Theoretical and experimental evidence of a site-selective Mott transition in Fe2O3 under pressure

E. Greenberg, I. Leonov, S. Layek, 1 Z. Konopkova, M. P. Pasternak, L. Dubrovinsky, R. Jeanloz, I. A. Abrikosov, G. Kh. Rozenberg 1 School of Physics and Astronomy, Tel Aviv University, 69978, Tel Aviv, Israel. 2 Theoretical Physics III, Center for Electronic Correlations and Magnetism, Institute of Physics, University of Augsburg, 86135 Augsburg, Germany 3 Materials Modeling and Development Laboratory, NUST “MISIS,” 119049 Moscow, Russia 4 DESY, HASYLAB, PETRA-III, P02, Notkestr. 85, Bldg. 47c, Hamburg, Germany. 5 Bayerisches Geoinstitut, University of Bayreuth, Bayreuth, Germany. 6 Department of Earth and Planetary Science, University of California, Berkeley, California 94720 7 Department of Physics, Chemistry and Biology (IFM), Linköping University, SE-581 83 Linköping, Sweden

( VI Fe M )2O3 [Aba2 structure]. Within the P21/n crystal structure, characterized by two distinct coordination sites (VI and VIII), we observe equal abundances of ferric ions (Fe 3+ ) and ions having delocalized electrons (Fe M ), and only at higher pressures is a fully metallic Aba2 structure obtained, all at room temperature. Thereby the transition is characterized by delocalization/metallization of the 3d electrons on half the Fe sites, with a site-dependent collapse of local moments. Above ~50 GPa, Fe2O3 is a strongly correlated metal with reduced electron mobility The insulator-metal transition, induced by pressure, composition or by other means, represents perhaps the most profound transformation of the chemical bond in materials. A specific subset, the Mott transition, is of particular importance because it is thought to depend on electron correlations that are essential to understanding the properties of transition-metal oxides important to fields ranging from materials chemistry to condensed-matter physics and even planetary science. Electronic and magnetic transitions in strongly correlated transition-metal compounds have thus been among the main topics of condensed-matter research over recent decades, being especially relevant to understanding hightemperature superconductivity as well as heavy-fermion behavior. 1,2,3,4,5,6,7 . The definitive electronic phenomenon in such compounds is the breakdown of d-or f-electron localization, causing a Mott (Mott-Hubbard) insulator-to-metal transition 1,2 . Such a transition does not necessarily imply a rearrangement of atoms, but in fact often exhibits an appreciable collapse in volume 8,9,10,11 . The initial concept of Mott is based on the relative importance of kinetic hopping (measured by the bandwidth) and onsite repulsion of electrons. However, recently another mechanism was proposed suggesting that a change of the crystal-field splitting rather than variation in the bandwidth may drive a Mott transition 10,12,13,14 . As a result, the Mott transition involves a simultaneous insulator-metal transition, magnetic moment collapse (change of the local spin state) and volume collapse.
Along with this, the existence in real materials of many additional degrees of freedom may result in new scenarios for the Mott transition; e.g., orbital degrees of freedom give rise to a scenario of an orbital-selective Mott transition 15,16,17,18 . Nevertheless, in some materials these paradigms cannot explain the experimentally observed details of electronic and structural transformations. An outstanding example is Fe2O3 hematite (Néel temperature TN =956 K 19 ), which crystallizes in a corundum-type structure with one type of FeO6 octahedron (slightly distorted). Photoemission spectroscopy 3 measurements show that Fe2O3 exhibits Mott insulating behavior with a large energy gap of ~ 2.5 eV 20 .
Upon compression, Fe2O3 is known to undergo a first-order phase transition above ~50 GPa, which is accompanied by a remarkable collapse of the lattice volume by ~10 % , 21,22,23,24,25,26, . The phase transition was associated with a "partial" transition to low-spin (LS) Fe 3+ state 24,27,28,29,30 . However, later Mössbauer studies indicated that at P > 80 GPa only a non-magnetic phase exists, without any sign of magnetic moments down to the lowest temperatures achieved, thereby suggesting a breakdown of 3delectron localization 25 . Furthermore, electrical transport measurements 25 show a sharp insulator-metal transition at a substantially lower pressure of ~50 GPa, which seemingly contradicts the existence of the high-spin state at pressures far above this transition (the high-spin state would not be expected to exhibit the electrical conductivity of a metal) 24,25,27,28 .
The crystal structure of the high-pressure phase of Fe2O3 observed above ∼50 GPa has been assigned either to an orthorhombic perovskite 22,24,31 or a Rh2O3-II-type 23,25 structure in early studies.
Only recently, based on single-crystal diffraction studies 32,33 , the lattice structure has been defined as a double-perovskite (DPv) phase. It has been proposed 23,34 that this structural transition drives the electronic and magnetic transformation. On the other hand, recent theoretical DFT+DMFT calculations 35 (DFT+DMFT: density-functional theory + dynamical mean-field theory of correlated electrons 36 ) predict that the electronic transition occurs within the hematite phase, i.e. prior to the structural transition, at high compression of V < 0.8 V0 (V0 is the equilibrium unit cell volume). According to an experimental equation of state (EOS), e.g. 22,23 , such volumes correspond to P > 70 GPa. We note that in ref. [35] the structural complexity of Fe2O3 near the phase transition has not been considered. Therefore the interplay between correlated electrons and the lattice structure could not have been studied. Thus, despite significant efforts and dozens of publications on this outwardly simple system, the evolution with pressure of the electronic and crystallographic structure of Fe2O3, and the mechanism of its electronic transition remain unresolved. Current theoretical models 35 do not explain the existing experimental results 24, 25,27,28,29,30,34 . 4 In the present work, we have studied Fe2O3 to pressures of about 100 GPa, combining Mössbauer spectroscopy, electrical transport and X-ray diffraction upon compression and decompression, along with first-principles quantum mechanical calculations (DFT+DMFT). Our study reveals a new type of insulator-metal transition, providing what is to the best of our knowledge the first evidence for a site-

