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HAL Id: jpa-00246431

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Submitted on 1 Jan 1991

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Coexistence of magnetic and mixed valence states in Ce5Rh4

J. Sereni, G. Nieva, J. Kappler, P. Haen

To cite this version:

J. Sereni, G. Nieva, J. Kappler, P. Haen. Coexistence of magnetic and mixed valence states in Ce5Rh4. Journal de Physique I, EDP Sciences, 1991, 1 (10), pp.1499-1510. �10.1051/jp1:1991222�.

�jpa-00246431�

(2)

J.

Phys.

I France1 (1991) 1499-1510 OCTOBRE1991, PAGE 1499

Classification

Physics

Abstracts

72.15E 75.30M 75.50E

Coexistence of magnetic and mixed valence states in CesRh4

J. G. Sereni

(I),

G. Nieva

(I),

J. P.

Kappler f)

and P. Haen (3) (~) Centro Atomico Bariloche, 8400 Bariloche,

Argentina

~)

I-P-C-M-S-,

Groupe

d'Etude des Matdriaux

Mdtalliques,

3 rue de l'Universitd, 67084

Strasbourg,

France

(~) Centre de Recherches sur les Trds Basses

Tempdratures (*),

Centre National de la Recherche

Scientifique,

B-P- 166, 38042 Grenoble Cedex 9, France

(Received13

March 1991, revised 3

April

1991,

accepted

24 June 1991)

Abstract.

Magnetic, specific

heat and

resistivity

measurements lead to assume that in the

CesRh4 compound

the three different Ce local environments induce two kinds of

ground

states.

The atoms in the

position

I order

magnetically

with a Ndel temperature of

T~

= 0.75 K and those

in

position

II and III are

responsible

for a Kondo-like behaviour. The Ce L~ii X-ray

absorption

witnesses the presence of a Mixed Valence

ground

state.

Inwoducdon.

In a recent

Study [I]

of the Structural and

magnetic properties

of the Ce-Rh

binary

compounds,

two different behaviours were well established as a function of the relative

Ce/Rh

= x concentration.

On the x w I

side,

the

CeRh~, CeRh~

and CeRh

compounds

are classical Mixed Valence

(MV)

systems with

high

values of the Ce valence measured

by Ljjj X-ray absorption ~AS),

a weak temperature

dependence

of the

susceptibility (x)

and a reduced cell volume with

respect

of the isostructural rare earth rhodiurn

(RE-Rh) compounds (see

Ref.

[I]

and Refs.

therein).

On the Ce rich side all the

compounds

show

magnetic

order at low

temperature iii.

The Curie-Weiss temperature

(0~(

decreases

monotonically

when x

increases,

with

unexpected large

values at the border

concentration,

I,e. for x m I but not too

large.

This suggests that

Ce~Rh4,

with x

=

1.25, 0~

=

200 K and T~q =

0.75

K,

is close to the limit between the MV and stable valence state

regimes.

Another characteristic of this

compound

is its reduced

volume,

which is 3 fb smaller than that obtained from the

(RE)~Rh4

volume

interpolation [2],

unusual for a Ce

magnetically

ordered

system.

This

compound gives

therefore the

opportunity

to compare in the same system the two behaviors which should a

priori

exclude

one each other.

(~)

Laboratoire associk h l'Universitk

Joseph

Fourier, Grenoble.

(3)

The aim of this paper is to

present

a detailed

study

of some

magnetic,

thermal and transport

properties

of

Ce~Rh4. Moreover, LjjjX-ray absorption spectra

are used to a direct determination of the Ce valence

u(T)

in this

compound.

Experimental

details.

The

samples

were

prepared by melting together

stoichiometric amounts of the components

(Ce

and Rh 99.99 fb

pure)

in an arc fumace under argon

atmosphere.

The

weight

losses in this

procedure

were

negligible.

The Cu Ka

X-ray pattems performed

on

Ce~Rh4

are characteristic of the orthorhombic

Sm~S14 type

structure, with lattice parameters

(a

=

7A17,

b

=

14.88 and

c =

7.6131)

in

good agreement

with

previous

results

[2]).

The

magnetic susceptibility

measurements were

performed using

a

vibrating sample magnetometer, operating

in

magnetic

fields up to 2T and between 2 and 300K. The

magnetization

was measured

by

an extraction method in fields up to 17 T at I.4 and 4.2 K

(S.N.C.I., Grenoble).

A conventional

four-probe

a-c-

technique

was used for

resistivity

measurements. The

samples

were

shaped

onto small rods of

> I mm in diameter and

~

10 mm in

length.

The very

low temperature measurements

(20mKw Tw1.2K)

were achieved on a

sample placed

inside the

mixing

chamber of a dilution

refrigerator.

The

specific

heat data were obtained with a semi-adiabatic

3He

calorimeter

using

the standard heat

pulse method, withing

the range of 0,4 to 30 K.

The

Lm X-ray absorption

spectra have been recorded on the EXAFS II

station, using

the

X-ray

beam delivered

by

the DCI

storage ring

at LURE in

Orsay.

