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

2. contents: 1. Charge frustration in molecular conductors 2. Quasi-one-dimensional DI-DCNQI 2 Ag ; 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-DCNQI 2 Ag ; 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-DCNQI 2 Ag ; 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 lattices with geometrical frustration are frequently generated.  -(BEDT-TTF) 2 X  -(BEDT-TTF) 2 X

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

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

8. antiferromagnetic spin system Spin Frustration ? -J charge ordering system “Charge Frustration” ? -V geometrical “charge frustration” in charge ordering systems P. W. Anderson, Phys. Rev. 104 (1954) 1008 J  S i S j (J >0)V  n i n j (V >0 ; repulsion ) Fe 3 O 4

9. 1D: zigzag ladder … PrBa 2 Cu 4 O 8 2D: triangular lattice …  -ET 2 X,  -ET 2 X A 2 FeO 4 3D: pyrochlore lattice (e.g. in spinels) … Fe 3 O 4, AlV 2 O 4, LiV 2 O 4, etc. examples of charge frustrated systems

10. charge frustration destabilizes charge order 1/4-filled extended Hubbard model Insulator H = t ij  ( c i  † c ｊ  + h.c. ) + U  n i↓ n i↑ + V ij  n i n j 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 = t ij  ( c i  † c ｊ  + h.c. ) + U  n i↓ n i↑ + V ij  n i n j 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 = t ij  ( c i  † c ｊ  + h.c. ) + U  n i↓ n i↑ + V ij  n i n j in the materials...frustration frequently relaxed by coupling to other degrees of freedoms : spin / orbital / lattice  -(BEDT-TTF) 2 RbZn(SCN) 4 horizontal type charge order with large lattice distortions, molecular rotations M.Watanabe et al., JPSJ 73, 116 (2004) X-ray structure study + [additional electron-lattice couplings]

13. charge frustration destabilizes charge order 1/4-filled extended Hubbard model H = t ij  ( c i  † c ｊ  + h.c. ) + U  n i↓ n i↑ + V ij  n i n j in the materials...frustration frequently relaxed by coupling to other degrees of freedoms : spin / orbital / lattice (DI-DCNQI) 2 Ag : + [additional electron-lattice couplings] 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-DCNQI 2 Ag ; 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-DCNQI 2 Ag K. Hiraki, K. Kanoda, PRB 54, 17276 (1996) DCNQI crystal structure Ag + : closed shell → 1/4-filled  -band of DCNQI molecular orbitals 1st principle band calculations T. Miyazaki et al, PRL 74, 5104 (1994) Q1D electronic structure (t ⊥ < 0.2t ∥ ) ( DMe-DCNQI 2 Ag )

16. DCNQI crystal structure phase transition Quasi-one-dimensional molecular conductor DI-DCNQI 2 Ag K. Hiraki, K. Kanoda, PRB 54, 17276 (1996)

17. Quasi-one-dimensional molecular conductor DI-DCNQI 2 Ag T. Itou et al., PRL 93, 216408 (2004)

18. NMR intensity 02000-4000-2000 NMR shift (ppm) 13 C NMR (powder) split of resonance lines First “direct” observation of charge ordering in 2:1 salts Wigner crystal-type charge ordering (no lattice displacement) K. Hiraki, K. Kanoda, PRL 80, 4737 (1998) Meneghetti et al, SSC 168, 632 (2002) Yamamoto et al, PRB 71, 045118(2005) but... IR, Raman : inconsistent ? 4k F superlattice peak in X-ray diffraction pattern of charge (and/or lattice) ordering was not settled … Nogami et al, J.Phys.IV 9, 357 (1999)

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

20. Interchain “spiral” frustration for charge order a+b c 0 1/4 1/2 3/4 0 1/4 1/2 3/4 V V’ ? DCNQI “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) A B

21. contents: 1. Charge frustration in molecular conductors [1] 2. Quasi-one-dimensional DI-DCNQI 2 Ag ; 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. ・ quasi-1-D extended Hubbard model + electron-lattice(adiabadic) couplings H =  t ( 1 + g P u i ) ( c i  † c i+1  + h.c. ) + U  n i↓ n i↑ + V  n i n i+1 + ( K P / 2 )  u i 2 + V ⊥  n i n j interchain Coulomb repulsion (un-frustrated) : mean-field Peierls (SSH) -type electron-lattice interaction 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

23. Monte-Carlo phase diagram for t=1, U = 6, V = 2.5, g P 2 /K P = 1 paramagnetic lattice dimerized Mott insulator uniform 1/4-filled metal paramagnetic charge order insulator dimer-Mott insulator + spin-Peierls singlet charge order insulator + spin-Peierls singlet 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

24. 3-dimensional interacting spinless fermion + coupling to lattice H 1D =  t (r ij ) ( c i † c j + h.c. ) + V (r ij )  n i n j H interchain = V ’ (r ij )  n i n j + V ’’ (r ij )  n i n j 1D chains : 1/2-filled spinless t-V model (U→∞ limit of extended Hubbard model) spiral interchain Coulomb repulsions Method u i : classical, uniaxial mean-field (Hartree-Fock) approximation for n i n j terms determine 〈 n i 〉, 〈 c i † c j 〉, u i self-consistently super-cell size : 2-sites in chain direction × 8=16 sites t (r ij ) = t [ 1 +  (u i - u j ) ] V (r ij ) = V [ 1 +  (u i - u j ) ] V ’ (r ij ) = V ’ [ 1 +  ’  (u i - u j ) ] V ’’ (r ij ) = V ’’ [ 1 +  ’’  (u i - u j ) ] coupling to lattice is introduced as H elastic = K P / 2  u i 2 ( SSH/Peierls-type ) Model H = H 1D + H interchain + H elastic

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) ・  /  =0.5,  ’/  =0.033,  ’’/  =0.098 : deduced from V(r ij ) ∝ r ij  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 AB

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

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,  =1,  =0.5,  ’ =0.033,  ’’ =0.098 mixed state charge frustration is relaxed ( CO : dimer : coex = 1:1:2 ) = Kakiuchi et al state charge disproportionationlattice distortion

28. finite-T property with mixed phase ground state : intermediate phase mixed state CO+dimer uniform metal 1/K=0.15 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 mixed state T*

31. complex conductance G(  =1kHz) 100 kHz 1 MHz 5 MHz T 1 =200KT 2 =75K dielectric constant F. Nad et al, J. Phys. Cond. Mat., 16 (2004) 7107 two characteristic temperatures seen in transport properties characteristic temperature T* : dimer order develops at T<T* CO+dimer mixed state T*

32. characteristic temperature T* within the ordered phase NMR intensity 02000-4000-2000 NMR shift (ppm) 13 C NMR (powder) K. Hiraki, K. Kanoda, PRL 80, 4737 (1998) T. Itou et al., PRL 93, 216408 (2004) anomalous broadening well above T N (= 5K) broad peak within ordered phase resistivity

33. summary charge ordered insulator small el-lat intlarge el-latt int dimerized Mott insulator frustration charge ordered insulator small el-lat intlarge el-latt int dimerized Mott insulator novel “mixed” phase frustration is relaxed ! ・ Hartree-Fock calc. on 3D spinless fermion 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