Metal-Insulator Transition and the Role of Electron Correlation in FeO2
MMetal-Insulator Transition and the Role of Electron Correlation in FeO Bo Gyu Jang
Department of Chemistry, Pohang University of Science and Technology, Pohang 37673, Korea.
Duck Young Kim ∗ Center for High Pressure Science and Technology Advanced Research (HPSTAR), Shanghai 201203, China.
Ji Hoon Shim † Department of Chemistry andDepartment of Physics and Division of Advanced Nuclear Engineering,Pohang University of Science and Technology, Pohang 37673, Korea. (Dated: July 19, 2016)Iron oxide is a key compound to understand the state of the deep Earth. It has been believedthat previously known oxides such as FeO and Fe O will be dominant at the mantle conditions.However, the recent observation of FeO shed another light to the composition of the deep lowermantle (DLM) [1] and thus understanding of the physical properties of FeO will be critical tomodel DLM. Here, we report the electronic structure and structural properties of FeO by usingdensity functional theory (DFT) and dynamic mean field theory (DMFT). The crystal structure ofFeO is composed of Fe and O − dimers, where the Fe ions are surrounded by the octahedralO atoms. We found that the bond length of O dimer, which is very sensitive to the change ofCoulomb interaction U of Fe 3 d orbitals, plays an important role in determining the electronicstructures. The band structures of DFT+DMFT show that the metal-insulator transition is drivenby the change of U and pressure. We suggest that the correlation effect should be considered tocorrectly describe the physical properties of FeO compound. Iron oxides are basic and important materials of theEarths interior. Among them, FeO and Fe O aretwo end members and the most well-known compounds.However other kinds of iron oxides with new stoichiom-etry, such as Fe O [2] and Fe O [3], are also discov-ered under the high pressure and temperature. Re-cently FeO , which holds an excessive amount of oxy-gen, is identified with both first-principles calculationand experiment near 76 GPa [1]. This new iron oxidereceives a great attention because it suggests an alter-native scernario for describing geochemical anomalies inthe lower mantle and the Great Oxidation Event. Thus,it is important to understand the correct electronic andstructural properties of FeO .FeO possesses a FeS -type pyrite structure. The crys-tal structure of Fe X ( X = O or S) can be obtained byreplacing X atom in B1 type Fe X with X dimer. FeOand FeS show a spin-state transition accompanied withMott-type insulator to metal transition under high pres-sure [4–8]. However, FeS is a non-magnetic compoundwhere the six Fe d electrons occupy the t g ground states[8–11]. NiS − x Se x also has a same crystal structure withFeO . It exhibits a complex phase diagram includingMIT and magnetic phase transition depending on com-position x , temperature, and pressure due to partiallyfilled e g orbital [12, 13]. Several previous studies have re-ported that the p orbitals of S dimer play an importantrole in describing electronic structures of this compounds[12, 13]. So we can expect that O dimer may also bean driving factor for determining electronic and physicalproperties of FeO . It is well known that standard density functional the-ory (DFT) fails to reproduce the physical properties andthe electronic structures of many TMO compounds be-cause electron correlation effect of d orbitals cannot bedescribed properly. Alternatively, DFT+ U which in-cludes the correlation effect of localized orbitals such as3 d gives better results for structural properties, mag-netic moments, and electronic structures. Dynamic MeanField Theory (DMFT) has been believed to be a more ad-vanced technique which deals with local electronic corre-lation problems exactly [14]. DMFT can describe weaklycorrelated electron system because it can capture boththe itinerant and localized nature of spectral function.DMFT has been combined with DFT (DFT+DMFT),and it has been widely used to describe the correlatedphysics of real materials in a first-principles manner.In this paper, we investigate structure properties andelectronic structure using DFT and DFT+DMFT ap-proaches. First, the electronic structure of experimen-tally reported FeO is calculated from DFT+DMFT. Thecalculated electronic structures indicate that σ * band ofO dimer plays an important role in determining thephysical properties of this system. We also study thatthe correlation effect of Fe d orbitals should be consid-ered to describe the crystal structure of FeO properly.Last, we find that MIT can occur by varying volume orchanging Coulomb interaction U . O dimer bond length isa governing parameter to determine the