Scaling in Angle Resolved Electrical Transport Measurements on κ-(BEDT-TTF)2Cu(NCS)2

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Scaling in Angle Resolved Electrical Transport Measurements on κ-(BEDT-TTF)2Cu(NCS)2

S. Friemel, C. Pasquier, D. Jérome

To cite this version:

S. Friemel, C. Pasquier, D. Jérome. Scaling in Angle Resolved Electrical Transport Measurements on κ-(BEDT-TTF)2Cu(NCS)2. Journal de Physique I, EDP Sciences, 1996, 6 (12), pp.2043-2050.

�10.1051/jp1:1996202�. �jpa-00247296�

Scaling ⁱⁿ Angle Resolved Electrical Transport Measurements

_on

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

S. Friemel

(*>,

^C.

Pasquier

and D. Jérome

Laboratoire de

Physique

des Solides

(**),

Université Paris-Sud, 91405 Orsay

Cedex,

France

(Received

7 &Iiv 1996, received in final form 14 June 1996,

accepted

17 June

1996)

PACS.74.70.Kn

Organic supercounductors

PACS.74.25.Fy

Transport

properties (electric

and thermal

conductivity.

thermoelectric elfects, etc.

PACS.74.60.Jg

Critical currents

Abstract. We report on

surgie crystal

electrical transport measurements _on

~-(BEDT-

TTF)2Cu(NCS)2

in _an externat

magnetic

field

applied

at dilferent

angles

with respect to trie superconducting layers. By _measuring ^trie

in-plane

resistivity _versus temperature we can reveal

a

thermally

activated behavior in trie vortex

liquid phase

and _are able to extract trie

angular dependence

of trie activation energy.

Voltage

_versus current measurements lead to

angle

depen- dent values for trie critical current Jc. Dur data _can be fitted

succesfully

within trie framework of trie

anisotropic

effective _mass model

resulting

_{m an} estimate for trie amsotropy parameter

~ =

(ab/(c

_~3 40 l10.

1. Introduction

Anisotropic superconductivity

has attracted wide interest for _a

long

time from the theoretical _as well _as from the

expenmental point

of view. Several

experiments

have been carned out, first _on

"artificially" anisotropic superconductors,

i,e.

multilayers

of conventional

superconductors _[1j,

then _on

intrinsically anisotropic superconductors,

1.e.

high-T~ superconducting cuprates [2-4].

Several models were

proposed according

to the wide range of anisotropy

existing

both in

extrinsically

and

intrinsically anisotropic superconductors [5j.

Intrinsically anisotropic superconductivity

is also observed in the

organic superconductors

~-(BEDT-TTF)~X

_[GI. ^In this paper we will

report

measurements on

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

This

compound

_can be

regarded

as a model

compound

for the

high-T~ superconductors,

as it exhibits a similar

crystal

structure of

alternating conducting

and

nonconducting layers.

The

conducting planes

consist of the

organic

^BEDT-TTF cations; conduction arises from the delocalized

~-doublebindings

of the BEDT-TTF'S central carbon atoms. The anorganic

Cu(NCS)2

anions _are

polymenzed

and form

insulating planes.

As T~ re 10 K and

H~2(0)

<

200

koe,

the

complete superconducting phase

_is accessible _in

expenment.

To

date, highly contradictory

values for the

anisotropy parameter

_~i ^{have been found for this}

compound, ranging

from _~i of the order of10 in

magnetization

_I?i and

resistivity

_[8j measurements to ~i > 200

(* ^{Author for}

correspondence je-mail: [email protected]) (**)

URA 2 CNRS

g

Les

Éditions

_{de Physique 1996}

2044 JOURNAL DE

PHYSIQUE

I N°12

extracted from

experiments

_on the

magnetic torque [9j, ac-susceptibility

_[10] and

specific

heat

[11j. Hence,

this crucial

point

_seems still _to be _{an open}

question.

In

previous

_{papers ~ve} have

presented

electrical transport measurements of the

in-plane resistivity

in

magnetic

fields

apphed perpendicuiar

to the

superconducting layers.

We have shown the effect of the

anisotropic superconducting properties

_on thermal fluctuations

[12]

and _on the vortex

dynamics

in the vortex

liquid

state

[13j.

The latter _can be

explained

in

the

picture

of _a very viscous vortex

liquid

with _an

anisotropy

parameter _~i m 110 -130. In this paper we further

investigate

the

anisotropic properties

of

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

resoiued

p(T)

and

VII)

measurements. We compare the _new data to the measurements at

perpendicular

fields

employing

different models. This also leads to _an estimate for the

anisotropy

parameter _~i.

2.

Experimental

Details

The measurements

presented

here _were

performed

_{on a}

high-quality single crystal

of

~-(BEDT-

TTF)2Cu(NCS)2

_grown in _a standard

electrocrystallization

_process

_[14].

