Orbital-selective pressure-driven metal to insulator transition in FeO from dynamical mean-field theory

Abstract

In this work we report the LDA+DMFT (method combining local-density approximation with dynamical mean-field theory) results of magnetic and spectral properties calculation for paramagnetic phases of FeO at ambient and high pressures (HPs). At ambient-pressure (AP) calculation gave FeO as a Mott insulator with Fe 3d shell in high-spin state. Calculated spectral functions are in a good agreement with experimental photoemission spectroscopy and IPES data. Experimentally observed metal-insulator transition at high pressure is successfully reproduced in calculations. In contrast to MnO and Fe2O3 (d5 configuration) where metal-insulator transition is accompanied by high-spin to low-spin transition, in FeO (d6 configuration) average value of magnetic moment √⟨μz2⟩ is nearly the same in the insulating phase at AP and metallic phase at HP in agreement with x-ray spectroscopy data [ J. Badro, V. V. Struzhkin, J. Shu, R. J. Hemley, H.-k. Mao, C.-c. Kao, J.-P. Rueff and G. Shen Phys. Rev. Lett. 83 4101 (1999)]. The metal-insulator transition is orbital selective with only t2g orbitals demonstrating spectral function typical for strongly correlated metal (well pronounced Hubbard bands and narrow quasiparticle peak) while eg states remain insulating.

Full text

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arXiv:1007.4650v1 [cond-mat.str-el] 27 Jul 2010
Orbital Selective Pressure-Driven Metal-Insulator Transition in FeO from Dynamical
Mean-Field Theory
A. O. Shorikov, Z. V. Pchelkina, V. I. Anisimov, and S. L. Skornyakov
Institute of Metal Physics, Russian Academy of Sciences, 620990 Yekaterinburg, Russia
2Ural Federal University, 620002 Yekaterinburg, Russia
M. A. Korotin
Institute of Metal Physics, Russian Academy of Sciences, 620041 Yekaterinburg, Russia
In this Letter we report the first LDA+DMFT (method combining Local Density Approxima-
tion with Dynamical Mean-Field Theory) results of magnetic and spectral properties calculation
for paramagnetic phases of FeO at ambient and high pressures (HP). At ambient pressure (AP)
calculation gave FeO as a Mott insulator with Fe 3d-shell in high-spin state. Calculated spectral
functions are in a good agreement with experimental PES and IPES data. Experimentally observed
metal-insulator transition at high pressure is successfully reproduced in calculations. In contrast to
MnO and Fe2O3 (d5configuration) where metal-insulator transition is accompanied by high-spin
to low-spin transition, in FeO (d6configuration) average value of magnetic moment
nearly the same in the insulating phase at AP and metallic phase at HP in agreement with X-Ray
spectroscopy data (Phys. Rev. Lett. 83, 4101 (1999)). The metal-insulator transition is orbital
selective with only t2g orbitals demonstrating spectral function typical for strongly correlated metal
(well pronounced Hubbard bands and narrow quasiparticle peak) while eg states remain insulating.
?< µ2
z> is
PACS numbers: 74.25.Jb, 71.45.Gm
Introduction.– For many years one of the central issues
of condensed matter physics is the metal-insulator tran-
sition (MIT) in d- or f-elements compounds [1]. The
most spectacular examples are pressure-driven transi-
tions from wide gap Mott insulators to metallic state for
transition metal oxides. For MnO and Fe2O3 (d5con-
figuration) metal-insulator transition is accompanied by
high-spin to low-spin transition (HS–LS). Recently MIT
in those materials was successfully described theoreti-
cally by LDA+DMFT(method combining Local Density
Approximation with Dynamical Mean-Field Theory) [2]
calculations [3, 4].
Iron oxide also exhibits MIT under high pressure. Re-
sistivity measurements showed that FeO becomes metal-
lic at pressures exceeding 72 GPa [5]. Correct description
of MIT under pressure in w¨ ustite (Fe1−xO) is crucial in
Earth science because iron oxides are believed to be ma-
jor constituents of Earth mantle.
At ambient pressure and room temperature FeO has
cubic rocksalt B1 structure [6]. Below N´ eel temperature
TN=198 K FeO transforms into rhombohedral structure
that could be viewed as a slight elongation along cube di-
agonal of the original cubic structure. Under pressure at
room temperature rhombohedral distortion is observed
at ≈ 15 GPa and this structure is preserved up to at
least 140 GPa [7, 8]. This transformation to rhombo-
hedral structure was believed to accompany long-range
magnetic ordering due to increasing of N´ eel temperature
with pressure [9]. However recent neutron diffraction
study of w¨ ustite at room temperature under pressure [10]
showed the absence of magnetic peaks corresponding to
antiferromagnetism. At high pressures and temperatures
(P >120 GPa and T >1000 K) FeO transforms into NiAs
B8 phase [11].
In contrast to MnO and Fe2O3 it is not clear if FeO
undergoes HS–LS transition with increase of pressure.
Controversial experimental evidences were obtained for
this problem. M¨ ossbauer spectroscopy [12] shows that
quadrupole splitting appears between 60 and 90 GPa at
room temperature. The authors interpreted that as LS
diamagnetic state. On the other hand high pressure X-
ray emission spectroscopy
satellite feature in Fe Kβ line associated with HS Fe2+
state does not disappear up to 143 GPa.
Electronic structure calculations in standard Density
Functional Theory (DFT) methods predict an antiferro-
magnetic metallic ground state [14] in contrast to exper-
imentally observed insulator with an optical band gap of
2.4 eV [15].The LDA+U method [16] has been success-
fully applied to investigate strongly correlated transition
metal oxides and predicted an insulating ground state
in FeO at ambient pressure [17]. Further investigation
done by Gramsch et al. [18] for stoichiometric w¨ ustite
has showed that using the value of Coulomb parameter
U that reproduces experimentally observed energy gap at
ambient pressure one can obtain metal-insulator transi-
tion in LDA+U calculations for unrealistically high pres-
sures only.
MIT in transition metal oxides with pressure can
be successfully described using LDA+DMFT calcula-
tions [3, 4]. In the present work we demonstrate that
LDA+DMFT method reproduces MIT for FeO with pres-
sure. However in contrast to MnO and Fe2O3 MIT is
not accompanied by high-spin to low-spin transition and
[13] demonstrates that the

