Pressure-induced spin pairing transition of Fe 3+ in oxygen octahedra
D. M. Vasiukov, L. Dubrovinsky, I. Kupenko, V. Cerantola, G. Aprilis, L. Ismailova, E. Bykova, C. McCammon, C. Prescher, A. I. Chumakov, N. Dubrovinskaia
PPressure-induced spin pairing transition of Fe in oxygenoctahedra D. M. Vasiukov,
1, 2, ∗ L. Dubrovinsky, I. Kupenko, V. Cerantola, G. Aprilis,
1, 2
L. Ismailova, E. Bykova, C. McCammon, C. Prescher, A. I. Chumakov, and N. Dubrovinskaia Laboratory of Crystallography, Universit¨at Bayreuth, D-95440 Bayreuth, Germany Bayerisches Geoinstitut, Universit¨at Bayreuth, D-95440 Bayreuth, Germany Institut f¨ur Mineralogie, Universit¨at M¨unster, D-48149 M¨unster, Germany ESRF-The European Synchrotron CS40220 38043 Grenoble Cedex 9 France Skolkovo Institute of Science and Technology,Skolkovo Innovation Center, 143026 Moscow, Russia Photon Science, Deutsches Elektronen-Synchrotron, D-22607 Hamburg, Germany Institut f¨ur Geologie und Mineralogie,Universit¨at zu K¨oln, D-50674 K¨oln, Germany (Dated: June 28, 2018) a r X i v : . [ c ond - m a t . s t r- e l ] O c t bstract High pressure can provoke spin transitions in transition metal-bearing compounds. These tran-sitions are of high interest not only for fundamental physics and chemistry, but also may haveimportant implications for geochemistry and geophysics of the Earth and planetary interiors. Herewe have carried out a comparative study of the pressure-induced spin transition in compoundswith trivalent iron, octahedrally coordinated by oxygen. High-pressure single-crystal M¨ossbauerspectroscopy data for FeBO , Fe O and Fe (Fe . Si . )(SiO ) are presented together withdetailed analysis of hyperfine parameter behavior. We argue that ζ -Fe O is an intermediate phasein the reconstructive phase transition between ι -Fe O and θ -Fe O and question the proposedperovskite-type structure for ζ -Fe O .The structural data show that the spin transition is closelyrelated to the volume of the iron octahedron. The transition starts when volumes reach 8.9–9.3 ˚A ,which corresponds to pressures of 45–60 GPa, depending on the compound. Based on phenomeno-logical arguments we conclude that the spin transition can proceed only as a first-order phasetransition in magnetically-ordered compounds. An empirical rule for prediction of cooperative be-havior at the spin transition is proposed. The instability of iron octahedra, together with stronginteractions between them in the vicinity of the critical volume, may trigger a phase transition inthe metastable phase. We find that the isomer shift of high spin iron ions depends linearly on theoctahedron volume with approximately the same coefficient, independent of the particular com-pounds and/or oxidation state. For eight-fold coordinated Fe we observe a significantly weakernonlinear volume dependence. PACS numbers: 75.30.Wx, 76.80.+y, 61.50.Ks . INTRODUCTION The spin-pairing transition in transition metal compounds, also known as spin crossoveror spin transition (the first observation published in 1931 ), is an important phenomenonthat can cause drastic changes in physical properties of materials, including alterations involume, compressibility and electrical conductivity. Upon crossover from high spin (HS) tolow spin (LS), the ionic radii change dramatically (for example, for Fe from 78 to 61 pm,and Fe from 64.5 to 55 pm ) that leads to a reduction of chemical bond lengths andmay cause structural changes. Reduction of the radii means that the LS ion can substitutefor other cations without significant change of the crystal structure, which is importantfor chemistry and especially for geochemistry as it may lead to variations in partitioning ofelements (particularly iron, one of the most abundant elements in the Earth and a componentof major mantle-forming minerals). Magnetic properties are also affected: for example,octahedrally-coordinated ferrous iron (Fe ) in the LS state is diamagnetic. Such versatilebehavior has motivated ongoing attempts to find practical applications for this phenomenon,for instance, as storage media and in displays , temperature-sensitive contrast agents formagnetic resonance imaging , and as a mechanical actuator (see review 6). Thermally-induced spin crossover is a frequent phenomenon in coordination complexeswith suitable ligands when the crystal-field splitting parameter D q is close to the mean spin-pairing energy E p . Most of such compounds are complexes of iron (see the recent review 7on this topic).A pressure-induced spin transition can be observed even in compounds with low ambient D q , because the crystal-field splitting parameter increases upon compression. However,until recently such investigations were rare. The swift development of the diamond anvilcell (DAC) technique yielded several striking discoveries, such as, for example, spin crossoverin ferropericlase at lower mantle conditions . M¨ossbauer spectroscopy (MS) coupled withsingle crystal X-ray diffraction (XRD) is an extremely powerful combination for investigationof spin transitions. High-pressure crystallography using synchrotron facilities with focusedhigh-energy X-rays and fast 2D detectors, and use of DACs with a large opening angle enable careful investigation of the geometry of the FeO octahedron before and after thespin transition and provide a basis to search for correlations between crystal chemistry andhyperfine parameters of the compounds under investigation.3n this paper we focus on ferric iron (Fe ) octahedrally coordinated by oxygen for thefollowing reasons: ( i ) the Fe O octahedron is a common structural element in differentcompounds and minerals (iron-containing garnets, perovskite-structured materials includ-ing ferrites, simple (Fe O ) and complex oxides, etc.), ( ii ) this polyhedron is of interest forphysics, as a spin transition in an ion with d -configuration may provoke an insulator-metaltransition , ( iii ) oxygen has the second highest value of electronegativity after fluorine, sothat the Fe-O bond shows a marked ionic character, and ( iv ) high quality experimental dataon spin transitions in some Fe O -containing compounds are already available. Comple-mented by our new experimental results, they may be useful for a comparative analysis aimedat establishing regularities in the pressure-induced spin transition of trivalent iron in the oxy-gen octahedron. The following compounds were examined: iron borate (FeBO ), hematite(Fe O ), skiagite-rich garnet (Fe (SiO ) ), goethite (FeOOH), calcium ferrite (CaFe O ) andandradite (Ca Fe (SiO ) ) (Table I).FeBO has a calcite (CaCO )-type structure ( R ¯3 c space group) . At ambient condi-tions the structure consists of slightly distorted corner-shared oxygen octahedra enclosingferric iron and BO triangles oriented in the structure perpendicular to the 3-fold axis. Ironborate is antiferromagnetic with weak ferromagnetism due to small canting of iron spinsfrom antiparallel alignment with N´eel point T N = 348 K . A nuclear forward scattering TABLE I. List of compounds examined in the present work. References to literature data used inthe comparative analysis are provided. Hereafter an em dash means the absence of data.Chemical compound Crystallographicdata M¨ossbauer spectroscopy data kind ofmaterial/referenceFeBO Ref. 11 powder, conventional MS, and single-crystal,MS with SMS/this studyFe O Ref. 12 single-crystal, MS with SMS/ this studyFe (Fe . Si . )(SiO ) Ref. 13 single-crystal, MS with SMS/ this studyFeOOH Ref. 14 powder/Ref. 14CaFe O Ref. 15 powder/Ref. 16Ca Fe Si O Ref. 17 — undergoes a phase transition to a nonmagnetic state at46 GPa . Single-crystal MS data led to conclusion that it is due to a HS → LS transition. Arecent detailed high-pressure single-crystal XRD study confirmed earlier suppositions that it is an isosymmetric transition . Thus, FeBO is an excellent reference compound forinvestigation of relations between crystal chemistry and hyperfine parameters of trivalentiron as a function of pressure and geometry of the Fe O octahedron.Hematite is a well-known iron sesquioxide (Fe O ) with a corundum-type (Al O ) struc-ture consisting only of Fe O octahedra. Each octahedron connects with three neighborsvia edges in honeycomb-like layers and the layers are interconnected through common tri-angular faces of octahedra (space group R ¯3 c ). It is antiferromagnetic (canted-type atambient conditions) with a high N´eel temperature of 948 K. Upon compression at ambienttemperature up to about 100 GPa, it undergoes three phase transformations: pressure-induced Morin transition with reorientation of iron magnetic moments and loss of cantingat 1.7 GPa , structural transition to the ζ -Fe O phase with a triclinic, distorted-perovskitestructure (space group P ¯1) at 54 GPa , and a transition to the orthorhombic θ -Fe O phase (space group Aba