Mössbauer spectroscopy
Mössbauer spectra of Fe2O3, characteristic of various pressure ranges and recorded at room and low temperatures, are shown in Figure 1(a, b, c). In agreement with previous publications 24,25,27,28 , the only observed spectral component upon compression is that of the high-spin state up to nearly 48 GPa (hematite phase Figure 1(a)). At P ≥ 48 GPa two new equally abundant components emerge: a nonmagnetic quadrupole-split component, with no sign of magnetic correlations down to 8 K (Figure 1(b)), and a magnetically split component characterized by significantly reduced hyperfine field Hhf (SI Figure   S1). Taking into account the reported double perovskite-type structure in this pressure range 32 , the two components are designated by DPvnm and DPvm, respectively. At P ≥ 56 GPa the only spectral 5 components are DPvnm and DPvm with equal abundances, until at P ≥ 62 GPa the abundance of a nonmagnetic component starts to increase (Figure 2(a)) to the point that above 75 GPa the Mössbauer spectra show a single, quadrupole-split component, designated as the high-pressure (HP) state ( Fig.   1(c)). The lack of any signs of magnetic correlations on Mössbauer timescales (≈ 10 -7 s) down to 4 K ( Figure 1(c)) prompted us to designate this single HP component as a non-magnetic state.
Upon decompression, the DPv components reappear, with a hysteresis of ~6 GPa (Figure 2(b)). In the pressure range of 47 > P > 44 GPa, the two DPv components are replaced by a single HS component designated as DPvdec (Figs. 1(d), S1). However, a component with hyperfine parameters identical to those of the hematite phase appears only below ~35 GPa, with complete transition back to hematite at ~25 GPa (Figs. 1(d), 2).

