Nuclear relaxation and electronic correlations in quasi-one-dimensional organic conductors. II. Experiments

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Nuclear relaxation and electronic correlations in quasi-one-dimensional organic conductors. II.

Experiments

P. Wzietek, F. Creuzet, C. Bourbonnais, D. Jérome, K. Bechgaard, P. Batail

To cite this version:

P. Wzietek, F. Creuzet, C. Bourbonnais, D. Jérome, K. Bechgaard, et al.. Nuclear relaxation and

electronic correlations in quasi-one-dimensional organic conductors. II. Experiments. Journal de

Physique I, EDP Sciences, 1993, 3 (1), pp.171-201. �10.1051/jp1:1993123�. �jpa-00246707�

Classification

Physics

Abstracts

76.60E 74.70K 75.40E 75.50E

Nuclear relaxation and electronic correlations in quasi-one-

dimensional organic conductors. II. Experiments

P. Wzietek

('~~),

F. Creuzet

("*),

_C. Bourbonnais

("~),

_D.

_Jdrome('),

K.

Bechgaard (3)

and P. Batail

(')

(1) Laboratoire de

Physique

des Solides, Universitd de Paris-Sud, bit. 510, 91405

Orsay,

France (2) Centre de Recherche _en

Physique

du Solide, Universitd de Sherbrooke, Sherbrooke,

Qudbec,

Canada JIK-2Rl

(3) H. C. Oersted Institute, DK-2100

Copenhagen,

Denmark

(Received 22

April

J992,

accepted

in

final form

4 September 1992)

Abstract. In this paper we collect and detail _recent results

conceming

~~Se and '~C nuclear relaxation rate measurements obtained _on several representatives ^{of the} (TMTSF)~X and (TMTTF)2X series of

charge

transfer salts _{as a} function of temperature and hydrostatic _pressure.

From the temperature ^and pressure

dependences

of

Tj',

for the compounds (TMTTF)2PF6, (TMTTF)2Br,

(TMTSF)~PF~

and

(TMTSF)~Cl04,

_{we are} in _a position to extract the nature, the

amplitude,

the statics, the

dynamics

and finally the

dimensionality

of

spin

correlations that characterize the unified

phase diagram

of both series of materials.

1. Introduction.

In this second paper of the

series,

_we review and

complete

the

analysis

of the

??Se

_and

~~C nuclear relaxation data obtained for

typical

members of the series

(TMTSF)~X

(X

=

PF~

and

CIO~)

and their

sulphur analogs (TMTTF )2X (X

₌

PF~

and

Br)

_as a function of temperature and

hydrostatic

_pressure. The

pronounced quasi-one-dimensional anisotropy

of these series of materials has been for

long

time considered _{as a}

key ingredient

in the succession of

phase

transitions orchestrated

by

^either the

hydrostatic

_pressure, the anion _or the

sulphur-

selenium substitution _{or even} the

application

of a

high magnetic

field

[Ii.

The

spatial anisotropy

of the electronic _structure

[2]

_promotes the

building

_up of

antiferromagnetic

correlations which _are

omnipresent

in these systems. ^An

important

and related energy scale of these correlations is found for

sulphur compounds

at low pressure and it

corresponds

to the

temperature

T~(100 230K)

below which the

resistivity

loses its metallic character _to

become

thermally

activated

[3] (see Fig, I).

In

compounds

^like

(TMTTF)~Pf~and

(TMTTF )~ASF~, X-ray

measurements

[4] performed

^below _T~ have shown the existence of

(*) Present address _: Unitd Mixte de Recherche CNRS-St-Gobain, 39 Quai L. Lefranc, B-P-135, 93303 Aubervilliers Cedex, France.

~i

p ~~(n cm)

^{~~ ~~~}

~~"~~~~'~~'

i

o°

(TMTTF),Br

~-i

~~-2

(TMTSF)~PF,

~-3

lO~'

~-5

~~-8

(TMTSF)~CIO,

~~-7

io ioo

T(K)

Fig,

I. Resistivity _vs, temperature ^for

representatives

of (TMTTF )~X ^and

(TMTSF)2X

series. After [3] and [I Ii.

another energy scale

Tjp(

40 60

K)

that marks the onset of _a ID lattice

instability

at the wavevector 2

k~

^{and which evolves} to a true 3D

phase

transition _at

Tsp(

lo 20

K)

with _a static lattice distortion of the

spin-Peierls (SP)

character

[3-7].

With the

application

^of _pressure, T~ ^{decreases and for}

(TMTTF)~PF~,

lo kbar of pressure is sufficient _to

yield

the SP state

unstable with respect to the formation of

antiferromagnetic (AF) long

_range order below _a Neel critical

point T~

_S 17 K

[5, 8].

In these pressure

conditions,

the AF

phase

transition presents

the _same features _as those found for

(TMTTF)~Br

at ambient pressure where

T~m

loo K

(Fig. I)

and

T~

m 15 K

[3, 5, 9, 10].

At

higher

_pressure, the temperature range above

T~

^with metallic

properties

increases and

beyond

some critical pressure which

depends

on the

anion

X,

the transport

properties

remain metallic down _to the

vicinity

of

T~

where AF critical fluctuations dominate (T

m

Tn). Therefore,

the characteristics of the AF transition

smoothly

evolve toward those found for the selenides series

(TMTSF [X

with

centrosymmetrical

anions

(X

=

PF~, ASF~, TaF~..

^{and for which}

T~

~ 10 K at ambient pressure

(Fig. 1) [8].

