HAL Id: jpa-00246431
https://hal.archives-ouvertes.fr/jpa-00246431
Submitted on 1 Jan 1991
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
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�
J.
Phys.
I France1 (1991) 1499-1510 OCTOBRE1991, PAGE 1499Classification
Physics
Abstracts72.15E 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 MatdriauxMdtalliques,
3 rue de l'Universitd, 67084Strasbourg,
France(~) Centre de Recherches sur les Trds Basses
Tempdratures (*),
Centre National de la RechercheScientifique,
B-P- 166, 38042 Grenoble Cedex 9, France(Received13
March 1991, revised 3April
1991,accepted
24 June 1991)Abstract.
Magnetic, specific
heat andresistivity
measurements lead to assume that in theCesRh4 compound
the three different Ce local environments induce two kinds ofground
states.The atoms in the
position
I ordermagnetically
with a Ndel temperature ofT~
= 0.75 K and thosein
position
II and III areresponsible
for a Kondo-like behaviour. The Ce L~ii X-rayabsorption
witnesses the presence of a Mixed Valenceground
state.Inwoducdon.
In a recent
Study [I]
of the Structural andmagnetic properties
of the Ce-Rhbinary
compounds,
two different behaviours were well established as a function of the relativeCe/Rh
= x concentration.
On the x w I
side,
theCeRh~, CeRh~
and CeRhcompounds
are classical Mixed Valence(MV)
systems withhigh
values of the Ce valence measuredby Ljjj X-ray absorption ~AS),
a weak temperature
dependence
of thesusceptibility (x)
and a reduced cell volume withrespect
of the isostructural rare earth rhodiurn(RE-Rh) compounds (see
Ref.[I]
and Refs.therein).
On the Ce rich side all the
compounds
showmagnetic
order at lowtemperature iii.
The Curie-Weiss temperature(0~(
decreasesmonotonically
when xincreases,
withunexpected large
values at the borderconcentration,
I,e. for x m I but not toolarge.
This suggests thatCe~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 stateregimes.
Another characteristic of thiscompound
is its reducedvolume,
which is 3 fb smaller than that obtained from the(RE)~Rh4
volumeinterpolation [2],
unusual for a Ce
magnetically
orderedsystem.
Thiscompound gives
therefore theopportunity
to compare in the same system the two behaviors which should apriori
excludeone each other.
(~)
Laboratoire associk h l'UniversitkJoseph
Fourier, Grenoble.The aim of this paper is to
present
a detailedstudy
of somemagnetic,
thermal and transportproperties
ofCe~Rh4. Moreover, LjjjX-ray absorption spectra
are used to a direct determination of the Ce valenceu(T)
in thiscompound.
Experimental
details.The
samples
wereprepared by melting together
stoichiometric amounts of the components(Ce
and Rh 99.99 fbpure)
in an arc fumace under argonatmosphere.
Theweight
losses in thisprocedure
werenegligible.
The Cu KaX-ray pattems performed
onCe~Rh4
are characteristic of the orthorhombicSm~S14 type
structure, with lattice parameters(a
=
7A17,
b=
14.88 and
c =
7.6131)
ingood agreement
withprevious
results[2]).
The
magnetic susceptibility
measurements wereperformed using
avibrating sample magnetometer, operating
inmagnetic
fields up to 2T and between 2 and 300K. Themagnetization
was measuredby
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 forresistivity
measurements. Thesamples
wereshaped
onto small rods of> I mm in diameter and
~
10 mm in
length.
The verylow temperature measurements
(20mKw Tw1.2K)
were achieved on asample placed
inside the
mixing
chamber of a dilutionrefrigerator.
The
specific
heat data were obtained with a semi-adiabatic3He
calorimeterusing
the standard heatpulse method, withing
the range of 0,4 to 30 K.The
Lm X-ray absorption
spectra have been recorded on the EXAFS IIstation, using
theX-ray
beam deliveredby
the DCIstorage ring
at LURE inOrsay.
The energyresolution,
in the 5-6 kev range, istypically
m1.5 eV. Additionalpremirrors
are used in order toreject parasite
harmonics. To avoid some extra contributions due to Ce oxidation thesamples
werepowdered
inhigh purified
argonatmosphere.
From the XANESanalysis
traces ofCeO~
areestimated to be lower than I fb.
