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Dielectric Susceptibility of Quasi One-Dimensional Charge and Spin Density Wave Conductors at Low
Temperatures
P. Monceau, F. Nad
To cite this version:
P. Monceau, F. Nad. Dielectric Susceptibility of Quasi One-Dimensional Charge and Spin Density Wave Conductors at Low Temperatures. Journal de Physique I, EDP Sciences, 1996, 6 (12), pp.2121- 2133. �10.1051/jp1:1996207�. �jpa-00247300�
J. Phys. I France 6 (1996) 2121-2133 DECEMBER1996, PAGE 2121
Dielectric Susceptibility of Quasi One-Dimensional Charge and
Spin Density Wave Conductors at Low Temperatures
P. Monceau (~~*) and F. Nad (~>~)
(~) Centre de Recherches sur les Très Basses Températures (**), CNRS, BP 166, 38042 Grenoble Cedex 9, France
(~) Institute of Radioengineering and Electronics, Russian Academy of Sciences, Mokhovaya11,
103907 Moscow, Russia
(Received 12 July1996, revised 29 July 1996, accepted 19 August 1996)
PACS.77.22.Gm Dielectric Ioss and relaxation PACS.71.45.Lr Charge-density-wave systems
PACS.75.30.Fv Spin-density waves
Abstract. We present a short review
on dielectric susceptibility properties of quasi one- dimensionaI charge and spm density waves. Emphasis is made
on new features we have observed
m recent measurements performed at very Iow frequencies and at Iow temperatures: a critical
slowing down of the real part of the dielectric susceptibility towards a temperature Tg and the bifurcation between two relaxation time processes near Tg. We interpret these data as resulting
from a transition of the charge and the spm density wave into
a glassy-Iike state.
1. Introduction
In quasi one-dimensional (lD conductors) with large enough degree of anisotropy a new elec- tronic coherent state develops below some critical value Tp as a result of the Peierls instability.
This new state is charactenzed either by a modulation of the charge density (charge density
wave, CDW) [1-8] or by a modulation of the spin density (spin density wave, SDW) [4,5,9].
Many compounds have been found to exhibit the CDW instability. Histoncally the first
were the mixed-valency platinum compounds, or Krogmann salts, K2Pt(CN)4Bro_3(3H20) Ill, then the organic tetrathiafulvalenetetracyanoquinodimethane (TTF-TCNQ) Ill, the tri
and tetra transition metal chalcogenides, NbSe3, TaS3, (TaSe4)21, [2], the molybdenum
oxides (bine bronze Ko_3Mo03 18]. Spin density wave instability is the more intensively studied in the organic Bechgaard's salts (TMTSF)2X built up of segregated stacks of tetramethylte-
traselenafulvalene (TMTSF) and X (PFO, A5Fo, molecules [9].
2. Energy Gap
The energy gap below Tp becomes apparent in the temperature dependent conductivity of
varions ID conductors [1-6] as well as in direct measurements of optical absorption [10,11].
(*)Author for correspondence (e-mail: monceaukÉlabs.polycors-gre.fr) (**) associated with University Joseph Fourier, UPR 5001 CNRS
© Les Éditions de Physique 1996
Qualitatively similar results have been obtained for organic ID conductors (monocrystals and
films) TTF-TCNQ which aise show the existence of a fundamental absorption edge [12,13].
Owing to these features the ID conductors with density waves (DW) are similar to semicon- ductors with narrow energy gap.
However. considerable differences between semiconductors and ID conductors exist, even
for these simple properties. Among them it should be noted, for example, the large broad- ening of the absorption edge of the order of value of the energy gap [loi, which is probably
associated ,vith thermodynamic fluctuations near Tp aiid quantum fluctuations at low tem-
peratures. Fluctuations have especially a strong influence on the soft one-dimensional DW
superlattice [10,14]. Additionally in the absorption spectra of even very pure samples, a fi- nite absorption is observed within the energy gap which has the form of spectral fines and
cari be associated with intrinsic deformations in the DW. As a result of these DW deforma- tions soliton-hke excitations and appropriate bound electronic states within the energy gap
cari develop [15-17].
