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Magnetic-relaxation and flux-pinning study in Tl0.5Pb0.5Sr2Ca1−xPrxCu2Oy superconductor
PHYSICA ELSEVIER
Physica C 257 (1996) 367-370
Magnetic-relaxation and flux-pinning study in T10.sPb0.sSr2Cal_xPrxCu2Oy superconductor Q. Hong, J.H. Wang * Department of Chemistry, State University of New York at Buffalo, Amherst, NY 14260, USA
Received 22 August 1995
Abstract Magnetic relaxation of the Tlo.sPb0.sSr2Cal_xPrxCu2Oy (1212) superconductor is studied by monitoring its magnetic moment as a function of time after the removal of magnetic field. The relaxation process is found to be well described by the Anderson-Kim model in the time window of our experiment. The flux-pinning potential within the superconductor is extracted through numerical fitting of the experimental data to the Anderson-Kim model. The dependence of the flux-pinning potential on the Pr doping level is investigated at different temperatures. It is found that at low temperatures, i.e., T < 20 K, the pinning potential decreases as the Pr content increases, while at higher temperatures above 30 K, there is a maximum of pinning potential at P r content x = 0.05. This suggests that for applications at liquid-nitrogen temperature in a magnetic field, it is advantageous to use the material at the Pr content of this level to minimize dissipation of energy due to flux motion.
1. Introduction W h e n a hard superconductor is placed in a magnetic field of strength in between its lower and upper critical fields, i.e. He1 and He2, respectively, it first enters a meta-stable state. A t zero temperature, this meta-stable state is clearly described in B e a n ' s original work as the critical state [1]. In short, he visualized that the induction B in the superconductor would not be equal to the equilibrium value B ( H ) but rather varies from point to point. The flux-line density is no longer uniform across the superconductor specimen and consequently a macroscopic current J ( = ~7 × B ) will flow in the region where V × B 4: 0. Since flux lines in superconductors repel
* Corresponding author. Fax: + 1 716 645 6949.
each other, the regions o f high line density tend to expand towards regions o f low density. This tendency, as suggested by deGennes [2], can be described by a pressure p in the two-dimensional flux-line system. The force density acting on the flux lines due to this pressure is simply - ~ p / a x and this has to be balanced by a pinning force due to the structural defects. The flux-line distribution is thus implicitly determined b y the condition
Here fm is the m a x i m u m pinning force in the material. A state thus realized is the critical state. A t finite temperatures, this critical state is disturbed by thermally activated flux j u m p s across the pinning barriers. In the theory formulated by Anderson and K i m [3], and Campbell and Evetts [4],
0921-4534/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved SSDI 0921-4534(95)00771-7
Q. Hong, J.H. Wang / Physica C 257 (1996) 367-370
368
thermal activation of vortices occurs in the form of bundles and the energy barrier U is modulated by a Lorentz force on the vertices proportional to the transport current density J. In the critical-state model, it is assumed that this is equal to the critical current density Jo of the material. The dependence of the energy barrier U on the current density is given by U = Uo(1 -
J/Jc),
(2)
where Jc is the current density without the Lorentz driving force. The jumping frequency f of flux lines across the energy barrier is described by the following Arrhenius relation:
where k B is the Botzmann constant characteristic attempting frequency in 106-1012 Hz. This equation gives us critical current density J at a given frequency f ; we have
j = j c ( 1 _ kBr \
fo
--~-0 l n T ) ,
and f0 is a the range of the effective measurement
(4)
which can be rewritten as j___ J c ( 1 _
kBT
t
( ) 1-
U0
~0 '
2. Experiment procedure The superconductor T10.sPb0.sSr2Ca1_xPrxCu2Oy in the form of pellet has been made using the procedures described in our previous paper [5]. A small rectangular piece was cut from the pellet and mounted on the SQUID (Quantum Design) probe for measurement. First, the superconductor was field cooled to the desired temperature and after the temperature was stable the applied field was removed. The magnetic-relaxation measurements were taken by monitoring the remanent magnetic moment of the superconductor as a function of time. This is done by using a SQUID magnetometer operating at the 3 cm scan length. The magnetic field inside the superconducting magnet under such a scan length can be thought of as uniform.