Experhnental
results.MAGNETIC MEASUREMENTS. The
temperature dependence
of the inversesusceptibility
x~
~(T)
is shown infigure
I. Itpresents
an unusual behavior for a 4fsystem.
The thermal Variation ofx~~
can be assimilated to a Curie-Weiss lawonly
athigh
temperature(T
m 200-250K)
; this lead to a Curie constant C of about 0.88emu/mole Ce, larger
than the free ionCe3+ Value,
and to anextrapolated
Curie-Weisstemperature (0~(
m200K, particularly large.
For T < 100K,
x ~(T~
exhibits apronounced
downward curvature, whichcannot be
represented by
a Curie-Weissbehavior,
even in firstapproximation.
Thiscorresponds
to arapid
increase of x oncooling. Then,
the Variation of x vs. T exhibits amaximum below lK
(inset
ofFig, I)
characteristic ofmagnetic
order. Theordering
temperature
cannot beprecisely
determined from thisplot,
but thespecific
heat datareported
in the
following
show thatantiferromagnetic (AF)
order occurs at atemperature
T~q =
0.75 K.
Figure
2 shows themagnetization
M versusapplied
field at 4.2 and lA K. Thehigh
field linear Variation of M leads to a saturationmagnetization M~
of about 0.34 ~L~/Ce at I.4 K(intercept
of thisstraight
line for H =0).
A Value of the same order can beexpected
forT- 0 because the thermal Variation of
M~
between 4.2 K and lA K isquite
small.ELECTRICAL RESISTIVITY. The electrical resistivities of
Ce5Rl14
and of thecompound
La5Rh4
areplotted
versustemperature
infigure
3. Theresistivity
ofLa~Rh~
exhibitsquite
large
values: a roomtemperature
valuep(RT)m130~LI1cm
and a residual valueM 10 MAGNETIC AND MIXED VALENCE STATES IN
Ce5Rh4
1501w
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 inversesusceptibility ~per
mole Ce) ofCe5Rh4
for 2< T
< 300 K.
Inset : x(T~ for Tw4.2 K.
5
14K 2K
~ O
~
? O°
f
' f
2 t
~
o
~
o o
~°
Ce~Rh,
~0
5 10 15 20lTl
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 anegative
curvature above m150 K. It can be noted also that aLa~Rh4 sample
measuredby specific
heat[3]
shows asuperconducting
transition at 1.2 ± 0.05K,
while no indication ofsuperconductivity
has been observed above 1.2 K for the presentresistivity sample.
Starting
from p(RT~
m140~LI1cm,
theresistivity
ofCe5Rh4
is alsocontinuously
decrea-sing,
without any markedanomaly,
as can be seen from the mainplot
offigure
3. This decrease is almost linear between 10 K and 2K,
with aslope
Bm 0.6
~LI1cm/K. Then,
as shown in theright-hand
sideinset,
p(Ce~Rh4)
exhibits arapid drop
below 1.5K,
andfinally
it reaches a residual value pom 21.5
~LI1cm
below 0.2 K.Together
with thisresistivity drop
wehave
plotted
its derivative3p/3T.
The latter exhibits asharp peak
at 0.75K, exactly
at theo-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 50
0 50 loo 150 20Q ~j~j 300
Fig.
3.- Main curves thermal variation of the electrical resistivities ofCe~Rh4
andLasRh4>
for1.2 w Tw 300K;
right-hand
side inset variation ofp(Ce~Rh~)
below 1.8K and of its derivative 3p/3T.Upper
left corner insetplot
of p po below I K forCesRh4
in alog-log
scale,showing
T~ and T~ variations.value of
T~
as definedby
thespecific
heatpeak.
Another indication that thisdrop
of p(Ce~Rh4)
is due tomagnetic OrdefIng
isgiven by
theplot
Ofp po below I K drawn in the upper inset of
figure
3 an almostT'variation
is observed between ~0.4 and~0.2K;
a
T~
term occurs below 0.15 K. This isquite
similar to the behavior of theresistivity
belowT~q of other AF ordered Ce
compounds
such asCeAl~
orCeB~.
