4kF CDW induced by long range Coulomb interactions

1
4kF CDW induced by long range Coulomb interactions

• F. Ya Nad
• Institut of Radio-Engineering and Electronics,
  Moscow
• Pierre Monceau
• Centre de Recherche sur les Très basses
  Températures, Grenoble
• M. Nagasawa
• Dept. Natural Science and Material Science, Tokyo
  Denki Univ.
• T. Nakamura and K. Furukawa
• Institute for Molecular Science, Okazaki, Japan
• In collaboration with
• S. Brazovski (LPTMS, Orsay), J.M. Fabre
  (Montpellier)

2
Structure of (TM)2X Bechgaard-Fabre salts
Transfer integral parallel to the stacks is one
order of magnitude larger than in either of the
transverse direction Slightly dimerized zig-zag
stacks of donors Stacks delimit cavities filled
by monovalent anions X The degree of
dimerization increases from the  Se  to the
 S  donors
J.L. Galigne et al. Acta Cristallog, 1979 K.
Bechgaard et al. Sid St. Comm., 1980
Symmetry of anions Centrosymmetric anions
(CSA) spherical Br- octahedral PF6-,
AsF6-,SbF6- Non-centrosymmetric anions
(NCSA) tetrahedral ClO4-, BF4-,ReO4- linear
SCN-
3
In 1D organic charge transfer salts, the ground
state is governed by various interactions electro
n-electron, electron-phonon, magnetic and
interaction with anions For non interacting (or
weakly interacting) electrons, a 2kF CDW can
develop due to the Peierls instability with q
2kF In the case where electron-electron
interactions are dominant, a modulation at 4kF
can develop (generalization of the classical
Wigner lattice) The formation of a 4kF CDW
depends of the magnitudes of on-site U and net
neighboring site V relative to the mean kinetic
energy determined by the width of the energy band
W 4t (t transfer integral) In the case of
(TMTTF)2X salts W 0.5 eV U 4-5 eV
V 2-3 eV ? U/W and V/W much larger
than 1 (F. Castet, A. Fritsch and L. Ducasse
1996 Calculations based on the extended Hubbard
model indicate the possibility of charge
disproportionation or charge ordering (CO) in
(TMTTF)2X salts
4
Models
-Important role of long-range Coulomb interaction
and charge- induced e-e correlations -Charge
disproportination resulting from strong
electronic interactions Seo and Fukuyama
J.Phys. Soc. Japan, 66 (1997) 1249 lattice
model in the Mean Field approximation at T0
taking into account the onsite U and the
nearest intersite V repulsion potentials.
Charge disproportionation occurs at
VgtVcr These states are accompanied by
different types of spin of AFM spin
arrangments.

• Interplay between electronic correlations and
  lattice effects in 1D quarter-filled bands
• Ung et al. Phys. Rev. Lett. 73 (1994) 2603
• S. Mazumdar et al. Phys. Rev. B62 (2000)
  13400
• -Anion potentials Anions can play a dominant
  role if they are allowed to undergo small
• displacements (along arbitrary directions)
  leading to local changes of the on-site
  electronic
• energies
• J. Riera and D. Poilblanc, Phys. Rev. B62
  (2000) R16243
• J. Riera and D. Poilblanc, Phys. Rev. B63
  (2001) 241102

5
CO at ECRYS 2005

• -M. Dumm Electomagnetic response
• M. Nagasawa Non linear transport in Br salt
• K. Kanoda (DI-DCNQI)2X
• T. Ito X-ray study of charge and
  anion orderings
• S. Mazumdar CO in 1/4 filled band charge
  transfer solids
• -S. Brazovski
• T. Takahashi CO, everywhere
• -S. Brown NMR