3. Results and discussions
here ~'0 = 1/f0- This equation predicts a logarithmic decay of the critical current density in the superconductor. From Bean's critical-state model [1], the magnetization M(t) of the superconductor can be obtained from the above current density J. Consequently, the time dependence of magnetization is obtained M(t)=M0
By using the Anderson-Kim and Bean critical-state model to fit our data, we extract the pinning potential U0 and its dependence on the Pr concentration in the superconductor at different temperatures.
(6)
where M 0 is the magnetization of the superconductor at the start of relaxation and this equation is the basis for the study of magnetic relaxations of superconductors. In this report, we use the above Anderson-Kim model to study the magnetic relaxation and flux pinning in the T10.sPb0.sSraCal_xPrxCuzOy superconductor. We investigate the magnetic-relaxation rate as a function of magnetic field and temperature.
3.1. Dependence of relaxation rate on the applied magnetic field The remanent magnetic moment m of the pelletform unsubstituted (T1,Pb)Sr 2CaCu20y superconductor as a function of time for a number of field strengths at the temperature of 35 K is measured and the results are displayed in Fig. 1. We found that the magnetic relaxation data can be reasonably well described by Anderson-Kim model in the time window of our experiment. Experimental data from another family of high-T~ superconductors are also found to agree well with this theory [6-10]. The relaxation rate, defined b y dM(t)/d In(t), for the remanent magnetization at different fields is obtained by least-squared fitting of the relaxation data to the Anderson-Kim equation (6). The result showing the dependence of relaxation rate on the applied field at 35 K is displayed in Fig. 2. As one can see from this figure the relaxation rate increases monotonically as the applied field H increases from 200 G to 5000 G.
Q. Hong, J.H. Wang//Physica C 257 (1996) 367-370
0.260
Remanent magnetic moment vs. field
~ v
(Tl,,Pb)Sr2CaCuzOyat T--.35 K
~" 2.6 E
0.240 E
369
2.4
0.220
E 0.200
~ 2.2 o E
e--~H=200 G s--EH=400 G -a--a H=600 G
.o_ 2.0 t-
0.180
1.8 5.0
6.0 7.0 8.0 In(t) (t in s e c o n d )
9.0
Fig. 1. Relaxation of remanent magnetic moment of unsubstituted (T1,Pb)-1212 at different magnetic field. Straight lines are obtained by fitting the data to the Anderson-Kim model.
The initial increase of the relaxation rate from H = 200 G to 1000 G can be explained by using Bean's model, which predicts a H 2 dependence for the relaxation rate when H is lower than twice the full penetration field Hp [1]. This condition is implied from the study of remanent magnetization as a function of field as shown in Fig. 3. From this figure, we can identify that the saturation field (which equals 2Hp) for the remanent magnetization is roughly 1000 G, which is consistent with the observation in Fig. 2. The reason for the continuous increase of the relaxation rate after the saturation field in Fig. 3 is not clear at this time. A possible explanation is that as the magnetic field increases, more flux quanta will be generated and the number of flux pinning centers
0.0030 0.0025 E
0.0020 0.0015
"o
0.0010
0.0005 0.0000
10'00 . 2 0. 0 0.
3. 0 0. 0 . 4 0. 0 0
5000
Applied field H (G) Fig. 2. Dependence of relaxation rate d M ( t ) / d l n ( t ) applied field at 35 K for unsubstituted (T1,Pb)-1212.
on the
0
3000 . 4000 . 1000 . . . 2000 . . . . 5000 6000 H (G)
Fig. 3. Dependence of remanent magnetic moment on the applied field at 35 K for unsubstituted (TI,Pb)-1212.
available inside the superconductor is not enough to pin the movement of the magnetic flux. And this may result in the giant relaxation rate observed.
