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HAL Id: jpa-00247287

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Hall Effect Anomalies and Phase Transitions in the Organic Superconductors, κ(BEDT-TTF)2Cu(NCS)2

and β-(BEDT-TTF)2I3

Keizo Murata

To cite this version:

Keizo Murata. Hall Effect Anomalies and Phase Transitions in the Organic Superconductors,

κ(BEDT-TTF)2Cu(NCS)2 and β-(BEDT-TTF)2I3. Journal de Physique I, EDP Sciences, 1996, 6

(12), pp.1865-1873. �10.1051/jp1:1996195�. �jpa-00247287�

(2)

Hall Elllect Anomalies and Phase Transitions in trie Organic Superconductors, ~t-(BEDT-TTF)2Cu(NCS)2

and fl-(BEDT-TTF)213

Keizo Murata

(*)

Electrotechnical

Laboratory,

1-1-4, Umezono, Tsukuba lbaraki, 305

Japan

(Received

13

May1996,

revised 22

August, accepted

.5

September1996)

PACS.74.70K

Organic superconductors

PACS.72.15Lh Relaxation limes and mean free

patins

PACS.72.15Eb Electrical and thermal conduction in

crystalline

menais and

alloys

Abstract. Trie Hall coefficient, Ru

(T)

for

organic

conductors is

strongly

temperature

depen-

dent even if they are metallic. The temperature

dependence

of Ru

(T)

is found tu exhibit une-

to-one

correspondence

with trie structure of the Fermi surface, hence con be called "Standard"

for each surface. Ii turned Dut that the

simple temperature-independent

Ru

(T)

is

only

realized in a material where trie Fermi surface is round and

simple

for these low dimensional systems.

The "Standard"

Ru(T)

for each Fermi surface is obtained

empirically

by comparing

RH(Tl's

of

relatively high

pressure, where low temperature navet stores or excitations

are suppressed.

In some cases,

Ru(T)

deviates

abruptly

from trie standard

Ru(T)-behavior,

which suggests a

phase transition or lis precursor. We show the

examples

of

~-(BEDT-TTF)2Cu(NCS)2

and of

fl-(BEDT-TTF)213

in which the anomaly in

RH(T) corresponds

tu a

peak (r-

GO

K)

of antifer-

romagnetic

fluctuation, and tu 20

K-phase

transition which is a~sociated with low-Tc supercon-

ductivity, respectively.

As seen in these two

exarnples,

trie Hall eflect is

strongly

influenced by trie electronic state, and therefore, can be ~ useful trot for

locating phase

transitions.

1. Introduction

The Hall effect is

generally

known to show carrier

density

in metallic and

semiconducting systems by

trie

relation, RH(T)

=

1/~e,

where n is trie carrier

density

and e, trie electron

charge.

A

simple

consequence of this relation is that metallic materials show a

temperature tndependent RH (T),

at least wheu trie Fermi energy is much

higher

thon 300 K. In trie

past

several years, we bave examiued trie Hall effect of

orgauic

couductors aud

supercouductors

from

quasi-oue-

to

quasi-two-dimeusioual (QID, Q2D)

couductors aud fouud almost

always

a

temperature

dependent RH (T). Although

simulations of

RH(T)

aud its

proof

are very dilficult due to restricted

experimeutal

information aud

evideuce,

at least for trie

Q2D system,

we fouud

empirically

oue-to-oue

correspondence

with trie

temperature depeudeuce

of

resistivity, p(T),

trie temperature

dependence

of Hall

effect, RH(T),

and trie structure of trie Fermi

surface,

~N"hich are shown

schematically

in

Figure

1.

(*)

Present address:

Dept.

of Mat. Sci., Fac. of

Sci.,

Osaka

City

Univ., 3-3-138,

Sugimoto, Sumiyoshi-

ku, Osaka 558, Japan

e-mail:

muratak©soi.oeaka-cu.ac.jp

@

Les

Éditions

de

Physique

1996

(3)

1866 JOURNAL DE

PHYSIQUE

I N°12

J-tYPe ~ ~ '"'~~°~

~~

~

>o

~

K-type ~

'"'

'°~ /

< o

~

T-type ~

lin

'°g

tl-(BEDT-TTF~I

~~

i~ j

4

~ og

~

20kbar 2 bar

Fermi

surface RH Vs

Temp

p vs

Temp

Fig.

1. Schematic sketch of trie Fermi Surface, trie Hall coefficient ~ers~s temperature and resistivity

~ersus temperature for fl-, ~- and T-types of

quasi-two-dimensional

organic conductors.

