The temperature dependence of the lower critical field in YBa2Cu3O(6+x) single crystals was determined by magnetization measurements with the applied field parallel and perpendicular to the c-axis. Results are compared with data from the literature and fitted to Ginzberg-Landau equations by assuming a linear dependence of the parameter kappa on temperature. A value of 7 plus or minus 2 kOe was estimated for the thermodynamic critical field at T = O by comparison of calculated H (sub c2) values with experimental data from the literature

Bennett, L. H.

Gayle, F. W.

Kaiser, D. L.

Swartzendruber, L. J.

English

NASA Technical Reports Server

N92-21637
LOWER CRITICAL FIELD MEASUREMENTS IN
YBa2Cu3Os+ x SINGLE CRYSTALS
D.L. Kaiser, L.J. Swartzendruber, F.W. Gayle and L.H. Bennett
Materials Science and Engineering Laboratory
National Institute of Standards and Technology
Gaithersburg, MD 20899
The temperature dependence of the lower critical field in
YBazCu30_+ x single crystals has been determined by magnetization
measurements with the applied field parallel and perpendicular to the
c-axis. Results were compared with data from the literature and
fitted to Ginzberg-Landau equations by assuming a linear dependence
of the parameter _ on temperature. A value of 7 ± 2 kOe was
estimated for the thermodynamic critical field at T = 0 by comparison
of calculated Hc2 values with experimental data from the literature.
INTRODUCTION
The lower critical field (Hcl) of the
high temperature superconductor
YBazCu3Os+ x (YBCO) is an intrinsic
material property which depends upon
temperature and crystallographic
orientation. Accurate measurement of Hcl
is complicated by flux pinning and edge
effects (as illustrated in Fig. i) and by
uncertainty in the demagnetizing factor.
Consequently, early reported Hcl values
in single crystals 1-s were up to an
order of magnitude larger than later
values. 6-12
In this study, H¢I measurements were made
on twinned and detwinned crystals and
the data were compared with results of
previous investigations for orientations
with the applied field parallel and
perpendicular to the c-axis of the
crystal. The experimental data were
fitted to Ginzberg-Landau equations for
the dependence of Hcl on temperature and
upper critical field (He2) values were
calculated for the two orientations of
interest.
EXPERIMENTAL PROCEDURE
The YBCO crystals used in the present
study (Fig. 2) were grown from Y-Ba-Cu-O
melts 13 and subsequently annealed in
oxygen gas at 420°C for 80 h to obtain
superconducting transition temperatures
T c > 90 K. (Thus, the oxygen content
6+x > 6.8514). Two crystals were
selected for measurement. The first
crystal (AN3-5) exhibited characteristic
{ii0} twin planes and was nearly cubic
with dimensions 120 x 135 x 120 _m 3 (c-
dimension = 120 #m). Due to the cubic
morphology, the demagnetizing factors
were nearly identical in all three
dimensions. The second crystal (AN9-5)
was fully detwinned via a thermo-
mechanical process developed in our
laboratory 15 and had dimensions a × b ×
c = 200 x 250 x I00 _m 3.
Magnetic measurements were made using a
superconducting quantum interference
device (SQUID) magnetometer, with the c-
axis of the crystal aligned either
perpendicular or parallel to the applied
field H. The crystal was first cooled
in zero field to a predetermined
temperature and the magnetization was
then measured as the applied field was
increased to a value in excess of Hcl.
For temperatures greater than about 60
K, sharp breaks from linearity in the M
vs. H curves were observed for both
crystals, making the estimation of Hcl
relatively precise. Below 60 K, the
249
https://ntrs.nasa.gov/search.jsp?R=19920012394 2020-03-17T13:07:49+00:00Z
-100
k=
-200
(b)
Hc1-/
0
Applied Field/(I-D) (Oe)
%.
"x
I I
200
Fig. I. Hypothetical magnetization curves after cooling in zero field for a sample:
(a) at equilibrium (i.e., an ellipsoid with no flux pinning); (b) with some pinning
and edge effects; (c) with strong pinning; and (d) with perfect diamagnetic character
(i.e., magnetization is proportional to the applied field after correction for the
demagnetizing factor, D). For the equilibrium case (a), there is a well-defined,
sharp break at Hcl, which allows for an accurate determination of H=i. Pinning and
edge effects (b and c) make it difficult to estimate the true Hcl. In case (b), the
observed onset occurs at applied fields below Hcl due to flux penetration at the
sharp edges and corners of the crystal. In case (c), pinning causes a gradual
departure from linearity, making the estimate of Hci less accurate.
Fig. 2. Scanning electron
micrograph of as-grown YBCO
single crystals. The smallest
dimension of a crystal generally
lies along the c-axis of the
unit cell.
250
ORIGINAL PAGE
BLACK AND WHITE PI--IOFOGRAP_
departure from linearity was more
gradual and He± was estimated from the
initial point of departure from
linearity.
RESULTS AND DISCUSSION
Temperature-dependent Hcl data from the
present study and previous investiga-
tions 4,6-8,1°-Iz for H II c and H ± c are
presented in Fig. 3. The earliest
reported He± values I-3'S were
erroneously high due to difficulties in
defining Hcl and are not included in the
two plots. The curves shown in each plot
