The metal-insulator transition of VO2 revisited

1
The metal-insulator transition of VO2revisited

• J.-P. Pouget
• Laboratoire de Physique des Solides,
• CNRS-UMR 8502,
• Université Paris-sud 91405 Orsay

 Correlated electronic states in low
dimensions  Orsay 16 et 17 juin 2008 Conférence
en lhonneur de Pascal Lederer
2
outline

• Electronic structure of metallic VO2
• Insulating ground states
• Role of the lattice in the metal-insulator
  transition of VO2
• General phase diagram of VO2 and its
  substituants

3
VO2 1st order metal-insulator transition at 340K

Discovered nearly 50 years ago still the object
of controversy!
in fact the insulating ground state of VO2 is
non magnetic
4
Bad metal
insulator
metal
in metallic phase ? T very short mean free
path V-V distance
P.B. Allen et al PRB 48, 4359 (1993)
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Metallic rutile phase
A
B
cR
ABAB (CFC) compact packing of hexagonal planes of
oxygen atoms V located in one octahedral cavity
out of two two sets of identical chains of VO6
octahedra running along cR
(related by 42 screw axis symmetry)
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V 3d orbitals in the xyz octahedral coordinate
frame
eg
V-O s bonding
orbital located in the xy basis of the octahedron
bonding between V in the (1,1,0) plane
(direct V-V bonding along cR 1D band?)
t2g
V-O p bonding
orbitals  perpendicular  to the triangular
faces of the octaedron

bonding between V in the (1,-1,0)
plane in the (0,0,1) plane
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well splitted t2g and eg bands
LDA
3dx²-y² a1g or t// (1D) band of Goodenough Is
it relevant to the physics of metallic VO2?
t2g
3dyz and 3dxz Eg or p bands of
Goodenough
1d electron of the V4 fills the 3 t2g bands
eg
V. Eyert Ann. Phys. (Leipzig) 11, 650 (2002)

8
Electronic structure of metallic VO2
LDA
Single site DMFT
UHB
LHB
U
t2g levels bandwidth2eV weakly
reduced in DMFT calculations
a1g
Eg
Hubbard bands on both Eg (p) and a1g (d//)
states no specificity of d// band!
Biermann et al PRL 94, 026404 (2005)
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Fractional occupancy of t2g orbitals
orbital/occupancy LDA single site DMFT
EFG measurements x²-y² (d//) f1
0.36 0.42 0.41 yz (p)
f2 0.32 0.29
0.26-0.28 xz (p) f3 0.32
0.29 0.33-0.31

Biermann et al PRL 94, 026404 (2005) JPP
thesis (1974) 51V EFG measurements between 70C
and 320C assuming that only the on site d
electron contributes to the EFG VXX
(2/7)eltr-3gt (1-3f2) VYY (2/7)eltr-3gt
(1-3f3) VZZ (2/7)eltr-3gt (1-3f1)
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VO2 a correlated metal?

• Total spin susceptiblity
• Neff (EF)10 states /eV, spin direction
• J.P. Pouget H. Launois, Journal de Physique 37,
  C4-49 (1976)
• Density of state at EF
• N(EF)1.3, 1.5, 2 state/eV, spin
  direction
• LDA Eyert Ann Phys. (Leipzig) 11, 650 (2002),
• LDA Korotin et al cond-mat/0301347
• LDA and DMFT Biermann et al PRL 94, 026404
  (2005)
• Enhancement factor of ?Pauli 5-8

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Sizeable charge fluctuations in the metallic
state

• DMFT quasiparticle band lower (LHB) and upper
  (UHB) Hubbard bands
• LHB observed in photoemission spectra
• VO2 close to a Mott-Hubbard transition?

LHB
Koethe et al PRL 97, 116402 (2006)
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Mott Hubbard transition for x increasing inNb
substitued VO2 V1-XNbXO2?