Very often, the DW superlattice is incommensurate with the pnstine crystal lattice and
in the case of ideal pure ID crystals the DW should move without resistance (ideal Frôhlich
conductivity) due to the translational invanance. In real ID crystals impurities and defects prevent from the motion of the DW as a whole. Such a motion is Orly possible when an electric field above a threshold value ET is applied [2-8]. ET strongly depends on the concentration of impurities and defects. However, for E < ET (practically in the DW ground state) the
DW cari contribute heavily to the complex conductivity in the frequency range h~o < A (A
is the Peierls gap), owing to the collective oscillations of the pinned DW. The contribution of this DW pinned mode has been measured in many experiments on several CDW and SDW
conductors [2-5, 18, 19].
As an example, Figure 1 shows the frequency dependent conductivity of several ID CDW conductors [3]. The fundamental absorption edge near huJ cf 2A (cf 10~~ Hz) cari be seen. The
maximum in conductivity in the frequency range 10~° 10~~ Hz corresponds to the collective
pinned CDW mode. The shape of this peak differs strongly of that resulting from an harmonic oscillator; that is probably due to the ramdam distribution of impurities and pinning potentials.
3. Dielectric Susceptibility in trie Microwave Frequency Range
The initial measurements of the dielectric susceptibility of ID CDW conductors have been carried eut in the millimeter wave spectral range.
An important contribution for correct measurements (precision within
mJ 1%) of the conduc-
tivity and the dielectric susceptibility of organic ID single crystal samples with small cross- section area (mJ loo
~1~ and a length about 1 mm has been made by Schegolev and Buravov [20].
The main point of the method was the measurement of the shift of the resonance frequency
and the variation of the resonance fine width when a ID single crystal is introduced within
a microwave resonator. In the frame of quasi static approximation, the frequency dependent complex conductivity a(~o) and complex susceptibility cari be deduced from these data. How-
ever the quasi static approximation is Orly satisfactory in the case where the used samples
have sizes far less than the wavelength of the electromagnetic radiation in vacuum and with thickness less than the skia depth. These conditions impose limitations on the magnitude of the minimal conductivity of the samples under investigation.
With this method the first measurements of microwave (mJ 10~° Hz) conductivity and di- electric susceptibility have been carned eut on single crystals of high conducting complexes based on TCNQ molecules [21,22]. Then it was found for the first time that the real part of the dielectric susceptibility (the dielectric constant) has an anomalously large value
mJ
10~
N°12 DIELECTRIC SUSCEPTIBILITY OF 1D CONDUCTORS 2123
,"', ,« ",
x x
«~ k
' NbSe3
11,x'"~, ~~
~ x"
~~ ~', ~~3
~ x
Mm
l j) (TaSe4)21
t ,
/ x,
« «« " ",
l
~
é K~,3"°°3
/ ~~~~~
,
«
« « « « « « « «'
~
KCP
~~(
Fig. I. Frequency dependent conductivity of several quasi one-dimensional CDW conductors from reference [3]. The fuit Iines represent the adsorption edge near the Peierls gap, the peaks m the 10 10~~ Hz frequency range are the response of the collective pinned CDW mode.
along the high conductivity axis [21]. The microwave properties of high punty organic sait
TTF-TCNQ have been studied by the same technique [23-25]. An abrupt decrease of the microwave conductivity was found below mJ 60 K which, similar to the results of Schegolev et ai. [21], was several orders of magnitude lower than the d-c- conductivity. A huge dielectric
constant
mJ
10~ 10~ appears in the same temperature range.
Figure 2 shows the temperature dependence of the real part of the microwave dielectric
constant along the chairs [24] of several organic isostructural compounds, based on TCNQ
molecules: TTF-TCNQ, TSeF-TCNQ, TMTTF-TCNQ, DSeDTF-TCNQ. For TTF-TCNQ, f'
increases when T is increased from 4.2 K, goes through a maximum and drops towards zero
at 38 K with some indication that f' goes negative for T > 38 K (remember that 38 Il is the
locking temperature between both CDWS on TCNQ and TTF chairs). This huge dielectric
constant has been ascribed to the collective mode of the pinned CDW as calculated by Lee,
Rice and Anderson [26]. They found:
,
2 uJ) Q(
~ 3 A2 ~ ~ol'
where the first term is the single partiale contribution in presence of the Peierls gap zl (~o) =
4~Ne~ /m*, N being the total electron density and m* the electron effective band mass). Trie
~
~
~~O
x
~/x,
~,
Ô ~À'
w .
