Complex magnetic ordering in the oxide selenide Sr 2 Fe 3 Se 2 O 3

Sr 2 Fe 3 Se 2 O 3 is a localised-moment iron oxide selenide in which two unusual coordinations for Fe 2+ ions form two sublattices in a 2:1 ratio. In the paramagnetic region at room temperature the compound adopts the crystal structure first reported for Sr 2 Co 3 S 2 O 3 , crystallising in space group Pbam with a = 7.8121 Å, b = 10.2375 Å, c = 3.9939 Å and Z = 2. The sublattice occupied by two thirds of the iron ions (Fe2 site) is formed by a network of distorted mer -[FeSe 3 O 3 ] octahedra linked via shared Se 2 edges and O vertices forming layers, which connect to other layers by shared Se vertices. As shown by magnetometry, neutron powder diffraction and Mössbauer spectroscopy measurements, these moments undergo long range magnetic ordering below T N1 = 118 K, initially adopting a magnetic structure with a propagation vector (½–δ, 0, ½) (0 ≤  ≤ 0.1) which is incommensurate with the nuclear structure and described in the Pbam1’(a01/2)000s magnetic superspace group, until at 92 K ( T INC ) there is a first order lock-in transition to a structure in which these Fe2 moments form a magnetic structure with a propagation vector (½ , 0, ½) which may be modelled using a 2 a × b × 2 c expansion of the nuclear cell in space group 36.178 B a b21m (BNS notation). Below T N2 = 52 K the remaining third of the Fe 2+ moments (Fe1 site) which are in a compressed trans -[FeSe 4 O 2 ] octahedral environment undergo long range ordering, as is evident from the magnetometry, the Mössbauer spectra and the appearance of new magnetic Bragg peaks in the neutron diffractograms. The ordering of the second set of moments on the Fe1 sites results in a slight re-orientation of the majority moments on the Fe2 sites. The magnetic structure at 1.5 K is described by a 2 a × 2 b × 2 c expansion of the nuclear cell in space group 9.40 I a b (BNS notation). An equivalent case A and can be


Introduction
Multi-anion compounds adopt a diverse range of structures and have received recent attention in several contexts. Oxide sulfides and oxide selenides enable band gap tuning for semiconductors and transparent conductors 1,2,3 and are of interest as potential thermoelectric materials. 4 Superconductors based on iron arsenides 5 and selenides 6 also often contain oxide, or hydroxide 7 slabs separating the iron arsenide or selenide layers. In oxide chalcogenides ordering of the oxide and heavier chalcogenide (S 2-, Se 2or Te 2-) anions is the norm as a result of their differing sizes and chemistry. 8  and which crystallise in different structures, both with non-centrosymmetric space groups (CaFeSeO also has a centrosymmetric polymorph). 11 The oxide selenide Sr 2 Fe 3 Se 2 O 3 has recently been reported by Lai et al., 15 along with the sulfide analogues for both Fe 15 and Co, 16  were ground together inside an argon-filled dry glovebox (Glovebox Technology Ltd, UK) using an agate pestle and mortar. The ground powder was pressed into a pellet, placed inside an alumina crucible, and sealed inside an evacuated silica ampoule. Various heating protocols were then investigated as described in the results section.

Diffraction Measurements.
Laboratory X-ray powder diffraction (XRPD) measurements to monitor phase purity and the course of the reactions were performed on a Panalytical Empyrean diffractometer using CuK  radiation.
High resolution XRPD measurements for structure solution and analysis were performed on beamline I11 17 at the Diamond Light Source, Ltd, UK, and additional measurements were made on beamline ID22 at the European Synchrotron Radiation Facility (ESRF), France. NPD measurements were performed from 10 -300 K on the WISH instrument 18

at the ISIS Pulsed Neutron and Muon
Facility, UK with the samples contained in indium-sealed thin-walled vanadium cylinders. Structure solution and Rietveld refinements were performed using the TOPAS Academic software. 19 Electron diffraction measurements at EMAT, Antwerp, were acquired with a Philips CM20 transmission electron microscope operated at 200 kV with the sample prepared by grinding the crushed powder in ethanol and depositing a few drops of the suspension on holey carbon TEM grids.