2) at 67 GPa . The perovskite-type phase consists of two types ofiron coordination polyhedra — octahedra and bicapped triangular prisms. The structuraldetails of this phase are still not fully clarified because of its low (triclinic) symmetry anddifficulties in collecting a sufficiently full XRD dataset in the DAC . The orthorhombicphase contains ferric iron in distorted triangular prisms only and Fe is in a LS state, assuggested by available XRD and MS data . There has been only limited informationabout the behavior of trivalent iron at the spin transition in Fe O polymorphs, and weprovide here new experimental data.Skiagite is an iron end-member in the silicate garnet family with ideal chemical formulaFe Fe (SiO ) . Samples used in the present study are a solid solution of skiagite andiron-majorite (Fe (FeSi)(SiO ) ), which have been described by Ismailova et al . Their ex-act chemical composition Fe (Fe . Fe . Si . )(SiO ) was determined from single-crystal XRD and microprobe analysis . It corresponds to approximately 23 mol % of ironmajorite component in the samples. Skiagite-majorite solid solution has a cubic crystalstructure (space group Ia ¯3 d ). The cubic X-site is populated by ferrous iron, whereas Fe and (Fe Si ) share the octahedral position (Y-site). XRD data revealed isosymmetriccrossover accompanied by a drop of the octahedron volume above 50 GPa . We collected5¨ossbauer spectra of the skiagite-majorite sample on compression up to 90 GPa and foundthat the spectra change in the same pressure range where XRD data indicate the phasetransition. Although iron occupies two structural positions and has multiple electronicstates, our new data allowed unambiguous interpretation of the mechanism and origin ofthis transition.Goethite ( α -FeOOH) is a widespread mineral with a diaspore-type ( α -AlOOH) structure(space group Pnma ). Iron octahedra share edges to form double chains along the c -axis (in Pbnm setting), which are further linked in a three-dimensional structure by sharing vertices.At ambient conditions goethite is a collinear antiferromagnetic with N´eel temperature T N = 393 K . A sharp spin transition accompanied by hydrogen bond symmetrization wasrevealed at 45 GPa .Calcium ferrite (CaFe O , recently discovered as the mineral harmunite ) belongs to theorthorhombic crystal system (space group Pnma ). Calcium has eight-fold coordinationand ferric iron populates two crystallographically nonequivalent octahedra with differentdegrees of distortion. These two different octahedra form infinite double chains along the c -axis (in Pbnm settings). Each chain contains octahedra of only one type. Within the chainsoctahedra share edges and different chains are linked by common vertices of octahedra. Atambient pressure calcium ferrite undergoes a phase transition to an antiferromagnetic statebellow 200 K . In previous work an isosymmetric phase transition was observed above 50GPa and explained by a spin transition of trivalent iron. Recently, this was associated witha Mott transition .Andradite (Ca Fe [SiO ] ) is a member of the garnet family. In this garnet structure,calcium is located in the cubic site (X-site) and ferric iron fully occupies the octahedralposition (Y-site). Spin crossover in andradite takes place between 60 GPa and 70 GPa .Here we present our new high-pressure single-crystal MS data for FeBO , Fe O , andFe (Fe . Si . )(SiO ) and analyze the behavior of hyperfine parameters at spin tran-sitions of ferric iron. We also discuss possible structural changes coupled with spin transi-tions, analyze the compressibility of the ferric iron octahedron, and the relationship betweenthe isomer shift and the polyhedron volume.The manuscript is organized as follows. First, new experimental data are presented, fol-lowed by a detailed analysis of hyperfine parameter behavior at the spin transition. Then, thecompressibility of the ferric iron octahedron is determined and possible structural changes6oupled with the spin transition are discussed. Finally, the dependence of the center shifton polyhedron volume is examined. II. EXPERIMENTAL DESCRIPTION
Iron borate single crystals were grown from a Fe O –B O –PbO/PbF flux as describedin Ref. 41. Hematite single crystals studied in the present work were taken from the samesynthesis batch as the crystals used in Ref. 31. Skiagite-iron-majorite single crystals weresynthesized in a multi-anvil apparatus at 9.5 GPa and 1100 C from a powdered mixture ofchemically pure oxides: Fe − x O, Fe O and SiO .High-quality single crystals with an average size of ∼ × × µ m for iron borate andhematite, and ∼ × × µ m for skiagite-iron-majorite were pre-selected on a three-circleBruker diffractometer equipped with a SMART APEX CCD detector and a high-brillianceRigaku rotating anode (Rotor Flex FR-D, Mo-K α radiation) with Osmic focusing X-rayoptics.For pressure generation BX90 DACs were used. The size of diamond culets was 250 µ m.Rhenium gaskets were pre-indented down to a thickness of ≈ µ m and holes of ≈ µ mdiameter were drilled in the center of indents. The cells with sample and a small ruby sphereplaced in the pressure chamber were loaded with Ne (Ar for FeBO single-crystal experiment)by means of a gas-loading system . Pressure in the pressure chamber was estimated beforeand after MS measurements by the ruby fluorescence method and an average value wastaken and the deviation was included in the uncertainty. For heating of Fe O we used aportable double-sided laser-heating system with infrared laser ( λ = 1071 nm) in continuousmode. In this case KCl was used as a pressure transmitting and thermal insulation medium.M¨ossbauer absorption spectra of powdered FeBO were collected using a conventionalWissEL spectrometer in constant-acceleration mode with a nominal 10 mCi Co(Rh) pointsource at 19 C. The folded spectra consist of 256 channels. The single-crystal M¨ossbauerexperiments with iron borate, hematite and skiagite were performed at ambient temperature(22 C) at the Nuclear Resonance beamline (ID18) at the European Synchrotron RadiationFacility (ESRF) using the synchrotron M¨ossbauer source (SMS) . The SMS is the pure nu-clear reflection of a FeBO crystal which is mounted on a velocity transducer and operatedin sinusoidal mode. The SMS is linearly polarized due to polarization of the synchrotron7adiation. In this case the folded spectra contain 512 channels. The average beam spot sizefor these experiments was 8 × µ m . The line width of the SMS was determined beforeand after collection of each spectrum of the samples by measurements of the reference singleline absorber (K Mg Fe(CN) ). All experiments were conducted in transmission geometry.The M¨ossbauer spectra were fitted using MossA software , version 1.01a. Spectra fromthe conventional radioactive source were processed using pseudo-Voigt line shapes. Forprocessing of spectra collected with SMS, a transmission integral fit was used assuming aLorentzian-squared line shape of the SMS and a Lorentzian line shape of the absorber. Allcenter shifts were calibrated relative to α -Fe at ambient conditions.The visualization of the structures and calculation of the distortions of polyhedra wereperformed using VESTA software , version 3.3.2. Calculations of the equations of state(EoS) were performed using EosFit7 . III. RESULTSA. Iron borate
Recent high-pressure single-crystal XRD experiments with FeBO showed a sharp tran-sition with large volume discontinuity at 50 ± and confirmed earlier supposition that it is isosymmetric phase transition. The single crystal XRD data provide importantinformation about geometrical characteristics of the Fe O octahedron. At ambient con-ditions the iron octahedron is slightly trigonally elongated along the 3-fold axis. Undercompression this distortion diminishes and completely disappears around 36 GPa. At thetransition, the octahedron volume decreases by 10.5 %, which is a clear indication of thetransition to LS state. The octahedron remains ideal across the transition and it is onlyabove 56 GPa that a trigonal compression along the 3-fold axis begins to grow slowly .M¨ossbauer spectra of iron borate were collected from ambient pressure to 70 GPa. Theevolution of the M¨ossbauer spectra is shown in Fig. 1b. At ambient conditions the spec-trum consists of one magnetic component with the following hyperfine parameters: centershift (CS) δ CS = 0 . ε = 0 . and hyperfinemagnetic field H hf = 34 . IG. 1. a) Structure of FeBO comprised by corner-shared Fe O octahedra and BO trianglesperpendicular to the 3-fold axis. b) Pressure evolution of iron borate M¨ossbauer spectra. Atambient pressure the spectrum is a single magnetic sextet (blue) that demonstrates increasing H hf at compression up to 54 GPa, then a paramagnetic doublet (green) appears that can be attributedto LS Fe . At 61 GPa only the paramagnetic component remains. c) Doublet has center shiftlower by ≈ .
13 mm/s than sextet. The squares and circles correspond to the experiment withpowder sample measured using a radioactive M¨ossbauer source and the stars are data from thesingle-crystal experiment measured using SMS. Hereafter, if error bars are not visible they aresmaller than the symbol size.
