Site-selective doping of ordered charge states in magnetite

Charge ordering creates a spontaneous array of differently charged ions and is associated with electronic phenomena such as superconductivity, colossal magnetoresistances (CMR), and multiferroicity. Charge orders are usually suppressed by chemical doping and site selective doping of a charge ordered array has not previously been demonstrated. Here we show that selective oxidation of one out of eight distinct Fe2+ sites occurs within the complex Fe2+/Fe3+ ordered structure of 2%-doped magnetite (Fe3O4), while the rest of the charge and orbitally ordered network remains intact. This ‘charge order within a charge order’ is attributed to the relative instability of the trimeron distortion surrounding the selected site. Our discovery suggests that similar complex charge ordered arrays could be used to provide surface sites for selective redox reactions, or for storing information by doping specific sites.

C harge ordering is associated with notable electronic phenomena such as superconductivity in copper 1 and bismuth 2 oxides, CMR in manganese oxide perovskites 3 and multiferroicity in iron oxides 4 . Charge orders are usually suppressed by doping although in a few cases such as CMR manganese oxides, the entire array rearranges into a new periodicity 5 . The concept of charge ordering was first proposed to account for the Verwey transition at T V ≈ 125 K in magnetite 6,7 . The lowtemperature order proved difficult to determine, but microcrystal X-ray diffraction has shown that the crystal structure changes from the cubic spinel type (space group Fd 3m) to a complex monoclinic Cc superstructure below T V 8, 9 . The Fe 2+ sites within the Fe 2+ /Fe 3+ charge-ordered array show a combination of orbital ordering and bonding to two Fe neighbours to form linear three-atom trimeron units, spin-polarised orbital molecules 10 . Orbital molecules associated with charge ordering have also been reported in other materials, such as CuIr 2 S 4 11 , AlV 2 O 4 12,13 , GaV 2 O 4 14 and CaFe 3 O 5 15 . Complex charge orders may lead to spontaneous formation of structurally inequivalent cations of the same charge, for example, ordering of V 4+ /V 5+ over eight inequivalent sites in α′-NaV 2 O 5 16 , and notably in the Cc magnetite superstructure where charges are localised over sixteen distinct octahedrally coordinated sites, eight for Fe 2+ and eight for Fe 3+ . Inequivalent cations of the same charge should, in principle, have slightly different redox potentials, but site selective doping of a charge ordered array has not previously been demonstrated.
Previous work has shown that magnetite can be hole-doped over a small range, up to x ≈ 0.035, with suppression of T V and a change from sharp first order to broad second-order Verwey transitions reported around x = 0.012 17

