PHYSICAL REVIEW B
VOLUME 45, NUMBER
1
1
JANUARY 1992-I
Thermoelectric power of the Kondo-lattice system: CepdSn
D. T. Adroja, B. D. Padalia, and S. N. Bhatia
Indian Institute
of Technology,
Potoai, Bombay 400076, India
S. K. Malik
Tata Institute of Fundamental
Research, Homi Bhabha Road, Bombay 400005, India
(Received 7 May 1991)
Thermoelectric power (TEP) of the antiferromagnetic compound CePdSn has been measured in the
temperature range 20 —300 K. It is positive at 300 K, exhibits a broad maximum at 100 K, and becomes
negative at low temperatures.
The maxima in TEP indicate the presence of Kondo and crystalline
electric4eld effects. These results are analyzed using the Bhattacharjee-Coqblin model, which explains
the gross features of the experimental TEP curve except the negative sign observed at low temperatures.
I. INTRODUCTION
(T~=14.5 K)
The Ce-based ternary equiatomic compounds of the
type CeTX (T= transition metal and X=metalloid) exhibit interesting physical properties. '
For instance,
CePtSi (Ref. 1) and CePtIn (Ref. 7) show heavy-fermion
behavior with a nonmagnetic ground state while CePdIn
(Ref. 3) is a heavy-fermion
system with a magnetic
ground state. The compounds CeNiSn (Ref. 8) and
CeRhSb (Ref. 9) exhibit valence fiuctuation behavior with
the formation of a pseudogap at the Fermi level. The continuous evolution of valence fluctuation behavior from
the heavy-fermion behavior has been observed in the
CePt& „Ni„Si system, which is important for the understanding of the boundary between the heavy-fermion
state and the valence fluctuation state. Although the origin of the anomalous properties of the Ce-based compounds is not yet fully understood, these are considered
to be due to the strong hybridization of nearly localized
Ce 4f electrons with the conduction electrons and are associated with the formation of many electron states in the
proximity of the Fermi level.
Among the various anomalies observed in physical
properties of the Ce-based system, measurements of the
transport properties, e.g. , resistivity and thermoelectric
power, are necessary to gain insight into the different
scattering mechanisms and their relative importance.
Since thermoelectric power (TEP) is very sensitive to the
different energy scales, this measurement provides an estimate of crystalline-electric-field
(CEF) splitting of the
4f levels. The TEP of the anomalous Ce compounds exhibits giant value at low temperatures and shows the
maximum at intermediate temperatures.
At 300 K, the
TEP of most of the Ce-based systems exhibits a positive
sign (e.g. , in CeCuzSiz, CeA12) while for the Yb-based systems, it has a negative sign.
In an earlier paper, ' we have reported on the magnetic susceptibility, electrical resistivity, and specific-heat
measurements
on antiferromagnetic
CePdSn. The magnetic ordering temperature of CePdSn (T&=7.5 K) is
anomalous compared to that of the isostructural GdPdSn
45
when considered from the de Gennes
scaling point of view. This suggests the presence of
Kondo-type interactions in this compound which may
give rise to a relatively stronger exchange interaction between the Ce-4f electrons and the conduction electrons
resulting in the anomalously high Neel temperature. The
presence of crystalline-electric-field effects is also inferred
from magnetic susceptibility, electrical resistivity, and
specific-heat data. In the continuation of our studies on
CePdSn, we report here the results of thermoelectric
power measurements on this compound. The experimental data on TEP are analyzed on the basis of the
model which takes into account
Bhattacharjee-Coqblin
both the Kondo and the CEF effects. This model explains the gross features of the experimental TEP curve
except for the low-temperature behavior.
II. EXPERIMENTAL
DETAILS
The compound CePdSn was prepared by melting
stoichiometric amounts of the constituent elements of
purity better than 99.99%%uo in an arc furnace. The singlephase nature of the compound was checked by powder
x-ray-diffraction studies. A rod-shaped sample of length
= 1.5 cm was used for the TEP measurements. The sample was clamped between two small copper plates which
were thermally anchored to the cold station of a closedcycle refrigerator. The temperature difference along the
length of the sample was measured with a copperConstantan therrnocouple.
The thermoelectric voltage
was measured across Au (50 pm) wires attached on two
ends of the sample with conducting silver paint. The
differential method was used for TEP measurements with
Au serving as the reference. An absolute accuracy of
and a relative accuracy of =2 /o could be achieved.
10'
III. RESULTS AND
DISCUSSION
The compound CePdSn crystallizes in the orthorhombic TiNiSi-type structure (space group Pnma) with four
formula units per unit cell. The unit-cell volume of
477
1992
The American Physical Society
BRIEF REPORTS
478
700
t
I
CePdSn
560—
0
0
E
420—
0
0
0
o0
0
0
0
o oo
Do 0
oo ooo
oo
ooo
ooo oo
o ooo
0o
oo
45
oooo~
I
1
I
1
I
l
I
CePdSn
273
o
0-
252—
O
E
Cg
o 231
280—
Cy
-4-
210-
0
189—
140
168
I
50
1
-8
30
20
10
TE MPERATURE(K)
0
I
I
00
CePdSn follows the usual lanthanide contraction indicating the trivalent or near trivalent nature of the Ce ions in
this compound. This is consistent with magnetic susceptibility data on this compound. '
Figure 1 shows the
resistivity of CePdSn as a function of temperature. The
resistivity is 700 pQcm, decreases
room-temperature
linearly with decreasing temperature from 300 K, but
shows a curvature starting at about 80 K. It exhibits a
broad maximum at 20 K and a sharp drop at about 7.5
K, the latter of which is due to the antiferromagnetic ordering of the Ce moments. The curvature in the resistivity has been analyzed earlier' on the basis of crystallineelectric-field effects. The minimum in the resistivity (as
also the anomalously high T~) suggests the presence of
Kondo-type interactions in this compound.
