Dc Hall effect measurements on ttf-tcnq

HAL Id: jpa-00208676

https://hal.archives-ouvertes.fr/jpa-00208676

Submitted on 1 Jan 1977

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.

Dc Hall effect measurements on ttf-tcnq

J.R. Cooper, M. Miljak, G. Delplanque, D. Jérome, M. Weger, J.M. Fabre, L.

Giral

To cite this version:

J.R. Cooper, M. Miljak, G. Delplanque, D. Jérome, M. Weger, et al.. Dc Hall effect measurements on ttf-tcnq. Journal de Physique, 1977, 38 (9), pp.1097-1103. �10.1051/jphys:019770038090109700�.

�jpa-00208676�

DC HALL EFFECT MEASUREMENTS ON TTF-TCNQ (*)

J. R. COOPER and M. MILJAK

Institute of

Physics

^{of the}

University,

^POB

304, Zagreb, Yugoslavia

G.

DELPLANQUE (1),

^D.

^JÉROME

^{and M. WEGER}

(2)

Laboratoire de

Physique

^des

Solides, Orsay,

^France

J. M.

FABRE

^{and L. GIRAL}

Laboratoire de Chimie

Organique

Structurale USTL 34060

Montpellier,

^France

(Reçu

^le 14 ^mars

1977, accepte

^{le 25 mai}

1977)

Résumé. ²⁰¹⁴ Des mesures de l’effet Hall ont été réalisées sur des monocristaux de TTF-TCNQ ^dans

la région métallique ^à

pression

atmosphérique ^{et sous}

pression

de 6 kbars. Avec l’orientation du

champ magnétique utilisée dans cette étude (H

parallèle

à l’axe cristallin a), la valeur moyenne du coefficient de Hall en bas champ ^{vaut -} 4,2 ^± 0,6 ^x 10-11

Vcm/AG à

température ^ambiante.

Cette valeur est en accord approximatif ^{avec les autres} estimations de la densité électronique. ^Nous

avons détaillé l’influence des contacts

électriques

^et comparé ^la dépendance ^de RH ^en fonction de la

température ^avec celle d’un travail

précédent

^sur HMTSF-TCNQ.

Abstract. ²⁰¹⁴ Some DC Hall effect measurements have been made on

single

crystals of TTF-TCNQ

in the metallic region, ^at atmospheric pressure and under pressure of 6 kbars. For the field orientation

employed ^{here (H} parallel ^{to the} crystalline ^a axis) the average value of the low field Hall coefficient is ²⁰¹⁴ 4.2 ± 0.6 ^x 10-11 Vcm/AG ^{at room} temperature ^{which is} approximately consistent with other estimates of the electron density. ^The influence of the electrical contacts is discussed in detail and the temperature dependence of RH ^is compared ^with previous ^{work on} HMTSF-TCNQ.

Classification

Physics ^Abstracts

72.20M - 72.80L

1. Introduction. ^-

Although

the electrical _proper- ties of several

organic charge

transfer salts based on the

TCNQ

acceptor molecule have been studied intensi-

vely [1],

^{not much} attention has been

paid

^{to one of}

the basic

transport properties,

the Hall efi’ect.

Recently

we measured the Hall coefficient

[2, 3] (RH)

^for

single crystals

^{of the}

charge

transfer salt

HMTSF-TCNQ

which remains a

good

conductor down to very low

temperatures [4]

^{and found}

large

^{values of}

RH

^below

200 K.

Together

with other evidence

[5, 6]

this result indicated that the

conductivity

^{at low T arose from a}

rather small number of

high mobility

^{carriers ( ~ 0.1}

carriers _per

TCNQ

^{molecule at 100 K}

falling

^to

about 0.002 at 10

K).

^{It was} thus very consistent with a

previous

^{band structure} calculation

[7]

^{in which}

hybridisation

^between acceptor and donor chains is

important

^{and leads to a} semi-metallic state at low temperatures.

Since in _{many ways}

TTF-TCNQ

has become the

prototype

^{of the}

high conductivity charge

^transfer

salts it is

obviously interesting

^to compare

RH

^for

these two materials and this is the aim of the present paper.

Up

^{to now we have made} measurements as a

function of

temperature

in the metallic

region

^both

at

atmospheric

pressure and under ^an

applied

^pres-

sure of 6

kilobars,

^{for one}

particular magnetic

^field

orientation (H // a

axis).

While this work was in _progress and after

comple-

tion of the

experiments

^under pressure, ^we become

aware of recent microwave measurements of the Hall

mobility [8]

ⁱⁿ

TTF-TCNQ

^{at room}

temperature

^and

interesting

theoretical calculations

[9] involving

^diffu-

sive electron

transport perpendicular

^{to the chains.}

These calculations

predict

^an enhanced Hall mobi-

lity [8, 9]

associated with the diffusive motion and there (1) Present address : Laboratoire Mineralogie Cristallographie

USTL, ³⁴⁰⁶⁰ Montpellier.