were obtained by fitting all displayed
data points using the Ginzberg-Landau
equation 16
Hcl = Hc(ln _ + 0.08)/J2 _, (i)
where H c is the thermodynamic critical
field at temperature T as given by
Hc = Hc0 (I - t 2). (2)
Here Hc0 is H c at T = 0, t is the reduced
temperature T/T c and _ is the Ginzberg-
Landau parameter (the ratio of the
penetration depth _ to the coherence
length _). Data for both H II c and H ± c
can be well-fitted by assuming that
varies linearly with temperature:
= a + bt. (3)
Good fits of Eq. (I) may be obtained for
a wide range of Hc0 values, leading to a
wide range of values for the parameters a
and b in Eq. (3). The range of
permissible Hc0 values is limited
considerably by requiring that Hc2 values
calculated from a second Ginzberg-Landau
equation
Hc2 = J2 _ H c (4)
be in reasonable agreement with
experimental Hc2 data from the litera-
ture. This comparative analysis yields a
value of 7 kOe for Hc0, _ = i00 + 85t for
H ± c and _ = 22 + 22t for H II c. The
calculated curves and data for Hc2 are
compared in Fig. 4. Considering the
large uncertainties in the experimental
Hc2 data and the obvious differences in
T c for samples from different studies,
agreement of the calculated curves with
the data is a matter of judgement. The
maxima seen in the calculated Hc2 curves
are unphysical, indicating that the
linear form used for _ should be
modified, e.g., by the addition of a
quadratic term in t. However, the large
uncertainty in the Hc0 value used here
(7 i 2 kOe) does not justify such an
additional term. Considering the large
variations in the experimental He2 data,
our Hc0 value is in reasonable agreement
with the value of i0 kOe estimated by
Worthington et al. 6 The resulting
uncertainties in _ values calculated
from our equations are also of order
±30%.
Our H c i data for the detwinned crystal
AN9-5 shown in Fig. 3a (H II c) are in
good agreement with the data of Krusin-
Elbaum et al. I° for twinned crystals.
This result indicates that twin bounda-
ries have only a small effect on H cI, as
noted in our earlier investigation. 17
Our H c i data for the twinned crystal
AN3-5 shown in Fig. 3b (H ± c) are in
reasonable agreement with the data from
previous investigations.4'6-s'1°-12
Anisotropy in H cI (Hcl II C/Hcl ± c) as
calculated from the two curves in Fig. 3
was 3.1 + 0.I for I0 K < T < 80 K.
The calculated Hcz values for H il c
(Fig. 4a) are in reasonable agreement
with the data of Welp et ai.18 near the
superconducting transition and follow
the general trend of the data of lye et
al. 19 and Worthington et al. 2 . For H±c
(Fig. 4b) the calculated values at high
temperature show good agreement with the
experimental data of Gallagher et al. 3
and Welp et al. 18 Anisotropy in Hc2
(Hc2 I c/Hc2 II c) as calculated from the
two curves in Fig. 4 was 4.3 i 0.2 for
i0 K < T < 80 K.
251
Ov
l
0.9
0.8
0.7
0.6
0.5
0.4
0.3-
0.2
0. I
0
300
+
Q [] Ref.[7]
+ Ref.[12]
_o o Ref.[10]
x This Work
+ O
+ +
(a) a 11 c + +
0 ' 2'0 ' 40 60 8'0
Temperature (K)
100
2OO
O
¢..)
100
0
0
[] Ref.[7]
[]
, * Ref.[8]
mm_.. _ + • Ref.[6]
• - m u_...._ • Ref.[4]
x a n""-¢_ m Ref.[ I li
x"_ o + Ref.[ 121Q
• _ o o Ref.[ 10]
×
-,_ o x This work
• .
(b) Hie _ m x_
! i ! ! i ! ! i !
20 40 60 80
Temperature (K)
I00
Fig. 3. Temperature-dependent H=I data for (a) H l[c (strong pinning) and (b) H l c
(weak pinning). Our data are for (a) the detwinned crystal AN9-5 and (b) the twinned
crystal AN3-5. The curves were generated by fitting the data to the Ginzberg-Landau
equation for Hcl and temperature-dependent _ equations given by (a) _ = 22 + 22t, and
(b) _ = I00 + 85t (t = T/To).
252
200
(D
O
O4
100
0
0
0
0
(a) H 11 o
' 2'o '
+ Ref.[19]
o Ref.[20]
_x x Ref.[21
xx_ Ref.[ 181
000 X ;+_&
Ooe , X+a__
l ! V ° l l _" '_
40 60 80
Temperature (K)
I00
(D
0
0.5
0
(b) H_I_c
I i
0 20
v Ref.[3]
x Ref.I2]
A Ref.[18]
o Ref.[20]
J191
40 60 80 100
Temperature (K)
Fig. 4. Temperature-dependent Hc2 curve (solid line) calculated from the Ginzberg-
Landau equation for Hc2 and the temperature-dependent x equation for (a) H II c and
(b) H ± c. Experimental Hc2 data from the literature are shown for comparison. The
extrapolations to lower temperatures (T < 60 K) are unreliable and the maxima in the
curves probably do not exist.
253
CONCLUSIONS
Temperature-dependent Hcl results were
determined from magnetization measure-
ments on detwinned and twinned single
crystals of YBCO for H II c and H ± c.
The results from the present study and
previous investigations for each
orientation were fitted to Ginzberg-
Landau equations assuming a linear
temperature dependence for the parameter
m. Hcz values calculated from the
Ginzberg-Landau equation and the
temperature-dependent m relations were in
reasonable agreement with experimental
Hcz data from the literature near the
superconducting transition temperature.
Values of Hc0 = 7 ± 2 kOe, m = i00 + 85t
for H ± c, and m = 22 + 22t for H II c
were estimated from the analysis.
Acknowledgments
We gratefully acknowledge the technical
assistance of H.J. Brown with the
magnetization measurements.
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255



Lower critical field measurements in YBa2Cu3O(6+x) single crystals

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