• Nb isoelectronic of V but of larger size
• lattice parameters of the rutile phase strongly
  increase with x
• Very large increase of the spin susceptibility
  with x
• NMR in the metallic state show that this
  increase is homogeneous (no local effects) for
  xltxC
• magnetism becomes more localized when x
  increases (Curis Weiss behavior of ?spin for x
  large)
• beyond xC 0.2 electronic conductivity becomes
  activated
• electronic charges become localized
• local effects (induced by the disorder) become
  relevant near the metal-insulator transition
• metal-insulator transition with x due to
  combined effect of correlations and disorder
• concept of strongly correlated Fermi glass (P.
  Lederer)

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Insulating phase monoclinic M1
Short V-O distance
tilted V-V pair
V leaves the center of the octahedron 1- V
shifts towards a triangular face of the
octahedron xz et yz orbitals (p band) shift
to higher energy 2- V pairing along cR x²-y²
levels split into bonding and anti-bonding
states stabilization of the x²-y² bonding level
with respect to p levels
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Driving force of the metal-insulator transition?
The x²-y² bonding level of the V4 pair is
occupied by 2 electrons of opposite spin
magnetic singlet (S0)

• The 1st order metal- insulator transition induces
  a very large electronic redistribution between
  the t2g orbitals
• Insulating non magnetic V-V paired M1 ground
  state stabilized by
• - a Peierls instability in the d// band ?
• - Mott-Hubbard charge localization effects?
• To differentiate more clearly these two processes
  let us look at alternative insulating phases
  stabilized in
• Cr substitued VO2
• uniaxial stressed VO2

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R-M1 transition of VO2 splitted into
R-M2-T-M1transitions
V1-XCrXO2 J.P. Pouget et al PRB 10, 1801 (1974)
VO2 stressed along 110R J.P. Pouget et al PRL
35, 873 (1975)
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M2 insulating phase
(site A)
(site B)
Zig-zag V chain along c
V-V pair along c
Zig zag chains of (Mott-Hubbard) localized d1
electrons
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Zig-zag V4 (S1/2) Heisenberg chain (site B)
?spin
?tot
M2
T
R
T
M2
In M2 Heisenberg chain with exchange
interaction 2J4t²/U600K50meV Zig-zag
chain bandwidth 4t0.9eV (LDA calculation V.
Eyert Ann. Phys. (Leipzig)11, 650
(2002)) UJ/2t²4eV U value used in DMFT
calculations (Biermann et al)
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Crossover from M2 to M1via T phase
Dimerization of the Heisenberg chains (V site B)
tilt of V pairs (V site A)
2J intradimer exchange integral on paired sites B
Jintra increases with the dimerization
Value of 2Jintra ( spin gap) in the M1 phase?
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Energy levels in the M1 phase
AB
??dimer
??
B
S
??dimer
eigenstates of the 2 electrons Hubbard molecule
(dimer)
T
?s
Only cluster DMFT is able to account for the
opening of a gap ?? at EF (LDA and single site
DMFT fail) ??dimer2.5-2.8eV gt??0.6eV
(Koethe et al PRL 97,116402 (2006))
?s?
S
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Estimation of the spin gap ?s in M1

• Shift of ? between the T phase of V1-XAlXO2 and
  M1 phase of VO2
• 51V NMR line width broadening of site B in the T
  phase of stressed VO2 T1-1 effect
• for a singlet triplet gap ? 1/T1exp-?/kT
• at 300K (1/T1)1800bars2 (1/T1)900bars
• If ??s-?s one gets for s0 (M1phase)
• ?s2400K with ?0.63 K/bar

2J(M1)?s gt2100K
G. Villeneuve et al J. Phys. C Solid State
Phys. 10, 3621 (1977)
M2
T
J.P. Pouget H. Launois, Journal de Physique 37,
C4-49 (1976)
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The intradimer exchange integral Jintra of the
dimerized Heisenberg chain (site B) is a linear
function of the lattice deformation measured by
the 51V EFG component VYY on site A
M1
Site B
T
M2
Site A
JintraB(K) 270K 11.4 VYYA (KHz)
For VYY 125KHz (corresponding to V pairing in
the M1 phase) one gets Jintra1150K or ?s2300K
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M1 ground state

• ?s 0.2eVltlt?? is thus caracteristic of an
  electronic state where strong coulomb repulsions
  lead to a spin charge separation
• The M1 ground state thus differs from a
  conventional Peierls ground state in a band
  structure of non interacting electrons where the
  lattice instability opens equal charge and spin
  gaps ?? ?s

