PHYSICAL REVIEW B
VOLUME 58, NUMBER 18
1 NOVEMBER 1998-II
Thermopower measurements of high-temperature superconductors: Experimental artifacts due
to applied thermal gradient and a technique for avoiding them
M. Putti, M. R. Cimberle, A. Canesi, C. Foglia, and A. S. Siri
INFM-CNR, Diparimento di Fisica, Università di Genova, Via Dodecaneso 33, 16146 Genova, Italia
~Received 5 May 1998!
We discuss thermoelectric measurements of high-temperature superconductors around the superconducting
transition. The Seebeck effect coefficient has been widely used to study the dissipative phenomena of the
vortex lattice and its interaction with quasiparticles, in conjunction with the resistivity to which it is correlated
in the framework of all existing theories. As is well known, Seebeck effect measurements are far from the
accuracy of resistivity measurements because the presence of a thermal gradient across the sample may alter
the shape of the curve. We make a quantitative analysis of the errors involved in ac measurement techniques;
the error percentage grows considerably in the low-dissipation region where the Seebeck effect vanishes. We
propose a method that drastically reduces the experimental artifacts; moreover, we present the Seebeck effect
measurements of a Y-Ba-Cu-O thin film, performed with the standard steady-flux ac technique and with the
one proposed here, and we discuss the results in light of our calculations. @S0163-1829~98!06842-8#
I. INTRODUCTION
Among the several new phenomena that high-temperature
superconductors ~HTSC’s! present compared to lowtemperature superconductors, one of the most intriguing is
nonzero Seebeck effect in the superconducting state. Its
origin, widely studied both theoretically1–4 and
experimentally,5–13 was explained at first in terms of a twofluid counterflow picture.1 This model hypothesizes that, in
the presence of a temperature gradient, there is a current of
unbound quasiparticles locally canceled by a supercurrent
that drives vortices transversal to the temperature gradient,
generating the longitudinal Seebeck voltage S. Other frameworks consider the role of bounded5 and unbounded3 quasiparticles, and normal current drag forces,4 but all models
emphasize a strict correlation between S and the magnetoresistivity r. The proportionality between S and r has been
qualitatively proved,7 but for a deeper analysis higher experimental resolution is needed, while, as is well known, the
accuracy attained in resistivity measurements is not achievable in thermoelectric measurements. This is due to the
smallness of S in the mixed state ~<5–1 mV/K! and to the
fact that the temperature difference DT across the sample has
to be so small in order not to alter the shape of the S(T)
curves. The need of a small DT is more pressing when the
thermoelectric power changes rapidly with temperature, as in
superconducting transitions, and the general requirement
DT!DT C , where DT C is the amplitude of the transition,
must be satisfied.
The first HTSC thermoelectric measurements using a dc
differential technique showed very poor temperature resolution and a poor signal-to-noise ratio. As in other cases, the
required increase in sensitivity was obtained by using an ac
technique with synchronous detection, but this sophisticated
technique produced an undesired effect.
Howson et al., who propose an ac technique, observed a
sharp peak in the temperature dependence of the thermopower in the vicinity of the critical temperature.14 They
0163-1829/98/58~18!/12344~6!/$15.00
PRB 58
suggested that this peak,15,16 never observed by means of dc
techniques because of their lesser thermal resolution, had a
fluctuative origin. Three years later Logvenov et al.17 and
then Aubin et al.18 demonstrated that the peak was a spurious effect generated by the temperature modulation and amplified by the presence of a constant temperature gradient
across the sample and by poor thermal contact between the
sample and the heat sink. In addition, Aubin et al.18 proposed a technique which used two heaters at the sample ends
to avoid the setup of a constant temperature gradient.
On the basis of the equations of Aubin et al.,18 we have
developed a mathematical analysis that allows one to simulate the thermoelectric voltages measured with different experimental techniques. In particular, we will discuss the results of the simulation for two measuring setups: the
traditional steady-flux one and one which maintains the
sample floating. We will show that experimental artifacts
may be easily observed if great care is not taken in the
project of the experimental setup and that these artifacts
manifest themselves not only in the well-recognizable form
of a peak, but also in the more insidious form of a temperature shift and deformation of the superconducting transition.