(2) Now returned to : The Racah Institute of Physics, ^The

Hebrew University ^of Jerusalem, ^Israel.

(*) Work in France supported partly by ^{contracts CNRS ATP-}

A207 and DGRST 75-7-0820. ^!

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:019770038090109700

1098

is

supporting experimental

evidence for such an

enhancement from the microwave work.

At present ^{we cannot make a direct}

comparison

between our values and the microwave results since the

magnetic

field orientations were different in the two

experiments

^{(H // a and H // c}

respectively)

and in fact it appears that ^even the

sign

^of

RH

^is

different. We chose the H // a orientation because

initially

^we believed that for the

crystal

^sizes

normally

available this was the most favourable

geometry

^for

avoiding

^a

spurious

reduction in

RH

associated with the extreme

anisotropy.

As discussed in detail sec-

tion 2.2 we now have a better

understanding

^{of these}

geometrical aspects

^{and are}

currently extending

^the

present

^{work to the H // c} orientation in order to make a direct

comparison

with the microwave data.

For the moment then we wish

simply

^to

report

^data in the other field orientation for a number of

samples

and to

emphasize

the differences between

TTF-Q

and

HMTSF-Q

^{in the}

region

^{60-300 K.}

2.

Experimental

^{details. - 2 .1 GENERAL. -}

Single crystal samples

^of

TTF-TCNQ

^were grown

by

^the

diffusion

method,

from solutions of TTF and

TCNQ

in acetonitrile. The

crystals

^{were not}

particularly large,

^{as shown in table}

I,

^{nor of}

especially high quality.

A number of other

experiments

^{were made}

on

samples

^{from the same} batch. Peak conductivities 10-20 times the room

temperature

^{value of}

500 ± ¹⁵⁰ (Q

cm)-1

were observed for the

long (b) axis,

while the a-axis

conductivity

^{was also in}

agreement

with values in the literature

[10], namely

^{1-2 (Q}

cm)-1

^{at room tem-}

perature, increasing by

^{a factor of 3 or so down to}

100 K

[12]. Samples

^{from the same batch were used}

in the recent

specific

^heat

study

^where

sharp phase

transitions were observed

[11]

and also for some

unpublished susceptibility

^work which showed a rather small low T Curie term

[12].

^{Therefore we are confi-}

dent that our materials are as pure ^as those of other

investigations.

The

geometry

^{of the}

experiment

is discussed in

more detail

below,

^{current was}

passed along

^{the b-}

axis,

^the

magnetic

^field

(H) applied along

^{the a-axis}

and the Hall

voltage ( VH) developed along

the shortest side of the

crystal

^- the c* axis.

In the first

experiments

electrical ^{contacts were} attached

directly

^{to the}

crystals

with silver

paint (Dupont 4929)

^{in the same} way ^as for HMTSF.

This method _gave an

adequate signal

^to noise ratio for the measurements at a pressure of 6 kilobars but it was

barely adequate

^{at ambient} pressure, and the situation could not be

improved by increasing

^the

measuring

^current.

Following

^reference

[13],

^we

finally improved

^the

signal

^to noise ratio

by making

the silver

paste

contacts to

evaporated gold

^contact

areas on the b-a faces of the

crystals.

We consider that the results for the latter

samples

^{(no" 6-8 in}

table I and

figure 3)

^{are the most reliable.}

A few results were obtained

using

^DC

(samples 1,

2 and

5)

^but

mostly

^{a low}

frequency

⁽⁷⁰

Hz)

^AC

technique

^was

employed

with lock-in

detection,

and currents between 1 and 3 mA RMS. The

linearity

of the Hall

voltage

^with

measuring

^current

(I)

^was

checked for several

samples.

In the

experiments

^at

Orsay

the field was

swept slowly

^{from zero to ± 21 kG}

using

^a

superconducting solenoid,

while for those in

Zagreb

^an

electromagnet

was

used,

^{the field}

being

^increased

quickly

^{from 0 to}

± 10

^kG.

Examples

^{of the}

signal

^to noise obtained with the two methods are shown in

figure

^2.

YH

^{was found to} vary

linearly

with field except

(possibly)

for the lowest

temperature point

⁽⁶⁸

K)

^at

atmospheric

pressure. The Hall coefficient

RH

^{is thus}

given by

the formula

where W is the width of the

sample

^{in the a direction}

parallel

^{to H and}

VH

^the average Hall

voltage (gene- rally -

⁵⁰

nV)

for ± ^H.

