One-dimensional physics in organic conductors (TMDTDSF)2X, X ...

HAL Id: jpa-00246576https://hal.archives-ouvertes.fr/jpa-00246576

Submitted on 1 Jan 1992

HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, estdestinée au dépôt et à la diffusion de documentsscientifiques de niveau recherche, publiés ou non,émanant des établissements d’enseignement et derecherche français ou étrangers, des laboratoirespublics ou privés.

One-dimensional physics in organic conductors(TMDTDSF)2X, X = PF6, ReO4 : 77Se-NMR

experimentsB. Gotschy, P. Auban-Senzier, A. Farrall, C. Bourbonnais, D. Jérome, E.

Canadell, R. Henriques, I. Johansen, K. Bechgaard

To cite this version:B. Gotschy, P. Auban-Senzier, A. Farrall, C. Bourbonnais, D. Jérome, et al.. One-dimensionalphysics in organic conductors (TMDTDSF)2X, X = PF6, ReO4 : 77Se-NMR experiments. Journal dePhysique I, EDP Sciences, 1992, 2 (5), pp.677-694. <10.1051/jp1:1992173>. <jpa-00246576>

https://hal.archives-ouvertes.fr/jpa-00246576

https://hal.archives-ouvertes.fr

J. Phys. I France 2 (1992) 677-694 MAY 1992, PAGE 677

Classification

Physics Abstracts

74.70K 75.30F 76.60E 71.45

One-dimensional physics in organic conductors

(TMDTDSF)~X, X=

PF~, Re04 :~~Se-NMR experiments

B. Gotschy II" *). P. Auban-Senzier (I), A. Farrall ('), C.Bourbonnais II" **),

D. Jdrome ('), E. Canadell (~), R. T. Hertriques (3), 1. Johansen (4)

dud K. Bechgaard (4)

(I) Laboratoire de Physique des Solides, Bit. 510, Universitd Paris-Sud, F-91405 orsay, France

(2) Laborato~re de Chimie Th60rique, Universit6 Paris-Sud, F-91405 orsay, France

(3) Laboratorio Nacional de Engenharia et Tecnologia Industrial, Departamento de Quimica, P-

2686 Sacavem, Portugal(4) H. C. oersted Institute, Universitetsparken 5, DK-2100 Copenhagen, Denmark

(Received16 October I99I, accepted in final form 23 January 1992)

Rksumd. Nous pr£sentons une 6tude RMN (spectres et mesures du temps de relaxation

Ti) sur le noyau ??Se, pour les compos6s (TMTSF)2Reo4, (TMDTDSF)2Reo4 et

(TMDTDSF)2PF6. Pour tous ces compos£s, la d£pendence en temp6rature du facteur d'augmen"tation de la relaxation (TTi)~ suit le coma de la susceptibilit6 statique uniforme xs(T) dans le

r6gime paramagn£tique. Des £carts h cette variation sont observ6s pour (TMDTDSF)2PF6 en

dessous de la tempdtature de localisation T~ qui sont expliquds en tenures de corn£lations

antiferromagn6tiques. La susceptibilit6 montre une divergence en racine carr6e de la temp6rature

au voisinage de la transifiion de phase vets un stat onde de densit6 de spin. La th6crie d'£chelle

pour le modble de gaz d'dlectrons quasi-unidimensionnels ddcrit parfaitement le comportement

RMN de ces systbmes organiques mixtes soufre-sd16nium. Bien que la densitd de charge

dlectronique sur [es sites de s616nium d£terminde par un calcul de type HUckel dtendu suggdre une

influence non ndgligeable du ddsordre, [es rdsultats ne permettent pas de d£crire de fagon

satisfaisante la forme des spectres observ£s pour le noyau ??Se.

Abstract. We present an NMR analysis (spectra and relaxation data) of ??Se nuclei for

(TMTSF)2Reo4, (TMDTDSF)2Re04 and (TMDTDSF)2PF6. In all compounds the temperaturedependence of the relaxation enhancement (TTi)~~ follows the square of the temperature

dependent uniform static susceptibility xs in the paramagnetic regime. Deviations from this

behaviour are visible in (TMDTDSF)2PF6 below the charge localization temperature T~ and are

explained in terms of antiferromagnetic correlations. The staggered susceptibility follows a square

root temperature divergence in the vicinity of the phase transition towards a spin density wave

state. The scaling theory for the quasi-one-dimensional electron gas model accounts very well for

the NMR behaviour of these mixed molecule systems. Although the electron charge density on Se

sites determined using an extended Hiickel type calculation suggests a non negligible influence of

disorder on the ??Se Knight shifts, the results cannot account in a satisfactory way for the

observed shape of the ??Se spectra.

(*) Permanent address : Physikalisches Institut der Universitaet Bayreuth, Germany.(**) Permanent address : Centre de Recherche en Physique du Solide, Ddpartement de Physique,

Universitd de Sherbrooke, Qudbec, Canada JIK-2Rl.

678 JOURNAL DE PHYSIQUE I N° 5

Introduction.

Organic conductors based on molecules of tetramethyl-tetrathiafulvalene (TMTTF) or

tetramethyl-tetraselenafulvalene (TMTSF) and with the general structure (TMTTF)~X or

(TMTSF)2X have been intensively studied recently [I]. The nature of the inorganic anion X,

govems in a crucial way especially the low temperature properties of these salts. Various

phase transitions between competing ground states have been identified in this series of

materials : spin-Peierls (SP) to spin density wave (SDW) states in (TMTTF)~X salts [2] and

SDW state to superconductivity in (TMTSF)~X materials [3]. All members of the (TM)~Xseries are isostructural and there exists no major difference at first sight between a compoundsuch as (TMTTF)2PF6 which exhibits an insulating behaviour below room temperature and

(TMTSF)~Cl04 which displays a metal-like conduction and superconductivity below 1.2 K.

