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The metal-insulator transition of VO 2 revisited

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

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  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 l’honneur 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: ρ ~T very short mean free path: ~V-V distance P.B. Allen et al PRB 48, 4359 (1993)

  5. 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)

  6. 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

  7. 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)

  8. 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)

  9. 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)

  10. 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

  11. 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)

  12. 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)

  13. 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

  14. 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

  15. 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)

  16. 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

  17. 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)

  18. 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?

  19. 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

  20. 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)

  21. 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

  22. 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

  23. 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

  24. 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?

  25. 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)

  26. {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 »

  27. 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

  28. 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))

  29. 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!

  30. 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!

  31. 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

  32. Supplementary material

  33. 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!

  34. metallic LDA

  35. 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)

  36. LDA phase métallique R phase isolante M1

  37. 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!

  38. 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

  39. LDA: Phase M2 zig-zag V2 paires V1

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