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Charge frustration and novel electron-lattice coupled phase transition

Charge frustration and novel electron-lattice coupled phase transition in molecular conductor DI-DCNQI 2 Ag. Hitoshi Seo. Synchrotron Radiation Research Center, Japan Atomic Energy Agency / SPring-8. Yukitoshi Motome. Department of Applied Physics, University of Tokyo. contents:.

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Charge frustration and novel electron-lattice coupled phase transition

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  1. Charge frustration and novel electron-latticecoupled phase transition in molecular conductor DI-DCNQI2Ag Hitoshi Seo Synchrotron Radiation Research Center, Japan Atomic Energy Agency / SPring-8 Yukitoshi Motome Department of Applied Physics, University of Tokyo

  2. contents: 1. Charge frustration in molecular conductors 2. Quasi-one-dimensional DI-DCNQI2Ag ; experimental background 3. Spinless fermion model coupled to the lattice ― mean-field analysis － 4. Summary

  3. contents: 1. Charge frustration in molecular conductors [1] 2. Quasi-one-dimensional DI-DCNQI2Ag ; experimental background 3. Spinless fermion model coupled to the lattice ― mean-field analysis － [2] 4. Summary [1] H. Seo, M. Ogata, Phys. Rev. B 64 (2001) 113103 J. Merino, H. Seo, M. Ogata, Phys. Rev. B 71 (2005) 125111 [2] H. Seo, Y. Motome, in preparation (review) H. Seo, J. Merino, H. Yoshioka, M. Ogata, J. Phys. Soc. Jpn. 75 (2006) 051009 (poster) Y. Otsuka, H. Seo, Y. Motome, T. Kato, P-30 preprint submitted to J. Phys. Soc. Jpn. [cond-mat/arXiv:0807.4004]

  4. contents: 1. Charge frustration in molecular conductors [1] 2. Quasi-one-dimensional DI-DCNQI2Ag ; experimental background 3. Spinless fermion model coupled to the lattice ― mean-field analysis － [2] 4. Summary [1] H. Seo, M. Ogata, Phys. Rev. B 64 (2001) 113103 J. Merino, H. Seo, M. Ogata, Phys. Rev. B 71 (2005) 125111 [2] H. Seo, Y. Motome, in preparation (review) H. Seo, J. Merino, H. Yoshioka, M. Ogata, J. Phys. Soc. Jpn. 75 (2006) 051009 (poster) Y. Otsuka, H. Seo, Y. Motome, T. Kato, P-30 preprint submitted to J. Phys. Soc. Jpn. [cond-mat/arXiv:0807.4004]

  5. Molecular (Organic) Conductors molecules assemble by weak van-der-Waals interaction → closed packed latticeswith geometrical frustration are frequently generated. k-(BEDT-TTF)2X q-(BEDT-TTF)2X

  6. Molecular (Organic) Conductors molecules assemble by weak van-der-Waals interaction → closed packed latticeswith geometrical frustration are frequently generated. k-(BEDT-TTF)2X q-(BEDT-TTF)2X 1/2-filled Mott insulating state → Heisenberg spin-1/2 system

  7. Molecular (Organic) Conductors molecules assemble by weak van-der-Waals interaction → closed packed latticeswith geometrical frustration are frequently generated. k-(BEDT-TTF)2X q-(BEDT-TTF)2X 1/2-filled Mott insulating state → Heisenberg spin-1/2 system 1/4-filled charge ordering system anisotropic triangular lattices

  8. geometrical “charge frustration” in charge ordering systems P. W. Anderson, Phys. Rev. 104 (1954) 1008 Fe3O4 Spin Frustration “Charge Frustration” -V -J ? ? antiferromagnetic spin system charge ordering system J S Si Sj (J >0) V S ni nj (V >0; repulsion)

  9. examples of charge frustrated systems 2D: triangular lattice …q-ET2X, a-ET2X A2FeO4 1D: zigzag ladder … PrBa2Cu4O8 3D: pyrochlore lattice (e.g. in spinels) … Fe3O4, AlV2O4, LiV2O4, etc.

  10. charge frustration destabilizes charge order   1/4-filled extended Hubbard model H = tijS(cis†cｊs + h.c. ) + USni↓ni↑ + VijSninj Insulator 1D zigzag ladder: H.Seo & M.Ogata, PRB 64, 113103 (2001) S.Ejima et al., PRB 72, 033101 (2005) 2D anisotropic triangular lattice: J.Merino, H.Seo, & M.Ogata, PRB 71, 125111 (2005) H.Watanabe & M.Ogata, JPSJ 75, 063702 (2006) S.Nishimoto, M.Shingai, Y. Ohta, cond-mat/0803.0516

  11. charge frustration destabilizes charge order   1/4-filled extended Hubbard model H = tijS(cis†cｊs + h.c. ) + USni↓ni↑ + VijSninj in the materials ... frustration frequently relaxed by coupling to other degrees of freedoms : spin / orbital / lattice