The ability to span a wide variety of physical properties in the (TM)2X series either byconsidering salts with different anions or by using high pressure has strongly stimulated the

development of a theoretical framework for the understanding of quasi-one-dimensional (Q-l-D) conductors.

A new organic conductor based on the hybrid molecule of TMTTF and TMTSF, the so-

called tetramethyl-dithiadiselenafulvalene (TMDTDSF), has provided a series of intermediate

compounds whose physical properties lie in between those of (TMTTF)~X and (TMTSF)~Xseries. This picture is supported by the fact, that the unit cell parameters of (TMDTDSF)~PF6

are nearly midway between those of (TMTTF)2PF6 and (TMTSF)~PF6 [4].

In a previous paper, transport properties and lH-relaxation data of (TMDTDSF)~PF6 have

been reported [4]. The divergence of the relaxation rate at 7 K, has been attributed to a SDW

ordering establishing at the same temperature. However, protons iri (TMDTDSF)~PF6belong exclusively to the methyl groups and as such may not be appropriate to probe the

temperature dependence of the electronic degrees of freedom over an extended temperatureregime since the quantum or thermally activated rotation of those groups provides an

additional channel of spin-lattice relaxation (in particular above 30 K [5]). Thus, the nuclear

relaxation caused by hyperfine interaction with the conduction electrons, a property which

yields a valuable information about the electronic system, is completely obscured at high

temperatures. Furthermore, the protons are located at the outer extremities of the

TMDTDSF molecule. Though the spatial part of the electronic wave function is usuallyspread in organic conductors over the whole molecule, we expect only a small fraction of the

conduction electron spin density on CH~ groups. This can be concluded from spin density

maps in (TMTSF)~X compounds [6]. Thus, the hyperfine interaction which for protonssimply scales with the spin density will be small, resulting in long relaxation times if the

coupling to conduction electrons is the main source of nuclear relaxation and implies time

consuming experiments. A third relaxation mechanism, though experimentally not yetconfirmed, might be caused by a rotation of the PF6 anions [7]. Therefore, selenium atoms

(?~Se, I=

1/2) which are located on the central region of the TMDTDSF molecule, being free

from extrinsic relaxation channels, could be considered as good nuclei to study the relaxation

of electronic origin.Detailed ~~Se-NMR experiments have already been carried out in (TMTSF)~PF6 18-10].

The aim of our measurements was to establish a complete temperature dependent profile of

the nuclear spin lattice relaxation time Ti in (TMDTDSF)~PF~ and to compare our results

with ??Se relaxation data of (TMTSF)~PF~. The temperature dependence of the NMR data

will be discussed in the frame of a scaling theory for the Q" I-D electron gas model [9, 11, 12].

It was previously found that it is precisely from the analysis of the temperature profile of the

relaxation that a great deal of information about the statics, the dynamics and the

dimensionality of electronic correlations can be extracted. In this theory the temperature

N° 5 ??Se-NMR in (TMDTDSF)2X, X=

PF6, Re04 679

dependent electronic susceptibility xs enters in an essential way. Thus, in order to allow a

quantitative comparison with the theory, a new experimental study of xs for

(TMDTDSF)2PF6 is also presented in this paper.A second point of interest concems the reported orientational disorder of the TMDTDSF

molecules in the stacks. The unsymmetrical TMDTDSF molecule can have two orientations

in the unit cell, depending whether S or Se atoms are closest to the anions. On the other hand,

though disorder is a common feature of the (TMDTDSF)2X family, the degree of disorder

seems to depend on the nature of the anion [13]. In crystals with small anions like PF6 the

disorder is complete, whereas for Re04 as an anion the degree of disorder seems to be

smaller. So, it is interesting to compare 77Se NMR measurements in (TMDTDSF)2PF6 and

(TMDTDSF)~Re04. In the latter compound the tetrahedral anion Re04 exhibits an anion

ordering phase transition (AO) into an insulating ground state at T~o=

163 K [14]. Again,T~o for the mixed molecule compound is intermediate between the AO transition of

(TMTTF)2Re04 (T~o=

156 K [15]) and that of (TMTSF)~Re04 (T~o=

180 K [16]). Thus,77Se NMR data in (TMTSF)~Re04 and (TMDTDSF)~Re04 are also reported and

discussed.

Experimental.

All crystals examined in this study were grown electrochemically. The crystals had typicaldimensions of 5 x 0.5 x 0.2 mm~.

Magnetic susceptibility results are obtained from two experimental techniques : a Faradaybalance and an ESR spectrometer (9.4 GHz), in the range of temperatures (4.2 K, 300 K).

Using the Faraday balance, static susceptibility was measured on powdered samples of

(TMDTDSF)~Re04 and (TMDTDSF)~PF~ with respective weights 6.8 mg and 20.6 mg. We

checked on the first compound the good linearity of the magnetization with the magneticfield, at room temperature, between 0 and 7T. Magnetization data give the static

susceptibility from which it is possible to reach the spin susceptibility xs(T) by removing the

T-independent core diamagnetism xd, calculated from the Pascal's constants. We used

xd "