As it is well known, the AF state becomes in _tum unstable

beyond

a critical pressure P

~

ar 7

(20)

kbar

for selenides

(sulphurs) [8, II, 12] leading

for

(TMTSF )~X

to the observation of

superconduc- tivity

at the lower temperature ^scale T~ ^{l K} [I Ii-

Despite

^{the absence of firm evidence for}

superconductivity

ⁱⁿ

sulphur compounds

at very

high

_pressure

[8, 13],

the unified

phase diagram

shown in

figure

2 _can be constructed in which

antiferromagnetism

acts as the central

pivot

^{for both series of materials. Here it is w~rthwhile to note that members of}

,

,~T

loo

' '

,

CONDUCTOR

,

~o ^' ,

q ^{SF -}

~i

^~ _~fi

$

_lo

l$ _SP

§

~ SOW

i

sc

O lo 20 30 40 50

PRESSURE

(kbar)

i i

i i

»

»~

_

» O

« « ji

#

b

C C _/

« /

~ W ~ c

~

>

2

~

~

_~

t

§ a

>

?

~ ~ t _~

Fig.

2. Unified

phase diagram

and energy scales of (TMTTF )~X ^and (TMTSF

~X

series _{as a} function of

hydrostatic

_{pressure or} anion X substitution. The

phase diagram

also includes the

sulphur-selenide

compound

(TMDTDSF)~PF~.

the

recently synthetized

mixed

sulphur-selenium

series

(TMDTDSF )~X (X

₌

PF~, ...) [14]

_are

easily incorporated

to this

phase diagram.

^For

example, (TMDTDSF)~PF6 compound

with T~ m loo

K, Tjp

m

20 K and

T~

m

7 K is located in the

right

hand side of the SP-AF

boundary [14].

What catches the attention in this combined

phase diagram

is

certainly

the existence of

multiple

_energy or temperature ^{scales. One} can also look _at these _as various

length

scales connected with electronic

(spin

or

charge)

_or lattice correlations and which _can be of different

spatial

dimensionalities. It is

clearly

^{of basic}

importance

to

bring

out the

microscopic origin

of

the rich _structure of this

phase diagram

and

especially

to assess the fundamental role

played by

electronic correlations when

extremely anisotropic

conditions

prevail [15, 16].

This _can be

only

achieved

by

^successive confrontations between theoretical

predictions

and

experiments.

It is

along

these lines that _over the past ten years a great ^{deal of efforts} was devoted to the

comparison

of nuclear relaxation _rate measurements in these materials with the

T/

^'

predictions

obtained in the framework of the

quasi-one-dimensional

electron gas model

[5, 14b, 17-23].

As

extensively

reviewed and discussed in the first paper, hereafter noted _as

I,

the great interest in

Tj

^' measurements for the

understanding

of the

phase diagram

of

figure

2 follows from the basic

expression

T/

=

2

y( _{T(gp~ )~}

^~

ld~q

[A~(~ x

[ (q, w~)/w~, ill

which is

directly

related _to the statics, the

dynamics

and the

dimensionality

of

spin

correlations at all

length

scales. These _are connected _to the temperature

dependence

of

spin

correlations and thus _to the temperature ^{variation of}

T/

^' itself.

Putting

the

emphasis

_on the temperature

profile

of

Tj

rather than in its

frequency

_or

field dependence

marks _an

important

difference with

respect

to

previous

NMR

analysis

of low dimensional materials. In the

past,

a lot of

interest _was indeed devoted to the

study

of

spin dynamics

in these systems as it _can be obtained via the field

dependence.

From _a series of works initiated

by

Boucher _et a/.

[24],

it _was found that diffusive

long

wave

length spin

excitations for one-dimensional

spin

chains lead to a

characteristic square ^root

frequency dependence Tj w/

^"~ of the relaxation _rate. The effect of diffusion _was

previously

noted in connection with the EPR linewidth measurements

[25].

The observation of this law in several

insulating

materials

[26]

demonstrated that from the

T/

measurements it _was

possible

_{to get} clear information about the

dimensionality

of the

long

wavelength spin

fluctuations. Later _on, Soda _et al.

[27], presented

in the _same

spirit

_a detailed

analysis

of the

frequency dependence

of

'H

_and

'DTj'

data of the two-chain

organic

conductor

TTF-TCNQ

and showed that for both chains, uniform

spin

fluctuations _are diffusive and one-dimensional in character.

Following

these lines of

thought,

^{similar studies} were

carried _on several series of

organic

materials

[28-30] including

the

Bechgaard

salts

[31-32].

In order to establish the existence of _a diffusive

component

^of

spin

fluctuations from the field variation of

T/

^'

however,

_one must be in _a

position

to

give

_a

precise

evaluation of the relative

weight

of the uniform

(Tj

^'

[q 0]

and the

staggered (Tj

^'

[q

_~

Qol) Parts

^of the relaxation rate, which necessitates _a full temperature

study

of each contribution. At _a

given temperature,

diffusion of low-dimensional

long wavelength spin

fluctuations _can be assessed

only

if

T/

^'

[q

0 w

Tj

^'

[q Qol,

which _tums out to hold in the

high

temperature ^{domain for}

organic

conductors

[5, 21-23, 27, 30].

At T

m 300 K and for _a field of 64 koe _{or so,} Stein _et al.

[32], reported

^the observation of _a weak

frequency dependence

for the

'H

relaxation of

(TMTSF)~PF~

and

(TMTSF)~CIO~

at ambient pressure which _was attributed to a diffusive component. ^Within

experimental

error, all the

'~C

_{and the}

??Se

_data

presented

^{in this work}

however,

do _not show any

frequency dependence

at ambient temperature ^{and for fields} up to 9 tesla. A

possible explanation

for this could reside in the

amplitude

of the extemal field which is not

sufficiently large.

