Negative Magnetoresistance in (TMTTF)2Br

(1)

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Negative Magnetoresistance in (TMTTF)2Br

M. Basletić, D. Zanchi, B. Korin-Hamzić, A. Hamzić, S. Tomić, J. Fabre

To cite this version:

M. Basletić, D. Zanchi, B. Korin-Hamzić, A. Hamzić, S. Tomić, et al.. Negative Magnetore- sistance in (TMTTF)2Br. Journal de Physique I, EDP Sciences, 1996, 6 (12), pp.1855-1864.

�10.1051/jp1:1996193�. �jpa-00247286�

(2)

J.

Phys.

l France 6

(1996)

1855-1864 DECEMBER1996, PAGE 1855

Negative Magnetoresistance in (TMTTF)2Br

M.

Basletié (~),

^D.

^Zanchi (~),

^B. Korin-Hamzié

(~,*),

^A. ^Hamzié (~

),

S. Tomié

(~)

^and ^J-M- ^Fabre

(~)

(~) Department of

Physics, Faculty

of Science. HR-10000

Zagreb,

Croatia

(~) Laboratoire de

Physique

des

Solides,

Université

Paris-Sud,

91405

Orsay

Cedex. France (~) ^Institute ^of

Physics

of trie University, PCB 304, HR-10000

Zagreb,

Croatia

(~) ^Université ^de

Montpellier II,

USTL, 34095

Montpellier,

France

(Received

il March 1996, revised 2

July1996,

accepted 19

August 1996)

PACS.74.70.Kn

Organic superconductors

PACS.72.15.Gd

Galvanomagnetic

and orner magnetotransport elfects

Abstract. We report trie transverse magnetoresistance measurements ai ambient pressure

in the organic conductor

(TMTTF)2Br

_in the temperature _range ^between ^4.2 K and 40 K and

in

magnetic

fields _up tu 8.5 T. We bave round isotropic,

negative

and temperature dependent

magnetoresistance

which becomes

neghgible,

close tu 40 K. We interpret trie observed behaviour within trie picture of

strongly

correlated quasi-one dimensional systems.

1. Introduction

The

highly auisotropic

_orgauic couductors

(TMTCF)2X (C

=

Se,

S: where TMTSF is tetram-

ethyltetraselenafulvalene,

TMTTF is

tetramethyltetrathiofulvaleue

aud X is _au avion:

Cl04, PF6, Re04, Br...)

_are the series of isostructural

compounds

in which _a wide

variety

of

phe-

nomena related to trie low-dimeusional nature of trie electrouic

spectrum

are fouud

iii.

These

indude

superconducting, antiferromagnetic (spin-density

_wave

SDW)

_or

spin-Peierls ground

state; a number of

peculiar maguetic

^field ^effects ^such as a

large

and

anisotropic positive

_mag-

netoresistance,

trie appearance of

magnetic

field-induced SDW'S

(FISDW),

I.e. _a cascade of SDW

phases appearing

for

increasmg H,

etc... It is

generally accepted

that

exchanging

Se for S and

for using

a different anion X and _an externat pressure lead to trie unified

phase diagram

for trie

(TMTCF)~X

series

(Fig. l),

where trie

properties

of _one

compound

at _a

given

_pressure

are

analogous

to those of another

compound

under

higher

_pressure _[2].

Trie selenium based

(TMTSF)2X

salts exhibit _a

high conductivity

at the _room

temperature

and _a metallic behaviour down _to trie low

temperatures,

^where ^trie mcommensurate SDW

ground

state is established. Trie externat pressure increases trie transverse

couphng

^and above à la kbars trie SDW

ground

state is

suppressed

in favor of

superconductivity.

Trie

application

of _a

magnetic

field

along

trie

least-conductiug

_axis

destroys

trie

superconducting ground

state

aud induces trie FISDW

phases

due to _a

progressive

unidimensioualisation of electronic states uuder field.