The energy

resolution,

in the 5-6 kev range, is

typically

m1.5 eV. Additional

premirrors

are used in order to

reject parasite

harmonics. To avoid some extra contributions due to Ce oxidation the

samples

were

powdered

in

high purified

argon

atmosphere.

From the XANES

analysis

traces of

CeO~

are

estimated to be lower than I fb.

Experhnental

results.

MAGNETIC MEASUREMENTS. The

temperature dependence

of the inverse

susceptibility

x~

~(T)

is shown in

figure

I. It

presents

an unusual behavior for a 4f

system.

The thermal Variation of

x~~

can be assimilated to a Curie-Weiss law

only

at

high

temperature

(T

m 200-250

K)

; this lead to a Curie constant C of about 0.88

emu/mole Ce, larger

than the free ion

Ce3+ Value,

and to an

extrapolated

Curie-Weiss

temperature (0~(

m200

K, particularly large.

For T < 100

K,

x ~(

T~

exhibits a

pronounced

downward curvature, which

cannot be

represented by

a Curie-Weiss

behavior,

even in first

approximation.

This

corresponds

to a

rapid

increase of x on

cooling. Then,

the Variation of x vs. T exhibits a

maximum below lK

(inset

of

Fig, I)

characteristic of

magnetic

order. The

ordering

temperature

cannot be

precisely

determined from this

plot,

but the

specific

heat data

reported

in the

following

show that

antiferromagnetic (AF)

order occurs at a

temperature

T~q =

0.75 K.

Figure

2 shows the

magnetization

M versus

applied

field at 4.2 and lA K. The

high

field linear Variation of M leads to a saturation

magnetization M~

of about 0.34 ~L~/Ce at I.4 K

(intercept

of this

straight

line for H =

0).

A Value of the same order can be

expected

for

T- 0 because the thermal Variation of

M~

between 4.2 K and lA K is

quite

small.

ELECTRICAL RESISTIVITY. The electrical resistivities of

Ce5Rl14

and of the

compound

La5Rh4

are

plotted

versus

temperature

in

figure

3. The

resistivity

of

La~Rh~

exhibits

quite

large

values: a room

temperature

value

p(RT)m130~LI1cm

and a residual value

(4)

M 10 MAGNETIC AND MIXED VALENCE STATES IN

Ce5Rh4

1501

w

Q

Ce~ Rh,

.'

i~

(

400 _.

f

l$

,/., ~

~

,,"

'

j

200

/~

W

".

/ /

o

° 2 T (K> 4

0

0 100 200 300

Fig.

I. Thermal variation of the inverse

susceptibility ~per

mole Ce) of

Ce5Rh4

for 2

< T

< 300 K.

Inset : x(T~ for Tw4.2 K.

5

14K 2K

~ O

~

?

f

' f

2 t

~

o

~

o o

Ce~Rh,

~0

5 10 15 20

lTl

Fig. 2. High field magnetization of

Ce~Rh4

up to 17 T, at T

=

IA and 4.2 K.

po close to 9.5

~LI1cm

below 10 K.

Moreover,

the thermal variation of p

(LasRh4)

exhibits a

negative

curvature above m150 K. It can be noted also that a

La~Rh4 sample

measured

by specific

heat

[3]

shows a

superconducting

transition at 1.2 ± 0.05

K,

while no indication of

superconductivity

has been observed above 1.2 K for the present

resistivity sample.

Starting

from p

(RT~

m140

~LI1cm,

the

resistivity

of

Ce5Rh4

is also

continuously

decrea-

sing,

without any marked

anomaly,

as can be seen from the main

plot

of

figure

3. This decrease is almost linear between 10 K and 2

K,

with a

slope

B

m 0.6

~LI1cm/K. Then,

as shown in the

right-hand

side

inset,

p

(Ce~Rh4)

exhibits a

rapid drop

below 1.5

K,

and

finally

it reaches a residual value po

m 21.5

~LI1cm

below 0.2 K.

Together

with this

resistivity drop

we

have

plotted

its derivative

3p/3T.

The latter exhibits a

sharp peak

at 0.75

K, exactly

at the

(5)

