Structural and magnetic order in CoCl2 intercalated graphite

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Structural and magnetic order in CoCl2 intercalated graphite

J. Rogerie, Ch. Simon, I. Rosenman, J. Schweizer, R. Vangelisti, P. Pernot, A.

Perignon

To cite this version:

J. Rogerie, Ch. Simon, I. Rosenman, J. Schweizer, R. Vangelisti, et al.. Structural and magnetic order in CoCl2 intercalated graphite. Journal de Physique I, EDP Sciences, 1992, 2 (3), pp.291-305.

�10.1051/jp1:1992135�. �jpa-00246484�

Classification

Physics

Abstracts 75.25

Structural and magnetic order in Cocl~ intercalated graphite

J.

Rogerie

(1.

2),

Ch. Simon

(I),

I. Rosenman

(I),

J. Schweizer _(2>

3),

^R.

Vangelisti (4),

P. Pemot

(4)

and A.

Perignon (4)

ii) Groupe

de

Physique

des Solides (*), Universitds Paris 7 et 6, 75251 Paris Cedex 05, France (2) DRF-DN, Centre d'Et1~des Nuc16aire de Grenoble, France

(3) Institut Laue

Langevin,

Grenoble, France

(4) Laboratoire de Chimie du Solide Min6ral

(**),

Universit6 de Nancy I, Vandceuvre [es Nancy, France

(Received J2

July

J99J, revised 25 November J99J,

accepted

28 November J99J)

Rdsumd. Nous

pr£sentons

des r£sultats de diffraction de rayons X et de neutrons obtenus _sur

un monocristal de CoC12 ins£rd dons le

graphite

ok la transition de Kosterlitz-Thouless peut ^dtre testde _car c'est _un

systdme

2D XY. La

longueur

de corrdlation du

magndtisme

dons le

plan

des couches augmente

lorsque

la

temp£rature

est abaissde, elle

diverge

h 4,5 K. L'ordre antiferroma-

gn6tique

suivant l'axe _c

apparflt

d'abord, h 6,5 K, mais la mise _en ordre 2D n'est pas modifide.

C'est _{pour cette} raison que

l'analyse

2D est

justifi£e.

Nous _avons ensuite

analys£

[es intensit£s

magn6tiques

et [es

longueurs

de corr61ation _en fonction de la

temp6rature

et montr6 la

prdsence

de d6fauts (vortex)

qui

abaissent l'aimantation mesurde dons [es

plans ferromagn6tiques

_comme it est

pr£vu

dans [es

syst~mes

2DXY.

Abstract. We present ^{the results of}

X-ray

and

magnetic

neutron diffraction studies _{on a}

single crystal

of _a rust stage

Cocl~

intercalated

graphite

which is _a

typical

2D XY system ^{in which the} Kosterlitz-Thouless theory can be tested. The correlation length ^{of the}

in-plane ferromagnetism

increases _as the temperature ^{is lowered and}

diverges

at 4.5 K. The c-axis

antiferromagnetic

order appears first _at 6.5 K, but the mechanism of the 2D

ordering

is not modified. For this _reason the 2D

analysis

is

justified.

We have then

analysed

the

magnetic

intensities and the correlation

lengths

_as functions of temperature and shown the presence of defects (vortices) which lower the measured

magnetization

in the

ferromagnetic planes

_as predicted ⁱⁿ the 2D XY systems.

1. Introduction.

The search of a

good

2D XY system ^{to test the} Kosterlitz-Thouless

(KT) theory [I]

is still _a

challenge [2]

and

Cocl~

intercalated in

graphite

_was

proposed

a

long

time ago as a

possible

candidate

[3]. Many

measurements of

magnetic susceptibility [4-6]

_were

performed

_on

samples

with various

stages

^of intercalation

[7].

The

shape

^of the

peak

^{observed in} these

(*) UA CNRS 17.

(**) UA CNRS 158.

292 JOURNAL DE PHYSIQUE I N° 3

experiments

was

interpreted

_{as a} 2DXY

transition,

modified

by

the

in-plane

six-fold

symmetry,

^the 3D

coupling

and the

in-plane

finite size effects

[6,81. Specific

heat

measurements have shown that

strong

2D fluctuations exist above the critical

temperature [91.

A

quite

extensive _neutron

scattering study

has been

performed

_on the second stage

compound [10-131, showing

a 3D

antiferromagnetic coupling along

the c-axis and _an

in-plane ferromagnetic ordering. However,

there is _a

large

c-axis disorder after intercalation

(a

mosaic of _more than 10

degrees),

and the

samples

which _were

previously

used

present

a

polycrystal-

line nature

(HOPG

I-e-

Highly

Oriented

Pyrolytic Graphite

_or stacked Kish

graphite).

Moreover the almost

complete

absence of correlations

along

c-axis in second

stage (there

is

no modulation of the

(hkf

lines

along

^f in the

crystal)

makes fine

magnetic crystallography

very difficult to achieve. The determination of the

magnetic

order needs _a

good knowledge

of the

crystallographic

structure as any structural defect has

consequencies

_on the

magnetic

diffraction. For this _{reason, we} have used for _our

study

_a

single crystalline

first stage

compound

where the

crystalline

order is much

bener, though

the presence of _a 3D

coupling.

