Pressure tuning of charge ordering in iron oxide

A Verwey-type charge-ordering transition in magnetite at 120 K leads to the formation of linear units of three iron ions with one shared electron, called trimerons. The recently-discovered iron pentoxide (Fe4O5) comprising mixed-valent iron cations at octahedral chains, demonstrates another unusual charge-ordering transition at 150 K involving competing formation of iron trimerons and dimerons. Here, we experimentally show that applied pressure can tune the charge-ordering pattern in Fe4O5 and strongly affect the ordering temperature. We report two charge-ordered phases, the first of which may comprise both dimeron and trimeron units, whereas, the second exhibits an overall dimerization involving both the octahedral and trigonal-prismatic chains of iron in the crystal structure. We link the dramatic change in the charge-ordering pattern in the second phase to redistribution of electrons between the octahedral and prismatic iron chains, and propose that the average oxidation state of the iron cations can pre-determine a charge-ordering pattern.


Results
Phase III and two options for its crystal structure. In all experiments, we start from normal conditions (Fe 4 O 5 -I phase) (Figs. 1a and 2) and gradually decrease the temperature in the cryostat. At about 200 K and 2 GPa, we observe the appearance of weak and blurred superlattice reflections, indicating the emergence of scattered fragments of a charge-ordering pattern (Fig. 3b). With further temperature decrease and pressure increase, these reflections become progressively stronger and clearer (Fig. 3c). We verify that these reflections do not belong to the earlier-reported charge-ordered Fe 4 O 5 -II phase 32 , and label this phase as Fe 4 O 5 -III. Meanwhile, the presence of Fe 4 O 5 -II is noticeable at 5-7 GPa at the lowest temperature point of 30 K (Fig. 2). Upon heating at about 18 GPa, we can follow the superlattice reflections of Fe 4 O 5 -III up to at least 270 K (Fig. 2). Thus, pressure strongly enhances the temperature of the chargeordering transition, compared to 150 K at ambient pressure 32 . We can index the single-crystal diffraction patterns of Fe 4 O 5 -III in either orthorhombic or monoclinic unit cells (Fig. 3d). Eventually, we determine two candidate crystal structures, namely, Fe 4 O 5 -IIIa with a monoclinic C2/m lattice (Fig. 4) and Fe 4 O 5 -III-b with an orthorhombic C222 1 unit cell (Fig. 5), which can equally well fit the experimental X-ray diffraction patterns (Table 1 and  Supplementary Table 1 32 , could result from a lattice instability related to competition between the Fe 4 O 5 -III-a and Fe 4 O 5 -III-b phases. A similar type of incommensurability was observed, for example, in the spin-Peierls compound, TiPO 4 34,35 . In magnetite, the formation of iron trimers in its chargeordered phase is perfectly traced by anomalous shortening of some Fe-Fe distances as found by single crystal X-ray diffraction method 4 ; hence we also apply this approach to Fe 4  Fe-Fe distances. For example, at 11.7 GPa and 180 K, the Fe-Fe distances in the prismatic chains of the Fe 4 O 5 -III-a structure show a periodicity consisting of one 2.8143 Å and two 2.8176 Å distances; since these two values are very similar, we cannot draw any conclusions about the formation of coupled units in these chains. Compared to the average Fe-Fe distance of~2.8165 Å along the same crystallographic direction (b-axis), the distances between two neighboring octahedrally-coordinated Fe2_2 atoms in the single chains of Fe2 octahedra are reduced, to 2.6597 Å, and likewise those between Fe3_4 atoms in the double chains of Fe3 octahedra are reduced to 2.7279 Å (Supplementary Table 2). These dramatic shortenings in the distances suggest the formation of dimers (Fig. 4a, c). In the other octahedral chains of this Fe 4 O 5 -III-a phase, equal contractions in two neighboring Fe-Fe distances indicate the formation of trimers.