o-I TlKl i

,

[e~

4 ~

~~~ '

i

/

E ~

/

~ ~

/

~Q

~ ~

~~ T

#=

o-o

I

1'5 ~

~ Q

15 ~

cL

5!1

~

~

25 Q

~ 5

~~

~

~fl o

4~

0 5 5

0

0 50 loo 150 20Q ~j~j 300

Fig.

3.- Main curves thermal variation of the electrical resistivities of

Ce~Rh4

and

LasRh4>

for

1.2 w Tw 300K;

right-hand

side inset variation of

p(Ce~Rh~)

below 1.8K and of its derivative 3p/3T.

Upper

left corner inset

plot

of p po below I K for

CesRh4

in a

log-log

scale,

showing

T~ and T~ variations.

value of

T~

as defined

by

the

specific

heat

peak.

Another indication that this

drop

of p

(Ce~Rh4)

is due to

magnetic OrdefIng

is

given by

the

plot

Ofp p

o below I K drawn in the upper inset of

figure

3 an almost

T'variation

is observed between ~0.4 and~0.2

K;

a

T~

term occurs below 0.15 K. This is

quite

similar to the behavior of the

resistivity

below

T~q of other AF ordered Ce

compounds

such as

CeAl~

or

CeB~.

For

CeA[,

(T~q

= 3.8

K),

a

T3

variation of p below 3

K,

then a

T~

variation below 0.4 K have been

reported [4]. However,

the latter

data,

like new measurements

[5a],

can be

reanalyzed [5b]

as the sum of a

T'and

a T~ term, the latter

becoming

dominant below 0.4K. A low

temperature

T~ term

plus

terms of the order of

T'were

also observed in the variation of the

resistivity

of

CeB~

below T~q

[6].

Let us now tum to the variations of p~, the

«magnetic

contribution »

(due

to

Ce).

In

principle,

p~ can be determined

by subtracting

from p

(Ce~Rh4)

the

resistivity

of a reference

non-magnetic compound, assuming

that the latter represents the same

phonon plus

defect contributions as the former. In Ce

compound

studies it is usual to subtract the

resistivity

of the

corresponding

lanthanum

compound.

Here

however,

the choice of p

(La~Rh4)

as reference must be discussed. The

high

RT value of p

(La~Rh4)

and the existence of a

negative

curvature in its thermal variation are

possible

evidences that this

compound

does not behave

strictly

like

a normal metal. The latter

generally

show linear variation of p near RT. A

non-linearity

of p

can result from the presence of two different

types

of carriers with

different

effective masses

at the Fermi level. The occurrence of such non-linearities is a well

kribwn

effect in transition metals

[7]

due to the existence of a narrow d-band in addition to the s-band : the curvature of p can be

positive

or

negative, depending

on the

sign

of the derivative of this d-band at the Fermi level. In the case of

La~Rh4>

the conduction band

might

be

mostly

of d

character,

while

the narrow band

might

be of 4f

character,

as it has been underlined

by

Wohlleben and

(6)

M 10 MAGNETIC AND MIXED VALENCE STATES IN

CesRh4

1503

coworkers

[8]

for other La intermetallic

compounds.

Its existence would agree with the

relatively high

value of the electronic

specific

heat

(y~

=

20

mJ/mole K~)

measured

[3]

on this

compound.

Other choices for reference

resistivity

could be

p(Y~Rh4)

or p

(Lu~Rh4),

with

possibly

lower RT values. The authors of reference

[8]

claim that the best choice is

always

the

resistivity

of a Lu-based reference

compound. However,

the lattice

parameters

of a Y or a Lu

compound

are

generally

farther from those of the

corresponding

Ce

compound

than those of the La-based one ; so are the

phonon

spectra and the resistivities. These considerations led us to

adopt

anyway for reference p

(La~Rh4)

as

plotted

in

figure

3.

However,

another

difficulty

occurs which is that uncertainties exist in the absolute values of both p

(Ce~Rh4)

and p

(La~Rh4),

which are

only

due to the errors made on

measuring

the

geometrical

dimensions of the

samples.

It results that each

resistivity

curve in

figure

3 can be affected

by

a

multiplicative

factor

given by

the

geometrical uncertainty.

In the

present

case

the diameters of the

samples

could be

precisely determined,

as well as the distance between the

voltage

contacts, the total error

remaining

within a few percents. Thus we have

plotted

in

figure4

four curves labelled I to

4, representing

the differences

p~=ap(Ce~Rh4)- bp(La~Rh4),

with different values of the factors a and b. For curve

I,

we chose

a = b

=

I,

in order to show the direct result of subtraction of the

experimental

curves of

figure3.

The other values are, for curve2: a= 0.97 and

b=1.03;

for curve3 :

