Measurements of Nernst effect, resistivity and Hall angle on epitaxial films
of Y$_{1-x}$Pr$_x$Ba$_2$Cu$_3$O$_{7-\delta}$(Pr-YBCO, 0$\leq x\leq$0.4) are
reported over a broad range of temperature and magnetic field. While the Hall
and resistivity data suggest a broad pseudogap regime in accordance with
earlier results, these first measurements of the Nernst effect on Pr-YBCO show
a large signal above the superconducting transition temperature(T$_c$). This
effect is attributed to vortex-like excitations in the phase incoherent
condensate existing above T$_c$. A correlation between disorder and the width
of the phase fluctuation regime has been established for the YBCO family of
cuprates, which suggests a T$_c\approx$110K for disorder-free
YBa$_2$Cu$_3$O$_{7-\delta}$.Comment: 5 pages, 6 figure

M. B. Maple

Peng Xiong

Pengcheng Li

R. C. Budhani

R. L. Greene

Soumen Mandal

English

arXiv

Measurements of Nernst effect, resistivity and Hall angle on epitaxial films of Y1-xPrxBa2Cu3O7-&#948; (Pr-YBCO, 0&#948;x&#948;0.4) are reported over a broad range of temperature and magnetic-field strength. While the hall and resistivity data suggest a broad pseudogap regime in accordance with earlier results, these first measurements of the nernst effect on Pr-YBCO show a large signal above the superconducting transition temperature (Tc). This effect is attributed to vortexlike excitations in the phase incoherent condensate existing above Tc. A correlation between disorder and the width of the phase fluctuation regime has been established for the &#947;BCO family of cuprates, which suggests a Tc&#8776;110 k for disorder-free YBa2Cu3O7-&#948;</SUB

Li, Pengcheng

Mandal, Soumen

Budhani, R. C.

Greene, R. L.