3.67 x10~~ emu/mole and x~ =

3.71 x10~~ emu/mole respectively for the

(TMDTDSF)~Re04 and (TMDTDSF)~PF~ compounds [17].Because of the low intensity of the sample signal, the contribution of the teflon sample-

holder to the total signal could not be neglected and fortunately could be derived from the

temperature dependence of the signal obtained with (TMDTDSF)~Re04. Below the anion

ordering transition, the spin susceptibility of this salt goes to zero exponentially while entering

a semi-conducting phase [14]. At low temperature, the only remaining magnetization comes

from the sample holder and from the sample core diamagnetization. We have fitted this

contribution with a law of the type : M=

A/T + B. After removing this contribution, we

obtained the genuine temperature dependence of the spin susceptibility for

(TMDTDSF)~Re04 with a room temperature value, xs=5.s8x10~~emu/mole. These

Faraday results are in fair agreement with the spin susceptibility data obtained from ESR

measurements performed on a single crystal. Faraday and ESR data are displayed together in

figure I. ESR data were normalized to the room temperature value obtained with the Faradaybalance technique. Furthermore, a calibration of the room temperature ESR susceptibility

against (TMTSF)2PF6 leads to xs =

5.3-5.8 x10~~ emu/mole (see Tab. I). The temperature

dependence of xs is roughly linear above the anion ordering transition and can be fitted below

163K by a law of the type xs~T~~exp(-A/T) (activated paramagnetism), with an

activation gap A=

970 K (see Tab. I and Fig. I).


~ ~~~~

~~i~~~~l it)a o

&o

EPR~i

o°

~ 0.0004 .

( ~°

£#0.0002

~i

~l.oa

TEMPERATURE (K)

4a._~i o "