a =

1.03 and b

=

0.97 and for curve 4 : a

= 1.05 and b

= 0.95.

All those curves show structures which are not obvious in the p

(Ce~Rh4)

curve of

figure

3.

In each case, p~ goes

through

a maximum

pQ~~

at a temperature

T$[~.

For curve

I,

pQ~~

= 32

~LI1cm

and

7$[~

m

25

K,

while these values go from

pQ~~

= 30

~LI1cm

and

7$[~

m 20 K for curve

2,

to

pQ~~

= 35

~LI1cm

and

7$[~

m 30 K for curve 4. In all cases, the

variations of p~ above

T$[~

are not monotonic on

increasing

T : after a

quite

steep

decrease,

curve I shows a

plateau

between ~100 and 200

K,

followed

by

a less

rapid

decrease. For

curve

2,

the

plateau

becomes a slow decrease between 100 and 200

K,

while a maximurn

occurs close to 200K in curves 3 and 4. Let us

emphasize

that the variations of

p~ below

7$[~

are not

really

affected

by application

of

multiplicative factors,

because p

(La~Rh4)

tends to its residual value below 10 K.

Thus,

p~ exhibits a

quasilinear

variation

35

~ ,

'l',

~

(

,

",,,

_,---_

', ',

""~~~~~'

3

"',,,

E '

'~~---~~~~

~~

"',

C- , ~~

~

~~

''

"

"_

~~

'~

~ -,~

2

~ ~- ~,~

lo

]30

~.,

~'

~

Ill

',

]

',

5 ~

~

T(Kl

",

~°0 5 10 15

0

0 50 loo 150 200 ~ ~j 300

Fig.

4. Variation of the «

magnetic

» contribution p~

= ap

(Ce~Rh4)-bp (La~Rh~)

where a and b are

normalizing

factors

(see text).

Curve I : a

= b

=

I ; Curve 2: a

= 0.97, b

=

1.03 ; Curve 3

a =

1.03, b

=

0.97 ; Curve 4 a

= 1.05, b

=

0.95. Inset detail of curve I below 17.5 K.

(7)

below 10

K,

as does- p

(Ce~Rh4)

itself. This is illustrated for curve I in the inset of

figure

4. In

this case, the value of the

slope

is

B=0.57~LI1cm/K

and the residual value is

p$

= 9.5

~LI1cm.

The values of B and

p$

derived from curves 2 to 4 differ from the former

by only

a few

percent, according

to the

multiplicative

factors considered. In the case where p

(Y~Rh4)

or p

(Lu~Rh4)

would be choosen as reference it can be

expected

that the above remarks would remain

valid,

even that the variations of p~ obtained would not

seriously

differ from those of

figure

4 up to m50K. The reason for this is that

p(Y~Rh4)

and p

(Lu~Rh4)

can be

supposed

also almost

temperature independent

below

m 10 K and

slowly increasing

up to m50K. In such a case, one can still

expect

a linear variation of p~ below 10 K and a maximum around 20-30 K.

Only

the

high temperature

variations of p~ would

perhaps

differ from those drawn in

figure

4.

SPECIFIC HEAT. The

specific

heat

data, displayed

in

figure 5,

show the characteristic contribution of a

magnetic phase

transition at T~q =

0.75

K,

but with

C~(

T~~~ = 2.8

J/K

mole

Ce,

I-e-

only

22 fb of the theoretical value. The best fit of

C~

for T <

T~

was found

using

the

function

C~

= A In

T~ T)/T~ B,

in the 0.7

~ T ~ 0.45 K range, with

A

=

lJ/moleK

and

B=0.5J/moleK.

Such a

logarithmic temperature dependence

of

C~

is

predicted by

the two-dimensional

Ising

model

[9].

Also in

figure 5,

one can see that

magnetic

fluctuations are

important

for T

~

TN

and that

they

contribute to

C~ already

up to

temperatures

of about 3

T~.

This corroborates the

assumption

of a low

dimensionality

of the

magnetic

lattice and that the value M~

(IRK) =0.34~Ls/Ce

is

representative

of the saturation

magnetization

in the

magnetic phase.

3

?~

/$ II Ce~Rh,

w j

i~

: : ~o.,

~ i ~

' ~

~ ; ~0.2

÷- j i

LJ~ /

"._ o

I 0 1 2

~j~j 3

i

"""..,.,,__

/

~

0

° ~

T K) ~

Fig.

5.-

Specific

heat of

CesRh~

as a function of temperature, for 0.4 w Tw 3 K. Inset : thermal variation of entropy, normalized to R In 2.

The inset of

figure

5 shows the thermal variation of the

entropy,

after subtraction of the

phonon

contribution and of an electronic term y~ = 20

mJ/mole K~ given [3] by

the reference

compound La~Rh4.

It is remarkable that at T

=

4 K the

entropy gain

is

only

40 fb of the total

expected

R In 2 value.

The

specific

heat data at

higher temperatures (5

w T « 30

K)

are

presented, figure 6,

in a

C/T

vs.

T~ plot.

In the 7 w T w 14 K range, the results can be fitted

by

a

C/T

= A +

fl T~ law,

with A

=

450 mJK~ ~ mole

(that

is A

=

90 mJK~

~/Ce at.)

and fl

=

4A mJK~ ~ mole

(that

(8)

bf 10 MAGNETIC AND MIXED VALENCE STATES IN

Ce5Rh4

1505

is

fl

= 0.49 mJK~

~/Ce at.)

which

corresponds

to a

Debye temperature

of

0D

= 280 K. Such a

