The metal insulator transition of vo 2 revisited
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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


Outline

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


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

insulator

metal

in metallic phase: ρ ~T

very short mean free path: ~V-V distance

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


The metal insulator transition of vo 2 revisited

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)


The metal insulator transition of vo 2 revisited

V 3d orbitals in the xyz octahedral coordinate frame

eg:

V-O

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?)

t2g

V-O

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


The metal insulator transition of vo 2 revisited

LDA:

well splittedt2gand egbands

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

Is it relevant to the physics of metallic VO2?

t2g

3dyzand 3dxz: Egor π* bandsofGoodenough

1d electron of the V4+

fills the 3 t2g bands

eg

V. Eyert Ann. Phys. (Leipzig)

11, 650 (2002)


The metal insulator transition of vo 2 revisited

Electronic structure of metallic VO2

LDA

Single site DMFT

UHB

LHB

U

t2g levels

bandwidth~2eV: weakly reduced in DMFT calculations

a1g

Eg

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?

LHB

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)


The metal insulator transition of vo 2 revisited

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 (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

V1-XCrXO2

J.P. Pouget et al PRB 10,

1801 (1974)

VO2 stressed along [110]R

J.P. Pouget et al PRL 35,

873 (1975)


The metal insulator transition of vo 2 revisited

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)

χspin

χtot

M2

T

R

T

M2

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~J/2t²~4eV

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

AB

Δρdimer

Δρ

B

S

eigenstates of the 2 electrons Hubbard molecule (dimer)

Δρdimer

T

Δσ

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))

Δσ?

S


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

M2

G. Villeneuve et al

J. Phys. C: Solid State

Phys. 10, 3621 (1977)

T

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


The metal insulator transition of vo 2 revisited

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 : 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

{u//[110]}

[110]

  • X-ray diffuse scattering experiments show the presence of {1,1,1} planes of « soft phonons » in rutile phase of

    (metallic)VO2 (insulating) TiO2

[001]

smeared diffuse

scattering ┴ c*R

cR*/2

+(001) planes

{u//cR}

R critical point of VO2

Γ critical point of TiO2

(incipient ferroelectricity

of symmetry A2Uand

2x degenerate EU)

Pcritical point of NbO2

aR*/2

EU

aR*/2

A2U

(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

[110]

[111]

cR

[1-10]

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 »


The metal insulator transition of vo 2 revisited

phase diagram of substitued VO2

Sublatices A≡B

Sublatices A≠B

dTMI/dx≈0

R

dTMI/dx ≈ -12K/%V3+

M1

xV5+

x

V3+

0.03

0

Reduction of V4+

Oxydation of V4+

VO2

M

V1-XMXO2

M=Cr, Al,Fe

M=Nb, Mo, W

VO2+y

VO2-yFy

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:

    ΔU=N(EF)Δσ²/2

    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!


Acknowledgements

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


Supplementary material

Supplementary material


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!


The metal insulator transition of vo 2 revisited

metallic

LDA


T 0 spectral function half filling full frustration

metallic VO2: single site DMFT

T=0 Spectral function half filling full frustration

D~2eV

zig-zag de V phase M2

D~0.9eV

ω/D

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


The metal insulator transition of vo 2 revisited

LDA phase métallique Rphase isolante M1


The metal insulator transition of vo 2 revisited

Structure électronique de la phase isolante M1

LDA

LDA

AB

B

a1g

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)

{

Eg

Pas de gap au niveau de Fermi!


The metal insulator transition of vo 2 revisited

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


The metal insulator transition of vo 2 revisited

LDA: Phase M2

zig-zag V2

paires V1


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