X-ray diffraction
Powder and single-crystal X-ray diffraction were performed at room temperature, respectively, during compression to 62 GPa followed by decompression, and up to 101 GPa on compression alone 37 .
Our studies show that upon compression a first-order structural phase transition with a symmetry change takes place in the pressure range of 53 to 57 GPa, with a concomitant volume decrease of ~9% (Figures 3, S2, S3). Single-crystal diffraction 32,33 shows that the new intermediate-pressure phase can be described as a distorted double perovskite-type (DPv-Fe2O3) using a monoclinic unit-cell with P21/n symmetry 32 (the symmetry is actually triclinic P-1 33 , however we use a monoclinic model to constrain the atomic arrangement as done in ref. 33). This structure has the general formula A2B'B''O6 and consists of a three-dimensional network of tilted corner-sharing B'O6 and B''O6 octahedra with A-cations located in bicapped trigonal-prismatic voids (8 nearest neighbors) ( Figure S4, interatomic distances are given in SI Table 1). The unit-cell volume as a function of pressure for hematite and DPv-Fe2O3 is shown in Figure 3, combining both powder and single-crystal 33 data. It is noteworthy that upon decompression from 62 GPa the DPv phase remains stable down to 35 GPa (Figures 3, SI Figures S2, S3). However, at P ~ 50 GPa a discontinuous volume increase of ~7% is observed, while the DPv structure remains 6 unchanged ( Figure 3) and only the monoclinic distortion of the unit cell decreases (SI Figure S5). The structural transition back to hematite begins only below 35 GPa.
A transition to a new high-pressure polymorph is observed upon compression of the DPv-Fe2O3 phase above 67 GPa (Figure 3), with a diffraction pattern that is successfully indexed based on an orthorhombic Aba2 space group that has only one type of Fe cation 33 (SI Figure S4).

Electrical resistance measurements
Our electrical resistance measurements show an abrupt ~6 orders of magnitude decrease of resistance at about 40-60 GPa on compression (Fig. 4), in agreement with the reported insulator-metal transition at ~55 GPa 25,38 . Upon further compression, we observe a substantial change in the pressure dependence of the resistance, indicating an additional change of conductivity features at ~70 GPa ( Fig.   4(a)). Similar behavior is seen during the decompression cycle, with a hysteresis of ~ 6 GPa. It is noteworthy that upon pressure release the resistance rises only by ~3 orders of magnitude at about 50-40 GPa, saturating below 40 GPa. Furthermore, to avoid a structural transition back to the corundum structure, we terminated decompression at 37 GPa and performed recompression measurements up to 83 GPa. The pressure-temperature dependence of electrical resistance upon recompression shows an abrupt drop at 45-60 GPa, with the onset of metallization below 53 GPa ( Fig. 4(b)). Similar to the hematite phase 38 the temperature dependence of the resistance of the insulating DPv phase is associated with a variable-range hopping mechanism below ~50 GPa: the electrical conductivity varies as = C exp(T0/T) 1/4 , though we notice a significantly reduced Mott temperature value, T0, ( Fig. 4(b); SI Fig.   S6(b)). Meanwhile, within the metallic region above ~50 GPa, the resistance exhibits a clear deviation from the Fermi-liquid-like T 2 behavior, showing a minimum at temperature T = 110 -150 K for the DPv phase and at about 75 K for the HP phase ( Fig. S6(a), for details see Supporting Info). This behavior is presumably associated with a Kondo effect 39 .