Its size is about 125 x 400 _x 20

~lm~.

On top ^{of the}

platelike sample.

four

gold

contacts were

evaporated using

a

shadow mask

technique.

The two outer

pads (current contacts)

also _cover the two outer sides of the

crystals

to short-circuit the

superconducting planes

and _{ensure an}

homogeneous

current

flow. The measurements _were carried out in _a rotatable

sample

holder with _a relative

angular

resolution of 0.2°. The external

magnetic

field _was

always applied perpendicular

to the current

flow,

but with variable

angle

8 between the

superconducting layers

and the field direction.

A standard four

probe _setup

_was used. The

p(T)

characteristics _were measured

employing

a

low

frequency

lock-in

technique,

whereas for the

~~(I)

curves a

pulsed

de-method _was used to minimize

heating

effects. For the latter the

voltage drop

_over the

sample

_was determined with

a

Keithley

K191 nanovoltmeter. For

temperature

measurements, a

carbon-glass

resistor _was

employed,

which _was

carefully

calibrated

against

shifts in the _presence of _a

magnetic

^field.

3. Results and Discussion

3.1. REsisTiviTY _vERsus TEMPERATURE MEASUREMENTS. In this section _~i>e will _con-

centrate _on the temperature

dependence

of the

resistivity

with respect to the

angle

bet~veen

the

magnetic

field and the

superconducting layers.

Measurements _were

performed

at different external fields.

Figure

1

gives

_an

example

of the data at H

= 12 koe. In this Arrhenius _repre- sentation it _can be

clearly noticed,

that the

resistivity

is

thermally

activated at all

angles.

As

reported previously

_[13] for the _case of _a

magnetic

field

applied perpendicular

to the _supercon-

ducting planes le

= 90°

),

this behavior _can be understood in the

picture

of

thermally

activated flux flow

(TAFF).

The

resistivity

can then be described _as

p(T)

=

poexp(-LT(H,T)/kBT),

where

U(H, T)

denotes the activation energy and kB the Boltzmann _constant. In reference

[13j

we were able to sho~v, that the activation energy

U(H, T)

_can be ascribed to energy barners ansing from

plastic

deformations

in the vortex

liquid,

_i.e, the creation of double kinks in the three dimensional flux lines. It then follows

U(H, T)

=

Upi

"

Uo(1- T/T~),

where T~ denotes

the transition

temperature,

and Uo c~

H~~/2.

_{We will}

now

analyze

the

angular dependent

data _in the _same way as the data at 8

= 90°. For this _{purpose, we}

employ

linear lits _to

the

apparently

linear

parts

of the _curves and derive the

angular dependent

activation energy.

These _are

plotted

in

Figure

2 for H

= 12 koe and another field

investigated (H

= 450

De).

It turns out, that the activation energy increases

slowly

from its

perpendicular le

=

90°)

value aiid has _a rather

sharp peak

at 8

= 0. To understand this

behavior,

_we further

analyze

these data

employing

two models

designed

to descnbe anisotropic, or

layered superconductors,

Om0°

_

0.1 ~~

) j.j[

~

^{~ ~~} _ÎÎ~

~ 42°

E-3 ~(Î

10 8 6 4

T(K)

Fig.

l.

Arrhemus-plot

of trie

resistivity

_versus temperature characteristics. Solid hnes: _{m a} mag- netic field H ₌ 12 koe applied at dilferent

angles

8 with respect to trie superconducting planes. Trie

angle

between trie field and trie

planes

_mcreases from left to

right.

For comparison, aise trie _curve for H _m 0 is plotted

(dashed fine).

Jo

450 Oe

o

g

c 12 koe

é

o

§

$

_{o o}

~

~ o

o

200 _{o o}

D°~

^° ° o

~ ~

0

~ ~

~0 -30 0 30 60 90120

8 1°)

Fig.

2.

Angular dependence

of trie activation energy for H

= 12 koe and H

= 450 Oe,

respectively.

respectively.

The first model _was

proposed by

Iles et ai.

[lsj

for

layered superconductors:

it

predicts

_a breakdown of the concept ^{of the usual 3D flux hne} structure~ when the

magnetic

field is

applied parallel

to the

superconducting planes.

For _an

arbitrarily

onented field

only

the

perpendicular

_component of the

magnetic

^field should be relevant for the formation of the flux-hne-structure. This idea leads to _a

scahng

formula for all field and

angular dependent quantities QI

Q(H, 8)

=

Q(H

_*

sine,

8

=

90°), (1)

1.e. the behavior _at different

angles

and fields of _a certain

quantity Q

is

completely

descnbed

by

its

dependence

_on field directed

perpendicular

to the

planes.