6
Unified Phase Diagram
Sequence of electronic phases of (TMTSF)2X and
(TMTTF)2X, (belonging to the same family) with
pressure as the relevant parameter which allows
to move a given compound throughout a unified
(T-P) phase diagram
Missing -Anion ordering -structureless
transition in (TMTTF)2SbF6 and (TMTTF)2ReO4
Phase diagram description following sequences of
electron states determined by changes in anions,
superstructures,. S. Brazovski and V. Yakovenko
1986)
C. Bourbonnais and D. Jérome, Advances in
Synthetic Metals (1999
7
AC conductivity of (TMTTF)2AsF6
8
First characterizations of (TMTTF)2X salts
Normalized resistivity of (TMTTF)2SbF6 (.),
(TMTTF)2AsF6 (- - -) and (TMTTF)2PF6 (------)
4kFcharge localization ? maximum of ? at T? IR
vibronic intensity measurements indicate
localized electrons on molecules which imply the
presence of a gap of charge (2??) on the stacks,
whose effect becomes relevant below T? ??/? No
effect on the magnetic susceptibility at T? ?
spin-charge separation
R. Laversanne et al. J. Physique Lett. (1984)
Magnetic susceptibility of (TMTTF)2AsF6
Electric resistivity of (TMTTF)2PF6
P. Vaca and C. Coulon, Phase Transitions (1991)
9
Charge Gap
1- T? T? metallic type of conductivity 2- T?
maximum of G AsF6 - 230K
SCN - 265K 3- T T? conductivity
decreases
10
 Structureless  transitions
Thermopower of some (TMTTF)2X salts
Dielectric constant of some (TMTTF)2X salts
?
?
H. Javadi, R. Laversanne and A.J. Epstein Phys.
Rev. B37 (1988) 4280
C. Coulon, S.S.S. Parkin and R. Laversanne,
Phys. Rev. B31 (1985) 3583

• -Anomaly in the dielectric constant at microwave
  frequencies
• -a break in the T dependence of the thermopower
  ?increase of the charge gap
• no supersrtucture
• No change in intensity of the main Bragg peaks
• A phase transition with a purely electronic
  origin?

11
Conductance of (TMTTF)2X salts
Br
PF6
SCN
ReO4
AsF6
SbF6
Non-centrosymetric anions
Centrosymetric anions
SCN (linear) anion ordering at
TAO169K Superstructure with q (0,1/2,1/2)
?CO2000K Low magnetic state (AF) ReO4
(tetrahedron) Structureless transition at
TCO227.5K ?CO1400K Anion ordering transition
at TAO154K ?CO2000K
AsF6 and SbF6 (octahedron) Abrupt bend at TCO
(100.6K for AsF6 and 154K for SbF6) Thermally
activated decrease of conductivity with
?CO400-500K Transition into a magnetic order
state at TMO
12
Real part of dielectric constant of (TMTTF)2X
salts
? ImG/?
AsF6
SbF6
ReO4
PF6
1- For all anions at T T?, there is no
anomaly 2- for CSA and ReO4 anions, ?diverges at
TCO. Huge magnitudes of ? - 2.106 for AsF6,
5.105 for ReO4
13
Charge disproportionation
C13 NMR spectra for (TMTTF)2AsF6
NMR measurements in an external field of 9T
(freq 96.4 MHz)
Below TCO, doubling of the spectral line due
to two inequivalent molecules with unequal
electron densities Charge disproportionation
31 from T1-1 measurements
Spectral splitting (charge disproportionation
order parameter) versus temperature
D.S. Chow et al. Phys. Rev. Lett. 85 (2000) 1698
At high temperatures the unit cell consists of
two equivalent TMTTF molecules related by
inversion about the counterion The breaking of
the inversion symmetry within the unit cell below
TCO, and the spontaneous dipole moment
associated with the charge imbalance on the two
molecules yield the ferroelectric behaviour.
14
Vibrational modes in (TMTTF)2X
ag stretching CC mode infrared active though
electron-molecular (emv) coupling Neutral TMTTF
?3 1639 cm-1 Meneghetti et al.
TMTTF ?3 1567 cm-1 J.Chem.
Phys. (1984) TMTTF0.5 ?3
1603cm-1 Resonance frequency of emv coupled
mode is a function of the charge (0.5 ?) on the
molecule
Temperature dependence of the ?3 mode
AsF6 T20K charge disproportionation 0.63
and 0.37 (2?0.26) T10K
------ 0.60 and
0.40 (2?0.20) PF6 T20K
------ 0.56 and
0.44 (2?0.12)
M. Dumm et al. ISCOM 2003
15
Dielectric constant of (TMTTF)2X with NCSA anions
ReO4
SCN
ReO4 salt at TAO does not show any peak but, a
jump-like decrease of the ? magnitude SCN
a) at TgtTAO no anomalies characteristic of a
CO transition b) at TTAO , q(0,1/2,1/2) a
small wide maximum two orders of magnitude
smaller than in CSA
16
Ferroelectric character
The ferroelectric state is triggered by the
uniform shift of anions yielding a macroscopic
ferroelectric polarization which is gigantically
amplified by the charge disproportionation on the
molecular stacks ( S. Brazovski, ISCOM 2003,
cond-mat 0306006, 0401309)
CSA and ReO4 salts show at TCO a second order
phase transition described by the Curie
law A ? ---------- ?
T- TCO ? 1/ ? (T) is close to be linear Ratio
AL / AH (AL at T? TCO AH
at TgtTCO) in CSA AL / AH 2 in ReO4 AL / AH
1.5
PF6
SbF6
ReO4
AsF6
CSA orentional disorder is weak because the
great symmetry of CSA NCSA possibility of
formation and stabilisation of a CO state depends
on the degree of disorder induced
by the orientational disordered NCSA ReO4 anion
has an intermediate degree of charge
symmetry(tetrahedron) orientation
disorder does not prevent the formation of a CO
state SCN strong non-symmetrical charge
distribution leading to an inner
disordered electric potential, that impeds the
formation of a CO state
17
Summary of data
Also BF4 T? 215-230K TCO83K TAO39K
18
Relaxation rate
19
Imaginary part of the permittivity of(TMTTF)2AsF6
T ltTCO
T gt TCO 101 K
20
Motion of domain walls
Frequency of the maximum in ? the same at T97
K and T105 K (TCO 101K)
The slow relaxation processes involved in the
shoulder of ? may correspond to the motion of
the domain wall structure developped in the
ferroelectric state
Freezing of the ferroelectric domainstructure
below 90K TCO - 10K
21
Relaxation rate in (TMTTF)2AsF6