DFT+DMFT calculations
state of Fe2O3 by employing the DFT+DMFT approach, a combination of ab initio band structure methods and dynamical mean-field theory of correlated electron systems 36 . We employ a fully charge selfconsistent implementation of the DFT+DMFT method and compute the electronic structure and phase stability of Fe2O3 under pressure. As a starting point, we calculate the electronic and structural properties of the low-pressure R-3c phase in the paramagnetic state (i.e., at slightly elevated temperature, T = 390 K, that should not otherwise affect our conclusions). In agreement with previous studies 35 , we obtain a Mott insulating solution with a relatively large d-d energy gap of about 2.5 eV. The calculated equilibrium lattice constant 5.61 a.u. and bulk modulus ~187 GPa are in good agreement with the X-ray diffraction measurements. Our result for the local magnetic moments is ~4.76 B, documenting that at ambient pressure the Fe 3+ ions are in a high-spin state (S = 5/2) with localized 3d electrons. We note that our calculations predict the HS-LS transition in the R-3c Fe2O3 to occur upon compression above ~72 GPa, i.e., at substantially higher compression than ~50 GPa found in our experiments (see Supplementary Material p.10).
Upon compression above ~50 GPa, the corundum R-3c phase undergoes a structural transition to the DPv phase. We calculate the electronic properties of that phase using the monoclinic P21/n symmetry and crystal structure parameters as obtained by diffraction at ~54 GPa, and use a cluster expansion of the DFT+DMFT approach in order to treat correlations in the Fe 3d bands of the structurally distinct Fe A and Fe B sites. Our results for the spectral function ( Fig. 5) reveal the existence of a site-selective Mott phase, in which the 3d electrons on only half of the Fe sites (octahedral B sites) are metallic, while the A sites remain insulating. The possibility of a site-selective Mott phase has recently been discussed for the rareearth nickelates, but without experimental or theoretical confirmation 40,41 . We note that the Fe B a1g and eg  orbitals show a sharp quasiparticle peak at the Fermi level, which is associated with a pronounced (orbital-selective) enhancement of the effective electron mass, m*/m. In fact, we estimate m*/m ~ 6 for 8 the Fe B a1g and ~ 4 for the eg  orbitals at temperature ~390 K. In contrast to that, the Fe B eg  orbitals remain insulating. In agreement with our experiment, we observe that the insulator-to-metal transition is accompanied by a remarkable site-selective collapse of local moments. Indeed, the local magnetic moment at the Fe A sites is ~4.63 B, which differs substantially from the magnetic moment at the B sites ~ 0.89 B. This confirms that in the DPv phase the octahedral Fe B ions are in a low-spin state (S = 1/2), while the Fe A sites remain high-spin (S = 5/2). Moreover, our results for the spin-spin correlation function () = mz()mz(0) (see inset of Figure  We note that upon lattice expansion of the DPv structure by ~8.5 %, our calculations predict a phase transition into a conventional Mott insulating state. Indeed, our Mössbauer, electrical resistance and Xray diffraction measurements show that upon decompression the electronic and structural transitions do not coincide; they are separated by a pressure interval of ~20 GPa. This implies a transition between 9 site-selective and conventional Mott phases for the DPv structure upon decompression and recompression: a remarkable decoupling of the electronic and lattice degrees of freedom in Fe2O3. We conclude that we are documenting intrinsic electronic properties of the DPv phase of Fe2O3, as indicated by the small hysteresis in electrical resistance upon decompression and recompression near the onset of insulator-metal transition ( Fig. 4: contrast the recompression results for hematite in previous studies 25,38 ).

Discussion
Summarizing our theoretical and experimental results, we find evidence that the metallization Å, respectively, at 54 GPa) that allows for the site-selective insulator-metal transition (SI Table 1). The volume change upon metallization is identical to that observed in CaFe2O4 42 , suggesting a similar mechanism of electronic transition for these sites: namely, closure of the Mott-Hubbard gap associated with a spin transition 10,12,13 in accord with our theoretical calculations. Because the DPv structure of Fe2O3 consists of chains of octahedra linked along the crystallographic c direction, and separated by the 8-coordinate sites in the a and b directions (SI Fig. 4), we would expect this phase to exhibit anisotropic electron mobility, with higher conductivity in the c than the a or b directions.
We note that metallization does not occur in the hematite phase upon compression. In the region where the MS data find both the hematite and the DPv phases, the remaining hematite phase is still in a highspin state (even when half of the Fe in the DPv phase are already non-magnetic, metallic). In addition, the P(V) data in Fig 3 show that there is no appreciable change in unit-cell volume of hematite during compression (no deviation from the hematite EOS), even in the region of coexistence. This is in full accordance with our theoretical calculations, which show that in hematite the IMT associated with a HS-LS state transformation takes place at pressure ~ 72 GPa (at volume ~ 0.74 V0) (SI Fig. 7).
Upon decompression, we observe a sharp reversal in electronic properties at about 45 GPa, with a metal-to-insulator transition and retrieval of a magnetic state (Figures 1c and 4), which can be described Formation of an intermediate electronic state, the so-called "orbital-selective" phase, has been claimed to occur in multi-orbital transition-metal oxides 15,16,17,18 . In the orbital-selective phase, due to the inclusion of orbital degrees of freedom, a partial localization can take place, in which some orbitals are conducting, while others are localized. As a result, localized spins and itinerant electrons coexist in a system. In Indeed, the appearance of the P21/n DPv phase can be understood as a result of the interplay between cohesive (lattice) energy and local magnetic moments. While the former favors the denser high-pressure 11 phase (e.g., Aba2), the local magnetic moments enter into the total energy as -Imz 2 /4 (here, I is a Stoner exchange interaction, mz 2  -square of the local magnetic moment), and therefore favor the corundum structured (space group R-3c) phase, i.e., the phase with high local magnetic moments. As a result, the intermediate DPv phase, with site-selective electronic and magnetic properties, is stabilized at intermediate pressures of about 50-60 GPa. This is presumably an electronic phase transition that results in the appearance of (at least) two electronically/magnetically different sublattices of Fe-cations; i.e., it always leads to a structural transformation, due to electron-lattice coupling. We point out that similar behavior only associated with the site-selective HS-LS transition is found to occur in a two-orbital Hubbard model with crystal-field splitting 43

