Monitoring the formation of infinite-layer transition metal oxides through in situ atomic-resolution electron microscopy

Abstract

Infinite-layer transition metal oxides with two-dimensional oxygen coordination exhibit intriguing electronic and magnetic properties due to strong in-plane orbital hybridization. The synthesis of this distinctive structure has primarily relied on kinetically controlled reduction of oxygen-rich phases featuring three-dimensional polyhedral oxygen coordination. Here, using in situ atomic-resolution electron microscopy, we scrutinize the intricate atomic-scale mechanisms of oxygen conduction leading to the transformation of SrFeO_2.5 to infinite-layer SrFeO₂. The oxygen release is highly anisotropic and governed by the lattice reorientation aligning the fast diffusion channels towards the outlet, which is facilitated by cooperative yet shuffle displacements of iron and oxygen ions. Accompanied with the oxygen release, the three-dimensional to two-dimensional reconfiguration of oxygen is facilitated by the lattice flexibility of FeO_x polyhedral layers, adopting multiple discrete transient states following the sequence determined by the least energy-costing pathways. Similar transformation mechanism may operate in cuprate and nickelate superconductors, which are isostructural with SrFeO₂.

Main

SrFeO₂ crystallizes in an infinite-layer structure, where divalent iron (Fe²⁺) is stabilized in a two-dimensional (2D) FeO₄ layer with corner-shared, square-planar oxygen coordination^1,2,3,4,5. This unique oxygen coordination of iron has garnered substantial attention, as the irons in most oxides are coordinated three-dimensionally by oxygen^6,7. The absence of apical oxygen in SrFeO₂ imparts highly anisotropic properties, such as 2D magnetism, implying strong Fe 3d to O 2p hybridization leading to in-layer magnetic interactions^1,3,5,8. In recent decades, except for some cuprates⁹, the synthesis of infinite-layer transition metal oxides, including nickelates^10,11, cobaltates¹² and ferrites¹, has been achieved through kinetically controlled reduction of oxygen-rich precursor phases, such as perovskite or brownmillerite, using a hydride¹³ or metallic¹⁴ reductant. During the deintercalation of apical oxygen, a small amount of hydrogen might be unintentionally introduced as donors and impact any unconventional physical properties observed thus far. The origin of nickelate superconductivity has recently come under scrutiny due to the possible hydrogen incorporation¹⁵; however, concerns have been allayed through the synthesis of superconducting nickelates without the use of hydrides¹⁴. Obtaining a pristine SrFeO₂ structure devoid of hydrogen could be achieved by high-temperature annealing of oxygen-rich precursor phases in a hydrogen-free reducing environment. However, considering the relative instability of SrFeO₂ compared with its thermodynamically stable end phases—iron and strontium oxide^2,16—capturing the rapid transformation to metastable SrFeO₂ with atomic resolution presents a challenge.

The transformation from three-dimensional (3D) polyhedral to 2D square-planar oxygen coordination involves not only the removal of some oxygen but also the reconfiguration of the remaining ones. Conversely, the strontium and iron in SrFeO₂ experience minimal positional changes, largely maintaining their original locations. This transformation is critically important, yet its atomic-scale mechanism, particularly the conversion from 3D polyhedral to 2D square-planar oxygen coordination, has remained largely elusive. This is primarily due to the challenges in directly observing the rapid oxygen conduction process. The model proposed by Inoue et al. has provided substantial insights into the fundamental aspects of this atomic reconfiguration, particularly highlighting the exchange between apical and equatorial oxygen ions^4,17,18. However, direct atomic-scale observation is still required to fully comprehend the energy cost at each stage of oxygen release and the subsequent reorganization, along with the associated structural modifications of the host lattice.

Here, we successfully captured the fast dynamic motion of individual atoms during the phase transformation of SrFeO_2.5 to SrFeO₂ using high-resolution transmission electron microscopy (HRTEM) under negative spherical aberration (C_s) imaging (NCSI) condition^19,20,21,22. This transformation was observed during the annealing of ultrathin transmission electron microscopy (TEM) specimens (typically sub-10 nm in thickness) in a hydrogen-free vacuum environment of TEM. Through in situ atomic-resolution observations and quantitative image analysis supported by atomic simulations, we uncover a previously unknown oxygen conduction mechanism. This mechanism is facilitated by the lattice dynamics, characterized by the cooperative yet shuffle displacement of iron and oxygen ions, as well as the lattice flexibility of FeO_x polyhedral layers in accommodating the oxygen conduction by adopting multiple polyhedral configurations.

Results and discussion

Nucleation and growth of infinite-layer SrFeO₂

A 30-nm-thick brownmillerite SrFeO_2.5 (001) film grown epitaxially on SrTiO₃ (001) substrate serves as the starting material^23,24 (Extended Data Fig. 1 and Supplementary Fig. 1a,b). The in-plane lattice of SrFeO_2.5 film is elastically strained to match that of SrTiO₃ substrate with establishing a coherent interface (Supplementary Fig. 1c–e). SrFeO_2.5 comprises alternating rows of corner-shared FeO₆ octahedral and FeO₄ tetrahedral layers. The key distinction between these two iron oxide layers lies in the presence of one-dimensional oxygen vacancy (V_O) channels within the FeO₄ tetrahedral layer along the [010] direction. These channels, composed of vacant atomic sites, provide a rapid diffusion pathway for oxygen ions²⁵, a characteristic common to other transition metal oxides sharing similar structures (Supplementary Table 1). Due to the one-dimensionality of the V_O channels, the oxygen conduction and associated phase transition exhibit high anisotropy depending on the orientation of these channels with respect to the oxygen removal and supply environment^17,26. Considering this, we prepared cross-sectional TEM specimens for heating experiments along the two orthogonal [100] and the [010] zone axes of the SrFeO_2.5 (001) film (Extended Data Fig. 1). In the [100] sample, the V_O channels run parallel to the plane surfaces of TEM specimen, while in the [010] sample, the channels run perpendicular to the plane surfaces of TEM specimen.

The phase transformation of SrFeO_2.5 to SrFeO₂ begins at approximately 450 °C under the high-vacuum condition of TEM column (~10⁻⁵ Pa). Once initiated, the transformation completes within just 30 s (Supplementary Video 1). This rapid process is in stark contrast to the hydro-reduction process, which typically takes several hours at similar temperatures^1,17. The nucleation of SrFeO₂ phase occurs at various locations in the SrFeO_2.5 film, primarily at its surface (Supplementary Video 1), occasionally at the SrTiO₃ interface (Supplementary Video 2) or within the film’s interior (Supplementary Video 3). Notably, the surface of the SrFeO_2.5 film emerges as the favoured site for nucleation, due to the ease of oxygen release at the initial stages of nucleation. Before the nucleation of SrFeO₂ phase, the oxygen configuration within the tetrahedral layers fluctuates, occasionally exhibiting the contrast similar to the octahedral layers (Extended Data Fig. 2). The fluctuation in the oxygen configuration is attributable to the dynamic motion of oxygen through the V_O channels, as it migrates and escapes into the environment. After nucleation, a nanometre-sized SrFeO₂ phase grows rapidly with the propagation of multiple ledges on adjacent layers (Supplementary Video 3). We confirmed that the final product of phase transformation is SrFeO₂ through integrated differential phase contrast (iDPC) imaging and electron energy-loss spectroscopy (EELS) analysis, supported by theoretical calculations (Methods and Extended Data Fig. 3).