It is

interesting

to recall that Fermi surfaces of trie

fl-,

~-, o- and r-types can be

developed

from a

siugle

round Fermi surface as showu lu

Figure

2.

By

companug

Figures

1 and

2,

it is

worth

noting

that trie Fermi surface of trie

fi-type

is trie most

simple

amoug

ail,

1.e. a round Fermi surface is located

just

inside trie first Brillouin zone. When trie Fermi surface folds

due to contact with trie Brillouin zone

boundary,

there appears a

nearly singular

curvature

m trie Fermi surface. Arouud the

siugular

curvature lu the Fermi

surface,

vF varies

strougly

with

k,

aud

consequently

trie r

scattering

lifetime becomes

sensitively k-dependeut.

This is trie pnmary reasou for trie temperature

depeudeuce

of

RH(T).

Marked

examples

of these

siugular

curvatures are trie

edges

of trie leus orbit of trie

~-type,

and trie

edges

of trie star-

shaped

Fermi surface of trie r-type.

(In

r-type

couductors,

there must be another reason for temperature

dependeuce

m

RH (T).

The

system

con uot be treated withiu trie framework used for

degeuerate

menais due to trie Fermi energy which is in trie same order of

magnitude

as trie

room

temperature.)

For the ideal 1D

system

with

k-independent

r, m the relaxation time

approximation

lu the semiclassical treatmeut,

symmetric (in k-space)

relaù~ation time does not

produce

Hall

voltage,

smce a~y, which is

proportional

to trie Hall

voltage,

vamshes

according

to trie

integral,

a~y o~

f

dl x £, where £ = vfr

[ii. Therefore,

trie Hall

voltage,

when it is detected in trie actual

QID system,

it is due to the imbalance from the symmetry. In other

words, RH (T)

is very much

(4)

>-type

0

-

~

K-type

~-type

-

~ ~

a-type

~ ~

example:

tx-(BEDT-TIF)~MHg(SCN)4

Fig.

2.

Typical

two-dimensional Fermi surfaces reconstructed from trie

original

round surfaces.

dominated

by

trie

dispersion (or diffusion) along

trie second and third conductive axes. Then trie Hall

signal

con either be

positive

or

negative irrespective

of trie value or

polarity expected

from trie

charge

transfer. So it is more dilficult in lD thon in 2D to draw ont trie "standard"

RH(T) correspondiug

to trie Fermi surfaces. Schematic

(= rougir) image

of trie Fermi surface

is less sulficieut to defiue

RH (T)

iii

QID.

Trie

importance

of trie

transport properties aloug

trie less couductive axes are

poiuted

ont to

iuterpret

trie

temperature depeudeut RH(T)

iii TTF-

TCNQ [2].

Auother

interpretation

for trie temperature

depeudent RR(T)

is, for

instance,

in

terms of a precursor of trie

phase

transition or of collective

excitation,

such as CDW in TTF-

TCNQ

[2] and SD~V in

(DMET)2Au(CN)2 [3,4].

These

apparently

different causes

resulting

in trie

temperature dependent RH (T)

are

actually

uot

iudepeudeut,

siuce trie

dispersion along

trie less couductive axes

strougly

influences trie variation of trie Hall effect as well as trie

phase

transitions. It is a matter of course that materials with lower

dimeusiouality

are more

likely

to show low

temperature

iustabilities. lu other

words,

materials

properties

at lower dimension are more sensitive to trie 2ud aud 3rd axes trausfer euergy or to trie

warpiug

of trie Fermi surface. This situation makes it more dilficult to draw out

typical

aud standard

RH(T)

for lower dimeusioual materials. Eveu lu trie 2D materials, with

iucreasiug

pressure,

low temperature iustabilities are more

suppressed,

aud

thus,

"standard"

RH (T)

for each Fermi

surface,

eveu

though

it is

schematic,

is

relatively easily

obtaiued.

lu this paper, we revisited

RH (T)

of trie

~-type

and

fl-type

couductors and show that

RH (T)

ceases

chaugiug

with pressure a

beyoud

certain pressure, where a

typical

aud "Standard

RH (T)

for each Fermi surface are realized. Wheu suddeu deviatious from those

RH(T)

are

fouud,

it

(5)

1868 JOURNAL DE

PHYSIQUE

I N°12

~

5

~ .9

)

~

Î~

~ ~

É

#

'

~

i

# 1

à

~

'

0 50 100 150 200 250 300

Temperature (K)

Fig.

