ECRYS-2011, August, 15-27, 2011
at the Institute of Scientific Studies in Cargese, Corse
Charge Fluctuation, Charge
Ordering and Zero-Gap State in
Molecular Conductors
Toshihiro Takahashi
Department of Physics, Gakushuin University, Mejiro
1-5-1, Toshima-ku, Tokyo 171-8588, Japan
3 keywords: Charge Fluctuation
Charge Ordering
Zero-Gap State
三題噺
“San-dai-banashi”
A style of Japanese traditional
comic story, “rakugo”.
Three keywords are given
independently by the audience.
The storyteller, “rakugo-ka”, makes
ad lib a consistent comic story using
all the keywords.
Outline

Introduction to NMR technique to probe
charge degree of freedom

Charge fluctuation and charge ordering in θ-phase
BEDT-TTF salts

Charge disproportionation in the zero-gap state of
α-BEDT-TTF2I3

Coupling with the permanent electric dipolar
moment of anion in TMTSF2FSO3

Charge disproportionation in λ-type BETS salts

Summary & Remarks
Outline

Introduction to NMR technique to probe
charge degree of freedom

Charge fluctuation and charge ordering in θ-phase
BEDT-TTF salts

Charge disproportionation in the zero-gap state of
α-BEDT-TTF2I3

Coupling with the permanent electric dipolar
moment of anion in TMTSF2FSO3

Charge disproportionation in λ-type BETS salts

Summary & Remarks
Simple Picture of Charge
Ordering (CO)
 1/4-filled system, D2A or DA2, without large dymerization
One carrier per two molecules
 Coulomb interaction, U & V, …
finding a charge arrangement to minimize Coulomb energy
 As including transfer
=>rich variety of phenomena
Charge Ordering vs. Charge
Disproportionation
 Long-range Charge Ordering (CO) vs. Charge




Disproportionation (CD)
Charge Frustration
Melting of CO
Charge Fluctuation/Charge Dynamics
Various Optical/Dielectric responses
How can NMR detect CO/CD?
Note that;
 Not detecting “charge” but “spin”density
 Not detecting Long Range CO but just the distribution
of local charge (spin)
 What we observed in CO/CD systems in common
were anomalous broadening of NMR spectrum.
How can CO/CD affect NMR spectrum and other
NMR parameters?
Brief introduction to NMR
(Nuclear Magnetic Resonance)
 Nuclear spin carries angular momentum,
m and
magnetic moment, J = I .
 Zeeman splitting in strong magnetic field: DE = g H 0
 Resonance condition: w 0 = gH0
H0
m =gJ =g I
Magnetic moment; m
Angular momentum;
J= I
w 0 = gH0
Zeeman splitting for I=1/2
Resonance Condition;
w = w0 = gH0

NMR can detect CO/CD
 Nuclei in material see local fields given by the
environments in addition to the external field.
 What we detect with NMR are the information of the
local field;
H0
w = g H0 + Hloc
H0 + Hloc
Local field distribution

Hloc
Central shift
Local field at each nuclear site
Interaction with electrons
 Orbital motion and Chemical shift
 Spin interaction and Knight shift

Orbital motion


Spin
Local fields are produced by surrounding electrons!
Interaction with electrons
 Orbital motion and Chemical shift
 Spin interaction and Knight shift


Shielding current

Magnetic shielding current gives local field. Chemists concerns
the isotropic part of the chemical shift tensor.
It is usually small compared with the spin contribution.
Interaction with electrons
 Orbital motion and Chemical shift
 Spin interaction and Knight shift



Spin magnetization
Interaction with electrons
 Orbital motion and Chemical shift
 Spin interaction and Knight shift



Spin magnetization
Lone-pair spin contribution is also anisotropic and much larger
than orbital contribution in the present systems.
Hyperfine interaction
 Hyperfine interaction
 Hyperfine interaction tensor
 Knight shift
~ proportional to electron spin susceptibility
~ anisotropic due to the hyperfine tensor
K = K iso + Kanis ( 3cos2 q -1)
for a pure p-electron with
uniaxial symmetry
Hyperfine interaction
 Inhomogeneity of Knight shift
causes inhomogeneous
broadening.
 Inhomogeneous width should be
proportional to the Knight shift.
~ proportional to electron
spin susceptibility
~ anisotropic due to the
hyperfine tensor