Moreover, we will show that the floating-sample technique
reduces substantially the constant temperature gradient
across the sample, so that spurious effects in the measurements are reduced drastically. Finally, we will present the
measurements performed on a YBa2Cu3O7 ~YBCO! thin film
by means of the two different techniques and discuss the
results, comparing them with the simulation.
II. ac TECHNIQUE
Heating one end of a sample by a power P(t)5 P 0 @ 1
1sin(vt)#, which oscillates with a frequency v, generates a
temperature distribution along the sample that can be indicated by
T ~ x,t ! 5T I 1 q 0 ~ x ! 1 q 1 ~ x ! sin~ v t ! ,
12 344
~1!
©1998 The American Physical Society
PRB 58
THERMOPOWER MEASUREMENTS OF HIGH- . . .
where x is the position, T I is the time-independent reference
temperature, and q 0 (x) and q 1 (x) are, respectively, the temperature increment due to the presence of the constant and
oscillating heat fluxes. The voltage generated between the
positions x a and x b is given by
V~ t !5
E
T b~ t !
T a~ t !
~2!
S„T ~ x,t ! …dT.
as R i , and the temperature gradients q 80 and q 81 are considered to be independent of the position.
As a result of the finite thermal resistance R e , the temperature T a at the position x a is time dependent and, compared to T s , is enhanced by a quantity proportional to (x b
2x a )R e /R i . Therefore, in this configuration, the instantaneous temperature at a point x can be written as
The total derivative dT is
~3!
F
1 q 18 ~ x2x a ! 1 ~ x b 2x a !
where q 80 [d q 0 /dx and q 81 [d q 1 /dx.
By expanding S„T(x,t)… with a Taylor series, we have
S„T ~ x,t ! …>S ~ T I ! 1
dS
dT
U
F
F
TI
1 d S
1
@ q 0 1 q 1 sin~ v t !# 2 .
2 dT 2
xa
S„T ~ x,t ! …@ q 80 1 q 81 sin~ v ! t # dx.
~5!
V ~ t ! >V 0 1V 1 sin~ v t ! 1V 2 sin~ 2 v t ! 1••• ,
where V 0 is the mean value of the signal and
E
xa
E
xb
xa
F
F
S ~ T I ! q 81 1
S
q 20
2
dS
dT
3
V 25
xb
2
U
q 18 1
TI
dS
dT
U
~ q 0 q 81 1 q 1 q 80 ! 1
TI
3 2
q q 8 1 q 0 q 1 q 08
8 1 1
US
q1
d 2S
q 81 2 2
2
dT
Re
sin~ v t ! ,
Ri
~9!
TI
DG
d 2S
q 1 ~ x ! 5 q 18 ~ x2x a ! 1 ~ x b 2x a !
Re
.
Ri
V 1 5S ~ T s ! DT 1 1
3
S
~6!
U
dT 2
V 2 52
TI
~7!
dx,
q 21
q 0q 1
q 80 1
q 81
2
2
DG
dx
~8!
are, respectively, the amplitude of the first and second harmonics of the measured voltage and are detected with a
lock-in amplifier locked to these frequencies. Now we apply
these relations to two different experimental configurations.
A. Steady-flux configuration
Here we consider a configuration with constant heat flow
along the sample. Following the analysis by Logvenov
et al.17 and Aubin et al.,18 the sample is coupled to the heat
sink at temperature T s via the thermal resistance R e . The
thermal resistance between the positions x a and x b is denoted
G
G
Re
,
Ri
Substituting these relations in Eqs. ~7! and ~8!, we obtain for
V 1 and V 2 the following results:
Substituting Eq. ~3! into Eq. ~4! and separating the different
harmonics components, we obtain
V 15
G
G
q 0 ~ x ! 5 q 08 ~ x2x a ! 1 ~ x b 2x a !
~4!
Unlike Aubin et al.,18 we have extended our analysis to the
second derivative to achieve more quantitative results. Only
the integral in dx leads to a contribution to the total voltage
V(t), whereas the integral containing dt is zero because the
integration must be taken over an integer number of cycles.