In the phase transformation recorded in real time under a NCSI HRTEM imaging condition, all constituent atoms, including oxygen, are clearly resolved (Fig. 1a). Across the moving phase boundary, the cation lattice frameworks of SrFeO_2.5 and SrFeO₂ remain highly commensurate, as strontium and iron atoms require only slight positional adjustments during the transformation. Given that the interlayer spacing of strontium layers (d_Sr–Sr) contracts by ~0.7 Å in SrFeO₂ from SrFeO_2.5 (Extended Data Fig. 4a,b), by mapping the d_Sr–Sr over a sequence of HRTEM images we were able to visualize the evolution of SrFeO₂ phase and the morphology of the phase boundary with SrFeO_2.5 (Fig. 1b,c and Extended Data Fig. 5). The phase boundary advances via step flow of multiple ledges on adjacent layers that effectively squeezes out oxygen from the SrFeO_2.5 in front of the boundary (Extended Data Fig. 5, Supplementary Fig. 2 and Supplementary Videos 1 and 2). The multiple ledges arrange into a shear-band-like slanted stack, roughly along the {011} plane (Extended Data Fig. 5). The volume change (contraction) resulting from the release of oxygen ions at the moving front of ledge is accommodated by gradual lattice bending over several nanometres (~5 nm).

Fig. 1: Structural evolution of the SrFeO_2.5–SrFeO₂ phase boundary captured by in situ HRTEM.

a, HRTEM images 6.84 s apart showing the phase transformation of SrFeO_2.5 to SrFeO₂ and their boundary migration at 450 °C (Supplementary Video 1). The dashed white line marks the phase boundary. In the SrFeO_2.5 [100] zone axis sample, the V_O channels are aligned laterally. Scale bars, 2 nm. b, Phase boundary outlined in a. c, Interplanar spacing map of the strontium layers, d_Sr–Sr, used for phase identification. Alternating red (tetrahedral layers) and blue (octahedral layer) stripes belong to SrFeO_2.5, while uniform blue region corresponds to the SrFeO₂ phase (refer to Extended Data Fig. 4). d, Intralayer iron–iron distance map, δ_Fe–Fe, visualizing the evolution of normally aligned V_O channels ahead of the moving phase boundary. The chequerboard pattern appearing in the SrFeO_2.5 [100] specimen indicates 90° reconfiguration, which brings the laterally aligned V_O channels to the normally aligned ones (yellow rectangles). Uniform green colour far below the phase boundary indicates the pristine SrFeO_2.5 [100] without reconfiguration. The structural evolution of atomic structure during the phase transformation is labelled in sequence of (i) initial SrFeO_2.5 [100], (ii) 90°-reconfigured to SrFeO_2.5 [010], (iii) SrFeO_2.5 [010]-SrFeO₂ phase boundary and (iv) SrFeO₂ [110] end phase. e,f, Atomic models (e) and HRTEM images (f) corresponding to each stage from (i) to (iv). The normally aligned V_O channels are indicated by yellow rectangles. The whole phase transformation process can be described as (i) to (ii), 90° reconfiguration of the V_O channels ahead of the moving front of phase boundary; (ii) to (iii), progress of the topotactic reduction with phase boundary migration; and (iii) to (iv), completion of the topotactic phase transformation to SrFeO₂. Scale bars, 5 Å.

Reconfiguration of V_O channels by atomic shuffle displacements

The oxygen release and rearrangement processes at the moving front of the phase boundary were observed to be highly anisotropic (Extended Data Fig. 6). Tracking the phase boundary motion on the in situ HRTEM movies revealed that the boundary moves approximately two to three times faster in the [010] sample than that in the [100] sample. The anisotropy in the oxygen release and rearrangement originates from the way how the V_O channels are aligned with respect to the oxygen sink, determining the kinetics of oxygen conduction, as schematically illustrated in Extended Data Fig. 1.

In the SrFeO_2.5 [100] sample where the V_O channels run parallel to the plane surface of TEM specimen, we observed that the crystallographic reorientation occurs in the vicinity of the phase boundary before the transformation to SrFeO₂ phase²⁶ (Supplementary Video 4). Specifically, the crystallographic reorientation results in the 90° reconfiguration of the SrFeO_2.5 [100] to [010] direction, aligning the V_O channels perpendicular to the top and bottom surfaces of TEM lamella specimen as in the [010] sample, shortening the total length of V_O channels to the oxygen sink and facilitating the subsequent phase transformation (Fig. 1d–f). These normally aligned V_O channels are visualized by mapping the intralayer iron–iron distance (δ_Fe–Fe) projected in the plane of visualization (Fig. 1d and Extended Data Fig. 4c). In the pristine [100] sample where the V_O channels are aligned horizontally, the measured δ_Fe–Fe is a uniform 2.7 Å (green). In contrast, in the pristine [010] or the 90°-reconfigured [100] sample where the V_O channels are aligned normally, the δ_Fe–Fe exhibits a chequerboard pattern of 2 Å (navy) and 3.9 Å (yellow), with the latter corresponding to the V_O channels. The 90° reconfiguration of V_O channels is confirmed by the appearance of a chequerboard pattern near the phase boundary in the δ_Fe–Fe map (Fig. 1d and Extended Data Fig. 7). Once the 90° reconfiguration takes place ahead of boundary, the phase boundary advances rapidly (Extended Data Fig. 6b, red), indicating that the alignment of V_O channels with respect to the environment governs the overall transformation rate.

The in situ atomic observation and simulation revealed that the 90° reconfiguration of V_O channels towards the shortest dimension of system is facilitated by collective yet shuffle atomic displacements. The HRTEM video was analysed frame by frame, capturing the atomic process leading to the 90° reconfiguration of the SrFeO_2.5 [100] to the [010] orientation (Fig. 2a and Supplementary Video 5). At the completion of the reconfiguration, the structural features of the SrFeO_2.5 [010] are perfectly restored, including the anti-ferrodistortive (AFD) rotation (β ≈ ±7°) of FeO₆ octahedral layers and the appearance of V_O channels (δ_Fe–Fe = 3.9 Å) within the tetrahedral layers (Extended Data Fig. 1d). To track the progression of 90° reconfiguration, the δ_Fe–Fe between two adjacent unit cells was monitored until the reconfiguration was fully accomplished (Fig. 2b and Supplementary Video 6). While the overall process completes quickly within seconds, a transient state, referred to as ‘(ii)’ in Fig. 2, was observed to exist between the two end states, ‘(i)’ for SrFeO_2.5 [100] and ‘(iii)’ for SrFeO_2.5 [010]. This transient state persists for an extended period, exhibiting intermediate values of δ_Fe–Fe and β values that were halfway between those of SrFeO_2.5 [100] and SrFeO_2.5 [010].