Typical Materials, exhibiting CO
 1/4-filled Organic molecular
conductors, of the chemical form
of A2D
 Q-1D system
DI-DCNQI2Ag (K. Hiraki, 1998)
TMTTF2X (PF6, AsF6, …) (D.S. Chow,
2000)
 2D ET salts
-ET2I3,
(Y. Takano, 2001)
-ET2RbZn(SCN)4 (K. Miyagawa, 2000,
R. Chiba, 2001)
X-ray, Raman & IR spectroscopy also
confirmed CO in various materials
Outline

Introduction to NMR technique to probe
charge degree of freedom

Charge fluctuation and charge ordering in θ-phase
BEDT-TTF salts

Charge disproportionation in the zero-gap state of
α-BEDT-TTF2I3

Coupling with the permanent electric dipolar
moment of anion in TMTSF2FSO3

Charge disproportionation in λ type BETS salts

Summary
-(ET)2MZn(SCN)4 (M=Rb,Cs)
H. Mori et al.,
Phys. Rev. B57, 12 023(1998)
Electric and Magnetic property
electric resistivity
spin susceptibility
RbZn
salt
CsZn
salt
Charge ordered transition in (ET)2RbZn(SCN)4
Charge Order
T<190K
Spin-singlet
T<30K
Unusual broadening above TMI
K. Miyagawa et al.,
2000
Mechanism of the broadening above TMI ?
at 204K
Observed excess width
is anisotropic!
~proportional to the
central shift
TMI
Angular dependence
of the 2nd moment is
proportional to K2
Inhomogeneous
broadening due to the
distribution of K
Inhomogeneous and homogeneous
13C-NMR lineshape in -RbZn
Metal state
LR-CO
TMI
Below 30 K
T2-1 enhancement
due to slow
dynamics of CD
T2 measurement
Double peak about 90 K & 70 K
Inhomogeneous broadening due to CD
(Chiba, 2004)
Inhomogeneous and homogeneous
linewidth
Dynamics of Inhomogeneous local field
T2-1
life time of Zeeman Level
tc-1
correlation frequency
2nd moment for the inhomogeneous field
T2-1 » t c -1
T2-1 »
Dw 2
Inhomogeneous and homogeneous
13C-NMR lineshape in -CsZn
Crossover into
different broadening
Inhomogeneous
broadening due to
large CD
Slow dynamics ~kHz
Motional narrowing
T dependence of 1/T2 in -RbZn
& -CsZn
Explained by expanded
exponential correlation;
(t) = <2>exp(-(t/tc))
with tc~exp(-/kBT)
Salt
Rb


/kB
7600 K
<2>1/2 3.3 kHz
Cs

5100 K
1.4 kHz
Angular dependence of NMR
lineshape of -CsZn
295 K
101 K
spin vanishes!
5K
Nonmagnetic ground state
Comparison of -CsZn and -RbZn
salts at 5K
charge rich
charge poor
charge : ~ +0.5
charge ordered state
-phase Salts
T MI
Rb-salt
s-P
CO
T MI
Cs-salt
s-P?
Spin-singlet
without CD !
Domains with
finite  coexist!
Chiba, PRB 2007
CD
CD
What is the origin of slow
dynamics of CD in -phase salts?
Competition between different types of CO may
be responsible.
 -RbZn salt with LR-CO of (0, 0, 1/2) below 190K
 Diffuse X-ray scattering with q=(1/4, k, 1/3) is
observed above TMI.
 Spin-singlet ground state with LR-CO.
 -CsZn salt without LR-CO
 Diffuse X-ray scatterings with q1=(2/3, k, 1/3) and
q2=(0, k, 1/2) are observed below 120K.
 Coexistence of spin-singlet domain and
paramagnetic domain without any sign of CO.
Outline