The quadrupole shift gradually decreases with increasing pressure and becomes closeto zero above 30 GPa. Such behavior can be understood if one takes into account theabove-mentioned changes in the octahedron distortion. With pressure increase the trigonaldistortion decreases and becomes zero above 35 GPa. This means that there is no latticecontribution to the electric field gradient (EFG) from the first coordination sphere. How-ever, there is still a lattice contribution from next coordination spheres as the iron Wyckoffposition does not have cubic symmetry. The quadrupole shift alters accordingly. Indeed, ε above 35 GPa is small but non-zero.The iron ions are on the 3-fold axis; therefore the EFG should be symmetric, i.e., theasymmetry parameter η = 0 and the principal component V zz of the EFG tensor is collinearwith the 3-fold axis . As the magnetic moments lie in the plane perpendicular to the 3-foldaxis and remain in the plane until the spin transition occurs , the angle θ between H hf and V zz of the EFG remains constant, and we can convert ε to quadrupole splitting (QS) ∆9 IG. 2. a) Effect of pressure on modulus of FeBO quadrupole splitting. The values for the doublet(green) and sextet (blue) differ by one order of magnitude at 54 GPa. b) The growth of hyperfinefield over the entire pressure range indicates an increase of N´eel temperature of FeBO . Thesquares and circles correspond to the experiment with powder sample measured using a radioactiveM¨ossbauer source and the stars are data from the single-crystal experiment measured using SMS.The colors conform to those in Figs. 1b and 1c. to have values for HS and LS states that can be compared. In our case the quadrupole shiftin the high-field condition ( g N µ N H hf (cid:29) eQV zz /
2) is | ε | = eQV zz (cid:32) θ − (cid:33) = ∆ (cid:32) θ − (cid:33) , (1)where Q is the quadrupole moment of the nucleus and e is the elementary charge. For θ = 90 ◦ , | ε | = ∆ / V xx , which has anopposite sign compared to V zz (as the EFG tensor is traceless). Therefore, as the quadrupoleshift is positive, the V zz is negative. The respective | ∆ | is plotted in Fig. 2a.At 54(1) GPa a new nonmagnetic doublet appears with δ CS = 0 . ≈ .
13 mm/slower than the CS of the magnetic component, Fig. 1c) and | ∆ | = 1 . T g . At 61 GPa the magneticsextet disappears completely, and only the doublet is observed up to 70 GPa. Our results arein general agreement with the previous study , although our data show smoother pressuredependencies of the hyperfine parameters, and higher pressure of the transition comparedto Ref. 24. 10 . Iron sesquioxide FIG. 3. a) Structure of Fe O (hematite) at ambient conditions consisting of Fe O octahedra.b) M¨ossbauer spectrum of hematite showing a single magnetic sextet of HS Fe . The spin-flopMorin transition results in a disappearance of the 2nd and 5th lines due to the particular orientationof the single crystal relative to the incident beam. M¨ossbauer spectra of Fe O were collected up to 82 GPa. We conducted independentexperiments with three DACs (one of them contained two crystals measured separately). Se-lected spectra are presented in Figs. 3b, 4b and 5c. The behavior of the hyperfine parameterswith pressure is shown in Fig. 6.The M¨ossbauer spectrum of α -Fe O (hematite) is a single magnetic sextet of HS ferriciron (Fig. 3b). At ambient temperature hematite undergoes a pressure-induced spin-flopMorin transition at 1 . . At this transition the spins flip 90 ◦ from the basal planeto the direction collinear with the 3-fold axis without change in the atomic arrangement.The noticeable effect of this transition is the disappearance of the 2nd and 5th lines of thesextet in the M¨ossbauer spectrum (Fig. 3b) due to the use of a single-crystal sample: inthis particular experiment the angle between the wave vector of the γ -ray and the magneticmoments is close to zero after the transition. The hyperfine magnetic field is increasedby 1.0(1) T (Fig. 6d) and ε changes from − . . IG. 4. a) Crystal structure of ι -Fe O with iron octahedra as in hematite but with a differentpacking motif. b) M¨ossbauer spectrum after laser heating of α -Fe O ( ∼ α -Fe O and ι -Fe O , respectively. agreement with data for the Morin transition at ambient pressure .There is no significant change of hematite component with further compression up to49 GPa. The δ CS expectedly decreases (Fig. 6a) and H hf reduces from 52.26(5) T to50.15(6) T (Fig. 6d). Note that the latter behavior is not related to the reduction of the N´eeltemperature , but is caused by a decrease of the H hf saturation value with pressure increase(a similar behavior was observed in FeBO ). Although single-crystal XRD experimentsdid not detect any significant changes in the octahedral distortion up to 25 GPa , the ε value almost doubles up to 0.355(9) mm/s at 49 GPa. Since iron is located on the 3-fold axisin α -Fe O , we can convert the quadrupole shift to ∆ (similar to FeBO in section III A).The result is plotted in Fig. 6b.According to data in Ref. 58, α -Fe O is metastable above 40 GPa at room temperature(RT) and orthorhombic ι -Fe O (space group P bcn ) becomes the stable phase. This poly-morph has a Rh O -II structure type with a single crystallographic position of octahedrally-coordinated iron and different from the corundum packing motif. In this phase two ironoctahedra form a building block sharing a common face. Connected via common vertices,this subunit forms a layer with herringbone-type packing and, in turn, the layers are inter-12 IG. 5.
Structures of high-pressure Fe O polymorphs and evolution of M¨ossbauer spectra at the respective transitions.a) At 54 GPa α -Fe O undergoes a phase transition to ζ -Fe O with distorted perovskite-type structure that consists of twotypes of FeO octahedra with different volumes (B-position, small octahedron is blue) and FeO bicapped trigonal prisms(A-position). b) At 67 GPa ζ -Fe O transforms to θ -Fe O built of FeO trigonal prisms. c) At 50 GPa the M¨ossbauerspectrum changes to a superposition of the magnetic sextet of ι -Fe O (purple component) and the signal of ζ -Fe O : doublet(blue) and sextet (green, H hf = 31 . ι -Fe O component disappears rapidly with increasing pressure and is absentabove 55 GPa. The intensity of the sextet with smaller field starts to decrease at 60 GPa and by 70 GPa the spectrum consistsonly of one doublet. connected through common edges of iron octahedra (Fig. 4a). Ab initio calculations for Al O showed that the kinetic barrier between corundum andRh O -II structures depends on whether the transition is forward (corundum → Rh O -II)or backward (Rh O -II → corrundum). The forward barrier is almost pressure independent,while the backward one strongly decreases with decompression, so the phase with Rh O -II13tructure is not recoverable. Our experiments and decompression data in Ref. 60 show thatthese conclusions are also valid for the Fe O system.In order to determine hyperfine parameters of ι -Fe O we performed a separate experi-ment (stars in Fig. 6) with laser heating ( ∼ α -Fe O (orange in Fig. 4b) and the second being the signal from ι -Fe O (purple in Fig. 4b). The hyperfine parameters of the purple sextet are δ CS = 0 . ε = 0 . H hf = 49 . ι -Fe O at 43 GPa (circle in Fig. 6a and d). The transmission integral fit givesa 0.4 mm/s line width for ι -Fe O that is distinct from the natural absorber line width(0.097 mm/s) of hematite. The CS values of α -Fe O and ι -Fe O are the same withinexperimental uncertainty (Fig. 6a) as iron occupies an octahedron with similar volumes inboth structures. The main distinctions of the ι -Fe O sextet are practically zero quadrupoleshift over the entire pressure range and H hf which is lower by 1.5–2 T compared to hematitevalues (Fig. 6d).With further compression of α -Fe O the M¨ossbauer spectrum changes drastically at50(1) GPa (Fig. 5c): it becomes a superposition of the ι -Fe O component (purple), and anew magnetic sextet ( δ CS = 0 . ε = 0 . H hf = 31 . δ CS = 0 . . α -Fe O disappears completely. The line width of the new components is0.4 mm/s.As single-crystal XRD experiments revealed a phase transition to triclinic ζ -Fe O (spacegroup P ¯1) at 54(1) GPa , the new components should be associated with the ζ -phase.The structure of the ζ -Fe O modeled (in monoclinic symmetry ) as a double-perovskitetype, consists of bicapped trigonal prisms (A-site) and two kinds of alternating octahedra(B (cid:48) - and B (cid:48)(cid:48) -sites). The octahedra have the same abundance but differ from each otherin volume (8.6 and 7.5 ˚A at 54 GPa). The discrepancy with XRD data in transitionpressure is apparently related to the use of different methods for pressure determination(ruby fluorescence vs position of the (111) XRD line of Ne).The behavior of hyperfine parameters is in good agreement in all conducted experiments(Fig. 6a,b,d). However, in two independent experiments the observed difference between therelative amount of components in ζ -Fe O after the transition from α -Fe O is significantly14 IG. 6.