.a~°°*b

* lo

j

~~~~~~~l~iT)°

o EPRlo

I/TEMPERATURE

Fig, I. Top : Temperature dependence of the spin susceptibility for (TMDTDSF)2Re04, showingthe anion ordering transition at TAO

~

163 K, bottom A plot of the type Log (TX s) versus I/T for the

same data gives, below 163 K, an activation gap Am

970 K. These results come from Faraday balance

(*) and ESR measurements (O).

Table 1.

~«~

~ESR 16'l dNMR (~)

(TMTSF)2Re04 1000 (°) 150

(TMDTDSF)2Re04 970 050

xs (300 K~ [10~4 emu/mole]

Faraday ESR Calibration NMR Calibration~P ~~~

(Ref : (TMTSF)2PF~) (Tj Tx /=

Co)

(TMTTF)~PF6 6.4 (*) 220

(TMTSF)~PF6 3.06 (**)(TMTSF)2Re04 2.73 (**) 3.6 2.95

(TMDTDSF)2Re04 5.58 5.3-5.8 5.09~

300

(TMDTDSF)2PF6 4,35 3.7-3.9 100

(°) TOMIC S., Thbse, Universitd Paris-Sud (1986).

(*) CouLoN C., Thbse, Universitd de Bordeaux (1982).(**) See references [35] and [36].

N° 5 ??Se-NMR in (TMDTDSF)~X, X=

PF~, Re04 681

The direct measurement of the sample holder's contribution is no longer possible for

(TMDTDSF)~PF~ since no ordering of the centrosymmetric anions occurs in that system.

Therefore, Faraday spin susceptibility results are reliable only in the high temperature range

when the holder's signal is small and constant. In figure 2, we have combined these last results

with the spin susceptibility derived from ESR measurements previously published [4]. The

room temperature value, Xs =

4.35 x10~~ emu/mole, was obtained from an ESR calibration

against (TMTSF)~PF~ [4]. The same linear temperature dependence is observed down to

60 K associated with a reduction of Xs by a factor 2 between 300 K and 60 K. This decrease is

actually larger than what is currently observed in compounds such as (TMTTF)2Br where

Xs (60 K)/Xs(300 K)=

0.67 [18].

..

o

o

EPRa °

ao

.o

IoE °

~ ~

*~

oo ~

~

°e

~©S

,b

~f'c~

~f T00

(K)

Fig.

from araday

esistivity elow = 100 K.


The NMR experiments were performed with a commercial Fourier transform pulsed

spectrometer, operated at a frequency of 75.6 MHz (stationary field Bo=

9.5 T). For the

measurements of the spin lattice relaxation the nuclear magnetization was inverted. After a

variable time delay ran echo sequence was applied and the echo was sampled as a function of

the delay. Extensive pulse phase cycling was used to extract the z-component of the

magnetization. One half of the echo was Fourier-transformed and the imaginary partintegrated. At high temperatures the recovery of the magnetization was observed to be

exponential over more than one decade inr.

Single crystal spectra were recorded using a standard echo sequence. Figures 3 and 4 give

some examples of NMR lineshapes obtained when the static field is perpendicular to the

stacking axis for (TMTSF)~X and (TMDTDSF)~X series.

The four selenium compounds display a well resolved spectrum showing four resonance

lines according to the four magnetically non equivalent sites in the unit cell (see Fig. 4 for

(TMTSF)~PF~). Figure 3 (left) shows the temperature dependence of ??Se NMR of

(TMTSF)~Re04. This compound undergoes a phase transition towards an insulating ground

Fig. 3. -Left ??Se NMR spectra at different temperatures for a single crystal of (TMTSF)2Re04(a Bo). From top to bottom : 285 K, 186 K, 178 K, 165 K, 152 K, 135 K. T~o

=180 K. Right :

??Se NMR spectra at different temperatures for a single crystal of (TMDTDSF)2Re04 (a I Bo). From

top to bottom : 230 K, 200 K, 180 K, 150 K, 130 K, 120 K. T~o=

163 K. Frequency axis is in ppmagainst the ??Se resonance of liquid H2Se04.

N° 5 ??Se-NMR ba (TMDTDSF)2X, X=

PF6, Re04 683

300 O -300

PPm

ioooo sooo o -sooo -ioooo

ppm

Fig. 4. Top :??Se NMR spectra for a single crystal oi I'I'MiSF)2PF6 (a I Bo) at room temperature.

Bottom :??SeNMR spectra for few aligned crystals of (TMDTDSF)2PF6 (aIIBO) at T=165K.

Frequency axis is in ppm against the ??Seresonance of liquid H2Se04.

state at TAO=

180 K, driven by an ordering of the non-centrosymmetric anions. The volume

of the unit cell doubles below TAO and the resolved spectrum can be attributed to locallyresolved chemical shifts as the shifts related to Xs (Knight shifts) vanish exponentially in the

semiconducting ground state.

As far as the ??Se-NMR of mixed S-Se compounds are concemed, a broad structureless

resonance line is observed with a width of about 1000ppm near room temperature. The

??Se-NMR lineshape of (TMDTDSF)~PF~ is nearly temperature independent down to low

temperatures. A broadening of the line at very low temperature can be attributed to

fluctuating precursors of the AF ordering at 7K. The temperature dependence of

(TMDTDSF)2Re04 NMR spectra is however different, figure 3 (right), since the ??Se

lineshape is resolved in the anion ordered phase at low temperature. Four non-equivalentselenium sites are observed in agreement with an altemate packing of TMDTDSF molecules

along the a-axis.

It is tempting to attribute the origin of the non-resolved spectrum at high temperature to a

distribution of local Knight shifts due to the existence of some residual disorder in the

molecular packing. These data tend to suggest that the strong disorder evidenced by Laue

scattering experiments in PF6 salts is also present with Re04 anions [13]. A better

understanding of the effect of disorder on the lineshape will await an improved knowledge of

the Knight shift and Knight shift anisotropy in these low dimensional conductors.


To improve the signal to noise ratio especially at high temperatures for relaxation

experiments, several crystals aligned along the stacking (a-) axis were used. ??Semeasure-

ments in (TMTSF)~PF~ seem to support the idea that the hyperfine interaction is mainlyisotropic in the plane perpendicular to the stacking axis. In this compound the anisotropy of

Ti was about 15 §b [8]. If we assume that the same is valid for (TMDTDSF)2PF6, the error

made by using aligned needles due- to the anisotropy of Ti is somewhat within the

experimental error of about ± 10 §b.

3

OI c

W WE W

O

' °

I I-O~2

O

ii

I jog(T-T~) lOi .

II~

~. .

,

O 'O

ig.

T~= 100 K

Tj

line s1/2.


PF6, Re04 685

allowing the onset of magnetic ordering at 7 K and the establishment of 3D magnetic critical

fluctuations up to 25 K as shown by the square root divergence of Tj This regime will be

discussed more extensively in the next section. Figures 6 and 7 show the dependence of

Tj as a function of temperature for (TMDTDSF)~Re04 and (TMTSF)~Re04, respectively.

The behaviour of Tj versus T is similar to (TMDTDSF)~PF~ with the same slight upward

curvature at high temperature. However, the values of Tj~ at room temperature are quite

different. As will be shown below, this can be attributed to different values of Xs. Both

systems undergo a transition into a semiconducting ground state driven by an ordering of the

non centrosymmetric anions at TAO=

180 K for (TMDTDSF)2Re04 and TAOm

163 K for

(TMTSF)~Re04. The susceptibility becomes activated, leading to a sharp drop of

Tj

5I

~ »

E ~~

4 j3~-~

3

2

X~Tla.u.

2

/

/~

o"

loo 200 300

T/K

Fig. 6. Temperature dependence of Tj for ??Se in a polycrystalline sample of (TMDTDSF)~Re04.The clear change in the curvature of Ti is the signature of anion ordering at T~o

=

163 K. For details of

the fit see text. The insert shows Tj versusX)T above T~o.

~ l .5

wE~

iW

i .o

2

X2Tla.u.

O.5 ~'

/

/

~/~

O-O

loo 200 SOD

T/K

Fig. 7. Temperature dependence of Tj for ??Se in a polycrystalline sample of (TMTSF)2Re04. The

clear change in the curvature of T/ is the signature of anion ordering at TAO=

180 K. For details of the

fit see text. The basert shows Ti~versus

Xl T above T~o. Xs was taken from reference [35].


Discussion.

In order to test the possible influence of disorder on the ??Se Knight shift of (TMDTDSF)~X

we decided to carry out model molecular orbital calculations. The simplest way to tackle the

problem is by considering a TMDTDSF molecule in the vicinity of two nearest neighboursalong the chain. As mentioned above, once the dimerization along the chain is taken into

account, eight different units of this type can be generated (Fig. 8). Because of the

stoichiometry the mean charge per TMDTDSF donor in (TMDTDSF)~X is +1/2e.

Consequently it should be possible to gain some insight conceming the influence of disorder

on the selenium Knight shift by calculating the selenium electron-spin density associated with

the highest occupied molecular orbital (HOMO) of the central (TMDTDSF )+ ~~~ in the eight[(TMDTDSF)+

~~~]~trimeric units schematically shown in figure 8.