The Fe 4 O 5 -III-b structure exhibits similar features. Its prismatic iron chains show a periodicity in the Fe-Fe bond lengths consisting of one 2.8118 Å and two 2.8189 Å distances, where the difference between the two is too small to allow any conclusions about the formation of any bonded units (Fig. 5). In contrast to Fe 4 O 5 -III-a, the Fe 4 O 5 -III-b structure does not contain any trimers (Fig. 5). Both octahedral chains of the Fe 4 O 5 -III-b structure exhibit only dimers with a Fe-Fe bond length of 2.6777 Å in the single chains of Fe2 octahedra, and 2.7387 Å in the double-chains of Fe3 octahedra (Supplementary Table 2). Both Fe 4 O 5 -III-a and Fe 4 O 5 -III-b crystal structures show a strong rapprochement between free Fe3 atoms (Fe3_3 in phase III-a and Fe3_2 in phase III-b, which are unincorporated into the dimer and trimer units) and the neighboring Fe1 atoms in the prisms, which are connected to these Fe3 octahedra via one shared edge (these Fe3-Fe1 pairs are highlighted as white dashed ellipsoids in Figs. 4d and 5d).   The Fe-Fe distances in these Fe3-Fe1 pairs become nearly the same as the average Fe-Fe distances in both prismatic and octahedral chains (Supplementary Table 2), thereby suggesting an enhancement of interactions between the iron ions occupying the prisms and octahedra.
We analyze the Fe-O bond lengths of all iron cations in both Fe 4 O 5 -III structures using a common bond valence sum (BVS) method (see Experimental Details) 36 . We estimate the average BVS values of the Fe1 atoms sitting in the prisms as +2.11 and +2.13 in Fe 4 O 5 -III-a and Fe 4 O 5 -III-b structures, respectively. The BVS analysis suggests that the dimers formed at the double chains of Fe3 octahedra of both structures consist of moderately overcharged valence-mixed Fe 2.5+ ions; whereas, the dimers formed at the single-chain Fe2 octahedra have a charge as high as +5. 4 (Figs. 4 and 5). Likewise, this analysis shows that, compared to a combination of one Fe 2+ and two Fe 3+ ions, the trimers in the Fe 4 O 5 -III-a structure are either strongly overcharged (+8.29 for the single chains of Fe2 octahedra) or strongly undercharged (+7.57 for the double chains of Fe3 octahedra) (Fig. 4).
Phase IV and charge ordering in chains of trigonal prisms. In all three experimental runs at pressures above 12 GPa and temperatures below 150 K, we observe the appearance of additional structural reflections ( Supplementary Fig. 1), suggesting the beginning of another transition to a further phase, labeled as Fe 4 O 5 -IV (Fig. 2). Below 150 K this transition is nearly complete at 25 GPa, but at slightly higher temperature (200 K), minor traces of Fe 4 O 5 -III are still observable even at 36 GPa (Fig. 2). Upon heating to room temperature at 36 GPa, Fe 4 O 5 -IV gradually transforms to the original Fe 4 O 5 -I phase; meanwhile, a noticeable fraction of Fe 4 O 5 -IV persists even at 293 K (Fig. 2).
The single crystal X-ray diffraction images of Fe 4 O 5 collected at 25.2 GPa and 120 K correspond to almost pure Fe 4 O 5 -IV ( Supplementary Fig. 1), and we determine its monoclinic P2 1 /m symmetry and atomic positions. The structure shows an overall dimerization along the c-axis involving both octahedral and prismatic chains (Fig. 6). We calculate BVS values of the iron ions in this structure using the above method 36 , and find an average value for the prismatic Fe1 atoms of +2.26. This value deviates from +2 established for these prismatic sites in the original Fe 4 O 5 -I phase 12,32 , and taking into account the emergence of dimeric ordering in these chains, we conclude that the prismatic sites in Fe 4 O 5 -IV are filled with mixed-valent iron cations. In the same way, the average BVS values of the iron in the single chains of Fe2 and double chains of Fe3 octahedra in Fe 4 O 5 -IV are found as +2.63 and +2.554, respectively (Fig. 6). These values are also consistent with the dimeric ordering in the chains. These BVS results indicate that Fe 4   the dimerization direction. This leads to a lattice volume collapse by about 0.5% at 120 K (Fig. 7a). This volume collapse may be attributed to a more homogeneous charge distribution in the Fe 4 O 5 -IV phase, which should lead to a volume contraction. By fitting the third-order Birch-Murnaghan equation of state 37,38 to the compression data of the Fe 4 O 5 -III phase at 120 K (Fig. 7a) (2) 12.328 (7) 12.328 (7) 5.4282 (4)   The electron transfer from the prisms to octahedra leads to a short-range reorganization of ordering type equal to +2.554, i.e., nearly optimal for the formation of Fe 2+ -Fe 3+ pairs. In contrast, the longest dimers are formed in Fe1 prismatic chains with an average BVS value of +2.26, which deviates the most from +2.5. Furthermore, we note that the above d units FeÀFe =d gap FeÀFe ratios increase linearly with a deviation of their average BVS values from +2.5, tending to 1 for the limiting case of Fe 2+ or Fe 3+ (Fig. 7c). This regularity indicates that the resulting length of the dimers is determined by the balance of Fe 2+ and Fe 3+ cations in each linear chain.