In this _case, the time scale

w/

^' set

by

^{the electronic}

spin-flip

_process

involved in _a scalar

hyperfine

interaction like

(I),

is too

long

with respect to the characteristic

time scale r~

(w~

_r~ ml

)

of processes that do _{not conserve}

spin along

the chains

(e,g.

interchain

tunneling

of uniform

spin fluctuations)

and which cut-off ID diffusion

[24].

If the field necessary to make _{w~ r~}

~ l is very

large,

_one

approaches

the so-called collisionless _or non-diffusive limit

[33]

where collisions have little influence _{on q} 0

spin

fluctuations and _can therefore be

neglected.

In the absence of field

dependence

for the observed

Ti ',

we will

therefore _assume that the collisionless limit is achieved _so that the whole

T/' analysis presented

^{here for} the

sulphur

^and the selenides series focuses

entirely

_on the temperature ^and the pressure

dependences.

This

clearly

contrasts with other

interpretations [31-32]

which associate _a diffusive component to the relaxation _rate of the

Bechgaard

salts in the very low temperature ^domain

(T

4 K

).

Although,

ⁱⁿ

principle,

relaxation time measurement

techniques

do _not need _to be

detailed,

in section 2 _{we comment on some}

particular

_aspects of _our

experimental approach

which have

enabled _us to obtain

high quality

data necessary for _a

quantitative analysis.

Section 3 presents a collection of nuclear

spin-lattice

relaxation results _on

(TMTTF)2PF6, (TMTTF)~Br, (TMTSF)~PF~

and

(TMTSF)~CIO~

_{as a} function of temperature ^and

hydrosta-

tic pressure and which _cover the essential features of the unified

phase diagram

of

figure

2. The

analysis

of the data is made in section 4. There,

predictions

of I for the

quasi-one-dimensional

electron gas model for lD correlation effects, critical behavior and _crossover

phenomena

_are

description

of these

complex

systems can come out from such _an

analysis.

The last part ^{of section 4 is devoted} to a

quantitative analysis

of the temperature ^and pressure

dependences

of the

magnetic susceptibility

_as it _can be extracted from the relaxation rate

measurements in the

paramagnetic regime.

Such _an

analysis

is based _on the well established

empirical relationship (Tj T)~

^' _oz

X/(T)

_{at P}

= I bar between the measured relaxation rate and

magnetic susceptibility

_over a

large high temperature

^domain.

Although

^this way of

obtaining x~(T)

does _not lead _to its absolute value, there _are clear

advantages

ⁱⁿ

using

the NMR

approach

under pressure

compared

to other kinds of

magnetic

measurements.

Indeed,

two standard methods have been used _so far for the

spin susceptibility investigation

in

organic

salts _: the

Faraday

and the EPR

techniques

and these become less accurate when _one reaches

high

_pressure. The

Faraday

^method

yields

_to the absolute value of the electronic

spin

susceptibility,

but it

requires

corrections for the

diamagnetic

contribution from inner-shell

electrons

[34, 35].

Some

Faraday susceptibility

measurements under pressure have been

carried _out

by

Forro _et al.

[36]

on

(TMTSF)~X

but _numerous corrections must be made for the pressure cell and the

transmitting

medium

diamagnetism

contributions. EPR is _{a more} direct method for _Xs measurement but its

sensitivity

decreases

rapidly

when the _resonance line width increases. Under pressure, EPR is _a rather difficult

technique

since the

sensitivity

^of the

spectrometer

may vary under pressure and

actually only

^{few results for}

organic

conductors _are available

[37].

In _{contrast to} other theoretical

interpretations

of

Xs(T)

in

organic

conductors

[38],

_our

approach

is

uniquely

based _on the effect of electron-electron interaction in the framework of the ID electron gaz model _as

developed

in I. When _constant pressure data _are

compared

to the

results of _a constant volume

theory,

it follows that for _a

non-singular quantity

like

x~(T),

it is necessary ^to evaluate the effect of tliermal

expansion

on the

susceptibility.

For this, the full temperature and pressure

dependences

of

Xs(T)

^need to be known and these _can be

extracted from its relation _to

(Tj T)~

^"~

2.

Experimental.

All

experiments

have been

performed

_on

single crystal samples prepared by

electrochemical

methods

[20].

For the

sulphur compounds, selectively

^'~C 95 % enriched

(TMTTF)2PF6

and

(TMTTF)2Br samples

have been used.

Compared

_to

powder samples,

this has the

advantage

of

eliminating

the

Tj anisotropy

and _an

exponentional

relaxation _can be recorded. Furthermore, the

powder

spectrum is broadened

by

the

Knight

shift

anisotropy.

The

experiments

are

performed

_on ??Se in the 45 MHz range for the

(TMTSF)~PF~

and

(TMTSF)2Cl04 compounds.

For the

sulphur compound (TMTTF)~PF~

the central '3C sites have been

observed at 45 MHz in the low temperature range and 33 MHz _at

high temperature. Finally, (TMTTF)2Br

data have been

acquired

at 60 MHz

(P

=

I

bar)

and 30 MHz

(P

=

13

kbar).