I ~Se ~ -Se

~~~ Se

jTMDTDSF)~ X

~~ -Se

.3 -Se 4 -Se

~Se -Se

~

-Se -Se

5 ~Se 5 -Se

-Se -Se

Se4p~ s 3p~ X -Se -Se

? ~Se B -Se

-Se -Se

-Se ~Se

Fig. 8. Left, illustration of the overlap of thear

orbitals in the (TMDTDSF)2X stacks. Right,

schematic representation of the eight different environments of a TMDTDSF donor when nearest

neighbour interactions along the chain are considered.

An effective one-electron Hamiltonian of the extended Hiickel type [23] and a basis set of

single f Slater type orbitals were used in the calculations. All valence electrons were taken

into account. The exponents (f) and the atomic parameters (H,, ) used are summarized in

table U. The off-diagonal matrix elements of the Hamiltonian were calculated according to

the modified Wolfsberg-Helmholz formula [24]. The geometry of the trimeric units 1-8 was

fixed in the following way. First, an ideal DTDSF molecule (I,e., hydrogen atoms were used

instead of the methyl groups) was build on the basis of accurate structures for other

(TMTSF)2X and (TMTTF)~X salts. The geometrical parameters for this ideal DTDSF were


PF~, Re04 687

Table II. Exponents and parameters used in the calculations.

Atom Orbital H,, (eV) f

Se 4s 20.5 2.440

4p 13.2 2.070

S 3s 20.0 1.817

3p 13.3 1.817

C 2s 21.4 1.625

2p IA 1.625

H Is -13.6 1.300

chosen to be : C~=

C~ 1.357 h, C~-Se : 1.876 h, Cp-Se : 1.896 h, Cp=

Cp 1.332 h,C~-S :

1.7361, Cp,-S :1.7451, Cp,

=

Cp.. 1.343 h, Se-C~-Se : 114.2°, C~-Se-Cp 94.2°,

S-C~-S : 114.0°, C~-S-Cp,. 96.3°, where C~ and Cpjp, refer to carbon atoms of the inner and

outer double bonds respectively. Second, the center and the direction of the inner

C=

C double bond of the three molecules were assumed to be in the same position as in the

average structure of Thorup etal. [25]. Since electron repulsions are not explicitelyconsidered in extended HUckel calculations, we will assume that the relative change of

electron and spin densities along the series of trimers 1-8 are very similar. The calculated

selenium HOMO electron densities for the central donor (D+ ~~~) of the eight trimeric units

flJ+~~~]~

of figure 8 are reported in table HI. These electron densities spread over 0.0128 e,

I-e- around 10§b of the total selenium HOMO electron density. Disorder clearly has a

noticeable effect on the selenium HOMO electron density. In addition, two remarks should

be placed here. First, the values of table III reflect the influence of different electron transfer

integrals on the selenium electron density of the central donor. It is well known, that single-f

type calculations underestimate the magnitude of these transfer integrals [26], so that the

electron density difference of table III are likely to be too small. Second, the electrostatic

Table III. -Selenium HOMO electron density calculated for the central donor molecule

(D+~~~) of different trimeric units. See figure 6 for labeling.

Unit Electron Unit Electron

0.1332 5 0.1340

2 0.1344 6 0.1405

3 0.1358 7 0.1277

4 0.1368 8 0.1400

interaction with the anions has not been considered. Since there are two possible ways to

place a TMDTDSF donor with respect to the acceptor, there are twice as much different

environments for a selenium atom. This is likely to induce a considerable additional spread.With these two observations in mind it is clear, that the 10 §b spread of the selenium HOMO

electron density should only be considered as a lower limit. A more quantitative estimation

would require calculations of the spin densities including explicitely both electron repulsion


and donor-acceptor interactions. Although the lo §b spread does not account for the observed

shape of the ??Se spectra, we believe these results suggest quite a sizeable control of the ??Se

Knight shifts by disorder.

Electronic degrees of freedom modulate the hyperfine interaction in conductors. Especiallyin the (TM)~X salts and their derivatives this tums out to be the dominant mechanism for

nuclear relaxation. However, the individual properties of each salt are well reflected in the

details of the nuclear relaxation, though the general behaviour can be described by an

uniform theory.We first look at the Tj versus T data of (TMDTDSF)~PF~ in the non ordered phase well

above T~ where the lattice softening effect are sufficently small to be ignored. From the EPR

data of figure 2 and X-ray measurements [13], this corresponds to the temperature domain

T~30K. Within this paramagnetic domain figure 3 shows, that at sufficiently high

temperatures, Tj presents an upward curvature which is typically found in Q-I -D conductors

[8, lo, 27]. This behaviour is well known to result from the uniform (qm

0) spin fluctuations

which dominate the relaxation. Previous calculations [9, 12] have shown, that in the presence

of spin fluctuations characterized by harmonic paramagnon dynamics, the small q integrationof the basic expression for Tj [28], namely :

Tj=

2 y((1/2 ar)~ T d~q(A~ ~X[ (q, w~)/w~ (1)

where A~ is the hyperfine coupling constant and Xi is the imaginary part of the transverse

retarded spin response function, can be uniquely expressed in terms of the temperaturedependent static and uniform magnetic susceptibility Xs, that is

Tj ~[qm

0]=

2 y((1/2 ar)~ (Ao(~ T ld~qX[ (q, w~)/w~q=0

~~~

~

cO TjXs(T)j~~~~~~

In one dimension this reduces for q m0 to

Tjiiqmoi=

coTxj(T) (3)

with Co=

dry( (Ao(~. We want to emphasize, that this expression is obtained in the so-called

collisionless (non-diffusive) limit where there is no field dependence as long as T~ w

~

with

w~ as the electronic Larmor frequency. This limit is consistent with the absence of field

dependence of Ti up to 6 T in systems such (TMTTF)~PF~ or (TMTTF)~Br and it provides an

indication for the validity of equation (3) [29]. From the Xs and T/ data we see, that the plot

of figure 9 shows, that the relation (3) for D=

I is indeed well satisfied for T ~150 K. So,

this result is of interest since it shows, that both Tj and Xs are influenced by ID paramagnons

which are decoupled from long wavelength charge excitations as can be observed in the

resistivity measurements.

From figure 9 deviations to the Tj ~~ TX j law become clearly visible below T~. These

deviations come from the antiferromagnetic spin fluctuations centered at qm2 k~ in one

dimension and which are expected to grow as the temperature is lowered. The correspondingcontribution of this large q value to Tj is well known [12, 30]. Indeed at small w, one has :

Ti ~(q"

2 kF)"

Yl/(4 ar)jN (EF)l~ (AQO(~ ~k(2 kF, T)=

Cl (4)


PF~, Re04 689

50.5

W '~~E '» *

.~ E .