Results
Structural studies of doped magnetite microcrystals. We compare results for three magnetite microcrystals. Details of the syntheses and magnetic and structural investigations are shown in "Methods". Sample #1 is the highly stoichiometric magnetite (x = 0) previously used to determine the Cc superstructure 8 , and a sharp Verwey transition at 123 K is observed in the magnetisation measurements shown in Fig. 1. Sample #2 is an Fedeficient Fe 3(1-δ) O 4 material that also has a sharp transition at T V = 102 K, from which the estimated hole doping is x = 3δ = 0.0116. Zn 2+ substitutes at tetrahedral cation sites that are not directly involved in the charge ordering, so a Fe 3-z Zn z O 4 sample was used to access higher hole-doping levels. This sample #3 shows a broad Verwey transition at T V = 92 K from which doping x = z = 0.0228 is estimated.
Our samples #2 and #3, respectively, lie in the firstand second-order Verwey transition regimes. It was originally thought that second-order samples did not show a structural transition at T V , but a subsequent study reported that a distortion of the cubic cell is present in the second-order regime, modelled with a rhombohedral R 3m cell 18 . A recent Mössbauer and room temperature diffraction study suggested a change of lattice symmetry for Fe 3-z Zn z O 4 between firstand second-order regimes 19 , but no corresponding change in phonon spectra was    Fig. 1 Characterisation of magnetite samples. a Zero-field cooled magnetisations of the powder for sample #1 and the microcrystals #2 and #3, normalised to 140 K values. The fields used were 100 Oe (#1 and #2) and 500 Oe (#3). The Verwey transition for each sample is indicated by a vertical arrow. b Low-temperature splitting of the cubic-(440) powder X-ray diffraction peak for sample #3, demonstrating that a lattice distortion occurs at the Verwey transition between 85 and 90 K. c Thermal evolution of unit-cell parameters derived from fits to powder X-ray profiles for #3 showing the monoclinic splitting at low temperatures. Values for sample #1 at 90 K 8 , shown as stars, demonstrate that the magnitude of the monoclinic distortion is greatly reduced by doping.
found by inelastic neutron scattering 20 . A lattice distortion is clearly seen in the low-temperature powder diffraction patterns of sample #3 (Fig. 1b), and our microcrystal structural analysis shows that the same Cc supercell as for the undoped material is present. Hence, there is no change of low-temperature structural symmetry on passing from firstto second-order Verwey regimes. Instead, this anomaly may be attributed to the site-selective doping discovered below.
The crystal structures of samples #2 and #3 below their Verwey transitions were determined from X-ray diffraction data using the same microcrystal method as for #1 8 . Both structures show the same qualitative charge ordering arrangement as for the x = 0 material. In order to quantify any small changes in the charge localisation, three local symmetry mode parameters are used, as defined in "Methods". Q rad measures the radial expansion of the FeO 6 octahedra, equivalent to the average Fe-O distance, and hence is sensitive to the size difference between Fe 2+ and Fe 3+ cations. The tetragonal Jahn-Teller distortion due to the orbital order of high-spin 3d 6 Fe 2+ is given by Q JT , as defined in ref. 6 . (Fe 3+ is orbitally non-degenerate and so is not subject to Jahn-Teller distortion.) The shortening of the distances from each Fe 2+ to its two neighbours in each trimeron is quantified by the Q tri mode. Oxidation of an Fe 2+ cation within the chargeordered array is expected to lead to an decrease in Q rad as Fe 3+ is smaller than Fe 2+ , an increase in Q JT due to loss of Fe 2+ Jahn-Teller compressions that have negative Q JT values, and an increase in Q tri as shortened Fe-Fe distances are lost. Hence, −ΔQ rad , ΔQ JT and ΔQ tri are all expected to increase with hole doping of Fe 2+ sites. Doping trends in these parameters mostly evolve smoothly with x as shown in Fig. 2. To display the combined changes for the 8 Fe 2+ sites, the differences −ΔQ rad , ΔQ JT and ΔQ tri between values for undoped sample #1 and for the doped samples #2 and #3 are shown as a bar chart in Fig. 3. In total, 44 of the 48 Fe 2+ ΔQ values are positive, demonstrating that the structure refinements are sensitive to the small changes induced by 1-2% hole doping. Most sites have values of the summed total distortion change ΔQ tot = −ΔQ rad + ΔQ JT + ΔQ tri in a common range between 0.01 and 0.12 Å, but it is striking that one site, B42 in crystal #3, has an outlying value of ΔQ tot = 0.21 Å comprising large changes in all of the radial, Jahn-Teller and trimeron modes.
Chemical doping of magnetite through introduction of Fevacancies in sample #2 or Zn-substitution in sample #3 occurs at high temperatures, so the defects are located randomly through the lattice with respect to the charge order that emerges below T V . Hence, a statistically uniform oxidation of Fe 2+ sites that happen to be adjacent to a defect is expected, and this accounts for the distribution of similar ΔQ tot values for most of the Fe 2+ sites in Fig. 3. However, it is evident that site B42 is substantially more oxidised in crystal #3 (site labels in the charge-ordered structure are shown on Fig. 3 of ref. 9 ), and this reveals a remarkable siteselectivity between the spontaneously created inequivalent Fe 2+ sites within the charge-ordered magnetite structure. It is notable that this effect is seen at such a small hole-doping level. The x = 0.0228 doping of sample #3 is only around one-fifth of the x = 1/ 8 = 0.125 level needed to fully oxidise one of the eight distinct Fe 2+ sites in the charge-ordered array, and so corresponds to oxidation on average of only 0.7 of the 32 Fe 2+ sites in the monoclinic unit cell. No selective doping of B42 or any other site is evident for crystal #2 at the lower doping of x = 0.0116. Hence, it is likely that the previously reported changeover from firstto second-order Verwey transitions near x = 0.012 is due to the localisation of holes at the B42 site above this limit, although studies of further samples would be needed to confirm this. Longrange ordering of trimerons likely persists throughout the existence range of doped magnetites (up to x ≈ 0.035 17 ), and robustness of disordered local trimeron distortions to high temperatures above T V has also been reported recently 21 .
The low-temperature structure of magnetite was previously shown to consist of a network of corner-sharing trimerons, in which the extra t 2g electron of the central Fe 2+ donor is significantly delocalised onto two adjacent B-site acceptors 8 . Seven of the eight structurally distinct trimerons have Fe 3+ cations as the two acceptors, i.e., they have charge configuration Fe 3+ -Fe 2+ -Fe 3+ . However, the B42 site is unique in having a Fe 2+ -Fe 2+ (B42)-Fe 3+ configuration, where another Fe 2+ acts as a terminal charge acceptor. The present discovery that B42 is more easily oxidised that other Fe 2+ sites can thus be attributed to the anomalous nature of the B42 trimeron. Electron-electron repulsion between the localised electrons of the adjacent Fe 2+ 's in this trimeron lowers the potential for ionisation of the B42 site relative to other Fe 2+ ions.

