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HAL Id: jpa-00210455

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Submitted on 1 Jan 1987

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Conduction electron spin resonance measurements on TTF-TNNQ and (TMTTF)2BF4 under hydrostatic

pressure

L. Forró, J.R. Cooper, G. Sekretarczyk, M. Krupski, K. Kamarás

To cite this version:

L. Forró, J.R. Cooper, G. Sekretarczyk, M. Krupski, K. Kamarás. Conduction electron spin resonance

measurements on TTF-TNNQ and (TMTTF)2BF4 under hydrostatic pressure. Journal de Physique,

1987, 48 (3), pp.413-418. �10.1051/jphys:01987004803041300�. �jpa-00210455�

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Conduction electron spin resonance measurements on TTF-TCNQ and

(TMTTF)2BF4 under hydrostatic pressure

L. Forró (1,2), J. R. Cooper (1), G. Sekretarczyk (3), M. Krupski (3) and K. Kamarás (4) (1) Institute of Physics of the University, Bijenicka 46, P.O.B. 304, 41001 Zagreb, Yougoslavia

(2) CEA/IRDI/DMECN/DTech/SESI, C.E.N. de Fontenay-aux-Roses, B.P. n° 6, 92265 Fontenay-aux-Roses Cedex, France

(3) Institute of Molecular Physics Polish Academy of Sciences, Smoluchowskiego 17/19, 60-173 Poznan, Poland

(4) Central Research Institute for Physics, P.O.B. 49, H-1515 Budapest, Hungary (Requ le 3 septembre 1986, accept6 le 13 novembre 1986)

Résumé. 2014 Nous présentons des mesures de résonance paramagnétique sur les électrons de conduction de deux conducteurs organiques : un système bi-chaînes tétrathiofulvalène-tétracyanoquinodiméthane (TTF-TCNQ) et une

mono-chaîne bis tétraméthyl-tétrathiofulvalène borontétrafluoride ((TMTTF)2BF4). Dans les deux cas la raie de résonance s’élargit fortement sous l’influence de la pression ; ceci est en contradiction avec le mécanisme d’Elliott.

Quant au facteur g, il ne dépend pas de la pression, alors que la susceptibilité paramétrique diminue à température

ordinaire de - 8 ± 1 %/kbar pour TTF-TCNQ et de - 3 ± 1 %/kbar pour (TMTTF2BF4.)

Abstract.

-

Conduction electron spin resonance (CESR) measurements under hydrostatic pressure on two chain

organic conductor tetrathiofulvalene-tetracyanoquinodimethane (TTF-TCNQ) and single chain organic conductor

bis tetramethyl-tetrathiofulvalene borontetrafluorid ((TMTTF)2BF4) are presented. In both cases the CESR

linewidth increases strongly with pressure in contradiction with the Elliott-mechanism for spin relaxation. The g- factor is pressure independent for both compounds while the spin susceptibility decreases by - 8 ± 1 %/kbar for TTF- TCNQ and - 3 ± 1 %/kbar for (TMTTF)2BF4 at room temperature.

Classification

Physics Abstracts

72.30P

-

72.15N

1. Introduction.

Conduction electron spin resonance (CESR) measure-

ments at ambient pressure have been carried out on a number of effectively one-dimensional (lD) organic conductors, including TTF-TCNQ [1], TMTTF-TCNQ [2], (TMTSF)2PF6 [3], TMTSF-DMTCNQ [1] etc...

and have been very useful in elucidating their unusual

magnetic properties. It is indeed peculiar that organic

metals with scattering times as low as 10-14-10-15 s do

give an observable CESR signal even at room tempera-

ture. Note that very few ordinary isotropic metals show

CESR and then usually only at very low temperatures.

The ESR linewidth (AH) reflects the spin lattice

relaxation rate and in ordinary metals it is usually

determined by the spin-phonon interaction. However in many organic metals, mainly two chain compounds,

4H has an unusual temperature dependence : namely it

increases with decreasing temperature [1]. Thus the proportionality between dH and the phonon population

is not obeyed in two chain systems like TTF-TCNQ

although it is roughly followed in single chain systems like (TMTTF)2BF4 [4].