Pressure dependence of Fe O hyperfine parameters. a) The doublet (blue) of ζ -Fe O has a CS that is lower by ≈ . before the transition (orange). The CS of the new sextet (green) is larger than thevalue for hematite at ambient pressure. b) ∆ of the doublet is approximately equal to QS in α -Fe O before the transition.c) The relative amount of components after the transition to ζ -phase shows that ι -Fe O (purple) vanishes at 55 GPa, andabove 60 GPa the green sextet starts to disappear. At 70 GPa the doublet remains the single component in the spectrum.d) The hyperfine field of ι -Fe O is lower by 1.5–2 T than values for α -Fe O over the entire pressure range. H hf of the greensextet is around 30 T at 50 GPa and increases with increasing pressure. The colors conform to those in Fig. 5c. Squares, starsand half-filled diamonds correspond to data from three different DACs. Half-up and half-down filled symbols distinguish twodifferent crystals in the third DAC. The circles at 43 GPa are parameters of ι -Fe O from Ref. 56. larger than statistical uncertainty (Fig. 6c). This discrepancy and small difference in H hf values of the green sextet (Fig. 6d) might indicate that electronic states of iron ions in ζ -Fe O are sensitive to non-hydrostatic stress. Despite this difference, the data show thesame general trends.With further compression ι -Fe O vanishes quickly and is absent in spectra above 55 GPa(Fig. 5c and Fig. 6c). There is an approximately constant ratio between areas of the remain-ing sextet and non-magnetic doublet up to 60 GPa. Above this pressure the green sextet also15tarts to gradually disappear and the CS and QS pressure dependences of the doublet haveinflections around 60 GPa (Fig. 6a,b). The quadrupole shift of the ζ -Fe O magnetic sex-tet remains zero within statistical uncertainty during compression. Note that the increaseof the hyperfine field of the green sextet (Fig. 6d) could signify that H hf is far from itssaturation value, and therefore the magnetic critical point in ζ -Fe O is considerably lowerthan that of hematite before the transition (the data in Ref. 60 confirm this conclusion). At70 GPa the doublet remains the only component of the spectra, in agreement with a singlestructural position of iron in orthorhombic θ -Fe O . In this phase the line width decreasesto 0.13 mm/s. Upon decompression from 61 to 50 GPa, M¨ossbauer spectra reveal a fullyreversible behavior ( ι -Fe O starts to appear again at 50 GPa).The interpretation of the M¨ossbauer components of ζ -Fe O within the framework of theproposed double-perovskite structure is as follows. The peculiar feature of the green sextetis the CS value which is even higher than that of hematite at ambient conditions (Fig. 6a).Since the isomer shift of iron increases with increasing iron coordination number , we canconclude that this sextet corresponds to HS Fe in the bicapped trigonal prisms, i.e., the A-site (with 8 oxygen neighbors). Accordingly, the blue doublet is assigned to the signal fromthe octahedral B-site and corresponds to the LS Fe , as this component is non-magneticand has CS lower by 0.23(2) mm/s than HS ferric iron before the transition (Fig. 6a).The interpretation connected with the double-perovskite structure encounters a numberof difficulties, however. Firstly, the model structure has two types of octahedra with differentvolumes (corresponding to HS and LS states of the iron ion). One would therefore expectthat ζ -Fe O should give three components in M¨ossbauer spectra. Contrary to that, ourexperimental data do not show any sign of an additional component. We emphasize that the ι -Fe O sextet (Fig. 5c) cannot be this third component due to high H hf (Fig. 6d), becausethe ζ -Fe O magnetic critical temperature is significantly lower than that in α -Fe O and H hf is far from saturation . Moreover, the volumes of both octahedra in ζ -Fe O at 54 GPa(8.6 and 7.5 ˚A ) are too small compared to the rest of the examined data (see section IV B 1).Secondly, according to the model structure of the ζ -Fe O phase , one could expectthat after the HS → LS transition in the octahedra, the M¨ossbauer spectrum will have twocomponents with area ratio 1:1 (HS iron in bicapped trigonal prisms and LS iron in oc-tahedra). The subsequent transition to θ -Fe O should result in an abrupt vanishing ofone component. However, our data clearly show that the green sextet disappears gradually16Fig. 5c), and at 65 GPa the area ratio between the doublet and the sextet is around 4:1(Fig. 6c).Thirdly, it is not clear why a strong change of the coordination polyhedron (octahedronto trigonal prism) at the ζ -Fe O to θ -Fe O transition does not lead to discontinuities in thehyperfine parameters (Fig. 6a,b). Moreover, the data show that QS values of α -Fe O and ζ -Fe O doublets are almost the same at 50 GPa (Fig. 6b). Such behavior is at variance withthe general trend of the increase of ∆ at the HS −→ LS transition of Fe in the octahedra .To overcome these disagreements, we note that ι -Fe O and θ -Fe O have the same pack-ing motif (Fig. 4a and 5b), the only difference being the type of iron polyhedron (octahedron vs trigonal prism). Moreover, at the α - to ζ -Fe O transition our experiments show a si-multaneous appearance of ι -Fe O together with the ζ -phase (Fig. 5c and 6c). Data inRef. 60 clearly demonstrate that ζ -Fe O transforms to ι -Fe O under decompression, notto α -Fe O . These facts indicate that ζ -Fe O is an intermediate phase in the reconstructivetransition between ι -Fe O and θ -Fe O . The stabilization of the intermediate phase over afinite pressure range and the complex dynamics of this reconstructive transition arise dueto changes of iron spin state (and, accordingly, ionic radius) across it.The double-perovskite structure (Fig. 5a) therefore does not appear to be a suitable can-didate for this intermediate phase. Based on our M¨ossbauer data, it is reasonable to assumethat the trigonal prisms are already present in the ζ -Fe O structure and associate the bluedoublet (Fig. 5c) with them. This explains the smooth behavior of the doublet hyperfineparameters at the transition from ζ - to θ -Fe O (Fig. 6a,b). The green sextet corresponds toHS Fe (we cannot say anything about its polyhedron besides that a coordination numberhigher than six is plausible) and its progressive disappearance above 60 GPa might indicatethat changes in the shape of polyhedra and interatomic distances proceed gradually. Atheoretical investigation of the possible pathways between ι -Fe O and θ -Fe O structuresshould clarify this problem.In concluding this section, it is important to note that trigonal prismatic coordination( D h symmetry group) does not lead to the habitual splitting of 3 d -levels on e g , t g manifoldsas octahedral, tetrahedral ( e , t ) and cubic environments. Instead, the d -levels split into alow-lying d z singlet and d x − y , d xy doublet, and high-energy d xz , d yz doublet . It is evidentthat in the trigonal prism, the crystal field does not quench orbital moments at all and it isconvenient to use the designations d , d ± and d ± for 3 d -orbitals.17n the case of the trigonal prism, the intermediate spin state can be readily stabilizedin addition to HS and LS states, as the energies of d and d ± levels are sensitive to thegeometry of the prism . To exclude this possibility we use the fact that the metal-liganddistance is approximately the same for both octahedral and trigonal prismatic coordina-tion . Comparison of the average Fe-O distance in θ -Fe O (1.82(4) ˚A at 74 GPa ) withtypical values for LS Fe in oxygen octahedra shows unambiguously that iron ions are inthe low-spin state in this phase, in agreement with conclusions based on M¨ossbauer data.For LS Fe in the trigonal prism, there are two possible electronic ground states: non-degenerate A (cid:48) (with one electron on the d orbital) and the doubly degenerate E (cid:48) state(with three electrons on the d ± orbitals). The highly distorted trigonal prisms in θ -Fe O indicate the Jahn-Teller nature of the iron ion and, therefore, support the E (cid:48) electronic state.The peculiarity of E (cid:48) is a huge orbital moment 2 µ B (for a purely ionic state), exceedingthe spin contribution to the total magnetic moment. Hence, LS Fe in a trigonal prism issubstantially different from the octahedral case and this should be taken into account in theanalysis of physical properties of ζ - and θ -Fe O . C. Skiagite-iron-majorite solid solution
Below 50 GPa the M¨ossbauer spectrum of the studied solid solution is a superpositionof two paramagnetic doublets corresponding to ferrous iron in the X-site and ferric ironin the Y-site (Fig. 7b). At 1.4 GPa the hyperfine parameters are δ CS = 1 . . and δ CS = 0 . . , which is in excellent agreement with . As the garnet structure is cubic, evenin the case of single-crystal M¨ossbauer experiments the doublet components should haveequal areas for any orientation . A small asymmetry of the X-site doublet areas appearsdue to the Gol’danskii-Karyagin effect (GKE) . Note that the GKE is not possible for theY-site, as all diagonal elements of the mean-square displacement tensor are equal due to thesymmetry of this position.The signal from Y-site Fe is not detected in the M¨ossbauer spectra, despite the samplecontaining 23 mol. % of iron-majorite. Apparently, the small amount of octahedral divalentiron is not distinguishable within the statistics of data collection. The interpretation that theY-site doublet (blue, Fig. 7b) is the signal from iron in a mixed valence state is implausible.18 IG. 7. a) Skiagite-iron-majorite solid solution with typical garnet structure. Its framework isformed by corner-shared SiO tetrahedra (Z-site, blue) and (Fe,Si)O octahedra (Y-site, gold), andthe distorted cubic voids (X-site) are populated by Fe . In the pressure range 50 60 GPa, skiagite-iron-majorite solid solution undergoes an isosymmetric phase transition with ≈