ForCeA[,
(T~q= 3.8
K),
aT3
variation of p below 3K,
then aT~
variation below 0.4 K have beenreported [4]. However,
the latterdata,
like new measurements[5a],
can bereanalyzed [5b]
as the sum of aT'and
a T~ term, the latter
becoming
dominant below 0.4K. A lowtemperature
T~ term
plus
terms of the order ofT'were
also observed in the variation of theresistivity
ofCeB~
below T~q[6].
Let us now tum to the variations of p~, the
«magnetic
contribution »(due
toCe).
Inprinciple,
p~ can be determinedby subtracting
from p(Ce~Rh4)
theresistivity
of a referencenon-magnetic compound, assuming
that the latter represents the samephonon plus
defect contributions as the former. In Cecompound
studies it is usual to subtract theresistivity
of thecorresponding
lanthanumcompound.
Herehowever,
the choice of p(La~Rh4)
as reference must be discussed. Thehigh
RT value of p(La~Rh4)
and the existence of anegative
curvature in its thermal variation arepossible
evidences that thiscompound
does not behavestrictly
likea normal metal. The latter
generally
show linear variation of p near RT. Anon-linearity
of pcan result from the presence of two different
types
of carriers withdifferent
effective massesat 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 bepositive
ornegative, depending
on thesign
of the derivative of this d-band at the Fermi level. In the case ofLa~Rh4>
the conduction bandmight
bemostly
of dcharacter,
whilethe narrow band
might
be of 4fcharacter,
as it has been underlinedby
Wohlleben andM 10 MAGNETIC AND MIXED VALENCE STATES IN
CesRh4
1503coworkers
[8]
for other La intermetalliccompounds.
Its existence would agree with therelatively high
value of the electronicspecific
heat(y~
=
20
mJ/mole K~)
measured[3]
on thiscompound.
Other choices for referenceresistivity
could bep(Y~Rh4)
or p(Lu~Rh4),
withpossibly
lower RT values. The authors of reference[8]
claim that the best choice isalways
theresistivity
of a Lu-based referencecompound. However,
the latticeparameters
of a Y or a Lucompound
aregenerally
farther from those of thecorresponding
Cecompound
than those of the La-based one ; so are thephonon
spectra and the resistivities. These considerations led us toadopt
anyway for reference p(La~Rh4)
asplotted
infigure
3.However,
anotherdifficulty
occurs which is that uncertainties exist in the absolute values of both p(Ce~Rh4)
and p(La~Rh4),
which areonly
due to the errors made onmeasuring
thegeometrical
dimensions of thesamples.
It results that eachresistivity
curve infigure
3 can be affectedby
amultiplicative
factorgiven by
thegeometrical uncertainty.
In thepresent
casethe diameters of the
samples
could beprecisely determined,
as well as the distance between thevoltage
contacts, the total errorremaining
within a few percents. Thus we haveplotted
infigure4
four curves labelled I to4, representing
the differencesp~=ap(Ce~Rh4)- bp(La~Rh4),
with different values of the factors a and b. For curveI,
we chosea = b
=
I,
in order to show the direct result of subtraction of theexperimental
curves offigure3.
The other values are, for curve2: a= 0.97 andb=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 offigure
3.In each case, p~ goes
through
a maximumpQ~~
at a temperatureT$[~.
For curveI,
pQ~~
= 32~LI1cm
and7$[~
m
25
K,
while these values go frompQ~~
= 30~LI1cm
and7$[~
m 20 K for curve
2,
topQ~~
= 35~LI1cm
and7$[~
m 30 K for curve 4. In all cases, the
variations of p~ above
T$[~
are not monotonic onincreasing
T : after aquite
steepdecrease,
curve I shows a
plateau
between ~100 and 200K,
followedby
a lessrapid
decrease. Forcurve
2,
theplateau
becomes a slow decrease between 100 and 200K,
while a maximurnoccurs close to 200K in curves 3 and 4. Let us
emphasize
that the variations ofp~ below
7$[~
are notreally
affectedby application
ofmultiplicative factors,
because p(La~Rh4)
tends to its residual value below 10 K.Thus,
p~ exhibits aquasilinear
variation35
~ ,
'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 arenormalizing
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.
below 10
K,
as does- p(Ce~Rh4)
itself. This is illustrated for curve I in the inset offigure
4. Inthis case, the value of the
slope
isB=0.57~LI1cm/K
and the residual value isp$
= 9.5
~LI1cm.