The second model _we will

employ

_is the

anisotropic

effective _mass

model,

which follows from the Lawrence-Doniach

equations [16j.

^{This niodel is further}

generalized by

the

scahng approach proposed by

Blatter et ai,

il îj.

Here again the

magnetic

field is scaled with _an

angular dependent scahng

function

SIR),

QIH, 8)

=

QIH

_*

E(8),

8

=

9Ù°). ₁₂₎

2046 JOURNAL DE

PHYSIQUE

I N°12

400

...~..pm ...v...pire

300

$

...A...pm

~_

...o...p50

~ ...u...p30

~°

²⁰⁰ _{-.-perp_}

ioo

~

ioo iooo ioooo

H*e18) ioe)

Fig.

3. Activation energy

dependence

_on the

magnetic

field for fields

apphed perpendicular

to the

layers (closed symbols)

and at dilferent

angles

8 with respect to trie planes

(open symbols).

The

magnetic

field for trie

angular dependent

values is scaled

according

to trie models

explained

in trie

text. Trie fines _are

guides

to trie _eye. Trie bar represents trie _errer due to trie

experimental uncertainty

m

angle

and field.

with

SIR)

=

Il _/12

* cos2 8 +

sin~ 8, (3)

where _i denotes the

anisotropy parameter,

_{~i =}

(ab/(c

"

mc/mab. (ab,(c

and _mab,mc

are the

in-plane

and

out-of-plane

coherence

lengths

and effective _masses,

respectively.

It _can

easily

be _seen, that the first model follows

formally

from the second

by setting

_i to

infinity,

as

already pointed

out

by

Blatter et ai.

[lîj.

This _can be understood within the framework of the

anisotropic

^effective mass model _as

neglecting

the

interlayer couphng,

_i.e,

setting

the effective

mass m~ for motion

perpendicular

to the

layers

to

infinity.

In

Figure

3 _we

plot

the activation energy found in measurements with the

magnetic

field

apphed perpendicular

to the

planes

and

additionally

the

angle

resolved activation

energies

at 12

koe,

for which the

magnetic

field is scaled for different values of i

following equations il, 2, 3).

^It turns out, ^that the overall

fitting quality

is

quite

convincing. The lits for different _~i differ

considerably only

at low fields

Ii.e.

8 _-

0),

whereas at

higher

fields

le

-

90°)

the

cos~

₈

term in the

scaling

function

(3)

^becomes

negligible

and both models result in

approximately

the _same behavior. In the

regime,

where the field is directed almost

parallel

to the

layers,

the best fit _can be achieved with _a value of _{~i m} î0. Values for _{~i in} the range 40 < ~i < 110 still result in lits, which lie well within the _error

resulting

from _our

expenmental

resolution in

angle

and in field

(for

low

applied fields).

Furthermore, the model of Kes et ni.

(or

_~i

=

ce)

does

not seem to be

appropriate

to describe _our data for 8 _- 0. At the lower

field,

H

= 450

De,

similar results could be achieved in _an

analogous analysis (not

shown

here).

3.2. VOLTAGE _VERSUS CURRENT MEASUREMENTS. We _now tum to

angle

resolved _mea-

surements of

VII)

charactenstics and

analyze

the critical current determined from these _curves

in the _same context as before. We measured

Viii

_curves at dilferent externat

magnetic

fields

(12 koe,

48 koe and 96

koe)

and

temperatures (4.4 K,

5.0

K,

G-o K and î-o

K). Typical

curves at 4.4 K and 48 koe _are

displayed

for _some

angles

_in

Figure

4. From these _curves,

we extract the

angle dependent

critical current. We do _not

employ

_a

voltage

criterion, but take the

intercept

of _a linear fit _to the

high-current parts

^{of the} curves with the _x-axis

[18j.

2.0

e»34°

~'~

Î~

14°

$~ _lO°

E _6°

~Î

4°

O°

O.O

0 10 20 30 40

(mA)

Fig.

4.

Voltage

_versus current _curves at 4A K and 48 koe for dilferent

angles

of the

applied magnetic

field.

u t2kOe

o 48kOe

A 96kOe

~

c

E~

^D°

°c~~

~~

£Î~

^~

~~

dP£

~

flɧ~ "ofioéQ%

0

W m 0 30 60 90120

e 1°)

Fig. 5.

Angular

dependence of trie critical current at T

= 4.4 K.

This decision _was motivated

by

the fact. that the _{curves are} rather

rounded, seemingly

due to the

thermally

activated flux flow.

Accordingly,

the determination of the cntical current

by

_a

voltage

cnterion would result in too low values. The

resulting

values at T

= 4.4 K _are shown _in

Figure

5. Their

dependence

_on

angle

is rather similar to the behavior of the activation energy described above.