Introduction to NMR technique to probe
charge degree of freedom

Charge fluctuations and charge ordering in θ-
phase BEDT-TTF salts

Charge disproportionation in the zero-gap state of
α-BEDT-TTF2I3

Coupling with the permanent electric dipolar
moment of anion in TMTSF2FSO3

Charge disproportionation in λ type BETS salts

Summary
Various ground states
in  -(BEDT-TTF)2I3
Ambient Pressure
Metal-Insulator Transition with CO
Under hydrostatic pressure
Anomalous NGS state with high mobility
Under Uniaxial strain
SC within CO-state
CO
NGS
along a-axis
Metal
SC
along b-axis
Tajima et al.
(2003)
Zero Gap State under pressure
Fermi Surface
Y
Contact Point & Zero Gap State (ZGS)
M
Ambient
Pressure
x (k )
electron
G
X
hole
pa=2kbar
CP
Dirac cone
pa >
M
3kbar
Γ
CP
(contact point)
(pa=4kbar)
Kobayashi et al., JPSJ (2005)
The first ZGS in a bulk system was
confirmed!
All peculiar ground states are explained on the
basis of unified band parameters!
CO / ZGS (NGS) / SC
Further questions:
How does CO behave under pressure?
What is the relation between CO and the ZGS?
How about in other isostructural salts?
Development of CD above TMI
 CO of CD aboveTMI
Because of site-dependence?
Precursor effect of CO?
 Pattern of CO： C > B cf. Ｘ-ray
 Relation to the ZGS under pressure
S
S
H
C
S
S
S
S
S
S
C
S. Moroto 2003
Y. Takano 1999
a-ET2I3 140K
257K
200K
Measurements under pressure
 P = 0.1 ~ 1.1 GPa
 H0 = 7 T (75 MHz) in
the ab-plane
H0
-ET2I3
Pressure cell
by Prof. W. Kang, Ewha Womans Univ., Seoul
T-dependence of Local
Susceptibilities under pressure
Local susceptibility is the smallest on ‘B’ molecule.
B molecule is a charge-poor site!
Charge Ordering determined by
Synchrotron X-ray Diffraction
CD in the metallic state
at ambient pressure:
‘B’ molecule is chargerich!
~ inconsistent to the NMR
results?
Title: Charge Ordering in $¥alpha$-(BEDT-TTF)$_2$I$_3$ by
Synchrotron X-ray DiffractionAuthors: by Toru Kakiuchi, Yusuke
Wakabayashi, Hiroshi Sawa, Toshihiro Takahashi, Toshikazu
NakamuraPublished: October 25, 2007J. Phys. Soc. Jpn., Vol.76,
No.11, p.113702
Kakiuchi et al., JPSJ (2007)
Theory explains this difficulty
Contact Point & Zero Gap State (ZGS)
Transfer energies evaluated from
first principle calculation by Kino
n A = n A' = 1.463, A,A' = +0.54
n B = 1.363,
B = +0.64
n C = 1.711
C = +0.29
B molecule is charge-rich!
Contact Point
Dirac cone
Katayama et al., JPSJ (2008)
Theory explains this difficulty
Local susceptibility is proportional to the
density of state around the contact point, and
not to the local charge!
c spin (T) µT
Katayama et al., Eur.Phys. (2009)
Theory explains this difficulty
U=0.4, Vp=0.05, Vc=0.17
nA = nA' =1.463,
nB =1.363,
nC =1.711
Local susceptibility is determined by
the density of states around the
contact point.
Conclusions
1. Non-stripe CO develops at low
temperatures and under pressure.
It does not break the lattice
symmetry.
T
ZGS
2. Charge-rich ‘B’ molecule has the
smallest local susceptibility. It is
consistent with X-ray and
theoretical analysis.
3. Non-stripe CO may be relevant
to the stabilization of the ZGS.
ZG
What is the origin of CO in the
metallic state of -I3 salt?
T
Non-stripe CO should come from a
band nature together with Coulomb
interaction.
ZGS
Characteristic time of charge
dynamics, if any, should be much
shorter than the NMR time scale.
The mechanism of CD is quite
different from the case of the salt.
ZG
Outline

