1 / 40

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.

shepry
Download Presentation

The metal-insulator transition of VO 2 revisited

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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

More Related