So we have
E
Re
Ri
with
@ q 0 1 q 1 sin~ v t !#
2
V~ t !5
F
T ~ x,t ! 5T s 1 q 80 ~ x2x a ! 1 ~ x b 2x a !
dT5 @ q 80 1 q 81 sin~ v t !# dx1 vq 1 ~ x ! cos~ v t ! dt,
xb
12 345
1 dS
2 dT
dS
dT
U
2DT 0 DT 1 a1
Ts
3
3
DT 20 DT 1 1 DT 31
2
8
U
DT 21 a2
Ts
U
3 d 2S
4 dT 2
DS
a 21
d 2S
U
dT 2
D
Ts
1
,
12
S
DT 0 DT 21 a 2 1
Ts
~10!
D
1
,
12
~11!
and DT 1 5 @ q 1 (x b )
where DT 0 5 @ q 0 (x b )2 q 0 (x a ) #
2 q 1 (x a ) # are experimentally measured quantities and a
5( 21 1R e /R i ) is the only free parameter and expresses the
quality of the thermal contact between the sample and heat
sink.
As we can see from Eq. ~10!, V 1 contains other terms
besides the desired term SDT 1 : a first-order term proportional to dS/dT and a second-order term proportional to
d 2 S/dT 2 . The parameter a depends on the thermal contact
between the sample and heat sink; if it is not good, that is, if
a@1/2, then both the terms grow, generating the pronounced
peak observed by Howson et al.; anyway, also for a very
good thermal contact, a51/2 and the spurious terms are reduced, but not canceled. Instead, we note that the first-order
term is proportional to the constant temperature difference
and is zero if DT 0 is null; in this way, the greatest part of the
spurious term is canceled.
Moreover, Eq. ~11! tells us that, for DT 0 >DT 1 , the
second-harmonic term V 2 is proportional to the difference
V 1 2S(T s )DT 1 and therefore V 2 may be used as an indicator
of the spurious size.
PUTTI, CIMBERLE, CANESI, FOGLIA, AND SIRI
12 346
PRB 58
Besides, to obtain a frequency region where the oscillating temperature gradient is noteworthy, the thermal resistance R e to the heat sink should be carefully determined. To
this end, availing ourselves of the analogy between electrical
and thermal circuits and using the approximation of concentrate constants, we represent our setup as in Fig. 1~b!, where
R i and R e are the thermal resistance, respectively, of the
sample and of the contact with the heat sink. The quantities
C/2 represent the thermal capacitance of the two sample
ends.
q a ( v ) and q b ( v ) are the oscillating temperatures at the
two sample ends between which the thermoelectric voltage is
measured. q b ( v ) is determined by the series of the thermal
resistance R i and capacitance C/2, so that the temperature
difference DT 1 ( v )5 q a ( v )2 q b ( v ) at the sample ends can
be written as
DT 1 ~ v ! 5 q a ~ v ! 2 q b ~ v ! 5 q a ~ v !
FIG. 1. Floating-sample configuration: ~a! schematic diagram
of the sample mounting and ~b! equivalent electrical circuit.
B. Floating-sample configuration
As in the previous case, in any generic experimental configuration, to make the first-order term ineffective we must
annul the constant temperature gradient. In fact, from Eq. ~7!
it follows that, for q 0 50, V 1 becomes
V 1 5S ~ T I ! DT 1 1
U
U
1 d 2S
8 dT 2
1 d 2S
5S ~ T I ! DT 1 1
8 dT 2
@ q 1~ x b ! 32 q 1~ x a ! 3 #
D
ivti
,
11i v t i
with t i 5R i C/2.
This implies that large values of DT 1 ( v ) are possible
when t i v @1. On the other hand, for v @1/t i , DT 1 ( v ) is
proportional to T a ( v ), which is due to the low-pass filter
formed by R e and C/2 with a cutoff frequency t e 5R e C/2.
Thus DT 1 ( v ) has a maximum if 1/t i , v ,1/t e , which
means in particular 1/t i ,1/t e or rather R i .R e . However,
since in this frequency interval q a ( v ) is proportional to R e ,
R e should be not too small.