Discussion
The above results show that the complex spontaneous charge ordering in magnetite creates electron-localised Fe 2+ sites of distinguishable redox activity. Although the charge-ordered superstructure of magnetite is very complex, accurate determination of the many variable structural parameters gives exquisite sensitivity to tiny changes in local charge states through the local radial, Jahn-Teller and trimeron-distortion modes. The discovered doping selectivity is remarkable, as it corresponds to a 'charge order within a charge order'. It is also notable that the rest of the charge, orbital and trimeron network remains robust while the B42 sites are oxidised, at least up to the 2% doping in this study. This suggests that similar complex charge-ordered arrays could be used to provide surface sites for selective redox reactions, or for storing information by doping-specific sites. It is notable that the B42 trimerons lie parallel to the cubic-(100) plane of magnetite which can be grown as thin films, so it might be possible to access and directly measure the difference in ionisation potential between the B42 and other in-plane trimerons (Fig. 4b) using scanning nanoprobe microscopies.
In summary, this work demonstrates that it is possible to selectively dope one site within the spontaneously created chargeordered array of magnetite without disrupting the rest of the electronically ordered network. This opens new possibilities to create a 'charge order within a charge order', and such materials could be used to provide surface sites for selective redox reactions, or for storing information by doping-specific sites.

Methods
Sample preparation. Sample #1 is a highly stoichiometric magnetite Fe 3(1-δ) O 4 with 3δ = 0.0000 originally provided by Prof. J. Honig that has been used in previously studies 8,9,21 . Samples #2 and #3 were synthesised through a modified route from Honig 17 . Small microcrystals of Fe 3(1-δ) O 4 (sample #2) or of Fe 3-z Zn z O 4 (sample #3) were obtained through firing Fe 2 O 3 or an Fe 2 O 3 /ZnO mixture at 1580°C under Ar flow. The stoichiometry of sample #2 Fe 3(1-δ) O 4 22 was adjusted by reannealing the crystals in a vertical furnace with a fixed CO 2 /H 2 buffer gas flow, to control the oxygen partial pressure according to the thermodynamic equilibrium of magnetite 17 and reference tables derived from the JANAF database 23 .
Magnetisation. Magnetic measurements were recorded with a Quantum Design SQUID magnetometer after zero-field cooling in fields of 100 Oe (samples #1 and #2) or 500 Oe (sample #3) during warming. Microcrystals were fixed in Eicosane within the gelatine capsule. Hole-doping levels x = 0.0116 and 0.0228 of samples #2 and #3, respectively, were estimated from their measured Verwey transition temperatures using the T V -x doping correlation plot in ref. 17 .
X-ray diffraction. Microcrystal X-ray diffraction data were collected on the diffractometer ID11 at ESRF (France). The wavelengths were all close to λ = 0.16 Å. The microcrystals (40-60 μm) were suspended in paratone oil in a litholoop. Cooling in a magnetic field from ambient temperature to 80-90 K (as described in ref. 6 ) was used to align the magnetic easy axis of the crystal with the field, thus helping to create a unique monoclinic c-axis below the Verwey transition. Temperature was controlled with a nitrogen cryostream. Data sets were recorded at 90 K (samples #1 and #2) or 80 K (sample #3), with varying omega-step sizes, exposure times, beam fluxes and at different phi settings, for high redundancy and to observe both low angle fundamental diffraction peaks and high-angle weak superstructure reflections.
Data reduction and integration for sample #2 were performed using the same procedure as for #1 in ref. 8 , via Bruker SMART and SAINT software 24 . For crystal #3, data were indexed and integrated using CrysalisPro 25 using an increased integration box (×2), and a filter for reflections above 50,000 counts to ensure detector linearity. Integrated results for each collection run were then processed using Sadabs 26 , applying a spherical absorption correction. The data were finally merged for refinement using Xprep 27 to a maximum resolution of 0.28 Å. Structure refinements were carried out using SHELXL software 28 and took both monoclinic and orthorhombic twin domains into account (excluding inversion twinning). Samples #2 and #3 were found to show substantial monoclinic twinning. All 168 of the variable atomic coordinates were refined independently, subject to the origin constraints of space group Cc. High-resolution powder diffraction patterns for sample #3 were recorded at the ID22 beamline of ESRF from 55 to 325 K using a helium cryostat with λ = 0.354224 Å. Rietveld refinements were performed using Fullprof software 29 , and the monoclinic unit-cell parameters at 80 K were used as the values for the singlecrystal refinement.
Distortion modes. Local distortion mode parameters are used to quantify the magnitude and changes of local distortions of the low-temperature magnetite structure with doping. Distortions of FeO 6 octahedra have been previously described by local modes Q in the O h point group 8 .
The radial expansion (breathing) mode Q rad is calculated from Eq. (1).
where d i are the six Fe-O distances in the octahedron and <d> is the global average octahedral Fe-O distance. This breathing mode describes changes in the cation size, and so is sensitive to charge ordering of large Fe 2+ against small Fe 3+ . The orbital ordering is characterised by the tetragonal Jahn-Teller mode Q JT , calculated as described in Supplementary Information to ref. 8 .
A trimeron mode Q tri sensitive to Fe-Fe distances is similarly defined for each Fe 2+ in Eq. (2).
This is summed over the two Fe-Fe distances BB i within the trimeron, where <BB> is the average of all nearest-neighbour B-B distances within the structure.

Data availability
Data that support the findings of this study have been deposited at https://doi.org/ 10.7488/ds/2783.