.

, O

~2 'I.*

~.

~'i.oo-S Xz~/~

~l.0

4~k'~

0 2

X~Tla.u.

Fig. 9. Tj versusXl T of ??Se in a polycrystalline sample of (TMDTDSF)2PF6. The straight line is a

fit to equation (I), which determines the q =0 contribution. Deviations from this linear behaviour are

caused by the q m2 k~ contribution. The insert shows the 2 k~ part of T/ versus

Xl T. It was calculated

by sub~acting the q =0 contribution from Tj~.

where in the presence of a correlation gap A~ the auxiliary susceptibility can be written in the

following scaling form :

k(2 kF, T)=

Jf(T~/EF) k(T/T~). (5)

Here g(T~/E~)m (T~/E~)~~° gives the power law contribution for energy scales above

T~ where 0~ yo ~

l. At lower temperatures one has k(T/T~)m

(T/T~)~ Y It tums out, that

below T~ elaborate calculations show, that y reaches the maximum value y =

I which is exact

in absence of magnetic anisotropy [21]. It should be mentioned, that the scaling form (5)neglects all transients when the electronic system evolves to the regime of strong electronic

Umklapp processes near T~. Therefore Ci is a temperature independent quantity as long as

the strong coupling regime prevails for the uniform charge degrees of freedom and the model

for the temperature dependence of Ti becomes

Tj=

Co TX I(T)+ Ci. (6)

From figure 9 one can see, that the low temperature deviation to the Tj TX / law does

extrapolate to a temperature independent contribution like (4). One can now single out the

deviations to the uniform contribution (see insert of Fig. 9). The quantity (Ti T)~~near

2 k~ is according to (4) directly proportional to k(2k~, T). Figure lo shows the resultingk(2 k~, T) versus T variation and it gives nice confirmation of the power law behaviour of

k(2k~,T) together with the relevance of ID Umklapp processes and the value of

y =

I in this compound. From the same figure one can observe that the strong couplingregime of correlations which leads to y =

I seems to be fully established only below 80 K or

so, I-e- below the resistivity minimum at T~ mloo K. There exists thus a sizeable temperature

domain, between 80 and loo K, dominated by transients associated to the crossover from the

weak to the strong Umklapp coupling regime. These effects are non-universal and depend on

microscopic details of the system. In this respect, the comparison with previous observations


~ 2

d'

~~

i~

~~

O

O/K

ig. 10.- emperature

MDTDSF)~PF6.

(2k~,T)~ (T/E~)~? (y« I). Lowtemperature

data were fittedwith y = I strong

scattering regime).


PF6, Re04 691

the interplay between the SP and the AF ordering it is necessary to specify such a mechanism.

Microscopic calculations for the quasi ID electron gas in the presence of non-zero interchain

single electron hopping ti and a lD correlation gap A~ ~ ti have shown, that the transverse

single electron band motion is frozen and has no chance to develop at low temperature II Ii.

Transverse one-particle virtual motion being always possible, it will lead to an effective AF

interchain exchange interaction Ji~

2 #rv~(t[/A~)~, where t[~ ti is renormalized by lD

many-body effects (see II Ii). This coupling is two-particle like and leads to an interchain

electron-hole pair propagation which is necessary to the transverse ordering of AF

correlations. According to the microscopic results of reference II Ii the critical parameter

rAp(fAp r ~~~) vanishes at the critical point and is given by

rAF =8 (2 y)- IL j(T/T~)- Y ii

»y& (T T~)/T~ (T- T~) (8)

where (=

Ji/#rv~ and 0~

8~

l is a positive constant, that gives the contribution of the

exchange to the transition above T~. Owing to the spin-charge separation of the ID electron

gas problem [21], the 2 k~ susceptibility exponent y namely

Y =2 yp i y~ (9)

contains two independent contributions, one linked to the spin (y,) degrees of freedom and

the other for the charge (y~). In presence of strong Umklapp effects and a correlation gap

one has y~ =0. As for the spin part, the bosonization technique tells us that y, is directly

connected to the spin compressibility K, [33], that is

y, =2 #rv, K, (lo)

where v, is the long wavelength spin degrees of freedom velocity introduced previously. It

tums out, that K,=

(2 #rv,)~ coincides with the zero temperature susceptibility per spin of

the mode. Under the influence of SP fluctuations which favor the formation of spin singletdimers, Xs does not saturate to the temperature independent value 2K, but is sizeablydepressed at low temperature as it is clearly seen from the EPR data of figure 2 below 40 K or

so. As suggested in reference [34] in the context of precursors to the SP ordering of the

(TMTTF)~PF6 compound, y, can be taken as a temperature dependent quantity which can

be directly related to the observed depression in Xs. That is

y(T)=

2 y,(Tlp)- i xs(Tlp)/xs(T) (i1)

where Tip is the ID energy scale for the SP lattice softening. From X-ray and EPR data it

corresponds roughly to 40K. Taking y,(T(p)~~=

l in absence of SP effects, the ratio

Xs(T(p)/Xs(T)can then be estimated for the observed depression in Xs(T) in figure 2. From

this semi-phenomenological approach, it is clear that as long as y (T) is positive, spin degreesof freedom are still present and they can bring the critical parameter rAp to zero at a finite

value for T~. From (8) the latter is given by

T~=

Tp ii (& y(T))- i ii +ii (& y (T))- nil/Y~T~ (12)

This is clearly anon vanishing quantity as long as y (T ) is positive. From ( II ) a rough estimate

would predict, that if the depression of the susceptibility due to SP ordering remains less than

50 fb, the onset of AF ordering is still possible. From the Tj versus T data of figure 5, AF

critical effects are observed up to 20 K or so, which is consistent with less than 50flb of

JOURNAL DE PHYSIQUE I T 2. N' 5, MAY 1992 27


reduction of Xs(T) down to 20 K and with the AF ordering arising in the same temperature

range. It is worthwhile to note at this point that the depression of the susceptibility seen in

(TMDTDSF)~PF~ is similar to the one already reported for the (TMTTF)~SbF~ compound in

the same range of temperature [32]. For the latter, it was proposed that even if ID precursors

effects are neglected, the kinetic interchain coupling can play a role in the interplay between

the SP and the AF ground states.

