charge frustration and novel electron-lattice coupled phase transition
DESCRIPTION
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:. - PowerPoint PPT PresentationTRANSCRIPT
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