In contrast to

previous experiments

made _on protons, ^{for which}

methyl

_group rotation effects

strongly

contribute _to the relaxation _{over a}

large

temperature ^domain

[9, 32, 40, 41, 42],

these nuclei

only probe

the fluctuation field

produced by

the electrons since _no other molecular motion _at the Larmor

frequency

is

expected

to contribute to the relaxation. On the other

hand,

relaxation measurements on

naturally

abundant

??Se present

some technical difficulties due _to

a very poor

signal-to-noise ratio, especially

at

high

temperature and under pressure. We are

usually

led _{to use}

composite samples

made of _a few

(2-4) aligned crystals.

The data _at low temperatures except ^for

(TMTTF)~Br

were obtained _{on a} conventional

broadband NMR spectrometer ^{where the}

wnplitude

of the

z-magnetization

_was measured

by

integrating

the free induction

decay signal.

In other

experiments

_a commercial Fourier

transform spectrometer ^{has been used. The}

spectra

^{of ??Se in}

(TMTSF)~PF~

and

(TMTSF)~CIO~

_are made up of 4 well resolved lines

corresponding

to 4

non-equivalent

Se sites

[43],

with _a residual linewidth of 2 kHz due

mainly

to the

dipolar broadening by

the

methyl

_{group protons.} For

Se,

the

knight

shift is known to be much

larger

than the chemical shift and it govems the

position

of the lines

[31].

The

Tj

^{is found} to be site

independent

within the

experimental

_error

(±

lo

%)

which is consistent with _a rather weak

spatial anisotropy

of

knight

shifts and with

spin density

calculations

[44].

The relaxation is

exponential

_over

nearly

two decades for the

magnitude

of

magnetization.

We should _comment here _{on some}

particular points conceming

the

experiments

_on ??Se _at

high

temperature

(100-300 K).

Its relaxation rate is

larger

than that of '3C and

special

_care

must be taken when

Tj

is of the order of the free induction

decay length Tf. Owing

to the time

consuming adjustment

of the

w-pulse

at every temperature, we have used the inversion- recovery sequence with

special

care on the

phase cycling

_necessary to extract the _z component of the

magnetization.

In

addition, during

the

signal averaging,

the coherent noise, _e,g. the

acoustic

ringing,

has been

suppressed by altematively changing

the

length

of the detection

pulse (from approximately

w/2 to 3

w/2).

In both sulfur

compounds

studied it is the central carbons that _were observed. These _can take two

non-equivalent positions

ⁱⁿ the unit

cell, giving

two resonance

frequencies separated by

the difference of

knight/chemical

shifts. In

highly

^enriched

samples,

however, each line will

split

in

general

into _a doublet due to C-C

dipolar coupling.

For central

carbon,

the

strength

of this

coupling (few kHz)

is

comparable

to the

separation

of Larmor

frequencies.

In such _{a case,}

as it is well known for

strongly coupled spin

_systems

[45a],

several difficulties appear in the relaxation measurements.

First, partially

relaxed spectra

depend

in _a

complicated

_{way on} the initial

non-equilibrium

state of the system, ^and thus, the

preparation procedure (pulse calibration,

_etc. is

subject

to

severe

conditions,

to avoid the

mixing

of

population

differences

resulting

in

non-exponential

decays. Moreover,

for _a

coupled pair

of

spins

the observed

Tj's

_are

always weighted

averages of transition

probabilities

of the _two

spins,

where the

weight

factors

depend

on the ratio _:

coupling

constant

(J~/shift

difference

(A) (these

factors _{are :}

cos~q~

and

sin~q~

with tan _{q~ m} J/2 A which _can be

easily

shown

by calculating

the transition

probabilities

^{between the}

exact

eigenstates

of the

system).

This

point

is of

particular importance,

because it _can, in

principle,

introduce

systematic

_errors into the temperature

dependence

of

Tj.

In all

experiments

_on

(TMTTF)2Br,

the

crystal

_was oriented in _a way to cancel the

dipolar interaction,

I-e- the b' axis

approximatively parallel

to the

applied

field

[45b].

We then observed two lines of 2 kHz width

separated by

about 100 ppm ^at 300 K. This is close _to the value found

by

Bemier _et al.

[45c],

for

(TMTSF)2Cl04.

The relaxation _rates of the _two lines

are different

by

a factor of 3 or so, which is also consistent with the

knight

shifts ratio of l.5 in

(TMTSF)2Cl04.

This ratio does _not exhibit any variation with temperature ^and pressure.

A _more detailed discussion is needed for the _case of

(TMTTF)~PF~

where _we used the _same

crystal

orientation.

(Hoflc*)

_as the _one of _a

previous

work at low temperature

[5]

in order _to

get

a consistent _set of data. The

typical

_spectrum is shown in

figure

3b. Here, the

dipolar splitting

is close to the shift difference _so that the two central lines

overlap.

We found that, within the

experimental

_error, the relaxation is characterised

by

a

single Tj

for all the spectrum, and

this,

_qt all temperatures. ^{Since the}

averaging

of transition

probabilities

cannot account itself for such _a difference between these _two

compounds (the weight

factors ratio is estimated to be of the order of

10),

we

performed

an additional

experiment

at

higher field,

where all lines

become resolved

(Fig. 3a).

Here the relaxation shows the _same characteristics _as for

(TMTTF)~Br.

This

clearly

^{shows that the}

averaging

is due _to

spin

diffusion between the

spin pairs

^of

adjacent

TMTTF molecules. The

spin

diffusion rate, related _to the

coupling strength

between

neighbouring spin pairs

is of several hundreds Hertz.

Therefore,

it is faster than the

(a)

(b)

20 lo -lo -20

f

(kHz)

Fig.