Magnetometry.
All measurements used a Quantum Design MPMS-XL SQUID magnetometer. The susceptibility was determined by measuring the magnetisation as a function of temperature on warming from 2 to 300 K after cooling both in a zero applied field: zero-field-cooled (ZFC) and in the measuring field: fieldcooled (FC) of 50 mT. Magnetisation isotherms (-5 ≤  0 H/T ≤ +5) at several temperatures were each measured after cooling the sample from 200 K (i.e. well above the highest magnetic ordering transition) to the measurement temperature in a +5 T field and then measuring the magnetisation while sweeping the field in steps down to -5 T and back to +5T. Successive isotherms were collected from highest to lowest temperature. Between the measurement of successive isotherms, the field was changed to 0T and the sample warmed to 200 K, then the field was changed to +5 T prior to cooling. This was in an attempt to remove any influence of the previous measurement on the next.
Samples were sequestered from air in gelatin capsules.

57
Fe Mössbauer spectra were collected using a constant-acceleration, cryostatic spectrometer (Janis 10 K CCR, model CCS-800/204N) with a Lakeshore 335 temperature controller. The radiation source 57 Co(Rh) was kept at room temperature. A Mössbauer thickness of 1 20 was achieved by   homogenously mixing 25 mg of Sr 2 Fe 3 Se 2 O 3 with graphite to fully pack a cylindrical cavity (1.77 cm 2 cross-section, 0.1 cm thick) in an acrylic disc, which was sealed air-tight. Spectra were analysed using the Recoil software package 21 to deconvolve the data into separate iron environments. Extracted chemical shift values are quoted relative to a thin α-Fe foil calibration.

Synthesis.
A preliminary synthesis using only SrO and FeSe in equimolar quantities was found to produce the reported phase with a large proportion of SrSe impurity. The synthesis was then modified by the inclusion of Fe 2 O 3 and Fe to target (FeO) x (SrSe) y compositions with x > y to minimise impurities and infer the composition. Sample purity and Bragg peak asymmetry were found to vary greatly with the synthesis temperature, even with the correct compositional ratio of elements.  Figure 1) showed well-formed spots with no evidence for streaking in the regions investigated. Structural solution was performed using charge flipping, as implemented in TOPAS Academic, 21 with Pbam symmetry imposed, using high resolution PXRD data collected with the I11 instrument. The algorithm was successful in identifying the locations of all ions in the unit cell, allowing the identity of the ions on each site to be subsequently deduced by comparison of their inter-ionic distances with those in relevant binary compounds.  15 in which single crystal X-ray diffraction confirmed this choice of space group Pbam. Rietveld refinement against synchrotron powder X-ray diffraction acquired using I11 achieved a good agreement to the data for sample B shown in Figure 2 and sample A shown in Figure S1. The result of the structural analysis (Table 1) is entirely consistent with the report of Lai et al. 15

Figure 2
Rietveld refinement against the PXRD pattern (I11) of Sr 2 Fe 3 Se 2 O 3 sample B taken at room temperature (note that this sample was intentionally prepared with a slight excess of SrSe in the reaction mixture, hence the presence of significant amounts of this phase in the sample).
The Sr 2 Fe 3 Se 2 O 3 structure is shown in Figure 3. For further discussion of the structure the reader is also referred to the works of Lai et al. 15,16 The key features of the structure are as follows: there are two iron coordination environments shown in Figure 3

Magnetometry.
Our magnetic susceptibility measurements show transitions consistent with those observed using magnetometry and heat capacity measurements by Lai et al. 15 In what follows we adopt their notation. The transitions are shown in Figure 4(b) at ~125 K (T N1 ), 50 K (T N2 ) and 40 K (T′). T N1 coincides approximately with the Verwey transition of Fe 3 O 4 , and while only 0.05 % of this phase (below the detection limit of bulk diffraction measurements) would be required to produce such a transition in the magnetisation, the heat capacity measurements of Lai et al. 15 show that this feature is associated with the bulk of the sample. Figure 4(a) shows a change in the shape of the hysteresis loops, obtained after field-cooling from room temperature at 5 T, on passing through the 50 K (T N2 ) and 40 K (T′) transitions. Below T' a metamagnetic transition appears at about 0.6 T in the magnetisation isotherm. This feature persists to lower temperatures and is evident in the virgin curve of the magnetisation isotherm at 2 K obtained after zero-field-cooling in the report of Lai et al. 15 In our field-cooled (5 T) isotherm at 2 K a higher-field feature is evident above 2 T which was also observed in the hysteresis loop of Lai et al. 15 The behaviour suggests that there may be a fielddependence to the magnetic ordering which would require neutron diffraction investigations beyond the scope of those performed here.