simple behaviour,

with a linear term

(AT),

is not

expected

in a stable 4f system for which an eventual

exponential

T

dependence

would be observed due to

crystal

field

(CF)

excitations.

However,

the calculated electronic contribution : C~j = C~~~~ C

D(280)

where

CD(280)

is the

Debye

function for

0D

= 280

K,

shows a maximum at about 20 K. The total

entropy

evaluated up to 35K is about 78fb of RIn

2;

it becomes 90fb of RIn 2 if the

y~ term of 20

mJ/mole K2

is included.

6 I

I

..

I

4

_.

"'

°~ ;~

~

.~

,,/

Ce~Rh,

~

~

,l'

~ ;"

0

0 200 400 600

T2j ~2j

Fig.

6. Variation of

C~/T

vs. T~ up to 30 K for

Ce5Rh4.

X-RAY ABSORPTION.

Examples

of Ce

Luj X-ray absorption spectra

in

Ce5Rh4,

at room

temperature

(continuous line)

and 40 K

(black dots),

are

given figure

7. The

double-peak shape

of the spectra is characteristic of

Liii

lines observed in Ce intermetallic

compounds

in a

a-Ce state. The

Ljjj

valence of MV systems, extracted from the ratio 3 of the

occupation probabilities

of the two

integral

valence states

(u

=

3 + 3

),

is

generally accepted

as a

finger- print

of the

ground

state of the RE and

gives

additional informations about the

macroscopic

2

Liii

C~ Ce Rh

z ~ ~

o

P

# I

o

~ l

j

1.2

2

< ~i ,.

Z e "'->-->,

[

? , ''

z

~'~0 100 200 300

T (Kl

0

5700 5720 574n 5760

ENERGY (eV)

Fig.

7. Ce Lii

X-ray absorption

spectra of

Ce5Rh4 Powder

for T

= 40 K

(black circles)

and 300 K

(continuous line).

Inset : thermal variation of the Ce valence.

(9)

properties, especially

when the valence is studied as a function of temperature

and/or

pressure. The inset of

figure

7 represents the thermal variation of the valence between 40 and 300 K. The valence could be determined with a

precision

Au

m 0.004.

Discussion.

A detailed

study

of the

crystalline

structure of

Ce5Rh4

has been carried out

[2]

in order to

analyse

the local environment of each

type

of Ce atom. The structure of

Ce~Rh4

was found

isotopic

to that of

Gd~S14 [10].

As for the

latter,

small

displacements

of the relative RE-Si

positions

increase the number of

neighbours

of the RE atoms

compared

to the

Sm~S14-type

structure.

Following

the nomenclature used in reference

[10],

it was

reported [2]

that for

Ce~Rh~ (within

the

Sm~S14 structure)

there are 8 atoms in

position

I

(Cei)>

8 in

position

II

(Cejj)

and 4 in

position

III

(Cejjj)

per unit cell

ii-e-

4 formula

units). Cei

has 11 Ce and 7 Rh

as first

neighbours, Cen

has II Ce and 6 Rh first

neigbhours

and

Cejjj

has 8 Ce and 9 Rh first

neighbours. Concerning

the

spatial

atomic

distribution,

the

Cei

atoms form chains

along

the

(0, 2.4,

0 and

(0,1.7,

0

planes,

with a Ce-Ce-Ce

angle

of 1501 The minimum

Cercei

distance is 3.784

A,

between atoms

belonging

to both mentioned

planes.

The

Cejj

atoms

are

placed

at the comers of canted squares

(of

3.97

A

of

side),

which also form chains with an

angle

of 140C The

Ceni

have no other

Ceii

atoms as nearest

neighbours.

As mentioned

before,

the

entropy gain

in the

magnetic

transition is

only

AS

= 0A R In 2.

This, together

with the

crystallography

of this

compound strongly

suggests that

only

8 atoms

(on 20)

are involved in the

magnetically

ordered

phase. By taking

into account the available volume of each kind of atom, the

Cej

atoms appears to be closer to a

magnetic (trivalent) ground

state than the

Cejj

atoms.

Furthermore,

the low

dimensionality

of the

magnetic

structure, reflected in the

C~

vs, ln T behaviour at T<

T~,

is in

good

agreement with the

spatial

distribution of the

Cej

atoms. The rest of the entropy

(0.6

R In

2)

should be related to the

Cejj

and

Cejjj

atoms. Similar

specific

heat behaviour was

already

observed in the

compounds Ce~sn~

and

Ce~sn~ [11]

the structure of which shows two sites of Ce atoms : In

Ce~sn~

half of the atoms are trivalent and carry a

magnetic

moment while the other half are MV in

Ce~sn~

one third of the Ce atoms are MV while the other are

magnetic.

The fractional number

(8/20)

of the Ce atoms involved in the

magnetic phase

of

Ce~Rh4

also

explains

the low saturation

magnetization

value.

Moreover,

it is

possible

to

recognize

the

magnetic

contribution of the

Cen

and

Ceii

atoms in the

high magnetic

field

slope

of the M

vs. H variation

(see Fig. 2)

x~~

=

2.3 x

10~3 emu/mole Ce,