Indeed,

the

magnetic specific

heat mesurements

[9]

have shown that 2D strong fluctuations above the transition temperature ^{still exist in the first} stage

compound

and it is then

possible

to

study

^the

sening

_up of _a

magnetic in-plane

2D order in it. The

magnetic susceptibility

presents in this stage a double

peak

_structure, the

interpretation

of which is still

controversial: it is

interpreted

_as the successive

ordering

in the

layer plane (upper temperature)

and 3D

antiferromagnetism (lower temperature) [4,12].

An altemative

interpretation

_was

superparamagnetism

due _to the islandic structure of the intercalated

layers

and their

coupling by dipolar

effect

[14, 15].

The

spin

arrangement ^itself was studied in _a

powder [16]

and then confirmed in _a HOPG

[17].

The structure is similar to that of the second stage

compound.

In this paper, we present a

complete study

of the structural and

magnetic

order. In _a first part, we present ^the

X-ray

diffraction _{on a}

single crystal

of first stage

Cocl~

intercalated in

graphite. Then,

in _a second

part,

we

give

_a

complete study

of the low

temperature (2 K) magnetic

structure. In _a third part, we

present

^the

temperature

^{variation of} the correlation

lengths

which shows that the

interpretation

of the two

peak

structure is

quite

different from that

previously proposed

_: the upper temperature ^{is the 3D}

ordering

^{and the}

lower _one

corresponds

to the

divergence

of the

in-plane

correlation

length.

Part four is devoted _to the

study

of

higher

_stage

compounds

where the 3D

ordering

does not occur. A last part ^is a discussion of _our

results,

in

particular

of _our observed transition

temperatures

^which

are lower than the usual _ones and _a discussion of the effect of the 3D

ordering

on the

in-plane

correlation

length.

2.

Samples

and

crystalline

characterization.

The

specimens

_were

prepared

in _{a two-zone} fumace

using

natural

single crystals

as host material. First stage

compounds

have been obtained

by

direct action of the gaseous dihalide

with _{an excess} of chlorine _gaz

(580

°C 0.7 Atm of

Chlorine,

30

days).

The chemical

analysis,

made _on natural

graphite powder (Ceylon

80~&§ ~200 _~L) intercalated under the _same conditions

[18]

has

given

an average formula _:

C5_23CoC12.12.

When

compared

to the ideal

ratio of

Cocl~

obtained from the

inplane

cell dimensions

assuming

2 carbon _atoms per

graphite cell,

I,e. 2 _x

(3.56/2.46)2

=

4,19. Such _a

stoichiometry

shows that

only

about 85 fb of the available volume is filled with the intercalant. The fact that there is _some chlorine excess, here 6

fb,

is _now

accepted [19].

This

stoichiometry corresponds

to a Co

filling

factor of 80 fb.

Moreover it should be mentioned that the intercalation in

single crystalline samples

^is _more

difficult than in

powdered samples,

so the actual

filling

factor in _our

sample

^is

probably

_even

lower than 80 fb.

We

give

both

X-ray

and _neutron diffraction results. The

X-ray crystallography

at _room

temperature was

performed

at

Nancy University.

^The

crystalline

and

magnetic

structure has been

investigated by

neutron diffraction at the Institut

Laue-Langevin

_{on a} two axis cold

neutron source 2D multidetector

spectrometer

^D16

[20].

For the neutron

scattering

experiments,

the

sample

was sealed in _an aluminium container and mounted in _a variable temperature cryostat ^{of the} _{« orange »} type

[20].

As _{we are} here

mainly

interested in the

magnetic

_{structure, we} have used

X-rays

to check the

quality

of the

intercalation,

and _we have used the neutron

scattering

data _to

analyse

the

magnetic scattering.

For this _reason the neutron diffraction

pattems

are corrected for the different effects which broaden them _: the mosaic of the

sample,

the resolution of

spectrometer,

^{and the} correlation

length

of the order.

In _most of the _{cases we} will discuss _now, the mosaic of the c-axis will dominate the

broadening

: 9.6° _at the full width at half maximum

(FWHM)

_as measured

by

a

rocking

_curve

of the

(001) peak,

to be

compared

_to the

in-plane

one of

2°,

_as measured _on the

(hk0) peaks (see below).

2,I STAGE HOMOGENEITY.- The

stage

^index

(s

=

I)

and the intercalation

homogeneity

were checked

by (00f) X-ray diffractograms using

o 2 _{o scans} in reflection mode. From the FWHM of the

peak,

_we deduce the correlation

length along

the c-axis

(if

=

500

A).

_The

comparison

between the calculated and observed intensities

(without taking

into account the thermal coefficient and the

absorption)

leads _to the

following crystallo-chemical description

_:

the intercalate

layer

consists of _a

three-layer

sandwich of Cl-Co-Cl

along

the _c axis

(Tab. I).

The c-axis electronic

density gives

_a direct

representation

of the

layer stacking [2 II- Figure

I shows the electron

charge density

obtained from the Fourier transform of the diffraction pattem

compared

to the

computed

_one

according

to the parameters ^{of table I. This}

figure

is

consistent with the

assignment

of _a Co

layer

at the center of the intercalate sandwich and Cl- Co-Cl

layers

_are

slightly compressed

between the

graphite bounding layers compared

with

pristine

material

[22].