Neutron Powder Diffraction.
Variable temperature NPD measurements ( Figure 5) were carried out on both sample A and sample B on warming. Sample A was measured in narrow temperature steps from 1.5 K to 150 K, while diffraction patterns with better statistics were collected on sample B at 20, 55, 97, and 135 K corresponding to key ordered states. Rietveld refinements against data from both samples produced identical models for the magnetic ordering. On cooling we observe magnetic ordering transitions as follows. Below 118 K (equated with T N1 ) magnetic Bragg peaks begin to appear. On cooling further these peaks shift remarkably in d-spacing until 92 K is reached ( Figure 5). We identify this temperature as a fourth magnetic transition for this compound which is not evident in the magnetic susceptibility measurements. We give this the symbol T INC because it is associated with the transition between commensurate and incommensurate magnetic ordering as described below. Below 51 K (T N2 ) an additional set of magnetic reflection appears, which increase sharply in intensity as the temperature is lowered, as can be seen in the change in intensity of the peak at 3.8 Å between 48 and 42 K in Figure 5..
Analysis of the commensurate reflections was performed using the ISODISTORT software, 33 coupled with Rietveld refinement in Topas Academic v6. 19 Rietveld refinement of the incommensurate magnetic structure was performed using FullProf. 34 Magnetic scattering in all diffraction patterns above T N2 = 51 K could be accounted for solely by ordering on one of the Fe sites. In principle the magnetic contribution to the Bragg scattering alone does not allow us to distinguish whether the Fe1 or the Fe2 site is responsible. However the Fe2:Fe1 ratio of 2:1 enabled us to deduce, from the size of the ordered moment, that the Fe2 site (the mer-FeSe 3 O 3 site which accounts for two thirds of the iron sites) must be the one ordered in this regime (with an ordered moment of 3.04(1)  B at 55 K) otherwise the less numerous Fe1 sites would each carry an ordered moment of 4.75(2) µ B at 55 K, which exceeds the maximum saturated value expected for Fe 2+ . This result is consistent with the Mössbauer data (see below). We firstly consider the magnetic structure that pertains between T N2 (51 K) and T INC (92 K). This can be accounted for ( Figure 6 shows the refinement against 55 K data) by commensurate ordering of the Fe2 moments with propagation vector k = (½, 0, ½). Trials of the possible magnetic ordering modes in the expanded unit cell gave a good fit to the data with a combination of mU 2 (ξ 1 ,0) modes (following the notation 35,36 of Miller and Love used in ISODISTORT). This may be described in the magnetic space group B a b2 1 m (36.178) (BNS notation). 37 The ordering scheme is as shown in Figure 7, in which the moments are directed along the c axis with antiferromagnetic coupling (J 1 ). In the direction of the a axis, the moments are antiferromagnetically aligned along the vertex-sharing 180° Fe(2)-O-Fe (2) pathways (J 2 ), and ferromagnetically aligned along the 99° Fe(2)-Se-Fe (2)   We note that the resulting magnetic space group is polar, indicating that the magnetic transition at T INC breaks the spatial inversion symmetry. Indeed, the magnetic order, which transforms as the mU 2 (ξ 1 ,0) irreducible representation, couples a displacive distortion with the Γ 4 -(σ) symmetry through the linear quadratic invariant 1 2 in the free energy. This lattice distortion can give rise to a net dipolar moment in the structure and it is probably the origin of the frustration release in the inter-ladder couplings (J 4 -J 7 in Figure 7).  38,39,40,41 Attempts to model the magnetic scattering using a cycloidal magnetic structure produced poor fits (see Figure S8). Rietveld refinement against the neutron diffraction pattern at 96 K is shown in Figure 9 42 The Fe2 moments that were already ordered above T N2 remain principally directed along the c axis with the mU2 ordering scheme, however to fully account for the magnetic intensities below T N2 they acquire a canting in the ab plane described by a combination of mS3+S4+ modes. A comparison of the fit with and without this Fe2 site canting is given in the supporting information ( Figure S3). This rearrangement of the spins becomes established at 40 K and may be associated with the T' transition in heat capacity measurements of Lai et al. 15 The canting puts the Fe2 moments in a plane with their nearest Fe1-O bond and the corresponding Fe1 moment, with antiferromagnetic alignment between each of the Fe1 moments and the Fe2 moments canting as shown in Figure 11(a). The ordering scheme thus derived is purely antiferromagnetic, and can be described in the I a b magnetic space group in a 2a nucl × 2b nucl × 2c nucl cell (Table S6). In light of the weak ferromagnetic component of the susceptibility evident in the magnetometry below T′ at 40 K, ordering modes which gave a net ferromagnetic canting of one or both sets of spins were attempted but none gave improvement to the fit, suggesting that the zerofield magnetic structure (i.e. as measured in the NPD experiment) is purely antiferromagnetic.
Moreover the determined magnetic space group does not allow any ferromagnetic moment in any crystallographic direction. Indeed, the magnetisation versus field curves shown in Figure 4 are close to linear at low fields, which is consistent with AFM ordering without an applied field.
To explain the canting of the Fe2 sublattice with the mS3+S4+(ε 1 ,ε 2 ) modes it is necessary to take into consideration a nuclear distortion with the right symmetry to allow a trilinear invariant in the free energy, coupling the two magnetic distortions. To conserve the translational symmetry of the parent structure, the nuclear distortion needs to have a propagation vector q=(0 ½ ½), the T point of the first Brillouin zone, and to transform as the T2 irreducible representation with order parameter direction P(δ 1 ,δ 2 ). This allows us to derive a trilinear invariant 1 ( 1 1 + 2 2 ) + 1 ( 1 2 − 2 1 ) describing the coupling, mediated by the T2(δ 1 ,δ 2 ), between the magnetic mU 2 (ξ 1 ,0) and mS3+S4+(ε 1 ,ε 2 ) distortions. Any monoclinic nuclear distortion was outside the resolution of the WISH diffractometer, and we did not observe any superstructure reflections consistent with q= (0 ½ ½).
We used the X-ray diffractometer ID22 at the ESRF to investigate whether the magnetic ordering at T N2 gives rise to a small monoclinic distortion of the nuclear cell or the presence of 0 ½ ½ peaks, that might be associated with the T' transition in the heat capacity data of Lai et al. 15 Our measurement at 5K showed no apparent symmetry lowering distortion ( Figure S4), but a careful observation of the diffraction pattern indicated the presence of a very weak reflection, not present at ambient temperatures, that could be indexed as the 0 5/2 ½ reflection ( Figure S5). Even if this reflection is statistically significant, its spurious nature cannot be excluded, but its position and the propagation vector are consistent with the symmetry analysis. A refinement with the distorted monoclinic symmetry Im is not possible due to the weak character of the distortion (i.e. the low intensity of the proposed 0 5/2 ½ reflection) and the high number of free parameters. Even considering this extra nuclear distortion, on the ground state magnetic space group, the weak ferromagnetic moment is still not allowed from the resulting symmetry. Note that we needed to use an attenuated beam on ID22 to avoid sample heating when performing this experiment: with the full intensity beam sample heating was evident as had been observed and described in measurements down to 75 K by Lai et al.
on the same instrument (see their Figure S4). 15 Figure 12 summarises the evolution of the ordered moments over the entire temperature range.   Figure 7(b)). (c) Arrangment of moments between ladders. (d) magnetic unit cell below T N2 , which is a 2a × 2b × 2c expansion relative to the nuclear cell (see Table S6). Sr and most Se sites not shown in (d) for clarity.   (3) 3.1253 (7) 3.1406 (7) 2.617 (2)