3.2. Dependence of the pinning potential on Pr concentration There has been a persistent interest in improving the flux-pinning strength by introducing artificially flux-pinning centers into the superconductor [ 11-15]. For example, the commonly used N b - S n superconductors are often mechanically cold treated to generate extended dislocations, grain boundaries, etc, which serves flux-pinning centers for the magnetic flux lines penetrating into the superconductors. As we know from previous work, in order for a non-superconducting region to effectively pin a magnetic flux quantum, its linear dimension must be at the same order of the coherent length ~ of the superconductor. This provides us with a rationale to introduce flux-pinning centers simply by chemical element doping or substitution, for the coherent length ~ in high-Tc superconductors is of the order of the lattice constant in the z direction. In our previous study of (T1,Pb)Sr2CaCu2Oy superconductors [5], it is shown that T~ can be increased from 80 K to about 100 K by substituting the divalent Ca by trivalent rare-earth Pr ions. Accompanying the increase in Tc, there is usually an improvement in the critical current density Jo of the superconductor at the same temperature. This leads us to speculate that substitution of Pr might increase the flux-pinning potential in this material. Since the
370
Q. Hong, J.H. Wang / Physica C 257 (1996) 367-370
analysis of the transport critical current density is complicated by the weak links between the grains, an alternative method to eliminate the weak-link effect is desired to study the flux-pinning property. Because the inter-grain critical critical current density is much smaller than the intra-grain critical current density, the contribution from intra-grain current to the magnetic moment of the superconductor dominates [16]. It is thus justifiable for us to obtain the intra-grain flux pinning potentials from a magnetic measurement. To study the flux-pinning potentials as a function of Pr substitution and temperature, we measured the magnetic relaxation rate after removal of a 1 T field for a series of Pr substituted samples. The results are fitted against the Anderson-Kim model of Eq. (6) by choosing ~'0 = 10-9 s and the pinning potential is extracted. The relaxation results agree very well with the Anderson-Kim model for all the samples we measured at 1 T and a typical graph is shown in Fig. 4. Fig. 5 shows the dependence of the so-obtained flux-pinning potential U0 on Pr concentration and temperature. We find that at 10 K the pinning potential decreases as the Pr substitution level increases. On the other hand, at elevated temperatures, Uo increases first and then decreases as the concentration of Pr increases. The maximum value of U0 occurs when x = 0.05. This suggests that for highcurrent applications of these materials at relatively 0.20
,
0.15
E
o
o
oT=10 K
o ° O o o o o ~ o T = 2 0 K
O T=30 K T---40 K
0.10
.~T=50 K r3- . --~--. . , ~ . - ~ . ~
.......
.'~*,,~.~.~
~7 " I " - - 6 0 K
E 0.05
. o.
o <~
¢.-ooo
0.00 5.5
....
6.5
'
'
7.5
8.5
9.5
In(t) (t in s e c o n d ) Fig. 4. Magnetic relaxation of T10.sPbo.sSr2Ca0.ssPro.15Cu2Oy at different temperatures after the removal of a magnetic field of 1 T.
0.5
\\
TT'J=I , 3 - ~ T=30
0.3
:3 0.2 0.1
\ \z~---.~~"d ~7-XTT=60 ~
0"00,0
,
~
i
,
r
,
i
0.1 0,2 0.3 0.4 Pr concentration
Fig. 5. Dependence of the magnetic flux-pinning potential on Pr concentration at different temperatures.