3.

Temperature dependence

of Hall coefficient of

K-(BEDT-TTF)2Cu(NCS)2

ai ambient and other pressures.

Magnetic

field is

perpendicular

tu trie

plane.

is an indication of a

phase

transition or some

peaking

in electronic excitation. Thus trie Hall effect is a useful and sensitive tool for

observiug

a

phase

transition.

2.

~z-(BEDT-TTF)2Cu(NCS)2

This material shows a

hump

in the

resistivity

versus

temperature

around loo K and under- goes a

superconducting

transition at 10 K. The

resistivity hump

had been controversial until

a series of materais from trie

insulating

to more metallic ones

appeared systematically.

It is understood since that trie materials con be

categorized

from insulator to metal in trie or-

der, N-(BEDT-TTF)2Cu[N(CN)2)Cl, N-(d~, BEDT-TTF)2Cu[N(CN)2)Br, ~-(h8, BEDT-TTF)2 Cu[N(CN)2)Br,

and

N-(BEDT-TTF)2Cu(NCS)2.

This

insulating

state is driven

by

electron

correlation,

like a Mott insulator which bas been discussed in correction with NMR

experi-

ments

[à-7j

as well as

theoretically [8j.

Trie

hump

at 100 K in

N-(BEDT-TTF)2Cu(NCS)2

con then be understood as a crossover from trie Mott insulator to a metal

by lowering

trie

temperature.

In ail of trie

N-compounds, (TIT)~~

of

~~C-NMR

exhibits

a

peak.

In

~-(BEDT-TTF) 2Cu(N CS)2

and in

~-(BEDT-TTF)2Cu[N(CN)2)Br,

this

peak

is located around 55 60 K

indicating

a maximum in trie

antiferromagnetic

fluctuation but net trie real transition because trie fine

shape

of NMR is still visible below 55 60 K. Previous to these NMR

studies,

there bave been several reports that indicate anomalous

change

around 60 70 K, which bave been referred to m reference

[9j.

Trie Hall

coefficient, RH(T),

which is

positive, gradually

increases on

decreasmg

trie

RH(T) temperature.

Below 60 70

K,

trie

slope

of

(dRH(T)/dT( suddenly

increases and shows a

peak

around 10 K

[9,10j.

No

appreciable change

is observed around 100 K

similarly

to

NMR-(TIT)~~

and to static

susceptibility [5, 6j.

This sudden increase m

(dRR(T)/dT(

below 60 70 K coincides

exactly

with trie

peak

in

(TIT)~~

of

~~C-NMR.

Now trie 60 70 K

transition,

we con compare trie

RH(T)

studied under

higher

pressures.

If we

overlap

trie

RH(T)

of P = 0 with other

RH (T)

of

higher

pressures, it is quite evident that trie 60 70 K is

really

an anomalous temperature as shown m

Figure

3. We therefore could bave a

strong implication

of a transition around 60 70 K net from trie

slope change

m

jdRH(T)/dT(

but rallier from trie contrast between trie ambient and

higher

pressures m trie Hall effect. We exammed trie

specific

heat across this

temperature

range, but could trot detect

(6)

any

singular signal il ii.

This is reasonable if trie 60 Ii

anomaly

is of

purely

electronic

origin.

In such a case, an

anomaly

m

specific heat,

even if one

exists,

can be buried in trie lattice contribution to trie

specific

heat.

Moreover,

this is consistent with trie fact that this is trie

peak

in the

antiferromagnetic

fluctuation in

~-(BEDT-TTF)2Cu(NCS)2

but trot trie transition obtained from observation of the

fine-shape

of NMR

[12].

The suppression

by

pressure of the 60 70 K "transition" observed

by

Hall effect

study

under pressure in

~-(BEDT-TTF)2Cu(NCS)2

may

actually

occur. In a similar

material,

~-(BEDT-TTF)2Cu[N(CN)2)Br,

the

suppression

of the

magnetic

fluctuation

peak by

pressure

is observed

by (TIT)~~

of NMR

[6].

About the "standard"

RH(T),

Sushko et ai. studied in

~-(BEDT-TTF)2Cu[N(CN)2)Cl

in trie pressure range of 4.5 10

kbar,

and found almost no

change

m

RH(T)

with pressure

[13].

It is

important

to note that this is trie pressure region where

already superconductivity

is

suppressed similarly

as m

~-(BEDT-TTF)2Cu(NCS)2.

3.

fl-(BEDT-TTF)213

As seen

Figure 4, RH (T)

of this material varies

extremely

little with temperature down to 20 K.

