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

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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�

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 temperature

dependence

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.

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)~X

series are isostructural and there exists _no

major

difference at first

sight

between _a

compound

such _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

by considering

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)~X

series. 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)~PF6 belong 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

temperature regime

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

usually spread

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 protons

simply

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 yet

confirmed, 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

typical

dimensions of 5 _x 0.5 _x 0.2

mm~.

Magnetic susceptibility

results _are obtained from two

experimental techniques

_{: a}

Faraday

balance 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

magnetic field,

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 _x

10~~

_{emu/mole and x~}

= 3.71 _x

10~~

_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}

Faraday

balance

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 EPR

lo

I/TEMPERATURE

Fig,

I.

Top

_:

Temperature dependence

of the

spin susceptibility

for (TMDTDSF)2Re04,

showing

the 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 ^A m 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 _x

10~~ _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

EPR

a °

a o

.o

o I

E ^°

~ ^~

~ *

o ~ o

~

° e

~©

S

,b

~f'

~

c

f

~

T

00

(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 _part integrated.

At

high temperatures

^the recovery of the

magnetization

_was observed _to be

exponential

over more than _one decade in _r.

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 ppm

against

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 ??Se _resonance 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

locally

resolved 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-equivalent

selenium 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.

??Se

_measure-

ments in

(TMTSF)~PF~

_seem to

support

^the idea that the

hyperfine

interaction is

mainly isotropic

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

O

I c

W W

E W

O

' ^°

I I-O

~2

O

ii

I jog(T-T~) lO

i .

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 TAO m 163 K for

(TMTSF)~Re04.

The

susceptibility

becomes

activated, leading

to a

sharp drop

of

Tj

5 I

~ »

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

versus

X)T

_above

_T~o.

~ ^{l .5} Ew

~ i

W 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}

neighbours along

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

Se

_{4p~ s 3p~ X -Se -Se}

? ~Se B -Se

-Se -Se

-Se ~Se

Fig.

8. Left, illustration of the

overlap

of the ar 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

explicitely

considered 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.

Especially

in 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

(q

m

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

integration

of 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

temperature dependent

static and uniform

magnetic susceptibility

_Xs, that is

Tj

~[q m

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 m 0 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}

corresponding

contribution 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

5 0.5

W

'~~

E '» *

~ E . .

.

, O

~2 _'I

.*

~ _.

~'i.o

o-S Xz~/~_~ ^l.0

4~

k'~

0 2

X~Tla.u.

Fig.

9.

Tj

_versus

Xl

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}

m 2

k~

contribution. The insert shows the 2k~ 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

resulting k(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

coupling regime

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~

m loo 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).

_Low

temperature

data

_{were fitted} with 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 singlet dimers,

_Xs does not saturate to the temperature

independent

value

2K,

but is

sizeably depressed

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 degrees

of 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 DEPHYSIQUEI 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,

C

i 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

polynom

of

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

_versus

x)

_{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

Knight

shifts. 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 m 0

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

susceptibility

below 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

support during

his

stay

at

Orsay.

We

acknowledge

P.

Wzietek,

E.

Barthel,

S.

Ravy

and J. P.

Pouget

for 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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Organic

and Inorganic Low Dimensional

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