Charge frustration and novel electron-lattice coupled phase transition

in molecular conductor DI-DCNQI2Ag

Charge frustration and novel electron-lattice coupled phase transition

in molecular conductor DI-DCNQI2Ag

Hitoshi SeoHitoshi Seo

Yukitoshi MotomeYukitoshi Motome

Synchrotron Radiation Research Center, Japan Atomic Energy Agency / SPring-8Synchrotron Radiation Research Center, Japan Atomic Energy Agency / SPring-8

Department of Applied Physics, University of TokyoDepartment of Applied Physics, University of Tokyo

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

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]

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]

Molecular (Organic) Conductors

molecules assemble by weak van-der-Waals interaction → closed packed lattices with geometrical frustration are frequently generated.

-(BEDT-TTF)2X -(BEDT-TTF)2X

Molecular (Organic) Conductors

-(BEDT-TTF)2X -(BEDT-TTF)2X

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

Molecular (Organic) Conductors

-(BEDT-TTF)2X -(BEDT-TTF)2X

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

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 Si Sj (J >0) V ni nj (V >0; repulsion)

Fe3O4

1D: zigzag ladder … PrBa2Cu4O8

2D: triangular lattice … -ET2X, -ET2X A2FeO4

3D: pyrochlore lattice (e.g. in spinels) … Fe3O4, AlV2O4, LiV2O4, etc.

examples of charge frustrated systems

charge frustration destabilizes charge order

  1/4-filled extended Hubbard model

Insulator

H = tij ( ci† c ｊ + h.c. ) + U ni↓ni↑ + Vij ni nj

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

charge frustration destabilizes charge order

  1/4-filled extended Hubbard model

H = tij ( ci† c ｊ + h.c. ) + U ni↓ni↑ + Vij ni nj

in the materials ... frustration frequently relaxed by coupling to other degrees of freedoms : spin / orbital / lattice

charge frustration destabilizes charge order

  1/4-filled extended Hubbard model

H = tij ( ci† c ｊ + h.c. ) + U ni↓ni↑ + Vij ni nj

in the materials ... frustration frequently relaxed by coupling to other degrees of freedoms : spin / orbital / lattice

-(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

+ [additional electron-lattice couplings]

charge frustration destabilizes charge order

  1/4-filled extended Hubbard model

H = tij ( ci† c ｊ + h.c. ) + U ni↓ni↑ + Vij ni nj

in the materials ... frustration frequently relaxed by coupling to other degrees of freedoms : spin / orbital / lattice

(DI-DCNQI)2Ag :

+ [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.

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]

Quasi-one-dimensional molecular conductor DI-DCNQI2Ag K. Hiraki, K. Kanoda, PRB 54, 17276 (1996)

DCNQI

crystal structureAg+ : 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-DCNQI2Ag )

DCNQI

crystal structure

phase transition

Quasi-one-dimensional molecular conductor DI-DCNQI2Ag K. Hiraki, K. Kanoda, PRB 54, 17276 (1996)

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

137.1K

118.5K

89.7K

69.0K

45.0K30.1K20.2K10.2K6.1K5.1K4.0K

183.4K174.9K164.4K

3.0K

250.5K240.3K231.6K208.3K203.8K

280.9K

NM

R in

tens

ity

0 2000-4000 -2000NMR shift (ppm)

13C 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 ?

4kF 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)

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 orderlattice uniform

charge orderlattice dimerization

charge uniformlattice dimerization

B

C

three kinds of ordering out of simple kind of chains

Interchain “spiral” frustration for charge order

a+b

c

01/4

1/23/40

1/41/2

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

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]

・ quasi-1-D extended Hubbard model + electron-lattice(adiabadic) couplings

H = t ( 1 + gP ui ) ( ci† ci+1 + h.c. ) + U ni↓ni↑ + V ni ni+1

+ ( KP / 2 ) ui2

+ V⊥ ni njinterchain Coulomb repulsion (un-frustrated) : mean-field

Peierls (SSH) -type electron-lattice interaction

electron-lattice coupled model for quasi-1-dim. molecular conductorsY. 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

paramagneticlattice dimerized

Mott insulator

uniform 1/4-filled metal

paramagneticcharge order insulator

dimer-Mott insulator+ spin-Peierls singlet

charge order insulator+ spin-Peierls singlet

electron-lattice coupled model for quasi-1-dim. molecular conductorsY. Otsuka, H. Seo, Y. Motome, T. Kato, submitted to JPSJ[cond-mat/arXiv:0807.4004] P-30

3-dimensional interacting spinless fermion + coupling to lattice

H1D = t (rij) ( ci † cj + h.c. ) + V (rij) ni nj

Hinterchain = V ’(rij) ni nj + V ’’(rij) ni nj

1D chains : 1/2-filled spinless t-V model (U→∞ limit of extended Hubbard model)

spiral interchain Coulomb repulsions

Method ui : classical, uniaxial mean-field (Hartree-Fock) approximation for ni nj terms determine 〈 ni 〉 , 〈 ci

† cj 〉 , ui self-consistently super-cell size : 2-sites in chain direction×8=16 sites

t (rij) = t [ 1 + (ui - uj) ]V (rij) = V [ 1 + (ui - uj) ]V ’ (rij) = V ’ [ 1 + ’(ui - uj) ]V ’’ (rij) = V ’’ [ 1 + ’’(ui - uj) ]

coupling to lattice is introduced as Helastic = KP / 2 ui2

( SSH/Peierls-type )

Model H = H1D+ Hinterchain+ Helastic

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(rij) ∝ rij

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

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 disproportionation lattice distortion

T=0 : as fermion-lattice coupling is increased, CO → Mix→ dimerparameters : 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 disproportionation lattice distortion

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) 113103J. Merino, H. Seo, M. Ogata, Phys. Rev. B 71 (2005) 125111

characteristic temperature T* : dimer order develops at T<T*

CO+dimer

mixed state

characteristic temperature T* : dimer order develops at T<T*

CO+dimer

mixed state

T*

T*

complex conductance G(=1kHz)

100 kHz1 MHz5 MHz

T1=200K T2=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*

T*

characteristic temperature T* within the ordered phase

137.1K

118.5K

89.7K

69.0K

45.0K30.1K20.2K10.2K6.1K5.1K4.0K

183.4K174.9K164.4K

3.0K

250.5K240.3K231.6K208.3K203.8K

280.9K

NM

R in

tens

ity

0 2000-4000 -2000NMR shift (ppm)

13C NMR (powder) K. Hiraki, K. Kanoda, PRL 80, 4737 (1998)

T. Itou et al., PRL 93, 216408 (2004)

anomalous broadening well above TN (= 5K)

broad peak within ordered phase

resistivity

summary

charge ordered insulator small el-lat int large el-latt int

dimerized Mott insulator

frustration

charge ordered insulator small el-lat int large 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