Samples
The Fe2O3 powder (99.5% pure) used in this study is commercially available from Riedel-de Haën.
For Mössbauer studies, 30% enriched 57 Fe2O3 was used. For single-crystal X-ray diffraction, the same hematite single crystals described elsewhere 32,53 were used.

Custom 4-pin diamond anvil cells (DACs) made at Tel-Aviv University 54 and Bayerisches
Geoinstitut, with anvil culet diameters of 250 or 200 μm and Re gaskets, were used to induce high pressure. Neon was used as a pressure-transmitting medium. Pressure was determined using the ruby R1 fluorescence line as a pressure marker, and the Ne unit-cell volume in the case of XRD studies. 57 Fe Mössbauer studies were performed up to 80 GPa using a 10 mCi 57 Co (Rh) point source in a variable temperature (5 -300 K) cryostat. Spectra were analyzed using a Spin-Hamiltonian fitting 13 program 55 from which the isomer shift (IS), the quadrupole splitting (QS), the hyperfine field (Hhf) and the relative abundances of the spectral components were deduced. The reported velocity is with respect to -Fe. The spectrum at 79 GPa and 4 K was collected using energy-domain synchrotron Mössbauer spectroscopy carried out at the beamline ID18 at ESRF 56 . This spectrum was collected with the source at RT and, therefore, is affected by the 2 nd order Doppler shift.
Electrical resistance measurements were performed up to 90 GPa. The Re gasket was covered with an insulating layer of an Al2O3-NaCl mixture (3:1 atomic ratio), which also serves as the pressure medium. Platinum foils with a thickness of 5-7 μm were cut in triangular form and used as electrical probes for resistance measurements. The foils were connected to copper leads, at the base of the diamond anvil, using a silver epoxy. Resistance was measured as a function of pressure and temperature using a standard four-probe method in a custom-made cryostat. At each temperature, the voltage was measured as a function of a series of applied currents, for determining the resistance from the obtained slope. Pressure was measured by ruby fluorescence both before and after each measurement. The reported uncertainties are given according to the standard errors obtained from the respective software used for fitting the data.

Theoretical Methods
We calculate the electronic structure and spin state of paramagnetic Fe2O3 using the DFT+DMFT computational approach (DMFT: dynamical mean-field theory). The DFT+DMFT method 36      DPv phase were performed during decompression to 37 GPa, and following recompression (empty hexagons and half-filled pentagons, respectively). Measurements of the hematite phase were collected during a separate decompression cycle to ambient pressure (symbols "□"). 28   In the insulating region (b), the temperature dependence of the resistance of the insulating DPv phase, below ~50 GPa, and the hematite phase is associated with a variable-range hopping mechanism (=Cexp(T0/T) 1/4 (4) 1.83 (3) 1.85(4)