Again,

the cntical current increases

slowly

from its 8

= 90° value and has

a rather

sharp peak

at 8

= 0. This

general

feature also tutus out at the other

temperatures investigated (not

shown

here).

We _now compare the

angle

resolved critical _currents to the values found for H

applied perpendicular

to the

superconducting planes. Figure

6 shows the critical currents at 8

= 90°

and T

= 4.4 K for dilferent fields, denved in the _same way as descnbed above.

Additionally,

we

plot

the

angle dependent

values at 12 koe, 48 koe and 96 koe with scaled values of the

magnetic

field for dilferent _~i.

Again,

the overall

fitting quahty

is quite convincing. But _as in the

previous

section due to the scatter in the data _{it can not}

unequivocally

be

decided,

which

~i results _in the best fit.

Nevertheless,

values of _i lower than about 40 _seem to be excluded. But in

contrary

to the

p(T) measurements,

^{the model} of Kes et ai. _seems not

entiiely inappropriate

to describe the

data,

also

taking

into account the accuracy in the determination of the critical

currents

employing

the method described above.

2048 JOURNAL DE

PHYSIQUE

I N°12

40

-perp.

30

o i2kOe

20 ~~~

~~~~~

40

30

yn40 ~

E

i#OO

0 20 40 60

H *

£le) jkoe)

Fig.

6. Critical current

dependence

_on the

magnetic

field at T

= 4A K for fields

apphed perpendic-

ular to trie

layers (closed symbols)

and at dilferent

angles

8 with respect to trie

planes (open symbols).

The

magnetic

field for trie

angular dependent

values is scaled

according

to trie models

explained

in trie

text. Trie sohd fine for trie

perpendicular

values is

a

guide

to trie eye.

3.3. DiscussioN. In this section _{we want} to compare ^our results to the values for _i and to

angle

resolved measurements

reported

in hterature.

First, compared

to the values

given by

magnetization I?i

^and

resistivity

_[8j

measurements,

^{where values of} _~i m 10 20 _are

reported,

our lower hmit of 40 _seems to be too

large.

This may be due to the

fact,

that for

example

in

resistivity

measurements, _{~i is}

usually

determined from the

anisotropy

^{in the} upper cntical

magnetic

field

Hc2 perpendicular

and

parallel

to the

layers. Here,

errors may anse from

a)

the method

employed

to determine

Hc2

from the measured _curves

b)

^the _accuracy, which _can be achieved to

align

the

magnetic

^field

parallel

to the

superconducting layers

and

c)

the fact that

H~2,c(0)

is Pauli hmited to about 190 koe

(Hpaui~

# 18.4

koe/K*T~ [19j).

In contrary, our

method does not test the _upper cntical field and does not

depend

on a

perfect ahgnment

in the

parallel position,

but involves several values close to 8

= 0.

In

fact, angle

resolved measurements of the

magnetic torque

[9j ^and

ac-susceptibility [loi

reveal much

larger

values of _~i. Farrell et ai. _[9] find _a value of

~i ^m

200, Mansky

et al.

[loi

1 = 160 350. These values _{are not} far from _our values found for the

angle

resolved

p(T>

measurements, and fit

perfectly

into _our

J~(8) dependence. Accordingly,

1N~e believe that it is not the measunng method

(resistivity, magnetization, ac-susceptibility etc.)

which is

decisive for the value found for _i, but

instead,

whether the

angle ^dependence

^{of the measured}

value _is taken into account. The _more reliable values _{seem to} result from

angle dependent

measurements.

4. Conclusion

In summary, we have

presented angle

resolved measurements of

p(T)

and

VII)

characteris- tics in order to determine the

anisotropic properties

of

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

The

p(T)

measurements reveal activated behavior at low

temperatures;

the

angular dependence

of the

activation energy can be fitted

by scaling

the

magnetic

field

according

to the

anisotropic

ef- fective _mass model. The _same

property

was found for the

angle dependence

of the cntical

currents. Both methods result in _a lower limit for _~i of about 40. From

p(T; H, Hi

_measure-

ments _an Upper limit of _{~i m} 110 could be

estimated,

whereas the

VII;

T,

H, 8)

characteristics

do not agree with such _an estimate.

Acknowledgments

We thank P. Batail for

providing

the

samples.

We

acknowledge

fruitful discussions with N.

Kopnin

and M.

Stenger.

We further

acknowledge

M. Nardone for technical

help.

One of _us

(C.

P-i

_was

supported by

DRET under _contract n° 94C8024.

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^A more accurate way ^to determine the critical currents was to fit the

VII)

characteristics

to the

appropriate

theoretical models. The results of lits _in the TAFF

picture

do not dilfer

considerably

from the values determined

by

the

simple

method described above.

They

will be

presented

elsewhere:

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