NASA Technical Reports Server (NTRS) 19920012394: Lower critical field measurements in YBa2Cu3O(6+x) single crystals

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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 melts 13 and subsequently annealed in
oxygen gas at 420°C for 80 h to obtain
The lower critical field (Hcl) of the superconducting transition temperatures
high temperature superconductor Tc > 90 K. (Thus, the oxygen content
YBazCu3Os+ x (YBCO) is an intrinsic 6+x > 6.8514). Two crystals were
material property which depends upon selected for measurement. The first
temperature and crystallographic crystal (AN3-5) exhibited characteristic
orientation. Accurate measurement of Hcl {ii0} twin planes and was nearly cubic
is complicated by flux pinning and edge with dimensions 120 x 135 x 120 _m 3 (c-
effects (as illustrated in Fig. i) and by dimension = 120 #m). Due to the cubic
uncertainty in the demagnetizing factor. morphology, the demagnetizing factors
Consequently, early reported Hcl values were nearly identical in all three
in single crystals 1-s were up to an dimensions. The second crystal (AN9-5)
order of magnitude larger than later was fully detwinned via a thermo-
values. 6-12 mechanical process developed in our
laboratory 15 and had dimensions a × b ×
In this study, H¢I measurements were made c = 200 x 250 x I00 _m 3.
on twinned and detwinned crystals and
the data were compared with results of Magnetic measurements were made using a
previous investigations for orientations superconducting quantum interference
with the applied field parallel and device (SQUID) magnetometer, with the c-
perpendicular to the c-axis of the axis of the crystal aligned either
crystal. The experimental data were perpendicular or parallel to the applied
fitted to Ginzberg-Landau equations for field H. The crystal was first cooled
the dependence of Hcl on temperature and in zero field to a predetermined
upper critical field (He2) values were temperature and the magnetization was
calculated for the two orientations of then measured as the applied field was
interest.
increased to a value in excess of Hcl.
For temperatures greater than about 60
EXPERIMENTAL PROCEDURE K, sharp breaks from linearity in the M
vs. H curves were observed for both
The YBCO crystals used in the present crystals, making the estimation of Hcl
study (Fig. 2) were grown from Y-Ba-Cu-O relatively precise. Below 60 K, the
249
-100 (b)
k=
Hc1-/
%.
-200 "x
I I
0 200
Applied Field/(I-D) (Oe)
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.
ORIGINAL PAGE
250
BLACK AND WHITE PI--IOFOGRAP_
departure from linearity was more calculated curves and data for Hc2 are
gradual and He± was estimated from the compared in Fig. 4. Considering the
initial point of departure from large uncertainties in the experimental
linearity. Hc2 data and the obvious differences in
Tc for samples from different studies,
RESULTS AND DISCUSSION agreement of the calculated curves with
the data is a matter of judgement. The
Temperature-dependent Hcl data from the maxima seen in the calculated Hc2 curves
present study and previous investiga- are unphysical, indicating that the
tions 4,6-8,1°-Iz for H IIc and H ± c are linear form used for _ should be
presented in Fig. 3. The earliest modified, e.g., by the addition of a
reported He± values I-3'S were quadratic term in t. However, the large
erroneously high due to difficulties in uncertainty in the Hc0 value used here
defining Hcl and are not included in the (7 i 2 kOe) does not justify such an
two plots. The curves shown in each plot additional term. Considering the large
were obtained by fitting all displayed variations in the experimental He2 data,
data points using the Ginzberg-Landau our Hc0 value is in reasonable agreement
equation 16 with the value of i0 kOe estimated by
Worthington et al. 6 The resulting
Hcl = Hc(ln _ + 0.08)/J2 _, (i) uncertainties in _ values calculated
from our equations are also of order
where Hc is the thermodynamic critical ±30%.
field at temperature T as given by
Our Hci data for the detwinned crystal
Hc = Hc0 (I - t2). (2) AN9-5 shown in Fig. 3a (H IIc) are in
good agreement with the data of Krusin-
Here Hc0 is Hc at T = 0, t is the reduced Elbaum et al. I° for twinned crystals.