Small satellites in the curves of

figure

I _are series determination effects which arise from the finite number

(11)

of terns available in the Fourier transform.

Neutron diffraction _was

performed

at 20 K and the results _are also listed in table I. The measured correlation

length if

is

larger

than 250

A

_{which is the}

experimental

resolution.

Table I. The parameters

ofthe first

_stage

ofcocl~

intercalated in

graphite.

Data _at 300 K _are obtained

from X-ray study

while those at 20 K _come

jfom

_neutrons.

la)

The altitude

of

the

different

atoms

ofthe

cell.

lb)

The cell and _structure parameters : ac,

ac~ci~,

^are

respectively

the cell parameters

of

the

graphite lattice,

and the intercalate

lattice, dc_c

is the

in-plane

distance

between carbon atoms,

fj~, flare

the

in-plane

and c-axis correlation

lengths.

a)

Atom Co Cl C

T(K)

Altitude

(A)

₀ 1.38 4.695 300

b)

ac

(A) _acoci~ (A) dc-c (i) _Ic (A) ii iA) fib IA) T(K)

2.456 3.56 1.417 9.42 500 500 300

2.452 3.54 1.415 9.32 ~250 500 20

294 JOURNAL DE

PHYSIQiJE

I N° 3

c c

4

cl

fl

_cl

I

o 3

Fig.

I.

Charge density

p (z)

along

c-axis from _a Fourier

synthesis

of the

(00f) integrated

intensities.

The continuous line is

experimental

density obtained from X-ray diffraction and the dashed line is the calculated

profile.

2.2 CRYSTAL STRUCTURE. From

(hk0) X-ray diffraction,

the

hexagonal

lattice constants

are determined

by using

diamond

powder

_as a reference. The

in-plane

correlation

length

f~,

_~ ^{is determined}

by

the FVfHM method and

given

in table I. The

in-plane

structure _was

shown

by

monochromatic Laue

photographs [221.

The Laue

diagram

_agrees with the

existence of _a

CoC12 hexagonal

lattice close to that of the

pristine Cocl~ [23]

and

quasi- parallel

to the

graphite

lattice

(Fig. 2).

However the diffuse spots associated with the intercalate form _{an arc} which shows _an orientation of the

crystallographic in-plane

_axes not well defined with respect to the carbon lanice. The

angular dispersion

^{betwen the} two a-axes can reach 2° _as shown

by

^{the double rotation}

technique [24].

We also _note the existence of

diffuse lines _at 30° to the a-axis of

graphite

which _cannot be attributed to another intercalate lattice _at

30°,

but to a disordered _state.

2.3 LAYERS _STACKING. The

layer stacking

refers to the arrangement of _a

given layer

relative to its

neighbouring

_ones. The two

in-plane

sublattices do not interfere and diffract

independently

^{in this}

compound (Fig. 2).

The

Cocl~ layers stacking

can be determined from the

profile

of the intensities measured

along (10f)

rods of

graphite

and intercalate lattices.

Figure

3 presents the

(10f) Cocl~

rods obtained

by X-ray (a)

and neutron

(b)

diffraction. The

neutron diffraction pattems are corrected

by

^the

geometrical

effects _{: we} have summed the

diffracted intensities of different detector cells and different

sample positions taking

into

account the effect of the mosaic _as

long

as it is

responsible

of the measured width

(larger

than

the instrumental resolution and than the width of the diffuse

ridge).

We have _to take into account the very

anisotropic

mosaics of the

sample

_: the c-axis mosaic

(measured by

_a

rocking

curve of the

(001) peak)

is 9.6° _at the full width at half maximum

(FWHM),

and the

in-plane

orientational _one

(measured

_on the

in-plane rocking

_{curve on}

(hk0 ) peaks)

^{is 2°}

(see

below in

«

crystal

structure

»).

The

(10f)c~~i~ ^pattem

^obtained

^{by X-ray}

or

by

neutron diffraction agrees with _an

identity period

of 3

Ic

where

I~

is the lattice constant

(9.32 A

_{at 20 K}

_by

_neutron diffraction and

9.39

A

_{at 300 K}

by X-ray analysis).

This result entails _an

a

-p

_-y

stacking

similar to that of the

pristine Cocl~.

^Numerous faults

perturb

the ideal

stacking

and _we have

computed

the diffraction pattem

(appendix I)

with a model which takes into account these

faults, following

Marti _et al.

[25].

The diffraction

pattems

^of

figures

3a and 3b _are different since both

techniques

_are not sensitive to the _same featl~res _:

X-rays

_are

mainly

sensitive to the cobalt atoms while neutron diffraction is sensitive to all the defects _as the chlorine _{atoms are} the main neutron scanerers. Calculations and

parameters

^{used in this} calculation _are defined in

*

,

,'

,

/

. / / / / /

°i

~d

* «

Q~

296 JOURNAL DE PHYSIQUE I N° 3

la)

/~ '

w e

" E

g

~

d

#

S "

,

W /

e a /

C ~

~ O

O o

o j~~

0 5 lo 15 0 2

1 ₁

Fig.

3. The (

lot)

diffraction pattem ^{of the} intercalant. a) By

X-ray

at 300 K. b) By neutron at 20 K.

The full line is the fit

by

the model

explained

in

appendix

I and the dashed _one represents ^the

scattering by

the disordered part of the

compound.