2.2 CONTACT ARRANGEMENTS. ^- The two contact

arrangements used for results

reported

^{here are}

shown in

figures

^{la and lb. In} view of the extreme TABLE I

Summary of

^room temperature ^Hall

effect

^results

for TTF-TCNQ samples

^at

atmospheric

^pressure

FIG. 1. ^- Possible contact arrangements for Hall effect measu- rements. (a) Using end contacts, samples ^1-5. (b) Using evaporated

Au strips ^without end contacts, samples ^6-8. (c) Original ^{Van der}

Pauw method. (d) ^{Modified to be a} null method and so equivalent

to la and lb for small contacts and thin samples.

anisotropy

^{of these}

crystals,

and because further work is

envisaged

^{for other}

magnetic

^field orientations

(especially H // c*)

^{it seems} worthwhile to discuss the

geometrical aspects

^{in more detail}

following

^the

papers

by

^{Van der Pauw}

[14,15].

^He first showed that it is

possible

^{to measure the low}

field

^Hall coefficient for any thin

arbitrarily shaped, isotropic sample [14]

simply by placing

four small contacts on the circum- ference

(Fig. 1c)

^and

measuring

^the

change

^{in resis-}

tance

RBD,AC

^on

applying

^a

magnetic

^field

perpendi-

cular to the

plane

^{of the}

sample

^(For

anisotropic

substances other Hall tensor

components

^{can be} determined

by rotating

^{H into this}

plane).

^{The Hall}

coefficient is

given by :

FIG. 3. ^- Temperature dependence ^of RH ^for TTF-TCNQ ^com- pared ^{with that of} HMTSF-TCNQ. TTF-TCNQ ^{at ambient}

pressure, open triangles results for two cooling cycles ^on sample 7,

open circles, sample ^{8. Solid} circles, sample 3, at 6 kbars. Crosses-

HMTSF-TCNQ ^at atmospheric pressure. Inset. Pressure dependence of RH at ^room temperature ^for TTF-TCNQ samples ³ (solid circles)

and 4 (open circles).

where W is the thickness of the

sample along

^H.

Unfortunately

^as it stands this is not a null method but we now realize that it can be

simply

^{modified to}

give

^a null method as shown in

figure

^{1 d. It is clear}

that the contact

arrangements

ⁱⁿ

figures

^{la and lb}

are

equivalent

^{to that in}

figure

^{1 d}

provided

^{that the}

current is uniform in the field direction and the contacts are small.

Van der Pauw also estimated the effect of finite size contacts for the

special

^{case of an}

isotropic

FIG. 2. ^- Examples ^of signal ^to noise obtained with the two experimental arrangements used in the present ^work. Upper trace, field sweep method used for measurements under pressure. Lower trace, time sweep method used for ambient _pressure work, following ^reference [13].

1100

circular

sample

^with

uniformly spaced

^contacts.

To first order the relative error in

RH

^is

given by :

where d is the

length

^{of the contact}

along

the circum- ference

(c)

^{of the}

sample.

Eq. (1)

remains valid for

anisotropic samples [15]

but in order to

apply

^eq.

⁽²⁾

^{we have to} take the aniso-

tropy

^{into account. This is}

easily

done since Van der Pauw

[15]

and others have shown that the ^current- field distribution in an

anisotropic sample

^{is the same}

as that in an

isotropic

^one with dimensions

multiplied by

factors such as

(Q1

C12

U,)116/al/2

in the various

principal

directions

1,

^{2 and 3.}

From our

point

^of view the work mentioned above has several

interesting practical

consequences.

(1)

^{For low field} measurements, ^i.e.

RH indepen-

dent of

H,

^{it is not} necessary ^to have a

completely

uniform current distribution. However the effective geometry ^{should be two}

dimensional,

^{i.e. the}

sample

very thin or at least uniform in the direction of H.

As shown in table I the

typical

dimensions of the

TTF-TCNQ crystals

^{were 3 x 0.4 x 0.03}

^mm’

^for

the

b,

^{a and} c* directions

respectively. Taking

^conduc-

tivity anisotropies

^of

500(Ub/Ca)

^and

200(Uc/Ua) [10]

leads to an

equivalent isotropic sample

of dimensions 0.44 ^x 1.3 ^x 0.06

mm’

at room temperature. ^Since H is

parallel

^{to a in the}

present experiments

^{we are}

very far from thin disc

geometry,

^{and so one}

possible

source of error is a non-uniform current distribution in the a direction. The

anomalously large

^values

of RH

for

samples

^{1 and 3} may be caused

by

^{such errors.}

This is one reason

why

^{we have more} confidence in the results for

samples

^{6-8 where Au}

strips

^were

evaporated

on the a-b faces because these contacts should be

more uniform.

