Magnetoconductivity of Bi2Sr2Ca1−xYxCu2O8+δ in fluctuation regime
C. P. Dhard, S. N. Bhatia, P. V. P. S. S. Sastry, J. V. Yakhmi, and A. K. Nigam
Citation: J. Appl. Phys. 76, 6944 (1994); doi: 10.1063/1.358082
View online: http://dx.doi.org/10.1063/1.358082
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Published by the American Institute of Physics.
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Magnetoconductivity
of BipSr2Cal +JxCu20s+s
in fluctuation
regime
C. P. Dhard and S. N. Bhatia
Department of Physics, Indian Institate of Technology, Bombay 400 076, India
P. V. P. S. S. Sastty and J. V. Yakhmi
Chemistry Division, Bhabha Atomic Research Centre, Bombay 400 085, India
A. K. Nigam
Tata Institute of Fundamental Research, Bombay 400 005 India
The magnetoconductivity of polycrystalline Bi,Sr,Ca,-,Y,Cu,Os+&
x=0,0.05 and 0.20 samples in
the magnetic field of 4 T was measured. The excess conductivity has been analyzed in the light of
Aronov-Hikami-Larkin
and Bieri-Maki formalisms together with Thompson’s correction of the
Zeeman term of both theories. The later theory was found within the clean limit to describe the data
adequately and yielded the estimate for the phase braking time r+=lX10-13
s. The
Maki-Thompson-Zeeman
contribution (Aot,,rrJ in these samples is found to be negligible.
The short coherence length coupled with the high transition temperature provide an excellent opportunity to study
the rounding of the transition in the oxide superconductors.
The fluctuation enhanced conductivity, i.e., excess conductivity (Aaj in zero field is representable by the AslamazovLarkin (AL) and Maki-Thompson (MT) terms.’ The magnetic field affects the excess conductivity through the orbital
angular momentum giving rise to AL-orbital (AUK)
and
MT-orbital (ho,)
terms and through the spin angular momentum yielding ALZeeman (ho&
and MT-Zeeman
(AC&
terms. Aronov, Hikami, and Larkina (,AHL) have
derived the expressions for these terms from the standard
theory in the dirty limit. However this theory is not applicable to high T, superconducting (HTSC) materials as they
fall within the clean limit with the mean free path Z*&,(O)
[Z-100 A and tab(O)=15 A for YBa,Cu,O, (YBCO)]. Later
Bieri and Maki3 (BM) proposed another theory of ha(H)
which was valid for the clean limit but it gave results identical to the AHL theory. Both AL contributions are not sensitive to the mean free path of the electrons. Therefore, their
values remain essentially unchanged in both dirty and clean
limits. However the MT contribution depends sensitively on
I since the vertex renormalization is essentially controlled by
I in the clean limit. The expressions obtained by Bieri and
Maki3 in this limit for all the four terms are identical to the
AHL expressions with the difference that the terms AoALz
and Ao,,
had (o,/4~-kT)~
instead of ( w,/~&T,)~
as their
prefactors and S was defined by S=1.203[1/&,(0)]
S&,
where S,, is given by (Ref. 2) SAHL=16&O)kT7,$rrd2~.
Later it was pointed out by Thompson4 that both these theories were wrong in treating the Zeeman splitting energy, correction to this leaves the three terms, viz., Au,,,
AC-,
and Aotiz unchanged but modifies the fourth Au,.
Experimentally almost all the attention appears to have
been focused on YBCO only and to the best of our knowledge no attempt has been made to study the
Bi,Sr,CaCu,Os+, (BSCCO) system in this light. Earlier
Matsuda et aL5 analyzed the magnetoconductivity of YBCO
thin t%ns in terms of AHL formalism without Thompson
correction. All four contributions were required giving the
value of the phase breaking time ~-+=10-‘~ s at 100 K. However Semba et al.” found no evidence for the hoin their
6944
J. Appl. Phys. 76 (lo), 15 November 1994
data on single crystals of YBCO. They found 7+==5X lo-r4 s
which is the shortest time reported so far. Sugawara et al.’
have analyzed their Au(H) data measured on chemical vapor
deposition (CVD) films of YBCO in BM theory with
Thompson’s correction’ (BMT), and find the bow, term to
be essential in both the ho-(H) vs E [= (T- T’ff)/TFf, TFf is
the mean field transition temperature] as well as Au(H) vs H
data. In polycrystalline YBCO Matsuda et aZ.’ also found
vanishing values of ACT,, using uncorrected AHL expressions. And our recent analysis on similar samples in the light
of corrected AHLJBM expressions support these results.”
We have measured the magnetoconductivity of polycrystalline Bi,Sr&a, -,Y,Cu20s+ 6 samples with x =O, 0.05, and
0.20 and find the ACT,, contribution to be negligible.
