ (0.17 mA cm−2) in LiFePO4)29.

## Discussion

In classical insertion compounds, a long and commonly held belief consists of associating hysteresis with the substantial disorder or motion of cations within the host structures. This leads to the straightforward extrapolation that hysteresis in Li-rich compounds originates from the TM cation migration triggered by the anionic redox process. However, the relationship between cation migration and hysteresis is not universal and breaks down for compounds having voltage hysteresis without cation migration, such as Na2/3[Mg0.28Mn0.72]O2 (ref. 30) and Na2RuO3 (ref. 31). An additional counter-example is NaCrSSe, showing negligible hysteresis but with substantial Cr migration32. Therefore, cation migration is not necessarily associated with structural reorganizations triggered by the anionic redox process and should not be blamed for voltage hysteresis unless clear evidence is established. Huge voltage hysteresis is frequently found in the Li-rich cation-disordered rock-salt phases pioneered by the groups of Ceder and Yabuuchi33,34,35,36. This might lead to the belief that cation disorder may play a key role in hysteresis. However, large hysteresis exclusively appears in anionic redox process for cation-disorder compounds like LTFO. This is supported by the presence of minor hysteresis37 in fully disordered compounds, like Li2VO2F, having sole cationic redox (V3+/V5+) and somewhat highlights the independence of voltage hysteresis from cation disorder. Lastly, a redox inversion model rooted in the sequential oxidation of M then O on charging and reduction of M then O on discharging (instead of O then M) was also used to explain hysteresis in a few Li-rich rock-salt compounds (Li1.3Ni0.27Ta0.43O2)2,17. Although elegant, this model, relying on thermodynamics rather than on kinetics, has limitations since it could not explain the hysteresis in some compounds, such as Li2Ru0.75Sn0.25O3 and LTFO, that are free of redox inversion.

By contrast, our explanation of the voltage hysteresis involving O(2p)-to-TM(nd) charge transfer is of higher universality. O(2p)-to-TM(nd) charge transfer is common to numerous Li-rich compounds in which the anionic redox process is described by a first-step cationic oxidation followed by a charge redistribution between TM and O. A few examples are Li2Ru0.75Sn0.25O3 (Ru6+)5, Li2IrySn1-yO3 (Ir>5.5+)7 and Li2MnO3-based phases (Mn7+)38. Although this mechanism is named differently by authors (reductive coupling or ligand-to-metal charge transfer), it invariably assumes the existence of an intermediate cation-oxidized excited state that has, however, never been observed so far. This lack of evidence no longer exists owing to this unique LTFO system for which we could successfully capture the intermediate Fe4+ species as evidence of a reductive coupling mechanism (O(2p)-to-TM(nd) charge transfer) for anionic redox.

Moreover, our study also provides a general understanding of the amplitude variation of voltage hysteresis in the large family of Li-rich rock-salt compounds. First, as a qualitative trend the voltage hysteresis magnitude is increased from covalent (Li2Ru0.75Sn0.25O3) to medium covalent/ionic (Li1.2Ni0.13Mn0.54Co0.13O2) and more pronounced ionic (Li1.17Ti0.33Fe0.5O2) systems (Fig. 6c), regardless of the cation order/disorder (remembering that the local structure for LTFO is very similar to that in the layered oxides as seen from transmission electron microscopy (TEM) results). This can be interpreted as: the higher the covalence, the larger the electron delocalization over the M–O bonds, leading to lower kinetic barriers for electron transfer that will result in smaller voltage hysteresis. This trend can also be extended to more covalent sulfides or even selenides, as supported by the much smaller hysteresis that they display9,31,39. It is worth mentioning that disorder is not a prerequisite for large hysteresis since it is also present in cation-ordered Li4+xNi1−xWO6 phases with d0 W6+ cations16. It is also reported that F substitution could alleviate hysteresis in cation-disordered compounds although it increases the ionicity40,41. This does not break the covalence–ionicity trend in hysteresis either, as F substitution lowers the TM valence and so increases the cationic-redox contribution at the cost of anionic redox, therefore with less hysteresis. Additionally, huge hysteresis can also be found in d10 metal/metalloid-based compounds, like those of d0-metals that show high ionicity such as the previously reported Li–Te–Fe–O (ref. 42) and Li4FeSbO6 (ref. 25) (Supplementary Table 7).

A burning question from a practical point of view is how to escape this hysteresis jail that plagues the use of anionic-redox materials. A first direction consists of increasing the dp hybridization through increasing covalence of the TM–O bonds or through less electronegative and softer anions such as S or Se. A second is to use the local structure for preventing ligand dimerization and by the same token local structural distortion, like what has been undertaken with P2-Na0.6[Li0.2Mn0.8]O2 (ref. 19) and Na2Mn3O7 (ref. 43) phases. Apparently, in such ribbon or mesh superstructures, oxygen redox could proceed by involving O 2p localized holes or delocalized π states44 that are free of the reductive coupling process, like those having redox from ‘TM–O’ bonding states (for example LiCoO2 (ref. 1) and Nax[Ni1/3Mn2/3]O2 (ref. 45)) rather than lone-pair states. Therefore, we believe this fresh view of the hysteresis of Li-rich compounds has revealed the crucial importance of ligand-to-metal charge transfer in the anionic redox process, which should help chemically cure the energy efficiency roadblock penalizing anionic-redox based materials and thereby their implementation in real-world applications.