DFT+DMFT calculations of the electronic and structural properties of the R-3c phase of Fe2O3
We calculate the electronic structure and phase stability of the corundum R-3c phase of Fe2O3 using the fully charge self-consistent DFT+DMFT approach 62,62,62,62,62,62 implemented with plane-wave pseudopotentials 62,62,62,62,62 . To this end, we calculate the total energy and local moment of the Fe ions of the R-3c phase as a function of lattice volume. The calculations are performed in a paramagnetic state at temperature T = 1160 K. We use the average Coulomb interaction U = 6 eV and Hund's exchange J = 0.86 eV for the Fe 3d shell as was estimated previously 62 . The U and J values are assumed to remain constant upon variation of the lattice. Overall, our results for the electronic and lattice properties of the R-3c phase agree well with experimental data. We first discuss the spectral properties of paramagnetic Fe2O3. In Fig. S7 (a) we present the evolution of the spectral function of Fe2O3 calculated as a function of lattice volume. At ambient pressure, we obtain a Mott insulating solution with an energy gap of ~2.5 eV, in agreement with optical and photoemission experiments 62,62,62 . Upon compression, the energy gap gradually decreases, resulting in a Mott-Hubbard insulator-to-metal transition (MIT), which is associated with a high-spin (HS) to low-spin (LS) state transition Error! Bookmark not defined. . In fact, as shown in Fig. S7 (b), the MIT is accompanied by a remarkable redistribution of the Fe 3d charge between the t2g and eg orbitals. Fe t2g orbital occupations are found to gradually increase upon compression. In particular, at a pressure above ~75 GPa, the a1g orbital occupancy is about 0.7, while the eg  occupation ~0.85. On the other hand, the Fe eg orbitals are strongly depopulated (their occupation is below 0.2).
In Fig. S8 we show our results for the evolution of the total energy and local magnetic moment of paramagnetic Fe2O3 as a function of lattice volume. We fit the calculated total energy using the third-order Birch-Murnaghan equation of states separately for the low-and high-volume regions. Our results for the equilibrium lattice constant a=5.61 a.u. and bulk modulus K0 ~187 GPa (K0'=dK/dT is fixed to 4.1) are in good quantitative agreement with the XRD data. At ambient pressure, the calculated local magnetic moment is ~ 4.76 B, implying a high-spin S=5/2 state of the Fe 3+ ions (3d 5 configuration with three electrons in the t2g and two in the eg orbitals). Our result for the spin-spin correlation function ()=mz()mz(0) calculated by DFT+DMFT for the equilibrium volume V0 and T=390 K is seen to be almost constant, independent of , and close to the unit (see Fig. S9). This implies that the Fe 3d electrons are strongly localized to form fluctuating moments. Upon compression of the R-3c lattice to V/V0 ~ 0.74, the total energy and local moment show a remarkable anomaly. In fact, the local moment is seen to retain its high-spin value down to about 72 GPa, while upon further compression, it exhibits a sharp HS-to-LS transition (see inset of Fig. S8), with a LS moment ~ 1.5 B at pressure above ~ 90 GPa.
Our calculations reveal that the HS-LS transition in the R-3c structure of paramagnetic Fe2O3 is associated with a Mott-Hubbard MIT. Moreover, the MIT is accompanied by an isostructural collapse of the lattice volume by ~ 12%, implying a complex interplay between electronic and lattice degrees of freedom. The structural change takes place upon compression above ~ 72 GPa. In addition, we find that the bulk modulus in the HS phase (K0 ~187 GPa) is considerably smaller than that in the LS phase (245 GPa), resulting in a remarkable decrease of the compressibility at the phase transition.
Furthermore, our theoretical results for the R-3c phase of Fe2O3 show that the MIT occurs at a remarkably high pressure value of ~72 GPa. It is considerably higher than the structural transformation into the DPv phase found experimentally (~50 GPa). We also calculate the total energy for the DPv phase of paramagnetic Fe2O3 using the crystal structure parameters obtained at ~54 GPa. Our results reveal that the DPv phase is energetically favorable in comparison to the corundum R-3c, i.e., the DPv phase is thermodynamically stable under pressure. In addition, as discussed in our paper, we obtain that the DPv phase is a site-selective Mott insulator, in which the 3d electrons on only half of the Fe sites (octahedral B sites) of DPv Fe2O3 are metallic, while the others (A sites) remain insulating. Our theoretical results for the phase stability Fe2O3 thereby confirm a structural transition from the corundum R-3c to the DPv structure of Fe2O3, in agreement with our experimental data. Overall, our results for the electronic structure, equilibrium lattice constant, and structural phase stability of paramagnetic Fe2O3 agree remarkably well with experimental data.

Evolution of the transport properties across the insulator-to-metal transition
Evolution of the transport properties across the transition can be interpreted similar to Machavariani et al. 62 by assuming that the sample is a mixture of two phases, metallic and insulating, with different transport characteristics. The overall conductivity is determined by a relative volume of both phases and by the shape and distribution of the clusters of each phase. We can estimate the relative volume of each phase from the room temperature resistivity measurements, assuming roughly that the clusters are spherical and that the conductivities of the two phases, 1 and 2, are not changed across the transition. In the framework of the symmetrical effective medium theory of Bruggeman 62 , the relative volumes V1 and V2=1-V1 are given by