Charge frustration and novel electron-lattice coupled phase transition

in molecular conductor DI-DCNQI2Ag

Hitoshi Seo

Yukitoshi Motome

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

Department 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 … PrBa2Cu4O82D: 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