high temperatures, it is better to dope the materials at about x = 0.05. References [1] C.P. Bean, Phys. Rev. Lett. 8 (1962) 250; C.P. Bean, Rev. Mod. Phys. 36 (1964) 31. [2] P.G. deGennes, Superconductivity of Metals and Alloys, chapter 3 (Addison-Wesley, Reading, MA, 1989) p. 83. [3] P.W. Anderson and Y.B. Kim, Rev. Mod. Phys. 36 (1964) 39. [4] A.M. Campbell and J.E. Evetts, Adv. Phys. 21 (1972) 199. [5] Q. Hong and J.H. Wang, Physica C 217 (1994) 439. [6] R. Hergt, R. Hiergeist, J. Taubert, H.W. Neumueller and G. Ries, Phys. Rev. B 47 (1993) 5405. [7] Y. Feng, L. Zhou, K.G. Wang, Y.H. Zhang, X. Jin, Y.T. Zhang, J.R. Jin and X.X. Yao, J. Appl. Phys. 74 (1993) 5096. [8] D.-L. Shi and M. Xu, Phys. Rev. B 44 (1991) 4548. [9] M. Balanda, A. Bajorek, A. Szytula and Z. Tomkowicz, Physica C 191 (1992) 515. [10] J. Paasi, M. Polak, M. Lahtinen, V. Plechacek and L. Soderlund, Cryogenics 32 (1992) 1076. [11] G.K. Bichile, K.M. Jadhav, R.L. Raibagkar, L. Hassan, D.G. Kuberkar and R.G. Kulkarni, Supercond. Sci. Techn. 6 (1993) 233. [12] K. Tenya, H. Miyajima, Y. Otani, Y. Ishikawa, S. Kohayashi and S. Yashizawa, J. Phys. Soc. Jpn. 62 (1993) 1006. [13] J. Schwartz and S. Wu, J. Appl. Phys. 3 (1993) 1343. [14] M.A. Kirk, Cryogenics 33 (1993) 235. [15] J.R. Thompson et al., Appl. Phys. Lett. 60 (1992) 2306. [16] A.P. Malozemoff, in: Physical Properties of High Temperatures Superconductors, vol. I, chapter 3, ed. D.M. Ginsberg, (World Scientific, Singapore, 1989) and references therein.
Physica C 257 (1996) 367-370
Magnetic-relaxation and flux-pinning study in T10.sPb0.sSr2Cal_xPrxCu2Oy superconductor Q. Hong, J.H. Wang * Department of Chemistry, State University of New York at Buffalo, Amherst, NY 14260, USA
Received 22 August 1995
Abstract Magnetic relaxation of the Tlo.sPb0.sSr2Cal_xPrxCu2Oy (1212) superconductor is studied by monitoring its magnetic moment as a function of time after the removal of magnetic field. The relaxation process is found to be well described by the Anderson-Kim model in the time window of our experiment. The flux-pinning potential within the superconductor is extracted through numerical fitting of the experimental data to the Anderson-Kim model. The dependence of the flux-pinning potential on the Pr doping level is investigated at different temperatures. It is found that at low temperatures, i.e., T < 20 K, the pinning potential decreases as the Pr content increases, while at higher temperatures above 30 K, there is a maximum of pinning potential at P r content x = 0.05. This suggests that for applications at liquid-nitrogen temperature in a magnetic field, it is advantageous to use the material at the Pr content of this level to minimize dissipation of energy due to flux motion.
1. Introduction W h e n a hard superconductor is placed in a magnetic field of strength in between its lower and upper critical fields, i.e. He1 and He2, respectively, it first enters a meta-stable state. A t zero temperature, this meta-stable state is clearly described in B e a n ' s original work as the critical state [1]. In short, he visualized that the induction B in the superconductor would not be equal to the equilibrium value B ( H ) but rather varies from point to point. The flux-line density is no longer uniform across the superconductor specimen and consequently a macroscopic current J ( = ~7 × B ) will flow in the region where V × B 4: 0. Since flux lines in superconductors repel
* Corresponding author. Fax: + 1 716 645 6949.