(* Author for

correspondence: (e-mail: bhamzic©olimp.irb.hr)

©

Les

Éditions

_de _Physique ₁₉₉₆

(3)

1856 JOURNAL DE

PHYSIQUE

I N°12

3100 ',,

CONDUCTOR

uJ CL

", à

$

_la

ce

Éf sp SDW

~

~ l

SC

~~~~~~~~

5 kbar

à

~

°

~ tD ~ O

" " " "

~ ~ ~ ~

~ ~

~ ~ ~ ~

~' ~' ~'

Fig.

1. The

position

of

(TMTTF)2Br

in the unified T P

phase diagram

for trie

(TMTCF)2X

serres.

SP,

SDW and SC refer to

spiu-Peierls,

_spin

density

_wave and

superconducting ground

states,

respectively.

Trie dashed fine marks

Tp,

i.e. trie limit between metallic like conductor and locahsed

(CL)

behaviour. The ambient _pressure locations of several compounds _are mdicated.

The _more

anisotropic,

e. more

lD,

sulfur based salts

(TMTTF)2X,

_on trie other

hand,

bave

a much smaller

conductivity

at trie _room temperature, enter a

charge

localization

regime

below 200

K,

and _are very

good

insulators at low

temperatures

where trie

spin-Peierls

transition

occurs

[2,3].

Trie existence of trie

resistivity

minimum at trie

temperature Tp

is

iuterpreted,

within trie 1D electron gas

theory _[4],

_as _a direct consequence of _a

significantly stronger coupling

to trie aniomc

potential

_via

Umklapp scattering,

which induces _a small dimerization

along

trie snacks

[5,6].

^Trie

repulsive

interactions between electrons lead _to trie creation of _a correlation gap

Ap

^and to a

semiconducting

^behaviour below

Tp.

^For ^T <

Tp

^trie

development

of lD

antiferromagnetic

fluctuations _goes

along

with trie electron localization. Trie externat _pressure reduces trie dimerization and this decreases

Ap

^and ^shifts

Tp

^towards ^lower temperatures. Trie

spin-Peierls grouud

state _crosses _over to trie

antiferromagnetic

SDIV state commeusurate with trie lattice. When

higher

_pressure _is

applied, Ap

^is

suppressed, _Tp

_is _no

longer

visible

(due

to a

charge delocalization),

and trie iucommensurate SDW state emerges. Trie

antiferromag-

netic charactenstics of trie sulfur _serres become similar to those of trie selemde _serres and trie

superconducting grouud

state _cau be

expected

at

higher

_pressures.

Amoug

ail trie knowu

(TMTTF)2X materials, (TMTTF)2Br

bas trie smallest _avion aud _c lattice

parameter [7j,

^trie

highest couductivity

at trie _room

temperature (aa

= 100

(Qcm)~I

aud that is

why

it occupies a

key position

m trie unified

(TMTCF)~X phase diagram.

Trie

superconductivity,

with

Tc

"

K,

for this

compound

_was observed under 2à kbar _[8]

(for comparison,

trie

correspoudiug

value _was 8 kbar in

(TMTSF)~PF~ iii),

thus

confirming

trie

predictions

of trie unified

phase diagrani. (TMTTF)2Br

shows _a metallic behaviour dowu to

Tp

re là0 K

[7,9],

aud _a

semicouductiug

_one belo~v

Tp.

^On ^trie ^orner

hand,

trie

magnetic susceptibility xs(T)

does uot show _auy

anomaly

_near

_{Tp [3j,} mdicating

trie

separation

betweeu

charge

and spiu

degrees

of freedom [6]. ^Below

Tp

^the

charge degrees

of freedom become frozen _eut without trie _occurrence of _any additional lattice _or

magiietic

distortions, while trie spin

susceptibility

_is left unaffected

by

trie electron localization. A SDW

phase

transition

(4)

N°12 NEGATIVE MAGNETORESISTANCE IN

(TMTTF)2Br

1857

at TN m 10 là K [9] is revealed

by conductivity [ii, thermopower _[10]

and

susceptibility

data

[iii,

while the NMR measuremeuts have shown the existence of _a commeusurate SDW

ground

state

[12,13].

The critical _pressure where

Ap

_~ 0 for

(TMTTF)2Br

sait is about 5 kbars

[14].

^At pressures

higher

than 10

kbars, (where Ap

^is

ummportant

and trie

ground

state is trie iucommeusurate

SDW),

trie

progressive