## Methods

### Synthesis of LTFO

To prepare Li1.17Ti0.33Fe0.5O2, a co-precipitation method was used to obtain the Ti–Fe hydroxide precursor. First, stoichiometric amounts of TiOSO4 (Chem Cruz) and FeSO4·7H2O (Alfa Aesar; >99%) were dissolved together in deionized water to obtain a salt solution with a Ti/Fe concentration of 2 M. Then, the co-precipitation reaction was performed at room temperature by dropwise addition of 2 M KOH (Alfa Aesar; 99.98%) aqueous solution and Ti/Fe salt solution simultaneously into 800 ml water while maintaining the pH at 11. The whole process was performed in a continuous stirred tank reactor (CSTR, Eppendorf BioFlo 320) with a stirring speed of 1,000 rpm and a solution adding speed of 1 ml min−1. Next, the precipitate was aged overnight and then washed with deionized water several times before transferring it to a vacuum oven and drying overnight at 80 °C. The Ti–Fe precursor (0.5 g) was then mixed with 2 g LiOH·H2O (Sigma-Aldrich; ≥99.0%) and dispersed into 16 ml deionized water, after which the suspension was placed into a 20 ml autoclave for the hydrothermal reaction at 220 °C for 12 h. Finally, the target LTFO product was obtained by filtering the suspension, washing the solid with water three times and then fully drying it in a vacuum oven at 80 °C.

### Electrochemical characterizations

To assess the electrochemistry of LTFO, a 2032-type coin cell was applied, otherwise a Swagelok cell was used for readily recovering the powder for special ex situ characterizations. The cathode electrode was prepared by mixing 70 wt% LTFO powder with 20 wt% carbon Super P as the conductive agent and 10 wt% polytetrafluoroethylene (PTFE) as the binder together and making it into freestanding films. The coin cells were then fabricated in an Ar-filled glovebox, with lithium foil as the anode and a Whatman GF/D borosilicate glass fibre sheet as the separator. LP30 electrolyte was used, with a composition of 1 M LiPF6 in ethylene carbonate (EC)/dimethyl carbonate (DMC) in a volume ratio of 1:1. Galvanostatic cycling was applied in the electrochemistry test, unless specified otherwise. GITT measurements were performed by periodically pulsing and relaxing the cells and the details are given in the relevant places of the main text. The EIS test during relaxation was performed with a three-electrode Swagelok cell, of which the reference electrode was a copper wire dipped with a small amount of lithium. The impedance spectra were measured by applying a periodic 10 mV potential wave with frequencies ranging from 200 kHz to 1.4 MHz.

### Structural characterizations (XRD, NPD, TEM and ICP-AES)

Synchrotron XRD patterns (wavelength λ = 0.4579 Å) were collected via the mail-in service of the 11-BM beamline at the Advanced Photon Source at Argonne National Laboratory. NPD experiments were perfomed using the high-resolution powder diffractometer SPODI (wavelength λ = 1.5482 Å) at Forschungs-Neutronenquelle Heinz Maier-Leibnitz (FRM II) at the Technical University of Munich. In situ XRD was carried out using a laboratory X-ray diffractometer (BRUKER D8 Advance) equipped with a Cu Kα radiation source (λKα1 = 1.54056 Å, λKα2 = 1.54439 Å) and a Lynxeye XE detector. A homemade airtight cell with a Be window was used. All the Rietveld refinements of the XRD and NPD patterns were performed using the FullProf program46. ICP-AES analysis was conducted on a PerkinElmer NexION 2000 ICP mass spectrometer. The samples for ICP-AES were first dissolved in aqua regia and then diluted with deionized water in a volumetric flask to the appropriate concentration before the measurements.

### TEM

TEM samples were prepared by crushing the crystals with an agate mortar and pestle in DMC and depositing drops of suspension onto a carbon film supported by a copper grid. Samples for TEM were stored and prepared in an Ar-filled glovebox. A special Gatan vacuum transfer holder was used for analysis and transportation of the samples from the Ar-filled glovebox to the TEM column to prevent interaction between the samples and air. ED patterns, HAADF-STEM images and STEM-EDX compositional maps were acquired on a probe aberration-corrected FEI Titan Themis Z 80-300 electron microscope at 200 kV equipped with a Super-X system for EDX analysis.

### OEMS measurements

Freestanding electrodes made from 70% LTFO, 20% carbon Super P and 10% PTFE binder were used to perform the OEMS experiments with an in-house developed cell47. To ensure reproducibility, three OEMS experiments were run simultaneously. Two of them used a LP30 electrolyte while the other one used LP47 electrolyte (1 M LiPF6 in EC/DEC wt. 3:7). A lithium foil anode and one piece of a Whatman GF/D glassfibre separator were used to construct the half cell. The gas signal was collected by resting the cell for 4 h before and after two cycles to stabilize the background signal.