Fig. 2: Atomic shuffle displacement leading to 90° reconfiguration of V_O channels—experiment and simulation.

a, Time sequence HRTEM images showing the 90°-reconfiguration process of SrFeO_2.5 [100] to [010] (Supplementary Video 5). Images (i) and (iii) represent the two end states, while image (ii) is a transient state that spans a relatively long time. The white line connecting iron and oxygen in the octahedral layers depicts the evolution of AFD rotation during the reorientation as indicated by angle β. b, Intralayer iron–iron distance, δ_Fe–Fe, of the two adjacent unit cells defined in a measured as a function of time (Supplementary Video 6). The δ_Fe–Fe values in the plot are the average of measurements from three-consecutive two-adjacent unit cells, with error bars indicating the standard deviation. The uniform δ_Fe–Fe values are split into one smaller (δ_{Fe–Fe_1}) and one larger (δ_{Fe–Fe_2}) values via a transient state (ii), with the latter being the vertically aligned V_O channel in SrFeO_2.5 [010]. c, Structural models from DFT simulations corresponding to states (i), (ii) and (iii) in a, which correspond to (1), (6) and (11), respectively, in a series of structural models calculated by DFT (Extended Data Fig. 8a). d, Top view of the structural models (i), (ii) and (iii) in c. The yellow arrows indicate the direction of V_O channels lying in the tetrahedral layers. e, Visualization of atomic shuffle displacement vectors by overlapping the two atomic arrangements from tetrahedral layers corresponding to (i) and (iii) in d. Superposition of the tetrahedral layers before and after the 90° reconfiguration and connecting the positions of each atom define the displacement vector.

Source data

The process leading to the 90° reconfiguration of V_O channels is facilitated by a shuffle-like displacement of iron and oxygen ions within the FeO₄ tetrahedral layer, akin to the atomic shuffle mechanism proposed for deformation twinning^27,28,29. It appears that there is no way to reposition all iron and oxygen ions to achieve the necessary 90° reconfiguration by a simple shear displacement process. To delve deeper into this phenomenon, we performed first principles calculations, taking into account the shuffle displacements for the 90° reconfiguration (Fig. 2c,d). In this process, each iron and oxygen atom is subject to a unique displacement vector (Fig. 2e and Supplementary Video 7). This shuffle displacement can be visualized by overlaying the two atomic arrangements before and after the 90° reconfiguration and connecting the position of each atom to define the corresponding displacement vector (Fig. 2e).

Twelve successive configurations, generated by the first principles nudged elastic band method, depicting the shuffle displacement process, are shown in Extended Data Fig. 8a and Supplementary Video 8. The initial and final configurations with the reaction coordinate (1) and (12) correspond to the SrFeO_2.5 [100] and the [010] zone axis orientation, respectively. To enable a direct comparison between experimental observations and the theoretical calculations, we simulated the HRTEM images using the atomic configuration files corresponding to each reaction coordinate (Extended Data Fig. 8b and Supplementary Video 8) and conducted cross-correlation analysis to assign proper reaction coordinates to the experimental HRTEM images (Extended Data Fig. 8c). Notably, a relatively long-lived transient state is observed at the midpoint of the reconfiguration process, corresponding to the reaction coordinates (6) and (7) (or state (ii)).

The energy landscape calculated (Extended Data Fig. 8d, blue) along the reaction coordinate of shuffle displacement reveals the presence of a local energy minimum at the coordinates numbered (6) and (7). This energy minimum arises from the reduced Coulomb repulsion between oxygen ions due to their relocations. This particular reaction coordinate appears as a subtle yet distinct local maximum in the probability plot (Extended Data Fig. 8d, orange) assessed by Boltzmann statistics of each reaction coordinate (Methods), manifesting a relatively long-lived transient state compared with the rest of the reaction coordinates in the course of otherwise fast shuffle displacement. The atomic configuration of this transient state predicted by the calculation matches well with the experimentally observed one from the midpoint of the reconfiguration (Extended Data Fig. 8c, (ii)). The shuffle displacement leading to 90° reconfiguration of SrFeO_2.5 is facilitated by the free space available for the iron and oxygen ions around the V_O channels.

Given that the energy states before and after the 90° reconfiguration are equivalent, as demonstrated in Extended Data Fig. 8d, there appears to be no inherent driving force for this process. However, the 90° reconfiguration of the V_O channels can reduce the energy required for the subsequent oxygen release process. When the V_O channels are oriented perpendicular to the plane surfaces of the TEM specimen, as depicted in Extended Data Fig. 1f, there is a 10³-fold increase in the direct exposure of the V_O channels to the vacuum, compared with the configurations where the channels run parallel to the longest dimension of the specimen, as shown in Extended Data Fig. 1e. This anisotropy in oxygen conduction, where the conduction is much more efficient along the V_O channels, suggests a preference for the 90° reconfiguration of V_O channels to facilitate easier oxygen removal.

Atomic-scale mechanism of oxygen release and rearrangement

The 90°-reconfigured V_O channels expedite the release of oxygen. The subsequent oxygen rearrangement is facilitated by the lattice flexibility of iron oxide layers that dynamically accommodates the change in oxygen coordination by adopting various FeO_x polyhedral configurations. This raises fundamental questions as to which oxygen ion is removed first and which one later, and how the remaining ones are rearranged into the square-planar configuration. Time-resolved tracking of the atomic position and intensity change from real-time NCSI HRTEM recordings (Supplementary Video 9) provides valuable clues to the underlying atomic-scale mechanism. A series of transient states identified during the one-unit event of layer-by-layer phase transformation unveils the sequence of oxygen release and rearrangement, as well as the associated multiple polyhedral configurations, with each configuration being corroborated by density functional theory (DFT) calculations (Fig. 3).