3.-'~C _spectra of _a single crystal of

(TMTTF)~PF~ (Ho flc*)

at _room temperature ^for a)

Ho

9.4T, and b)

Ho

^{3.I T.} At

high

field, the relaxation times of the _two doublets _{are :}

5 _ms (left) and ~13

ms

(right).

At low fields, all the lines have the _same Tj at about 8 _ms.

relaxation at all temperatures

(the Tj inhomogeneity

_over the

spectrum

^{is about lo %} at 300 K and

disappears

at lower

temperature).

The relaxation rate has been calculated

by integrating

the

whole spectrum. ^As

long

_as the

Tj's

of both nuclei _are

governed by

the _same

phenomena,

as it is

(TMTTF)2Br,

this

procedure

is reliable for the

study

of the temperature

dependence

of the

relaxation _rate.

Measurements under pressure ^at

high

temperatures

(T

_~ loo K

)

have been

performed

with a

CuBe 8 _mm inner diameter cell cooled

by

a thermal

exchanger

with

liquid nitrogen.

^The

liquid

flow _was

automatically

controlled in order to minimize the temperature

gradients

in the cell.

The RF

circuity

was mounted _as close _as

possible

to the

sample (10 cm)

but _was

thermally

isolated and temperature controlled _{to ensure} the

long

time

stability required

^for

averaging.

When

performing high

_pressure

experiments

at low temperatures, ^{it is}

important

to circumvent any pressure loss _on

cooling, especially

_near the

freezing point

of the

pressurized

medium. To minimize this

effect,

_we have used an

extemally

controlled pressure system.

Isopentane

is

pressurized

in _a

primary

chamber where the pressure is controlled

by

a

manganine

gauge. A

capillary tubing

drives the pressure to the cooled cell where _an

intensifying piston

creates the

high

_pressure in the

experimental

chamber. Two different

liquids

_were used _{to create}

high

_pressure freon in the

measuring

chamber and

isopentane

in the low pressure stage ^{of the} intensifier. Since the

freezing point

of freon

(300

K at 14

kbar) always

occurs well above the _one of

isopentane,

losses could be

compensated

until

complete

freon solidification and therefore _are

kept

^{within 500 bar} at lo kbar.

All

experiments

under pressure and at

high

temperature ^{have been}

performed

at lower field

(about

3

Tesla)

but _we have checked that the relaxation _rate does _not exhibit any field

dependence

_up to the

highest

field _we used _{at room} temperature

(9 Tesla).

3. Results.

The '3C

Tj

^' temperature

dependence

^for

(TMTTF)2PF6 compound

at P

= I bar and 13 kbar

is shown in

figure

4. The low

temperature profiles clearly emphasizes

the different _nature of the

ground

state at each pressure. At ambient pressure, the system

develops

_a

spin-Peierls instability

_at

Tsp=19K

below which

T/' _{drops rapidly}

_{to zero.} Above

T~~ and below T~~ ^m 40 K _{or so,} there is also _a sizeable

depression

of the relaxation rate. These results _are

clearly

consistent with

X-ray

measurements

[4]

which show _a lD lattice

softening

below 60 K and _{a true} lattice distortion of the

spin-Peierls type

well below 19 K. Similar

depressions

take

place

for the EPR

spin susceptibility

at the _same temperature as shown in

figure

4. It is of interest _to

point

out here that

essentially

the _same features in the

X-ray [4] resistivity [3, 6],

and

Xs(T) (Faraday) [6-7]

results _were obtained in another

spin-Peierls compound, (TMTTF)2AsF6.

In

figure 6,

we report

Ti

^' and

Xs(T)

data below

Tsp

on a

semi-log

scale

showing

_an activated behavior with a gap

Asp

₌ ^3.5

Tsp,

that

apparently

satisfies _a BCS like relation for both

quantities.

Above 40 K,

Ti

^' is found _to be temperature

independent

_up to

65K _{or so,} where it starts to increase with _an

upward

curvature. The

Tj'

_and

_x~(T)

temperature

profiles

do _not show any

anomaly

_near

_T~

m 220 K where the

resistivity

minimum

occurs

(Fig. I).

This indicates the very

interesting property

^of

separation

between

charge

and

spin degrees

of freedom.

Furthermore,

the enhancement of

Ti

^' above 65 K is

directly

related to the _one of

Xs(T) [5]. Indeed, figure

7

clearly

shows the existence of the

following scaling

relation

Tj

^'

= C

j +

Co TX/(T) (2)

above T~~. This

emphasizes

that _an

important

contribution to the relaxation _comes from

long wavelength

uniform

spin

fluctuations. As for the _{constant term}

Cj,

it will be show _{to come} from ID AF correlations

(see

next

Sect.).

160

~,~

T,~'(s") (TIITTF)~PF,

~",

o

120

",

o

",~~

^o

~$

^{~~~ '°} ~~~" (K)

~

°

i ~

4

o

. ~

V

AA~

.. o ~

. , ~

~: ~

'eZtl:]...

^~

50

emperature (K)

Fig. 4.

13

_kbar

The low

data are _{from [5]. In}

the

_inset : power law _analysis

T/~ in

the

cRtical domain of the _AF transition at 13 kbar.

(imiifi~

PF~

.i

so i i o

0 ~ 20 30 10 50 60 10 T(Kl

Fig.

5. EPR

susceptibility

of (TMTTF )~PF~ as a function of temperature. The low temperature

region

is detailed iri the inset.