for H m 10 T. This value seems too

high

to be

only

the result of a Van Vleck contribution

(originated

in the CF

excitations)

and a

large part

of x~~ can be due to a mixed valent or Kondo

ground

state.

Further informations can be extracted from the thermal variation of the

susceptibility.

The curvature of the x~ vs. T curve for Tw100 K cannot be

explained by

the sole CF Effects

(the

structure of which

being already unknown). Effectively,

as shown in

figure 8,

in a

XT

vs. T

plot,

a linear variation is observed in the 4 w Tw 80 K range of

temperature.

This behaviour defines two terms :

I)

a dominant

magnetic

contribution at low

temperature,

which

can be attributed to the

Cej

atoms, with a Curie constant

Cj

= 0.095

emuK/mole

Ce and

it)

a temperature

independent susceptibility,

xo = 2.0 x 10 3

emu/mole

Ce

(note

that this value is in coincidence with that of

x~~).

Such an

analysis

leads to assume that the measured

susceptibility

is an addition of two kinds of

magnetic

Ce contributions. Since the CF structure is not

known,

such a low

temperature analysis

cannot

give

the concentration ratio of these two

kinds of Ce atoms.

Nevertheless,

it is reasonable to assume that at

high temperature

the

contribution of the

Cej

atoms to the

susceptibility

xi follows a Curie-Weiss

law,

xC/(T+0j)

with x the

Cej concentration, C=0.8emuK/molece

and an estimated

0j

m 10 K. Thus the

high temperature susceptibility

contribution of the

Cen

and

Cei~i

atoms

(10)

bf 10 MAGNETIC AND MIXED VALENCE STATES IN

Ce5Rh4

1507

can be obtained from:

xn(T~ =x(T~-xC/(T- 01).

A least square fit of

x(T)

for

150 w T w 300

K,

allows to calculate the variation of xi

(T~

as

displayed

in inset of

figure

8.

Within the error

bar,

the latter shows a Curie-Weiss variation above ~150 K with a

large 0~~

value

(m

340

K)

but becomes almost

temperature independent

below

~

100 K

only

a

very shallow minimum can be discerned in the 60-100 K

region.

Such a behavior is

typical

for the

susceptibility

of a MV system with a characteristic

temperature

defined from the

extrapolated 0~~ temperature. Following

the

theory

of

Krishna-Murthy [12],

this characteristic

temperature

is

T~

= 0~~~

/2

=

170 K while from Griiner's

theory [13]

T~= (0~~(/4.5

=

75K. This last temperature is close to that of the above mentioned minimum of

I/xi~(T) (I.e.

maximurn of

xn(T)

around 80

K).

The agreement between the ratio of the

magnetic

and the

non-magnetic

Ce atoms extracted from this

susceptibility analysis (x

=

0.28

)

and that obtained from the

magnetic entropy gain (x

=

0.33

)

confirms the

hypothesis

of a distribution of Ce atoms in two distinct sublattices with two different

magnetic

behaviours.

3

~~5~~4

___,..."'""

I 2 __;....""'

I ,:.""

E ,:.."

(

/" 5200

./""

I

~

j100

-.-~~'~

~

-~

'»"

~~0

TIK)

~0

100 200 300

Fig.

8. -Variation of the

susceptibility

~per mole of

compound)

of

Ce~Rh4

in a XT vs. T

plot,

for 4 ST «300K. Inset calculated thermal variation of the inverse

susceptibility

xi (see text), for 4 ST « 300 K ; the I indicates the relative

precision

of the fit.

On the other

hand,

values of the characteristic temperature

T~

for the

Cei~

and

Ceijj

atoms two to four times lower than those derived above can be extracted from

C~(T) by using

the

Desgranges-Schotte

model

[14], namely T~

=

T~~/0.448

= 44

K,

where

T~~~m20K

is the

temperature

of the maximurn of

C~i,

or

T~

=

grR/3

A

= 40K

(with

A normalized to the fraction of mixed valent

atoms).

The difference between the latter values and those derived from the

susceptibility

can be attributed to the fact that the

Ce~i

and

Cenj

atoms do not have the same environment and therefore may show different

T~

values. The lower

TK

may be dominant in

C~i(T~

in the range where the latter has been measured

(5

to 30

K)

while the

higher T~ might

be dominant in the

high temperature susceptibility,

since it is derived from x taken between 150 and 300 K. This existence of two

T~

for the mixed-valent

Ce atoms values can

explain

that

xi~(T) stays

almost constant below 100

K,

with no well

defined maximum. It is also

possible

that these

T~

values are not temperature

independent, leading

to

unexpected experimental

variations of x.

The above considerations allow also to built a

possible explanation

of the behaviour of the

magnetic resistivity