The samples were prepared by the matrix precursor
method by reacting B&O, with a Sr,CaCu20s precursor in
the presence of O2 at 900-950 “C. All the samples were
confirmed to be of single phase by x-ray diffraction (XRD).
dc conductivity was measured by the four probe method on
bar shaped samples.’ The current density used was typically
0.1 A/cm’. Samples were so oriented that the measuring current was perpendicular to the applied field. The sample temperature was measured with a Si diode/CGR thermometer,
placed in contact with the sample in a copper holder, and was
raised at the rate of 2 K/h. The data were taken at the interval
of 20 mK within the transition region.
At high temperatures (T&2T,)
the zero field and the
field data coincide for all the samples implying negligible
magnetoresistance to be present in the normal state and below TFf the transition broadens in the field. A field of 4 T
was used because for the higher fields the orbital terms show
deviations from the H2 behavior predicted by the above
theories.“73 In zero field, a single sharp peak in dp/dT is
symmetrical about the temperature T,, of its maximum,
whereas in the field this curve spreads towards lower temperatures. This spread is around 35 K for x=0 and increases
further with the Y concentration.
We have analyzed the total fluctuation conductivity
where
A q(H) = [ 4H, T> - g,(H, VI
aAH, T)
= lIp,(H,T)
is the background conductivity. Agf(H) contains the zero field conductivity (Ref. 11) Ao-(O) and the
modifications produced in it by the magnetic field. The estiQ 1994 American Institute of Physics
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Bi2SrZCa
TAJ3LB I. Various fitted physical parameters for BSCCO samples in the
clean and dirty limit. r+, r, and I are calculated at 100 K. In BM, L(O) and
&b(O) are constants, whereas in BMT-d(dirty) and BMT-c(clean) these are
temperature dependent.
E,(O)
i&
&b(O)
(4
7
1
(lo-14 9)
t-4
3
(lo-‘3
s)
x=0
AHL.
BM
BMT-d
BMTc
1.9
2.3
1.8
1.8
10.0
9.1
9.9
8.9
1.0
1.3
0.81
0.11
1.0
5.3
0.13
5.3
9.8
52.5
x=0.05
AHL
BM
BMT-d
BMT-c
2.5
2.6
1.8
1.8
11.4
10.2
9.9
8.6
4.0
1.7
0.86
0.12
1.1
5.3
0.16
5.3
11.0
58.6
x=0.20
AI-E
BM
BMTd
BMlk
CU,O,+~
h6t
10000
MT
AL
h
‘E
ALZ
MTZ
3.2
3.1
1.9
1.9
12.8
11.8
10.4
10.4
6.0
2.0
0.86
0.12
1.3
5.3
0.18
5.3
1994
\\
\
11.5
61.2
mation of background conductivity u,(H,T)
have been discussed in detail in Ref. 1.
The experimental data of AnAH, T) of x=0 was first
fitted to the combined expressions of zero field AL and MT
terms and field dependent AHL expressions of AL and MT
terms with Thompson’s correction by taking &(O), ,$,(O),
and Q-$as the adjustable parameters. r+ was assumed to vary
as r#=r&T
where 7fl is a constant. The values of fitted
parameters are shown in Table I. Good agreement can be
obtained with
&(0)=1.9
&
&,(O)=lO.O
A, and
r4=1X10-r3 s. The value of E,(O) agreed with that obtained
from the zero field data.’ The agreement further improved
when BM equations with Thompson’s correction were used
and the mean free path 1 was allowed to vary with temperature as I= lo/T where 1, is a constant. Here in the clean limit
&(O), .&CO), and Z,,T~ were taken as the free parameters.
&(O) slightly increased to 2.3 A and &(O) decreased to 9.1
A. We obtained Zo7~=6.8X10-8 A s. To get an estimate of
r+ from this product, we note that I= mF= r,,uF/T (i.e.,
Ia= rOuF) where r is the transport relaxation time and bF the
Fermi velocity of the carriers. The later is estimated as
(0.6-1.6)X107
cm/s from the relation &,(O) =fiu,JaA
with the in-plane energy gap parameter givenr’ by
2A.ikT,=3.5-8.
Now assuming r$=~ this product yields r+
(100 K)-1.3X10-r3
s for the lowest estimate of uF, i.e.,
uF=O.SX~O~ cm/s. This compares well with the value obtained by Sugawara et aL7 Batlogg,‘” from the resistivity
data, has obtained r=fifl.35kT=5.4X
10-12fT.
With
~~-10~ cm/s, this yields r+( 100 K)-5X10-14
s from our
estimates of ZOrfl and the rdr comes out to be -2.3.