io
T
N°12 DIELECTRIC SUSCEPTIBILITY OF lD CONDUCTORS 2125
4. Dielectric Susceptibility in trie Radio Frequency Range
In the frequency range below 10~ Hz the main method for the determination of the dielectric susceptibility is the measurement of the complex conductivity a(~o) and the calculation of the real and imaginary parts of the susceptibility using the simple equations [28, 30]:
~>
Im a(~d)
~~~ ~,> lRea(~d) «dl
,
where adc is the conductivity for de current. These equations can be used in the radio frequency
range because for these frequencies the penetration depth of the electromagnetic field is always larger than the thickness of the samples under investigation, namely
mJ loo pm.
However at variance with contactless microwave method of Schegolev et ai., low frequency
a-c- measurements will include contact resistance phenomena. Therefore, for such type of
measurements, the contact resistances should have an ohmic behaviour and a value much smaller than the resistance of the bulk sample.
Another important limitation (similar to microwave cavity perturbation technique also) is
the non ideal orthogonality of channels for measurements of the real part and of the imaginary part of the conductivity, that always exists in real devices. This non-orthogonality is usually characterized by a special coefficient o which, for the best devices, has a typical magnitude of about 10~~ 10~~ degree. As a matter of fact, this coefficient determines how many times
one component of the conductivity can be different of the other with keeping an appropriate accuracy in the measurements [31,32].
This a-c- method has been intensively used for the measurements of the susceptibility of ID CDW conductors in the frequency range lo~ 10~ Hz and in the temperature range Tp/2 <
T < Tp [28-30]. The data could not be explained by a Debye-type relaxation with a single relaxation time. It was shown that the results can be satisfactory descnbed by a model taking
into account the distribution of energy barriers and the distribution of relaxation times. When T is decreased, trie main relaxation time grows with a thermally activated behaviour with trie
activation energy in trie range of magnitude of trie Peierls energy gap [28-30].
These dielectric susceptibility measurements have been extended on Ko 3Mo03 samples at lower temperatures and lower frequencies [33.34j. In these conditions it has been shown that the temperature dependence of f'(T) is not monotonous but exhibits a maximum at low frequencies.
We will now present our results measured in similar conditions in Section 5 for CDW conductors and Section 6 for the SDW (TMTSF)2PF6.
5. Low Frequency Dielectric Response of CDW Conductors
We have carned ont low frequency dielectric susceptibility measurements of several ID CDW conductors, namely orthorhombic (o-TaS3) TaS3 (31,32], monoclinic TaS3 [35], Ko.3Mo03 [36],
in trie frequency range 10~~ 10~ Hz and in trie low T range 4.2 50 K. Trie measurements down to 11 Hz bave been performed with an impedance analyser HP 4192A. For measurements in trie range 10~~ -10~ Hz
we have used a home-made computer bridge [32]. The bridge is auto- balanced by computer generation in one bridge arm of the sin wave with such an amplitude
and phase to compensate the appropriate a-c- signal from the unknown impedance in the other
bridge arm. Trie magnitude of trie a-c- voltage for measurements was kept at a small value such as the electric Eac was smaller than o-1 ET
Figure 3 shows trie temperature dependence of trie real part f' of the complex susceptibility
of o-TaS3 at fixed frequencies [31]. Below trie Peierls transition temperature (Tp = 220 K), the magnitude of f' becomes very large as usual and reaches a maximum
mJ 7 x 10~
near 120 K.
10~
ÎÙ~ ',
"o,
o o,
"o 'o
£' 'o
j
'o
'o ~
ÎÙ~ ". 3
'O ~
O
o 5
lo~
~~ ~~~ ~~o 200 250
~
1000/T (K"~)
Fig. 3. Temperature dependence of the real part, e', of the dielectric susceptibility of o-TaS3 at
frequencies (Hz): 1 11, 2 Ill, 3 1-1 x 10~, 4 10~, 5 10~ (from Ref. [31]).