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metallic spectral function is observed only for t2gorbitals
while egstates remain insulating.
Method.– The LDA+DMFT method [2] calculation
scheme is constructed in the following way: first, a Hamil-
tonianˆHLDA is produced using converged LDA results
for the system under investigation, then the many-body
Hamiltonian is set up, and finally the corresponding self-
consistent DMFT equations are solved. The calculations
presented below have been done for crystal volumes cor-
responding to values of pressure up to 140 GPa and room
temperature. Since no structure transition has been ob-
served at low temperatures [8] and NiAs phase appears
above 1000 K only all calculation were performed for sim-
ple NaCl (B1) cubic crystal structure with lattice con-
stant scaled to give a volume corresponding to applied
pressure [5]. Ab-initio calculations of electronic struc-
ture were obtained within the pseudopotential plane-
wave method PWSCF, as implemented in the Quan-
tum ESPRESSO package [19]. HamiltoniansˆHLDA in
Wannier function (WF) basis [20, 21] were produced us-
ing projection procedure that is described in details in
Ref. 22.
The WFs are defined by the choice of Bloch functions
Hilbert space and by a set of trial localized orbitals that
will be projected on these Bloch functions. The basis
set includes all bands that are formed by O-2p and Fe-
3d states and correspondingly full set of O-2p, and Fe-3d
atomic orbitals to be projected on Bloch functions for
these bands.That would correspond to the extended
model where in addition to d-orbitals all p-orbitals are
included too.
The resulting 8x8 p − d Hamiltonian to be solved by
DMFT has the form
ˆH =ˆHLDA−ˆHdc+1
2
i,α,β,σ,σ′
?
Uσσ′
αβˆ nd
iασˆ nd
iβσ′, (1)
where Uσσ′
the occupation number operator for the d electrons with
orbitals α or β and spin indices σ or σ′on the i-th site.
The termˆHdcstands for the d-d interaction already ac-
counted for in LDA, so called double-counting correction.
In the present calculation the double-counting was chosen
in the following formˆHdc=¯U(ndmft−1
the self-consistent total number of d electrons obtained
within the LDA+DMFT,¯U is the average Coulomb pa-
rameter for the d shell andˆI is unit operator.
The elements of Uσσ′
αβmatrix are parameterized by U
and JH according to procedure described in [23]. The
values of Coulomb repulsion parameter U and Hund ex-
change parameter JHwere calculated by the constrained
LDA method [24] on Wannier functions [22]. Obtained
values JH=0.89 eV, U = 5 eV are close to previous
estimations [18].The effective impurity problem for
the DMFT was solved by the hybridization expansion
Continuous-Time Quantum Monte-Carlo method (CT-
QMC) [25]. Calculations for all volumes were performed
αβ
is the Coulomb interaction matrix, ˆ nd
iασis
2)ˆI. Here ndmftis
0
0,2
eg
t2g
0
0,2
0
0,2
0
0,2
0
0,2
-4-2024
Energy [eV]
0
0,2
APP
50GPa
55GPa
60GPa
70GPa
140GPa
Spectral function [1/eV]
FIG. 1: (Color online) Spectral function of Fe-d states vs.
pressure obtained in LDA+DMFT (CT-QMC) calculations
at room temperature.
in the paramagnetic state at the inverse temperature
β = 1/T = 40 eV−1corresponding to 290 K. Spectral
functions on real energies were calculated by Maximum
Entropy Method (MEM)[26].
Results and discussion.– The Fe d band is split by crys-
tal field in triply degenerated t2gand doubly degenerated
eg subbands. LDA fails to describe insulating ground
state of FeO at AP and for all volumes FeO is metallic.
Including Coulomb correlation effects in frames of
LDA+DMFT method results in high spin state wide gap
Mott insulator for ambient pressure phase (APP) of FeO
in agreement with experimental data.
energy gap value of about 2 eV agrees well with IPES
measurement [27] value 2.5 eV and optical spectrum [15]
value 2.4 eV. The occupation numbers for Fe d orbitals
are n(eg)=0.54 and n(t2g)=0.68. The average value of lo-
cal magnetic moment?< µ2
agree very well with high-spin state of Fe+2ion (d6con-
figuration) in cubic crystal field: 2 electrons in egstates
(n(eg)=1/2) and 4 electrons in t2g states (n(t2g)=2/3)
with magnetic moment value 4 µB. Spectral functions
A(ω) for all pressure values calculated by MEM using
The calculated
z> is 3.8µB. Those numbers