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Electronic parameters of the M1 Hubbard dimer

• Spin gap value ?s 0.2 eV
• ?s -U (U²16t²)1/2/2
• which leads to
• 2t (?s ??intra)1/2 0.7eV
• 2t amounts to the splitting between bonding and
  anti-bonding quasiparticle states
• in DMFT (0.7eV) and cluster DMFT (0.9eV)
  calculations
• 2t is nearly twice smaller than the B-AB
  splitting found in LDA (1.4eV)
• U ??intra-?s 2.5eV
• (in the M2 phase U estimated at 4eV)
• For U/t 7
• double site occupation 6 per dimer
• nearly no charge fluctuations no LHB seen in
  photoemission
• ground state wave function very close to the
  Heitler-London limit

wave function expected for a spin-Peierls ground
state The ground state of VO2 is such that ?s7J
(strong coupling limit) In weak coupling
spin-Peierls systems ?sltJ
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Lattice effects

• the R to M1 transformation (as well as R to M2 or
  T transformations) involves
• - the critical wave vectors qc of the  R 
  point star(1/2,0,1/2) , (0,1/2,1/2)
• - together, with a 2 components (?1,?2)
  irreductible representation for each qC
• ?i corresponds to the lattice deformation of
  the M2 phase
• formation of zig-zag V chain (site B) V-V
  pairs (site A)
• the zig-zag displacements located are in the
  (1,1,0)R / (1,-1,0)R planes for i1 / 2
• M2 ?1? 0, ?2 0 T ?1gt ?2 ? 0
  M1 ?1 ?2 ? 0
• The metal-insulator transition of VO2 corresponds
  to a lattice instability at a single R point
• Is it a Peierls instability with formation of a
  charge density wave driven by the divergence of
  the electron-hole response function at a qc which
  leads to good nesting properties of the Fermi
  surface?
• Does the lattice dynamics exhibits a soft mode
  whose critical wave vector qc is connected to
  the band filling of VO2 ?
• Or is there an incipient lattice instability of
  the rutile structure used to trig the
  metal-insulator transition?

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Evidences of soft lattice dynamics

• X-ray diffuse scattering experiments show the
  presence of 1,1,1 planes of  soft phonons  in
  rutile phase of
• (metallic)VO2 (insulating)
  TiO2

u//110
110
001
cR/2
smeared diffuse scattering - cR
(001) planes u//cR
R critical point of VO2
G critical point of TiO2 (incipient
ferroelectricity of symmetry A2U and 2x
degenerate EU)
P critical point of NbO2
aR/2
aR/2
EU
A2U
(R. Comès, P. Felix and JPP 35 years old
unpublished results)
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1,1,1 planar soft phonon modes in VO2

• not related to the band filling (the diffuse
  scattering exists also in TiO2)
• 2kF of the d// band does not appear to be a
  pertinent critical wave vector
• as expected for a Peierls transition
• but the incipient (001)-like diffuse lines
  could be the fingerprint of a 4kF instability
  (not critical) of fully occupied d// levels
• instability of VO2 is triggerred by an incipient
  lattice instability of the rutile structure which
  tends to induce a V zig-zag shift
• ferroelectric V shift along the 110 / 1-10
  direction (degenerate RI?) accounts for the
  polarisation of the diffuse scattering

110
111
cR
1-10
correlated V shifts along 111 direction give
rise to the observed (111) X-ray diffuse
scattering sheets the zig-zag displacement
destabilizes the p orbitals a further
stabilization of d// orbitals occurs via the
formation of bonding levels achieved by V pairing
between neighbouring 111  chains 
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phase diagram of substitued VO2
Sublatices AB
Sublatices A?B
dTMI/dx0
R
dTMI/dx -12K/V3
M1
xV5
x
V3
0.03
0
Oxydation of V4
Reduction of V4
VO2
M
V1-XMXO2
MCr, Al, Fe
MNb, Mo, W
VO2y
VO2-yFy
uniaxial stress // 110R
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Main features of the general phase diagram