The intensities _are corrected

by

the

geometrical

factor.

[27].

We worked _at low temperature

(2 K)

under _a

magnetic

field of 0.3 T

applied

in the

layers plane.

To be _{sl~re to see}

only

the cobalt atoms, we have

performed

the difference between this

pattem

^{and the}

pattem

^{obtained without}

magnetic

field

(the

system ^{is hence}

antiferromagnetic

and does _not diffuse at small

angles)

or at

higher

temperature. ^{We did} not observe any small

angle scattering

due _to the cobalt atoms. It is of _course

always

difficult _to be

sure of the result of _a

negative experiment, especially

if the

predicted magnetic signal

is small

(about

I fb of the nuclear small

angle signal). However,

_we believe that

previous

small

angle

experiments

_on

NiC12 samples [15]

_{were not} relevant in

Cocl~

and that the cobalt vacancies

randomly spread

_over the

layer.

^{This is} also the result of _{a recent}

X-ray

and TEM

study

on

CoC12-GIC

of

stages

^{I and 2}

by Speck

and Dresselhaus

[28]

which conclude that the intercalate

layers present

a porous ^{continuous structure rather than} an islandic discontinuous

one.

In conclusion, the

(00f)

line characterizes the

staging

and its faults while the

(10f)

_neutron diffraction line is sensitive to the

stacking

and to the

chirality

of the Cl-Co-Cl

layer.

The intercalated

layer stacking

remains

nearly

identical to that of the

pristine Cocl~

in

spite

of the presence of _a

graphite layer.

This effect characterizes the first

stage compound

and is not observed in the

higher

_stages. Similar results _are observed in

Cdcl~

and

Cucl~ [26].

For this _reason, the

complete magnetic study

can be achieved.

3. The

magnetic

structure.

All the

magnetic

_pattems

presented

have been obtained _{as a} difference between _two

equivalent pattems

at low and

high temperatures (20 K)

in order to remove the

non-magnetic

part ^{of the}

scattering.

The transformation of the intensities from

laboratory

coordinates (@, _q~

)

into

reciprocal

_space coordinates

(Q)

is

performed taking

into _account the

anisotropic

mosaics of the

sample [29].

The

magnetic

calculation takes into _account the correction due _to the geometry ^{of the}

neutron-spin

interaction

((S

x

Q)

_x

Q/Q~

where S is the

spin

director

vector and

Q

the _neutron transfer

one).

Figure

4 presents the

(00f) magnetic

diffraction pattem at 1.6 K. It indicates _a clear c-axis

antiferromagnetism

with cobalt

spins laying

in the

plane.

This structure induces _a

doubling

of the cell

along

the c-axis. This result is in agreement ^{with all}

previous

studies _on

polycrystals.

'Ii 3/z g~

0 20 40 60 80

26 (degree

Fig.

4. The

magnetic (00i)~~

line _at 1.6 K. The intensities _are corrected by the

geometrical

factors.

A

=

4.52

h.

From _a

comparison

between nuclear and

magnetic intensifies,

_we deduce that

only

60 fb of the

spins (1.44 ~B/Co atom)

are ordered

ferromagnetically

at low

temperature (1.6 K) (64

fb

if _we take into _account the

stoichiometry C~_~~coo,~4Cl~

^{obtained from the chemical}

analysis

(cf.

_part

2)

and the

staging

faults

although

the average

magnetization

saturates as will be _seen in the _next section. The

magnetic

correlation

length along

c-axis is 125

I _(about

₁₃

magnetic layers),

smaller than the

crystallographic

_one

(f)= 500i).

_{This is}

_probably

due _to the

importance

of the

stacking

faults. The corrected

(10f)~~ magnetic

diffraction line is flat in

f (Fig. 5). Usually,

in nuclear

diffraction,

such _a flat

(10f)

line is characteristic of 2D systems, I-e- of _a

complete

absence of correlations in the

stacking.

This effect does not exist in

magnetic

diffraction since the

spins

_are attached to the atoms, and _we have

computed

the

intensity given by

the 3D

antiferromagnetism (taking

into _account the

crystalline

defects and

300

250

3 200

f

_lS0

o

° 100

50

0

0 DA 0.8 1.2 1.6 2

~

Fig.

^5. The

(10i)~~ magnetic

diffraction pattem at 1.6K, corrected

by

the

geometrical

factors A

= 4.52

h.

_{The continuous line is the}

computed

diffraction

by

the

perfect antiferromagnetic

structure,

taking

into account the

crystalline stacking

correlations, and the horizontal line

corresponds

to a

calculation where

they

_are

neglected.

298 JOURNAL DE PHYSIQUE I N° 3

the resolution of the

spectrometer).

The

computation predicts

indeed the presence of _a small modulation of the

magnetic

^line

(Fig. 5)

which is too small _to be observed

here, given

the statistical _error bars.

However the

antiferromagnetic intensity

^is non zero and _can be obtained from the average value of the

scattering intensity

of the

(10f) _magnetic

_pattem.

_Compared

with the structural

intensity,

it confirms the value of about 64fb for the ordered cobalt

spins, previously

determined _on the

00i magnetic

line.