The spin susceptibility can also be obtained from the

intensity of the CESR signal. One of the most exciting things in the high temperature metallic phase of organic

conductors is the enhanced and temperature dependent spin susceptibility (Xs ). For example in TTF-TCNQ at

room temperature XS is enhanced by a factor of 3 to 5 times over the value calculated using a bandwidth

deduced from optical or thermoelectric power measurements. Furthermore this paramagnetic suscep-

tibility which is temperature independent in ordinary

metals falls by a factor of 2.5 on cooling down to 60 K [5].

These strange features of AH and X are believed to

arise from the 1D nature of the electronic band structure but after a lot of experimental and theoretical work a generally accepted explanation is still missing.

Attempts have been made to account for the tempera-

ture dependence of AH in terms of interchain coupling [6] or as a precursor to the Peierls instability [1J. The

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01987004803041300

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414

two mechanisms most often cited for the T dependence

and enhancement of ys are a) electron-electron interac- tions which enhance XS and introduce a log T depen-

dence [7] and b) polaron formation which gives a T dependent narrowing of the bandwidth [8].

By application of high pressure one hopes to get

insight into these mechanisms since it will produce

controlled changes in the onchain and interchain trans- fer integrals ti and t, . It will also increase the mean free

path (decrease the scattering time) and alter the charge

transfer. Thus the screening of the Coulomb interac- tions may be altered. Furthermore as we have been interested in the different ESR responses for two chain and single chain compounds for some time, we have

made a comparative study of TTF-TCNQ and (TMTTF)2BF4 under pressure. TTF-TCNQ has already

been measured by Berthier et al. [2]. However in their low field measurements at 40 MHz the linewidth was

comparable with the applied magnetic field, no infor-

mation could be obtained about the g-factor, and there

was also a possibility that the ESR intensity could have

been reduced because of changes in the skin depth

under pressure, giving an overestimate of the pressure

dependence of Xs.

Before discussing the present high field ESR data for

single crystals let us briefly mention some effects of pressure on other physical properties of both com- pounds.

TTF-TCNQ is one of the best studied organic

conductors under hydrostatic pressure. The compress-

ibility of the a, b, c lattice parameters is 0.26 %, 0.43 %

and 0.32 % per kilobar respectively [9]. The lattice parameters have strong temperature dependence, too, and it has been emphasized that thermal contraction of the lattice between 290-65 K has approximately the

same effect as the application of 5 kbars pressure at

room temperature. Calculating the change in tj with b-

axis spacing [11], the obtained increase in tl was in good agreement with the experimental results on the

pressure dependence of the plasma frequency, namely

d In tl/dp = 2 %/kbar [12]. But the strong increase of the conductivity d In Q /dp

=

28 %/kbar can not be explained with such a change in the one electron

bandwidth [10]. Generally, all the Fermi-level proper- ties exhibit anomalously large pressure dependence in TTF-TCNQ, for example proton relaxation rate 11 T

(- 23 %/kbar), spin susceptibility (- 8 %/kbar) [2], etc.

(TMITF)2BF4 has not been so thoroughly investi- gated under pressure. As far as we know, there are no available compressibility data. A priori this material is

expected to be less compressible than TTF-TCNQ because with full charge transfer from the TMTTF molecules to the anions it resembles more an ionic

crystal. However, thermal contraction and compress-

ibility measurements on a similar compound (TMTSF)2PF6 [13] give similar values to those of TTF- TCNQ. The first experiments on (TMTTF)2BF4 under hydrostatic pressure have been performed in Japan and

show a similar strong pressure dependence of the

electrical conductivity to that for TTF-TCNQ, namely

d In uldp = 19 % kbar [14].

2. Experimental details.

We have performed our pressure and temperature dependent ESR measurements at X-band using a high

pressure apparatus, which works at pressures up to 5 kbars and at temperatures from 80 to 350 K [15]. The

apparatus contains a cylindrical corundum resonator directly coupled to the waveguide by a matching

corundum wedge. The pressure chamber in which the resonator is placed is made of nonmagnetic beryllium

bronze. The temperature of the system was controlled by a nitrogen vapour flux pumped through a heat exchanger disposed outside the pressure chamber. In this work the pressure medium was petroleum ether.

Single crystals of TTF-TCNQ and (TNMF)2BF4

were placed in the resonator in an orientation which minimizes the skin effect and gives Lorentzian line-

shapes. Possible changes in the Q-factor of the re-

sonator in temperature and pressure were monitored

by the signal of a copper sulfate crystal in the orienta- tion (g -- 2.50) in which it does not disturb the sample signal (g = 2.01). The static magnetic field and mic-

rowave frequency were recorded continuously during

the experiment.