III. EXPERIMENTAL SETUP
TI
TI
3DT 1 @ q 21 ~ x b ! 1 q 21 ~ x a ! 1 q 1 ~ x a ! q 1 ~ x b !# ,
S
~12!
where the first derivative is not present. So the spurious term
affects the signal only to second order.
Furthermore, in order to minimize the spurious term and
at the same time to maintain a good effective temperature
gradient DT 1 5 @ q 1 (x b )2 q 1 (x a ) # , the temperature oscillation at the cold end should tend to zero, which means
q 1 (x a )50. This can be achieved using a timely frequency.
The attempt at a zero DT 0 was made before by Aubin
et al. using a technique with two heaters.18,6,11 In this paper
we present a technique that attains the same goal with only
one heater, so that the problems in the thermal control of the
experimental setup are reduced drastically.
Our experimental configuration, previously used for thermal diffusivity measurements,19 is schematized in Fig.
1~a!: the sample is mounted with one end fixed to a heater
and the other floating; the heated end is thermally anchored
to the heat sink via a thermal resistance R e . In this way the
constant heat flux, shortened to the heat sink by R e , does not
cross the sample and the constant temperature gradient is
sensibly reduced. Actually, a small constant flux is expected,
due to radiation and thermal conduction through the thermocouple and electrical wires: however, all these factors can
be kept under control experimentally.
From the above discussion it can be easily understood that
each kind of temperature distribution along the sample may
generate spurious effects. For this reason the experimental
apparatus has been studied in order that high thermal stability can be obtained.
The main features of the experimental setup are the following. A large hollow copper sphere ~7.4 cm diameter!,
which acts as heat reservoir, contains an Ag sample holder.
The sample is fixed to it by a silver vice coated with an
indium sheath to assure a good thermal contact. In the case
of the floating-sample configuration, the vice fixes the calibrated thermal resistance R e . The alternating temperature
gradient is applied to the sample with a heater consisting of
a precision strain gauge. One thermocouple Au ~0.07% Fe!
Chromel measures the temperature gradient across the
sample; a second thermocouple between the sample and heat
sink checks the mean temperature of the sample with respect
to the bath. Electrical contact to the 99.99% Cu wires was
made with Ag varnish painted to Ag pads, evaporated on
opposite ends of the sample.
The data acquisition system is fully automated. A personal computer is interfaced in an analogical mode with the
instrumentation. It generates power at the chosen frequencies, producing the temperature gradient along the sample,
and synchronously detects the thermoelectric voltages coming from the sample and from the thermocouples; then, it
makes a Fourier transform of these signals and saves the
module and phase of the required harmonic components. We
point out that in this way we have access to much more
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THERMOPOWER MEASUREMENTS OF HIGH- . . .
12 347
FIG. 2. Seebeck effect ~circles!, measured, and the resistivity
~solid line! of a YBCO thin film as a function of temperature. The
distribution of the time-averaged temperature along the sample in
the case of steady flux is schematized in the inset; T s is the temperature of the heat sink, x 0 is the position at the end of the sample
in contact with the heat sink, and x L is the opposite end; the sharp
rise of the temperature at x 0 is due to the thermal resistance between sample and reservoir. The first thermocouple is placed between x a and x b and the second one between x c 5(x b 1x a )/2 and
the heat sink.
information than using a lock-in amplifier.
Moreover, the computer provides, asynchronously, thermoregulation of the heat reservoir by means of a proportional, integrative, and derivative ~PID! system, and verifies
the sample thermal stability. To assure the greatest thermal
stability during the measurements, we avoid collecting thermopower data in the temperature slope. Therefore, measurements are performed at a fixed temperature and the temperature stability of the sample is checked with great care. The
collection of each datum, obtained from the average of two
to four measurements performed at the same temperature,
takes 100–500 s. During this time, the temperature of the
sample is stabilized within 1 mK.
A. Measurements with the steady-flux method
We have measured the Seebeck effect of YBCO thin film
using a configuration with constant heat flow. Details of the
sample preparation are given elsewhere.20
The experimental results from 80 to 96 K are reported in
Fig. 2 ~circles!, where, for comparison, we plot also the resistivity ~solid line!. We can see that the thermoelectric transition is broader than the resistive one and that a peak is
superimposed. This is what we expect from a bad thermal
contact between the sample and heat sink.