Figure

6

displays

the

(100) magnetic peak

_as it is observed _on the multidetector _: the

peak presents

an

asymmetric

line

shape

which is _a convolution of the

in-plane

correlation

length,

the

experimental

resolution and the Lorentz factor which is the convolution of the Warren tail

[30]

and the finite mosaic. We have fitted the

experimental lineshape

_on this basis. We have chosen _a Gaussian

in-plane

structure factor _as it is _a

good approximation

of _a

quasi-long

_range

order _as

pointed

out

by

Dutta and Sinha

[31]

and it is

impossible

to

distinguish

from other

forms in such _an

experiment.

The width of the Gaussian function is assumed to be

proportional

to the inverse of the

in-plane

correlation

length f~,

~. This correlation

length

is

larger

than the resolution at 1.6 K and _can be estimated to be

larger

than

5001.

_The

_shape

_of

the _curve at 1.6 K is defined

by

the resolution and the mosaic. The

right

width of this

peak

increases with the temperature. ^{This increase shows the decrease of the}

in-plane

correlation

length.

T=10 K

1,",,

,,'

'.

'; "'.,'

_.£

.' .' .'" '. .'.

m

..'

_~:

,_T=6 0

I ', _..

g

(

E 6 ^~ ~.

)

^''

T=4 5 II

I

4

~ fi

d

T=1 6 K

," .'

0

S 4 3 2 0 2 3 4 5

4 (degree)

Fig.

6. The temperature ^{variation of the} (100)

magnetic

peak. The fit is _a Lorenzian line

shape,

convoluted

by

the

experimental

resolution, the mosaic of the

sample,

and the flat

(10i)

line (Warren

shape).

~P is the 2 0

angle

with the center of the detector _{at a} fixed

position

for Q

= (100) for

~P

=

0.

In

conclusion,

the low temperature

magnetic

structure consists in _a

long

range antifer-

romagnetic

order

along

the c-axis

(125 I)

_and

a

long

_range

ferromagnetic

arrangement ^{in the}

plane (more

than 250

I).

_{No modulation of the}

_{(10i) magnetic}

_line

was observed because of the

crystallographic

defects. The

complete integrated

intensities of both

(00f)

and

(10i)

_lines

_give

a number of ordered

spins

of 64

fb, indicating

that 1/3 of the

spins

are

disordered _{even on a} very short

length

scale. This

point

will be discussed in the last part.

4.

Temperature dependence.

Figure

6

gives

the

temperature

^{variation of the}

(100) magnetic

diffraction line where _a dear

broadening

_can be _seen when the

temperature

increases. This is related to a decrease of

f~,~

and _we have fitted the _curves

according

to the model described

previously

for 1.6 K.

Figures

7a and 7b show the

temperature dependence

of the

integrated intensity

of

in-plane ((100)

and

out-of-plane ((001/2)

lines and of the inverse of the correlation

lengths I/f~

~ and

I/f~.

(b)

t120 30

loo

u iii

^{i~i 25}

^£1,,~i,[

~ _~

i

~~

~f

^{" ~~} '%

~~

(

~~ loo ©4

~~

~'

~~ ~~

f

_~~

p

00112

~~ '

~

i

~

0 0

0 2 4 6 8 lo 12 0 2 4 6 8 lo 12

T(K) T(K)

Fig.

7. a) The temperature ^{variation of the}

integrated

intensities of the (001/2)

magnetic peak

and of the (100)

magnetic

part. b) The temperature variation of the inverse of the correlation

lengths

obtained from the half width at half maximum of the diffraction pattems.

ij

are the cristalline correlation

lengths.

The continuous line is _a fit by a KT model _as described in _{text ;} T~~ ^{is the KT 2D}

ordering

temperature, and

T~

is the 3D AF

ordering

temperature.

Two critical temperatures appear on these

figures.

One

corresponds

to the appearance of the 3D

antiferromagnetism:

the

extrapolation

of the

(001/2) peak intensity gives TN

₌ 6.5 K _± 0.3 K

(Fig. 7a).

The

intensity

of the maximum of the

(100) peak

varies

initially

in the _same way as the

(001/2) peak

but does not go ^to zero above

T~.

The other critical

temperature

^is

given by

the

extrapolation

of the variation of the inverse of

in-plane magnetic

correlation

length (Fig. 7b).

This temperature,

T~D,

^{is about 4.5 K±0.5 K. Above}

T~,

_{a strong} 2D

ferromagnetic

order remains with _a correlation

length

which is much smaller than _at 1.6 K. It is _a short range 2D

quasi

order. At

T~,

_no

anomaly

_was observed in the

variation of the

in-plane magnetic

correlation

length.

^This result demonstrates that

previous interpretations

of the upper and lower temperatures, ^{deduced from the}

magnetic susceptibility studies,

as T~D ^and

T~ respectively

were wrong. The upper

temperature corresponds

to the

disappearance

of the

long

_range c-axis

antiferromagnetism.

The lower _one

corresponds

to the

divergence

of the

in-plane

correlation

length,

and _we have called it T~D ^for this _reason.

However _at this

temperature

^{the out-of}

plane f~

correlation

length

is

already quite large,

so

the actual order is 3D.

Along

the

c-axis,

a critical

broadening

_was

observed,

above 5.5

K,

and

close to the

T~ temperature (6.5K).

This is similar to the results of the second stage

compound [10, Ill

where the 3D order has _a smaller correlation

length.

5. Correlation between neutron

scattering

and

magnetic susceptibility.