3. Results and discussion.

The first ESR parameter whose change is obvious

under pressure is the linewidth. Figures 1 and 2 display

the temperature variation of AH for TTF-TCNQ and

Fig. 1.

-

CESR linewidth versus temperature for a single crystal of TTF-TCNQ at 1 bar (0) and 5 kbars (x) in the

orientation Hdc 11 c *.

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Fig. 2.

-

CESR linewidth versus temperature for a single crystal of (TMTTF)2BF4 at 1 bar (0) and 5 kbars (x) in the

orientation Hdc II b * .

(TMTTF)2BF4 at ambient pressure and at 5 kbars

respectively. In both cases AH increases linearly with

pressure. For TTF-TCNQ AH increases by factor of 2.7 for 5 kbars and this factor is constant in the measured temperature range 80-310 K. This relative increase in AH is in good agreement with the earlier low field studies.

The linewidth in TTF-TCNQ at ambient pressure does not satisfy the Elliott relation [16] for spin

relaxation which is often used for isotropic metals :

where Ag is the deviation of the g-factor from the free

electron value and Tf is the electron scattering rate along the chains measured in resistivity. Namely the

observed linewidth AH is a factor of 100 less than that

expected from equation (1) [17]. Furthermore, as the resistivity decreases on cooling the linewidth should

decrease too. However the actual temperature depen-

dence of AH is the opposite (Fig. 1). It is presently

believed that the very narrow linewidth (and also its

anomalous temperature dependence) is the consequ-

ence of the quasi-one-dimensional electronic structure.

In a strictly 1D system the Fermi surface consists of two

points at kF and - kF and both the forward (q = 0) and

backward (q- 2 kF ) scatterings do not give spin relax-

ation [18]. Hence to account for the observed finite

linewidth one has to include 3D effects like interchain

scattering, because every process which makes the system resemble an isotropic metal will broaden the line. In the first attempt at a mathematical formulation

Weger included the TII IT .1. factor in the Elliott formula

[6]. This is the ratio of onchain scattering time and

interchain tunnelling time and is a measure of the

dimensionality of the system :

T11 is given by the golden rule of perturbation theory

to be T-’ = 2 iTIh 1 T .L IZ Ti. Inserting this into

equation (2) one gets for the linewidth :

where (1. is the interchain overlap integral.

It is tempting to attribute the spectacular increase of AH with pressure in figure 1 to the increased transverse transfer integral and onchain scattering time. Supposing

a pressure dependence similar for (1. as for (I, it turns

out that the decisive factor is Ti. This is not surprising

since in a single particle picture a -- w p 2 r and from

optical measurements it is known that the change in plasma frequency is an order of magnitude less than the

change in conductivity with pressure [10]. The lengthen- ing of Till by pressure changes both cr and AH by nearly

the same factor. However the origin of such a large sensitivity of the electron lifetime to pressure remains a

somewhat controversial question.

There is a striking difference in the temperature dependence of d In uldp and d In åBldp. The latter is

constant at 33 %/kbar (Fig. 1) in the measured tempera-

ture range, while the former falls from 28 % kbar at room temperature to 10 %/kbar at 100 K. The latter temperature dependence was attributed to the increas-

ing role of the Frohlich collective mode in the conduc-

tivity as the temperature is lowered. The extra conduc-

tivity depends very weakly on pressure in the incom- mensurate regime, so the overall pressure effect is reduced. Similarly one can consider different contribu- tions to the linewidth :

The first and second terms are the usual single particle spin relaxation by phonons for momentum changes

near to 0 and 2 kF. The third term could enter as the

temperature is lowered and collective Frohlich modes build up. However nothing is known about the effect of such modes on spin relaxation but if anything they

should reduce the spin flip rate for those electrons which are condensed in the collective state. Whether these long life-time fluctuating CDWs give a contri-

bution to the spin flip rate of the uncondensed electrons

by scattering them is questionable. However with the appearance of CDWs, the population of the soft 2 kF phonon modes increases thus increasing the spin flip scattering rate, and will increase the second term in

equation (4). Irradiation experiments have shown that there is some extra contribution to the linewidth as the temperature is lowered towards the phase transition [19], and that this contribution is as sensitive to defects

as the Frohlich conductivity. The temperature inde-

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416

pendence of AH (5 kbars)/AH (1 bar)

=

2.7 means that

any relaxation mechanism associated with the CDW fluctuations is either negligible or has the same pressure

dependence as the single particle mechanism which is dominant near room temperature.