iucrease of trie

positive maguetoresistauce

with

increasing

_pressure _was found

[7]. However,

the

magnetoresistance

^data at lower _pressures and for T _<

Tp, (where

the existence of

Ap

suppresses any

single-partiale

transverse

tunueling).

have net beeu

presented

_UP to now.

There _are few results _on the

uegative magnetoresistauce

in the

organic

conductors. lu the two-chain orgamc conductors the

magnetic

field

dependeuce

^of the Peierls transition

tempera-

ture was found

[15,16].

The small

isotropic

and

negative magnetoresistance

in

TTF-TCNQ

_[15]

below Peierls transition follows _a

T~~

behaviour. This effect _was ascribed to the small increase

m the

charge

_carrier

density

caused

by

the band

splittiug.

The

negative

aud

anisotropic

magnetoresistauce has beeu observed in the series of

(DMTTSF)2X

salts

[17],

^which are

isomorphous

with

(TMTCF)2X

but show metallic-like behaviour dowu to the low

temperatures,

^where ^the

resistivity

saturates without trie _occurrence of

superconductivity.

The

maguetoresistauce

bas beeu

iuterpreted

iii terms of 2D weak localization due to trie disorder iii trie avion lattice.

lu this work _we

preseut

_au

experimeutal investigation

^of trie

maguetoresistauce

of

(TMTTF)2

Br at ambieut _pressure aud for T _< 40 K. Dur data

reveal,

for trie first

time,

_a

uegative maguetoresistauce

iii _eue member of trie

(TMTCF)2X family.

Trie results will be

aualysed

in trie framework of correlated

quasi-1D

couductors [6].

2.

Experimental

Results

Three

siugle crystals

_were studied.

Samples

_were mounted in trie classic four-in-fine array geometry ^with

gold

wires stuck with silver

paint

on

pre-evaporated gold

contacts

(trie voltage

contacts encircled trie

crystal,

whereas trie curreut contacts covered

completely

trie euds of

trie

samples).

Trie resistauce _was measured with _au ou-fine de

set-up,

^with curreut reversed ai each field value. Trie de curreut,

aloug

trie best

couductiug

direction

(a axis)

_was

kept

low

euough

iii order to avoid Joule

heatiug

aud

possible

uou-ohmic effects. Wheu trie

sample

resistauce exceeded 10~ Q

(for temperatures

^below ¹⁰

K),

trie

voltage

_respouse _was measured

by

electrometer with

iuput impedauce

_> 10~~ Q. Trie liuear I V _curves obtaiued at 4.2 K aud 8 K coufirmed that ail _our data refer to trie ohmic

couductivity regiou.

At each

temperature,

trie

maguetic

^field

(up

to 8.5

T)

_was

aligued aloug

^trie ^c* ^aud ^b' ^directions

(1.e. perpeudicular

to trie

current).

Trie _room

temperature couductivity

_aa values for three

samples

_were

55,

72 and 30

(Q cm)~~

for

samples 1,

2 and 3,

respectively. Samples

were cooled

slowly (3 K/heur)

in order to avoid irreversible resistance

jumps,

well kuowu to appear lu ail

orgauic

couductors. We observed very few cracks which bave net exceeded _a few _per cent of trie

sample

resistance.

Figure

2 shows trie temperature

dependence

of trie uormalized resistauce

R/Rmjn (where

Rmin

_is the minimum value of the resistance

just

above

Tp

m 1à0

K)

^for trie three

samples

measured in this work. Ail the

samples

exhibited

qualitatively

the _same behaviour. The

temperature dependence

of the

resistivity p(T)

below lào K _can be

analysed

_usmg _a

phe- uomeuological

law for _a

simple

semiconductor

p(T)

₌ _pmm

exp[A(T) /kT] (1)

m which ail the thermal evolution of

p(T)

is included in the function

~h(T),

^defiued as T-

depeudent

_energy _gap. Trie

prefactor

is determiued _as _pmm

=

p(Tp)

t.e. trie

resistivity

value

(5)

1858 JOURNAL DE

PHYSIQUE

I N°12

~~

~

4

+

lO~

~ sample 1 ⁺ ^à

~

[

^sample ² _~+ _~ ^~

lO~