We have observed two critical

temperatures

T~D ^and

T~ by

neutron

scattering.

In the first stage

compound,

two

peaks

_appear on the

magnetic susceptibility [5].

We have decided to

study

the _neutron

scattering

and the

magnetic susceptibility

in the _same

sample.

This has been

300 JOURNAL DE PHYSIQUE I N° 3

done _{on a} first stage ^HOPG intercalated

sample. Figure

8

presents

^the obtained results. It is clear _on this

figure

that

T~ corresponds

to the

highest temperature peak

^of the

susceptibility.

The

peak

of

susceptibility

at the lowest temperature

corresponds

to the 2D

ordering temperature

T~D. ^These

temperatures

are

higher

than in the

single crystalline sample presented previously.

This

point

will be discussed below. The

computation

of the actual

behavior of the AC

magnetic susceptibility

in such _a

system,

a first

stage Co-GIC,

with

strong

c-axis

coupling

is out of the KT model

[5, 6].

~

. .

. .

"

.

l.6 (~l _.'

T ~'~ lb) .

(

( ^~ _{~ .}

(

l.2

j

^$

^j

^~'~ .

~ $ _; % _w

~£ ~ ~ 'T ^~

~ DA _.

~ J 2°Qj fi

~

= , ; ^~ N

~ DA

d

°'~

~

~ 0

~ ~ ~ ~ ~ ~~ 0 2 4 6 8 lo

T(K) T(K)

Fig. 8.

-Comparison

in _a HOPG intercalated sample, between the temperature ^{variation of the}

magnetic susceptibility

at 1.0 Oe excitation field (a), and the intensity of the (001/2) magnetic

Bragg

peak (b).

6. The

higher

stages.

The neutron

scattering

in second stage was

extensively

studied

by

Suzuki _et al.

[10-13].

The correlation

length along

the c-axis is much smaller

(30 I)

and there is _a coexistence between

long

_range

(3D)

and very short range

(2D)

order.

However,

we believe that it is

possible

to

give

_an

interpretation

of their data similar to _our

interpretation

of the results _on the first

stage compound.

In the second

stage compound,

the

fitting

of

(100) magnetic peak

is _more difficult and

they

did not

study

the

temperature

^{variation of this}

peak.

We have

investigated

a third stage

compound (in

_a

powdered sample

on the two-axis

spectrometer DIB)

and found _no

antiferromagnetic peaks although

_a

peak

_was observed in

magnetic susceptibility

measurements at around T~D = 8 K. We have also

investigated

_a bi- intercalated

compound GBIC-Cocl~-GaC13.

The

sample

_was

prepared

from _a

single crystal,

but _we could _not observe

by

neutron

scattering

the

(100)

nuclear

peak

of the intercalate because the

in-plane

order is very weak. The

(00f) _magnetic

line after the correction

by

the Lorentz factor is flat and decreases

slowly

with temperature ^{between 1.6 K and 10}

K,

in _a way which is very similar to the

integrated intensity

of the

(100) peak

of the first stage

compound.

Unfortunately,

it _was not

possible

to determine the

in-plane

correlation

length

_{as a} function of

temperature

^{because of the absence of the}

(100) peak.

In this

sample,

_a

peak

_was also observed in the

susceptibility

measurements near T~D ₌ ^{6 K}

[32].

In

conclusion,

_we believe that the

higher

_{stages present a}

divergence

^of the

in-plane

correlation

length

which is very similar _to that of the first stage

compound

and

corresponds

to the

peak

of

magnetic susceptibility.

The 3D order decreases as the stage ^increases. In the second

stage compound,

a short range 3D

antiferromagnetic

order _was observed. In

higher stages

^{and in the} bi-intercalated

compound,

no 3D

ordering

_was observed. The

comparison

between the

magnetic properties

of the first and the

higher

_stages shows that the 2D

ordering

is

only weakly

influenced

by

the 3D

coupling.

This allows _us to

study

this 2D

ordering

_even in the first stage

compound.

7. Discussion.

In this

part,

we will discuss three

points

: the

validity

of the 2D XY KT model which is

usually

used to fit the

magnetic susceptibility

in the

higher

stages ^{the critical}

temperatures

^that we

have

found,

which _are very low

compared

to other

studies,

and the

partial ordering

at low

temperatures.

7,I THE VALIDITY oF THE 2D XY MODELS. We have shown in the

previous

sections that

the

temperature

^{variation of the}

in-plane magnetic

correlation

length

is

mainly

driven

by

the 2D

properties

of the

layer

and the 3D

antiferromagnetic

order does _not affect it. For this

reason, we will _now discuss the 2D XY model and

interprete

our results within this

framework.

The Kosterlitz-Thouless model

[Ii

of the 2DXY transition _assumes that the transition is driven

by

^the

separation

of vortex-antivortex

pairs

which _are

responsible

for the ther-

modynamical stability

of the low

temperature phase.

The correlation

length f

above T~D ^is

given by

(1/t)

=

(I/to) exp(-

b/t~~~) with t

=

(T T~D)/T~D (I)

This behavior _assumes that the system is

purely 2D, ferromagnetic

XY and infinite. In the present case, many deviations exist.

First,

there is _a 3D

coupling

which appears at

T~,

and the

system presents strong

^3D

correlations,

which however do not

strongly modify

the 2D

ordering.