I

(Kj

20 0 7 5

to' io'

~~~0)

(TMTTF),PF,

~' ~~~~

10° io°

lo" to"

to-' to-'

10~~ lO~~

0.5 1.0 1.5 2.0 2.5

10/T

Fig.

6.-Therrnally activated behavior of

q' _(right

_scale) and _Xs (left scale) _{as a} function of I/T for (TMTTF )2PF~ ^below

Ts,

at I bar.

At P

= 13 kbar, the

spin-Peierls

state of

(TMTTF)~PF~

is _no

longer

stable

[5, 8]. Instead, figure

4 shows that

T/' develops

_a

singular

behavior which

corresponds

to the _onset of

magnetic ordering

at

T~

=17 K. From the

log-log plot

^{in the} insert, the power law

~i ~A/ ₍₃₎

I (K)

0 50 loo 150 200

Tl'(S~')

(TMTTF),PF, 60

40

20

0

0.0 0.5 1.0 1.5 2.0

X~T(a.u.)

Fig.

7. Linear

dependence

of the measured

Tj (Fig.

3) _on

Tx)(T (Fig.

5 for (TMTTF )~PF~ at I bar.

takes

place

_near

T~

where in the notation of

I, iA~

₌

[(T T~ )/T~ ]~

^° and

d

m

1/2 _± 0.05. It is attributed to an AF type ^{of critical}

ordering (see

next

Sect.).

The reduced width

Atn

_m

(Tn T~)/T~

m

0.6 for the emergence of these critical fluctuations above

T~

is rather

large.

^At

higher

temperature, the relaxation rate becomes temperature

independent

and the

plateau

^{of relaxation is} seen up ^to 80

K,

^where an increase of

Ti

^' _emerges with _a much less

pronounced upward

curvature than the _one found _at I bar. If _{we assume} that the

empirical

relation

(2)

is still

valid,

these data show that the

amplitude

^{of uniform} fluctuations is

sizeably

reduced under pressure.

Looking

_now at the effect of anion substitution in the

sulphur

series,

figure

8 shows the

temperature profiles

of the '3C relaxation _rate for each NMR line of the

non-equivalent

center carbons of

(TMTTF)2Br

at I bar

[23].

At this pressure, the

compound

presents a

resistivity

minimum at

T~m

^{loo K}

(Fig. 2)

and it is known _to become

antiferromagnetic

below

T~m15K.

For both NMR

lines,

the relaxation _rate shows _a clear

singularity

_near

T~

^{which is}

quite

similar to the _one found for the

PF6 compound

at 13 kbar

(Fig. 4).

The critical behavior _can be best fitted _to the _same

expression (3)

with the critical exponents

jm

0.45 and 0.5

respectively

to each line. As for the critical

width,

its

amplitude

~t~

_~ ^{o,6 is consistent with the} one found for

(TMTTF)~PF~

at 13 kbar. The

slight departure

=

worth

noting

that the above '3C data confirms the

previous

^'H

T/

^' temperature ^{variation of} reference

[9]

obtained up to 30 K and above which the

methyl-group

rotation contribution to

T/

^' becomes

important.

The close

similarity

to the

PF~

salt under pressure is

again obviously

clear in the

paramagnetic regime. Indeed,

the

resistivity (Fig, I)

and relaxation rate

(Fig. 8)

data _are consistent with _a

complete separation

between

charge

and

spin degrees

^of freedom.

The

plateau

of relaxation is well defined up to 75 K where the increase of

T/'

becomes apparent.

Furthermore, using

the EPR

susceptibility

data shown in

figure 9a,

_we have checked in

figure

9b that for both NMR

lines,

relation

(2)

is well satisfied.

We _{now tum our} attention _to the

Bechgaard

salt

compound (TMTSF)~PF~, figure10a

shows the ??Se

T/

^' _vs. T

profiles

_at P

=

I bar, 5.5 and lo kbar up to 300 K. From the data,

we see that the

upward

curvature of

Tj

^' with T is still present ^{in the}

high

temperature

regime

but its

amplitude

decreases with pressure. There is no

resistivity

minimum

reported

for the

Bechgaard

salts

(T~

~

Tn,

_see

Fig. I)

and the

paramagnetic regime

is well characterized

by

metallic

properties [I I].

At low

temperature

^{and for P} _~ ^P

~ ^m

6.9 kbar

[I1, 46],

the

ground

state is

antiferromagnetic.

This is illustrated

by

the

figure 10a,

where at I bar and 5.5

kbar,

T/~

is

clearly singular

at

T~m12K

and

T~=8.7K. Figure

lob shows that the critical variation _near the transition still

obey equation (2)

where

again

1Y ₌ 1/2 _± lo % _{over a} decade in temperature. ^{The critical width}

Atn

_- ^0.8

(1 bar), (5.5 kbar)

is also

large

and is similar _to

those found in

sulphur compounds.

At lo

kbar~P~,

AF

ordering

is unstable and

(TMTSF)~PF~ undergoes

_a

superconducting phase

^transition near lK. Nevertheless,

figure10a,

shows that _a rather

large

enhancement of the relaxation rate below 30K still remains. This enhancement is

independent

of the symmetry ^{of the anion since} very similar results _are found for the ??Se

Tj

^' data of

(TMTSF)~Cl04

in the so-called relaxed _state at ambient pressure

(~

P

~

(Fig.

II

).

This

large

enhancement above

P~

has also been confirmed

by

other groups

[40, 47].

It has also been

reported

for

(TMTSF)2FS03

at 10kbar

~ P

~ ⁼

7

kbar) [17].

From the data of

figures 4, 8,

lo and

II,

it is

interesting

to observe that this

temperature

^{scale for selenides is}

clearly

lower than the _one found for the emergence of the

Ti

^'

plateaus

in the

sulphur compounds thereby suggesting

that the AF component ^{of relaxation} is less

developed

in the

Bechgaard

salts. As for the

high

pressure

region,

the

upward

curvature

of the relaxation

profiles

is rather well

pronounced

^{for both}

(TMTSF)2PF6

and

120

T,~'(s~') (TMTTF)zBT

loo '

,

~ ^,

'

'

~~ ^~~~

^~~~~

t

~

lo

"'~ '~[

.

~$

_{60 T-T»}

(~~/

'

i ^'

4 ^'°

,

*

.

20 ^°

, .

~ .

°

~

~

0 50 i

0

50 200 250 300

Temperature (K)

Fig.

8. Tj vs. T data for the two central carbon sites in (TMTTF

)~Br

at 56 kG. The insert shows the power law

divergence

_{near T~.}

1-a

Xs (a.u.) _(TMTTF),Br

to ^e

e

e .

O-S

~ .

~ ~

.. ^{. . .} .

~~

' ' 0.6

.

o 0.4

,

j~ j

O-Z

0 0.0

50

~

1500 (Q)

..

~ .

.

$°& _~Q

l ,*»»»

0~1000

~~ O

O ~

500 ^o

~ ~

o

a

o ~

a

o ~

o

~

, ~

loo 300(K)

so

T~~~(3~~) (TMT3F)~C10,

P - I bar

60 ,~

,'

. '

~.A

40

~A

20

O

0 lo 20 30

TEMPERATURE (K)

Fig,

ll. Low temperature ~?Se

Tj~

_vs. T data of

(TMTSF)~Cl04

in the relaxed state full circles, 31.9 kG f b' full

triangles,

6.o kG

(powder)

_{open squares,} 31.9 kG # _{c* open}

diamond-shaped,

21 kG # b'.

~~Se