p~,

assuming

the latter is

suitably

determined

by subtracting

p

(La~Rh4)

(11)

from p

(Ce~Rh4).

The

general

behaviour of p~ in a Kondo lattice

compound

is

typically

an

increase as In T at

high temperature,

as a result of Kondo effect when the excited CF levels

are

populated

;

then,

due to

depopulation

of these

levels,

a decrease of p~ occurs on

cooling

at a

temperature

related to the

splitting

energy A between the

ground

state and the excited CF levels.

Finally,

another In T variation of p~ can be

observed, corresponding

to a Kondo effect in the

magnetic ground

state. Such a

general

behaviour has been first

theoretically

calculated

[15]

and

compared

to

experimental

observations for Ce

compounds

such as

CeAl~

and

CeA13. However,

for a

compound

coherence effects occur,

leading

to a decrease of p~

(with

a Fermi

liquid behavior) and/or magnetic

order can occur,

depending

on

competition

between Kondo effect and RICKY interactions.

Experimental

observations can also differ from the

general

behaviour

predicted

in reference

[15], depending

on the CF level scheme and the relative values of the characteristic

temperature(s)

of the

system.

Further theoretical

developments

have been made

[16]

which consider such different situations.

In the present case,

starting

from

high temperatures,

the structures observed in the variations of p~ around

200K, figure 4,

are attributable to CF

effects, assuming

these structures are not an artefact

resulting

from the subtraction of p

(La~Rh4). However,

it is not

possible

to say whether this CF effect is related to the

Cei

or to the

Cejj and/or Cei~j

atoms.

It is also not easy to say whether the further Kondo-like increase of p~ between

m 100 K and

the 20-30 K maximum is relative still to excited CF states or to a

magnetic ground

state. In the first case, the decrease of p~ below 20 K would result from a

depopulation

of the lowest

excited CF level of the trivalent

Cei

atoms. This would be consistent with the fact that these

Cei

atoms should have a characteristic

temperature

much lower than that the of

Cejj

and

Cei~i

we assumed

previously 01~

10

K,

I-e-

T~(Cei)

of the order of a few

Kelvins,

or even

lower than

T~.

In the second

hypothesis

the decrease of p~ below 20 K would result from the onset of coherence. It is not

impossible

that both effects coexist.

Finally,

the almost linear

variation of p~ between

~ 2 and ~10 K is characteristic of a coherent behavior.

A

comparison

with the variations of p~ observed

[llb]

in the two systems

Ce~sn~

and

Ce3Sn7

seems to be

interesting since,

like in the present case, very different CF structures and

T~

values can be

expected

for the two kinds of Ce atoms

existing

in these systems. In

Ce~sn~,

p~ shows

only

a rounded maximum centered near 150-200 K. Variations

resembling

those of

curves I or 2 in

figure

4 are observed in p~ of

Ce~sn~

: p~ exhibits a maximum around 60

K,

but it shows also a

change

of

slope (or

a small

maximum, depending

on the factors chosen to normalize the raw

resistivities)

around 180-200 K. What is

presently

known about the CF level scheme in these

compounds

allow

only

a

rough explanation

of these variations of p~. In both cases, this

scheme,

as deduced from neutron

experiments [llb]

consists in three

doublets,

with

splitting energies

between the

ground

state and the excited ones of 70 and 155 K for

Ce2Sn5

and of 160 and 250 K for

Ce~sn~.

A further

comparison

with the

Ce~Rh4

case would need a neutron

study

of the latter. In all cases, a better

interpretation

of the variations of p~ would also

imply

to

study

these variations when Ce is

diluted,

as it has been

made in many cases such as

Lai _~Ce~Cu~Si~ [17], Laj _~ce~Al~ [18]

and

Laj _~Ce~Cu~ [19].

Replacing

Ce

by

La can induce the

disappearance

of

magnetic

order and

coherence,

thus lead to the observation of the low

temperature

Kondo variation in the

ground

state and allow a

better observation of CF effects at

higher temperatures.

Let us now discuss the

Ljjj

XAS results. Numerous

examples

of Ce

compounds

defined as trivalent state systems

by macroscopic properties

are not

purely

trivalent from the

X-ray absorption point

of view

[20].

This is the case of

Heavy

Fermions

(CeRu~si~,

u

=

3.10)

or

ferromagnetic (CePd,

u =

3.03) compounds

; in these cases the

Lm