Fig. 3: Atomic-scale mechanism of oxygen release and rearrangement—in situ HRTEM image analysis.

a, Time sequence HRTEM images showing the phase transformation of the SrFeO_2.5 [010] after 90° reconfiguration (Supplementary Video 9). The four distinct states (i)–(iv) were identified during the transformation of octahedral and tetrahedral layers to square-planar layers. AFD rotation and polar distortion in states (i) and (ii), respectively, are indicated by arrows and lines. The dashed arrows in states (iii) and (iv) correlate to the concurrent intensity change of the two oxygen, the apical oxygen of FeO₆ octahedral and the equatorial oxygen of FeO₄ tetrahedral, indicating the oxygen migration from the former to the latter. Colour bar indicates intensity level after normalization. Octa., octahedral; tetra., tetrahedral. b, SrO column intensity of the four SrO layers defined in a (Exp., yellow marker). The same measurement on the simulated images (Extended Data Fig. 9) was added for comparison (Sim., grey). The upper (SrO with all oxygen) and lower (only strontium without oxygen) bounds are marked by the dashed line. The intensity values in the plot represent the average of measurements from the lateral four SrO columns, with error bars indicating the standard deviation. Green dashed boxes and white arrows highlight the intensity change. c, Intensity of the V_O channel (red) and FeO column (blue) along the tetrahedral layer defined in a. The correlated intensity changes of the apical oxygen in SrO and the oxygen occupying V_O channels are indicated by the dashed arrows pointing from b to c. d, Atomic models, corresponding to states (i) to (iv) in a, proposed by DFT calculation.

Source data

The FeO₄ tetrahedral and FeO₆ octahedral layers of SrFeO_2.5 undergo transformation to the FeO₄ square-planar layer following distinct yet highly correlated pathways, as summarized below.

• 1. The transformation of the tetrahedral layer to the square-planar layer begins with the release of the oxygen shared between two neighbouring tetrahedra (as they are the easiest to remove), followed by the sequential incorporation of the apical oxygen released from both the top and bottom adjacent octahedral layers. The experimental evidence supporting the release of oxygen from the tetrahedral layer is provided by the noticeable intensity trail across the V_O channels, together with the reduced intensity of FeO columns (Supplementary Video 9).

• 2. The transformation of the octahedral layer to the square-planar layer occurs through the sequential release of the two apical oxygen while retaining the strongly bound equatorial oxygen. Initially, the release of one apical oxygen results in a polar distortion arises in the resulting FeO₅ square-pyramidal layer. This polar distortion disappears as the FeO₅ unit further transitions to the FeO₄ square-planar layer by releasing the remaining apical oxygen. The released apical oxygen then moves towards the nearest tetrahedral layers and participate in subsequent rearrangement within the layer.

The analysis of HRTEM images and complementary DFT calculations, elucidating the transformation sequence of each layer and their interplay, are summarized in Fig. 3. In the FeO₆ octahedral layer, the initial yet most prominent change is observed as a decrease in the intensity of the apical SrO (SrO (1)) column, accompanied by the evolution of polar distortion in the equatorial oxygen and iron ions (from state (i) to (ii) in Fig. 3a–c), overriding the intrinsic AFD rotation. The reduction in the intensity of the SrO column can be attributed to the release of apical oxygen from the corresponding FeO₆ octahedra. As verified by DFT calculation (Fig. 3d), the release of apical oxygen causes a structural change of the octahedral layer, that is, the AFD rotation to polar distortion; the removal of the top apical oxygen truncates the FeO₆ octahedra into a FeO₅ square pyramid, causing the equatorial oxygen ions to move upwards and the iron ions to move downwards, counterbalancing the emerging dipole moment and resulting in a buckling with an amplitude of 24 pm. The released apical oxygen subsequently migrates towards the (upper) nearest tetrahedral layer.

The first noticeable change in the tetrahedral layer is the rise of the intensity at the vacant sites (V_O channels) beyond the background level and the simultaneous decrease of the intensity of the FeO columns (from state (i) to (ii) in Fig. 3a–c). These intensity changes indicate the release of the oxygen from the FeO columns, which is corner-shared between two neighbouring FeO₄ tetrahedra, and subsequent migration through the V_O channels to the vacuum outlet. As the oxygen release and evacuation continues in the tetrahedral layer, the oxygen coordination of iron atom reduces gradually from FeO₄. At some point in the course of the oxygen evacuation, the tetrahedral layer transitions to a completely new atomic arrangement, where the V_O channels are filled with oxygen (Fig. 3a, state (iii)). We note that this change happens simultaneously with the release of apical oxygen from the FeO₅ square pyramid in the upper layer (Fig. 3b,c, state (iii)). The transition layer is likely to adopt a FeO₃ trigonal-planar configuration by receiving the apical oxygen released from the FeO₅ square pyramid in the upper layer (Fig. 3d, state (iii)). The trigonal-planar configuration then transitions into FeO₄ square-planar configuration by completely filling up the vacant sites with the oxygen delivered from the FeO₆ in the lower octahedral layer (Fig. 3a–d, state (iv)). This unit event converts one octahedral and tetrahedral layers into two corner-shared FeO₄ square-planar layers and continues in the subsequent layers.

The proposed model, derived from the analysis of real-time HRTEM data, is validated by DFT simulations, confirming the sequence of oxygen release and rearrangement (Fig. 3d, Extended Data Fig. 9 and Supplementary Video 10). For instance, by tracking the variation of d_Sr–Sr (Extended Data Fig. 9f and Supplementary Video 11) during the phase transformation, the stepwise evolution of distinct transient states can be identified. These transient states exhibit different spacing, one measuring 4.16 Å and the other measuring 3.79 Å, between the two end phases (4.21 Å for SrFeO_2.5 and 3.49 Å for SrFeO₂). Each transient state persists for a specific duration within a second-level time span. The presence of such distinct, stepwise structural changes suggests that the phase transformation occurs discretely through a series of short-lived transient states. As validation, we carried out the same analysis on the simulated HRTEM images using the DFT results corresponding to each step shown in Fig. 3. The intensity measured from the simulated images is included as grey bars in Fig. 3, and the full results are summarized in Extended Data Fig. 9. The intensity changes of each atomic column associated with oxygen loss and redistribution measured from the simulated HRTEM images agree well with the experimental measurements.

Energy landscape along the observed oxygen release and rearrangement pathway

According to the DFT calculations, the equatorial oxygen in FeO₆ (O₁) exhibits the highest V_O formation energy (4.11 eV), indicating that these oxygen ions are the least likely to be removed (Fig. 4a–c). Conversely, the corner-shared oxygen between two neighbouring FeO₄ within the tetrahedral layer (O₃) exhibits the lowest V_O formation energy (3.25 eV). Given the substantial amount of oxygen that needs to be removed in SrFeO_2.5, it is evident that this type of oxygen is the most easily removable one. Notably, the V_O formation energy is substantially reduced for all types of oxygen at the phase boundary (Fig. 4b,c). Once the corner-shared oxygen is removed, the FeO₄ unit adopts a FeO₃ trigonal-planar configuration by receiving an apical oxygen from the upper octahedral layers and, subsequently, another one from the lower octahedral layers, achieving the square-planar configuration (Fig. 4d). Regarding the apical oxygen (O₂) in perfect SrFeO_2.5 (Fig. 4a,c), each oxygen atom is shared between the FeO₆ octahedral and FeO₄ tetrahedral layers at its vertices. The energy required to remove this apical oxygen is high (3.76 eV) when both connecting polyhedra maintain their regular oxygen coordination. However, when the oxygen coordination of the polyhedra is disrupted by losing oxygen, such as from the FeO₆ octahedra to a FeO₅ square pyramid (as in pathway 1 in Fig. 4d), or from the FeO₄ tetrahedra to a FeO₃ trigonal-planar (as in pathway 3), our DFT calculations show that the activation energy required to migrate the apical oxygen is lowered substantionally (Fig. 4e), facilitating the release and migration towards the tetrahedral layers. This energy difference in displacing the apical oxygen, depending on the local oxygen coordination, determines the energetically favoured pathway and controls the sequence of oxygen removal and rearrangement processes (Fig. 4d,e). Consequently, the phase boundary propagates in a layer-by-layer fashion, akin to falling dominoes, following the reaction pathway with the least energy cost in the energy landscape.