Now let us tum to (TMDTDSF)2Re04 and (TMTSF)2Re04. At high temperatures, above

TAO, both systems relax according to equation (3). In this temperature region the electronic

susceptibility shows a linear increase with temperature (Xs WA + BT ). The constants A and

B were adapted to give a good approximation of the real high temperature Xs data (data of

(TMDTDSF)~Re04 as published here, data for (TMTSF)2Re04 were taken from reference

[35]). Thereafter the calculated susceptibility was normalized to its value at room temperature(x~(RT )

=I ). The idea of this treatment is to get rid of possible troubles encountered by the

calibration of x~. On the other hand there is usually no doubt about the temperature

dependence of Xs, as long as only relative values are concemed. To account for a better

comparison of all systems the normalization was also made for Xs of (TMDTDSF)2PF6. Later

in this paper, we will show how the ??Se relaxation can provide the absolute values of

Xs for (TMDTDSF)2PF6, (TMDTDSF)~Re04 and (TMTSF)2Re04. Following the above

discussion, Ci

in equation (4) should be set to zero in the high temperature regime (metallic

phase, weak coupling). Using the above approximations in equation (3) one gets a polynomof degree 3 in T, which can be fitted easily to the NMR data of figure 5. The agreement

between the fit and the data is quite good. The inserts in figure 6 and figure 7 show

Tj versusx) T above TAO for both compounds. The linear dependence with a zero intercept

for Tj~ at zero temperature is obvious. Below the anion ordering temperature, both

components show a semiconducting behaviour. Low temperature data were fitted to a law of

the form :

T/=

CT~ exp(- 2 A/T) (13)

were C is a constant. This is of course still the simple relation of equation (3), where for

Xs an activated paramagnetism was assumed. A is of the order of 000 K. Even a small error

in the temperature measurement for Tj~or Xs has a strong influence on the analysis and

therefore the direct fit seems to be more reliable. The values of A as extracted from the fit are

given in table I.

So far, we have made no use of the coefficient Co, which is the slope of Tj~versus

Xl T in the high temperature regime. Co contains the details of the ??Se hyperfine interaction

(hfi) and, since our Xs data are normalized to unity, the value of Xs at room temperature. So,from an analysis of Co an absolute calibration of Xs should be possible. In other words, a

measure of T/~can be used to probe the electronic susceptibility [8]. However, the

conduction electrons are in #r-orbitals and the observed hyperfine interaction is caused by a

dipolar interaction together with a polarization of lower orbitals (core polarization), which

makes it impossible to calculate correctly. Thus for the following analysis we made the

assumptions, that the hyperfine interaction is the same for both (TA4TSF)2X and

(TMDTDSF)2X. This assumption is supported by very similar molecular and cristalline

geometries in the two compounds. Furthermore, only values from powdered samples will be

used. We want to remind the reader, that the resonance of (TMDTDSF)~X is«

powderlike»

as a consequence of the intrinsic disorder which leads to a continuous distribution of Knightshifts. We hope to include this effect, at least to some extent, in the powder mean values of

the hfi. So, if Co and the absolute value of Xs are known for one compound,

x~ for other Se-containing materials in which Tp ~(T ) has been measured, can be derived by a


PF6, Re04 693

simple scaling argument. The values for Xs, thus found by this procedure, have been

summarized in table I. Co was taken from measurements in (TMTSF)2PF~ in reference [8]

and Xs from reference [36]. The determination of Xs via Ti measurements has also been used

in an other context, namely under pressure [8, 29].

Summary.

The magnetic and NMR studies of the mixed S-Se salts presented and discussed in this article

complete earlier works performed on sulfur or selenium compounds. (TMDTDSF)2PF6 is a

unique material in the sense that all regimes predicted by the theory can be observed

experimentally. A lD regime with dominant q m0 spin fluctuations is observed between 300

and 180K (T/~ ~TX/(T)) whereas the contribution to the relaxation coming from

2 k~ spin fluctuations takes over gradually below 180K and follows the strong Umklapp

scattering temperature dependence (XsDw(2k~)~Tp~) only below T~=100K. The

2 k~ spin-phonon coupling contributes to a further lowering of the uniform susceptibilitybelow 60 K. However, the tendency of the lD antiferromagnetic chain towards dimerization

is not strong enough to stabilize a SP ground state. Instead, SDW ordering is achieved below

7 K with 3D 2 k~-SDW fluctuations detectable via Tj~ measurements up to 25 K or so,

(Tj T T~ ~~~).

Acknowledgements.

One of us (B.G.) wants to thartk the Deutsche Forschungsgemeinschaft for financial supportduring his stay at Orsay. We acknowledge P. Wzietek, E. Barthel, S. Ravy and J. P. Pougetfor several discussions.

This work has been partly supported by the ESPRIT-Basic Research Action MOL-

COM 312i and the DRET Contract n° 88/198.