(2)

^The

voltage

^{and current leads}

(including RB)

can be

interchanged

^so

reducing

^{the source}

impedance

seen

by

^the

voltage measuring

^device.

(3)

^{If it is not}

possible

^{to obtain a null}

by adjusting

the

potentiometer RB (Fig. ld)

^{then the contacts can be}

rotated

cyclicly. Empirically

^{we have}

^always

^found

that a null can be made in one of the other four

configurations

^and consistent values obtained for

RH.

It is _very useful to know this because in several of the

early experiments

^we

prematurely stopped

^{the measu-}

rements at lower

temperatures

^{when it became}

impos-

sible to balance out the resistive

voltage

^{in zero field.}

However we should

point

^{out that the}

position

^{of the}

null is often

inconveniently

temperature

dependent.

(4)

^{The contacts} should be

small,

and the effect of finite contact

size, including

^{current contacts cover-}

ing

the ends of the

crystal

^can be estimated from eq.

(2).

As noted elsewhere

already (3),

^{it turns out}

that the condition

L/T >

³

JA

^{(where A} is the ani- sotropy ^{in the}

conductivity,

^{in this case}

(Jb/O’c)’

^is

sufficient to ensure that end contacts do not cause more than a 30

%

reduction in

RH.

^{This is not a} pro- blem here since A is of the order of 200 at room

tempe-

rature and we had

L/T

values from 70-150. Never- theless A does increase at lower

temperatures

^{so to be}

on the safe side it is

probably

^{better not to use end}

contacts at all

[16],

^but

just

^{to use contacts on the}

sides of the

crystal

^{as we did for our later}

samples,

numbers 6-8 in table I.

Certainly

^{end contacts should}

not be

employed

^for the other

crystal

orientation H // c* where A is > ^{500 and}

LIT usually

^lower

(of the order of

10).

The effect of finite contacts on the a-b faces can

also be estimated

according

^to eq.

(2)

^{and the}

possible

corrections are listed in table I. In one or two instances the measured values of

RH

may be as much as 30

%

too low because of finite contact sizes.

Imperfections

in the

samples

^{such as}

inhomogeneities, grain

^boun-

daries,

etc., ^{can also}

give

^{rise to a} non-uniform or

non-ideal current distribution and so lead to errors

in

RH.

However the conductivities at room tempera-

ture were all around 500 (Q

cm)-1,

^{as shown in}

table I, ^{with low}

temperature peaks

10-20 times

larger,

which indicates that the defect concentration

was

reasonably

^{low. As mentioned in section}

2(i) samples

^{from the same} batch exhibited

sharp phase

transitions in both

specific

^heat

[11]

and conducti-

vity [12].

3. Results. ^- The results obtained for the

eight samples

^{measured at room}

temperature

^{are listed in} table

I,

^the

sign of RH

^was determined for four of them

by comparison

^{with a standard}

Ni

²

^%

^Mn

^alloy

known to be electron like

[17]

^{and was found to be}

negative.

^The

weighted

average of

RH

^{at room} tempe-

rature is ^- 4.2 ± 0.6 x

lO-11 Vcm/AG (omitting

the

anomalously high

values for

samples

^{1 and}

3).

This leads to a

mobility (RH Ull)

^{of about 2}

^cm2/Vs along

^the chain axis at room

temperature

^and pressure.

But if the corrections for finite size contacts listed in table I are

applied RH

^{could be as}

high

^as

As shown in the inset to

figure

³

RH

^is

strongly

pres-

sure

dependent

^{at room}

temperature. Although

there are

large

uncertainties for the

points

^{near atmo-}

spheric

pressure it seems clear

that RH I

^decreases

by

^a factor of 2-3

by

^{8 kbars.}

The temperature

dependence

for three different

samples,

^{two at ambient} pressure and one at 6 kbars is shown in

figure

^{3. For}

experimental

^{reasons the}

ambient _pressure measurements are

presently

^limited

to

temperatures

^{above 68} K. However the results under _pressure show that there are no gross

changes

in

RH

^on

cooling

below the

conductivity peak

^or

through

^{the first}

phase

transition (which is at 58 K for 6

kbars)

^but

just

^a

steady

increase in

RH.

^{In fact}

under _pressure

RH

^is

approximately proportional

^to

T- 1.

The dashed line at

RH

^{= - 4. 5 x}

10-11 Vcm/AG

in

figure

³

corresponds

^{to the}

expected

^{value of}

1/nec, taking

^{a band}

filling

^{of 0.58}

el/TCNQ

^molecule

- as

given by

the value of 2

kF

^from

X-ray

^{and neutron}

scattering.