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3
-12-10-8
-6
-4-2024
6
Energy [eV], EF=0 eV
0
1
2
3
4
5
Spectral function [1/eV]
DMFT
PES, IPES
23 eV
Intensity [Arb. units]
FIG. 2: (Color online) Total spectral function of FeO in am-
bient pressure phase calculated within LDA+DMFT (CT-
QMC) (β=40 eV−1)(solid blue line) in comparison with com-
bined PES and IPES experimental data (red dots) from
Ref. [28, 29].
Green function G(τ) from CT-QMC calculations are pre-
sented in the Fig. 1. The spectral function for ambient
pressure phase (APP) shows well defined insulating be-
havior for all d-orbitals. However the energy gap for eg
states is nearly two times larger than for t2gstates indi-
cating that the latter orbitals are closer to MIT than the
former ones. Figure 2 contains calculated total spectral
function compared with spectrum combined from PES
and IPES experiments [28, 29]. The theoretical and ex-
perimental curves are in a good agreement.
LDA+DMFT calculation made for small volume values
corresponding to high pressures gave metallic state for
FeO (see Fig. 3) starting from 60 GPa in agreement with
experiment [5]. One can see that t2g orbitals become
metallic whereas egones remain insulating. This behav-
ior reminds the orbital selective Mott transition (OSMT)
in ruthenates [30]. Occupation number values in Fe-d
shell are practically not changed comparing with APP
and are n(eg)=0.55 n(t2g)=0.68 at 140 GPa. The mag-
netic moment value decreases on a few percent only and
is 3.5µB at 140 GPa. The only interpretation for those
values is that an iron d-shell in high pressure metallic
phase of FeO still corresponds to high-spin state of Fe+2
ion. This conclusion agrees well with analysis of high
pressure X-Ray emission spectroscopy experiment made
in Ref. [13]. The occupation numbers and magnetic mo-
ment vs. pressure are presented in the Fig. 3. One can
see that all curves exhibit the kink at 60 GPa. We argue
that this feature is due to MIT and corresponding re-
construction of spectral function at Fermi level. Spectral
functions A(ω) for t2g in the Fig. 1 for pressure values
larger then 60 GPa become typical for strongly correlated
metal close to MIT: well pronounced Hubbard bands and
narrow quasiparticle peak. A(ω) for eg is still insulat-
ing with Hubbard bands only but energy gap value is
050
100 150
Pressure [GPa]
22
2,5 2,5
33
3,5 3,5
44
<M> [µB]
<M>
n(t2g)
n(eg)
Occupations
FIG. 3: (Color online) Magnetic moments (black squares) and
occupancies of t2g (red cicles) and eg (blue triangles) shells vs.
pressure obtained in LDA+DMFT (CT-QMC) calculations.
strongly decreased comparing with APP (see Fig. 1).
To understand these results the following simple model
was used. The model has two semicircle DOS of the same
width with 3 orbital and 4 electrons. One orbital is non-
degenerate and two other orbitals are degenerate. The
centers of gravity and DOS widths were taken from ab
initio LDA calculations. In this model non-degenerate
orbital stands for eg-orbital in FeO and two others for
t2g. Occupations in model in HS state are 1/2 for non-
degenerate orbital (the same as in realistic LDA+DMFT
calculation for FeO) and 3/4 for degenerate orbitals com-
paring with 2/3 in the case of t2g orbitals in FeO. The
Kanamori parametrisation of Coulomb repulsion (with
the same U=5 eV and J=0.89 eV) was used. Note, that
corresponding matrix elemetns Uσ,σ′
be the same for all orbitals. The model was solved using
DMFT (CT-QMC) method and obtained spectral func-
tions for two values of pressure (APP and 140 GPA) are
presented in the Fig. 4.
Theorbitalselective
(OSMT) was reproduced in these calculations.
DOSes for all three orbitals have the same width (in
contrast to OSMT [30] in ruthenates where two bands
have very different widths) and actual structure of DOS
is neglected we can conclude that effects of different
degeneracy of orbitals and deviation from half filling are
the driving force of this separate transition. It is known
that critical value of Coulomb interaction parameter
Uc needed for metal-insulator transition in half-filled
degenerate Hubbard model is Uc ≈
[31] (N is degeneracy and UN=1
for non-degenerate case).
degenerate t2g orbitals one needs larger effective U
value to become insulating than for less degenerate eg
orbitals.In addition to that for half-filled states an
estimation for effective Ueff value is U +(N −1)J while
for the occupancy one electron more then half-filling
α,β(eq. 1) are set to
metal-insulatedtransition
Since
√NUN=1
is critical U value
That means that for more
c
− NJ
c