~~~~~~ ~

+ A~ _'

~~

_{_,} ^'

~ ^,

,,"

lO 1 "

à ,

C

( lO~

~~~

lO~

~~

ÎÎ

~~

~ ^~/ 80

~

~°

~~40

(

20

~

lO~

°

o 50 ioo

o

T

(K)

lO

o 5 la 15 zo z5

100/T (1/K)

Fig.

2. Normalized resistance

R/Rm,n

_~s. temperature for trie three samples. Inset: The temper-

ature dependence of trie activation gap

àp(T)

deduced from trie

resistivity

data of trie

sample

2 with

trie

highest

_room temperature conductivity value.

just

above

Tp.

^As ^mentioued

previously,

this minimum is attributed to trie

opening

^of trie correlation _gap

Ap

ⁱⁿ ^trie ^electronic spectrum below

Tp. Assuming

that

A(T)

=

Ap(T)

and usiug

equation (1), Ap(T)

for

sample

2 is given in trie iuset of trie

Figure

2. As

shown, Ap(T)

starts from _zero _ai

Tp

^and ^reaches ^trie ^value ^of about 110 K at trie SDW

phase

transition

TN

" 11 K

(this

value _was determined from _our ESA data _on the

samples

from the _same

batch

[18] ). Furthermore,

there _is aise _a

change

in trie

slope

^of

A(T)

below 20

K, probably

related _to trie SDW

phase

transition. For T _< 10 K trie

change

_m trie

slope

of trie

resistivity

towards _some

saturating

value is

sample depeudeut,

aud this _cau be attributed to trie _presence of

impurity

levels _lu trie semicouductor euergy gap. We _can therefore _assume that below 8 K trie

conductivity

for ail _our

samples begms being

dommated

by

_a

temperature mdepeudeut

component, ^which

probably

results from

crystal

defects aud

impurities.

This component can

be

expected

to be

relatively

msensitive to _an

applied magnetic field,

and _one _can

anticipate

_a

vanishing magnetoresistance

at very low temperatures.

Trie

maguetoresistauce data, Ap /p

=

[p(H) p(0)] /p(0),

_are shown _m

Figure

3, _as _a function of

applied magnetic

field

(H((c*

and

H((b')

at several fixed

temperatures.

^The

magnetoresis-

tance _is

negative, approximately

hnear _up to 8.à T and

independent

of trie orientation of trie

apphed magnetic

field

perpendicular

to trie curreut. Such _an

isotropy suggests

that trie oh- served behaviour is dominated

by

trie

magnetic

field

couphng

to trie spms

only,

and is not due to trie

amsotropic

effect which would be caused

by

the orbital

coupling.

(6)

(TMTTF)2Br

1859

5

o '°*

fbo

"~ _°

~~q~

~'

^~

~~Î~j~

~~ "

~fO

'~

~ o o o~

~"

É'~i~

~~~ ~' ° ',O o

~ .',

/&

" ° ',

Î~

^~~

_T

=

8 K ~"~i,~ _T

=

16 ~

~

~il

~

Cu ^~°

à '

^~

e~,Ç

^'~

~~~~ikÎ°~°~°i

'Q,O

-5 ..,

~ fi

~~° _° Hllb>

~~~

T

₌

27 K T

=

36 K

-20

0 Z 4 6 8 0 Z 4 6 8

H (testa)

Fig.

3. Trie

magnetoresistance àp/p

_~s.

applied magnetic

field

(for H((c*

and

H((b')

_ai several fixed temperatures

(for sample 2).

The

temperature dependence

of trie

magnetoresistance

^for ^three

^samples (for

H

= 8.à T and 4

T)

is showu iii

Figure

4. It _cau be

clearly

_seeu that trie

maguetoresistance Ap/p

starts

being

observable below 40

K,

aud its

uegative

value _iucreases to about

18%

_at 8 K. At 4.2 K trie

maguetoresistauce

becomes

uegligible

^for ^ail ^three

^samples.

^For two of them, trie variation of

Ap/p

is about trie same, whereas for trie third

sample

trie

magnitude

of

Ap/p

is

20%

weaker aud vauishes above 30 K. We believe that such _a behaviour is due to trie lower

quality

of this

particular sample,

siuce it had aise trie lowest _room

temperature couductivity

value.

3. Discussion

lu order to discuss trie observed

maguetoresistauce behaviour,

let us

agaiu

recall trie uuified

phase diagram

for

orgauic quasi-lD systems

_[2] ^aud ^locate

(TMTTF)2Br (Fig. l).

Que _sees _im-

mediately

that three

temperature

scales characterize _our material. Trie

highest

is trie _crossover

temperature

Tp,

at which trie

charge degrees

of freedom start to

freeze,

which _meaus that trie electrous become _more aud _more localized at trie lattice sites. This behavior is

quite

^well illus- trated

(see Fig. 2) by

trie

progressive

iucrease of trie _euergy _gap _ou

loweriug

trie

temperature,

which is deduced from _our

experimental

data and _a

simple

law

given by equatiou (1).