Indian Academy of Sciences

ar
X
iv
:c
on
d-
m
at
/0
70
37
61
v2
 [
co
nd
-m
at
.s
up
r-
co
n]
 3
 J
ul
 2
00
7
Correlation between incoherent phase fluctuations and disorder in Y1−xPrxBa2Cu3O7−δ
epitaxial films from Nernst effect measurements
Pengcheng Li1,∗ Soumen Mandal2, R. C. Budhani2, and R. L. Greene1
1Center for Superconductivity Research and Department of Physics,
University of Maryland, College Park, Maryland 20742-4111
2Condensed Matter-Low Dimensional Systems Laboratory, Department of Physics,
Indian Institute of Technology Kanpur, Kanpur-208016, India
(Dated: February 6, 2008)
Measurements of Nernst effect, resistivity and Hall angle on epitaxial films of
Y1−xPrxBa2Cu3O7−δ(Pr-YBCO, 0≤ x ≤0.4) are reported over a broad range of tempera-
ture and magnetic field. While the Hall and resistivity data suggest a broad pseudogap regime in
accordance with earlier results, these first measurements of the Nernst effect on Pr-YBCO show
a large signal above the superconducting transition temperature(Tc). This effect is attributed to
vortex-like excitations in the phase incoherent condensate existing above Tc. A correlation between
disorder and the width of the phase fluctuation regime has been established for the YBCO family
of cuprates, which suggests a Tc ≈110K for disorder-free YBa2Cu3O7−δ.
PACS numbers: 74.25.Fy, 74.40.+k, 72.15.Jf, 74,62.Dh
The anomalously large Nernst voltage well above the
zero-field Tc in hole-doped cuprate superconductors is
now a well established experimental observation with a
dominant view that it is due to vortex-like excitations
in the phase uncorrelated superfluid above Tc.
1,2 Such
excitations nucleate in the presence of an external field
due to a non-zero pairing amplitude of incoherent phase
at T>Tc and drift down the thermal gradient generating
a transverse voltage. The appearance of the Nernst sig-
nal on approaching Tc from above, therefore, marks the
onset of a phase uncorrelated pairing amplitude. The
observation of an enhanced diamagnetism near the onset
temperature Tν of the anomalous Nernst signal in some
hole-doped cuprates strongly supports the vortex-like ex-
citations scenario.2,3 The fact that the regime of this large
Nernst effect overlaps with the temperature range where
a pseudogap is seen in the electronic excitation spectrum,
somehow also suggests that the anomalous Nernst effect
may be related to the pseudogap phenomenon, although
counterviews also exist on the prescription of vortex-like
excitations and correlation between Nernst effect and
pseudogap phenomenon.4,5 Rullier-Albenque et al.6 have
established a correlation between the width of the phase
fluctuation regime over which a large Nernst voltage is
seen and disorder in the CuO2 planes induced by electron
irradiation. The disordered samples show a wider range
of phase fluctuations. However, high Tc cuprates can
also be subjected to out-of-plane disorder by changing
the ionic radius of the rare earth and alkaline earth sites
while keeping the hole concentration fixed. The disorder
works as a weak scatterer and reduces Tc substantially.
7
The cuprate Y1−xPrxBa2Cu3O7−δ(Pr-YBCO)
presents a very interesting system to study the role of
out-of-plane disorder on the regime of incoherent phase
fluctuations in YBa2Cu3O7−δ cuprates because the
ionic radius of Pr3+ is larger by a factor of about 1.134
compared to the ionic radius of Y3+. In this paper,
we present the first measurements of the normal state
Nernst Effect in Y1−xPrxBa2Cu3O7−δ over a broad
range of composition. These data have been augmented
by measurements of Hall angle and in-plane resistivity
over a wide range of field and temperature. We note
that while the zero-field superconducting transition
temperature Tc drops with increasing Pr in a quasi
non-linear manner as reported earlier,8 the fluctuation
regime △Tfl=(Tν-Tc) widens. Most remarkably, an
interesting correlation emerges between Tν and Tc in the
YBCO family of cuprates with in-plane and out-of-plane
disorder.
The c-axis oriented epitaxial
Y1−xPrxBa2Cu3O7−δ(x=0, 0.1, 0.2, 0.3, 0.4) films
of thickness about 2500 Å were fabricated on (100)
SrTiO3 substrates by pulsed laser deposition using a
KrF excimer laser(λ=248 nm)with a typical repetition
rate and energy density of 5 Hz and 2 J/cm2 respec-
tively, which yields a growth rate of 1.6 Å/second. The
deposition temperature and oxygen partial pressure
during film deposition were set 800 0C and about 400
mTorr respectively.
The in-plane resistivity and Hall effect measurements
were done on the films patterned to a standard Hall bar
in a Quantum Design PPMS with a 14 T magnet. The
Nernst measurements were performed using a one-heater-
two-thermometer technique. The sample was attached on
one end to a copper block with a mechanical clamp and
the other end was left free. A small chip resistor heater
is attached on the free end, and a temperature gradient
is created by applying a constant current to the heater.
Two tiny Lakeshore Cernox thermometers are attached
on the two ends of the sample to monitor the temperature
gradient continuously. The Nernst voltage is measured
with a Keithley 2001 multimeter with a 1801 preamp
while the field is slowly ramped at a rate of 0.3 T/min
between -14 T and +14 T(H ⊥ ab). The system tem-
perature was well controlled to give stability of the tem-
perature of ±1 mK, which enables us to perform a high
2
resolution Nernst voltage measurement(typically ∼10 nV
in our setup). The temperature gradient is around 0.5-
2 K/cm depending on the temperature of measurement,
and the sample temperature is taken as the average of
hot and cold end temperatures. The Nernst signal is ob-
tained by subtracting negative field data from positive
field data to eliminate any possible thermopower contri-
bution. The Nernst signal was defined as
ey =
Ey
−∇T
(1)
where Ey is the transverse electrical field across the
sample and −∇T is the temperature gradient along its
length.
Fig. 1 shows the temperature dependence of in-plane
resistivity ρab for Y1−xPrxBa2Cu3O7−δ films with Pr
concentration from 0 to 0.4. The zero field supercon-
ducting transition temperature Tc decreases from 90 K
for the x=0 film to about 40 K for the underdoped
x=0.4 film in agreement with published work on these
cuprates.9,10,11 The in-plane resistivity increases with Pr
content, which suggests a decrease of carrier concen-
tration or carrier mobility due to out-of-plane disorder
caused by Pr. While the resistivity ρab(T ) remains metal-
lic in the normal state, a small upturn in ρab(T ) on
cooling is seen in the x=0.4 film just above Tc, which
may be due to charge localizations found in many other
cuprates. The resistivity has a linear temperature de-
pendence for the fully oxygenated Pr-free film, while it
deviates from linearity on increasing the Pr doping. The
temperature below which this deviation from linearity
sets in is about 190 K in the x=0.1 film and gradually
exceeds 300 K for the film with the highest Pr concen-
tration. This nonlinear ρab below 300 K for the higher
Pr-rich samples indicates a pseudogap regime above Tc.
This deviation of ρab(T) from linearity on cooling is not
monotonic. To illustrate this point we show in the inset
of Fig. 1 the temperature derivative dρab(T )/dT of all
the films. The dρab(T )/dT vs T plot of the films with
x≥0.2 goes through a maximum and the peak tempera-
ture shifts towards higher values with the increasing Pr
content. This observation is consistent with the resis-
tivity data of Y1−xPrxBa2Cu3O7−δ single crystals.
8 We
note that the peak temperature Tcr is much lower than
the pseudogap temperature, as found from the deviation
of the linear resistivity. Sandu et al.8 have identified
this critical temperature Tcr in the ρab(T) data of their
Y1−xPrxBa2Cu3O7−δ single crystals as a signature of the
onset of dissipation due to thermally excited vortex loops.
We will shortly compare Tcr with the onset temperature
Tν of the anomalous Nernst voltage, which is a direct
indicator of vortex loop excitations. At this juncture, it
is also worthwhile to point out that the overall behavior
of the ρ(T ) of these films is similar to that observed by
Convington and Greene12 in their Y1−xPrxBa2Cu3O7−δ
films. The important consequence of Pr doping is a sig-
nificant enhancement in resistivity without affecting the
linear temperature dependence of ρ at T≥120 K. This
0 50 100 150 200 250 300
0
200
400
600
800
1000
50 100 150 200 250
1
2
3
4
 x=0
 0.4
0.3
 0.2
 0.1
 