This result indicates that twin bounda-
temperature T/T c and _ is the Ginzberg-
Landau parameter (the ratio of the ries have only a small effect on HcI, as
penetration depth _ to the coherence noted in our earlier investigation. 17
length _). Data for both H IIc and H ± c Our Hci data for the twinned crystal
can be well-fitted by assuming that AN3-5 shown in Fig. 3b (H ± c) are in
varies linearly with temperature: reasonable agreement with the data from
previous investigations.4'6-s'1°-12
= a + bt. (3) Anisotropy in HcI (Hcl IIC/Hcl ± c) as
calculated from the two curves in Fig. 3
Good fits of Eq. (I) may be obtained for was 3.1 + 0.I for I0 K < T < 80 K.
a wide range of Hc0 values, leading to a
wide range of values for the parameters a The calculated Hcz values for H ilc
and b in Eq. (3). The range of (Fig. 4a) are in reasonable agreement
permissible Hc0 values is limited with the data of Welp et ai.18 near the
considerably by requiring that Hc2 values superconducting transition and follow
calculated from a second Ginzberg-Landau the general trend of the data of lye et
equation al. 19 and Worthington et al. 2 . For H±c
(Fig. 4b) the calculated values at high
Hc2 = J2 _ Hc (4) temperature show good agreement with the
experimental data of Gallagher et al. 3
be in reasonable agreement with and Welp et al. 18 Anisotropy in Hc2
experimental Hc2 data from the litera- (Hc2 I c/Hc2 IIc) as calculated from the
ture. This comparative analysis yields a two curves in Fig. 4 was 4.3 i 0.2 for
value of 7 kOe for Hc0, _ = i00 + 85t for i0 K < T < 80 K.
H ± c and _ = 22 + 22t for H IIc. The
251
l
+
0.9 Q [] Ref.[7]
0.8 + Ref.[12]
0.7
O 0.6 x This Work
_o o Ref.[10]
v 0.5
0.4
0.3-
+ O
0.2
+ +
0. I (a) a 11 c + +
0
0 ' 2'0 ' 40 60 8'0
100
Temperature (K)
300
[] Ref.[7]
[]
, * Ref.[8]
mm_.. _ + • Ref.[6]
2OO
• - mu_...._ • Ref.[4]
O x a n""-¢_ m Ref.[ I li
x"_ o + Ref.[ 121
Q
¢..)
• _ o o Ref.[ 10]
100 × -,_ o x This work
• .
(b) Hie _ _m x
0
! i ! ! i ! ! i !
0 20 40 60 80 I00
Temperature (K)
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
+ Ref.[19]
o Ref.[20]
200
_x x Ref.[21
(D
O
0 xx_ Ref.[ 181
O4
100 0
(a) H 11o
000 X ;+_&
Ooe , X+a__
0 l ! V ° l l _" '_
' 2'o '
0 40 60 80 I00
Temperature (K)
v Ref.[3]
x Ref.I2]
A Ref.[18]
(D o Ref.[20]
0
J191
0.5
(b) H_I_c
0
I i
0 20 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 IIc 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 Ku, H.D. Yang, J.W. Lynn, W.-H. Li,
and Q. Li, "Effects of Crystal
Temperature-dependent Hcl results were Anisotropy on Magnetization and
determined from magnetization measure- Magnetic Order in Superconducting
ments on detwinned and twinned single RBazCU3OT_x," Physica B 148B, 285-
crystals of YBCO for H IIc and H ± c. 288 (1987).
The results from the present study and 6. T.K. Worthington, Y. Yeshurun, A.P.
previous investigations for each Malozemoff, R.M. Yandrofski, F.
orientation were fitted to Ginzberg- Holtzberg, and T.R. Dinger, "The
Landau equations assuming a linear Effect of Flux Pinning and Flux
temperature dependence for the parameter Creep on Magnetic Measurements of
m. Hcz values calculated from the Single Crystal YiBazCu3OT_x," J. de
Ginzberg-Landau equation and the Phys. 49, C8-2093-2098 (1988).
temperature-dependent m relations were in 7. Y. Yeshurun, A.P. Malozemoff, F.
reasonable agreement with experimental Holtzberg, and T.R. Dinger,
Hcz data from the literature near the "Magnetic Relaxation and the Lower
superconducting transition temperature. Critical Fields in a Y-Ba-Cu-O
Values of Hc0 = 7 ± 2 kOe, m = i00 + 85t Crystal," Phys. Rev. B 38, 11828-
for H ± c, and m = 22 + 22t for H IIc 11831 (1988).
were estimated from the analysis. 8. L. Fuchter, C. Giovannella, G.
Collin, and I.A. Campbell, "Lower
Acknowledgments Critical Fields and Pinning in
YiBazCu307_x," Physica C 156, 69-72
We gratefully acknowledge the technical (1988).
assistance of H.J. Brown with the 9. A. Umezawa, G.W. Crabtree, J.Z. Liu,
magnetization measurements. T.J. Moran, S.K. Malik, L.H. Nunez,
W.L. Kwok, and C.H. Sowers,
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