4. Discussion. ^- In the

subsequent paragraphs

^we

discuss the

following

features of the results shown in

figure 3 ; (i)

^the

sign

^and

magnitude

^of

RH

^{at room}

temperature (ii)

^its pressure

dependence ^there,

^and

(iii)

the increase in

RH

^{at low} temperatures.

(i)

The formula for a

single anisotropic tight binding

^band

provides

^{a useful}

starting point.

^The

standard

expressions [18]

for the low field Hall coeffi- cient lead to the formula :

where b is the lattice constant

along

^the

high

^conduc-

tivity

^b axis. Therefore within the band

picture (and

as

long

^{as the band is not half}

full)

^{there should}

still be an observable Hall effect ^even in these extre-

mely anisotropic

materials.

Physically

^{this is}

^because,

to first order in

H,

the carriers

propagating

^{in the b}

direction are not deflected

by

^the

magnetic

^{field and}

thus the cancellation between the Lorentz force and the Hall field does not

depend

^{on the} transverse effective

mass.

Mathematically

it is because the transverse transfer

integral (t_L)

^occurs in both the Hall conduc-

tivity

^tensor

(aab)

^{and the} transverse

conductivity (O’aa)

and so cancels in

RH. Strictly speaking

^{the above}

formula holds in the relaxation time

approximation

where the

scattering

^{time i is constant over the Fermi}

surface. If this is not the case then

RH

^{should be}

multiplied by

^an additional factor of the form

where ^{and Vi-}

^are the electron velocities and the brackets indicate a Fermi surface _average. This factor could

possibly

^{lead to an} enhancement of _up to a

factor two in

RH.

If we take

kF

^{= 0.29}

nib [19]

^then eq.

(3) gives RH

^{= - 3.2 x}

10-11 Vcm/AG,

^{which is}

reasonably

close to the values observed between 100 and 300 K.

Therefore the classical

interpretation

^{of our results}

is that the Hall effect and

conductivity

^{are dominated}

by

^the

TCNQ

chains. This conclusion is consistent with both the

sign

^{of the} thermoelectric _power

parallel

to the b axis

[20]

^{and with a recent}

analysis

^of

the thermoelectric _power of

TTF l-x TSeF x TCNQ alloys [21].

ii)

^The pressure

dependence

^of

RH

^{is more difficult}

to

understand, especially

^as

optical

measurements show that the

plasma frequency,

^{i.e. the electron}

density,

^is

only weakly

pressure

dependent [22].

The obvious

interpretation

is that under _pressure the

conductivity

^{of the TTF} chains increases more

quickly [28]

than that of the

TCNQ chains, leading

^to

cancellation of the electron and hole

contributions

to

RH.

^{However as far as we} know there is

presently

no

independent

evidence for this

hypothesis.

^Another

possibility

^{which cannot be ruled out, is that at room}

temperature

^and pressure

RH

is enhanced

by

^{about a}

factor of two over the value

given by

eq.

(3).

^{From the}

study

^of

amorphous

materials it is known that

RH

is often enhanced when the

conductivity

^{is diffu-}

sive

[24]

^{(i.e. the mean free}

path %

^{one lattice}

spacing).

Several authors have noted that

taking

leads to an

apparent

^{mean free}

path

^{1 = 0.9 b at room}

temperature.

This estimate

depends only

^{on the known}

band

filling

and lattice

parameters,

^{so it is}

quite precise

and indicates that the

longitudinal

^diffusive

region

^is

approached

^{near room}

temperature. By analogy

^with

amorphous

materials this could lead to an

enhancement in

RH

which is then reduced under pressure.

In fact

according

^{to the recent work of}

Lyo [9]

^and

Ong

and Portis

[8],

^{in these}

charge

transfer salts

RH

can also be enhanced

by

^a

temperature independent

factor of five to ten even if

only

^the transverse conduc-

tivity

is diffusive while the

parallel

^one remains cohe- rent. However this sort of mechanism would not

explain

the observed _pressure

dependence

^{since at}

room temperature ^the transverse

conductivity

^cer-

tainly

remains diffusive in the 0-8 kbars _range. We also note that the microwave Hall effect

experi-

ments

[8]

^{were carried out on}

samples

^{which had been}

thermally cycled

^{to reduce} _all ^{and so had I}

b/5.

iii)

^{The low}

temperature upturn

ⁱⁿ

RH

^{is the most}

interesting

feature of the

present

^results.

Again

^we

believe that there are two

possible interpretations

which deserve consideration.