Although

this result is

quite simple,

and looks more like standard

metal,

tt is worth

remarktng,

since flot

RH (T)

is

exceptional

among the

Q2D organic

couductors.

By comparing

with

RH (T)

aud the Fermi surface of other

types,

it is noticed that this standard behavior of

RH(T)

is caused

by

the fact that the Fermi surface does not touch the first Brillouin zone

boundary, leaving

no

singular

area in the Fermi surface. In other

words,

no

particularly

anomalous

r-(mean

free

time)

area in

kF-space

is found.

Another

interesting

feature in this

region

is that even

though p(T)

and

RH (T)

exhibit metallic

behavior,

the mean free

path, t,

calculated

by

a

=

ne~r/m

is smaller than trie lattice constant around 300

K;

t

= 0.13

À

for 300 K and 130 at

temperature just

above

superconducting

T~

[14, là]. (The

lattice constants are 6.6

À,

9.1 in the 2D

plane

and 15.3

perpendicular

to the

plane.)

The mobilities are p

=

RH

x a is 0.2

cm~ IV

s at room

temperature

and 80

cm~

V

s at 20 K. From such

high

to low

temperatures

ail

through, RH (T)

is constant as if it is

contiuuously

a coherent metal. It is net well understood

yet why

metallic behavior is

exhibited with such

parameters

in

high (= room) temperature.

Turning

back to the relation between the Hall effect aud the

phase transitions,

we compare the

RH(Tl's

studied under vanous pressures. From

Figure 4, RH(Tl's

are identical above 7

kbar,

and we can thus obtain trie "standard"

RH(T)

for this material.

By comparing

with

this,

anomalies m

RH(T)

are

quite

dear at 17à K

[14]

and 20 K

[14-16].

This material bas two

supercouductiug

transition

temperatures,

8 K and 1-à K

[17,18].

Trie

superconductivity

of1.à K is associated with trie incommensurate

superstructure

fouud

by Emge

et ai.

[19]

with

a wave vector of

(0.08,

0.27,

0.20à)

that appear at 17à K. Trie

superconductivity

at 1.à K is

a metastable state

[20, 21]

which can be converted to 8 K state

through

2 K

by annealing

trie

sample

at around 103 K in trie time scale of 100 hours

[22, 23].

As for trie

properties

and rotes of trie Hall

effect, first,

ii is

interesting

from trie

viewpoint

of trie

transport property

itself that

already

at 17à

K,

where no

siguificaut change

in trie Fermi

surface relative to trie Brillouin zone

boundary

is

expected,

trie

RH (T)

is influenced

(reduced) by

8Slo. Next, a new transition was

strongly implied

at 20 K

by observing

a

sharp

kink there

and > 40Yo

drop

m

RH (Ti

below 20 K

[14]

which was then confirmed as a transition but not

trie crossover of trie

scattenng

mechanism

by specific

heat measurement

[24].

Since this 20

K transition was obvions m

RH(T)

and in

speofic heat,

it is noted that trie

RH(T) study

is

thus a

po~v"erful

tool for

locating phase

transitions.

Looking

around at other works concernmg trie 20 K

anomaly,

we are remmded of trie NMR

Korringa relation,

which does net continue

(7)

187o JOURNAL DE

PHYSIQUE

I N°12

5

Ù w+

~

~ OOOO'OOO°OaO

f

~ ,,,

Îf

~

Î__

#

g

à1

~Î~"~

h

'~>

~ '

a)

50 100 150 200 250 300

Temperature (K)

~'%

~

~ l '

~

~

~ °

' Q

j O

£ -

>

O >

~ fl

~

>

'

perature (K)

Fig.

4.

Temperature dependence

of Hall coefficient of

fl-(BEDT-TTF)213

ai anibient and orner pressures for T

= o 300 K

la)

and ils expansion for low temperature

16). Magnetic

field is perpen- dicular to trie

plane.

The values of pressure in a

clamp

cell

correspond

to low temperature. In

our

pressure medium and equipment, room temperature is

always

1.5 kb

independent

of

room temperature values. Arrow

in

(b)

shows a

example

of an

anomaly

m RH

(T)

for 5 kb. Data for 3 -10 kb

are for

trie same

sample.

TO fit with o kb data of a dilferent sample, trie value ai 100 K is adjusted taking

into account trie data from reference [28].

across this

temperature [2à,26].

Trie

~H-NMR

relaxation behavior becomes

non-siugle

aud

that situation is

comphcated [27].