The values of B andp$
derived from curves 2 to 4 differ from the formerby only
a fewpercent, according
to themultiplicative
factors considered. In the case where p(Y~Rh4)
or p(Lu~Rh4)
would be choosen as reference it can beexpected
that the above remarks would remainvalid,
even that the variations of p~ obtained would notseriously
differ from those of
figure
4 up to m50K. The reason for this is thatp(Y~Rh4)
and p(Lu~Rh4)
can besupposed
also almosttemperature independent
belowm 10 K and
slowly increasing
up to m50K. In such a case, one can stillexpect
a linear variation of p~ below 10 K and a maximum around 20-30 K.Only
thehigh temperature
variations of p~ wouldperhaps
differ from those drawn infigure
4.SPECIFIC HEAT. The
specific
heatdata, displayed
infigure 5,
show the characteristic contribution of amagnetic phase
transition at T~q =0.75
K,
but withC~(
T~~~ = 2.8J/K
moleCe,
I-e-only
22 fb of the theoretical value. The best fit ofC~
for T <T~
was foundusing
thefunction
C~
= A InT~ T)/T~ B,
in the 0.7~ T ~ 0.45 K range, with
A
=
lJ/moleK
andB=0.5J/moleK.
Such alogarithmic temperature dependence
ofC~
ispredicted by
the two-dimensionalIsing
model[9].
Also infigure 5,
one can see thatmagnetic
fluctuations areimportant
for T~
TN
and thatthey
contribute toC~ already
up totemperatures
of about 3T~.
This corroborates theassumption
of a lowdimensionality
of themagnetic
lattice and that the value M~(IRK) =0.34~Ls/Ce
isrepresentative
of the saturationmagnetization
in themagnetic phase.
3
-÷
?~
/$ II Ce~Rh,
w j
i~
: : ~o.,
~ i ~
' ~
~ ; ~0.2
÷- j i
LJ~ /
"._ oI 0 1 2
~j~j 3
i
"""..,.,,__
/
~0
° ~
T K) ~
Fig.
5.-Specific
heat ofCesRh~
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 theentropy,
after subtraction of thephonon
contribution and of an electronic term y~ = 20mJ/mole K~ given [3] by
the referencecompound La~Rh4.
It is remarkable that at T=
4 K the
entropy gain
isonly
40 fb of the totalexpected
R In 2 value.The
specific
heat data athigher temperatures (5
w T « 30K)
arepresented, figure 6,
in aC/T
vs.T~ plot.
In the 7 w T w 14 K range, the results can be fittedby
aC/T
= A +
fl T~ law,
with A=
450 mJK~ ~ mole
(that
is A=
90 mJK~
~/Ce at.)
and fl=
4A mJK~ ~ mole
(that
bf 10 MAGNETIC AND MIXED VALENCE STATES IN
Ce5Rh4
1505is
fl
= 0.49 mJK~
~/Ce at.)
whichcorresponds
to aDebye temperature
of0D
= 280 K. Such asimple behaviour,
with a linear term(AT),
is notexpected
in a stable 4f system for which an eventualexponential
Tdependence
would be observed due tocrystal
field(CF)
excitations.However,
the calculated electronic contribution : C~j = C~~~~ CD(280)
whereCD(280)
is theDebye
function for0D
= 280K,
shows a maximum at about 20 K. The totalentropy
evaluated up to 35K is about 78fb of RIn
2;
it becomes 90fb of RIn 2 if they~ 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 ofC~/T
vs. T~ up to 30 K forCe5Rh4.
X-RAY ABSORPTION.
Examples
of CeLuj X-ray absorption spectra
inCe5Rh4,
at roomtemperature
(continuous line)
and 40 K(black dots),
aregiven figure
7. Thedouble-peak shape
of the spectra is characteristic ofLiii
lines observed in Ce intermetalliccompounds
in aa-Ce state. The
Ljjj
valence of MV systems, extracted from the ratio 3 of theoccupation probabilities
of the twointegral
valence states(u
=
3 + 3
),
isgenerally accepted
as afinger- print
of theground
state of the RE andgives
additional informations about themacroscopic
2
Liii
C~ Ce Rhz ~ ~
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 LiiX-ray absorption
spectra ofCe5Rh4 Powder
for T= 40 K
(black circles)
and 300 K(continuous line).