MIT in this sys-tem which is sensitively affected by correlation strengthof Fe d orbitals.DFT calculation is performed with WIEN2k code a r X i v : . [ c ond - m a t . s t r- e l ] J u l FIG. 1. Crystal structure of FeO . Brown and red spheres in-dicate Fe and O atoms, respectively. (a) Fe atom surroundedby six O atoms makes octahedral symmetry where the Fe-Obond length is 1.808 ˚A. (b) O-O dimers in FeO crystal. Fe-Obond is omitted for clarity. The bond length of O dimer is1.896 ˚A and the distance between second nearest O atom is2.437 ˚A. [15], which uses a full-potential augmented plane-wavemethod. We use the generalized gradient approxima-tion by Perdew, Burke, and Ernzerhof (PBE GGA) toexchange-correlation functional [16]. A 12 × × k -points mesh is used for self-consistent calculation. Effec-tive one electron Hamiltonian is generated from WIEN2kcalculation and electronic correlation effect of Fe d or-bitals is treated by local self-energy, which is consid-ered by using continuous time quantum Monte Carlo(CTQMC) impurity solver. The detail of DMFT im-plementation to the DFT method has been introducedin ref.[17] explicitly. We consider a paramagnetic stateat temperature T=200 K. For structural optimization atdifferent volumes, we use the Vienna ab initio package(VASP) [18], where a plane-wave cutoff is set to 500 eVand a 10 × × k -points mesh is used.Figure 1 shows the experimental crystal structure ofFeO at 76 GPa which contains four Fe atoms and eightO atoms in the unit cell. It possesses a simple cubicstructure with a space group Pa¯3 where the four Featoms are located at (0, 0, 0), (0, 0.5, 0.5), (0.5, 0,0.5), and (0.5, 0.5, 0). The eight O atoms are located at ± ( a, a, a ) , ± (0 . − a, − a, . a ) , ± ( − a, . a, . − a ),and ± (0 . a, . − a, − a ), where a =0.3746 at the exper-imental structure. Fe atom surrounded by six O atomsmakes slightly distorted octahedral symmetry where theFe-O bond length is 1.808 ˚A. Each octahedron sharesoxygen atoms at vertex or it is connected by O-O bond-ing which makes O dimer as shown in Fig. 1. The bondlength of O dimer is 1.896 ˚A and the distance betweensecond nearest O atoms is 2.437 ˚A, which is quite largecompared to the O dimer bond length. Thus, one canexpect that O dimer forms σ and π molecular orbitalswhich may play an important role in this system.First, we perform calculations of the electronic struc-tures using DFT and its combination to the DMFT(DFT+DMFT) method on the reported crystal structureof FeO at 76 GPa. Figure 2 (a) displays spectral func- FIG. 2. (a) Calculated spectral functions from standard DFTand DFT+DMFT ( U =5 eV, J =0.8 eV, and T=200 K) (upperpanel) and orbital resolved spectra from DFT+DMFT (lowerpanel). Inset shows imaginary part of electron self-energy onMatsubara frequency for each orbitals. (b) Molecular orbitaldiagram of O − and schematic DOS of FeO . FeO showsmetallic behavior due to the broad O σ * band. tions from standard DFT calculation and DFT+DMFTcalculation. In DFT+DMFT, we use an on-site Coulombinteraction U = 5 eV and a Hund coupling constant J = 0.8 eV. Spectral function of DFT+DMFT calculationis slightly renormalized from that of DFT calculation,which indicates that correlation effect on spectral func-tion is very weak. The inset figure displays the imaginarypart of electron self-energy on Matsubara frequency. Fe t g and e g bands show mass enhancement of m*/ m of ∼ ∼ at 76 GPa. Its e g orbitals, which iswell above Fermi level by ∼ t g bands split into e πg doublet and an a g singlet due to distorted FeO octahe-dron symmetry [12]. Overall bandwidth of t g bands isaround 2 eV and locates just below Fermi level while thebroad σ * band of O dimer is just above Fermi level withthe bandwidth of around 3 eV. Thus, O dimer takestwo electrons from a nearest Fe atom forming hyperox-ide O − and electrons are occupied up to π * antibondingorbitals. A schematic electronic structures are shown inFig. 2 (b) based on the molecular orbital energy dia-gram. The π and σ bands from O dimer are completelyfilled making broad bands well below Fermi level. In thecalculated electronic structures of FeO at 76 GPa, thereis an overlap between the t g band and the σ * band dueto their large bandwidth, and it forms a metallic groundstate. We also perform DFT+DMFT calculation at agiven crystal structure with bigger U value but band gapdoes not open due to the broad σ * band at Fermi levelas shown in Fig. 2. Therefore, the metallic ground stateis robust regardless of the size of the correlation effect.Note that the bandwidth and the position of σ * bandis subject sensitively to the bond length of O dimer.In Fig. 2 (b), a schematic DOS shows a possible in-sulating ground state by reducing the bandwidth