Afterwards in the temperature range between loo K and 50 K, f' decreases exponentially
with an activation energy of the order of that of the Peierls gap. Below 50 K, f' measured at frequencies f > loo kHz continues to decrease monotonously. However for frequencies f < loo kHz, the f'(T, f) dependences show pronounced peaks. The magnitude and the
position of the peak maxima on the temperature scale are dependent on frequency. The f' peak is shift at lower temperature when the frequency is decreased.
In Figure 4 is plotted the frequency dependence of f'(~o) and f"(~o) at two selected tempera- tures. The high frequency branches (above 10~ Hz are very similar and they are well described by a power law f'
mJ
f"
mJ ~o~" On the contrary the dependences of f'(~o) and f"(~o) exhibit
a different behaviour in the low frequency range. It is worth noting that the loss function
(f") changes from practically symmetrical in the temperature range around 30 K to more and
more non symmetrical at lower temperature [32]. Ail these features of f'(~o,T) and f"(~o,T) dependences are typical for many different types of disordered materials with non-exponential
relaxation [37]. In the frame of dynamical scaling it can be shown that the effective width of trie loss peak f"(~o) measures the width of trie gaussian distribution of logarithms of trie relaxation times. It can be then concluded that above 30 K effectively trie distribution P(InT)
has a gaussian distribution while at lower T (below 25 K) the distribution becomes more and
more wider.
Trie temperature dependence of f' at fixed frequencies is shown in Figure 5 for o-TaS3. f' exhibits a sharp peak. The magnitude of this peak increases when the frequency is decreased.
The average relaxation time, T*, can be determined at the deflection point on f'(T) curve. T*
can be fitted either by a Fulcher-law: T
= Toexp(B/T Tc) with TO
"
10~~ s, B
= 200 K
and Tc m 13 K as well as by a slowing down equation: T*
= To(1- Tc/T)~~~ with Ta
=
10~~°
s. Tc
= 15 K and zv ce 24. The latter dependence is drawn in Figure 6 by a solid fine. In the same figure is plotted the dependence of Tp e (~o~)~~ where ~o~ corresponds to the
maximum of the loss function f". Above 32 K, T* (1/T) and T~(1/T) show a similar thermally
activated dependence with an activation energy of 780 K which is close to the Peierls energy gap in o-TaS3. These data are also in good agreement with those of Cava et ai. obtained at
higher temperature [29]. However below 32 K a branching between two relaxation processes
N°12 DIELECTRIC SUSCEPTIBILITY OF lD CONDUCTORS 2127
10~
£~ ~ ~~~AA
AA 38 ~
~ôA
& ~ AA
~ A~
106 ~a °° o~~~
o° O~g
~O~ j~
£~ ~Éô
° A
Og lÙ~ ~
~~4
o,1 la loo100010~ lo~ lo~ lo~
Frequency (Hz)
~~s
~~~
A
~
£' l8 K
a~~
107
,,
oaaoo omol ~'a
g o~ ~~~~
o oa a
aoag~
A~
06 °ag
go
~O ,
~ io
ao
105 ~~
io
~~4
O.ol loo lo~ lo~
Frequency (Hz)
Fig. 4. Frequency dependences of the real part e~ and imagmary part e" of the dielectric suscepti- biIity of o-TaS3 at T
= 18 K and T
= 38 K (from Ref. [32]
appears: T*(1/T) exhibits an upward curvature fitted by a slowing down equation and T~(1/T)
a downward curvature.
6. Low Frequency Permittivity of (TMTSF)2PF6 at Low Temperatures
We have performed similar a-c- conductivity measurements on the SDW compound (TMTSF)2 PF6 in the temperature range below half the SDW transition temperature (T~ = 12.5 K) and
in the frequency range 10~ -10~ Hz [38].
Figure 7 shows f'(~o) and f"(~o) dependences at several temperatures. In the high frequency
range (10~ -10~ Hz) f'(~o) and f"(~o) dependences are similar such as f'(~o)
mJ f"(~o)
mJ
~o~° with
a = o.6 o.7. With decreasing frequency f"(~o) shows a pronounced maximum the position of which shifts at lower frequency when T is reduced. Simultaneously the width of f"(~o) grows.