Fig. 4: Energetics of V_O formation and migration determining sequence of oxygen removal and rearrangement.

a,b, Atomic model of perfect SrFeO_2.5 (a) and SrFeO_2.5/SrFeO₂ boundary (b). Oxygen in different iron coordination is classified for the calculation of V_O formation energy; equatorial oxygen in FeO₆ (O₁ in SrFeO_2.5, O₁′ in SrFeO_2.5/SrFeO₂ boundary), apical oxygen in FeO₆ (O₂, O₂′) and equatorial oxygen in FeO₄ (O₃, O₃′). c, V_O formation energy calculated for the oxygen in different Fe coordination of SrFeO_2.5 (green) and SrFeO_2.5/SrFeO₂ boundary (orange). d, Oxygen migration pathways for apical oxygen in different iron coordination to the tetrahedral layer: (1) FeO₅ square pyramid; (2) ordinary FeO₆; (3) FeO₃ trigonal planar. e, Energy landscape along the different migration paths defined in d. Pathway passing through (1) to (3) is energetically favoured over (2) to (3), explaining the observed sequence of oxygen removal and rearrangement processes.

Source data

The oxygen conduction mechanism identified in this study differs from the typical high-temperature hopping process. Instead, it is facilitated by the lattice flexibility of FeO_x polyhedral layers, which accommodate oxygen conduction by adopting multiple polyhedral configurations. To illustrate this, we tracked the trajectory of atomic movements, highlighting their discrete nature in response to changes in oxygen coordination (Extended Data Fig. 10). These discrete movements result from changes in the oxygen coordination around Fe atoms within FeO_x polyhedral layers, differing from conventional vacancy-driven oxygen conduction that typically leaves a diffusive trace as result of random walks. Additionally, we analysed the moving rate of the phase boundary to assess its time (t) dependency, determining whether it follows diffusion control, indicated by a t^1/2 dependency, or interface reaction control, marked by a linear t dependency. The results, shown in Supplementary Fig. 3, reveal a linear t dependency in the boundary motion, suggesting that the process is driven by an interface reaction controlled type process. Specifically, this interface reaction involves oxygen rearrangement through discrete configurations of FeO_x polyhedral layers at the phase boundary, in contrast to conventional vacancy-driven diffusion process. Remarkably, upon cooling in the vacuum of TEM column, the reverse reaction takes place spontaneously (Supplementary Fig. 4). This suggests not only that oxygen is sufficiently mobile at low temperatures but also that the cation framework can adjust itself to form a new topotactic structure.

Conclusion

The atomic-scale mechanism underlying one of the most intriguing topotactic phase transformations in transition metal oxides, from 3D polyhedral to 2D square-planar configuration, has been revealed through real-time tracking of atomic motions during the phase transformation. The phase transformation was assessed by heating an ultrathin SrFeO_2.5 sample in the vacuum of TEM column, eliminating the need for a controversial hydride reductant. Due to the pronounced anisotropy in oxygen conduction, the rate-limiting step is governed by the atomic reconfiguration process, aligning the Vo channels along the shortest dimension of the sample. This reorientation is facilitated by the cooperative shuffle displacement of iron and oxygen ions within the lattice. The release and rearrangement of oxygen occur in a well-defined sequential pathway via transient states, as the energy required for oxygen release varies depending on the evolving local oxygen coordination. In contrast to conventional vacancy-driven oxygen conduction at high temperatures, this conduction mechanism is enabled by the lattice flexibility of FeO_x polyhedral layers, which can accommodate the removal or addition of oxygen through the adoption of multiple polyhedral configurations with varying degrees of iron–oxygen bond valence and covalence, as well as polar distortion or anti-polar rotation.

The insights gained from this observation not only shed light on the specific transformation mechanism in SrFeO₂ but also provide a foundation for understanding similar processes in other materials, such as cuprate and nickelate superconductors that share similar structural characteristics. By elucidating the intricate atomic-scale dynamics involved in the transformation of 3D polyhedral to 2D square-planar oxygen coordination, our research paves the way for further exploration and potential advancements in the field of infinite-layer transition metal oxides.

Methods

SrFeO_2.5 thin film growth and TEM specimen preparation

Epitaxial SrFeO_2.5 thin film was grown on atomically flat (001)-oriented single-crystalline SrTiO₃ substrates using pulsed laser epitaxy at 700 °C under 1 mTorr of oxygen partial pressure. An excimer (KrF) laser of 248 nm wavelength (IPEX 864, Lightmachinery) with an energy fluence of 1.3 J cm⁻² and a repetition rate of 4 Hz was used. The atomic structures and the crystallinity of the epitaxial thin films were characterized by high-resolution X-ray diffraction. The thickness of the thin films was determined as 30 nm, using X-ray reflectivity.

Cross-sectional TEM specimens were prepared along the [100] and [010] zone axis of the epitaxial SrFeO_2.5 thin films by using focused ion beam (FIB) milling. The prepared SrFeO_2.5 lamella by FIB were attached to silicon micro-electromechanical systems chip (Wildfire, DENSsolutions) for in situ heating experiments. At the final stage of FIB milling, a low energy Ga⁺ ion beam at 2 kV was used to reduce the beam damages.

As shown in Extended Data Fig. 1, the geometry of the SrFeO_2.5 thin film region of the TEM specimen is approximately 5.6 nm (lamella thickness) × 30 nm (as-grown thin film thickness) × 10⁴ nm (lamella length). If the V_O channels are aligned perpendicular to the plane surfaces of the [010] TEM specimen (Extended Data Fig. 1f), it would lead 10³ times more direct exposure of the V_O channels towards the vacuum, compared with the [010] specimen with V_O channels running along the longest dimension (Extended Data Fig. 1e).