At first sight the temperature dependence of AH (Fig. 2) of (TMTTF)2BF4 suggests that the original

Elliott formula (1) applies as is stated in the literature for most of the single chain compounds. However there is again a problem in understanding why the line is so

narrow, i.e. the magnitude of AH is not consistent with

equation (1). From the pressure dependence of AH it is

obvious that the Tr term alone cannot account for the

linebroadening, because Tp 1, as measured in the resis-

tivity, decreases with pressure, and consequently AH

should decrease. Only an interchain hopping rate increasing with pressure can broaden the line as obser- ved. So we propose an empirical formula for AH in single chain compounds :

In (TMTTF)2BF4 the pressure dependence of these scattering rates compete with each other : the latter wins and AH increases with pressure, although this

increase is only 45 % for 5 kbars, i.e. a factor of 3.5 less than for TTF-TCNQ.

One could ask what is the role of the pressure

dependence of Ag in the linebroadening. Figure 3

Fig. 3.

-

g-factor versus temperature for single crystals of

TTF-TCNQ and (TMTTF)2BF4 at 1 bar (0) and 5 kbars (x).

(The orientations in respect to static magnetic field are the

same as for Figs. 1 and 2.)

shows that Ag is pressure independent for both com- pounds. For (TMTTF)2BF4 this is comprehensible since g is a molecular property, and contracting the

lattice one does not expect to change molecular quan- tities. In the case of TTF-TCNQ the constancy of g

means more, since the molecular g-factors of each

chain are mixed together with the respective spin susceptibilities giving a common g value [20] :

It can be concluded that at room temperature the spin susceptibility of the donor (X p ) and acceptor chain

(X A ) changes at the same rate with pressure because the total g-factor is pressure independent. However

below 200 K at 5 kbars g seems to be below the ambient pressure values. Within the strong coupling

limit corresponding to equation (6) this implies an

increased contribution of the TCNQ chain in respect to the TTF chain in the total susceptibility (XT). From the

NMR measurements of Takahashi et al. [21] it is known that XA (i.e. XTCNQ) changes slope below 200 K, it

decreases faster than at higher temperatures. This

change is usually ascribed to a precursor effect, namely

1D fluctuations towards the semi-conducting phase.

Susceptibility measurements of KCP have proved ex- perimentally that these fluctuations can be suppressed by pressure [22] ; the temperature dependent suscepti- bility at normal pressure becomes nearly temperature independent at a preessure of 20 kbars. From the g- factor measurements of TTF-TCNQ such a tendency

can be postulated for the TCNQ chain, but measure-

ments at higher pressures are needed to confirm this.

It was demonstrated above that in TTF-TCNQ the

spin susceptibility of donor and acceptor chains vary in the same way under pressure at room temperature. In

figure 4 are shown the changes in total spin susceptibili- ty for both compounds at room temperature. For TTF-TCNQ d In x Idp = - 8 ± 1 % kbar and for

Fig. 4.

-

Normalized spin susceptibility versus pressure for

(TMTTF)2BF4 and TTF-TCNQ at ambient temperature.

Different symbols mark different runs.

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(TMT’rF)2BF4 d In X Idp

= -

3 ± 1 %/kbar. It is im- mediately clear that an increase of 2 % in tl in the

formula for the spin susceptibility of noninteracting

electrons cannot account for the change in X.

The motionally band narrowing model requires the phonon frequency w to be comparable to the bandwidth

4 ti, otherwise Migdal’s theorem holds and the phonons

have no effect on y [23]. One expects the phonon frequencies (external and internal) to be similar in

TTF-TCNQ and (TMTTF)2BF4, as well as their

pressure dependence. However the difference in d In X Idp of a factor of 3 between the two compounds

tends to go against the explanation of the pressure

dependence of X within this model.

Let us consider the changes in X under pressure

expected if Coulomb correlations are important.

TTF-TCNQ and (TMTTF)2BF4 have the same room

temperature susceptibilities of 6.0 x 10-4 emu/mole.

