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The metal-insulator transition of VO 2 revisited. 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 l’honneur de Pascal Lederer. outline.

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the metal insulator transition of vo 2 revisited

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 l’honneur de Pascal Lederer

  • 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
vo 2 1 st order metal insulator transition at 340k
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

bad metal
Bad metal



in metallic phase: ρ ~T

very short mean free path: ~V-V distance

P.B. Allen et al PRB 48, 4359 (1993)


Metallic rutile phase




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)


V 3d orbitals in the xyz octahedral coordinate frame



σ* bonding

orbital located in the xy basis of the octahedron

bonding between V in the (1,1,0) plane (direct V-V bondingalong cR :1D band?)



π* 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



well splittedt2gand egbands

3dx²-y²: a1g or t// (1D) band of Goodenough

Is it relevant to the physics of metallic VO2?


3dyzand 3dxz: Egor π* bandsofGoodenough

1d electron of the V4+

fills the 3 t2g bands


V. Eyert Ann. Phys. (Leipzig)

11, 650 (2002)


Electronic structure of metallic VO2


Single site DMFT




t2g levels

bandwidth~2eV: weakly reduced in DMFT calculations



Hubbard bandson both Eg (π*)

and a1g (d//) states

no specificity of d// band!

Biermann et al PRL 94, 026404 (2005)

fractional occupancy of t 2g orbitals
Fractional occupancy of t2g orbitals

orbital/occupancy LDA* single site DMFT* EFG measurements**

x²-y² (d//) f1 0.36 0.42 0.41

yz (π*) f2 0.32 0.29 0.26-0.28

xz (π*) f3 0.32 0.29 0.33-0.31

*Biermann et al PRL 94, 026404 (2005)

** JPP thesis (1974): 51V EFG measurements between 70°C and 320°C

assuming that only the on site d electron contributes to the EFG:

VXX = (2/7)e<r-3> (1-3f2)

VYY = (2/7)e<r-3> (1-3f3)

VZZ = (2/7)e<r-3> (1-3f1)

vo 2 a correlated metal
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 χPauli: 5-8

sizeable charge fluctuations in the metallic state
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?


Koethe et al PRL 97, 116402 (2006)

mott hubbard transition for x increasing in nb substitued vo 2 v 1 x nb x o 2
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 x<xC

magnetism becomes more localized when x increases (Curis Weiss behavior of χspin 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)


Insulating phase: monoclinic M1

Short V-O distance


V-V pair

V leaves the center of the octahedron:

1- V shifts towards a triangular face of the octahedron

xz et yz orbitals (π* 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 π* levels

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 (S=0)

Driving force of the metal-insulator transition?
  • 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 stressedVO2

r m 1 transition of vo 2 splitted into r m 2 t m 1 transitions
R-M1 transition of VO2 splitted into R-M2-T-M1transitions


J.P. Pouget et al PRB 10,

1801 (1974)

VO2 stressed along [110]R

J.P. Pouget et al PRL 35,

873 (1975)


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

zig zag v 4 s 1 2 heisenberg chain site b
Zig-zag V4+ (S=1/2) Heisenberg chain (site B)








In M2: Heisenberg chain with exchange interaction 2J~4t²/U~600K~50meV

Zig-zag chain bandwidth: 4t~0.9eV

(LDA calculation: V. Eyert Ann. Phys. (Leipzig)11, 650 (2002))


U value used in DMFT calculations (Biermann et al)

crossover from m 2 to m 1 via t phase
Crossover from M2 toM1via 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?

energy levels in the m 1 phase
Energy levels in the M1 phase






eigenstates of the 2 electrons Hubbard molecule (dimer)




Only cluster DMFT is able to account for

the opening of a gap Δρat EF

(LDA and single site DMFT fail)

Δρdimer~2.5-2.8eV >Δρ~0.6eV

(Koethe et al PRL 97,116402 (2006))



estimation of the spin gap in m 1
Estimation of the spin gap Δσ in M1

2J(M1)=Δσ >2100K

  • Shift of χbetween the T phase ofV1-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 Δ: 1/T1~exp-Δ/kT

at 300K: (1/T1)1800bars=2 (1/T1)900bars

If Δ=Δσ-Δ’s one gets for s=0 (M1phase)

Δσ=2400K with Δ’=0.63 K/bar


G. Villeneuve et al

J. Phys. C: Solid State

Phys. 10, 3621 (1977)


J.P. Pouget& H. Launois, Journal de Physique 37, C4-49 (1976)