each other, the regions o f high line density tend to expand towards regions o f low density. This tendency, as suggested by deGennes [2], can be described by a pressure p in the two-dimensional flux-line system. The force density acting on the flux lines due to this pressure is simply - ~ p / a x and this has to be balanced by a pinning force due to the structural defects. The flux-line distribution is thus implicitly determined b y the condition
Here fm is the m a x i m u m pinning force in the material. A state thus realized is the critical state. A t finite temperatures, this critical state is disturbed by thermally activated flux j u m p s across the pinning barriers. In the theory formulated by Anderson and K i m [3], and Campbell and Evetts [4],
0921-4534/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved SSDI 0921-4534(95)00771-7
Q. Hong, J.H. Wang / Physica C 257 (1996) 367-370
368
thermal activation of vortices occurs in the form of bundles and the energy barrier U is modulated by a Lorentz force on the vertices proportional to the transport current density J. In the critical-state model, it is assumed that this is equal to the critical current density Jo of the material. The dependence of the energy barrier U on the current density is given by U = Uo(1 -
J/Jc),
(2)
where Jc is the current density without the Lorentz driving force. The jumping frequency f of flux lines across the energy barrier is described by the following Arrhenius relation:
where k B is the Botzmann constant characteristic attempting frequency in 106-1012 Hz. This equation gives us critical current density J at a given frequency f ; we have
j = j c ( 1 _ kBr \
fo
--~-0 l n T ) ,
and f0 is a the range of the effective measurement
(4)
which can be rewritten as j___ J c ( 1 _
kBT
t
( ) 1-
U0
~0 '
2. Experiment procedure The superconductor T10.sPb0.sSr2Ca1_xPrxCu2Oy in the form of pellet has been made using the procedures described in our previous paper [5]. A small rectangular piece was cut from the pellet and mounted on the SQUID (Quantum Design) probe for measurement. First, the superconductor was field cooled to the desired temperature and after the temperature was stable the applied field was removed. The magnetic-relaxation measurements were taken by monitoring the remanent magnetic moment of the superconductor as a function of time. This is done by using a SQUID magnetometer operating at the 3 cm scan length. The magnetic field inside the superconducting magnet under such a scan length can be thought of as uniform.
3. Results and discussions
here ~'0 = 1/f0- This equation predicts a logarithmic decay of the critical current density in the superconductor. From Bean's critical-state model [1], the magnetization M(t) of the superconductor can be obtained from the above current density J. Consequently, the time dependence of magnetization is obtained M(t)=M0
By using the Anderson-Kim and Bean critical-state model to fit our data, we extract the pinning potential U0 and its dependence on the Pr concentration in the superconductor at different temperatures.
(6)
where M 0 is the magnetization of the superconductor at the start of relaxation and this equation is the basis for the study of magnetic relaxations of superconductors. In this report, we use the above Anderson-Kim model to study the magnetic relaxation and flux pinning in the T10.sPb0.sSraCal_xPrxCuzOy superconductor. We investigate the magnetic-relaxation rate as a function of magnetic field and temperature.
3.1. Dependence of relaxation rate on the applied magnetic field The remanent magnetic moment m of the pelletform unsubstituted (T1,Pb)Sr 2CaCu20y superconductor as a function of time for a number of field strengths at the temperature of 35 K is measured and the results are displayed in Fig. 1. We found that the magnetic relaxation data can be reasonably well described by Anderson-Kim model in the time window of our experiment. Experimental data from another family of high-T~ superconductors are also found to agree well with this theory [6-10]. The relaxation rate, defined b y dM(t)/d In(t), for the remanent magnetization at different fields is obtained by least-squared fitting of the relaxation data to the Anderson-Kim equation (6). The result showing the dependence of relaxation rate on the applied field at 35 K is displayed in Fig. 2. As one can see from this figure the relaxation rate increases monotonically as the applied field H increases from 200 G to 5000 G.
Q. Hong, J.H. Wang//Physica C 257 (1996) 367-370
0.260
Remanent magnetic moment vs. field
~ v
(Tl,,Pb)Sr2CaCuzOyat T--.35 K
~" 2.6 E
0.240 E
369
2.4
0.220
E 0.200
~ 2.2 o E
e--~H=200 G s--EH=400 G -a--a H=600 G
.o_ 2.0 t-
0.180
1.8 5.0
6.0 7.0 8.0 In(t) (t in s e c o n d )
9.0
Fig. 1. Relaxation of remanent magnetic moment of unsubstituted (T1,Pb)-1212 at different magnetic field. Straight lines are obtained by fitting the data to the Anderson-Kim model.