• ? 1/?1-T-TCO?
• This divergence correponds to the theory of a
  classical ferroelectric and is due to the
  softening of the oscillatory mode responsible for
  the FE transition

22
Relaxation rate in (TMTTF)2PF6
Diffuse phase transition in ferroelectrics with
compositional heteroginity, so-called relaxator
ferroelectrics
23
Effect of pressure
24
(TMTTF)2SbF6 under pressure
0.5 GPa
0.16 GPa
1 bar
Temperature dependence of the conductance of
(TMTTF)2SbF6 at 1kHz
25
Nagasawa et al., in press
26
Dielectric permittivity of (TMTTF)2SbF6
100 kHz
3 Mhz
Pressure 0.38 GPa
Ambient pressure
at 100kHZ, 300 kHz, 1 MHz, 3 MHz
27
TCO versus pressure for (TMTTF)2SbF6
V/t decreases with pressure ? decrease of
dimerization ? Shift of TCO at lower T
1 MHz
100 kHz
10 kHz
28
Effet of deuteration
29
Conductance of (TMTTF)2AsF6
hydrogenated
SbF6 salt
deuterated
30
Real part of the dielectric permittivity
100kHz
H
H
D
D
----------- 16K
-------- 13K
31
Deuteration effect on (TMTTF)2Re04
D
H
Shift of TCO of 7K No effect on TAO
TAO
1 MHz
32
Deuteration
Charge ordering is currently explained on the
base of the extended Hubbard model taking into
account Coulomb correlated electron interactions
on TMTTF chains. The magnitude of these
interactions is governed by the ration V/t with
V the potential of the next neighboring
interaction and t1/2(t1 t2) is the
effective intrachain transfer integral with t1
within dimers and t2
between dimers. Preliminary structural data
indicate an increase of the distance between
TMTTF molecules along their molecular chains (
T. Nakamura et al.) It is suggested that the
increase of TCO in deuterated samples is
associated with the growth of the ratio V/t (and
consequently an increase of dimerization? an
increase of TCO.)
33
Anion ordering transitions

• CSA
• 1- No indication of anion ordering and of
  formation of a superstructure with q ? 0 at T gt
  TMO
• 2- This is due to the charge symmetry of these
  anions, with all orintations in the cavities
  equivalent
• 3- the  structureless  transition at TCO gt TMO
  is associated with charge ordering on the TMTTF
  molecular chains
• NCSA
• 1- large anisotropy of the charge distribution.
  Various orientations within the molecular
  cavities are not equivalent
• 2- the short contacts between anions and S atoms
  favors orientational anion ordering with
  formation of a superstructure with q ? 0
• SCN superstructure with q (0, 1/2, 1/2)
  antiferroelectric behaviour
• ReO4 superstructure with q (1/2, 1/2, 1/2)