The reduced distances between the free Fe3 atoms in the doublechains of Fe3 octahedra and the neighboring Fe1 atoms in the prisms, observed in both Fe 4 O 5 -III-a and Fe 4 O 5 -III-b structures (highlighted as dashed ellipsoids in Figs. 4d and 5d), appear to be the most suitable channels for hopping of electrons from Fe 2+ ions occupying Fe1 prisms to the octahedral matrix. Only 1/3 of the Fe1 atoms are involved in these channels, and hence, if the electrons of prismatically-coordinated Fe 2+ ions are not delocalized within the framework of these trigonal prismatic chains, the Fe1 atoms may be maximally charged up to +2.33 on average. The actual BVS values of the two Fe1 atoms are +2.23 and +2.29 (Fig. 6), which satisfy this constraint well. The coexistence of Fe 4 O 5 -III and Fe 4 O 5 -IV phases over an extended pressure range (Fig. 2) suggests that this phase transition is rather prolonged. Likely, it is caused by the gradual pressure-driven electron transfer from the trigonal prismatic chains to the octahedral ones. The Fe 4 O 5 -III-b structure comprises only dimers; hence having free iron cations in all Fe3 chains provides twice as many channels for the charge hopping compared to the Fe 4 O 5 -III-a structure.
As mentioned above, we observe that a noticeable fraction of the Fe 4 O 5 -IV phase persists upon heating to 293 K at 35 GPa (Fig. 2). To examine the possibility of the room-temperature phase transition Fe 4 O 5 -I → Fe 4 O 5 -IV, we compress a single crystal of Fe 4 O 5 in a separate experiment to about 45 GPa, but we see no evidence for a phase transition. Previous works also did not find any structural phase transition in this range 12,39 . At the maximum pressure of 45 GPa, we laser-heat the sample up to 2000°C, and indeed we observe a structural transition to the same dimerized Fe 4 O 5 -IV structure (Fig. 2, Table 1 (Fig. 7c), and hence a distribution of Fe 2+ and Fe 3+ ions at least at the octahedral sites of Fe 4 O 5 -IV (HT) is more random than ordered. It can be that the transition mechanism at high temperature is different, and the dimerization observed could instead result from a Peierls transition 40 rather than from the formation of electrically-bonded Fe 2+ -Fe 3+ dimers with a shared electron. together with the overall structural dimerization including these Fe1 chains, unambiguously confirm the mixed-valent nature of the iron ions at the prismatic sites in this structure. The minor deviations of the BVS values from +2 for Fe1 atoms in the Fe 4 O 5 -III-a and Fe 4 O 5 -III-b phases do not allow us either to conclude a small shift in the oxidation state of these ions toward +3 or to rule that out. The co-existence of Fe 4 O 5 -III and Fe 4 O 5 -IV phases for an extended pressure range (Fig. 2) hints that this transition may follow the electron transfer between the octahedral and prismatic chains. This leads to a short-order reorganization of the charge-ordering pattern and the formation of inclusions of the novel structural order. Comparing the different charge-ordered patterns in Fe 4 O 5 -II 32 , Fe 4 O 5 -III-a, Fe 4 O 5 -III-b, and Fe 4 O 5 -IV (Figs. 4-6), we conclude that the average oxidation state of octahedrally-coordinated cations predetermines which ordering type would be optimal. For example, in order to form short trimers, the average oxidation state of iron should be~+2.7 (Fig. 7c). A moderate decrease in this BVS value leads to the formation of more loosely-bonded long trimers and dimers. For BVS values tending toward +2.5, a closely-packed dimeric order becomes preferable (Fig. 6). Thus, the average oxidation state of iron ions at the octahedral chains apparently pre-determines an optimal charge-ordering scheme. One can expect, for example in the newly-discovered Fe 7 O 9 and Fe 5 O 6 crystallizing in similar structures 14,22 , that the former with a nominal oxidation state of the octahedral ions of +2.8 at ambient pressure is prone to the formation of exclusively trimers; likewise, the latter in which their oxidation state is +2.5 is prone to dimer formation only. A pressure-stimulated electron transfer from the prismatic to octahedral chains can occur inhomogeneously in the bulk of the Fe 4 O 5 crystal and this can result in the formation of an anomalous charge-ordering pattern combining different co-existing ordering schemes (Fig. 7d).