Moreover in the KT

theory

the correlation

length

does not

really depend

_on the dimension of the space

[33].

Such _a

system

with 3D

coupling presents

a KT like transition

(which

is in fact

3D)

at a transition temperature

[33]

_:

TIT

"

TKT(1

+

9/1r/ _{(J'/J~) (2)}

(TKT

^{is the 2D}

temperature arJs~/2,

_s

=

1/2,

J'the

out-of-plane coupling).

This is the _case in intercalated

compounds

where the vortices should be in fact 2D. Friedel has

recently

shown that the

opposite assumption

I-e- 3D defects

(here

3D vortices with the axis in any direction of the 3D

space) gives

a

completely

different result, even with _a strong

anisotropy [34].

In this

model T~ ^is very small _as J' is not a

perturbative

term and the 2D transition

might

be

destroyed.

We _are

obviously

not in such _{a case.}

There is _a finite structural

in-plane

correlation

length f~,

_~ ^which is the upper bound for the

magnetic

correlation

length f.

The effect of this finite size _on the KT transition has been studied

theoretically by

Szeto et al.

[35].

We have observed that until

f

reaches the value

f~,

_~ at 4 K, no effect _can be observed _on the temperature

dependence

of

f.

For these _{reasons, we} fit the temperature

dependence

of

f by

a KT model _as is shown in

figure

7b

(fo

=

8.8

I,

b

=

1.6 and T~D = 4.4

K).

In this

model,

b

parametrizes

the inflexion

changing

of

I/f(T)

_as

predicted by

^the Kosterlitz-Thouless

model, to,

the

high

temperature

limit of the correlation

length,

is _a few times the unit cell parameter

(3.54i)

_and

T~D ^{should be the} Kosterlitz-Thouless transition

temperature.

^With s = 1/2 and

E~ being

the

energy of _{a vortex}

creation,

for

E~/kT WI,

_we find

T~~ =NJS~/2

=8.4K. The value

J

= 21.5 K of the XY

ferromagnetic exchange

interaction J _was measured

independently by

inelastic

magnetic

_neutron

scattering [36].

We will discuss in the next section the

discrepancy

between the measured T~D ^and

T~~.

The inflexion

point

_:

_T~

=

5.6 K

(Fig. 7b) corresponds

in

the model _{to a} correlation

length approaching

the size of the _core of the vortices:

302 JOURNAL DE PHYSIQUE I N° 3

f(T~ )

=

20, I

to. Beyond

^this

point,

the interaction energy between vortices is

different,

since these _{can no}

longer

be considered _as free vortices and the Kosterlitz-Thouless

theory

is _not

valid,

but this inversion of the _curvature remains _as it characterizes the smoothness of the

transition.

7.2 THE VALUES OF THE CRITICAL TEMPERATURES. The critical temperatures

T~~

and

T~~

^that we have found in the

single crystal (4

K and 6.5

K)

_are lower than those found

by

others

(8

K and 9

K).

The

interpretation

of this

discrepancy

is still _not

completely

clear. The presence of _a

high

rate of cobalt vacancies in the cobalt

layer

can be at the

origin

of this difference. Nicholls

[19]

has

recently proposed

_a model where the vacancies _are

completely disordered,

_{as was}

suggested by

_our small

angle

neutron

scattering

measurements which _were unable _to observe any

long

_range order in the vacancies. In this

model,

the presence of the

vacancies is treated in _{a mean} field

theory

where the average number of first

neighbors

decreases

(in

the present case 5 instead of

6).

Hence, the effective J

in-plane coupling

value decreases and then T~D ^{decreases. The decrease of}

T~

is _more difficult _to describe since _we have to know the

origin

of the 3D

coupling, dipole-dipole

interaction _or

super-exchange

across the chlorine and the

graphite layers.

Both models

give

reasonable values of

T~

but the

dipole-dipole

interaction model

[29] predicts

_a limitation of

f~

at

f~,~

^and a

destruction of the

antiferromagnetic ordering

temperature

TN

for _a value of

f~

_~ ^of a few

l~'s

which is indeed observed in

figure

7b. The

discrepancies

between the transition

temperatures among different

samples

then arise from the different

filling

factors of the cobalt atoms in the GICS. It should be mentioned here that it is very difficult to intercalate

graphite, particularly single crystals,

with

CoC12

to the first stage ^with a

high filling

factor

[17].

7.3 THE PARTIAL ORDERING AT Low TEMPERATURE. As _we have

already

mentioned,

only

64 fb of the

spins

are ordered _at low temperatures

although

the

peak intensity

saturates. The

integrated

intensities of the

Bragg peaks

^measured

by magnetic

neutron

scattering

do not

correspond

to the

magnetization

of _one of the _two sublattices but

correspond

to the local

magnetization averaged

_on a size

equal

to the correlation

length.

For

example,

the presence of vortices in the

layer

decreases the observed

integrated peak intensity

not because the

average

magnetization

should be _zero, but because the _{vortex cores}

give

_a

scattering

which is very flat in the

reciprocal

lattice and hence is _not taken into _account in _our

integration

of the

peak intensity.

We believe

(but

this remains somehow

speculative)

that the presence of such defects in the low temperature

phase

is due to the presence of the cobalt vacancies which

pin

the vortices.