Trie

electrou localizatiou is driven either

by

trie

4kF scattering

_process

(which

is relevant if trie band

is

half-filed),

_or if there is _a

4kF-gap A4k~

ⁱⁱⁱ a non half-filled

baud,

which is _our _case. Trie

correspoudiug

bare

4kF scatteriug amplitude,

_t _e. trie

streugth

of trie electrou-electrou Umk-

lapp

_process,

commouly

called _{g3 in} trie

"g-ology" decompositiou

of trie direct electrou-electrou

(7)

1860 JOLÎRNAL DE

PHYSIQUE

I N°12

O

fÎÎ ÎC~

~,

_

-5

/"'

@

(

/"

_ T ^'

Î

1

ç~ ^lO

~

~#

_sampie

.

j8.5

Tj

-15

~

^sample ² ^X ^8.5 ^T

+ (4 T) sampie 3 à (8.5 T) -ZO

la ZO 30 40

T (K)

Fig.

4. The temperature dependence of trie magnetoresistance for three samples and for H

= 8.5 T.

For

sample

2 the

magnetoresistance

data _are aise shown for H

= 4 T.

àp/p

= o for ail three

samples

ai 4.2 K. The fuit and dashed fines _are fit to

equation (4) (see text)

for H

= 8.5 T and 4

T, respectively.

interaction,

is

directly proportional

to

A4i~ [19]:

93 "

91à4kF /EF (2)

where gi is backward

scatteriug amplitude.

This relation _is _a crude

approximation,

but _as far

as we kuow this is trie

ouly

_eue that _cau be

applied

to _our _case.

For

temperatures

below

Tp

^the

spiu degrees

of freedom _are

decoupled

from the

charge

_Dues,

because of trie lD nature of ail trie motions

[20].

^The _spms on different chains become correlated at trie

temperature Tx2

Since trie

spin

_operator consists of electron-noie

(e-h) pairs

like

~ttr~,

this

temperature

bas trie

meaniug

of _a

two-partiale

_crosi-over from lD to 2D

(or 3D)

_regime.

Fiually,

_a

phase

transition to _a 3D

antiferromagnet

_occurs at

TN

Trie

spin-charge separatiou

is exact _as

long

_as trie electronic

spectrum

is

only

linear around Fermi level. Trie

non-lineanty

_can introduce small

mixing,

and

consequently,

trie effects of

maguetic

field to g3, as

pointed

ont in

[là]. Figure

5 shows

typical

lD

scatteriug

_process ⁱⁿ trie

case of Zeeman

splitted

linear electrouic spectrum, aud it is evident that

only

trie

spin

transfer

coupling

_gii _ceases to

couple

trie electrons

exactly

_m Fermi

points,

I.e. looses its relevance.

One should notice that trie bosonised Hainiltouiau for

charge degrees

of freedom

[20] depends ouly

_ou Fermi

velocity

and

scattering amplitudes _gijj 2g2

and g3, which _are ail

mdependent

on

magnetic

field.

Below

Tx2

trie

problem

_ceases to be

one-dimensional,

which

implies

that trie

spiii-charge separation

is _not vahd _any _more. This _meaus that trie

charges

start to feel trie

maguetic

field which is

coupled ouly

to the _spius. lu other

words,

below T~2 trie

spiu

becomes

coupled

to trie

charge,

aud

consequently,

trie

charge

fluctuations become field

dependent.

Trie effect of trie

magnetic

field to trie cntical SDW fluctuations bas been

analysed usiug

RPA

[21],

^but

ouly

in trie _g3

" 0 limit. These calculations bave shown that trie

spectral weight

of trie fluctuations for

trie SDW vector

parallel

to H is driven

upwards (by 2/LBH,

_pB is trie Bohr

magneton),

from trie fluctuations

perpendicular

to

H,

_t _e. trie fluctuations

parallel

to H become less cntical.

(More

reahstic

description

_~for trie TN < T _<

Tx2

_regime _is doser to _a

strong coupling,

and it is

expected

to be

represented

rather well

by

_a 2D

Heisenberg model).

Trie existence of trie additional _gap

2pBH,

for

spin

fluctuations

parallel

to trie

field,

_con be understood _more

(8)

(TMTTF)2Br

1861

iii

,~

EF EF

~ ~

>

k _k

k Fi -k Fi

kfj kfj

_{-k Fi -k} _Fi

kfj kfj

j j

g~ g~

EF EF

~ ~

>-

k _> k

-k _Fi -k Fi k~j

kfj -k~j

_{-k Fi} k~j

kfj

Fig.