  12. charge frustration destabilizes charge order   1/4-filled extended Hubbard model H = tijS(cis†cｊs + h.c. ) + USni↓ni↑ + VijSninj + [additional electron-lattice couplings] in the materials ... frustration frequently relaxed by coupling to other degrees of freedoms : spin / orbital / lattice q-(BEDT-TTF)2RbZn(SCN)4 horizontal type charge order with large lattice distortions, molecular rotations M.Watanabe et al., JPSJ 73, 116 (2004) X-ray structure study

  13. charge frustration destabilizes charge order   1/4-filled extended Hubbard model H = tijS(cis†cｊs + h.c. ) + USni↓ni↑ + VijSninj + [additional electron-lattice couplings] in the materials ... frustration frequently relaxed by coupling to other degrees of freedoms : spin / orbital / lattice (DI-DCNQI)2Ag :   this compound has been considered as a canonical quasi-1-dim 1/4-filled system.   spiral inter-chain coupling gives rise to charge frustration.   novel charge-lattice coupled phase is generated to relax the frustration.

  14. contents: 1. Charge frustration in molecular conductors [1] 2. Quasi-one-dimensional DI-DCNQI2Ag ; experimental background 3. Spinless fermion model coupled to the lattice ― mean-field analysis － [2] 4. Summary [1] H. Seo, M. Ogata, Phys. Rev. B 64 (2001) 113103 J. Merino, H. Seo, M. Ogata, Phys. Rev. B 71 (2005) 125111 [2] H. Seo, Y. Motome, in preparation (review) H. Seo, J. Merino, H. Yoshioka, M. Ogata, J. Phys. Soc. Jpn. 75 (2006) 051009 (poster) Y. Otsuka, H. Seo, Y. Motome, T. Kato, P-30 preprint submitted to J. Phys. Soc. Jpn. [cond-mat/arXiv:0807.4004]

  15. Quasi-one-dimensional molecular conductor DI-DCNQI2Ag K. Hiraki, K. Kanoda, PRB 54, 17276 (1996) crystal structure Ag+ : closed shell 　→ 1/4-filled p-band of DCNQI molecular orbitals 1st principle band calculations ( DMe-DCNQI2Ag ) DCNQI T. Miyazaki et al, PRL 74, 5104 (1994) Q1D electronic structure (t⊥< 0.2t∥)

  16. Quasi-one-dimensional molecular conductor DI-DCNQI2Ag K. Hiraki, K. Kanoda, PRB 54, 17276 (1996) crystal structure phase transition DCNQI

  17. Quasi-one-dimensional molecular conductor DI-DCNQI2Ag T. Itou et al., PRL 93, 216408 (2004)

  18. NMR intensity split of resonance lines -4000 -2000 0 2000 NMR shift (ppm) First “direct” observation of charge ordering in 2:1 salts K. Hiraki, K. Kanoda, PRL 80, 4737 (1998) 4kFsuperlattice peak in X-ray diffraction 13C NMR (powder) Nogami et al, J.Phys.IV 9, 357 (1999) Wigner crystal-type charge ordering (no lattice displacement) but ... IR, Raman : inconsistent ? Yamamoto et al, PRB 71, 045118(2005) Meneghetti et al, SSC 168, 632 (2002) pattern of charge (and/or lattice) ordering was not settled …

  19. Recent crystal structure analysis using synchrotron X-ray (T=50 K) Kakiuchi-Wakabayashi-Sawa-Itou-Kanoda, PRL 98, 066402 (2007) A A charge order lattice uniform B B C charge order lattice dimerization C charge uniform lattice dimerization three kinds of ordering out of simple kind of chains novel charge-lattice coupled ordering !

  20. V V’ Interchain “spiral” frustration for charge order DCNQI 3/4 1/2 1/4 0 c 3/4 1/2 1/4 0 a+b ? A B “charge frustration” K. Kanoda et al, J. Phys. IV France 131 (2005) 21 (proc. of ECRYS) Kakiuchi-Wakabayashi-Sawa-Itou-Kanoda, PRL 98, 066402 (2007)

  21. contents: 1. Charge frustration in molecular conductors [1] 2. Quasi-one-dimensional DI-DCNQI2Ag ; experimental background 3. Spinless fermion model coupled to the lattice ― mean-field analysis － [2] 4. Summary [1] H. Seo, M. Ogata, Phys. Rev. B 64 (2001) 113103 J. Merino, H. Seo, M. Ogata, Phys. Rev. B 71 (2005) 125111 [2] H. Seo, Y. Motome, in preparation (review) H. Seo, J. Merino, H. Yoshioka, M. Ogata, J. Phys. Soc. Jpn. 75 (2006) 051009 (poster) Y. Otsuka, H. Seo, Y. Motome, T. Kato, P-30 preprint submitted to J. Phys. Soc. Jpn. [cond-mat/arXiv:0807.4004]

