Pressure-Induced Site-Selective Mott Insulator-Metal Transition in Fe 2 O 3

Eran Greenberg, Ivan Leonov, Samar Layek, Zuzana Konopkova, Moshe P. Pasternak, Leonid Dubrovinsky, Raymond Jeanloz, Igor A. Abrikosov, and Gregory Kh. Rozenberg School of Physics and Astronomy, Tel Aviv University, 69978, Tel Aviv, Israel Institute of Metal Physics, Sofia Kovalevskaya Street 18, 620219 Yekaterinburg GSP-170, Russia Materials Modeling and Development Laboratory, NUST “MISIS,” 119049 Moscow, Russia DESY, HASYLAB, PETRA-III, P02, Notkestraße 85, Building 47c, Hamburg, Germany Bayerisches Geoinstitut, University of Bayreuth, Bayreuth, Germany Departments of Earth and Planetary Science and Astronomy, and Miller Institute for Basic Research in Science, University of California, Berkeley, California 94720, USA Department of Physics, Chemistry and Biology (IFM), Linköping University, SE-581 83 Linköping, Sweden

For the partially filled Fe 3d and O 2p orbitals we construct a basis set of atomic-centered symmetry-constrained Wannier functions [47]. In order to enhance localization of the Fe 3d Wannier orbitals, the O 2p orbitals were constructed using Wannier functions defined over the full energy range spanned by the p-d band complex; the localized Fe 3d orbitals are constructed using the Fe 3d band set. To solve the realistic many-body problem, we employ the continuoustime hybridization-expansion (segment) quantum Monte-Carlo algorithm. In the DPv phase, correlations in the Fe 3d bands of the structurally distinct Fe A and Fe B sites are treated using a cluster expansion of the DFT+DMFT approach. The calculations are performed in the paramagnetic state at temperature T = 390 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 [40]. The Coulomb interaction is treated in the density-density approximation. The spin-orbit coupling is neglected in these calculations. We employ the fully localized double-counting correction, evaluated from the self-consistently determined local occupancies, to account for the electronic interactions already described by DFT. The spectral functions were computed using the maximum entropy method. Further technical details about the method used can be found in Leonov et al. [42].

Experimental Methods
Custom diamond anvil cells (DACs) made at Tel-Aviv University and Bayerisches Geoinstitut, with anvil culet diameters of 250 or 200 μm and Re gaskets, were used to induce high pressure. 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 program [48] from which the isomer shift (IS), the quadrupole splitting (QS), the hyperfine field (H hf ) and the relative abundances of the spectral components were deduced. The reported velocity is with respect to α-Fe at room-temperature. The pressure uncertainties are 1-2 GPa. The spectrum at 79 GPa and 4 K was collected using energy-domain synchrotron Mössbauer spectroscopy carried out at the beamline ID18 at ESRF. 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 Al 2 O 3 -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.
Evolution of the transport properties across the P21/n phase transition can be interpreted similar to Machavariani et al. [55] by assuming that the sample is a mixture of two phases, metallic and insulating, with different transport characteristics. The overall conductivity σ 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, σ 1 and σ 2 , are not changed across the transition. In the framework of the symmetrical effective medium theory of Bruggeman [52], the relative volumes V 1 and V 2 =1-V 1 are given by (1) for decompression and recompression cycles. The σ 1 and σ 2 values are chosen as the estimated conductivities just before and after the transition, where the phases exist alone (at ~40.6 GPa and ~70.4 GPa for decompression and at 47 GPa and 76.6 GPa for recompression).
The calculations are made on the assumption that the geometrical coefficient B in the relation σ=B/R does not change under pressure (B depends on the thickness of the sample, the distance between the contacts and the width of the current flow).
The reported uncertainties are given according to the standard errors obtained from the respective software used for fitting the data. It is noteworthy, that there are some inconsistences in the transitions range observed by different methods. Thus for the structural 3 to DPv and corroborating electronic transitions XRD reveals a coexistence range of ~ 5 GPa, MS of ~ 7 GPa and for resistance measurements the range is extended to more than 10 GPa. A systematic reason for the observed inconsistences for different methods could be the two different types of manometries: the use of a Ne marker from which the pressure is deduced from the well-known Ne-EOS and the ruby method. Another systematic reason could be the different geometries of the signal collection methods: in the synchrotron XRD measurements the signal derives from a small central part of the sample, whereas in Mossbauer studies the signal is collected from a much larger; ∼2/3 of the sample diameter, resulting in possible pressure gradient effects. In resistivity measurements, the role of pressure gradients could be even more substantial due to using a solid pressure medium.