The process of electron transfer in Fe 4 O 5 from the trigonal prismatic to the octahedral iron chains towards charge equalization is perhaps not complete by 40 GPa, and with further pressurization the average BVS values of all iron cations can probably approach +2.5 even more closely. However, this could hardly change the dimeric charge-ordering pattern of Fe 4 O 5 -IV (Fig. 6), unless the material was to become metallic and the charge-ordering state suppressed; although the lattice symmetry may be sensitive to the charge balance. We propose that such electron transfer processes under pressure could also occur in other iron oxides crystallizing in kindred lattices, like the abovementioned Fe 5 O 6 14 and Fe 7 O 9 22 . However, for the ambientpressure cubic spinel phase of magnetite with inverse electronic configuration in which tetrahedral sites are filled by Fe 3+ ions and hence are already maximally charged, the possibility of an opposite electron transfer under pressure, from tetrahedral sites to the octahedral network has been suggested 41 . However, this conjecture was not in line with earlier work 42 , and was not confirmed in subsequent studies [43][44][45][46] . It was established for magnetite that its charge-ordered phase may be suppressed by applied pressure of about 8 GPa 47,48 . Thus, the behavior of Fe 4 O 5 is remarkably different from that of magnetite and demonstrates new perspectives for charge-ordered states in iron-rich oxides. At the moment, we cannot unambiguously ascertain the driving forces of the phase transitions observed in Fe 4 O 5 both at ambient and high pressures. In previous work investigating the Verwey transition in magnetite, it was determined that the intersite Coulomb interactions between the 3d electrons of the Fe ions alone, as well as phonon-driven lattice instability, could hardly stimulate this transition 49,50 . A more complex scenario, however, in which the strong electron correlations enhance the electron-phonon interactions and simultaneously reduce the mobility of the minority-spin t 2g electrons of Fe 2+ ions, increasing their tendency towards localization, could be an indication that electron-phonon interactions may be a driving force of the Verwey transition 49,50 . The phase transitions in Fe 4 O 5 could have similar or even more complex scenarios involving the charge, lattice, spin, and orbital degrees of freedom.
Mössbauer spectroscopy of Fe 4 O 5 at low temperature under high pressure. At ambient conditions, the Mössbauer spectra of Fe 4 O 5 can be well fitted by the superposition of a magnetic sextet and a paramagnetic doublet with relative areas of 80(2)% and 20 (2)%, respectively (Fig. 8c). The presence of the sextet component indicates the existence of magnetic order at room temperature. In the Fe 4 O 5 crystal, 25% of iron cations occupy the trigonal prisms, and 75% have octahedral coordination (Fig. 1a). Hence, we can assign the doublet to prismatic Fe1 atoms, and likewise the sextet to octahedral Fe2 and Fe3 atoms. We determine the hyperfine parameters of these components. For example, for the spectrum collected at 295 K and 2.1 GPa, we determine the center shift of the doublet to be δ CS = 1.125(12) mm/s and the quadrupole splitting to be Δ = 1.93(2) mm/s. For the sextet, we find the center shift to be δ CS = 0.568(15) mm/s, the quadrupole shift to be ε = 0.21(1) mm/s, and the hyperfine magnetic field to be H hf = 24.96 (13) T. The center shift of the Mössbauer spectral components depends primarily on the oxidation state of iron in a linear-like manner. We compare these center shifts with those reported for other iron oxides, e.g., δ CS = 0.36 mm/s for octahedral Fe 3+ ions in hematite (α-Fe 2 O 3 ) 51 and δ CS = 0.67 mm/s for octahedral mixed-valent Fe 2.5+ ions in magnetite 51 . The linear trend based on these data suggests that octahedrally-coordinated Fe 2+ ions should exhibit center shifts around δ CS = 0.98 mm/s; likewise the above-determined value of δ CS = 0.568 mm/s for the magnetic sextet in Fe 4 O 5 should correspond to an oxidation state of Fe 2.67+ , in excellent agreement with the BVS results (Fig. 1a). The large value of δ CS = 1.125(12) mm/s for the Fe1 doublet unambiguously corresponds to Fe 2+ , in line with both BVS estimations (Fig. 1a) and earlier data for ferrous-iron compounds 51 .