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4
0
1
Fe-d t2g
Fe-d eg
0
0,1
0,2
nondeg.
deg.
-404
Energy [eV]
0
1
-404
Energy [eV]
0
0,1
0,2
DOS [States/eV]
Spectral Function [1/eV]
APP
140 GPa
FIG. 4:
states (DOS) (solid lines) and correponding model semicir-
cle DOS(dashed lines). Right panels - spectral functions from
model DMFT (CT-QMC) calculations for two values of pres-
sure.Non degenerate orbital (black lines) reproduces eg-
orbitals and 2 times degenerate one reproduces t2g orbitals
(red line).
(Color online) Left panels - LDA densities of
an estimation is Ueff = U − J. Then for 2/3 filled t2g
orbitals one needs much larger U value to drive them
into insulating state than for half-filled egstates.
In conclusion.– We have performed LDA+DMFT cal-
culation for FeO at room temperature and values of pres-
sure from the ambient one till 140 GPa. In the agree-
ment with experiment spectral function for FeO at AP
demonstrates an energy gap of about 2 eV. At the pres-
sures higher then 60 GPa FeO is metallic but only for
t2gorbitals while egstates remain insulating that corre-
sponds to orbital selective Mott transition scenario. The
MIT obtained in our calculations is not accompanied by
change of spin state and FeO has HS with large local mo-
ment in APP and all HPP. This result agrees with high
pressure X-Ray emission spectroscopy data.
Acknowledgments.– The authors thank J. Kuneˇ s for
providing DMFT computer code used in our calcula-
tions, P. Werner for the CT-QMC impurity solver. This
work was supported by the Russian Foundation for Ba-
sic Research (Project No. 10-02-00046-a, 09-02-00431-a,
and 10-02-00546-a), the Dynasty Foundation, the fund of
the President of the Russian Federation for the support
of scientific schools NSH 1941.2008.2, the Programs of
the Russian Academy of Science Presidium “Quantum
microphysics of condensed matter” N7 and ”Strongly
compressed materials“, Russian Federal Agency for Sci-
ence and Innovations (Program “Scientific and Scientific-
Pedagogical Trained of the Innovating Russia” for 2009-
2010 years), grant No. 02.740.11.0217, MK-3758.2010.2.
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