Introduction to NMR technique to probe
charge degree of freedom

Charge fluctuation and charge ordering in θ-phase
BEDT-TTF salts

Charge disproportionation in the zero-gap state of
α-BEDT-TTF2I3

Coupling with the permanent electric dipolar
moment of anion in TMTSF2FSO3

Charge disproportionation in λ type BETS salts

Summary
Crystal Structure of (TMTSF)2FSO3
Bechgaard Salt with
asymmetric anion, FSO3
TMTSF molecule
a- axis
FSO3-
(TMTSF)2FSO3 under Pressure
Phase diagram
Resistivity
Thermoelectric power
Y. J. Jo et al., 2003
77Se-NMR
Lineshape
4 sharp peaks
~4 Se-sites in a
unit cell
Line broadening
Sharp component
appears
with short delay ~ 3 s
with long delay ~ 600 s
Coexistence of sharp
& broad components
77Se-NMR
T1-1
No anomaly at
90 K.
Double comp.
of T1-1 below 40
K.
Broader line
has shorter T1
Sharper line
has longer T1
Angular dependence of
77Se-NMR Lineshape
Angular dependence of
77Se-NMR Lineshape
Inhomogeneous width assuming CD of 0.6~0.4
Enhancement of
77Se-NMR
T2-1
0.65 GPa
Possibility of slow
Charge fluctuations
as in the q-ET salt.
Anomalous T2-1 enhancement was
not observed at ambient pressure.
Double Peaks of T21 around 90 K & 70
K.
90 K: the phase
boundary (I).
70 K: inside the
intermediate
phase.
Anion dynamics seen by
0.4 GPa
Coexistence of 3Drotated signal and
Anion-ordered signal
in the region between
boundary I & II.
19F-NMR
3D-rotated signal
Anion-ordered signal
Anion dynamics seen by
0.4 GPa
19F-NMR
3D-rotated signal
Anion-ordered signal
T-dependence of
19F-NMR
T1-1
0.4 GPa
Coupling with methyl-group
rotation in AO state?
BBP relaxation suggesting
3D-rotation
Conclusions
■
■
■
■
Metallic phase above I and
Nonmagnetic Insulating phase below II
were confirmed.
Large charge disproportionation was
found in the anomalous metallic phase
with below I.
Coexistence of the metallic and
insulating phase suggests the
boundary II is of first order.
19F-NMR & X-ray analysis strongly
suggest that; Boundary I associates
with the ordering of tetrahedrons;
Boundary II with the ordering of elec.
dipoles.
Metal
Anomalous
metal with
CD
Nonmag.
Insulator
What is the origin of CD in
FSO3 salt?
CD was observed in the region where
partial ordering of FSO3 appears.
Magnitude of CD is moderate compared
with the other CD systems.
CD may be due to the intramolecular
charge imbalance and the first indication
of the coupling between the electric
dipoles and the carriers.
+
+
-
-
Metal
Nonmag.
Insulator
Outline

Introduction to NMR technique to probe
charge degree of freedom

Charge fluctuations and charge ordering in θ-
phase BEDT-TTF salts

Charge disproportionation in the zero-gap state of
α-BEDT-TTF2I3

Coupling with the permanent electric dipolar
moment of anion in TMTSF2FSO3

Charge disproportionation in λ-type BETS salts

Summary
p-d interaction on -(BETS)2FeCl4:
77Se
NMR
K. Hiraki16, H. Mayaffre1, M. Horvatic2, C. Berthier12, H. Tanaka3,
A. Kobayashi4, H. Kobayashi5 and T. Takahashi6
1. Laboratoire de Spectrometrie Physique, Université Joseph Fourier
2. Grenoble High Magnetic Field Laboratory
3. Nanotechnology Research Institute, AIST
4. Department of Chemistry, University of Tokyo
5. Institute for Molecular Science
6. Department of Physics, Gakushuin University
Acknowledgement
We would like to thank prof. K. Takimiya (Hiroshima University)
Structure and electronic properties
H. Kobayashi et al., J. A. C. S. 118, 368 (1996)
H. Tanaka et al., J. A. C. S. 121, 760 (1999)
H. Akutsu et al., PRB58, 9294 (1998)
Hext
Brossard et al.
EPJ B1, 439(1998)
AFI
SC
Balicas et al.
PRL87, 067002(2001)
Mechanism of Field-Induced SC
 Orbital decoupling effect is
suppressed by applying external filed
strictly parallel to the conducting 2D
layer (a*c plane).
Hext
 Jaccarino-Peter mechanism:
Exchange field from magnetic ions
(Fe2+: S=5/2) compensates the
external field; SC appears when,
H0 + Hexch  Hc2,
where Hexch = J<S>/gB
 Our aims is to confirm the exchange
field seen by p-electrons through
77Se-NMR
p
Fe 5/2 spin
AFI
Balicas et al. PRL87, 067002(2001)
SC
7/16
H0 dependence of NMR shift at
M10 magnet GHMFL
1.5K
oct2005/apr2006
d f (MHz)
0.4
0.2
Se NMR 1.5 K
0.0
-0.2
-0.4
-0.6
-0.8
-1.0
-1.2
0
5 10 15 20
H0 (T)
H0 || a
H0 ^ a
25
30
35
5B J=32±2 T
Linewidth vs.
magnetization
Excess broadening
below 30K is very likely
due to CD!
Angular dependence of linewidth
in the Fe-salt
Dc p c p » 0.7
r » 0.5 ± 0.3
Angular dependence of spectral width is proportional
to that of the central shift, suggesting CD.
Angular dependence of linewidth
in the Fe- and the Ga-salt
H eff = 9 T
Dc p c p » 0.3
r » 0.5 ± 0.15
H eff = -17.5T
Dc p c p » 0.7
r » 0.5 ± 0.3
Fe ions are not relevant to CD!
Organic BETS layers should be responsible for CD!
15/16
Which mechanism gives the CD?
Magnetic Fe ions are not relevant to the line broadening.
It should be attributed to the inhomogeneity of the local
susceptibility, p, in the BETS layer, suggesting large CD,
while their dynamics have not yet been examined.
Mechanism of CO is not clarified yet.
Charge imbalance was already suggested in the Fe-salt
by;
microwave/Matsui PRB 2003
1H NMR/Endo JPSJ 2002
X ray/Komiyama JPSJ 2004
I-V characteristics./ Toyota PRB 2002
Dielectric Anomaly
H. Matsui, 2003
Outline