 
(
 c
m
)
T(K)
Tcr
 
d
/d
T(
 c
m
/K
) 
 
T(K)
0.0
0.1
0.2
0.4
0.3
FIG. 1: In-plan resistivity as a function of temperature for
the Y1−xPrxBa2Cu3O7−δ films(x from 0 to 0.4). Inset shows
the temperature derivative of the resistivity from the main
panel for all the films. The arrows indicate the temperature
where the peak of the derivative plot appears.
points towards enhanced scattering within CuO2 planes
without affecting the carrier concentration as seen in Zn
doped YBCO. At larger Pr concentrations(x≥0.5), the
ρ(T ) curves develop an S shape similar to that seen in
oxygen deficient YBCO in the vicinity of superconduct-
ing transition. This is a signature of reduction in carrier
concentration.
The temperature dependence of Hall resistivity for all
the films was measured in a 14 tesla field for both field
orientations. Consistent with prior work(see Ref. 7 and
8), the normal state Hall coefficient RH first increases as
the temperature is lowered from 300 K and then drops
near the superconducting transition. At a given temper-
ature, the Hall number decreases with Pr doping. It is
about 5 times smaller at T=300 K in the x=0.4 film than
for the Pr-free sample suggesting a strong localization of
mobile holes by the local field of the Pr ions. The tem-
perature dependence of the Hall angle cotθ(T ) for all the
films was calculated. We find that the cotθ(T ) data can
be fitted to the form cotθ = a + bT n with n close to 2. A
similar temperature dependence of cotθ(T ) in Pr-YBCO
samples has been observed in previous reports.9,10,11 A
deviation from the power law dependence of cotθ(T ) on
temperature is seen near Tc in all films. It has been sug-
gested that this deviation could be related to the opening
of the pseudogap.13 To find the temperature TH where
this deviation starts, we plot (cotθ−a)/bT n as a function
of temperature for the films(Fig. 2) with x=0.2 and 0.3.
As seen in the figure, (cotθ − a)/bT n is a constant of or-
der unity when the temperature is much higher than Tc.
It starts to increase sharply below a critical temperature
TH ∼105 K for these two Pr content films. We actually
find that TH remains nearly independent of the Pr con-
centration. Since TH which is close to Tcr found from
the resistivity, is much lower than the pseudogap temper-
ature, it has also been argued14 that the TH scale may
3
0 50 100 150 200 250 300
0.5
1.0
1.5
2.0
2.5
0.5
1.0
1.5
2.0
2.5
 
 
(c
ot
-a
)/b
Tn
T(K)
x=0.3
 
 T(K)
(c
ot
-a
)/b
Tn
x=0.2
TH
FIG. 2: (cotθ−a)/bT n(see text for details) versus temperature
for x=0.2 and 0.3 films. The arrows mark the temperature TH
at which the deviation from the high temperature behavior
starts.
0 2 4 6 8 10 12 14
0
1
2
3
4
5
75K
50K
40K
 
 
e y
(
V
/K
)
0H(T)
x=0.2
Tc~65K
35K
45K
55K
60K
65K
70K
85-190K
FIG. 3: The field dependence of the Nernst signal for the
x=0.2 film at different temperatures.
be related to the onset of superconducting fluctuations
or vortex-like excitations in the normal state.
The Nernst effect was measured in all Pr-substituted
films. Fig. 3 shows the field dependence of the Nernst
signal(ey) at different temperatures for x=0.2 film. A
qualitatively similar field dependence of ey was observed
for the other concentrations of Pr. These data are not
40 60 80 100 120 140 160
-0.5
0.0
0.5
1.0
1.5
2.0
0.3
 
