HAL Id: jpa-00246576 https://hal.archives-ouvertes.fr/jpa-00246576 Submitted on 1 Jan 1992 HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. One-dimensional physics in organic conductors (TMDTDSF)2X, X = PF6, ReO4 : 77Se-NMR experiments B. 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-dimensional physics in organic conductors (TMDTDSF)2X, X = PF6, ReO4 : 77Se-NMR experiments. Journal de Physique I, EDP Sciences, 1992, 2 (5), pp.677-694. <10.1051/jp1:1992173>. <jpa-00246576>
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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>
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).
680 JOURNAL DE PHYSIQUE I N° 5
~ ~~~~
~~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
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.
684 JOURNAL DE PHYSIQUE I N° 5
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.
N° 5 ??Se-NMR in (TMDTDSF)2X, X=
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].
686 JOURNAL DE PHYSIQUE I N° 5
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
N° 5 ??Se-NMR in (TMDTDSF)2X, X=
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
688 JOURNAL DE PHYSIQUE I N° 5
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)
N° 5 ??Se-NMR in (TMDTDSF)2X, X=
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
690 JOURNAL DE PHYSIQUE I N° 5
~ 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).
N° 5 ??Se-NMR in (TMDTDSF)2X, X=
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
692 JOURNAL DE PHYSIQUE I N° 5
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
N° 5 ??Se-NMR in (TMDTDSF)2X, X=
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.
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