valence remains

nearly

temperature

independent [21].

As shown in inset of

figure

7 the valence in

Ce5Rh4

increases from 3.14 to 3.16 with

decreasing temperature.

Such a variation of u is characteristic of a MV

(12)

M 10 MAGNETIC AND MIXED VALENCE STATES IN Ce5Rh4 1509

system and can be

compared

to that observed in

CeRh,

CeNi

[2 ii,

or

CePd3 [22],

with Kondo

temperatures

in the 100-300 K range. Note that for

compounds

with

T~ higher

than 300

K,

as

Cefe~

or

CeRh~

the

Ljjj

valence is

temperature independent [22].

Therefore in

Ce5Rh4,

the Lj~i XAS

study,

which of course does not discriminate the different Ce

contributions, yields

the presence of a MV state with a characteristic

temperature

lower than 300 K and then confirms the

macroscopic

result

analysis.

Conclusion.

The

properties

of

Ce~Rh4 reported

in the

present study

can be well

explained by

a distribution of the Ce atoms in distinct sublattices. The

respective

Ce environment induces two different kinds of

ground

states : Kondo with a low

T~

value and

magnetic

for the

Cei

atoms with a

magnetic

transition at

T~

= 0.75 K and Kondo-like for the

Cen

and

Cem

atoms, with characteristic temperatures

ranging

between 40 and 170 K. Further

knowledge

on

the local

magnetism

and CF

splitting

of each kind of Ce atoms is needed to confirm this

study

; this can be

provided by

neutron

scattering

measurements.

Acknowledgements.

We thank S. Hoffmann for his

help

in the

resistivity

measurements, Dr C. Godart for his assistance in the Lji~

studies,

Dr F.

Lapierre

for her interest to this work and Dr J. Pierre for critical

reading

of the

manuscript.

References

[I]

KAPPLER J. P., LEHMANN P., SCHMERBER G., NIEVA G. and SERENI J. G., J.

Phys. Colloq.

France 49

(1988)

C8-721.

[2] RAMAN A., J. Less Common Mel. 48

(1976)

lll.

[3] SERENI J. G., NIEVA G., SCHMERBER J., KAPPLER J. P., Mod.

Phys.

Lett. B 3

(1989)

1225.

[4] LAPIERRE F., HAEN P., BRIGGS A. and SERA M., J. Magn. Magn. Mater. 63 & 64 (1987) 76.

[5]

(a)

BEHNIA K., Thdse, Universitfi

Paris-Sud, Orsay (1990) (b)

LAPIERRE F., Private communication.

[6] MARCENAT C., JACCARD D., SIERRO J., FLOUQUET J., dNuKi Y. and KOMATSUBARA T.,

Physica

B 163 (1990) 147.

[7] See Mom N. F. and JONES H., in The

theory

of the

Properties

of Metals and

Alloys (Clarendon

Press, Oxford, 1936, and Dover

Publ.,

New York, 1958).

[8] WOHLLEBEN D, and WITTERSHAGEN B., Adv.

Phys.

34

(1985)

403.

[9] See for

example

: KADANOFF L. P., GOETzE W., HAMBLEN D., HECHT R., LEwis E.A. S., PALCIAUSKAS V. V., RAYL M., Swim J., ASPNES D. and KANE J., Rev. Mod.

Phys.

39

(1967)

395.

[10] IGLESIAS J. E. and STEINFINK H., J. Less Common Met. 26 (1972) 45.

[I I] (a) BOUCHERLE J. X., GIVORD F., LAPIERRE F., LEJAY P., PEYRARD J., ODIN J., SCHWEITzER J.

and STUNAULT A., in Valence Fluctuations and Heavy Fermions,

L.C.Gupta

and

S. K. Malik Eds.

~Plenum

Press, New York,

1987)

p. 485 ;

BOUCHERLE J. X., GIVORD F., LEJAY P., SCHWEITzER J. and STUNAULT A., Physica B1s6 & ls7

(1989)

809

(b) STUNAULT A., Thdse, Universitb

Joseph

Fourier, Grenoble

(1988).

[12] KRISHNA-MURTHY H. R., WILSON K. G. and WILKINS J. W.,

Phys.

Rev. Lett. 3s

(1975)

l101.

[13] GRUNER G. and ZAWADOWSKY A., Rep. Prog.

Phys.

37 (1974) 1497.

[14] DESGRANGES H. U. and SCHOTTE K. D.,

Phys.

Lett. 91A

(1982)

240.

[15] CORNUT B. and COQBLIN B.,

Phys.

Rev. Bs

(1972)

4541.

(13)

[16] MAEKAWA S., KASHIBA S., TAKAHASHI S. and TACHIKI M., in

Theory

of

Heavy

Fermion and Valence Fluctuations, T. Kasuya and T. Saso Eds.

(Springer-Verlag,

1985) p. 90 ;

GuEssous A., Thdse, Grenoble

(1987) unpublished.

[17] ALIEV F. G., BRANDT N. B., MOSHALKOV V. V. and CHUDINOV S. M., J. Low

Temp. Phys.

57

(1984)

61.

[18] 0NuKi Y., FURUKAWA Y. and KOMATSUBARA T., J.

Phys.

Sac. Jpn s3

(1985)

2734.

[19] SUMIYAMA A., ODA Y., NAGANO H.,

0NuKi

Y., SHIBUTANI K. and KOMATSUBARA T., J.

Phys.

Sac. Jpn ss (1986) 1294.

[20] ROHLER J., J. Magn. Magn. Mater. 47 & 48

(1985)

175.

[21] BEAUREPAIRE E., KAPPLER J. P., SERENI J. G., GODART C. and KRILL G., in Proc. Vlth EXAFS Conf., S. S. Hasnain Ed., Ellis-Horwood Ltd

(1991)

p. 505.

[22] BAucHsPiEss K. R., BOKSCH W., HOLLAND-MORITz E., LAUNOIS H., POW R, and WOHLLEBEN

D., in Valence Fluctuations in Solids, L.M.Falicov, W.Hanke and M.B.

Maple

Eds.

~North-Holland Publishing Company, 1981)

p. 417.

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