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


Site B



Site A

JintraB(°K) + 270K ≈ 11.4 VYYA (KHz)

For VYY= 125KHz (corresponding to V pairing in the M1 phase) one

gets : Jintra~1150K or Δσ~2300K

m 1 ground state
M1 ground state

Δσ~ 0.2eV<<Δρ 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 electronswhere the lattice instability opens equal charge and spin gaps Δρ ~ Δσ

electronic parameters of the m 1 hubbard dimer
Electronic parameters of the M1 Hubbarddimer
  • Spin gap value Δσ ~ 0.2 eV

Δσ= [-U+ (U²+16t²)1/2]/2

which leads to:

2t ≈ (Δσ Δρintra)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 ≈ Δρintra-Δσ ~ 2.5eV

(in the M2 phaseU 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 Δσ~7J (strong coupling limit)

In weak coupling spin-Peierls systems Δσ<J

lattice effects
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 (η1,η2) irreductible representation for each qC:

ηi 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 i=1 / 2

M2: η1≠0, η2= 0 T: η1> η2 ≠0 M1: η1= η2 ≠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?
evidences of soft lattice dynamics
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


smeared diffuse

scattering ┴ c*R


+(001) planes


R critical point of VO2

Γ critical point of TiO2

(incipient ferroelectricity

of symmetry A2Uand

2x degenerate EU)

Pcritical point of NbO2





(R. Comès, P. Felix and JPP: 35 years old unpublished results)

1 1 1 planar soft phonon modes in vo 2
{1,1,1} planarsoft 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





correlatedV shifts along [111] direction give rise to the observed (111) X-ray diffuse scattering sheets

*the zig-zag displacement destabilizes the π* orbitals

a further stabilization of d// orbitalsoccurs via the formation of bonding levels achieved by V pairing between neighbouring [111] « chains »


phase diagram of substitued VO2

Sublatices A≡B

Sublatices A≠B



dTMI/dx ≈ -12K/%V3+







Reduction of V4+

Oxydation of V4+




M=Cr, Al,Fe

M=Nb, Mo, W



uniaxial stress // [110]R

main features of the general phase diagram
Main features of the general phase diagram
  • Substituants reducing V4+ in V3+ : destabilize insulating M1* with respect to metallic R

formation ofV3+ 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 ΔU is a BCS like condensation energy

of a spin-Peierls ground state:


One gets: ΔU≈1000K per V4+ - V4+ pair (i.e. perV2O4 formula unitof M1)

with Δσ~0.2eV 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))

main features of the general phase diagram1
Main features of the general phase diagram
  • Substituants reducing V4+ in V5+ : destabilize insulating M1 with respect to new insulating T and M2 phases

butleaves unchangedmetal-insulator transition: dTMI/dx≈0

below R: the totally paired M1 phase is replaced by the half paired M2 phase

formation of V5+ looses also thepairing 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!

comparison of vo 2 and bavs 3
Comparison of VO2and BaVS3
  • Both are d1 V systems where the t2g orbitals are partly filled

(but there is a stronger V-X hybridation for X=S than for X=O)

  • BaVS3 undergoes at 70K a 2nd orderPeierls M-I transition driven by a 2kF CDW instability in the 1D d// band responsible of the conducting properties

at TMItetramerization of V chainswithout charge redistribution among the t2g’s

(Fagot et al PRL90,196403 (2003))

  • VO2 undergoes at 340K a 1st order M-I transition accompanied by a large charge redistribution among the t2g’s

Structuralinstability towards the formation of zig-zag V shifts in metallic VO2 destabilizes the π* 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!

  • 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

main messages
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 transitionis 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+ (S=1/2) pairing

  • The asymmetric features of the general phase diagram of substitued VO2 must be more clearly explained!
t 0 spectral function half filling full frustration

metallic VO2: single site DMFT

T=0 Spectral function half filling full frustration


zig-zag de V phase M2



X.Zhang M. Rozenberg G. Kotliar (PRL 1993)


Structure électronique de la phase isolante M1






Niveaux a1g séparés en états:

liants (B) et antiliants (AB)

par l’appariement des V

Mais recouvrement avec le bas des états Eg (structure de semi-métal)



Pas de gap au niveau de Fermi!


Structure électronique de la phase isolante M1

Single site DMFT

Cluster DMFT












Stabilise états a1g

Gap entre a1g(B) et Eg

Pas de gap à EF


LDA: Phase M2

zig-zag V2

paires V1