10 % discontinuityof (Fe,Si)O volume . b) M¨ossbauer spectra of skiagite-majorite solid solution before (50 GPa)and after (65 GPa) spin crossover. The green doublet corresponds to the X-site with HS Fe ,the blue and brown doublets correspond to the Y-site with HS and LS Fe , respectively, and theviolet singlet corresponds to the LS Y-site Fe . Mixed valence components are observed in compounds where iron polyhedra (participatingin intervalence charge transfer) are connected through common edges or faces , which isnot the case for iron populating the octahedral position in the garnet structure (see Fig. 7a).The M¨ossbauer spectra do not change substantially with compression up to 50 GPa.Above this pressure the Fe component starts to transform into an asymmetric doubletwith higher quadrupole splitting (Fig. 7b). The changes develop up to 65 GPa, so thetransformation pressure range is consistent with that determined from the XRD data within experimental error. Between these pressures the Y-site component shows dynamicalbroadening which indicates interconversion between spin states comparable with the meanlifetime ( ∼ − s) of the excited state of Fe.Since the structure of skiagite-iron-majorite preserves the cubic symmetry over the entireinvestigated pressure range, the intensities of the Y-site doublet lines should remain equal19
IG. 8. Pressure dependence of center shift (a) and quadrupole splitting (b). The hyperfineparameters of X-site Fe (green) show monotone behavior over the entire all pressure range.Above 50 GPa, the CS of Y-site Fe decreases with simultaneous growth of QS (blue and brownpoints). The colors conform to those in Fig. 7b and the squares and stars correspond to twoindependent experiments. after spin crossover . To describe the new feature (strong asymmetry of the new doublet)one could add a singlet to the more intense line of the new doublet and interpret it as ironin a different electronic state in the octahedral position (Fig. 7b, spectrum at 65 GPa).Indeed the value of the center shift of the singlet (0.57(2) mm/s at 65 GPa) is close to valuescharacteristic for LS Fe in oxygen octahedra . This observation could be an indicationthat octahedral ferrous iron undergoes a HS → LS transition. Due to collapse of the doubletinto a singlet, the dip of this component increases by a factor of two, hence the signal fromthis ion could become distinguishable.The asymmetry of the Y-site doublet could also be caused by a dynamical Jahn-Tellereffect of LS Fe , because in the low-spin state, ferric iron has the orbitally degeneratestate T g . There are several equivalent distortions that remove degeneracy, and the ironoctahedron can resonate between them. It could lead to non-trivial modifications of the lineshape, if the hopping characteristic time between equivalent distorted configurations is closeto the characteristic measurement time .We note, however, that while the proposed explanations of the asymmetry of the doubletdescribed above are ambiguous and further work (for example, low-temperature MS) maybe required to fully explain the observations, this uncertainty does not affect our major20onclusions in any way. The brown doublet (Fig. 7b) remains the signal of trivalent iron inthe octahedral site. The hyperfine parameters of ferric iron during the transition change inthe following way: at 65 GPa CS drops from 0.24 (at 50 GPa) to 0.03 mm/s and the QSvalue increases from 0.34 to 0.8 mm/s (Figs. 8a and 8b). These changes are consistent withtypical trends for spin transitions of ferric iron. Hyperfine parameters of divalent iron in thecubic position vary monotonically up to 90 GPa (Figs. 8a and b). IV. DISCUSSIONA. Hyperfine parameters at spin transitions in Fe O octahedra TABLE II. Hyperfine parameters of ferric iron in the studied compounds before and after the spintransition. All parameters refer to ambient temperature if not given explicitly.Compound δ HS − δ LS , mm/s ∆, mm/s H hf , Tbefore after before afterFeBO (Fe . Si . )(SiO ) O O All considered compounds demonstrate similar behavior through spin transitions. Themain features are (i) drop in CS value, (ii) disappearance of magnetic order at room temper-ature, and (iii)
LS state of ferric iron ion characterized by doublet with higher quadrupolesplitting (relative to HS values of Fe ). All data on hyperfine parameters of ferric iron incompounds of interest before and after spin transition are compiled in Table II.
1. Isomer chemical shift
The physical meaning of isomer shift in MS is an electron density on the probe nucleuswhich is almost fully created by s -electrons (with relativistic considerations there is also aminor p -electron contribution) . One can write it in such form21 IS = 2 π Ze [ (cid:104) r e (cid:105) − (cid:104) r g (cid:105) ]∆ ψ (0) = α · ∆ ψ (0) , (2)where Z is the proton number, (cid:104) r (cid:105) is the mean-squared nuclear radius of the excited andground states, and ∆ ψ (0) is the difference in electron density at the nucleus between themeasured and reference compounds. The constant α is negative in the case of Fe.The difference in the isomer shift between HS and LS states has been known since the earlydays of M¨ossbauer spectroscopy . As HS and LS ions have different radii, the metal-ligandbonds should be shorter for the LS configuration and, accordingly, an increased covalencyof chemical bonds. This suggests that in the LS state, the occupancy of 4 s -orbitals increasewhich leads to higher electron density at the nucleus and to lower isomer shift. However,modern density functional theory (DFT) calculations have not found a correlation betweenthe IS value and 4 s -L¨owdin population . In that paper the general inference was made thatthe metal-ligand bond length is important and that shorter bonds result in lower isomershifts. In any event, bond length is a determinative factor and the IS value is necessarilylower for the LS iron ion.In the compounds in the present study, the spin transition starts at CS values of0 . ± . i ) the transition is isosymmetric (as distinct to the case of hematite), ( ii ) thetransition is first-order, i.e., abrupt (unlike in skiagite-iron-majorite, for example), and ( iii )the M¨ossbauer spectra were measured at room temperature so the influence of changes inthe second-order Doppler (SOD) shift should be minimal (see discussion in Ref. 61).The difference in CS values between HS and LS states is half the difference comparedto coordination complexes ( ∼ . . The smaller difference is probably related tosmaller changes in the octahedral volume of Fe O (compare changes in bond length fordifferent ligands in Ref. 62, Table 1). The relatively large discontinuity in values for FeOOH(Table II) might be related to hydrogen bond symmetrization and corresponding significantchanges in the SOD shift (in this case the zero-motion contribution may change significantly).22 . Second-order Doppler shift and center shift The second-order Doppler shift results in reduction of γ -ray energy due to relativistictime dilatation in the reference frame associated with the moving nucleus δ SOD = − (cid:104) v (cid:105) c E γ = − (cid:104) (cid:15) k (cid:105) M c E γ , (3)where E γ is the γ -quantum energy, (cid:104) v (cid:105) is the mean-squared velocity of the nucleus in thecrystal, M is the nuclear mass, c is the speed of light and (cid:104) (cid:15) k (cid:105) is the mean kinetic energyof the nucleus. Under the assumption that the nucleus is a harmonic oscillator, the meankinetic energy is half of the vibrational internal energy and the SOD shift depends linearlyon the internal energy of the nucleus. At the HS → LS transition the magnitude of δ SOD should increase as the decrease of the iron ionic radius causes a reduction of the polyhedronvolume and, accordingly, leads to an increase of the force constants. Therefore, changes in δ SOD will have the same sign as changes in the isomer shift.Value of the SOD shift can be determined by means of nuclear inelastic scattering (NIS)data. From the NIS spectrum one can extract the partial phonon density of states (pDOS)of the M¨ossbauer isotope and the vibrational internal energy can be directly determined byintegrating the pDOS function (cid:15) v = 32 (cid:90) ∞ E coth (cid:18) E k B T (cid:19) D ( E ) dE, (4)where D ( E ) is the iron pDOS and k B is the Boltzmann constant.For the compounds in this study, there is NIS data only for the skiagite–iron-majoritesolid solution up to 56 GPa . As iron populates two different structural positions in thisgarnet, the corresponding pDOS is an average function of both. Nevertheless, these data canyield a reasonable estimation of changes in the SOD shift at the spin transition of Y-site Fe as δ CS of X-site Fe does not show any evident anomalies in the vicinity of spin crossover(Fig. 8a). There is a 4 meV increase of mean internal energy between 45 and 56 GPa thatcorresponds to 0.011(4) mm/s change of δ SOD . This is about 10 % of the observed variationin center shift upon HS-LS crossover.One can also use siderite (FeCO ) data to crosscheck this estimation. Siderite is isostruc-tural with iron borate and contains carbon and ferrous iron instead of boron and ferric iron,respectively. Siderite also undergoes a HS → LS transition at similar pressures ( ≈
45 GPa)23nd with similar changes in unit cell and octahedron volumes ; hence the phonon proper-ties of the crystal lattice should be similar to those of FeBO . Siderite NIS data show a 4 meVdiscontinuity at the spin transition , and the respective δ SOD change is 0.011(2) mm/s, sim-ilar to the estimation for the skiagite-iron-majorite solid solution.The center shift extracted from M¨ossbauer spectra is simply the sum of isomer and SODshifts ( δ CS = δ IS + δ SOD ). Thus, our estimations suggest that reduction of δ CS at thepressure-induced spin transition of Fe at ambient temperature is mainly caused by theisomer shift. The SOD contribution is not higher than 10 %.