In order to verify the validity of our analysis, we have
simulated the first- and second-harmonic signals mathematically using Eqs. ~10! and ~11!. To do this we use as the
thermoelectric curve S(T) the timely renormalized r (T)
curve that holds the fundamental characteristics of S(T).
From this curve we calculate the first and second derivatives
dS/dT and d 2 S/dT 2 , and we obtain V 1 (T) and V 2 (T) by
FIG. 3. ~a! measured Seebeck effect by the steady-flux method
~circles! and the simulated V 1 /DT 1 by Eq. ~10! ~solid line!, and ~b!
the measured ~circles! and the simulated V 2 by Eq. ~11! ~solid line!.
The parameters involved in the calculation are the experimental
values DT 0 50.45 K, DT 1 50.19 K, and the free one a52.46.
introducing the experimentally measured parameters DT 0
50.451 K and DT 1 50.19 K; the only free parameter is a
52.46. The result is shown in Fig. 3 by the solid line.
In Fig. 3~a! the Seebeck effect measured ~circles! and the
simulated V 1 /DT 1 ~solid line! are plotted. We can see that
the simulated curve reproduces the features of the measured
one with great accuracy. In Fig. 3~b! the measured ~circles!
and the simulated behaviors ~solid line! of the secondharmonic component V 2 are compared for the same values of
parameters. Also, in this case the two curves are very similar.
The parameter a can be evaluated independently. In the
inset of Fig. 2 we can see that the time-averaged temperature
measured at x c 5(x a 1x b )/2 is given by
q 0 ~ x c ! 5T s 1 @ q 0 ~ x b ! 2 q 0 ~ x a !#
S
D
Re 1
1 5T s 1DT 0 a,
Ri 2
from which a5 @ q (x c )2T s # /DT 0 : with the second thermocouple, we measure q (x c )2T s and obtain a51.1/0.45
'2.4, which is consistent with the value previously obtained.
Many series of measurements of the Seebeck effect have
been performed with different values of the parameters DT 0
and DT 1 : in all these cases we have observed the peak and
the simulation has been able to reproduce the experimental
results using parameters a ranging from 2.1 to 2.46.
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PUTTI, CIMBERLE, CANESI, FOGLIA, AND SIRI
PRB 58
As previously pointed out, the peak is evident in the case
of bad thermal contact between sample and heat sink; by
improving the thermal contact, we obtained thermoelectric
transitions where the peak is absent. However, we note that,
even though the thermal resistance R e is zero, the parameter
a amounts to 0.5; therefore, the spurious term is only reduced proportionally to a, and tends to broaden and alter the
transition in any case.
This fact is emphasized experimentally by the second harmonic V 2 . In fact, from Eqs. ~10! and ~11! we can see that
4V 2 /V 1 roughly represents the magnitude of the spurious
signal compared to V 1 . In careful thermoelectric voltage
measurements ~good thermal contact and small thermal gradients: DT 1 'DT 0 '0.05DT c ), we find 4V 2/V 1 '0.2, maximum in the low-temperature part of the transition.
B. Measurements with the floating-sample method
The same YBCO thin film was measured in the floatingsample configuration.
A thick Cu wire ~diameter 0.75 mm! of opportune length
was fixed between the heated end and the sample holder. The
Cu wire was calibrated in order to have a thermal resistance
R e that met the condition previously mentioned (R e <R i ).
From the measurements with the heat flow, we have determined that the sample thermal resistance R i is of the order
of 167 K/W, which is coherent with the value 156 K/W
obtained from knowledge of the substrate (SrTiO3) thermal
conductivity and its geometrical dimensions.
After mounting the sample in the floating configuration,
the external thermal conductivity turn out to be R e
'143 K/W, which is slightly smaller than R i .