Calculating the Pauli susceptibility with a total band- width 4 tj of 0.5 eV (which is a reasonable parameter for these compounds), one gets a value three times smaller than the measured one [5]. As is shown in figure 4 this enhancement is strongly pressure depen-

dent for TTF-TCNQ. Furthermore it is tempting to

attribute the strong temperature dependence of x (see Fig. 5) to the temperature dependence of the enhance- ment mechanism. Note in figure 5 that the pressure

dependence of X is slightly temperature dependent in TTF-TCNQ ; from - 8 ± 1 %/kbar at room tempera-

ture it changes to - 6 ± 2 %/kbar at 80 K.

When treating the electron-electron interactions it is usual to use the Fourier transform of the Coulomb interactions and to distinguish between the forward

scattering (g2 ) which corresponds to small momentum

Fig. 5.

-

Temperature dependence of the spin susceptibility

of TTF-TCNQ at 1 bar (0) and 5 kbars (x).

transfer q = 0, and the backward scattering (gl ) which displays the large momentum transfer with 2 kF. In real

space 92 corresponds to a long range interaction, which

is normally screened, while g1 is defined by the short

range onsite Coulomb interaction U. Calculation of the

high temperature magnetic susceptibility in the parquet

approximation [7] shows that:

where gl(T) = gll(l + g, In EFIT), g, - nF U, and

nF and X p are the density of states and the Pauli

susceptibility for the noninteracting electron gas.

Equation (7) holds for weak interactions, that is

U/4 t ..: 1.

Applying these results to the spin susceptibility of

TTF-TCNQ separated for each chain, it turns out that

91 TCNQ ::- 61, TTF

.

With such parameters the temperature

dependence and the enhancement of TTF-TCNQ come

mainly from the TCNQ chain.

For the enhancement of the factor of 3 in X at room temperatures one needs g, -- 0.5. This value does not

really fall within the weak coupling limit, nevertheless

equation (7) can be useful for a qualitative description

of the experimental results. Reduction of 9 1 to 0.3

accounts well for the observed decrease of 40 % of X at

5 kbars at room temperature. As ti depends little on

pressure, this reduction in g1 means an increased

screening of U under pressure. There could be several

reasons for this :

a) the increase in the onchain screening ;

b) interchain screening by the free electrons on the

neighbouring chains ;

c) excitonic screening of highly polarizable molecules [24]. This can be strongly pressure dependent since the polaron binding energy EB varies roughly like R- 4 (R is

the interchain distance) and reduces the effective

interaction to U - 2 EB ;

d) the screening of the short range interaction is

especially sensitive to the charge transfer (p) [25]. The screening is least effective near p

=

0.5 and the most effective near p

=

0.75.For TTF-TCNQ low tempera-

ture measurements have shown that p changes from

0.59 at normal pressure to 0.615 at 5 kbars [26] which

should considerably reduce U.

The decreased value of g1 under pressure qualitat- ively accounts for a temperature dependence of X at

5 kbars weaker than at ambient pressure. However it accounts only qualitatively since equation (7) cannot fit

the temperature variation of y with a temperature

independent g1 at any pressure. But as was mentioned in the introduction, a temperature drop from room

temperature to 100 K contracts the lattice as much as a 5 kbars pressure at room temperature, and all the

screening mechanisms discussed above can be switched

on by cooling the sample. (Note that in TTF-TCNQ at

normal pressure the charge transfer of 0.55 at room

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418

temperature increases below 220 K to 0.59 [27], which

may increase the efficiency of the screening).

Accepting the screening of the onsite Coulomb interaction as the source of the variation of X with

pressure, it is really simple to explain the much weaker decrease of y for (TMTTF)2BF4 at 5 kbars (Fig. 4). The charge transfer cannot help in screening since p

=

0.5 is the most unfavorable, and it does not vary with pressure. Furthermore the reduction of U on the TMTTF molecule via screening by metallic electrons of

neighbouring chains is less effective since the anions do not form conducting chains. The poor polarizability of

the closed shell anions also disadvantages the excitonic screening mechanism. The weaker screening of the

onsite U in (TMTTF)2BF4 is also shown in the tempera-

ture dependence of X [4]. Between 100 K and 300 K it increases only by 50 % (in TTF-TCNQ it is 100 %), although the thermal variation of the lattice is probably

similar to TTF-TCNQ.

In conclusion, the application of hydrostatic pressures

has confirmed the importance of the interchain hopping

in the spin relaxation processes. The increase in the linewidth has the same origin as the increased single particle conductivity: rl is a strong function of the pressure. The enhancement and unusual temperature dependence of y is ascribed to Coulomb interactions,

then from the present work it follows that U is strongly

pressure dependent in TTF-TCNQ and less in

(TMTTF)2BF4. This indicates that changes in charge

transfer with pressure and interchain screening mechan-

isms may be important for reducing the onsite Coulomb

interaction U.

