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
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