~~~'~~~~2 ~§ ~~~'~~~~2 ~~°4 /

%

o. 53 KG_w

b'

_{A : 56.5}

KG,I

~

/

. 31KGll

I

a 64

KG,/6

o

P =

I bar. The field

circles

and _triangles

correspond to

the

T~~(3 ^~)

/

T~~~(S'~)

60 is

(T~T~~)z~~o

/

~

C

(TVTTF) ~Br _SOD

40

iooo

20

w

(TVT3F)~PF,

~~ ~~~

(TMT3F)~C10,

O-O O.5 1-O 1.5 2.0 2.5

x

( T(w,u.)

Fig.

13. Plots of

Tj (Fig.

12) _vs. the measured TX

j(T)

of references [34, 35] for

(TMTSF)~PF~

and

(TMTSF)2Cl04

above 50K. The results of

figures

7 and 9b for

(TMTTF)~PF~ (squares)

and

(TMTTF)2Br

(dashed line) _are

reported

for

comparison.

tT~Tl'~

_,

SK

_l~~ ^*

o/

a

o

~/~

/

a

~/

.

/

4

4.

Analysis.

4. I THE _MODEL. It _{was soon} inferred that for each

compound

of the

sulphur

series at low

pressure, the existence of _a

resistivity

minimum at T~ ^w

T~

is _a direct consequence of the relevance of lD electronic

umklapp

_processes. Barisic and Brazovskii

[48]

and

Emery

et al.

[16],

^indeed

suggested

that the combined influence of the 4

k~

^anion

potential

and the apparent

slight

dimerization of the

organic

stacks _must open a gap

A~

ⁱⁿ the electronic

spectrum

^{of the}

chains _{at ±} 2

k~.

^{This leads} to an effective half-filled band _at low temperature ^{and electronic}

umklapp

effects will

strongly

influence the _{nature as} well _as the

amplitude

of correlations. If

one assumes that far from the critical

point

the

compounds

can be described

by

lD

physics,

repulsive

interactions between electrons will

invariably

lead _to the creation of _a correlation gap A~ ^{and of an}

insulating

behavior below T~ -

A~/w.

^These

properties

_are well known _to

follow from the lD

repulsive

Hubbard model and its continuum

generalization, namely

the _so- called lD electron gas model. As described in I and

largely

discussed in the literature

[49],

the direct electron-electron interaction in the latter model is

parametrized

in terms of four

couplings

constants g~ _{i ~} for left and

right moving

electrons.

They

all reduce to the one-site

repulsion

U in the Hubbard limit. This model is

particularly interesting

for the

present compounds

since the

amplitude

_{of g~ is}

directly

related to the

amplitude

of electronic

umklapp

processes and in _{tum to} the dimerization

responsible

for the

insulating

_{gap A~}

[48].

From its

amplitude,

an effective bare value of g~ can be found _{as a} function of pressure

[14, 50].

A very

peculiar

characteristic of the lD

physics

of this model is the

complete separation

between

long wavelength charge

and

spin

excitations. As _a consequence of this

spin-charge separation,

the

absolute value of

Xs(T)

allows the determination of gi ^and g~

(see

Sect.

5)

and this

independently

of g~ ^{and the} combination

2g~-gj

which _are connected to the

charge

excitations. The latters

strongly

influence the

strength

of AF correlations and the value of TN

lls, 50].

This property ^is

invariably

observed in all

sulphur compounds

that

present

a

resistivity

minimum. For

(TMTTF)2PF6

and

(TMTTF)2Br compounds

at ambient pressure for

example, figures

5 and 9a show that the

long wavelength spin degrees

of freedom which

contribute _to

Xs(T)

remain

clearly

unaffected in the temperature range where the

resistivity

minimum _occurs

[7].