Introduction to NMR technique to probe
charge degree of freedom

Charge fluctuations and charge ordering in θ-
phase BEDT-TTF salt

Charge disproportionation in the zero-gap state of
α-BEDT-TTF2I3

Coupling with the permanent electric dipolar
moment of anion in TMTSF2FSO3

Charge disproportionation in λ type BETS salts

Summary & Remarks
Summary-1
 Anomalous NMR line broadening was observed in
metallic states of various molecular conductors;




-(ET)2MZn(SCN)4, (M=Rb, Cs)
-(ET)2I3
(TMTSF)2FSO3
-(BEST)2MCl4, (M=Fe, Ga)
 Angular dependence of the width is proportional very
well to that of the central shift of the spectrum, which
suggests the appearance of CO/CD.
 Details of the nature of CO/CD are found quite
different among them.
Summary-2
 -(ET)2MZn(SCN)4, (M=Rb, Cs)
Long-range CO in the Rb-salt
CD due to the competition of different CO’s
 -(ET)2I3
Long-range CO; Non-stripe CO in the ZGS
CD due to band formation, enhanced by Coulomb correlation.
 (TMTSF)2FSO3
CD in the metallic state under pressure.
Coupling with electric dipoles on FSO3 anion may be relevant.
 -(BEST)2MCl4, (M=Fe, Ga)
BETS layers are responsible for CD in the metallic state.
Mechanisms responsible for CO/CD are full of variety!
Concluding remarks
 Increasing numbers of molecular conductors are
found to exhibit CO/CD.
 CO/CD are found to interplay with various types of
ground states.
 Even Superconductivity is found in the vicinity of
CO’ed state.
-(ET)2I3 under uniaxial strain (Tajima, 2003)
-(DODHT)2PF6（Tc = 3.1 K at 16.5 kbar: Nishikawa, 2003)
-(meso-DMBEDT-TTF)2PF6 （Tc = 4.3 K at 4.0 kbar: Kimiura,
2004）
CO/CD will open new possibility of molecular
conductors and other correlated systems!
Collabrators:
Ko-ichi Hiraki, Yoshiki Takano, Ken-ichi Arai, Shiro Harada,
Hidetaka Satsukawa
Dept. Physics, Gakushuin Univ.
N. Tajima, H.M. Yamamoto, R. Kato
RIKEN, JST-CREST,
and T. Naito,
Ehime Univ.
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Comparison with the other
isostructural -phase I3 salts
S
S
C
S
S
S
S
S
Se
Se
S
C
S
Single crystal 1 peace
with double bond carbons enriched with 13C
ET
S
S
Se
Se
C
Se
Se
C
Se
Se
S
Single crystal 1 peace
with double bond carbons enriched with 13C
BETS
S
S
S
Se
Se
S
Se
Se
BEDT-STF
Ensemble of small single crystals
with all Se sites enriched with 77Se isotope
S
S
Large amount of small single crystals
containing natural 77Se (7.5%)
Small single crystal
containing natural 77Se (7.5%)
-(BETS)2I3 v.s. -(ET)2I3
-BETS2I3 may correspond to
-ET2I3 under pressure of
~1.1 GPa
M. Inokuchi et al, BCSJ 68 (1995) 547
N. Tajima et al, EPL 80 (2007) 47002
Angular dependence of resonance
shift for the 3 peaks
Sinusoidal dependences
Relative phase
NMR shift from 73.170/MHz
0.25
A,A'
B
C
0.20
0.15
Red-Green
Black-Green
Black-Red
58°
78°
20°
0.10
0.05
0.00
-0.05
Amplitude ratio
-0.10
-70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70
angle/deg
Green : Red : Black
= 2.8：1：3.0
~ 0.6：0.2：0.6