References

[1] For a recent review see : Low Dimensional Conductors and Superconductors, NATO ASI series,

D. J6rome and L. G. Canon Eds. (Plenum Press, New York, 1987) ;

POUGET J. P., Organic and Inorganic Low Dimensional Crystalline Materials, NATO ASI

P. Delhaes and M. Drillon Eds. B168 (Plenum Press) pp. 185.

[2] CARON L. G., CREUzET F., BUTAUD P., BOURBONNAJS C., JtROME D. and BECHGAARD K.,

Synth. Met. 27, B123 (1988).

[3] TAKAHASHI T., JtROME D. and BECHGAARD K., J. Phys. Lett. France 43 (1982) L565.

[4] AUBAN P., JtROME D., LERSTRUP K., JOHANNSEN I., JORGENSEN M. and BECHGAARD K., J.

Phys. France 50 (1989) 2727.

[5] CREUzET F., TAKAHASHI T., JtROME D. and FABRE J. M., J. Phys. Lett. France 43 (1982) L755.

[6] K~NOSHITA N., Synth. Met. 19 (1987) 317.

[7] MCBRJERTY V. J., DOUGLASS D. C. and WUDL F., Solid State Commun. 43 (1982) 679.

[8] WzJETEK P., CREUzET F., BOURBONNAIS C., JtROME D., BATAIL P. and BECHGAARD K.,

preprint.[9] BOURBONNAIS C., WzJETEK P., CREUzET F., JtROME D., BATAJL P. and BECHGAARD K., Phys.

Rev. Lett. 62 (1989) 1532.

[10] CREUzET F., BOURBONNAJS C., CARON L. G., JtROME D. and MORADPOUR A., Synth. Met. 19

(1987) 277.

[I I] BOURBONNAIS C. and CARON L. G., Int. J. Mod. Phys. B 5 (1991) 1033.

[12] BOURBONNAJS C., preprint.


[13] LJU Q., RAVY S., SENHAJJ A., POUGET J. P., JOHANNSEN I. and BECHGAARD K., Synth. Met. 42

(1991) 1711.

[14] AUBAN P., JQROME D., JOHANNSEN I. and BECHGAARD K., Synth. Met. 42 (1991) 2285.

[15] PARKJN S. S. P., J. Phys. Colloq. France 44 (1983) C3-l105.

[16] MORET R., POUGET J. P., Comts R. and BECHGAARD K., Phys. Rev. Lett. 49 (1982) 1008.

ii?] Pascal's constants were taken from : SELWOOD P. W., Magnetochemistry (Interscience Publishers,

New York, 1956).

[18] WzJETEK P., BOURBONNAIS C., CREUzET F., JQROME D. and BECHGAARD K., Europhys. Lett. 12

(1990) 453.

[19] KANG W., Thbse, Universit6 Paris-Sud (1989).[20] COULON C., J. Phys. Colloq. France 44 (1983) C3-885.

[21] SOLYOM J., Adv. Phys. 28 (1979) 201;

EMERY V. J., Highly Conducting One Dimensional Solids, in J. T. Devreese, R. P. Evrard and

V. E. VanDoren Eds. (Plenum Press) pp. 247.

[22] BOURBONNAJS C., STEIN P., JtROME D. and MORADPOUR A., Phys. Rev. B 33 (1986) 7608 ;

MORIYA T. and UEDA K., Solid State Commun. IS (1974) 169.

[23] HOFFMANN R., J. Chem. Phys. 39 (1963) 1397.

[24] AMMETER J. H., BUERGI H. B., THrBEAULT J. and HOFFMANN R., J. Am. Chem. Soc. 105 (1978)6093.

[25] THORUP N. et al., to be published.[26] WHANGBO M. H., WILLIAMS J. M., BENO M. A. and DORFAfANN J. R., J. Am. Chem. Soc. 105

(1983) 645.

[27] BOURBONNAJS C., WzIETEK P., JtROME D., CREUzET F., VALADE L., CAssouX P., Europhys.Lett. 6 (1988) 177 ;

SODA G., JtROME D., WEGNER M., ALIzON J., GALLICE J., ROBERT H., FABRE J. M. and GIRAL

L., J. Phys. France 38 (1977) 931;

BouRBoNNAis C., HENRIQUES R. T., WzJETEK P., KONGETER D., VOIRON J. and JtROME D.,

Phys. Rev. B 44 (1991) 641.

[28] MORIYA T., J. Phys. Soc. Jpn 18 (1963) 516.

[29] WzJETEK P., Thbse, Universit6 Paris-Sud (1989).[30] BOURBONNAJS C., CREUzET F., JtROME D., BECHGAARD K. and MORADPOUR A., J. Phys. Lett.

France 45 (1984) L755.

[31] CREUzET F., BOURBONNAJS C., CARON L. G., JQROME D. and BECHGAARD K., Synth. Met. 19

(1987) 289.

[32] VACA P. and COULON C., Phase Transition 30 (1991) 49 and references therein.

[33] EFETOV K. B., Sov. Phys. JETP 43 (1976) 1221.

[34] BOURBONNAJS C., Proceedings of the NATO Advanced Study Institute on Low Dimensional

Conductors and Semiconductors, in D. J6rome and L. G. Canon Eds. (Plenum PublishingCorp.), pp. 155.

[35] FORRO L., COOPER J. R., ROTHAEMEL B., SCHiLL~NG J. S., WEGER M., SCHWErrzER D., KELLER

H. J. and BECHGAARD K., Synth. Met. 19 (1987) 339.

[36] MiLJAK M., COOPER J. R. and BECHGAARD K., J. Phys. Colloq. France 44 (1983) C3-893.

One-dimensional physics in organic conductors (TMDTDSF)2X, X ...

Documents

Transcript of One-dimensional physics in organic conductors (TMDTDSF)2X, X ...