3. Hyperfine magnetic field
At the HS → LS transition in octahedral coordination, the spin of ferric iron changesfrom 5/2 to 1/2. This means a huge drop of the iron magnetic moment, but Fe remainsparamagnetic in the LS state as distinct from LS Fe . Accordingly, the transition shouldcause a large drop of N´eel (Curie) temperature. Indeed, in all studied compounds that weremagnetically ordered in the HS state, the disappearance of magnetic ordering or a largedecrease of the H hf value at the spin transition are observed.Reliable experimental information about the T N pressure dependence is unfortunatelyabsent. To estimate the magnetic critical temperature in the vicinity of the spin transitionfor the considered compounds, one can apply Bloch’s law : T N ∝ J ∝ V ( − / , (5)where J is the exchange integral. For V it is more reasonable to use the volume of theoctahedron instead of the unit cell volume as it better determines the overlapping of elec-tronic wave functions. The obtained estimations are listed in Table III. Using the mean-fieldapproximation and assuming that the exchange integral does not change substantially, onecan obtain that the N´eel temperature after the spin transition will be 3/35 of T N beforethe transition . Although the constancy of the exchange integral through the spin transi-tion is doubtful , this result is satisfactory for rough estimations. The factor 3/35 meansthat existence of magnetic order at room temperature after the spin transition requires thatthe N´eel temperature before the transition should be around 3500 K. Even the large T N inhematite (1675 K, Table III) is substantially less than this value.24 ABLE III. Estimated N´eel temperatures from Bloch’s law in the vicinity of the HS → LS transitionin the studied compounds.Compound T N at ambientpressure, K T N just belowtransition, KFeBO
348 690FeOOH 393 649CaFe O
200 370Fe O
948 1675
The hyperfine magnetic field results from interaction of the nuclear spin with its ownelectrons and can be expressed as a sum of three contributions: Fermi contact interaction( H c ) and a dipolar interaction with orbital and spin momenta ( H L and H S , respectively) ofthe electrons : H hf = H c + H L + H S , (6) H c = 8 π g e µ B (cid:104) S (cid:105) (cid:88) ns (cid:20)(cid:12)(cid:12)(cid:12) ψ ↑ ns (0) (cid:12)(cid:12)(cid:12) − (cid:12)(cid:12)(cid:12) ψ ↓ ns (0) (cid:12)(cid:12)(cid:12) (cid:21) , (7) H L = g e µ B (cid:104) r (cid:105)(cid:104) L (cid:105) , (8) H S = g e µ B (cid:104) r ( S · r ) 1 r − S r (cid:105) , (9)where g e is the electron spin g -factor, µ B is the Bohr magneton, (cid:12)(cid:12)(cid:12) ψ ↑↓ ns (0) (cid:12)(cid:12)(cid:12) is the electrondensity at the nucleus for a given ns shell with spin parallel or antiparallel to the expectationvalue of the net electronic spin (cid:104) S (cid:105) , (cid:104) L (cid:105) is the expectation value of orbital momentum and r is the radial coordinate of electrons. As all terms in (6) depend on (cid:104) S (cid:105) or (cid:104) L (cid:105) , thecorresponding H hf of Fe in HS and LS configurations should be significantly different.The saturation H hf value of HS ferric iron in oxygen octahedra (electronic term A g ) isusually around 50–55 T. For this electronic configuration orbital momentum is absent, thesaturation value of (cid:104) S (cid:105) is 5/2 and the observed hyperfine field arises mainly from the Fermicontact interaction term. In the LS state ( T g term) the saturated values of (cid:104) S (cid:105) or (cid:104) L (cid:105) canreach 1/2 and 1, respectively. So in this case H c should be around 11 T, but H L and H S H L and H S may have different signs relative to H c , the resulting hyperfine fields may lie in the 0 to 20 T range.There are only a scarce amount of data for H hf of Fe O in the LS state. Magneticordering was observed in FeOOH with LS Fe that showed a hyperfine field of 7.2 T at6 K (Table II, but it is not clear if H hf was saturated) and magnetism was also reportedin FeBO below 50 K . In the latter case perturbations of NFS spectra were detected, butit was not possible to fit them satisfactorily. Moreover, spin transitions in Fe can lead tometallization with disappearance of magnetic moments (as in the case of CaFe O ). It isclear that further systematic studies of magnetic ordering in phases containing high-pressureLS trivalent iron are required.