34
Conclusions

• 1- Electron correlations due to long range
  Coulomb interactions on the molecular chains are
  the driven force of the formation of a charge
  ordered state , of the Wigner type in (TMTTF)2X
  conductors
• 2- Shift of the anions chains ( displacement
  transition) provides the stabilization of this CO
  state, which shows many features of a
  ferroelectric state
• 3- The form of charge symmetry of anions
  determine largely the possibility of
  stabilization of the CO state, the nature of the
  CO transition and the magnitude of the dielectric
  constant near TCO.
• 4- a new line in the unified phase diagram
• 5- huge effect of deuteration

35
References
F. Nad, P. Monceau and J.M. Fabre J. Physique IV
9 (1999) 10-361 F. Nad, P. Monceau, C. Carcel
and J.M. Fabre Phys. Rev. B62 (2000) 1753 F.
Nad, P. Monceau and J.M. Fabre J. Phys.Condens.
Matter 12 (2000) L435 P.Monceau, F. Nad and S.
Brazovski Phys. Rev.Lett. 86 (2001) 4080 F. Nad,
P. Monceau, C. Carcel and J.M. Fabre J.
Phys.Condens. Matter 13 (2001) L717 F. Nad and
P. Monceau J. Physique IV 12 (2002) Pr 9-133 F.
Nad, P. Monceau, H. Hiraki and T. Takahashi J.
Phys.Condens. Matter 16 (2004) 1 F. Nad, P.
Monceau, T. Nakamura and K. Furukawa submitted to
J. Phys.Condens. Matter M. Nagasawa, F. Nad,
P. Monceau and J-M. Fabre submitted to Solid
state Communications F. Nad, P. Monceau, L.
Kaboub and J-M. Fabre submitted to Europhysics
Letters
36
Quarter-filled systems without an uniform stacking

• role of the 4kF umklapp scattering in the
  Mott-Hubbard localization
• possibility of a Mott insulator in a
  quarter-filled uniform system
• (EDT-TTF-CONMe2)2AsF6 K. Heuzé et al.
  Adv. Mater. (2003)
• (DMtTTF)2X with X ClO4, ReO4 C. Coulon ISCOM
  (2003) S. Sylvain et al. (ISCOM 2003)
• Electronic localisation at 150K with appearance
  of a short range incommensurate
• modulation with q (-0.58, 0, 0.275)
• DI-DCNQI)2Ag Wigner crystal type of charge
  ordering
• K.Hiraki and K. Kanoda, Phys. Rev. Lett. 80
  (1998) 4737

37
(DI-DCNQI)2Ag
Resistivity
Magnetic susceptibility
K.Hiraki and K. Kanoda, Phys. Rev. B54 (1996)
17276
X-ray structural study of 4kF Wigner crystal Y.
Nogami et al. ECRYS 1999 The calculated 4kF
intensity with the modulation of the molecular
valence D-0.25D-0.75 is two orders of magnitude
too weak Need to use variations in the
intramolecular bond lengths
C13-NMR spectra
Temperature dependence of the NMR Knight shifts
which measure the relative populations of
electron in the molecular species
K.Hiraki and K. Kanoda, Phys Rev. Lett. 80
(1998) 4737
38
Dielectric permittivity of (DI-DCNQI)2Ag
Resistivity
Dielectric constant
?
100kHz
1MHz
5MHz
The dielectric permittivity increases sharply
below 220K, temperature at which a new charge
ordered state with charge disproportionation
occurs (NMR and x-rays). The increase of the
permittivity reflects the polarizibility of the
growing (soft) 4kF superstructure
39
The main effect of pressure and deuteration may
be explained within the common extended Hubbard
model Pressure -the distance R between
molecules decreases V determined by long range
interactions is proportional to 1/R t determined
by orbital overlap is proportional to 1/expR At
ambient pressure , V/t is large enough for the
formation of the CO state V/t decreases ?
decrease of charge diproportionation ? shift of
the maximum of ? ? shift of TCO at low
T Deuteration Deuteration may induce a negative
pressure effect ? a growth of the distance R
between molecules Then V/t will increase ? the
increase of TCO That is in agreement with the
growth of R in the anion sequence Br, PF6, AsF6,
SbF6, Preliminary X-ray studies show that the
the dimer length between TMTTF molecules is T
dependent And it grows near TCO At first sight,
it appears that the increase of TCO in deuterated
samples can be associated with the growth of V/t
with the growth of the ratio V/t due to the
increase of the distance R A more deep
theoretical analysis is clearly needed taking
into account the change of the dimeriztion Along
the chain axis.