### In situ Mössbauer spectroscopy

Operando and in situ 57Fe Mössbauer analyses were carried out in the transmission geometry in the constant acceleration mode and with a 57Co(Rh) source with radioactivity of 500 MBq. The velocity scale (±4 mm s−1) was calibrated at room temperature with α-Fe foil. To avoid using thick electrodes and a longer data collection time, the absorbers were prepared using 100% 57Fe. During cycling, a spectrum was collected every hour. The electrodes used contained 2–5 mg cm−2 LTFO mixed with 15% carbon black and 10% PTFE. The hyperfine parameters IS (isomer shift) and QS (quadrupole splitting) were determined by fitting Lorentzian lines to the experimental data. The isomer shift values were calculated with respect to that of an α-Fe standard at room temperature. The in situ cell was similar to the one used for XAS analysis (see below). Note that the spectrum of the pristine material consisted of two sub-spectra highlighting the fact that iron environments were not identical as can be expected regarding the distribution of the nearest neighbours of iron (Fe, Ti, Li). This nearest-next neighbour effect was responsible for the spectra broadening. For the sake of clarity, only the sum of the two doublets is presented48.

### XAS

Ex situ Fe and Ti K-edge XAS and in situ Fe and Ti K-edge XAS spectra during relaxation were collected in transmission mode at the ROCK beamline49 of the SOLEIL synchrotron facility in France. A Si(111) channel-cut quick-XAS monochromator with an energy resolution of 0.7 eV at 7 keV was used. The intensity of the monochromatic X-ray beam was measured using three consecutive ionization detectors. To prepare the ex situ samples, freestanding LTFO electrode films were cycled to the desired SoC, after which they were extracted from the cell and sealed with Kapton tape and placed in air-tight X-ray transparent plastic bags under argon for protection. For the in situ relaxation measurement, an electrochemical cell equipped with Be windows50 was placed between the first and second ionization chambers. The energy calibration was performed using Fe and Ti foils placed between the second and third ionization chambers. All XAS data were processed with the Athena program51. Fourier transformation was implemented for k2-weighted EXAFS oscillations in the k range of 2.7 to 9.8 Å−1 for both Fe and Ti K-edge spectra using a sine window function. The EXAFS fittings of Fe K-edge spectra before and after relaxation were performed in the R range of 1 to 3 Å.

### HAXPES

Ex situ HAXPES measurements were carried out at the GALAXIES beamline52 of the SOLEIL synchrotron in France. The powder-form samples were cycled to the desired SoC with Swagelok cells and then recovered, washed with DMC three times and then dried under reduced pressure overnight. The transferring of samples from the glovebox to the HAXPES chamber was always done under argon or reduced pressure to avoid air contact. A third-order reflection of a Si(111) double-crystal monochromator was used to obtain the photon excitation energy  = 10 keV. The photoelectrons were collected and analysed using a SCIENTA EW4000 spectrometer, with an energy resolution of 0.22 eV at 10.0 keV photon energy for the Au Fermi edge. No charge neutralizer was required and the analysis chamber pressure was kept around 10−8 mbar during the experiment. The measurements were performed using single-bunch mode to minimize the X-ray damage to the samples.

### DFT+U calculations

All the calculations performed were done with the Vienna Ab initio Simulation Package (VASP), within the generalized gradient approximation and using the Perdew–Burke–Ernzerhof potential for electron exchange and correlation energy53,54,55. For searching the ground-state structure of the LTFO supercell (Li14Ti4Fe6O24), a genetic algorithm (GA) method was implemented. The details and the rationality for using the ground-state structure for further calculations (analysed by the cation distribution) are given in Supplementary Fig. 15. A 600 eV energy cutoff and a 3 × 2 × 6 k-point mesh were further used to optimize the ground-state structure within a spin-polarized DFT + U framework, where Ueff = UJ (U and J are the parameters for describing on-site coulomb and exchange interactions) was set to 5.3 eV for Fe unless specified. The convergence conditions for all the calculations were set as 10−5 eV for electronic loops and 0.02 eV Å−1 for ionic loops. For Fukui function calculations, we removed 0.2 electrons from the fully relaxed pristine structure (222 electrons) and performed the electronic relaxation while fixing the geometric structure. We finally obtained the charge density difference using the following equation:

$$f_ - \left( r \right) = \rho _N\left( {{{\boldsymbol{r}}}} \right) - \rho _{N - 0.2}({{{\boldsymbol{r}}}}),$$

where $$f_ - \left( r \right)$$ is the Fukui function, $$\rho _N\left( {{{\boldsymbol{r}}}} \right)$$ is the charge density of the pristine structure (N = 222 denotes the number of electrons) and $$\rho _{N - 0.2}({{{\boldsymbol{r}}}})$$ is the charge density of the pristine structure with 0.2 electrons removed.