Figure 2 shows the TEP of CePdSn as a function of
temperature in the temperature range 20 —300 K. The
value of TEP at room temperature is =1 pV/K with a
positive sign. This positive sign is consistent with the
sign observed in most of the Ce-based Kondo and heavyferrnion systems. The magnitude of TEP of CePdSn increases with decreasing temperature (from room temperature) and reaches a maximum value of =4 pV/K at
about 100 K. On further decrease of temperature below
"
1
(2)
n(EF)
g2
1
100
I
I
I
150
I
200
I
I
250
I
300
T (K)
300
resistivity of CePdSn as a function of temInset shows the variation at low temperatures.
S= k~
I
I
]50
200
250
TEMPERATURE (K)
FIG. 1. Electrical
perature.
I
50
FIG. 2. Thermoelectric power of CePdSn as a function of
temperature. The solid and dotted lines represent two fits based
on the BC model (see text).
100 K, TEP shows a sharp drop and reaches a value of
—4. 2 pV/K at 21 K. From the trend of the experimental curve, it is likely that TEP may show a minimum at a
temperature below 21 K. However, due to our experimental limitations of the lowest achievable temperature
on the closed-cycle refrigerator, we could not observe this
minimum. The negative sign of the TEP of CePdSn observed below 50 K is an exception among the Ce-based
Kondo and mixed-valence compounds and has been observed earlier in CeAlz, CeA13, and CeCuzSiz. '
The maximum around 100 K in the TEP of CePdSn
can be understood on the basis of the BhattacharjeeCoqblin (BC) model' (special case of the two-level model) in a manner similar to that applied in the case of
CeA13. ' This model is based on the Kondo effect in the
presence of CEF in which TEP has been calculated exactperturbation
theory using the
ly in the third-order
which describes the resonant
effective Hamiltonian
scattering and takes into account both crystalline electric
fields and the combined spin and orbit exchange scattering for the case of two levels split by the crystalline electric field. The TEP power, S, in this model is given by
[Eq. (32), Ref. 13].
g C G)(hl;, 0)+ g' g[U', G, (h„,b,
where the symbols have the same meaning as in Ref. 13.
This equation, in conjunction with Eqs. 36(a) and 36(b)
and 38(a) —38(d) of Ref. 13 provide a closed form expression for the calculation of TEP. According to the BC
model, TEP exhibits a maximum in the temperature
,
)+ V', G~(b, „,h, )]
range between b, /3 to 6/6, where b is the energy separation between the CEF split levels.
In the analysis of TEP of CePdSn, following BC, we
have taken the electron density of states at EF,
n(E~)=2. 2 states/eV (which is the density of states of
BRIEF REPORTS
45
pure lanthanum), and the mixing parameter between the
conduction electrons and the 4f electrons Vzf =0.07
eV. ' The value of ground-state degeneracy a, (obtained
from susceptibility and resistivity analysis) is taken to be
2 and for simplicity the excited-state degeneracy a2 is
taken as 4, (although CEF splitting will lead to three doublets for the Ce + ion). The cutoff energy (D) is defined
in such a way that the exchange coupling parameters are
zero if the energy of the conduction electrons is greater
than D and has been taken to be 850 K, which is the
for CeA13.
value taken by Bhattacharjee and Coqblin'
The three remaining parameters, viz. , the direct scatterthe
ing potential V, the exchange integral
&, and
crystal-field splitting 6 were considered as variables. A
least-squares fit procedure was used to obtain the optimum values of these parameters. Two of the fits ob0. 073 eV, and
tained, one with V= —1.02 eV, J&&= —
5=400 K in the temperature range 50-300 K and the
second with V = —1.85 eV, J» = —
0. 078 eV, and
5=360 K over the temperature range 20 —300 K are
represented as solid and dotted lines respectively in Fig.
2. Good agreement between theory and experiment in
J
&
the high-temperature
range is evident from the figure.
However, this approach fails to explain the lowtemperature negative region of the TEP curve. The
overall CEF splitting in CePdSn has been estimated earlier to be about 300 K. ' Because of the approximations
involved, the value obtained in the present analysis may
However, independent
be considered as satisfactory.
determination of CEF parameters such as by neutron
scattering will be useful for improved understanding of
this system.
IV. CONCLUSIONS
The thermoelectric power measurements on CePdSn
reveal the presence of the Kondo and the crystallineelectric-field effects in this compound consistent with its
high TN and a resistivity minimum. The TEP results can
be understood on the basis of the Bhattacharjee-Coqblin
model, which explains the broad features of the experimental curve. However, the negative sign observed at
low temperatures is not reproduced by this model for the
parameters used and may be due to the onset of the antiferromagnetic ordering of the Ce moments.
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