In situ NCSI HRTEM imaging

A Cs-corrected (S)TEM (Grand ARM300F, JEOL) operated at 300 kV was used for in situ heating experiments. The in situ heating was performed using a heating holder (Wildfire, DENSsolutions). After initially ramping up to 350 °C, the annealing temperature was subsequently increased to 500 °C in increments of 50 °C, with the sample maintained for 1 h at each temperature step. We observed that the temperature window for phase transition was notably narrow; specifically, the phase transition did not occur at temperatures below 450 °C. Conversely, at temperatures exceeding 450 °C, the phase transition occurred concurrently with thermal decomposition. This limited temperature range posed a challenge in varying the temperature within the narrow operational window for observing the phase transformation. Real-time in situ movies were acquired at 450 °C to investigate the phase transformation using a 4 K × 4 K charge-coupled detector (CCD) camera (OneView, Gatan) at 25 frames per second (fps). The NCSI condition, which gives enhanced contrast (bright atomic columns on dark background) and minimal delocalization (~±0.03 nm), was used to resolve all atoms (including oxygen columns) under spherical aberration coefficient C_s = −13 μm combined with Δf = +6.2 nm Scherzer defocus^20,21. The electron dose rate was on the order of 10³–10⁴ e⁻ Å⁻² s⁻¹.

For the TEM specimen with the thickness of 5.6 nm (Supplementary Fig. 5), all atomic columns in the NCSI HRTEM images show linear intensity–thickness relationships that justify the use of the column intensity to trace the change in the number of atoms in the column (Supplementary Fig. 6). This is key to the direct interpretation of the intensity change associated with the migration and loss of oxygen.

HAADF-STEM imaging

The detector collection angle in the range of 70 to 175 mrad was set for high-angle annular dark-field (HAADF) imaging mode. The convergence semi-angle of a focused electron probe was 25 mrad.

Electronic structure analysis by STEM EELS

Atomic-resolution EELS has been carried out using an EEL spectrometer (GIF Quantum ER, Gatan) with an energy resolution of 0.6 eV at the acceleration voltage of 300 kV under STEM imaging mode. The probe convergence angle and collection angle were 23 and 36 mrad, respectively. To determine the valence state of iron ions before and after phase transformation, atomic-resolution EELS has been carried out with focusing the electron probe at individual oxygen (for O K edge) and iron (for Fe L_2,3 edge) column sites. Zero-loss peak was acquired simultaneously for the energy calibration. The electron dose rate was about 10⁴ e⁻ Å⁻² s⁻¹. The energy dispersion and dwell time per pixel were 0.1 eV and 0.2 s, respectively. There is no noticeable electron beam damages during data acquisition.

The presence of divalent Fe²⁺ ion in the square-planar oxygen coordination was confirmed by the chemical shift of EELS Fe-L_2,3 edge towards a lower energy, compared with the Fe-L_2,3 edge of tetrahedral or octahedral oxygen coordination of Fe³⁺ ions in SrFeO_2.5 (refs. ^30,31) (Extended Data Fig. 3) Moreover, the increased hybridization strength between Fe 3d to O 2p in SrFeO₂, compared with SrFeO_2.5, was confirmed by a shift in the EELS O-K edge to a higher energy—a key characteristic of the square-planar FeO₄ layers in SrFeO₂. This finding has been further supported by the DFT calculations on the density of state (DOS) and EELS O K edge of SrFeO₂ and SrFeO_2.5.

Oxygen configuration characterization by iDPC-STEM imaging

Differential phase contrast (DPC) signal was obtained by using a segmented field detector (SAAF Octa. JEOL) under STEM mode. The beam deflection was measured and converted to iDPC images using a commercial software (qDPC, HREM Research Ltd.). iDPC is a suitable imaging technique to visualize light elements such as oxygen when the sample thickness is not ideal for NCSI HRTEM. The convergence angle of electron probe for DPC was 25 mrad. The angular ranges for the inner and outer detectors were set to 0–16.7 and 16.7–33.3 mrad, respectively.

Viewing along the [100] zone axis, the apical oxygen of octahedra or tetrahedra is overlapped with strontium while the equatorial oxygen is visible without overlap with other elements (Extended Data Fig. 1). This image projection thus hinders unambiguous interpretation of the oxygen configuration in the newly formed phase. To avoid confusion, we performed a heating experiment along the [110] zone axis under the same temperature and characterized the atomic structure by iDPC imaging under STEM mode (Extended Data Fig. 3). Along this zone axis, the apical oxygen is isolated without overlap with strontium or iron. After transformation, compared with pristine SrFeO_2.5 structure, all the apical oxygen in the newly formed phase was lost, indicating that the newly formed structure is SrFeO₂ with square-planar coordinated infinite-layer structure.

Geometric phase analysis

Geometric phase analysis (HREM Research) software was used for the strain analysis of HRTEM images and HAADF-STEM images. For the strain maps shown in Extended Data Fig. 5 and Supplementary Figs. 1 and 2, the fractional change of the in-plane and out-of-plane lattice parameters from the reference SrFeO_2.5 phase, ε_xx and ε_zz, respectively, was used to differentiate SrFeO₂ from SrFeO_2.5 and identify the phase boundary. The lattice rotation map (R_xz) was used to visualize the lattice bending over ledge(s) in the phase boundary, which arises to accommodate the large mismatch in the out-of-plane lattice parameters between SrFeO_2.5 and SrFeO₂. For the epitaxial misfit strain analysis applied on HAADF-STEM images in Supplementary Fig. 1, the reference area was set on SrTiO₃ substrate region. Given that the SrFeO_2.5 film used in this study is compressively strained on SrTiO₃ substrate (misfit strain of −1.4%), the effect of lattice strain on the oxygen reconfiguration and conduction mechanisms needs further exploration.

Energy-filtered TEM for thickness estimation of TEM specimen

For the determination of TEM specimen thickness, energy-filtered TEM was conducted using an energy filter (Quantum spectrometer ER965, Gatan) combined with a 2 K × 2 K CCD camera (UltraScanXP 100FT, Gatan). An objective aperture with a diameter of 20 μm was used to select the transmitted beam for thickness map. Thickness maps were recorded using the imaging filter to remove inelastically scattered electrons outside an energy window of 0 ± 5.0 eV with the exposure time of 4 s. The mean free path for inelastic scattering of 94.6 nm was used for SrFeO_2.5.