of σ *bands. We speculate that this system may locate nearthe metal-insulator transition point, which is controlledby O dimer. In the following, we investigate further theeffect of pressure on the crystal structure and its effecton the electronic properties.We investigate the change of the electronic structureswith respect to volume. Before optimizing the crystalstructure at several volumes, we check if standard DFTcaptures the experimental structure at 76 Gpa prop-erly. However, standard DFT calculation overestimatesO dimer bond length by ∼ dimer bond length and Fe-O distance are de-termined by oxygen position parameter a in the unitcell. As the position parameter a increases, Fe-O dis-tance increases slowly while O dimer bond length de-creases rapidly. When Fe-O distance increases by 0.05 ˚A,O dimer bond length decreases by ∼ dimerbond length is easily affected by small change of Fe-Obond length. DFT calculation predicts Fe-O distance tobe shorter than that of experimental report and thus thecorresponding O dimer bond length is estimated to belonger. It is expected that the standard DFT calculationcannot describe a localized picture of Fe d orbitals prop-erly and overestimates the bonding strength between Feand O.Furthermore, we perform DFT+ U calculation to checkthe change of crystal structure depending on on-siteCoulomb interaction U . We find that O dimer bondlength is very sensitively affected by a choice of U valueas shown in Fig. 3 (a). Although the change in Fe-O dis-tance, which is directly affected by U , is small, O dimerbond length is rapidly changed as we discussed above.With an increase of U value, hybridization between O p orbitals and Fe t g bands decreases to make Fe-O bondlength increase. O dimer bond length is affected sensi-tively by this change and becomes closer to that of exper-imental value. This indicates that the correlation effecton Fe d orbitals should be considered to describe prop-erly the crystal structure of FeO , especially O dimerbond length.O dimer bond length also affects the electronic struc-ture of FeO . As O dimer bond length decreases, theinteraction between the adjacent dimers decreases mak-ing the band width of O σ * orbitals narrow. Splitting FIG. 3. (a) Variation of Fe-O and O-O distance in experimen-tal volume (20.8 ˚A /f.u.) at 76 Gpa with respect to Coulombinteraction energy U . (b) Calculated O dimer bond lengthwith respect to volume for several U value from DFT+ U cal-culation. Below critical O dimer bond length ( ∼ between bonding and antibonding orbitals of O dimerincreases by pushing up the O σ * orbitals above Fermilevel as shown in Fig. 2 (b). We notice that O σ * bandsare completely removed from Fermi level at U = 6 eV tomake a gap between Fe t g bands and O σ * band. FeO eventually turns into an insulator as described in Fig. 2(b) with dotted σ * band.We obtain the optimized structures at several volumeswith varying U value, as shown in Fig. 3 (b). O dimerbond length increases as volume increases with a choiceof U value up to 4 eV. However, this trend is reversedat higher U value. It can be understood from a com-petition between Fe-O bonding strength and correlationeffect of Fe 3 d orbitals. Note that stronger Fe-O bond-ing strength gives shorter Fe-O bonding, which resultsin longer O dimer bond length. The gray dashed refer-ence lines in Fig. 3 (b) exhibit a simple O dimer bondlength change in accordance with volume expansion with-out atomic position relaxation with respect to O dimerbond length at 20.8 ˚A . When the slope of O dimerbond length with respect to volume is steeper than that FIG. 4. Calculated momentum resolved spectral function for (a) 20.8 ˚A / f.u., (b) 21.8 ˚A / f.u., and (c) 22.8 ˚A / f.u. at T =200 K. The system is metallic for (a) and (b), and insulating for (c) which makes gap between O σ * band and Fe t g ( e πg and a g ) band. (d) Spectral functions show metal to insulator transition clearly. Small spectral weight near Fermi level disappearas O σ * band width decreases. of the guided line, the effect of Fe-O bonding strengthpredominates over the correlation effect. In this case,the O dimer bonding becomes weaker with increasingvolume at small U value. Although the O dimer bondlength keeps increasing at U = 4 eV, the slope is smallerthan the guided line, which indicates that the formationof O dimer becomes preferable at bigger volume. When U value is larger than 5 eV, the correlation effect becomesmore dominant than Fe-O bonding strength so that theformation of O dimer is much preferred. We alreadydiscussed that the tiny change in Fe-O bond, which isinduced by the change of U , makes big difference in O dimer bond length which can affect the electronic struc-ture of FeO