We note that the line widths of the sextet are roughly twice as large as those of the doublet (1.1 vs 0.5 mm/s) (Fig. 8c). This broadening results from electron exchange between the Fe 2+ and Fe 3+ cations occupying the octahedral sites; a similar effect was also observed in magnetite 52 . Upon cooling, the doublet component loses intensity and completely disappears around 150 K (Fig. 8b). Hence, Fe1 atoms occupying the oxygen prisms become magnetically ordered, and their contribution to the spectra largely overlaps with the stronger signal of Fe2 and Fe3 atoms. The Mössbauer spectra demonstrate a pronounced broadening around 150 K (Fig. 8b), where a charge ordering in Fe 4 O 5 was observed 32 .
For magnetite, it has been documented that charge ordering below the Verwey transition at 120 K leads to the appearance of many closely-overlapping magnetic sextets which can be resolved only under special conditions, such as single-crystal measurements in magnetic fields 52,53 . Here, we collect spectra from a polycrystalline Fe 4 O 5 sample and, together with other factors like potential phase co-existence (Fig. 2), this impedes an unambiguous fitting of the Mössbauer spectra at low temperatures. A simple single-sextet analysis of the spectra shows that the quadrupole shift has a discontinuity in its temperature dependence between 150 and 100 K (Supplementary Figure 2b and Supplementary Table 5). This feature is likely linked to changes in the magnetic properties (kink in inverse magnetic susceptibility in Fig. 7a).
The Mössbauer spectra collected in the charge-ordered states appear to be a superposition of several sextets. For instance, the spectrum acquired at 20 K and 2.6 GPa, i.e., in the stability region of the incommensurately-modulated Fe 4 O 5 -II phase with an infinite number of different environments for iron (Fig. 2), can be reasonably well described by three sextets (Fig. 8c). The center shifts of these sextets are about 0.6-0.85 mm/s, i.e., between δ CS = 0.36 mm/s for Fe 3+ ions in hematite 51 and 0.98 mm/s estimated above for octahedral Fe 2+ atoms, but at the same time quite far from both. We therefore conclude that in the charge-ordered phases of Fe 4 O 5 , the oxidation states of the octahedrally-coordinated iron did not split into Fe 2+ and Fe 3+ components, and hence, these ions are characterized by stable non-integer oxidation states. This finding is in line with the earlier conjecture 4,32 that the minority-spin t 2g electron of Fe 2+ ions is shared between all ions involved in the formation of either trimers or dimers.
We do not observe any noticeable changes in the spectra with pressure up to 8 GPa at low temperatures. This fact indicates that Fe 4 O 5 -II and Fe 4 O 5 -III charge-ordered phases are not readily distinguishable by Mössbauer spectroscopy (Figs. 2 and 8c). With further compression to 16.3 GPa across the beginning of the Fe 4 O 5 -III → Fe 4 O 5 -IV transition (Fig. 2), the hyperfine field distribution changes to an apparent bimodal form (Supplementary Figure 2c). We fit these spectra by a superposition of two sextets (Fig. 8c), and for example, at 11.3 GPa and 20 K in Fe 4 O 5 -III phase, their center shifts are δ CS = 0.66(3) and 0.82 (3) mm/s. Taking into account the second-order Doppler shift (we use the value of 0.11 mm/s for hematite) 54 and disregarding a possible pressure correction for the δ CS values, we estimate the average oxidation states of iron linked to the green and purple sextets to be +2.7 and +2.45, respectively (Fig. 8c). Therefore, this case also unambiguously demonstrates that the oxidation states of the octahedrally-coordinated iron in Fe 4 O 5 do not split into integer Fe 2+ and Fe 3+ components, even at 20 K. These +2.7 and +2.45 values correspond well to the average BVS values for the iron cations occupying the single chains of Fe2 and double chains of Fe3 octahedra, respectively (Figs. 4 and 5).