(i)

^Possible

relationship

between Hall constant and

transverse

tunnelling

^{matrix element. - In}

previous

work on

HMTSF-TCNQ [1, 7]

^{it was}

suggested

^that

at low temperatures ^the transverse motion of the electron is coherent

corresponding

^{to the band struc-}

ture of a semi-metal with about

1/500

^carrier per molecule. On the other

hand,

^at

high

temperatures the transverse motion is

diffusive;

the bands of the

TCNQ

chains and HMTSF chains are

independent

and contain about 0.7 carrier _per molecule. Let us

illustrate here some

qualitative

features of the diffu- sive ^H coherent transition

(DCT).

^{In a}

single

^chain

system ^{we would not}

expect

^{the Hall} constant to

change radically

between the two limits

(except

^for

the

possibility

^{of some} enhancement in the transverse diffuse

region [8, 9])

^because

they

^both

correspond

to the same number of carriers. But in a

system

^with

two types ^of

chain, donor-acceptor tunnelling

^will

cause a reduction of 2-3 orders in the carrier concen-

tration

[1, 7].

Assume that at time t ⁼

0,

the electron is on chain 1

1102

and that the

donor-acceptor tunnelling

matrix element is

given by tal.

Then at

time t,

^{the electron wave}

function ql

^is

given by :

One factor which arrests this coherent build _up is the

scattering

of the electron either on chain 1 or 2.

Let us assume that this

scattering

^{time is}

given by

’tv,

or

by :

when the two chains have different

scattering

^times

LV! 1 and LV2.

If ta L Tvlh >

^{2 7r} the wavefunction oscillates back and forth several times between the chains and we can consider it to be a coherent

superposition

^of

t/J 1

and

t/J 2.

If on the other

hand 11 Tvlh 1, ql

^{has no time to}

build _up on chain 2 before its

phase

^is

destroyed

^and

we do not have a coherent

superposition

^{but rather}

diffusive motion between chains. Therefore in this

picture

^we expect ^a

gradual changeover

^{from diffusive}

to coherent motion at a temperature ^{for which}

A similar

point

of view has

already

^been

expressed by Ong

^{and Portis}

[8]. If ti

^{is of the order of 5 meV for}

TTF-TCNQ

^{then this}

corresponds

to Lv ⁼

10-13

s

which is

roughly

^{the correct order of}

magnitude,

^at

60 K. Since

fully

coherent motion will

probably

^lead

to an increase of

102-103

in

RH

^{it is not} necessary that this condition be satisfied

exactly

^{in order to}

get

an increase of a factor of four or so

by

^{60 K.}

The differences between

HMTSF-TCNQ

^{and TTF-}

TCNQ

^are

clearly apparent

^{in this}

picture

^because

there is a lot of other evidence

showing that t.L

^is

several times

larger

in the former material and this is

why RH

^turns up ^at

higher temperatures

^{(160 K for a} factor of 2 increase in

RH

^as

opposed

^{to - 70 K for}

TTF-TCNQ).

^The

relatively strong

pressure

depen-

dence of

RH in HMTSF-TCNQ

may be ascribed to the increase in electronic mean free

path

^{under pres-}

sure since around 200 K the

conductivity

^{is still}

strongly

^pressure

dependent [5].

Although

^{the above}

interpretation

^{is the one which}

we

presently

^{believe to be correct we cannot be}

completely

^sure that condition

(6)

^{is even satisfied}

to within a factor of 10 in our

samples

^{which had}

conductivity peaks

^{of 10-20. The value Tv =}

^lO-13

^s

is

already

^{60 times}

larger

than that deduced from the

room

temperature conductivity

^{and thus we miss a}

factor of 3-6 at 60 K. If

conductivity

^is

mainly by TCNQ

chains the

discrepancy

^{will be even}

larger.

Furthermore the

value t.L

^{= 5 meV also}

represents

an upper limit. It was determined from NMR work

[25]

and arises from several _escape

paths,

^not

necessarily

in the a direction.

(ii)

^Possible

effect of

^1D

fluctuations

ⁱⁿ

RH. -

In view of the

uncertainty regarding

^{the transverse}

propagation

ⁱⁿ

TTF-TCNQ

^{at low T we wish to}

mention a different

interpretation

of the increase in

RH-

The latest

X-ray

^results

[19]

show that in

TTF-TCNQ

the 2

kF

diffuse lines start to appear around 150 K and

gradually

^{increase in}

intensity

^{at lower}

temperatures.

Since these lines in a sense

represent

fluctuations towards the low T

semi-conducting

^{state it is}

possible

that

they

could be associated with an increase in

RH.

Indeed several theories suggest the existence of a

pseudogap

in the electron

density

^{of states above the}

phase

transition at 53 K

[23].

^This

point

^{of view is}

consistent with the

temperature dependence

^of

RH

ⁱⁿ

TTF-TCNQ

^under pressure

(RH-1 ~ T)

^{and with}

the fact that in

HMTSF-TCNQ

^{the diffuse}

X-ray

lines are observed to near room

temperature [26].