Inset : thermal variation of the Ce valence.properties, especially
when the valence is studied as a function of temperatureand/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 aprecision
Aum 0.004.
Discussion.
A detailed
study
of thecrystalline
structure ofCe5Rh4
has been carried out[2]
in order toanalyse
the local environment of eachtype
of Ce atom. The structure ofCe~Rh4
was foundisotopic
to that ofGd~S14 [10].
As for thelatter,
smalldisplacements
of the relative RE-Sipositions
increase the number ofneighbours
of the RE atomscompared
to theSm~S14-type
structure.
Following
the nomenclature used in reference[10],
it wasreported [2]
that forCe~Rh~ (within
theSm~S14 structure)
there are 8 atoms inposition
I(Cei)>
8 inposition
II(Cejj)
and 4 inposition
III(Cejjj)
per unit cellii-e-
4 formulaunits). Cei
has 11 Ce and 7 Rhas first
neighbours, Cen
has II Ce and 6 Rh firstneigbhours
andCejjj
has 8 Ce and 9 Rh firstneighbours. Concerning
thespatial
atomicdistribution,
theCei
atoms form chainsalong
the(0, 2.4,
0 and(0,1.7,
0planes,
with a Ce-Ce-Ceangle
of 1501 The minimumCercei
distance is 3.784
A,
between atomsbelonging
to both mentionedplanes.
TheCejj
atomsare
placed
at the comers of canted squares(of
3.97A
ofside),
which also form chains with anangle
of 140C TheCeni
have no otherCeii
atoms as nearestneighbours.
As mentioned
before,
theentropy gain
in themagnetic
transition isonly
AS= 0A R In 2.
This, together
with thecrystallography
of thiscompound strongly
suggests thatonly
8 atoms(on 20)
are involved in themagnetically
orderedphase. By taking
into account the available volume of each kind of atom, theCej
atoms appears to be closer to amagnetic (trivalent) ground
state than theCejj
atoms.Furthermore,
the lowdimensionality
of themagnetic
structure, reflected in theC~
vs, ln T behaviour at T<T~,
is ingood
agreement with thespatial
distribution of theCej
atoms. The rest of the entropy(0.6
R In2)
should be related to theCejj
andCejjj
atoms. Similarspecific
heat behaviour wasalready
observed in thecompounds Ce~sn~
andCe~sn~ [11]
the structure of which shows two sites of Ce atoms : InCe~sn~
half of the atoms are trivalent and carry amagnetic
moment while the other half are MV inCe~sn~
one third of the Ce atoms are MV while the other aremagnetic.
The fractional number
(8/20)
of the Ce atoms involved in themagnetic phase
ofCe~Rh4
also
explains
the low saturationmagnetization
value.Moreover,
it ispossible
torecognize
themagnetic
contribution of theCen
andCeii
atoms in thehigh magnetic
fieldslope
of the Mvs. H variation
(see Fig. 2)
x~~=
2.3 x
10~3 emu/mole Ce,
for H m 10 T. This value seems toohigh
to beonly
the result of a Van Vleck contribution(originated
in the CFexcitations)
and a
large part
of x~~ can be due to a mixed valent or Kondoground
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 beexplained by
the sole CF Effects(the
structure of whichbeing already unknown). Effectively,
as shown infigure 8,
in aXT
vs. Tplot,
a linear variation is observed in the 4 w Tw 80 K range oftemperature.
This behaviour defines two terms :I)
a dominantmagnetic
contribution at lowtemperature,
whichcan be attributed to the
Cej
atoms, with a Curie constantCj
= 0.095
emuK/mole
Ce andit)
a temperatureindependent susceptibility,
xo = 2.0 x 10 3emu/mole
Ce(note
that this value is in coincidence with that ofx~~).
Such ananalysis
leads to assume that the measuredsusceptibility
is an addition of two kinds ofmagnetic
Ce contributions. Since the CF structure is notknown,
such a lowtemperature analysis
cannotgive
the concentration ratio of these twokinds of Ce atoms.
Nevertheless,
it is reasonable to assume that athigh temperature
thecontribution of the
Cej
atoms to thesusceptibility
xi follows a Curie-Weisslaw,
xC/(T+0j)
with x theCej concentration, C=0.8emuK/molece
and an estimated0j
m 10 K. Thus thehigh temperature susceptibility
contribution of theCen
andCei~i
atomsbf 10 MAGNETIC AND MIXED VALENCE STATES IN
Ce5Rh4
1507can be obtained from:
xn(T~ =x(T~-xC/(T- 01).