Mössbauer Spectroscopy.
The temperature dependence of the Mössbauer spectra has been described and interpreted by Lai et al. 15 Here we show the evolution of the spectra in the region from just above T N1 to just below T INC spanning the region where the magnetic ordering of the Fe2 moments is incommensurate and the Fe1 moments do not participate in long range order. The data and fits in Figure 13 show the onset of magnetic order between 125 K and 110 K and the evolution to 80 K, below T INC . At 125 K (Figure 13) in the paramagnetic region, the data are modelled by two doublets. The more numerous Fe2 moments produce a doublet with a chemical shift (relative to a thin Fe foil) of  = 1.001(2) mm s -1 and with a quadrupole splitting of E Q = 1.897(8) mm s -1 . The remaining doublet is ascribed to the Fe1 moments ( = 0.963(4) mm s -1 ; E Q = 1.46(1) mm s -1 ). As magnetic ordering occurs, the majority signal due to the Fe2 sites is described by a sextet confirming that it is the Fe2 moments that are participating in long range magnetic order below T N1 (see the potential ambiguity described above in the analysis of the NPD data). At 80 K (Figure 13), below T INC , the signal due to these Fe2 moments is described by a highly asymmetric sextet arising from the local magnetic field, B hf , due to the magnetic ordering and the quadrupole splitting due to the asymmetric coordination environment. 43 The minority Fe1 signal persists as a quadrupole doublet. In the region between T N1 and T INC , where the NPD data show incommensurate magnetic ordering of the Fe2 moments, the Fe2 sextet in the Mössbauer spectrum exhibits very broad lines. The data in this region (110 K and 97 K in Figure 13) were modelled using a quadrupole splitting similar to that used in the paramagnetic region above T N1 and in the commensurately ordered region below T INC , and a single value for the local magnetic field that steadily increased with decreasing temperature (Figure 14(a)), but they required much broader line widths in this region (Figure 14 Table 2.