5. Trie two-electron

scattering

_processes under Zeeman

splitting.

In order to preserve mo-

menta, ^the

spin-transferring couphng

_gii _is driven to irrelevance, _i-e- ii does non exist in the limit when trie eut-off around Fermi energy tends to _zero. Trie relevance of other processes ares net

change.

~ _~

l

EF

~

>

k

-k _Fi -k Fi

kfj kfj

Fig.

6. The creation of _an opposite-

(a)

and _a

parallel-spin (b)

electron-hale _pair. An additional energy

2pBH

is needed for the creation of trie

parallel-spin

electron-hale _pair.

intuitively estimating

what

euerfy

^we ^ueed ^to ^create ^a

^spiu

^excitation ^at ^q ⁼

^2kF ^Parallel (fil(~lF-i)

^and

perpendicular (lF~~ W-t

to trie

magnetic

field. It is evident, from

Figure

G,

that _a creation of e-h

pair

^with

opposite spins

costs

equal

_energy _as for H

= 0

(a).

Trie

creation of _a

parallel-spin

e-h

pair

at

2kF

is net

possible

if both

partiales

_are to be at trie Fermi surface

(b).

Trie minimum energy needed is

2pBH,

which

corresponds just

to trie field-

dependent part

of trie gap for

parallel

modes.

By constructing

trie local

thermodynamics

for

spins

around

2kF,

_we _expect that trie

parallel-to-perpendicular spin

fluctuations ratio will be

given by exp(-2pBH/kBT),

where kB ^is Boltzmauu constant.

Turning

uow to our

results,

let _us first

emphasize that,

since one-electron motion is lD in ail

regimes,

trie

ouly possible coupliug

of electrous with

maguetic

^field is trie Pauli _one. Trie tact that there is _no orbital

coupliug

leads tu trie

isotropic maguetoresistauce, iudepeudeut

of field direction. This _is well coufirmed

by

_our

results,

showu iii

Figure

3.

(9)

1862 JOURNAL DE

PHYSIQUE

I N°12

1

_ii

Z=2~

+

~

Fig.

7. The first order _une

particle self-energy

for

antiferromagnetic

fluctuations: two

degenerate

modes

perpendicular

and _une

parallel

tu

magnetic

field.

The

negative magnetoresistance (cf. Fig. 4)

is due tu trie meutioued

suppression

^of ^fluctua- tious

parallel

tu H in trie critical

regime. Namely,

^trie ^lD ^electrons bave less

antiferromagnetic

fluctuations to scatter at, 1-e- trie

only

left _are trie two modes

perpendicular

to H. We _can calculate trie

maguetoresistauce by usiug

trie

self-euergy (L)

corrections due to trie two per-

peudicular

and _one

parallel spin

modes.

Figure

7 shows trie

diagrams

takeu iuto accouut. Trie bosouic fines _are

2kF-spin

fluctuation

propagators,

and indices

(( and 1 deuote their direction

lu

maguetic

field. Trie

change

of trie resistauce

Ap

iii _a

maguetic

field H is:

Ap

=

[p(H) p(0)]

r-

Im

L(La

=

0)H

Im

L(w

=

0)H=o (3)

where _w is trie one-electron

frequency

which _we

put

to zero, since _we _are interested in DC resistance.

The

diagrams

iii

Figure

î

contribute, roughly speaking,

_as

exp(-Ajj /T)

and

exp(-Ai /T)

where

Ajj

^and

Ai

_are trie _gaps for

parallel

and

perpendicular

fluctuations

respectively _[21].

If _one _assumes

iutuitively

that

Ai

re

Ai

+

(pBH/T (where (

is _a uumerical constant of the

order of

2),

the

maguetoresistauce

is:

Ap(H) exp(-2pBH/kBT)

i

P(°1

^" ^~

P(°) exP(Ai/Ti

^~~~

where

Ai

= AD

lu(T/TN)

aud

~o

"

47rTfi@

rd 4.33

T,

aud _a is _a

prefactor haviug

the nuits of

resistivity,

thus

providiug

the correct

dimeusiouahty.

Dur data

(Fig. 4)

show that trie

uegative maguetoresistauce

is observed for 8 K < T <

40

K,

aud

Ap/p

₌ 0 _at 4.2 K. Trie _Upper

limitiug temperature

is field

independent (1.e.