DFT+DMFT calculations of the electronic and structural properties of the phase of Fe 2 O 3
As a starting point, we calculate the electronic structure and phase stability of the corundum 3 phase of Fe 2 O 3 using the fully charge self-consistent DFT+DMFT approach [39,41] implemented with plane-wave pseudopotentials [6,43,44]. To this end, we calculate the total energy and local moment of the Fe ions of the 3 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 [40]. 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 3 phase agree well with experimental data. We first discuss the spectral properties of paramagnetic Fe 2 O 3 . In which is associated with a high-spin (HS) to low-spin (LS) state transition [40]. In fact, as shown in Fig. S5(b), the MIT is accompanied by a remarkable redistribution of the Fe 3d charge between the t 2g and e g orbitals. Fe t 2g orbital occupations are found to gradually increase upon compression. In particular, at a pressure above ~75 GPa, the a 1g orbital occupancy is about 0.7, while the e g π occupation ~0.85. On the other hand, the Fe e g orbitals are strongly depopulated (their occupation is below 0.2).
In Fig. 2 we show our results for the evolution of the total energy and local magnetic moment of paramagnetic 3 Fe 2 O 3 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 highvolume regions. Our results for the equilibrium lattice constant a=5.61 a.u. and bulk modulus K 0 ~187 GPa (K 0 '=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 μ B, implying a high-spin S=5/2 state of the Fe 3+ ions (3d 5 configuration with three electrons in the t 2g and two in the e g orbitals).
Our result for the spin-spin correlation function χ(τ)=<m z (τ)m z (0)> calculated by DFT+DMFT for the equilibrium volume V 0 and T=390 K is seen to be almost constant, independent of τ, and close to the unit (see Fig. S6). This implies that the Fe 3d electrons are strongly localized to form fluctuating moments. Upon compression of the 3 lattice to V/V 0 ~ 0.74, the total energy and local moment show a remarkable anomaly. In fact, the local moment is seen to retain its highspin value down to about 72 GPa, while upon further compression, it exhibits a sharp HS-to-LS transition, with a LS moment ~ 1.5 μ B at pressure above ~ 90 GPa.
Our calculations reveal that the HS-LS transition in the 3 structure of paramagnetic Fe 2 O 3 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 (K 0 ~187 GPa) is considerably smaller than that in the LS phase (245 GPa where K 0 , and V 0 are the bulk modulus, and the unit cell volume at 1 bar and 300 K, respectively. The obtained fitting parameters for the 3 structure are: K 0 = 197.6(6) GPa and V 0 = 100.58 ( The | and + symbols correspond to Fe 2 O 3 and Ne pressure medium, respectively. The spectrum at 42.1 GPa, collected upon decompression, is fit well with the P2 1 n structure with the reduced monoclinic distortion (marked DPv dec ). Note that fitting of our data to the Rh 2 O3-II type structure, which according to Ref.
[28] appears upon heating to ~1.800 K at about 40 GPa, gives rather poor results and therefore such possibility was excluded.  Figure S4. Temperature dependence of electrical resistance at various pressures in the metallic region (a) and pressure dependence of Mott temperature, T 0 , for the hematite and insulating DPv phases (b). In the metallic region (a), above ~50 GPa, R(T) exhibits a Fermi-liquid-like R ~ T 2 dependence with a minimum: at T min ≈ 110 -150 K in the DPv phase and at T min ~ 75 K in the HP phase. This behavior could be a consequence of the Kondo effect -an indication of strong interaction between localized magnetic moments and the conduction electrons. We note the rather high value of T min for both phases. The solid lines represent results of the fit to R(T)=R(0) + aT 2 + bT 5 -cln(T), where R(0) is the sum of all contributions to the resistance at zero temperature. 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 (σ=Cexp(T 0 /T) 1/4 ). We note ~ 4 order of magnitude difference of the Mott temperature between hematite and DPv phases. Figure S5. Evolution of the Fe 3d and O 2p spectral function (a) and the partial Fe t 2g and e g occupations (b) of paramagnetic Fe 2 O 3 calculated by DFT+DMFT at T=1160 K as a function of lattice volume. Fe t 2g (a 1g and e g π orbitals) and e g , and O 2p orbital contributions are shown. The MIT associated with a HS-LS state transformation takes place at pressure ~ 72 GPa (at volume ~ 0.74 V 0 ). Figure S6. Fe 3d and O 2p spectral function (a) and spin-spin correlation function χ(τ)=<m z (τ)m z (0)> (b) of paramagnetic corundum Fe 2 O 3 as calculated by DFT+DMFT for the equilibrium volume V 0 , at temperature T=390 K. Fe t 2g (a 1g and e g π orbitals) and e g , and O 2p orbital contributions are shown. χ(τ) is seen to be almost constant, independent of τ, and close to the unit, implying a strong localization of the Fe 3d electrons.