The metal-insulator transition of VO2revisited

J.-P. PougetLaboratoire 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

• 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 itssubstituants

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

Discovered nearly 50 years agostill the object of controversy!

*

*in fact the insulating ground stateof VO2 is non magnetic

Bad metal

in metallic phase: ρ ~Tvery short mean free path: ~V-V distance

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

metal

insulator

Metallic rutile phase

cR

ABAB (CFC) compact packing of hexagonal planes of oxygen atomsV 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)

A

B

eg:

t2g

V-Oσ* bonding

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

bonding between V in the (1,-1,0) plane in the (0,0,1) plane

V 3d orbitals in the xyz octahedral coordinate frame

V-Oπ* bonding

orbital located in the xy basis of the

octahedron

orbitals « perpendicular » to the triangular faces of the octaedron

well splitted t2g and eg bands

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

3dyz and 3dxz: Eg or π* bandsof Goodenough

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

is it relevant to the physics of metallic VO2?

LDA:

1d electron of the V4+

fills the 3 t2g bands

t2g

eg

Electronic structure of metallic VO2

LDASingle site DMFT

Ega1g

t2g levelsbandwidth~2eV: weakly reduced in

DMFT calculations

ULHB

UHB

Biermann et al PRL 94, 026404 (2005)

Hubbard bands on both Eg (π*)and a1g (d//) statesno specificity of d// band!

Fractional occupancy of t2g orbitalsorbital/occupancy LDA* single site DMFT* EFG measurements**x²-y² (d//) f1 0.36 0.42 0.41yz (π*) f2 0.32 0.29 0.26-0.28xz (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°Cassuming 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)

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

• 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 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 xNMR in the metallic state show that this increase is homogeneous (no local effects) for x<xCmagnetism becomes more localized when x increases (χspin: Curie Weiss behavior of for large x)

• beyond xC ~0.2: electronic conductivity becomes activatedelectrons become localizedlocal 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

tiltedV-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(by ~0.3eV from LDA or DMFT)

2- V pairing along cR : x²-y² levels split into bonding and anti-bonding statesstabilization of the x²-y² bonding level with respect to π* levels

Short V-O distance

Driving force of the metal-insulatortransition?

• 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 VO2uniaxial stressed VO2

The x²-y² bonding level of the V4+ pair is occupied by 2 electrons of opposite spin: magnetic singlet (S=0)

R-M1 transition of VO2 splitted intoR-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)

M2 insulating phase

Zig-zag V chainalong c

V-V pairalong c

(site B)

(site A)

Zig –zag chains of (Mott-Hubbard) localized d1 electrons

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/2t²~4eVU value used in DMFT calculations (Biermann et al)

Zig-zag V4+ (S=1/2) Heisenberg chain (site B)

χtot

χspin

T M2

R T

M2

Crossover from M2 to M1via T phase

tilt of V pairs (V site A)

Dimerization of the Heisenberg chains (V site B)

2J intradimer exchange integralon paired sites B

Value of 2Jintra (= spin gap) in the M1 phase?

Jintra increases with the dimerization

Energy levels in the M1 phase

ΔρΔρdimer

Δρdimer

Δσ

eigenstates of the 2 electronsHubbard molecule (dimer)

Only cluster DMFT is able to account forthe opening of a gap Δρ at EF

(LDA and single site DMFT fail)

Δρdimer~2.5-2.8eV >Δρ~0.6eV(Koethe et al PRL 97,116402 (2006))

Δσ?

S

T

SB

AB

Estimation of the spin gap Δσ in M1 • Shift of χ 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 effectfor a singlet –triplet gap Δ: 1/T1~exp-Δ/kTat 300K: (1/T1)1800bars=2 (1/T1)900barsIf Δ=Δσ-Δ’s one gets for s=0 (M1phase)Δσ=2400K with Δ’=0.63 K/bar

2J(M1)=Δσ >2100K

G. Villeneuve et al J. Phys. C: Solid StatePhys. 10, 3621 (1977)

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

M2T

50 60 70 80 90 100 110 120 130200

400

600

800

1000

1200

Jintr

a (°

K)

Vyy (KHz)