Within this

picture

^{the low T} semi-metallic state of

HMTSF-TCNQ

would be associated with an incom-

plete

Peierls transition as mentioned

previously [3].

Such a

picture

^{has a number of}

interesting

^conse-

quences. It

implies

^{that in} both materials the ID fluctuations (i.e. the 2

kF anomalies)

^become stronger under pressure. In

TTF-TCNQ

^this may be due to an

increase in the mean field transition temperature

(Tp) ^[27]

combined with an increase in the electronic

mean free

path

^under pressure. We would expect ^the

smearing

of the anomalies in k _space to be of the order

Akb ~ 1/1

^and

clearly

^{for I ~ b the 2}

kF

^ano-

malies will be smeared out. Therefore

according

^{to this}

picture

^{one would}

expect

^{the 2}

kF anomaly

^to

persist

up ^to

higher temperatures

^under pressure, and in

general

there should be a connection between the

strength

^{of the 2}

kF

anomalies and the mean free

path

^I.

A

difficulty

with this

approach

is that in TTF-

TCNQ 4 kF

anomalies have been observed _up to room temperature

[19]

^{and a}

priori

^these may also

give

^{rise to a}

pseudogap.

^{In order to} get around this

objection

^{we have to}

postulate

^{that for} some reason

the 4

kF

anomalies do not affect the

conductivity

^or

Hall effect _e.g.

by being

associated with the TTF chains

only.

5. Conclusion. ^- In

conclusion,

^we have shown that DC Hall effect measurements are feasible on

single crystals

^of

TTF-TCNQ

^even in the metallic

region

^{and we now have a better}

understanding

^{of the}

experimental problems

associated with measurements in such

anisotropic

materials. For the field orientation used here the value at ambient _pressure is not very different from the classical value

llnec,

^{with n the}

concentration of electrons _per molecule on the

TCNQ

chain. The increase at low

temperature

may be due to

an

incipient changeover

^from transverse diffusive

conductivity

^{to a more coherent one. For a two band}

model characteristic of the two types of chains this

gives

^a much smaller number of free carriers and

consequently

^{a much}

larger

^{value of}

RH

^when any

degree

of coherence can build _up between the wave-

functions on the two

types

^of chain. Thus the

turn-up temperature

^{serves as a measure of the}

donor-accep-

tor

covalency.

Alternatively,

^as discussed in the next, the increase in

RH

may be associated with the occurrence of the

2 kF

anomalies in the

X-ray scattering

^which may become

sharper

^under pressure

mainly

because of the increased electronic mean free

path.

It

might

^be

possible

^to

distinguish

between these two

interpretations

in the future

by making

^{similar mea-}

surements on materials which

clearly

^have

only

^one

type ^of

conducting chain,

because in such a case

transverse

tunnelling

^{should not lead to a drastic}

reduction in the number of carriers. We believe that such measurements would also be of

especial

^interest

for those materials which remain metallic down to low

temperatures

^{in order to} determine the number of carriers.

Acknowledgments.

^{- We are}

particularly grateful

to S.

Barisic,

^A.

Bjelis,

^{R. H.} Friend and H. Gut- freund for

helpful

discussions and to N. P.

Ong

^and

A. M. Portis for

helpful correspondence

^and

preprints

of references

[8]

^and

[9].

The technical assistance of G. Malfait in the _pressure

experiments

^is

appreciated.

References

[1] ^{Recent work} by many groups will be summarised in :

a) Proceedings of the NATO-ASI Summer School on Chemistry and Physics of one-dimensional metals. Ed. H. G. Keller

(Plenum Press) ¹⁹⁷⁷ (our previous work is summarized in the article by JÉROME, ^{D. and} WEGER, M.).

b) Proceedings of the Conference of Organic ^Conductors

and Semiconductors held in Siófok, Hungary, Sept. 1976,

to be published early ^{in 1977.}

[2] COOPER, ^J. R., WEGER, M., DELPLANQUE, G., JÉROME, ^{D. and} BECHGAARD, K., J. Physique ^{Lett. 37} (1976) ^{L 349.}

[3] ^{Idem in} Proceedings ^{of Siófok} Conference, ^{to be} published

in 1977.

[4] BLOCH, ^A. N., COWAN, D. O. BECHGAARD, K., PYLE, ^R. E., BANKS, ^{R. M. and} POEHLER, ^T. O., Phys. Rev. Lett. 34

(1975) ^1561.

[5] COOPER, ^J. R., WEGER, M., JÉROME, D., LEFUR, D., BECH- GAARD, K., COWAN, ^{D. O. and} BLOCH, ^A. N., Solid State Commun. 19 (1976) ^749.