In order to measure the floating end temperature q 1 (x b ),
we collocated the second thermocouple at the position x b
~see the inset in Fig. 4!. In this way, from measurements
performed at a different frequency, it was possible to determine that the quantity DT 1 / q 1 (x b ) has a maximum
@ DT 1 / q 1 (x b )'1 # for v '0.63 cycle/s ~period of 10
s!: thus, at this frequency, we have a maximal oscillating
gradient compatibly with a minimal spurious signal @see Eq.
~12!#.
In Fig. 4 is reported the Seebeck coefficient measured
with the sample floating ~squares!, together with the resistivity of the sample ~solid line!. The oscillating temperature
gradient was DT 1 50.073 K, and the constant temperature
gradient across the sample was DT 0 50.06 K. This last value
~much lower than those coming into play in the steady-flow
method! is due to the thermal conductance of the thermocouple wires to the bath and can be further reduced. As one
can see, the peak in the Seebeck effect is absent; furthermore, the temperature and amplitude of the transition being
the same, the two curves nearly overlap, which is even more
important. Anyway, the thermoelectric transition is different
from the resistive one in the high-temperature region. In fact,
below 88 K, S(T) decreases faster than r (T) and remains
below the resistive curve down to 84 K.
In order to exclude the measurement of the Seebeck coefficient being affected by a spurious signal, we have estimated this last from Eq. ~7! using the experimental values
DT 1 50.07 K, DT 0 50.06 K, q (x b )50.07 K, and q (x a )
50.14 K. It turns out to be maximum between 80 and 85 K
FIG. 4. Seebeck effect ~squares!, measured by the floatingsample method, and the resistivity ~solid line! of a YBCO thin film
as a function of temperature. The distribution of the time-averaged
temperature along the sample in the floating-sample case is schematized in the inset. The ideal case is considered, with negligible
constant thermal gradient along the sample. The symbols are the
same as in Fig. 2; the first thermocouple is placed between x a and
x b and the second one between x b and the heat sink.
where, anyway, it is less than 7% of the measured voltage.
Also, in this case it is mainly due to the constant thermal
gradient; if DT 0 were zero, the spurious term should be only
the 0.5% of V 1 . Thus we can exclude the possibility that the
behavior of S(T) observed below 88 K may be due to an
experimental artifact. As a further check, we have performed
a measurement using a smaller oscillating power (DT 1
50.028 K and DT 0 50.02 K), and we have obtained the
same curve of Fig. 4.
IV. CONCLUSION
In this paper we have discussed experimental problems
related to thermopower measurements of the superconductors in the region around the superconducting transition. The
need of a high signal-to-noise ratio is opposed to the requirement of high thermal resolution, and therefore ac techniques
have been used more frequently. We have focused our attention on this kind of technique and on the experimental artifacts they can produce. On the other hand, not even dc techniques are free from problems. In fact, we can assume in a
general way that, around the superconducting transition, the
thermoelectric voltage measurement ~ac or dc! is affected by
the percentage error.
S D S D
DV
DT
B DT
'A
1
V
DT C
2 DT C
2
,
where DT is the effective temperature difference between the
points where the Seebeck effect is measured, DT C is the
amplitude of the transition, and A and B are constants. In the
ac techniques with constant heat flow, A and B depend on the
thermal contact between the heat sink and sample, and can
become very large, while in dc techniques they are of the
PRB 58
THERMOPOWER MEASUREMENTS OF HIGH- . . .
order of unity. On the other hand, the dc techniques must use
thermal gradients that are from 2 to 5 times larger than those
used in ac techniques to produce an equivalent signal-tonoise ratio.
The ac technique with a floating sample combine the possibility of applying a very low thermal gradient to the very
favorable conditions A50 and B'1 @see Eq. ~12!#; thus, the
error is drastically reduced.
Finally, we point out that precise measurements of the
Seebeck coefficient are necessary if transport properties are
used to investigate the various dissipative mechanisms in the
mixed state and, in particular, the interplay between vortices
and quasiparticles.
Up to now the relation S(T)5(S n / r n ) r (T) has been
widely used: here S n and r n are the Seebeck coefficient
and resistivity in the normal state. Such a relationship has
been attributed to several different mechanisms1,2,4,5 ~quasiparticle motion, vortex flow, weak link dissipation! and has
1
R. P. Huebener, A. V. Ustinov, and V. K. Kapulenko, Phys. Rev.
B 42, 4831 ~1990!.