Acknowledgments.

Useful discussions with S. Barisi£ , A. Bjelis, A. Janossy

and L. Zuppiroli are gratefully acknowledged. One of

us (L. F.) acknowledges the hospitality of Prof. A.

Graja and Prof. J. Stankowski during his stay at the Institute of Molecular Physics in Poznan.

References

[1] TOMKIEWICZ, Y., Phys. Rev. B 19 (1979) 4038.

[2] BERTHIER, C., COOPER, J. R., JEROME, D., SODA, G., WEYL, C., FABRE, J. M. and GIRAL, L., Mol. Cryst. Liq. Cryst. 32 (1976) 267.

[3] PEDERSEN, H. J., SCOTT, J. C. and BECHGAARD, K., Solid State Commun. 35 (1980) 207.

[4] DELHAES, P., COULON, C., AMIELL, J., FLANDROIS, S., TOREILLES, E., FABRE, J. M. and GIRAL, L., Mol. Cryst. Liq. Cryst. 50 (1979) 43.

[5] COOPER, J. R., MILJAK, M. and KORIN, B., Chemica Scripta 17 (1987) 79.

[6] WEGER, M., J. Physique Colloq. 39 (1978) C6-1456.

[7] BARISIC, S., BJELIS, A., in : Theoretical Aspects of

Band Structures and Electronic Properties of

Pseudo-One-Dimensional Solids, ed. by Komimura, D. Reidel (D. Reidel Publ. Co., Dordrecht) 1985 and references therein.

[8] ENTIN-WOHLMAN, O., KAVEH, M., GUTFREUND, H., WEGER, M. and MOTT, N. F., Philos. Mag.

B 50 (1984) 251.

[9] DEBRAY, D., MILLET, R., JEROME, D., BARISIC, S., GIRAL, L. and FABRE, J. M., J. Physique Lett.

38 (1977) L-227.

[10] COOPER, J. R., Phys. Rev. B 19 (1979) 2404.

[11] BERLINSKY, A. J., CAROLAN, J. F. and WEILER, L.,

Solid State Commun. 15 (1974) 795.

[12] WELBER, B., ENGLER, E. M., GRANT, P. M. and SEIDEN, Bull. Am. Phys. Soc. 21 (1976) 311.

[13] MOROSIN, B., SCHRIBER, J. E., GREENE, R. L. and ENGLER, E. M., Phys. Rev. B 26 (1982) 2660.

[14] MURATA, K., private communication.

[15] STANKOWSKI, J., GALEZENSKI, A., KRUPSKI, M., WAPLAK, S., GIERSZAL, H., Rev. Sci. In-

strum. 47 (1976) 128.

[16] ELLIOTT, R. J., Phys. Rev. 89 (1953) 689.

[17] FORRÓ, L., Ph. D. thesis 1985, unpublished.

[18] YAFFET, Y., Solid State Physics, V. 14, ed. by H.

Ehrenreich, F. Seitz, D. Turnbull (Academic,

N. Y.) 1965.

[19] SANQUER, M., BOUFFARD, S. and FORRÓ, L., J.

Physique 47 (1986) 1035.

[20] TOMKIEWICZ, Y., TARANKO, A. R., ENGLER, E. M., Phys. Rev. Lett. 37 (1976) 1705.

[21] TAKAHASHI, T., JEROME, D., MASIN, F., FABRE, J.

M., GIRAL, L., J. Phys. C 17 (1984) 3777.

[22] JEROME, D., SODA, G., COOPER, J. R., FABRE, J.

M. and GIRAL, L., Solid State Commun. 22

(1977) 319.

[23] MIGDAL, A. B., Soviet Phys. JETP 7 (1958) 996.

[24] LE BLANC, O. M., J. Chem. Phys. 42 (1965) 4307:

[25] MAZUMDAR, S. and BLOCH, A. N., Phys. Rev. Lett.

50 (1983) 207.

[26] MEGTERT,S., COMES, R., VETTIER, C., PYNN, R.

and GARITO, A. F., Solid State Commun. 31

(1979) 977.

[27] POUGET, J. P., Chemica Scripta 17 (1981) 85.

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