significantly. Comparison of O dimer bondlength between experiment and theory will be a usefultest to confirm the importance of the correlation effect.We suggest that exact measurements of O dimer bondlength with respect to volume can verify which U valueis proper for the correct description of this system.We find that FeO turns into insulator below criticalO dimer bond length about 1.7 ˚A. MIT is observed at U = 5 eV with varying the volume as shown in Fig. 3(b). It is also observed at constant volume by varying U value if the change of O dimer bond length is correctlycaptured at given U value as shown in Fig. 3 (a). Mo-mentum resolved spectral functions are calculated usingDFT+DMFT to investigate MIT more carefully as shownin Fig. 4. In all volumes, the DFT+DMFT results al-ways show weak correlation with mass enhancement ofm*/m less than 1.5. The bandwidth of t g and e g bandsdecreases from ∼ ∼ to 22.8 ˚A . The crystal field splitting be-tween t g and e g bands also decreases from 3.5 eV to 3 eVas Fe-O bond length increases. O σ * bands also show adecrease in width. The band width of σ * band is ∼ and decreases by ∼ . The tail of σ * band gradually moves from -1 eV to above Fermi level as the band width decreases,leading to MIT.It is worth to note that the MIT is a band insulatortype not a Mott-type because it is driven by the changeof the band widths and positions of O σ * and Fe t g bands, which are determined by O dimer bond length.As we discussed above, electronic structure is robust onlywith the change of U values while O dimer bond lengthis fixed. It is interesting that the correlation effect is verylimited directly to the spectral function, but it plays animportant role in the MIT through the change of the crys-tal structure. O dimer bond length, which controls MITin this system, is sensitively affected by the competitionbetween correlation effect and Fe-O bond strength.It should be also noted that O dimer bond length canbe easily tuned by external condition such as chemicaldoping and/or oxygen vacancy which can affect the cor-relation strength of Fe d orbitals [19]. As we discussedabove, small change of Fe-O bond length affects O dimerbond length significantly. If Fe-O distance increases onlyby ∼ dimer distance as shown in Fig. 3 (a). So the elec-tronic properties can be significantly changed by externalconditions.A stable phase of FeO was observed under deep lowermantle condition with very high pressure and tempera-ture. To simulate the mantle condition, we also inves-tigate the electronic structure of FeO at high tempera-ture up to 2000 K. When DFT+DMFT calculations areperformed on the experimental structure at 76GPa, elec-tronic structures of FeO exhibit metallic nature at anytemperature of our interest. So, we expect that the O dimer bond length is the most important parameter todetermine the physical properties under the lower mantlecondition. On the other hand, the magnetism also mightbe an important parameter to the electronic structures atvery low temperature, although FeS , which has a samecrystal structure, is reported to be a non-magnetic com-pound for whole temperature range [8–11].Using DFT and DFT+DMFT calculation, we inves-tigated electronic structure and structural properties ofFeO under high pressure. Calculated spectral functionfrom DFT+DMFT indicates that correlation effect onthe electronic structure of given crystal structure is small.However, the correlation effect of Fe d orbitals plays animportant role to determine crystal structure of FeO .Specifically, O dimer bond length is sensitively affectedby the choice of U value. We find that FeO shows MITat the critical O dimer bond length of ∼ U value or volume. Wesuggest that the correlation effect should be consideredto describe correct structural and electronic properties ofFeO .This research was supported by the National ResearchFoundation of Korea (NRF) grant funded by the Koreagovernment (MSIP) (No. 2015R1A2A1A15051540), andthe Supercomputing Center/Korea Institute of Scienceand Technology Information with supercomputing re-sources including technical support (KSC-2016-C1-0003).DYK acknowledges the financial support by the NSAF(U1530402). ∗ [email protected] † [email protected][1] Q. Hu, D. Y. Kim, W. Yang, L. Yang, Y. Meng, L. Zhang, and H.-K. Mao, Nature , 241 (2016).[2] B. Lavina, P. Dera, E. Kim, Y. Meng, R. T. Downs, P. F.Weck, S. R. Sutton, and Y. Zhao, Proc. Natl. Acad. Sci.U. S. A , 17281 (2011).[3] B. Lavina and Y. Meng, Sci. Adv. , e1400260 (2015).[4] K. Ohta, R. E. Cohen, K. Hirose, K. Haule, K. Shimizu,and Y. Ohishi, Phys. Rev. Lett. , 026403 (2012).[5] I. Leonov, Phys. Rev. B , 085142 (2015).[6] J. Badro, V. V. 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