Control experiments I—electron beam effects

Evaluating the effects of the electron beam is crucial in in situ TEM heating experiments. In this study, we carefully maintained the electron dose rate at approximately 1 × 10⁴ e⁻ Å⁻² s⁻¹. This rate was chosen to optimize the signal-to-noise ratio while minimizing potential electron beam-induced damages. Fortunately, the benefit of using HRTEM for atomic-scale imaging over STEM is its relatively lower electron dose rate, which is typically in the order of 10³–10⁴ e⁻ Å⁻² s⁻¹. We also performed the heating experiment at a reduced dose rate of ~10³ e⁻ Å⁻² s⁻¹ and obtained similar results. To further assess the impact of the electron beam, we conducted controlled experiments, the results of which are detailed in Supplementary Figs. 4 (~20-nm-thick TEM specimen) and 7 (~180-nm-thick TEM specimen). In these experiments, we activated the electron beam only for capturing images or obtaining diffraction patterns necessary for phase identification. By maintaining identical heating–cooling conditions but without electron beam exposure, we observed that the SrFeO_2.5 film in the 20-nm-thick TEM specimen transformed into SrFeO₂ at a temperature of 450 °C and then reverted to SrFeO_2.5 reversibly upon cooling to room temperature, consistent with the behaviour of the ultrathin TEM specimen. This confirms that the reversible transformation between SrFeO_2.5 and SrFeO₂ is primarily driven by temperature changes, rather than by stimulation from the electron beam.

Control experiments II—sample size effects

The synthesis of infinite-layer SrFeO₂ with the square-planar oxygen configuration is limited to only a few kinetically controlled processes such as hydro-reduction as SrFeO₂ is not a thermodynamically stable phase in most experimental conditions. Considering the relative instability of SrFeO₂, thermal annealing of the initial phase SrFeO_2.5 for a sufficiently long time is likely to induce the decomposition to the stable end phases. Whether kinetically driven oxygen deintercalation topotactic transition dominates thermodynamically driven decomposition depends on the annealing and sample conditions. In this context, providing a favourable condition for the fast deintercalation of oxygen can result in the dominance of SrFeO₂ formation over phase decomposition. This can be achieved by lowering the oxygen partial pressure in the annealing atmosphere, which enhances the escaping tendency of oxygen (chemical potential of oxygen). Not only the driving force but also the physical area through which oxygen escapes should be increased and the energy barrier for oxygen migration should be reduced to promote the fast deintercalation of oxygen. This can be accomplished by increasing the surface-to-volume ratio by optimizing the geometry, crystallographic orientation and sample size.

Note that the pressure of TEM column is in the level of 10⁻⁵ Pa, which is several orders of magnitude lower than the pressure adopted for most hydro-reduction processes^1,13. More importantly, while the size of powder samples prepared by mechanical grinding in all reported studies was in the range of 1–10 μm, the thickness of TEM specimens used in the present study was in the order of nanometre, resulting in a high surface-to-volume ratio, favourable for oxygen release. All these sample and environmental conditions can promote the fast deintercalation of oxygen before decomposition. In fact, in situ heating of the ultrathin TEM sample (5.6 nm in thickness) prepared for NCSI HRTEM imaging showed the fast transformation of SrFeO_2.5 to SrFeO₂. Upon cooling, the SrFeO₂ phase transforms back to SrFeO_2.5 reversibly, demonstrating that, for the ultrathin sample, kinetically driven oxygen deintercalation or intercalation completes before thermodynamically driven process sets in.

As demonstrated in Extended Data Fig. 6, the activation of V_O channel reconfiguration plays a pivotal role in determining the overall rate of phase transformation, thus acting as a critical rate-limiting step in this kinetically controlled process. We note that the reconfiguration of the V_O channels incurs a substantial energy cost, necessitated by the collective and cooperative shuffle displacements of all involved atoms, as depicted in the energy curve in Extended Data Fig. 8d. With increasing sample size, the energy required for this reconfiguration escalates due to the greater number of atoms needing displacement. Consequently, effective reconfiguration is primarily observable in exceedingly thin samples, such as those prepared for TEM, or only in the near-surface area of bulk sample where the V_O channels are not aligned towards the largest exposed surface.

We note that, as the phase transformation proceeds, the SrFeO₂/SrFeO_2.5 phase boundary moves downwards from the film surface, transforming the volume of the SrFeO_2.5 film swept by the phase boundary into SrFeO₂, leaving no residual SrFeO_2.5 phase in its wake. The released oxygen moves through the V_O channels and eventually escapes into the vacuum at the (010) edge of the film. Therefore, in this specific TEM sample scenario, the released oxygen is directly transported to the vacuum via the V_O channels without passing through SrFeO₂ phase. However, in the transformation of bulk SrFeO_2.5, oxygen diffusion through the SrFeO₂ phase probably plays a critical role. If this step is slow and becomes rate limiting, it might compete with the thermal decomposition process.

As a control experiment to investigate the effects of TEM specimen thickness on the oxygen deintercalation topotactic transition, we prepared thicker TEM samples with thickness of ~20 nm and ~180 nm. The rate of transformation to SrFeO₂ via oxygen deintercalation depends critically on the sample thickness. For the TEM specimen with a thickness of ~20 nm (Supplementary Fig. 4), the reversible transformation completes within 5 min in a heating–cooling cycle between 450 °C and 20 °C. However, reversibility diminishes with increasing TEM specimen thickness, and thermodynamics comes into play. For the ~180-nm-thick TEM specimen (Supplementary Fig. 7), the transformation from SrFeO_2.5 to SrFeO₂ was slower and more prolonged. Additionally, we observed the formation of a Fe-rich (Sr-deficient) phase on the film surface, indicating decomposition of the SrFeO_2.5 or SrFeO₂ ternary oxide into Fe–O and Sr–O binary oxides, with SrO being volatile; therefore, the chemical composition deviates from exact stoichiometry (due to the preferential loss of strontium). Intriguingly, the SrFeO₂ phase persisted without reverting to SrFeO_2.5 even after extended post-cooling air exposure at room temperature. This behaviour aligns with previous studies using micrometre-sized powder samples, presenting challenges in synthesizing a single phase SrFeO₂ through thermal reduction; such attempts either lead to the loss of reversibility or generate byproducts. Despite these challenges, our findings offer a novel avenue for achieving reversible phase transformation in infinite-layer transition metal oxides, potentially in ultrathin membrane forms. Further, it excludes the potential incorporation of hydrogen, which has been speculated as a mechanism that stabilizes metastable infinite-layer phase³².

As seen in the light-element sensitive iDPC-STEM image in Extended Data Fig. 3, no signature indicative of hydrogen incorporation was observed at the apical oxygen sites of the resulting SrFeO₂ phase. As a comparison, the hydride reduction process, involving hydrogen ions reacting with oxygen ions to form H₂O (ref. ³³) or metallic hydroxide¹³, probably operates via a different atomic-scale mechanism than what we observed in this study. The hydrogen intercalation into the brownmillerite lattice destabilizes and extracts lattice oxygen during annealing, significantly impacting the energetics of diffusion pathways³³. However, the reduction process, operating at low temperature, inherently involves oxygen ion conduction across an energy barrier within the brownmillerite lattice, controlled by reaction kinetics. Consequently, despite these differences, the kinetic pathway for oxygen conduction may still bear similarities.