  22. electron-lattice coupled model for quasi-1-dim. molecular conductors Y. Otsuka, H. Seo, Y. Motome, T. Kato, submitted to JPSJ [cond-mat/arXiv:0807.4004] P-30 ・ quasi-1-D extended Hubbard model + electron-lattice(adiabadic) couplings H = St ( 1 +gP ui ) (cis†ci+1s + h.c. ) + USni↓ni↑ + VSnini+1 Peierls (SSH) -type electron-lattice interaction + ( KP / 2 )S ui2 interchain Coulomb repulsion (un-frustrated) : mean-field + V⊥Sninj

  23. electron-lattice coupled model for quasi-1-dim. molecular conductors Y. Otsuka, H. Seo, Y. Motome, T. Kato, submitted to JPSJ [cond-mat/arXiv:0807.4004] P-30 Monte-Carlo phase diagram for t=1, U = 6, V = 2.5, gP2/KP = 1 uniform 1/4-filled metal paramagnetic lattice dimerized Mott insulator paramagnetic charge order insulator dimer-Mott insulator + spin-Peierls singlet charge order insulator + spin-Peierls singlet

  24. 3-dimensional interacting spinless fermion + coupling to lattice Model H =H1D+Hinterchain+Helastic H1D = St(rij)(ci †cj + h.c. ) + V (rij)Sninj 1D chains : 1/2-filled spinless t-V model (U→∞ limit of extended Hubbard model) Hinterchain = V ’(rij) Sninj+ V ’’(rij) Sninj spiral interchain Coulomb repulsions Helastic = KP / 2 S ui2 t(rij) = t [ 1 + a (ui - uj) ] coupling to lattice is introduced as V(rij) = V [ 1 + b (ui - uj) ] ( SSH/Peierls-type ) V ’ (rij) = V ’ [ 1 + b’(ui - uj) ] V ’’ (rij) = V ’’ [ 1 + b’’(ui - uj) ] Method ui: classical, uniaxial mean-field (Hartree-Fock) approximation for ninj terms determine 〈ni〉, 〈ci †cj〉, uiself-consistently super-cell size : 2-sites in chain direction×8=16 sites

  25. Choice of parameters ・ V’/V=0.5, V’’/V=0.1 (cf. from distances between centerof DCNQIs, V’/V=0.51, V’’/V=0.48) ・ b/a =0.5, b’/a =0.033, b’’/a =0.098 : deduced from V(rij)∝ rij-g Conditions for self-consistent CO and DM solutions ・ one interchain bond per each spiral is frustrated. ・ one interchain bond per each “array” is frustrated. (due to periodic boundary condition) → only two kind of patterns are possible A B

  26. T=0 : as fermion-lattice coupling is increased, CO → Mix→ dimer parameters : t=1, V=1.5, V’/V=0.5, V’’/V=0.1, a=1, b =0.5, b’ =0.033, b’’ =0.098 charge disproportionation lattice distortion CO+dimer charge order & lattice dimerization : frustration in 1/4 of interchain bonds

  27. T=0 : as fermion-lattice coupling is increased, CO → Mix→ dimer parameters : t=1, V=1.5, V’/V=0.5, V’’/V=0.1, a=1, b =0.5, b’ =0.033, b’’ =0.098 charge disproportionation lattice distortion mixed state ( CO : dimer : coex = 1:1:2 ) charge frustration is relaxed = Kakiuchi et al state

  28. finite-T property with mixed phase ground state : intermediate phase 1/K=0.15 CO+dimer mixed state uniform metal another scenario : frustrated CO state destabilized if one takes into account of quantum fluctuation H. Seo, M. Ogata, Phys. Rev. B 64 (2001) 113103 J. Merino, H. Seo, M. Ogata, Phys. Rev. B 71 (2005) 125111

  29. characteristic temperature T* : dimer order develops at T<T* CO+dimer mixed state

  30. characteristic temperature T* : dimer order develops at T<T* CO+dimer T* mixed state T*

  31. characteristic temperature T* : dimer order develops at T<T* two characteristic temperatures seen in transport properties CO+dimer F. Nad et al, J. Phys. Cond. Mat., 16 (2004) 7107 complex conductance G(w=1kHz) T1=200K T2=75K T* mixed state dielectric constant 100 kHz 1 MHz T* 5 MHz

  32. NMR intensity -4000 -2000 0 2000 NMR shift (ppm) characteristic temperature T* within the ordered phase 13C NMR (powder) resistivity K. Hiraki, K. Kanoda, PRL 80, 4737 (1998) T. Itou et al., PRL 93, 216408 (2004) broad peak within ordered phase anomalous broadening well above TN (= 5K)

  33. summary ・ Hartree-Fock calc. on 3D spinlessfermion model + lattice : reproduces Kakiuchi et al’s state ・ finite-T calc. : different T-depencence for CO and dimerization →characteristic temperature within ordered phase pointed out by Nad et al charge ordered insulator dimerized Mott insulator small el-lat int large el-latt int frustration charge ordered insulator dimerized Mott insulator small el-lat int large el-latt int novel “mixed” phase frustration is relaxed !

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