• Substituants reducing V4 in V3 destabilize
  insulating M1 with respect to metallic R
• formation of V3 costs U the energy gain
  in the formation of V4-V4 Heitler-London pairs
  is lost
• dTMI/dx -1200K per V4-V4 pair broken
• Assuming that the energy gain ?U is a BCS like
  condensation energy
• of a spin-Peierls ground state
• ?UN(EF)?s²/2
• One gets ?U1000K per V4 - V4 pair (i.e. per
  V2O4 formula unit of M1)
• with ?s0.2eV and N(EF)2x2states per eV, spin
  direction and V2O4 f.u.
• For large x, the M1 long range order is
  destroyed, but the local V-V pairing remains
• (R. Comès et al Acta Cryst. A30, 55 (1974))

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Main features of the general phase diagram

• Substituants reducing V4 in V5 destabilize
  insulating M1 with respect to new insulating T
  and M2 phases
• but leaves unchanged metal-insulator transition
  dTMI/dx0
• below R the totally paired M1 phase is replaced
  by the half paired M2 phase
• formation of V5 looses also the pairing energy
  gain but does not kill
• the zig-zag instability (also present in TiO2!)
• as a consequence the M2 phase is favored
• uniaxial stress along 110 induces zig-zag V
  displacements along 1-10

Note the non symmetric phase diagram with respect
to electron and hole  doping  of VO2!
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Comparison of VO2 and BaVS3

• Both are d1 V systems where the t2g orbitals are
  partly filled
• (but there is a stronger V-X hybridation for XS
  than for XO)
• BaVS3 undergoes at 70K a 2nd order Peierls M-I
  transition driven by a 2kF CDW instability in the
  1D d// band responsible of the conducting
  properties
• at TMI tetramerization of V chains without
  charge redistribution among the t2gs
• (Fagot et al PRL90,196403 (2003))
• VO2 undergoes at 340K a 1st order M-I transition
  accompanied by a large charge redistribution
  among the t2gs
• Structural instability towards the formation of
  zig-zag V shifts in metallic VO2 destabilizes
  the p levels and thus induces a charge
  redistribution in favor of the d// levels
• The pairing (dimerization) provides a further
  gain of energy by putting the d// levels into a
  singlet bonding state
• M1 phase exhibits a spin-Peierls like ground
  state
• This mechanism differs of the Peierls-like V
  pairing scenario proposed by Goodenough!

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acknowledgements

• During the thesis work
• H. Launois
• P. Lederer
• T.M. Rice
• R. Comès
• J. Friedel
• Renew of interest from recent DMFT calculations
• A. Georges
• S. Biermann
• A. Poteryaev
• J.M. Tomczak

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Supplementary material
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Main messages

• Electron-electron interactions are important in
  VO2
• - in metallic VO2 important charge
  fluctuations (Hubbard bands)
• Mott-Hubbard like localization occurs when
  the lattice expands (Nb substitution)
• - in insulating VO2 spin-charge decoupling
• ground state described by Heitler-London
  wave function
• The 1ST order metal-insulator transition is
  accompanied by a large redistribution of charge
  between d orbitals.
• for achieving this proccess an incipient lattice
  instability of the rutile structure is used.
• It stabilizes a spin-Peierls like ground
  state with V4 (S1/2) pairing
• The asymmetric features of the general phase
  diagram of substitued VO2 must be more clearly
  explained!

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metallic
LDA
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T0 Spectral function half filling full
frustration
metallic VO2 single site DMFT
D2eV
zig-zag de V phase M2 D0.9eV
?/D
X.Zhang M. Rozenberg G. Kotliar (PRL 1993)
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LDA phase métallique R phase isolante M1
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Structure électronique de la phase isolante M1
LDA
LDA
AB
B
a1g
Niveaux a1g séparés en états liants (B) et
antiliants (AB) par lappariement des V Mais
recouvrement avec le bas des états Eg (structure
de semi-métal)

Eg
Pas de gap au niveau de Fermi!
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Structure électronique de la phase isolante M1
Single site DMFT
Cluster DMFT
UHB
a1g
B
Eg
LHB
AB
UHB
U
LHB
a1g
Eg
Stabilise états a1g
Gap entre a1g(B) et Eg
Pas de gap à EF
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LDA Phase M2
zig-zag V2
paires V1