 
e y
(
V
/K
)
T(K)
 x=0
 x=0.1
 x=0.2
 x=0.3
 x=0.4
0.4 0.0
0.2
0.1
FIG. 4: The temperature dependence of the Nernst signal
taken at 14 T for the films. The arrows show the temperatures
at which the Nernst signal deviates from the high temperature
background.
shown in Fig. 3 for the sake of clarity. The rapid rise
of the Nernst signal for field less than the upper critical
field (Hc2) observed for T<Tc is due to the motion of
vortices driven by the temperature gradient. At higher
temperatures(T>Tc), the Nernst signal remains sizable
and has a non-linear field dependence. On increasing the
temperature well beyond Tc, the signal ey becomes ex-
tremely small. Here it tends to a negative linear field
dependence, which typically is attributed to quasiparti-
cles in the normal state.2
The temperature dependence of the Nernst signal
taken at 14 T for all the films is shown in Fig. 4. As
seen in the figure, this signal is extremely small for all
the films in the high temperature range well above Tc.
On decreasing the temperature, the Nernst signal starts
to increase rapidly at a certain temperature Tν , which
depends on the Pr concentration. The temperature (Tν)
below which the Nernst signal rises rapidly above the
high temperature normal state data is marked by arrows
in Fig. 4.
The large Nernst signal observed in the temperature
window of Tc and Tν has been interpreted as evidence
for vortex-like excitations or strong superconducting fluc-
tuation in most of the hole-doped cuprates.2 In Fig. 5,
we show the characteristic temperatures Tcr, TH and Tν
deduced from the measurements of resistivity, Hall angle
and Nernst effect respectively along with the zero-field
transition temperature Tc as a function of Pr concentra-
tion. We note that the onset temperature of the anoma-
lous Nernst signal Tν is lower than TH and Tcr, and the
difference between them increases in Pr-rich samples. It
has been found3 that in hole-doped cuprates, the onset
temperature of the anomalous Nernst signal compares
well with the temperature at which a fluctuating dia-
magnetism appears, it is clear that Tν is a true indicator
of the emergence of vortex like excitations in a phase in-
4
0.0 0.1 0.2 0.3 0.4
40
50
60
70
80
90
100
110
120
130
 
 
 Tc
 T
 TH
 Tcr
T(
K
)
Pr content x
FIG. 5: (color online). Doping dependence of the tempera-
ture scales deduced from the temperature derivative of the
in-plane resistivity(Tcr, open circle), Hall angle(TH , solid tri-
angle) and Nernst effect measurements(Tν , filled circle), solid
square is the superconducting transition Tc.
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140
0
20
40
60
80
100
120
140
160
 