V1-XCrXO2 X=1% stressed VO2% T=295K

M1

T

M2

JintraB(°K) + 270K ≈ 11.4 VYY

A (KHz)

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

For VYY= 125KHz (corresponding to V pairing in the M1 phase) onegets : Jintra~1150K or Δσ~2300K

Site B

Site A

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 formation of a gap Δρ mostly due to electron-electron interaction issustained by a recent high pressure experiment showing an abrupt increase of the metallicity of M1-VO2 above 10GPa

(E. Arcangeletti et al PRL 98, 196406 (2007))

The M1 ground state thus differs from a conventional Peierlsground state in a band structure of non interacting electronswhere the lattice instability opens equal charge and spin gaps Δρ ~ Δσ

Electronic parameters of the M1 Hubbard dimer• Spin gap value Δσ ~ 0.2 eVΔσ= [-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 statesin DMFT (0.7eV) and cluster DMFT (0.9eV) calculations2t is nearly twice smaller than the B-AB splitting found in LDA (~1.4eV)• U ≈ Δρintra-Δσ ~ 2.5eV(in the M2 phase U estimated at ~4eV)• For U/t ~ 7

double site occupation ~ 6% per dimernearly no charge fluctuations no LHB seen in photoemissionground state wave function very close to the Heitler-London limit*

*wave function expected for a spin-Peierls ground stateThe ground state of VO2 is such that Δσ~7J (strong coupling limit)

In weak coupling spin-Peierls systems Δσ<J

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 pointIs 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 isconnected 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• X-ray diffuse scattering experiments show the presence of {1,1,1}

planes of « soft phonons » in rutile phase of(metallic)VO2 (insulating) TiO2

(R. Comès, P. Felix and JPP: 35 years old unpublished results)aR*/2

aR*/2

cR*/2

R critical point of VO2

P critical point of NbO2

Γ critical point of TiO2(incipient ferroelectricity

of symmetry A2U and2x degenerate EU)

+(001) planes{u//cR}

[001]

[110]

A2U

EU

{u//[110]}

smeared diffuse scattering ┴ c*R

{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 transitionbut 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* ( for [111] / [1-11] chains) accountsfor the polarisation of the diffuse scattering

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

*the zig-zag displacement destabilizes the π* orbitalsa further stabilization of d// orbitals occurs via the formation of bonding levels

achieved by V pairing between neighbouring [111] « chains » (no X-ray diffuse scattering corresponding at this process seen)

[111][110]

cR

[1-11]

phase diagram of substitued VO2

R

M1

0.03x

V1-XMXO2

0

dTMI/dx ≈ -12K/%V3+

uniaxial stress // [110]R

xV5+V3+

M=Cr, Al, Fe

VO2+yVO2-yFy

M=Nb, Mo, W

Oxydation of V4+Reduction of V4+MVO2

dTMI/dx≈0Sublatices A≡B Sublatices A≠B

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 lostdTMI/dx ≈ -1200K per V4+-V4+ pair broken

Assuming that the energy gain ΔU is a BCS like condensation energyof a spin-Peierls ground state:

ΔU=N(EF)Δσ²/2One gets: ΔU≈1000K per V4+ - V4+ pair (i.e. per V2O4 formula unit of 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 diagram

• Substituants reducing V4+ in V5+ : destabilize insulatingM1 with respect to new insulating T and M2 phases

but leaves unchanged metal-insulator transition: dTMI/dx≈0below R: the totally paired M1 phase is replaced by the halfpaired M2 phase formation of V5+ looses also the pairing energy gain but does not killthe 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 VO2 and 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 order Peierls M-I transition driven by a 2kF CDW instability in the 1D d// band responsible of the conducting propertiesat TMI tetramerization of V chains without 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’sStructural instability 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//levelsThe pairing (dimerization) provides a further gain of energy by forming d//Heitler – London type bonding levelsThe M1 phase exhibits a spin-Peierls like ground state

This mechanism differs of the Goodenough’s scenario of formation of a Peierls-like gap at the Fermi level

acknowledgements• During the thesis work

H. LaunoisP. LedererT.M. RiceR. ComèsJ. Friedel

• Renew of interest from recent DMFT calculationsA. GeorgesS. BiermannA. PoteryaevJ.M. Tomczak