^trie

magnetoresistance

becomes

negligible

for H

= 4 T and 8.5 T at about trie _same

temperature)

aud _cau be taken _as trie

high-temperature

cut-off value for

equation (4). Taking TN

₌ ii

K,

our zero-field

resistivity

data

p(o)

and fixed field value

(8.5 T)

_we bave calculated

Ap/p(0)

values from

equation (4)

for different _o

(where

different _a

correspond

to

products

of trie _same pmm value and different uumerical

factors).

Once trie best agreemeut was obtained for trie data at 8.5 T

(fuit

fine.

Fig. 4),

trie _same _a value _was taken for

fitting

trie 4 T data

(dashed

fine,

Fig. 4).

One _sees that

quahtatively

_a rather

good agreement

^between our

experimental _points

and

equatiou (4)

is obtaiued

(for

4 T and 8.5

T)

_m trie

temperature

_range 18 K _< T _< 40

K,

but

ouly

with

Ao/T

_re 7

ii.

e. 1.6 times

larger value).

Ou trie other

baud,

it bas beeu

beyoud

this

approach

to calculate trie exact form of _a

(although

_we believe that it is related to trie

resistivity

due _to trie

spin fluctuations)

and thus any further

quantitative

_comparison of the used

fittiug

parameter a would be toc

presumptuous

at this

point.

Bath calculated _curves show _a _minimum _at _re là K. Trie field

depeudeuce

of

equatiou (4)

_is

mouotouous aud has _no

extreme,

^aud ^this minimum _is

simply

due to the fact that iii this _regime

there _is _a clear

change

of trie

slope

iii trie

temperature

variation of _our zero-field

resistivity (cf. Fig. 2).

Had it been not the _case, the calculated _curves would continue

decreasing

as

temperature

approaches TN- Apart

from

that,

and

bearing

_m mmd trie crude theoretical

assumptions, equation (4) provides

_a

satisfactory qualitative

fit for bath temperature ^and ^field

(10)

(TMTTF)2Br

1863

variation of the

magnetoresistance

of

(TMTTF)2Br

_in the

regiou

18 K _< T < 40

K,

_t.e. for

temperatures

where the

autiferromaguetic

fluctuations _are

important.

Equation (4)

cauuot be

applied

for T _<

TN,

where the SDW

grouud

state is well defiued. It has beeu

predicted theoretically _[21]

that the

opeuiug

of the small _{gap in} _eue of three Goldstoue

modes below

TN

is

expected

to have direct cousequeuces ou trie measurable

properties

like

maguetoresistauce.

The

quantitative aualysis

of these effects _is _a rather

complex problem

aud remaius opeu for future

investigations.

Withiu the

preseuted picture

we cauuot say what is the

maguetoresistauce

value

expected

at 4.2 K.

However,

_as

already meutioued,

the

vauishiug maguetoresistauce

at 4.2 K may be

simply

the cousequeuce of the fact that the

maguetic

^field has _no influence _ou defects aud

nov-maguetic impurities.

lu that _case, wheu the

temperature

is mcreased and

approaches

the

regime

^with

strong fluctuations,

the effects of the

applied

field _on the resistance start

being

visible. Above 8 K

(and

_up to 40

K)

the

negative magnetoresistance

qualitatively

_agrees with the

dependence given by equatiou (4). Fiually,

for T _> 40

K,

the

maguetoresistauce

becomes

negligible again.

In accordance with _our

previous discussion,

_we

suggest

that this upper

(predicted

field

independent _[21])

cut-off

temperature

is

just Tx2.

Dur

results would thus be trie first to show its existence.

4. Conclusion

In

conclusion,

we

report

^trie

isotropic

aud

uegative magnetoresistance

in the

organic

conductor

(TMTTF)2Br

at ambient pressure. The

maguetoresistauce

is the

largest

at about 8 K

(18%),

decreases with

increasmg temperature

and vanishes above 40 K. We

interpret

our results _as trie consequence of the Pauli

coupling

of electrous with

maguetic

field that

yields

to the

isotropic magnetoresistauce.

The

uegative maguetoresistauce

^is ^due to the reduced

scatteriug

of elec-

trous _ou the

autiferromaguetic

fluctuations which

develop

below the _crossover temperature

Tx2.