4. Quadrupole splitting
The main parameter of M¨ossbauer spectra that is usually used to discriminate betweenHS and LS states is the quadrupole splitting. The strength of the quadrupole interactiondepends on the electric field gradient created at the nucleus by the electron cloud (electroniccontribution) and by neighboring ions (lattice contribution) : q = (1 − R ) q e + (1 − γ ∞ ) q i , (10)where q , q e and q i are the EFG (total, electronic and lattice contributions, respectively), and R and γ ∞ are the Sternheimer factors of shielding and antishielding, respectively. Since theEFG is proportional to r − , firstly the electronic part generally is the dominant contributionto the EFG and secondly, in the case when the lattice contribution plays a principle role theEFG will be mainly dominated by the first coordination sphere (since the second neighborsat 2 r distance produce an EFG that is 8 times weaker). The above-mentioned correlationbetween decrease of the iron octahedron distortion and quadrupole shift in iron borate is agood example of the latter case.As fully-filled or half-filled e g and t g orbitals do not produce an EFG (see Table 4.2 inRef. 54), the quadrupole splitting in the case of HS Fe is mainly related to the latticecontribution and is generally small. In octahedrally coordinated Fe in the LS state, theelectron term is T g with one unpaired electron on the t g level and, therefore, for ferric ironat the spin transition the main contribution to the EFG changes from lattice to electronic26for ferrous iron the situation is opposite). This should cause a significant increase of the QSvalue and, indeed, this tendency is observed in all compounds with the exception of Fe O (Table II) where the polyhedron type may change.There is a large spread of QS values of the Fe LS state: from 0.9 mm/s in CaFe O andskiagite-iron-majorite to 2.5 mm/s in FeOOH (at 50 K). Note that the lowest value of∆ is significantly smaller than the corresponding value 1.9 mm/s reported for LS Fe incoordination complexes . The analysis of the EFG in LS Fe is analogous to the approachfor HS Fe . The additional electron on the t g level is replaced by a hole and the EFGwill be controlled by t g manifold splitting and temperature. This explains the spread of QSvalues in the LS state through the different degrees of octahedral distortion in the studiedcompounds. The temperature dependence of ∆ for LS Fe has been observed for FeOOHand CaFe O . B. Structure data
1. Volume of Fe O octahedron at spin transition FIG. 9. Volume of Fe O octahedra as a function of pressure for different compounds. Blacksquares correspond to iron borate, red circles to skiagite, green and blue triangles to two differentstructural positions in calcium ferrite, cyan diamonds to goethite, magenta hexagons to hematiteand brown stars to andradite. Fig. 9 shows the dependence of the octahedron volumes in the studied compounds as a27
ABLE IV. Crystal field parameters and the estimated polyhedron volumes at transition onset.Compound 10 D q (cm − ) B (cm − ) β V (˚A ) V t from eq. (11) (˚A ) exp. V t (˚A )FeBO
680 0.68 11.61 9.0 9.1Fe O
540 0.54 10.77 10.2 9.0FeOOH 15320
590 0.59 10.81 10.3 9.3Ca Fe Si O
593 0.59 10.9 9.2 8.9 function of pressure. One can see that the spin transition of Fe starts in the pressurerange 45–60 GPa and over a remarkably narrow range of octahedron volume — 8.9–9.3 ˚A .This suggests that the spin transition is controlled by the electronic density inside theoctahedron and explains why the spin transition starts within a narrow range of CS values(see section IV A 1).In crystal field theory the crystal field splitting parameter determines the strength ofthe electrostatic potential created by anions and is directly related to the distance betweencation and anions ( D q ∝ r − for an ideal octahedron, ch. 2 in Ref. 84). Using Tanabe-Suganodiagrams one can estimate the transition bond length at which the spin transition shouldhappen. So, for the polyhedron volume we can write: V t = V (cid:32) D q D tq (cid:33) / , (11)where V is the octahedron volume, and the indices 0 and t correspond to ambient pressureand at the spin transition, respectively. The results of this estimation for the compoundsunder consideration are collected in Table IV. One can see that this simplest model overes-timates the transition volume notably in the case of hematite and goethite. If predictionswould be accurate, the spin transition in these compounds would take place at 20–25 GPa.Note that this discrepancy is not related to covalent effects. The degree of covalency can beestimated using the nephelauxetic ratio β (smaller values of β indicate more covalent bonds,while unity means a purely ionic bond). Despite the fact that hematite and goethite aremore covalent than iron borate, Eq. (11) predicts nearly the correct octahedron volume forandradite, which has the same nephelauxetic ratio as hematite (Table IV).This problem is most likely related to octahedral distortions. In both hematite andgoethite, octahedral Fe-O bonds divide into two groups (three bonds in each) with different28 ABLE V. Equation of state parameters of the HS ferric iron octahedron in the studied compounds.The Birch-Murnagham (BM) EoS of both 2nd and 3rd order was used. For calcium ferrite, theaverage volume of two octahedra (for iron in two distinct crystallographic positions) was used.Compound EoS order V (˚A ) K (GPa) K (cid:48) FeBO O Fe (SiO ) O lengths: approximately 1.95 and 2.10 ˚A at ambient conditions. Electrostatic potentials withsymmetry lower than cubic contain additional terms that have different power dependencieson r (for instance, the term ∝ r − for a trigonally distorted octahedron, see ch. 2 in Ref. 84).Therefore, consideration of the proper electrostatic potentials for hematite and goethiteshould include a correct estimation of the transition volumes, but such an examination isbeyond the scope of this work.In all studied compounds, iron octahedra show very similar compressibility (Fig. 9).Skiagite-iron-majorite solid solution data deviate from the rest of the examined compoundsdue to the mixed population of the Y-site by iron and silicon, because the SiO octahedron issignificantly smaller than one for Fe O (for example, in the ilmenite- and perovskite-typeMgSiO polymorphs the volume is around 7.64 ˚A at ambient conditions ). Owing to this,XRD provides an average picture with a reduced volume of the (Fe,Si)O octahedron (Fig. 9).At spin crossover the volumes of iron octahedra decrease and approach those of siliconoctahedra, where the difference between the average volume of the (Fe,Si)O octahedra andthe rest of the data becomes small above 60 GPa (Fig. 9).The isothermal bulk moduli of Fe O octahedra in different compounds at ambient29onditions vary between 170 and 210 GPa (Table V). The K value correlates with theoctahedron volume at ambient pressure and, apparently, it is related to the length of Fe-Obonds (the shorter the bond, the more incompressible the octahedron). In the vicinity ofthe spin transition the average value of K is around 400 GPa (iron borate has the lowestvalue of 340(20) GPa). Currently, only iron borate and calcium ferrite have sufficient datapoints above the spin transition for estimation of the LS octahedron EoS . For FeBO the parameters of the EoS (BM, 2nd order) are V = 9 . and K = 225(65) GPa,and for CaFe O they are V = 9 . and K = 320(50) GPa. As LS ferric iron hasa significantly smaller ionic radius, one can expect that elastic moduli should increase atthe HS → LS transition. Indeed, an EoS comparison of HS and LS Fe O octahedra showsthat at 50 GPa, the bulk modulus changes from 340(20) GPa to 410(70) GPa and from400(20) GPa to 510(50) GPa for FeBO and CaFe O , respectively.
2. Cooperativity at spin transition
Available single-crystal XRD data show that pressure-induced spin transitions in inor-ganic compounds have a strong tendency to result in isosymmetric transitions. From thephenomenological theory of phase transitions, it follows that they can proceed either as first-order transitions or, beyond the critical point, a crossover in which there is no discontinuityin any free-energy derivative .The abundance ratio of different spin states would be controlled by Boltzmann factorif cations change spin states independently. However, since cations in different spin stateshave different ionic radii, a spin transition of one ion introduces a strain field to the crystallattice (one can consider the ion in a different spin state as an impurity). The couplingwith this strain field determines the strength of cooperative behavior at the spin transitionand, accordingly, the critical temperature ( T cp ) at which the first-order phase transition ischanged by crossover behavior. In general, the elastic interaction between impurities in acrystal is complex and may even lead to superstructures with cations coexisting in differentspin states . However, to our knowledge, no single-crystal XRD study of pressure-inducedspin transition has observed such superstructures. We therefore limit our discussion tosimple isosymmetric transitions, as they involve all principal features of the spin-transitionphenomenon. 30n the crossover regime, there is dynamical spin state equilibrium at the spin transition, socations permanently change their spin state. The rate of these changes ( t s ) is an importantparameter, since different experimental techniques have different characteristic measurementtimes ( t m , 10 − s for Fe MS). Hence, depending on the ratio t s /t m , one technique canshow an averaged spin state while another can show the apparent static coexistence of spinstates. Since phase coexistence is an inherent feature of first-order phase transitions, it is notnecessarily a trivial task to determine which mechanism of spin transition is observed, whichmay lead to wrong conclusions. In this respect diffraction techniques have an advantage,because they average over ensemble and not time period. Hence if a spin transition proceedsin a first-order manner, one will see peak splitting corresponding to spin-domains withdifferent volumes (see siderite example in Ref. 75), while for crossover it will be simply asingle phase with averaged volume. In addition, results of powder DAC experiments shouldbe considered with caution because of the tendency to broaden the transition region (seecomparison of powder and single-crystal experiments in Ref. 68).For the examined compounds (Table I) the condition of cooperativity is as follows: ifiron octahedra share common oxygen atoms and form an infinite framework, the compoundshows strong cooperative behavior at pressure-induced spin transitions (by “strong” we meanthat the critical point lies above room temperature). If this condition is fulfilled there arefavorable conditions for magnetic ordering by means of superexchange interactions. Indeed,all such studied compounds in the HS state are magnetically ordered at room temperaturein the vicinity of the spin transition (see Table III). However, if the compound undergoesan isosymmetric (according to XRD) HS → LS transition and magnetic ordering disappearsin the LS state, when, strictly speaking, the transition is not isosymmetric, because atsuch transition the symmetry relative to time reversal is changed. This leads to importantconsequences: ( i ) the spin transition in magnetically-ordered compounds can only proceedas a first-order phase transition, and ( ii ) the temperature of the critical point cannot belower than the N´eel (Curie) temperature of the HS phase in the vicinity of the spin transition.These conclusions are valid if the spin transition is the driving force of the transition.Among the studied compounds, only the spin transitions in the Y-site of the garnet struc-ture (andradite and skiagite–iron-majorite solid solution) show explicit crossover behaviorat room temperature within ∼