We come back to this discussion later.

One of trie

advantages

of trie

RH(T) study

is that we can

easily

extend trie work under pressure. Since anomalies are

always

seen in

RH (T),

as shown

by

an arrow in

Figure

4b for à kb for

example,

we cau

plot

those

temperatures agamst

pressure

together

with

T~'s

of trie

superconductivity,

as shown in

Figure

à. It is seen that trie

point

at 20 K at P

= 0

cannot be couuected to other points associated with trie

high T~'s. By annealing

at 103 K for

à0 -loo

hours,

8 K

supercouductivity

is observed

by specific heat,

aud 20 K

anomaly

in

RH (T) disappears [28].

What is known from

Figure

5 is that 1.5 K

superconductivity

is related with lîà K

through

20 K

anomaly,

while 8 K

superconductivity

is related

through

la K

anomaly.

With this

figure,

as

N-(BEDT-TTF)2Cu(NCS)2 superconductivity

is

suppressed

where

RR(T)

ceases

changiug

with pressure, it is

suggestive

that trie

superconductivity

is assisted with non-

conventional electromc excitation.

Although

trie reason to reahze 1-à K

superconductivity

m trie basic

background

of 8 K bas uot beeu solved

yet,

we

proposed previously

that trie

deusity

of states for the 1-à K state is

(8)

25

J'-(BEDT-TIF)~l~

Çi

R~(T)

Î 15

~ é

Î

la Low Temp

f

Metallic region

~ ~

O 2 4 6 8 la 12

Pressure (kbar)

Fig.

5. Trie temperature-pressure

diagram

of

fl-(BEDT-TTF)213 plotted

with Tc

(superconductiv- ity)

and THaii

(Hall

elfect

anomaly).

Ii is seen that ai Tuait ai 20 K for low Tc, trie store does non continue to trie

points

associated with trie

high

Tc state. The metallic region below trie temperature of trie Hall elfect

anomaly

is shown as "low temperature metallic

region".

This demonstrates trie

ambiguity

m trie definition of trie anomalous temperature.

smaller thon that of trie 8 K at trie 20 K transition

through possible nesting

of trie Fermi surface

[14, 24].

This

deusity

of state scenario can not be consistent with trie

~H-NMR results,

which tells about

3%/kbar/kbar

decrease in trie

deusity

of states in

spite

of some relaxation

anomaly

at P

= o

through

around 20 K

[2à].

Very recently,

Kanoda et ai. bave

reported

a detailed static

susceptibility

and

~~C-NMR

concemiug trie 20 K transition

[29]

which renewed trie

previous reports

ou

susceptibility [30].

Trie static

susceptibility

decreases with

temperature

aud levels off below 20 K.

By auuealiug

at 103

K,

trie level-off

susceptibility

iucreased. This is consistent with our

previous deusity

of state

picture implied

ou trie Hall effect measurement. Further. incommensurate structure are seeu to be

suppressed by

trie NMR fine

shape by aunealing

in trie time scale of 700 tirs.

4. Conclusion

The Hall effect of

orgauic

metaiiic couductors are

generally

very

temperature depeudent.

This is due to trie low dimensional nature of these inaterials. If trie materials are lower in

dimension, RH (T)

as well as trie low dimensional instabilities are more

sensitively

influenced

by

trie transfer energy

along

trie less conductive axes. This situation

might

be trie reason that we cari obtain

typical

"standard"

RH(T)

for each

typical

Fermi surface

especially

for 2D materials under

relatively higher

pressures, where delicate transfer energy structure is less

important.

Among these, fl-(BEDT-TTF)213

is trie

special

case, which shows almost temperature Inde-

pendent RH (T).

It is

explained

that trie Fermi surface is trie most

simple

without any

singular point

in

k-space

lu terms of

scatteriug

lifetime.

We note that for ail trie cases

~-(BEDT-TTF)2Cu(NCS)2, ~-(BEDT-TTF)2Cu[N(CN)2)Cl

and

fl-(BEDT-TTF)213, RH(T)

is

already

constant with pressure where

superconductivity

is

suppressed.

This

might

indicate that trie

superconductivity

is realized in trie environment of novel low dimensional instabilities.

(9)

1872 JOiÎRNAL DE

PHYSIQUE

I N°12

Finally regarding

trie standard

RH(T),

trie anomalies in

RH(T)

which are

usually

related to

phase

transitions are

clearly

found. Thus the Hall effect is a useful tool for

locating phase

transitions.

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