Dur calculatious

reproduce qualitatively

the

expenmeutal fiudiugs

which estimate Tx2 to about 40 K.

Acknowledgments

The authors _are

pleased

to

ackuowledge stimulatiug

discussions with A.

Bjelii,

K.

Maki,

E.

Origuac,

H. Schulz aud P. Wzietek.

References

iii

For the

geueral

introduction _see: Jérome D. aud Schulz

H-J-,

Adu.

Phu-s.

31

(1982) 299;

Ishiguro

T. aud

Yamaji K., Orgauic Supercouductors, Springer

Series _in Soiid-State Sci-

ences 88

(Spriuger-Verlag, Heidelberg, 1990).

[2] Jérome

D.,

Science 252

(1991)

là09.

[3] Coulon

C.,

Delhaes

P.,

^Flandrois ^S.,

Lagnier R., Bonjour

E. aud Fabre J-M-. J.

Phys.

France 43

(1982)

1059.

[4] ^For

example

_see:

Solyom J.,

Adu.

Phys.

28

(1979

201.

[Si

Emery V.,

Bruinsma R. and Bari§ié

S., Phys.

Reu. Lett. 48

(1982)

1039.

[6] Bourbonnais

C.,

Low Dimeusioual Conductors and

Super-conductors,

NA TO-AST

Series,

D. Jérome aud L.G. Caron Eds.

(Pleuum Press,

New

~"ork, 1987)

_p. 155.

(11)

1864 JOURNAL DE

PHYSIQUE

I N°12

[7] Parkiu

S-S-P-,

Creuzet

F.,

Jérome

D.,

Fabre J-M- aud

Bechgaard K.,

J.

Phys.

France 44

(1983)

975.

[8j Balicas

L.,

Behuia

K., Kaug W.,

Cauadell

E.,

Aubau-Seuzier P., Jérome

D.,

Ribault M.

aud Fabre

J-M-,

J.

Phys.

I France 4

(1994)

1539.

[9j ^{It is} ^showu

(Ref. [îj)

that

siguificaut

differeuces _are fouud betweeu

samples

_growu from differeut chemical solveuts. lu _our _case

(so

called

Montpellier samples) _Tp

_re 150 K aud

TN

_" ii K

(Ref. [18]).

[10j

^Parkin

S-S-P-,

Scott J-C-, Torrance J-B- and

Eugler E-M-, Phys.

Reu. B 26

(1982)

6319.

[1ii

Delhaes

P.,

Coulon

C.,

Amiell J.. Flandrois

S.,

Toreilles

E.,

Fabre J-M- and Giral

L.,

Moi.

Crys. Ltq. Cryst.

50

(1979)

43.

[12j

^Nakamura

T.,

Nobutoki

T., Kobayashi

Y.. Takahashi T. and Saito

G., Synth.

Met. 70

(1995)

1293.

[13j

^Barthel

E., Quirion G.,

Wzietek

P.,

Jérome

D.,

Christensen

J-B-, J»rgensen

M. and Bech-

gaard K., Europhys.

Lett. 21

(1993)

87.

[14j

Klemme

B-J-,

Brown

S-E-,

Wzietek

P.,

Kriza

G.,

Batail

P.,

Jérome D. aud Fabre

J-M-, Phys.

Reu. Lett. 75

(199à)

2408.

[là] Tiedje

T.. Carolau J-F- aud

Berliusky A.J.,

Con. J.

Phys.

53

(1975)

1593.

[16j

^Boufait

G., Lopes E-B-,

Matos

M.J., Heuriquès

R-T- and Almeida M., Soi. State Commun.

80

(1991)

391.

[lîj

Ulmet

J-P-,

Bachere

L., Askeuazy

S. aud Ousset

J-C-, Phys.

Reu. B 38

(1988)

î782.

[18j

^The

vauishing

ESR

susceptibility

and concomitant

divergence

of the ESR linewidth define trie critical

temperature

TN of trie SD~V

phase

transition of this

samples

at ii K.

[19j

Bari§ié S. and Brazovskii

S.,

"Recent

Developmeuts

_lu Condensed Matter

Physics",

Vol.

I,

J-T- Devreese Ed.

(Plenum,

New

York, 1981.)

_p. 327.

[20j

^{See for}

example:

Haldane

F-D-M-, J.Phys.

C14

(1981)

2à8à.

[21j Bjeli§

A. and Zanchi

D., Phys.

Reu. B 49

(1994)

à968.