2
K. H. Fischer, Physica C 200, 23 ~1992!.
3
E. Z. Meilikhov and R. M. Farzetdinova, Physica C 221, 27
~1994!.
4
P. Ao, J. Low Temp. Phys. 107, 347 ~1997!.
5
A. V. Samoilov, A. A. Jurgens, and N. V. Zavaritsky, Phys. Rev.
B 46, 6643 ~1992!.
6
M. Oussena, R. Gagnon, Y. Wang, and M. Aubin, Phys. Rev. B
46, 528 ~1992!.
7
H.-C. Ri, R. Gross, F. Kober, A. Beck, L. Alff, R. Gross, and R.
P. Huebener, Phys. Rev. B 47, 12 312 ~1993!.
8
H.-C. Ri, R. Gross, F. Gollnik, A. Beck, R. P. Huebener, P. Wagner, and H. Adrian, Phys. Rev. B 50, 3312 ~1994!.
9
V. Calzona, M. R. Cimberle, C. Ferdeghini, D. Marrè, M. Putti,
A. S. Siri, G. Grasso, and R. Flukiger, Physica C 235–240, 3113
~1995!.
10
V. Calzona, M. R. Cimberle, C. Ferdeghini, D. Marrè, and M.
Putti, Physica C 246, 169 ~1995!.
11
H. Ghamlouch, M. Aubin, R. Gagnon, and Ltaillefer, Phys. Rev.
B 54, 9070 ~1996!.
12 349
been verified qualitatively. Actually, when a deeper analysis
has been tried, contradictory S/ r behaviors have been measured. In Refs. 9 and 13 the ratio S/ r , measured at various
magnetic fields, has been observed to decrease towards zero
as the temperature decreases. In Ref. 12, on the contrary, the
authors observe that the ratio S/ r , constant in the highdissipation region, diverges in the temperature and field regions where the S and r signals tend to zero. These two
results, in the region of low dissipation, are opposite: in the
first case S goes to zero faster than r; in the second case S is
finite when r is zero.
We recall that, in the very region where the Seebeck effect vanishes, the spurious term is maximum and tends to
broaden the transition. Therefore, in light of the above discussed problems involved in the measurement of S, we suggest that, in these delicate measurements, an accurate check
of the experimental conditions should be made before giving
any physical interpretation.
12
J. A. Clayhold, Y. Y. Xue, C. W. Chu, J. N. Eckstein, and I.
Bozovic, Phys. Rev. B 53, 8681 ~1996!.
13
Y. Sato, I. Terasaki, and S. Tajima, Phys. Rev. B 54, 6676 ~1996!.
14
M. A. Howson, M. B. Salomon, T. A. Friedmann, S. E. Inderhees, J. P. Rice, D. Ginsberg, and M. K. Ghiron, J. Phys.: Condens. Matter 1, 465 ~1989!.
15
M. A. Howson, M. B. Salomon, T. A. Friedmann, J. P. Rice, and
D. Ginsberg, Phys. Rev. B 41, 300 ~1990!.
16
A. J. Lowe, S. Regan, and M. A. Howson, Phys. Rev. B 44, 9757
~1991!.
17
G. Yu. Logvenov, V. V. Ryazanov, R. Gross, and F. Kober, Phys.
Rev. B 47, 15 322 ~1993!.
18
M. Aubin, H. Ghamlouch, and P. Fournier, Rev. Sci. Instrum. 64,
2938 ~1993!.
19
V. Calzona, M. R. Cimberle, C. Ferdeghini, M. Putti, and A. Siri,
Rev. Sci. Instrum. 64, 766 ~1993!.
20
M. R. Cimberle, A. Diaspro, C. Ferdeghini, E. Giannini, G. Grassano, D. Marré, I. Pallecchi, M. Putti, R. Rolandi, and A. S. Siri,
in Proceedings of EUCAS 97, The Netherlands, edited by H.
Rogalla and D. H. A. Blank ~Institute of Physics, Bristol, 1997!,
Vol. 1, p. 213.