Conclusions
Sr 2 Fe 3 Se 2 O 3 with two unusual and highly anisotropic environments for Fe 2+ ions shows a complex succession of magnetic ordering transitions. Neutron powder diffraction measurements unveil the origin of the complexity in the magnetic susceptibility and Mössbauer spectra previously described 15 and reveal an additional region of magnetic behaviour where the onset of long range magnetic ordering on one of the Fe sublattices (Fe2) on cooling results first of all in an incommensurate region of long range order, presumably driven by frustration of some of the weaker exchange interactions.
The lowest temperature magnetic structure is dictated by the interactions between the two sublattices of long-range-ordered Fe moments. Given the complexity of the magnetic structures found for compounds composed of these highly anisotropic transition metal coordination environments 26,42 there is scope for tuning the details of the exchange interactions by chemical substitution on the transition metal, chalcogenide and electropositive metal sites.
Associated Content.

Supporting Information
The Corresponding Author.

For Table of Contents Only
Sr 2 Fe 2 Se 2 O 3 displays complex magnetic ordering over two Fe 2+ sublattices which is probed using powder neutron diffraction.

Figure S1
Rietveld refinement against PXRD pattern of Sr 2 Fe 3 Se 2 O 3 sample A taken at room temperature using the Mythen detector of the I11 diffractometer at Diamond Light Source.

S3
Description of the magnetic models using ISODISTORT As described in the main text, between 55 (T N2 ) and 91 K (T INC ), one of the two Fe sites shows commensurate magnetic order with k-point U (½, 0, ½  Bg_1(a,a) and Bg_2(a,a) gives a reasonable model, but does not give a satisfactory fit to the data, shown in Figure S3(a). The fit can be improved slightly by allowing all six terms to refine freely {mS3+S4+ Bg_1(a,b), mS3+S4+ Bg_2(a,b), mS1+S2+ Ag(a,b)} but even this gives a poor statistical and visual fit, which indicates that the data cannot be fitted with these modes alone, as shown in Figure S3

Figure S4
X-ray diffraction patterns of Sample A taken using the MAC detector of the ID22 diffractometer at the ESRF. The red pattern was taken at room temperature and the blue pattern at 5 K. No evidence of splitting in the strongest structural peaks is observed.

Figure S5
Powder X-ray diffraction of sample A taken at ID22 (λ=0.35440(Å)). The data taken at 5K (blue line) show the presence of a very weak peak at 5.6° coincident with the position of the 0 5/2 ½ reflection expected from the magnetic structure and symmetry analysis. This peak appears weaker in the pattern taken with the unattenuated beam (purple line), which while measured in the cryostat at 5K is estimated to be between 30 and 60 K based on the lattice parameters due to beam heating. The peak is absent in the room temperature diffraction pattern (green line).Note that the maximum peak height observed in the pattern was 40,000 counts.
Tables of unit cell information in the paramagnetic regime.

Table S1
Refined atomic parameters against synchrotron powder diffraction data for sample B, corresponding to the data in Table 1 in the main paper. Peakshape asymmetry was observed in this high resolution data. Attempting to refine the asymmetry as 2 phases with different lattice parameters produced an improved fit, but no differences in the occupancies or positions of the atoms could be discerned between the phases. Since no physical origin for this asymmetry could be established, it was instead handled with an arbitrary asymmetric peakshape function.

S9
Tables of structural information in the Fe1 and Fe2 ordered regime Table S5 refinement parameters from WISH at 20K for the nuclear cell of sample B, corresponding to the data in Table 1 in the main paper.

Instrument
WISH Temperature 20 K Nuclear symmetry Pbam (55) a (Å) 7.7945(2) b (Å) 10.1979 (3)    *This is a non standard setting of space group C c c (9.40 in BNS notation), used in order maintain the same axis orientation as used for the nuclear cell. The unit cell is a 2a × 2b × 2c expansion of the nuclear unit cell.
. S11 Figure S6. Rietveld refinements against Neutron Powder Diffraction data of Sample A. patterns at 1.5-91 and 125-150K were refined against with Topas Academic, patterns 92-119K were refined against with FullProf. The 150K refinement in Fullprof is also shown for comparison.  Figure S8. The cycloidal fits to PND data at 96 K show clear discrepancies with the experimental intensity in contrast with the incommensurate spin-density wave model shown in Figure 9 of the main text. Upper blue tickmarks: nuclear structure; lower red tickmarks: magnetic structure.