Magnetic properties of Fe 4 O 5 . The magnetization data for Fe 4 O 5 collected at ambient pressure (Fig. 8a) are similar to those reported earlier 32 , but show slightly smaller absolute values of susceptibility. In this work, we carry out measurements on several single crystals of Fe 4 O 5 , and likely, this discrepancy may be related to a minor ferromagnetic impurity which can potentially be present in the large polycrystalline sample examined earlier 32 . There are two main features of the magnetization data: (i) the transformation between canted and collinear magnetic ordering (around 90 K at ambient pressure), and (ii) charge ordering that manifests itself by a kink in the 1/χ curve (around 150 K at ambient pressure) (Fig. 8a). Both features are observed up to 1.83 GPa, the maximum pressure of our measurement, and shift toward higher temperature upon compression. The size of the canted moment increases abruptly, with a large change between 0.66 and 0.90 GPa and weak changes below or above this range. Given the observation of the Fe 4 O 5 -III phase at 200 K and 2 GPa (Fig. 2), we conclude that our magnetization data extend well into its stability range, and hence, this abrupt change in the moment likely results from the phase transformation. Moreover, the kink in the 1/χ curves shifts to higher temperatures (Fig. 8a) The magnetization data reveal close similarities between Fe 4 O 5 -II and Fe 4 O 5 -III. Both support the formation of a canted state at low temperatures. Moreover, both charge-ordered phases emerge from the same collinear magnetic order that sets in around 320 K at ambient pressure 32 . As seen from the Mössbauer spectra (Fig. 8b), the initial magnetic ordering remains above room temperature at these pressures. As established earlier 32 , a ferromagnetic spin alignment along the a-direction (in the coordinate framework of Fe 4 O 5 -I) is essential for the formation of dimers and trimers in the charge-ordered state 32 , and hence magnetic ordering is a key prerequisite of the charge ordering. The same type of magnetic order would even support dimer formation in Fe 4 O 5 -IV. This demonstrates that this magnetic ordering can produce different charge-ordered states in a single structural framework.
Conclusions. We determined the low-temperature high-pressure phase diagram of Fe 4 O 5 using single crystal X-ray diffraction and Mössbauer spectroscopy and by measurement of magnetic properties. We found two novel crystal structures of Fe 4 O 5 and observed the extended regions of their co-existence in the phase diagram. A dramatic change in the charge-ordering pattern in the second high-pressure phase was attributed to electron hopping from the octahedral to the prismatic iron chains. We propose that the average oxidation state of the iron cations in oxides of this family can pre-determine a charge-ordering pattern. Thus, Fe 4 O 5 demonstrates that the charge-ordering pattern can be changed by applied pressure or stress, and two or more charge-ordered phases can co-exist with each other inside one single crystal. Our work highlights the complexity of charge-ordering processes in iron-based and other transition metal oxides, but simultaneously it suggests a clue to these phenomena.    56,57 . The procedure was similar to that described in previous work 58,59 . The chemical composition of the samples was verified by means of scanning electron microscopy (SEM) using a LEO-1530 instrument and by microprobe analysis using a JEOL JXA-8200 electron microscope. The crystal structure of the samples was determined by means of single crystal and powder X-ray diffraction using a highbrilliance Rigaku diffractometer (Mo K α radiation, λ = 0.7108 Å).