 
T
(K
)
T
C
(K)
dT /dT
C
=0.36
110K
FIG. 6: (color online). Onset temperature Tν of anoma-
lous Nernst signal versus Tc for oxygen-doped and disordered
YBCO. Solid square: Pr-YBCO, open triangle: oxygen-doped
YBCO(ref. 16), open square: YBa2Cu3O6.6 with electron ir-
radiation(ref. 6), open circle: YBa2Cu3O7 with electron irra-
diation(ref. 6) and solid triangle: Zn-YBCO(ref. 15).
coherent condensate. We note that while the Tc drops
with increasing Pr, the width of the fluctuation regime
△Tfl(=Tν-Tc) actually broadens.
The observed increase in △Tfl can be associated pri-
marily with the out-of-plane disorder caused by the sub-
stitution of Pr at the Y sites of YBa2Cu3O7. This site
disorder may also have a spin component as the mo-
ment on the Pr sites can lead to pair breaking effects.
Rullier-Albenque et al.6 have studied the effects of in-
plane disorder on the Nernst effect in YBa2Cu3O7 and
YBa2Cu3O6.6. They note that the fluctuation regime
above Tc expands considerably with the disorder. In
Fig. 6 we plot the Tν vs Tc data of our films along with
the results of Rullier-Albenque and coworkers. Quite re-
markably, these data fall on a single curve with a slope
dTν/dTc ∼0.36. The figure also shows the characteris-
tic temperature Tν for Zn-doped YBCO.
15 It is known
that zinc causes a strong in-plane disorder with a drastic
suppression of Tc. The normalized temperature Tν of
the zinc doped YBCO also follows the general trend seen
in Fig. 6. A simple extrapolation of the curve shown in
Fig. 6 suggests that a disorder-free YBa2Cu3O7 should
have a Tc of 110K. In Fig. 6 we have also plotted the Tν
of the pristine oxygen-deficient YBa2Cu3O7−δ crystals.
16
Although these samples do not have any deliberately cre-
ated in-plane or out-of-plane disorder there is some ran-
domness in the occupancy of the plane site oxygen due to
a non-zero δ. This positional disorder of oxygen should
create local fluctuations in the potential seen by holes.
Moreover, the hole concentration of these samples de-
creased with δ. The Tν vs Tc curve for these samples
shows a large deviation from the data for the disordered
samples when the oxygen concentration falls below 6.6
per unit cell of YBCO. From these data it is clear that at
least below optimal doping the phase fluctuation regime
derives contributions from disorder as well as deficiency
of mobile carriers. We expect that electron irradiation of
YBa2Cu3O7−δ with δ >0.4 would enhance their Tν .
In summary, we have performed measurements of the
Nernst effect, resistivity and Hall effect on Pr-substituted
YBa2Cu3O7−δ films. We find that an anomalous large
Nernst signal survives above the superconducting tran-
sition temperature in the Pr-rich samples. This large
Nernst voltage is attributed to vortex-like excitations in
a phase incoherent superfluid existing above Tc. The
regime of temperature over which these fluctuations pre-
vail broadens with the Pr concentration. We attribute
this effect primarily to the out-of-plane disorder caused
by praseodymium, which is consistent with the measure-
ments on other YBCO cuprates with in-plane and out-of-
plane disorders. However, we do not completely rule out
the contribution of reduced carrier concentration, partic-
ularly in the Pr-rich sample(x≈0.5).
Acknowledgments
PL and RLG acknowledge support of NSF Grant INT-
0242867. The research at IIT-Kanpur has been sup-
ported by a grant from the Department of Science and
Technology under the project DST/INT/NSF/RPO-105.
We thank Saurabh Bose of help in sample preparation.
∗ Electronic address: pcli@physics.umd.edu 1 Z.A. Xu, N. P. Ong, Y. Wang, T. Kakeshita and S. Uchida,
5
Nature (London) 406, 486 (2000).
2 Y. Wang, L. Li and N. P. Ong, Phys. Rev. B 73, 024510
(2006).
3 Yayu Wang, Lu Li, M. J. Naughton, G. D. Gu, S. Uchida,
and N. P. Ong, Phys. Rev. Lett. 95, 247002 (2005).
4 A. S. Alexandrov and V. N. Zavaritsky, Phys. Rev. Lett.
93, 217002 (2004) and references therein.
5 I. Ussishkin and S. L. Sondhi, Int. J. Mod. Phys. B 18,
3315 (2004); I. Ussishkin, S. L. Sondhi and D. A. Huse,
Phys. Rev. Lett. 89, 287001 (2002).
6 F. Rullier-Albenque, R. Tourbot, H. Alloul, P. Lejay, D.
Colson and A. Forget, Phys. Rev. Lett. 96, 067002 (2006).
7 K. Fujita, T. Noda, K. M. Kojima, H. Eisaki, and S.
Uchida, Phys. Rev. Lett. 95, 097006 (2005).
8 V. Sandu, E. Cimpoiasu, T. Katuwal, C. C. Almasan, Shi
Li and M. B. Maple, Phys. Rev. Lett. 93, 177005 (2004).
9 Peng Xiong, Gang Xiao and X. D. Wu Phys. Rev. B 47,
5516R (1992).
10 Wu Jiang, J. L. Peng, S. J. Hagen and R. L. Greene, Phys.
Rev. B 46, 8694(R)(1992).
11 M. B. Maple, J. Magn. Magn. Mater., 177, 18 (1998).
12 M. Covington and L. H. Greene, Phys. Rev. B 62, 12440
(2000).
13 H. Y. Hwang, B. Batlogg, H. Takagi, H. L. Kao, J. Kwo,
R. J. Cava, J. J. Krajewski and W. F. Peck, Jr., Phys.
Rev. Lett. 72, 2636 (1994).
14 D. Matthey, S. Gariglio, B. Giovannini and J.-M Triscone,
Phys. Rev. B 64, 024513 (2001).
15 Z. A. Xu, J. Q. Shen, S. R. Zhao, Y. J. Zhang and C. K.
Ong, Phys. Rev. B 72, 144527 (2005).
16 N. P. Ong, Y. Wang, S. Ono, Y. Ando and S. Uchida,
Annalen der Physik (Leipzig) 13, 9 (2004).

Correlation between incoherent phase fluctuations and disorder in Y1-xPrxBa2Cu3O7-&#948; epitaxial films from Nernst effect measurements

Crossref