10 GPa. This is in agreement with the formulated cooper-ativity condition, since Y-site octahedra do not share oxygen atoms (Fig. 7a). Note that31his is a clear structure feature, where the spin transition of Mn ( d configuration) in theoctahedral site of the hydrogarnet henritermierite proceeds in the same way .An interesting transition takes place in yttrium iron garnet (YIG) Y Fe O in whichferric iron populates both the Y-sites and tetrahedral Z-sites. Although YIG is isostruc-tural to the garnets discussed above, it undergoes a different phase transition. At pressurescharacteristic for the Fe O spin transition (50 ± that is not related to the mechanical instability . YIG remainsferrimagnetic ( T C = 559 K at ambient conditions) up to amorphization, so a spin transitionaccording to our phenomenological arguments can proceed only in a first-order manner.The Fe O tetrahedron is a “metastable” polyhedron at high pressure due to the rela-tively large ionic radius of ferric iron (49 pm vs
26 pm of Si ) and the general tendency toincrease coordination number with pressure . Indeed, XRD and M¨ossbauer data of amor-phous YIG show evidence that iron has six-fold coordination in this state . Moreover,YIG is metastable at room temperature above 31 GPa and transforms to the perovskitestructure (in which the minimum cation coordination number is six) upon heating , whichis typical behavior for members of the garnet family. There is a large kinetic barrier betweenthe garnet and perovskite structures, which, to our knowledge, cannot be overcome by anygarnet at room temperature. Therefore, it is the instability of HS Fe O octahedra uponreaching the critical volume that serves as a trigger for this amorphization, allowing thekinetic barrier to be overcome (partially in this case). The cooperative behavior of ironoctahedra might be crucial for the process. Indeed, spin transition by crossover does notlead to such consequences for the garnet examples above (although they are also certainlymetastable at spin crossover pressures). The appearance of ι -Fe O at the transition of α -Fe O to ζ -Fe O (see section III B) might also be related to this phenomenon.In the case of solid solutions, the highest T cp value will be seen in the iron end-member.Reduction of the amount of iron in the system will decrease the cooperativity of iron octa-hedra and, accordingly, the critical point temperature. In natural systems pressure-inducedspin transitions are inferred to occur in the Earth and exoplanet interiors. In view of theabove considerations the iron spin transition in the Earth’s mantle should tend to crossoverbehavior for the following reasons: ( i ) mantle minerals are solid solutions with relativelylow concentrations of iron that promote a decrease of the cooperativity of iron ions, and ( ii )the temperatures of the mantle are high ( > . Center shift vs polyhedron volume FIG. 10. Center shift as a function of the octahedron volume. Within experimental uncertaintiesdata show a linear dependence. Purple and blue circles are data of FeBO (HS and LS, respectively),orange diamonds correspond to α -Fe O , and brown squares belong to FeCO (single-crystal datafrom Ref. 68). The red lines are linear fits to the underlying points (the middle line is a fit of theFeBO HS points). In the HS state, slope values are the same for both ferric (FeBO , α -Fe O ) andferrous (FeCO ) iron ions. The LS state in iron borate is more sensitive to changes of octahedronvolume. Single-crystal XRD experiments provide a unique opportunity to study the dependenceof CS on the polyhedron volume (Figs. 10 and 11). In addition to the compounds measuredin this work, we also used for comparison single-crystal M¨ossbauer data of siderite . Usingstructure data from Ref. 75 we obtained the following 2nd BM EoS parameters for theFe O octahedron: V = 13 . and K = 108(3) GPa. Hence the octahedron offerrous iron is larger by ∼ at ambient conditions (see Fig. 9) and more compressiblerelative to ferric iron octahedra.In all studied compounds the CS value varies linearly with octahedron volume. It is inter-esting that for the HS octahedra, linear fits have the same slope (Fig. 10) within uncertainty,regardless of valence state: 0.079(4), 0.079(5) and 0.082(4) mm/s · ˚A − for FeBO , α -Fe O and FeCO , respectively. Y-site Fe in skiagite-iron-majorite solid solution shows the samelinear dependence in the HS state (Fig. 10a) with slope 0.087(6) mm/s · ˚A − , but one shouldnote the systematic error in this value because the average (Fe,Si)O volume was used.33 IG. 11. Volume dependence of CS in skiagite-iron-majorite solid solution. a) CS of Y-site HSFe (pink circles) also depends linearly on octahedron volume, but LS data (blue circles) showalmost the same slope in contrast to FeBO . b) CS of X-site Fe (in distorted cube) has a muchweaker non-linear dependence. The red lines are linear fits to the underlying points. This similarity of slopes suggests that the volume dependence of CS is governed by thesame mechanism in all investigated compounds. The noted difference in pressure dependenceof isomer shift between Fe and Fe compounds is therefore simply related to the highercompressibility of ferrous iron (at least in the case of octahedral coordination). High-pressureNIS data of siderite show that δ SOD also depends linearly on octahedron volume with0.0050(1) mm/s · ˚A − coefficient, which is 6 % of the observed volume dependence of δ CS .The data clearly show that the CS discontinuity between two spin states is caused notonly by the volume difference, but also to changes in the electronic configuration, since theLS values do not lie on continuations of HS lines (Fig. 10 and 11a). In the LS state δ CS ismore sensitive to volume changes in the FeBO case (Fig. 10), while LS Fe in skiagite-iron-majorite shows roughly the same slope as the HS state (Fig. 11a). The number of datapoints is too small, however, for definite conclusions. Also note that in the latter case theCS values can be affected by strong overlap with singlet component (Fig. 7b).The volume dependence of δ CS for different types of coordination polyhedron can beobtained from the skiagite-iron-majorite data. The CS variation of cubic X-site Fe isnonlinear and considerably weaker than for the case of the octahedron (Fig. 11b). A linearfit of the data below 16 ˚A (pressure above 60 GPa) has a slope of 0.054(3) mm/s · ˚A − .34 . CONCLUSIONS We performed a comparative study of the spin transition in Fe O octahedra in a numberof different compounds using MS in combination with single-crystal XRD data. Analysis ofthe obtained data shows that the most universal and unambiguous evidence of the HS → LStransition among hyperfine parameters is a drop of the center shift value ( ≥ .
13 mm/s).One significant advantage is the temperature independence of the drop, which is not thecase for quadrupole splitting, since for the studied case the QS values for the LS state canbe close to HS values before spin transition. However, the temperature dependence of ∆within the LS state can be a reliable indicator.We argue that ζ -Fe O is an intermediate phase in the reconstructive phase transitionbetween ι -Fe O and θ -Fe O . The interpretation of M¨ossbauer data in the framework ofthe existing model for the structure of ζ -Fe O is not consistent with observations. Basedon behavior of hyperfine parameters in the Fe O system, we conclude a coexistence of HSand LS Fe in ζ -Fe O with LS Fe occupying trigonal prisms.Structural data reveal that for all studied compounds, the spin transition starts withina narrow range of octahedral volumes: 8.9–9.3 ˚A . Taking into account the compressibil-ity of Fe O octahedra, this corresponds to the 45–60 GPa pressure range. The simpleideal octahedral model from crystal field theory predicts transition volumes with reasonableaccuracy, but highly distorted octahedra require a more elaborate approach.Spin transitions usually lead to isosymmetric structural transitions. Two scenarios arepossible: supercritical, crossover behavior or first-order phase transition. The degree ofcooperativity in the behavior of iron octahedra (controlled by elastic interactions betweenions in different spin states) plays a crucial role, determining the position of the critical pointon the phase diagram. From phenomenological arguments, it follows that in magnetically-ordered compounds the spin transition can proceed only in a first-order manner. Moreover,experiments show that cooperative behavior is preserved at least at room temperature ifiron octahedra share common oxygen atoms. We argue that instability of iron octahedra onreaching the critical volume, together with cooperative behavior, is important for metastablephases as it may promote the overcoming of kinetic barriers, even at low temperatures.We note that these conclusions are applicable in general to spin transition phenomenon,regardless of the specific transition ion. 35e have demonstrated that the center shift of HS iron depends linearly on octahedralvolume with the same slope, regardless of oxidation state (0.08 mm/s · ˚A − ). NIS data showthat the SOD contribution to this dependence is less than 10 %. Such data can be used fordetermination of the isomer shift calibration constant. The center shift of ferrous iron incubic coordination is less sensitive to the volume changes and the dependence is nonlinear. ACKNOWLEDGMENTS
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