The temperature dependence of f'(T) at fixed frequencies between 111 Hz and MHz is
plotted in Figure 8. For a given frequency, f'(T,~o) shows a pronounced maximum. Trie position of this maximum is shifted to lower T with decreasing frequency. It should be noted
1,2 10~
0.01 .
10~ .
~ ôa
a
. a
f~~ 6
ooo a
. ù
~ ~~ o°~
o
a
~ à
, ù o a
2 lo~ ~
~~~ ~
~ .
0
0
(K)
Fig. 5. Temperature dependence of the real part é' of the dielectric susceptibility of o-TaS3 at
frequencies (m Hz) indicated in the figure. The two Iower curves correspond to f
= 11 kHz (x) and
100 kHz (A) (from Ref. [32]) ioo
~ tL
i° /P j
o,i ,'
& o,oi P~
'
o,coi ~,/~
o,oooi
~-5
20 30 40 50 60 70
1000iT (K"~)
Fig. 6. Temperature dependence of the relaxation time (o) determmed from deflection points of
e'(uJ,T) dependences of o-TaS3 and of the (fl) relaxation from the position of maxima of e"(IoguJ) dependences (from Ref. [32]
that trie high temperature parts of these curves (on the nght of the maximum) at different
frequencies merge practically into a single master curve.
As in the case of CDW systems, Figure 9 shows the temperature dependence of two relaxation time processes: the mean relaxation time T* from the deflection points in f'(T,~o) dependences, and the relaxation time from the maximum in f"(T,~o).
7. Low Temperature Glass Transition?
A qualitative physical model for the interpretation of the low frequency dielectric susdeptibility of CDW conductors described above has been proposed in [32]. In the temperature range
N°12 DIELECTRIC SUSCEPTIBILITY OF 1D CONDUCTORS 2129
b%Étnn
~° ~Ôù1x
o x~
O~ X
wmww«~
o ~ w
~ ù ~
O~#~~,~(~w
o x e
, ~ô x *
g à m (
o~ù~ ~
io6 ~°Î
à
~ X~Îe
oô m,
où x e
oh m*
oÔ~x°où
o
io2 io3 io4 io7
~~
O° °(iras
~
x~~ Éô
x~
~ iÎiÎ
x
~
~ axa
~
~
x
° ( nww,~
Zn ~~
~~
w axa
~ ~
x w °ÎÎ~
* il,
,,
@x~ x .
g
~ e ox
~
m .
o x .
~ e j n ~
xô
~ m
6 10 oxù
*
e °à#
x
~ j
e o
io~
~ ~ ~ ~ ~
io Jo io io' io io
Frequency (Hz)
Fig. 7. Frequency dependences of the real part e' and imagmary part e" of the electric permittivity of (TMTSF)2PF~ at given temperatures (in K): (z) 1,3, (x) I.G, (/~) 1.8, (1) 2A, (*) 3.2, (e) 4 (from
Ref. [38]
Tp/2 < T < Tp the interaction of the CDW with impurities has essentially a weak pinning
collective character. With decreasing the temperature below mJ Tp/2, because of the reduction of the screening and the resulting hardening of the CDW due to the exponentially vanishing
of the number of free electrons and holes, the pinning is essentially local induced by strong pinning impurities. Local CDW deformations at these pinning centers are nucleated in the
CDW superstructure which dominates the kinetic properties of the system.
The dielectric susceptibility results from the summation of polanzation effects and dipole
interactions between these randomly distributed solitons. We consider that the main cause of
f'(T) growth is the increase of the CDW ngidity with decreasing screening of its defects by
free carriers. The more rigid CDW tries to be more homogeneous. As a result the CDW co- herence length and the dielectric constant will increase. However at low temperatures dynamic retarding effects occur and the CDW has no enough time to respond to the a-c- perturbation and its response (i.e. the f' magnitude) decreases.
The divergence of f'(T), the dependence of the average relaxation time determined from
f'(T) well fitted by a slowing down relation with a finite Tc and the change of character of the distribution of relaxation times (from f"), from Gaussian to non Gaussian, are features