HRTEM image simulations

The HRTEM image simulation was performed by using the abTEM Python package³⁴ working with a multi-slice algorithm. The NCSI imaging condition used for the simulation is as follows: accelerating voltage 300 kV, spherical aberration coefficient C_s = −13 μm, chromatical aberration coefficient C_c = 1.6 mm, defocus Δf = 6.2 nm, convergence angle α = 0.5 mrad and focus spread Δf_s = 2.4 nm. All simulated images have been calibrated by the modulation transfer function of the CCD camera (OneView, Gatan), which is the major factor causing the Stobbs-factor problem on simulated and experimental image matching³⁵.

To determine the thickness of the TEM specimen used for NCSI HRTEM imaging, image simulation was carried out for SrFeO_2.5 structure as a function of sample thickness (Supplementary Figs. 5 and 6). As a quantitative evaluation, the cross-correlation factor (XCF) was calculated for each simulated and experimental image. An XCF of ‘1’ indicates a perfect match. Judging from both the image contrast and the XCF value, the sample thickness of 10-unit-cell (5.6 nm) yields the best match with the experimental image as shown in Supplementary Fig. 5. Once the sample thickness was determined, the image simulation was conducted for various transient states predicted by DFT calculations using the same simulation setup.

Theoretical calculations

All calculations were performed using DFT with the plane-wave-based Vienna Ab initio Simulation Package (VASP)^36,37,38. For the exchange-correlation function, the revised Perdew, Burke and Ernzerhof generalized gradient approximation (PBEsol) is adapted³⁹. We used the projector-augmented wave potentials that include ten valence electrons for strontium (4s², 4p⁶ and 5s²), eight for iron (3d⁷ and 4s¹) and six for oxygen (2s² and 2p⁴)⁴⁰.

To investigate the dynamics of ions, we designed 1 × 2 × 6 SrFeO_2.5 supercell. Energy barriers for the atomic shuffling and phase transformation to SrFeO₂ were computed using the nudged elastic band method, implemented in the VASP code⁴¹. A plane-wave cut-off energy of 500 eV with a Monkhorst–Pack grid with 6 × 6 × 6 and 2 × 2 × 2 k-point meshes were used for the structural relaxations and supercell calculations, respectively⁴². We applied the onsite Hubbard U correction of 5 eV using the Dudarev formalism for the correlated iron d electrons⁴³. We considered the G-type antiferromagnetic collinear spin ordering on the iron ions. All calculations were converged in energy to 10⁻⁵ eV per unit cell, and the structures were fully optimized with the force convergence of 10⁻¹ eV Å⁻¹.

Using the calculated energy for each shuffle step during the 90° reconfiguration of SrFeO_2.5, we estimated the relative probability of observing each step (Extended Data Fig. 8a) given by Boltzmann distribution⁴⁴

$${P}_{i}=\exp\left[\frac{-{E}_{i}}{{k}_{{\mathrm{B}}}T}\right],$$

(1)

where P_i is the relative probability of observing step i, T is the temperature, k_B is the Boltzmann constant and E_i is the enthalpy in each step. Relatively higher observation possibility can be recognized at the locations between configuration (6) and (7). We then carried out HRTEM image simulation for each configuration (Extended Data Fig. 8b) and cross-correlated them with all experimental HRTEM frame images from the in situ video (Supplementary Video 5) during the reconfiguration to find out the most likely configuration for each frame by estimating the XCF value.

The V_O formation energy (${E}_{{{\mathrm{vac}}}}^{\;f}$) was calculated using

$${E}_{{\;{\mathrm{vac}}}}^{f}={E}_{{{\mathrm{defective}}}}-{E}_{{{\mathrm{perfect}}}}+\frac{1}{2}{E}_{{{\mathrm{O}}}_{2}},$$

(2)

where E_defective is the energy of a structure with one V_O, E_perfect is the energy of the perfect crystal structure and ${E}_{{{\mathrm{O}}}_{2}}$ is the energy of an oxygen molecule in the gas phase. The calculated V_O formation energy has been compared with other oxides and summarized in Supplementary Table 2.

To investigate the effect of the structural phase transformation on the electronic and magnetic properties, we calculated the DOS at each reaction coordinate along the pathway from (1) to (3) shown in Fig. 4e. This analysis segmented the atomic model for each stage into three zones: SrFeO₂, SrFeO₂/SrFeO_2.5 phase boundary and SrFeO_2.5 (Supplementary Fig. 8). For these zones, the DOS calculations were performed at each stage. The results, detailed in Supplementary Figs. 9–12, reveal that only the SrFeO₂/SrFeO_2.5 phase boundary exhibits minor ferromagnetic metallic characteristics. In contrast, the regions of SrFeO₂ and SrFeO_2.5 predominantly exhibit G-type antiferromagnetic insulating properties, with the exception of tiny mid-gap states. Additionally, the DOS calculations indicate the persistence of G-type antiferromagnetic insulating properties throughout the atomic shuffling displacement leading to the 90° reconfiguration of V_O channels (Supplementary Fig. 13).

To obtain EELS O-K edge spectra of SrFeO_2.5 and SrFeO₂, the dielectric function was calculated using the supercell core-hole method. The following imaginary part of the dielectric function (${\epsilon }_{\alpha \beta }^{\left(2\right)}\left(\omega \right)$) in the long wavelength limit (q = 0) is used for calculating the loss spectrum:

$${\epsilon }_{\alpha \beta }^{\left(2\right)}\left(\omega \right)=\frac{4{\uppi }^{2}{{\mathrm{e}}}^{2}{{{\hslash }}}^{4}}{\varOmega {\omega }^{2}{m}_{{\mathrm{e}}}^{2}}\mathop{\sum }\limits_{c,k}2{\omega }_{k}\delta \left({\varepsilon }_{{{{ck}}}}-{\varepsilon }_{{{\mathrm{core}}}}-\omega \right)\times {M}_{\alpha }^{{\;{\mathrm{core}}}\to {{{ck}}}}{M}_{\beta }^{{\;{\mathrm{core}}}\to {{{ck}}}* }$$

(3)

$$I\left(\omega \right)\propto {{\omega }^{2}\left({\epsilon }_{11}^{\left(2\right)}\left(\omega \right)+{\epsilon }_{22}^{\left(2\right)}\left(\omega \right)\right)}^{0.5},$$

(4)

where $\varOmega ,\,\varepsilon$ and $M$ denote the unit cell volume, the orbital energies and the momentum matrix elements, respectively. $\alpha$ and $\beta$ denote the Cartesian indices of dielectric tensor. ω denotes the fequency, m_e, denotes the mass of electron, ẟ is the delta function, ħ is the reduced Planck’s constant, c is the speed of light and k is the wave vector. Here, we only consider in-plane components of the dielectric tensor due to the sample geometry of TEM sample. We applied a constant Gaussian broadening of 0.6 eV to the simulated EELS data to replicate the experimental data.