[6] SODA, G., JÉROME, D., WEGER, M., BECHGAARD, ^{K. and} PEDERSEN, E., ^Solid State Commun. 20 (1976) ^107.

[7] WEGER, M., Solid State Commun. 19 (1976) ^149.

[8] ONG, ^{N. P. and} PORTIS, ^A. M., preprint Sept. 1976, Phys. ^Rev.

B 15 (1977) 1782; ^also ONG, ^N. P., PORTIS, ^{A. M. and} KANAZAWA, K., ^{Bull. Am.} Phys. ^{Soc. 20} (1975) ^465.

[9] LYO, S. K., Phys. ^{Rev. B 14} (1976) ^3377.

[10] COHEN, ^M. J., COLEMAN, ^L. B., GARITO, ^{A. F. and} HEEGER, A. J., Phys. ^{Rev. B 10} (1974) ^1298.

[11] DJUREK, D., FRANULOVI0106, K., PRESTER, ^M. and TOMI0106, S., Phys. ^{Rev. Lett. 38} (1977) ^715.

[12] MILJAK, M. and COOPER, ^J. R., unpublished ^work.

[13] FARGES, J. P., BRAU, A., VASILESCU, D., DUPUIS, P. and NEÉL, J., Phys. Status Solidi 37 (1970) ^745.

[14] ^{VAN DER} PAUW, L. J., Philips ^Res. Rep. 13 (1958) ^1.

[15] ^{VAN DER} PAUW, ^L. J., Philips ^Res. Rep. 16 (1961) ^187.

[16] ^Professor BOK, J., private communication.

[17] ^Dr FERT, A., private communication ²⁰¹⁴ we are grateful ^to

him for this standard sample.

[18] ZIMAN, ^J. M., Electrons and Phonons (Clarendon ^Press Oxford) 1960, Chapter ^{XII Sect. 5.}

[19] POUGET, J. P., KHANNA, ^S. K., DENOYER, F., COMÈS, R., GARITO, ^{A. F. and} HEEGER, A. J., Phys. ^{Rev. Lett. 37} (1976) 437 and references therein, ^{see also} COMÈS, R., in reference [1, a], ^and KAGOSHIMA, S., ISHIGURO, ^{T. and} ANZAI, H., ^J. Phys. ^Soc. Japan ⁴¹ (1976) ^2061.

[20] CHAIKIN, ^P. M., KWAK, ^J. F., JONES, ^T. E., GARITO, ^{A. F. and} HEEGER, ^A. J., Phys. Rev. Lett. 31 (1973) ^601.

[21] CHAIKIN, ^P. M., KWAK, ^J. F., GREENE, ^R. L., ETEMAD, ^{S. and} ENGLER, ^E. M., Solid State Commun. 19 (1976) ^1201.

[22] WELBER, B., ENGLER, E. M., GRANT, ^{P. M. and} SEIDEN, ^P. E., Bull. Am. Phys. ^{Soc. 35} (1976) ^{311 and} private ^communi-

cation from SEIDEN, P. E. to D. J.

[23] LEE, P. A., RICE, ^{T. M. and} ANDERSON, P. W., Phys. ^Rev.

Lett. 31 (1973) 462;

BJELI0160, ^{A. and} BARI0160I0106, S., J. Physique ^{Lett. 36} (1975) ^{L 169.}

[24] ^{See for} example MOTT, ^{N. F.} and DAVIES, E. A., Electronic Processes in Non-Crystalline ^Materials (Clarendon Press, Oxford) 1971, section 2-12.

[25] SODA, G., JÉROME, D., WEGER, M., FABRE, ^{J. M. and} GIRAL, ^L.

Solid State Commun. 18 (1976) ^{1417. See also} SODA, G.

in references [1, a] ^and [1, b] ^{and also} SODA, G., JÉROME, D., WEGER, M., ALIZON, J., GALLICE, J., ROBERT, H., FABRE, J. M. and GIRAL, L., ^{to be} published

in J. Physique ³⁸ (1977).

[26] WEYL, C., ENGLER, E. M., ETEMAD, S., BECHGAARD, K. and JEHANNO, G., Solid State Commun. 19 (1976) ^926.

[27] COOPER, J. R., JÉROME, D., ETEMAD, ^{S. and} ENGLER, E. M., ^to appear in Solid State Commun. (1977) ^and COOPER, J. R., JÉROME, D., WEGER, ^{M. and} ETEMAD, S., ^J. Physique ^Lett.

36 (1975) L ^219.

[28] GUTFREUND, H. and WEGER, M., ^to appear in Phys. ^Rev.

( 1977).