A least square fit ofx(T)
for150 w T w 300
K,
allows to calculate the variation of xi(T~
asdisplayed
in inset offigure
8.Within the error
bar,
the latter shows a Curie-Weiss variation above ~150 K with alarge 0~~
value(m
340K)
but becomes almosttemperature independent
below~
100 K
only
avery shallow minimum can be discerned in the 60-100 K
region.
Such a behavior istypical
for thesusceptibility
of a MV system with a characteristictemperature
defined from theextrapolated 0~~ temperature. Following
thetheory
ofKrishna-Murthy [12],
this characteristictemperature
isT~
= 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 ofxn(T)
around 80K).
The agreement between the ratio of themagnetic
and thenon-magnetic
Ce atoms extracted from thissusceptibility analysis (x
=
0.28
)
and that obtained from themagnetic entropy gain (x
=
0.33
)
confirms thehypothesis
of a distribution of Ce atoms in two distinct sublattices with two differentmagnetic
behaviours.3
~~5~~4
___,..."'""
I 2 __;....""'
I ,:.""
E ,:.."
(
/" 5200./""
I
~
j100
-.-~~'~~
-~'»"
~~0
TIK)
~0
100 200 300Fig.
8. -Variation of thesusceptibility
~per mole ofcompound)
ofCe~Rh4
in a XT vs. Tplot,
for 4 ST «300K. Inset calculated thermal variation of the inversesusceptibility
xi (see text), for 4 ST « 300 K ; the I indicates the relativeprecision
of the fit.On the other
hand,
values of the characteristic temperatureT~
for theCei~
andCeijj
atoms two to four times lower than those derived above can be extracted from
C~(T) by using
theDesgranges-Schotte
model[14], namely T~
=
T~~/0.448
= 44
K,
whereT~~~m20K
is thetemperature
of the maximurn ofC~i,
orT~
=
grR/3
A= 40K
(with
A normalized to the fraction of mixed valentatoms).
The difference between the latter values and those derived from thesusceptibility
can be attributed to the fact that theCe~i
andCenj
atoms do not have the same environment and therefore may show different
T~
values. The lowerTK
may be dominant inC~i(T~
in the range where the latter has been measured(5
to 30K)
while thehigher T~ might
be dominant in thehigh temperature susceptibility,
since it is derived from x taken between 150 and 300 K. This existence of twoT~
for the mixed-valentCe atoms values can
explain
thatxi~(T) stays
almost constant below 100K,
with no welldefined maximum. It is also
possible
that theseT~
values are not temperatureindependent, leading
tounexpected experimental
variations of x.The above considerations allow also to built a
possible explanation
of the behaviour of themagnetic resistivity
p~,assuming
the latter issuitably
determinedby subtracting
p(La~Rh4)
from p
(Ce~Rh4).
Thegeneral
behaviour of p~ in a Kondo latticecompound
istypically
anincrease as In T at
high temperature,
as a result of Kondo effect when the excited CF levelsare
populated
;then,
due todepopulation
of theselevels,
a decrease of p~ occurs oncooling
at a
temperature
related to thesplitting
energy A between theground
state and the excited CF levels.Finally,
another In T variation of p~ can beobserved, corresponding
to a Kondo effect in themagnetic ground
state. Such ageneral
behaviour has been firsttheoretically
calculated[15]
andcompared
toexperimental
observations for Cecompounds
such asCeAl~
and
CeA13. However,
for acompound
coherence effects occur,leading
to a decrease of p~(with
a Fermiliquid behavior) and/or magnetic
order can occur,depending
oncompetition
between Kondo effect and RICKY interactions.
Experimental
observations can also differ from thegeneral
behaviourpredicted
in reference[15], depending
on the CF level scheme and the relative values of the characteristictemperature(s)
of thesystem.