BMT? have further also assumed E(O) and tab(O) to be
temperature dependent along with I, for both dirty and clean
limits. Assuming these temperature variations, values of the
parameters obtained are listed in Table I. Both the limits give
identical values of &(O) as 1.8 A whereas &,(O) works out to
be =9 A and 210 A for the dirty and clean limits, respecJ. Appl. Phys., Vol. 76, No. 10, 15 November
\
4 sr2cao95 y,.,,
cu,
0,
+A
I
1000
1
‘c:
F
t
MT0
kk
100
b
a
10
:/
,
eps
FIG. 1. Fluctuation and magnetoconductivity of BSCCO n=O and 0.05 in
(a) and (b). In (a) &(O) and cob(O) are temperature dependent while in (b)
they are constants. Note the change in relative order of AJ-Z and MT0
contributions in (a) and (b). All the four contributions to Ao((N,T), i.e.,
AL.0, MTO, ALZ, and MTZ and the excess magnetoconductivity Au,,, displayed here, are negative in magnitude.
tively, at 100 K. These values agree with those obtained by
BMT on single crystals of YBCO. Our analysis yields
r+fFO.2 and uF= 7X106 cm/s for the clean limit using the
Batlogg’s” value of r. This is the clean limit r and therefore
Dhard et al.
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6945
cannot be used in the dirty limit as has been used conventionally. To estimate 7 in the dirty limit we assumed
vF=1X107 cm/s. We get r+=1X10-r3
and r in this
Iimit=~~=1.3X10-‘5
s. Thus r,Jrd=62. This ratio is too
large. rd appears to be too small, its reasonable value should
be a smaller fraction of Q-.If uF is reduced further the ratio
rdr also gets reduced but it still remains too high. In the case
of AHL r is also very small. As this theory is valid for the
dirty case, 1 wilI be -&,(O). With ~~-10~ cm/s this yields
r6-lX10-r4
s and rdrd=lO.
Two points are to be noted about this analysis. The data
has been fitted over the range O.OlGeGO.2 and the nonlocal
effects have not been included. These effects apparently become visible at eaO.25 as shown by BMT.
The magnetoconductivity obtained by subtracting
hum(O) and AU-~(O) from Auf(H,T) is displayed in Fig.
l(a) along with the calculated values of the four field depenhas the smallest value over the
dent contributions. Arm
entire E range, being less than 1% of the total Au-~(H,T).
The fit does not deteriorate when the term Auis dropped
altogether. However the rms deviation jumps when the next
is dropped. This result is in conformity
larger term Au,,
with our previous conclusionlo on polycrystalline YBCO
(measured at 4 T) and with Semba et aL6 and Matsuda et al.’
who also found ACT- to be negligible in their magnetoconductivity of single crystal and polycrystalline YBCO, respectively, measured at 1 T. However Sugawara et al.’ found this
term to be present as a substantial fraction of the total magnetoconductivity at 13 T. Since the BMT equations predict
each of the four contributions to be proportional to -H2, the
Au-,
i.e.,
the
ratio
relative
magnitude
of
Au~(Au~,+Au,,+Au~+Aumz)
will not increase
with H and will be a function of E and r6, only. In actual
practice since Aum and Aumo show some saturation at
high fields near T,(at 60.015) the ratio may increase at
such fields. For the present data the equations predict the
ratio to be less than 1% over the entire E range of the data,
i.e., for 0.05~~GO.2, and to remain at negligible levels even
when r+ is increased to =10-t3 s. The anisotropy ratio
(AuM~+Au,)/(Aum+Aum+Au~-t-AumJ
works
out to be 5.6 at e=O.O5 and AuMTz forms 10% of this ratio.
The magnetoconductivity of the x=0.05 and 0.20
6946
samples behaves identically. The plot for x =0.05 is shown in
Fig. l(b). Aumz here is also negligible and the neglect of
this term does not alter the fits in any of these samples.
Though the AHL theory gives reasonable estimates of r$, it
underestimates r thus yielding a very large value for the ratio
rdr. This ratio is similarly overestimated in the BMT dirty
limit and underestimated in its clean limit. Only when E(O)
and &,(O) are taken as temperature independent does this
theory yield reasonable estimates of rdr. The values are
listed in Table I. All the parameters, viz., r+, t,(O) and
.E&,(O)~etc., increase systematically with Y concentration. r4
shows a slight increase with Y doping but still Aa,,
remains negligible. However this increase in r+ increases the
magnitude of the Aa,,
relative to those of the other two.
Instead of being the smallest term as in the Y-free sample, it
and becomes the second largest term.
over takes AuIn summary our analysis of the magnetoconductivity of
Y-doped polycrystalline BSCCO suggests the absence of
Aucontributions for the fields up to 4 T. The other three
terms Au,, , Au,, , and Au,
all contribute significantly.
Due to the absence of AaM,, the validity of the Thompson
correction could not be verified. Though BMT theory appears to agree with experiments, for a better estimate of r+
prior knowledge of some of the parameters, E(O), &(O), or
VF, will be useful. Data further appear to favor the temperature independent value of c,(O) and &(O) and discard their
functional forms given by the BMT equations.
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Yamamoto, and K Hirata, Phys. Rev. B 40, 5176 (1989).
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J. Appl. Phys., Vol. 76, No. IO, 15 November 1994
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Dhard et al.