More measurements will be necessary to confirm _or infirm this

model,

and in

particular

measurements under

magnetic

field.

8. Conclusion.

We have measured the

magnetic ordering

of

CoC12

intercalated in

graphite,

and _we have

shown that the 2D

ordering

_seems to be very

weakly

influenced

by

the 3D

ordering

which appears ^at

T~.

We have then

analysed

the 2D

ordering

in the Kosterlitz-Thouless framework.

In

particular

the

magnetic in-plane

correlation

length

varies _more

smoothly

with temperature than the c-axis _{one, as} is

predicted

in the 2D KT

theory. Only

part ^{of the}

spins (64fb)

contributes to the

magnetic Bragg peaks

in the low

temperature phase showing

the presence of local disorder. We attribute these _zones to the vortex cores

predicted

in the KT

theory.

The

presence of cobalt vacancies which

explains

the differences in the transition temperatures between different

samples

does _not

perturb

too

strongly

the mechanism of _appearance of the 2D

ordering.

Appendix

1.

Stacking

faults of

Coclz

first stage.

The calculation _was

performed according

to the

following procedure

_:

The

in-plane

lattices of

graphite

and intercalate

layers

are incommensurate, _so the _two orders do not interfere in the

(10f)

_{line. Since the effect of the}

_staging

_faults is

negligible compared

to the effect of the

stacking faults,

_we have assumed _{a pure} first

stage compound.

We _{use a} model

describing

the N

equidistant layers

as

homogeneous

Markov chains of first order

[25, 26, 36],

which represent a first

neighbour

interactions.

The

probability

to be in the state e~ in the

plane

_n is

p(e,)

= p,. The

probability

to be in

the state e~ in the

plane

_n if the

plane (n

^I

)

is

e~ is

Q(.

Let A be the matrix of coordinates of the

change

of basis which

diagonalized Q.

The diffracted

intensity

is

I(I)

=

Real

((PWI

AAA ^~'

W)

where A is _a

diagonal

matrix

Aj

₌

(I

+ A~

exp(-

2 I

grit)/(I

_A~

_exp(-

2

igri))

₊

+

(I

_{+ A~}

exp(2 igri))/(I

_A~

exp(2

I

gri))

The

peaks

_occur for A~

exp(±

2

art)

= I.

We also introduce _an

in-plane

translation

3

of the

(n

₊

I)th plane

with respect to the nth _one

by replacing

_A~

by A~exp(2iar3(ha*+kb*)).

The

physical meaning

of this translation is not

simple.

It is

actually

_an indirect way ^to introduce random

stacking

faults

[24]

which would have been very difficult _to calculate in the presence of commensurate

stacking

faults. The altemative calculation

(only

random

faults)

_was

performed

elsewhere and

supply

a

poorer fit

[36].

A

layer

of

Cocl~

is made of three

hexagonal

2D lattices stacked in rhomboedral

positions.

Let _u and d be the

symbols

for the upper and lower chlorine

planes,

ABC the three

possible positions

^of the 2D

hexagonal

lattice. The

following

table

gives

the different _states

(C

is the

permutation

of ABC and 8

exchange

of the _two chlorine

positions).

W~

=

b~~

+ 2

b~j

cos 2

ar(df

_±

_1/3).

State Positions W Structure factor Name

ei

A~ BC~

W+ II

li(ei

+ e~ + e~ + e4 + e~ ⁺

e~)

ej

C

(ej _B~ CA~ _j

W⁺ II

li(ei

+ e~ + e~ e4 e~

e~)

e~

C~

~(ei) C~ AB~ j2

4~+ II

/(ei

+

je~

+

j~ _e~)

_e~

8C~

~(ej B~ AC~ j~

W~ II

/(e4

+

j~

_{e~ +}

_je~)

_e4

8C(ej) A~ CB~ j4~-

^II

~/3(ei

₊

j~e~

₊

_je~)

_e~

8~

~(ei) C~ BA~

4~- 1/

/(e4

+

je~

₊

j~ _e~)

_e~

304 JOURNAL DE PHYSIQUE I N° 3

Since all

positions

_are

equivalent,

_p

=

1/6. The conditional

probabilities

_are listed _now

State _{n, state n +} I

Probability

e~,

C(e~)

I

=

1, 2,

3 2 _p

e~, C~ ~(e~) ^I =

4, 5,

6 2 _p

e~,

C(ei)

I

=

4, 5,

6 2

a

e~, ^C~

'(e~)

I

=

1, 2,

3 2 _a

e~,

8(e~)

I

= I _to 6

fl

e~, _e~ I

=

I _to 6 _e

e~,

8C(e~)

I

=

I _to 6 _v

e~, ^SC ~(e~

)

I

=

I _to 6 _v

with the condition _{s +} 2 _{a +} 2 _{p +} fl + 2 _v

=

I.

The

diagonalization gives

the

following eigenvalues

:

i

s+2a+2v-2p-fl

and the

eigenvalues

of the matrix

Is ^+2ja

⁺

^{2/p (fl v)J}

(p

₊

v)j~

s

+2j~a

₊

_2jp

The best fit is shown in

figure

3b with the parameters :

a p =

0.13, fl

_v

=

0.004,

_{s a p}

=

0.025,

_no

background,

755

planes

and 3

=

0.07.

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Phys.

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