Further theoreticaldevelopments
have been made[16]
which consider such different situations.In the present case,
starting
fromhigh temperatures,
the structures observed in the variations of p~ around200K, figure 4,
are attributable to CFeffects, assuming
these structures are not an artefactresulting
from the subtraction of p(La~Rh4). However,
it is notpossible
to say whether this CF effect is related to theCei
or to theCejj 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 adepopulation
of the lowestexcited CF level of the trivalent
Cei
atoms. This would be consistent with the fact that theseCei
atoms should have a characteristictemperature
much lower than that the ofCejj
andCei~i
we assumedpreviously 01~
10K,
I-e-T~(Cei)
of the order of a fewKelvins,
or evenlower than
T~.
In the secondhypothesis
the decrease of p~ below 20 K would result from the onset of coherence. It is notimpossible
that both effects coexist.Finally,
the almost linearvariation 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 systemsCe~sn~
andCe3Sn7
seems to beinteresting since,
like in the present case, very different CF structures andT~
values can beexpected
for the two kinds of Ce atomsexisting
in these systems. InCe~sn~,
p~ shows
only
a rounded maximum centered near 150-200 K. Variationsresembling
those ofcurves I or 2 in
figure
4 are observed in p~ ofCe~sn~
: p~ exhibits a maximum around 60K,
but it shows also a
change
ofslope (or
a smallmaximum, depending
on the factors chosen to normalize the rawresistivities)
around 180-200 K. What ispresently
known about the CF level scheme in thesecompounds
allowonly
arough explanation
of these variations of p~. In both cases, thisscheme,
as deduced from neutronexperiments [llb]
consists in threedoublets,
withsplitting energies
between theground
state and the excited ones of 70 and 155 K forCe2Sn5
and of 160 and 250 K forCe~sn~.
A furthercomparison
with theCe~Rh4
case would need a neutron
study
of the latter. In all cases, a betterinterpretation
of the variations of p~ would alsoimply
tostudy
these variations when Ce isdiluted,
as it has beenmade in many cases such as
Lai _~Ce~Cu~Si~ [17], Laj _~ce~Al~ [18]
andLaj _~Ce~Cu~ [19].
Replacing
Ceby
La can induce thedisappearance
ofmagnetic
order andcoherence,
thus lead to the observation of the lowtemperature
Kondo variation in theground
state and allow abetter observation of CF effects at
higher temperatures.
Let us now discuss the
Ljjj
XAS results. Numerousexamples
of Cecompounds
defined as trivalent state systemsby macroscopic properties
are notpurely
trivalent from theX-ray absorption point
of view[20].
This is the case ofHeavy
Fermions(CeRu~si~,
u=
3.10)
orferromagnetic (CePd,
u =3.03) compounds
; in these cases theLm
valence remainsnearly
temperatureindependent [21].
As shown in inset offigure
7 the valence inCe5Rh4
increases from 3.14 to 3.16 withdecreasing temperature.
Such a variation of u is characteristic of a MVM 10 MAGNETIC AND MIXED VALENCE STATES IN Ce5Rh4 1509
system and can be
compared
to that observed inCeRh,
CeNi[2 ii,
orCePd3 [22],
with Kondotemperatures
in the 100-300 K range. Note that forcompounds
withT~ higher
than 300K,
asCefe~
orCeRh~
theLjjj
valence istemperature independent [22].
Therefore inCe5Rh4,
the Lj~i XASstudy,
which of course does not discriminate the different Cecontributions, yields
the presence of a MV state with a characteristic
temperature
lower than 300 K and then confirms themacroscopic
resultanalysis.
Conclusion.
The
properties
ofCe~Rh4 reported
in thepresent study
can be wellexplained by
a distribution of the Ce atoms in distinct sublattices. Therespective
Ce environment induces two different kinds ofground
states : Kondo with a lowT~
value andmagnetic
for theCei
atoms with a
magnetic
transition atT~
= 0.75 K and Kondo-like for the
Cen
andCem
atoms, with characteristic temperatures
ranging
between 40 and 170 K. Furtherknowledge
onthe local
magnetism
and CFsplitting
of each kind of Ce atoms is needed to confirm thisstudy
; this can beprovided by
neutronscattering
measurements.Acknowledgements.
We thank S. Hoffmann for his
help
in theresistivity
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 criticalreading
of themanuscript.
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, UniversitfiParis-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 theProperties
of Metals andAlloys (Clarendon
Press, Oxford, 1936, and DoverPubl.,
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
andS. 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.[16] MAEKAWA S., KASHIBA S., TAKAHASHI S. and TACHIKI M., in
Theory
ofHeavy
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.