Methods
Single crystal X-ray diffraction under pressure. We selected high-quality single crystals of Fe 4 O 5 and loaded them into symmetric membrane diamond anvil cells (DACs) equipped with Boehler-Almax diamonds that enabled X-ray diffraction images to be collected over the widest range of angles. We employed three DACs with diamond anvil culet sizes of 400 and 300 µm. Together with the sample in the same cell, we loaded a ruby sphere and a chip of gold that was used for pressure determination (Fig. 2). An additional ruby sphere was placed on the outer surface of one diamond anvil to monitor the reference of its R 1 line at low temperature and ambient pressure. All of the DACs were filled with Ne pressure-transmitting medium. In total, we carried out three high-pressure single crystal X-ray diffraction experiments. The first one served as an initial scanning of the low-temperature phase diagram of Fe 4 O 5 , and it was performed at the ID27 beamline of the European Synchrotron Radiation Facility (ESRF, Grenoble, France) with a wavelength of λ = 0.3738 Å. The second and third runs involved more detailed investigations, and they were accomplished in a cold-finger He cryostat on the P02.2 beamline at the Deutsches Elektronen-Synchrotron (DESY, Hamburg, Germany) using a wavelength of λ = 0.2887 Å 60 . Additionally, we carried out a room temperature compression experiment with laser heating at high pressures on beamline ID09a at ESRF (λ = 0.41513 Å). At each (P,T) point on the phase diagram, we acquired single-crystal X-ray diffraction images upon continuous rotation of the cell with the sample around the vertical ω-axis with a step of Δω = 0.5°and an exposure time of t = 0.5 s/frame. The diffraction data were collected by a Perkin Elmer XRD1621 detector. We analyzed these data with CrysAlisPro software, and solved the crystal structures using JANA2006 software 61 . We analyze the Fe-O bond lengths of all iron cations in the different crystal structures of Fe 4 O 5 using a common BVS method 36 . In this method, a bond valence is determined as (S ij = exp[(R ij − d ij )/b 0 ], where d ij is the distance between atoms i and j, R ij is the bond valence parameter (empirically determined distance for this cation-anion pair), and b 0 is an empirical parameter about 0.37 Å), and then, a BVS value of a cation is determined as a sum of individual bond valences V i ¼ P j s ij 36 . In these calculations, we used b 0 =0.37 Å and the bond-valence parameters R ij determined at ambient conditions for Fe 2+ -O and Fe 3+ -O bonds as 1.734 and 1.759 Å, respectively 36 . Using literature data from the equation of state of hematite (α-Fe 2 O 3 ) determined from single crystal X-ray diffraction experiments up to 25 GPa 62 , we estimated a pressure dependence of the bond-parameter R ij for the Fe 3+ -O bonds, and applied these values in the BVS estimations as well. Since the total cation charge in the formula unit (+10) should be conserved at all pressures and temperatures, the calculated nominal BVS values were accordingly renormalized to meet this requirement. After performing these procedures, the calculations using different starting R ij values gave identical results within experimental uncertainty.
Mössbauer spectroscopy under pressure. For Mössbauer spectroscopic examination over a wide pressure-temperature range, we synthesized a polycrystalline sample of 20% 57 Fe-enriched Fe 4 O 5 . We also utilized a membrane DAC with diamond anvil culet sizes of 400 µm. The DAC was fixed inside a cryostat. We collected synchrotron Mössbauer source (SMS) 63 spectra on the Nuclear Resonance beamline ID18 at ESRF 64 . The SMS is based on a nuclear resonant monochromator employing pure nuclear reflections of an iron borate ( 57 FeBO 3 ) crystal. The source provides 57 Fe resonant radiation at 14.4 keV within a bandwidth of 15 neV, which is tunable in energy over a range of~±0.6 meV 63 . The beam of gamma-radiation emitted by the SMS was focused to a 10 × 15 µm 2 spot size. The velocity scale was calibrated relative to a natural α-Fe foil of 25 μm thickness. The center shift values are given relative to α-Fe. We monitored the width and the absolute position of the isomer shift of the source line before and after each measurement using a K 2 Mg 57 Fe(CN) 6 reference single line absorber.
Magnetic measurements under pressure. The bulk magnetization measurements under hydrostatic pressure 65,66 were performed in a CuBe pressure cell placed inside a Quantum Design MPMS 5S SQUID magnetometer. Daphne 7373 oil was used as a pressure-transmitting medium. One small piece of lead (~0.1 mg) was placed together with the sample inside the pressure cell, while another piece (~0.1 mg) was placed outside the pressure cell. Under pressure, the superconducting transition temperature of the inner piece decreases. The difference between the superconducting transition temperatures of the two lead samples determines the pressure value inside the pressure cell at low temperatures. Several small single crystals of Fe 4 O 5 with a total mass of~0.6 mg were placed into a gasket of the pressure cell along with the aforementioned piece of lead. The empty cell background data was subtracted 65 using an automatic background subtraction (ABS) procedure. Field-cooling measurements of the lead and Fe 4 O 5 samples were performed in fields of 2 mT and 0.5 T, respectively, from 300 K down to 4 K.

Data availability
The X-ray crystallographic information files (CIFs) for structures that support the findings of this study have been deposited at the Inorganic Crystal Structure Database (ICSD) with accession codes 434152, 434153, 434154, 434155, and 434156 (http://www2. fiz-karlsruhe.de/icsd_home.html). The authors declare that all other data supporting the findings of this study are available within the article and Supplementary Information files, and also are available from the corresponding author upon reasonable request.