The effect of

hydrostatic

_pressure is of interest since it reduces the dimerization and this will diminish the

amplitude

_{of g~.}

Therefore,

it will shift the

resistivity

minimum _at lower

temperature.

^{This has been found} to be consistent with the

resistivity

data of

Creuzet et al.

[8]

for

(TMTTF)~PF6

and

(TMTTF)~Br

under pressure and also with the

absence of

resistivity

minimum for all the

Bechgaard

salts at ambient pressure. These _are indeed less dimerized than the

sulphur compounds [16].

It is from these

experimental

facts and the central role

played by

the

antiferromagnetism

in the combined

phase diagram

of both series that the ID electron gas model has attracted considerable attention for the theoretical

interpretation

of these materials

[5 II-

As shown in I, ^the

quasi-ID generalization

of this model with the inclusion of the small transverse

hopping integrals

is necessary to assure the existence of

long

_range

ordering.

For both

sulphur

and selenides series the band _structure calculations _as well _as several

experiments

lead to the

anisotropic

_sequence of t~ ^m15 ti~

m 450 ti~ ^{between the} a, b and _c direction

hopping integrals. Despite

similar

anisotropy

ratio

ti~/t~

between the _two

families,

the

amplitude

of t~ ^differs

sizeably

however.

According

to Ducasse etal.

[2b]

_at I bar,

E~

m 300 K for

(TMTTF)~PF~ compound

while

E~

_m 2 500 K for the

(TMTSF)~PF~.

In presence of _a lD correlation gap

A~,

transverse

single

electron band motion is

essentially

frozen below T~ ^{and it is}

through

_an effective interchain

exchange

^mechanism

(IEX)

which has

a kinetic

origin

that interchain

propagation

of AF correlations _can lead to

long

_range order at a

finite

T~ [15].

As _we will discuss next, temperature

dependence

of NMR relaxation _rate

especially conceming

^the nature, the

amplitude,

the

statics,

the

dynamics

and the dimensionali- ty of

spin

correlations.

4.2 SCALING FEATURES.

Sulphur compounds.

Let's first look at the temperature ^{variation of the}

~~CTj'

in

(TMTTF)~PF~

at 13 kbar

(T~

m 17 K _; T~ m 75

K) [5]

and

(TMTTF)2Br

at P

=

I bar

(T~

=

15 K T~ m loo

K) [23]

which _are

typical antiferromagnets

of the

sulphur

series at low pressure. As

already

mentioned in section

3,

the

log-log plots

of the

figures

4 and 8 for the cRtical behavior lead _to the value

d

= 1/2 _± lo % in both _cases.

According

to the results of the

section of 2, the AF contribution to the nuclear relaxation rate,- for _a

quasi-

lD electron gas model with _a lD correlation gap A~ ^near

T~,

is

given by

i~l

[~ Q01

_~ ~

(Q0) _~Al'~ (~)

Here

©(Qo)

is _a temperature

independent quantity (cf. Eqs.(1-6)

and

(1-57)).

This

Ti

^'

expression

results from _a RPA treatment of the interchain AF

exchange (IEX) coupling

while the lD part ^{of the}

problem

^{is treated}

rigorously.

As for the cRtical index

d

=

1/2,

it is a 3D result that combines Gaussian exponents ^{for the AF}

susceptibility,

the correlation

length

and the relaxation time for fluctuations. The Gaussian cRtical width

Atn

m

(Tn T~)/T~

for the emergence of critical fluctuations above

T~

is obtained from the temperature

Tn

at which the cRtical contribution to

T/

^{' exceeds} the

paramagnetic

one. This

quantity

reflects the non-universal features of the model used. Whenever T~ ^w

TN,

^the transition is driven

by

the IEX

coupling

and from

(1-62),

it is

given by

~~fl "

"~[~~

_Y~

("i~Nf~F) f0a f0b f0clT/ (5)

where

according to1,

6 _S I and _y

=

I. For the IEX

mechanism,

the transverse coherence

lengths lo

~ and

lo

~

are small

quantities (~

l while

(wT~/v~) to

~

l _so that A tn ^{l which is}

large

in agreement ^{with the results of}

figures

4 and 8 for which _one has

Atn

0.6 for

sulphur compounds.

It should be stressed however, ^{that the}

anisotropy

with respect to the third

direction should be

quite large

in these

compounds (fo~w fo~)

so that it may appear

somewhat

surpRsing

that _no 2D critical effects _{are seen} above

T~.

The _reason for this is not clear _so far.

As discussed in I, the choice of _a different mechanism for the

phase

^transition can lead to a

quite

^different value for

Atn.

In this respect, a 3D

logarithmic nesting (NAF)

mechanism of

antiferromagnetism,

would lead to different precursors

(see Sect.1-6)

and _{to a} smaller

amplitude

^for

Atn [41].

In that _sense, the

amplitude

of the precursors ^to the transition _can

give

valuable indication _on the

type

^of

microscopic

mechanism involved in the

propagation

of AF correlations for the transition.

In the framework of the

quasi-ID

electron gas model, the presence of _a correlation gap A~

wT~

^{300 K for both}

compounds

in their

respective

_pressure conditions would _corre-

spond

to the temperature ^{scale for} strong ^electronic

umklapp scattering.

This

yields

a power law exponent y of the ID 2 k~ ^AF response function _x

(2 k~, T)

^{T~ ?}

)

that is

exactly equal

to

unity.

This exponent

together

witli the _exact relation

v = z = I for the coherence

length

^and