The initial increase of the relaxation rate from H = 200 G to 1000 G can be explained by using Bean's model, which predicts a H 2 dependence for the relaxation rate when H is lower than twice the full penetration field Hp [1]. This condition is implied from the study of remanent magnetization as a function of field as shown in Fig. 3. From this figure, we can identify that the saturation field (which equals 2Hp) for the remanent magnetization is roughly 1000 G, which is consistent with the observation in Fig. 2. The reason for the continuous increase of the relaxation rate after the saturation field in Fig. 3 is not clear at this time. A possible explanation is that as the magnetic field increases, more flux quanta will be generated and the number of flux pinning centers
0.0030 0.0025 E
0.0020 0.0015
"o
0.0010
0.0005 0.0000
10'00 . 2 0. 0 0.
3. 0 0. 0 . 4 0. 0 0
5000
Applied field H (G) Fig. 2. Dependence of relaxation rate d M ( t ) / d l n ( t ) applied field at 35 K for unsubstituted (T1,Pb)-1212.
on the
0
3000 . 4000 . 1000 . . . 2000 . . . . 5000 6000 H (G)
Fig. 3. Dependence of remanent magnetic moment on the applied field at 35 K for unsubstituted (TI,Pb)-1212.
available inside the superconductor is not enough to pin the movement of the magnetic flux. And this may result in the giant relaxation rate observed.
3.2. Dependence of the pinning potential on Pr concentration There has been a persistent interest in improving the flux-pinning strength by introducing artificially flux-pinning centers into the superconductor [ 11-15]. For example, the commonly used N b - S n superconductors are often mechanically cold treated to generate extended dislocations, grain boundaries, etc, which serves flux-pinning centers for the magnetic flux lines penetrating into the superconductors. As we know from previous work, in order for a non-superconducting region to effectively pin a magnetic flux quantum, its linear dimension must be at the same order of the coherent length ~ of the superconductor. This provides us with a rationale to introduce flux-pinning centers simply by chemical element doping or substitution, for the coherent length ~ in high-Tc superconductors is of the order of the lattice constant in the z direction. In our previous study of (T1,Pb)Sr2CaCu2Oy superconductors [5], it is shown that T~ can be increased from 80 K to about 100 K by substituting the divalent Ca by trivalent rare-earth Pr ions. Accompanying the increase in Tc, there is usually an improvement in the critical current density Jo of the superconductor at the same temperature. This leads us to speculate that substitution of Pr might increase the flux-pinning potential in this material. Since the
370
Q. Hong, J.H. Wang / Physica C 257 (1996) 367-370
analysis of the transport critical current density is complicated by the weak links between the grains, an alternative method to eliminate the weak-link effect is desired to study the flux-pinning property. Because the inter-grain critical critical current density is much smaller than the intra-grain critical current density, the contribution from intra-grain current to the magnetic moment of the superconductor dominates [16]. It is thus justifiable for us to obtain the intra-grain flux pinning potentials from a magnetic measurement. To study the flux-pinning potentials as a function of Pr substitution and temperature, we measured the magnetic relaxation rate after removal of a 1 T field for a series of Pr substituted samples. The results are fitted against the Anderson-Kim model of Eq. (6) by choosing ~'0 = 10-9 s and the pinning potential is extracted. The relaxation results agree very well with the Anderson-Kim model for all the samples we measured at 1 T and a typical graph is shown in Fig. 4. Fig. 5 shows the dependence of the so-obtained flux-pinning potential U0 on Pr concentration and temperature. We find that at 10 K the pinning potential decreases as the Pr substitution level increases. On the other hand, at elevated temperatures, Uo increases first and then decreases as the concentration of Pr increases. The maximum value of U0 occurs when x = 0.05. This suggests that for highcurrent applications of these materials at relatively 0.20
,
0.15
E
o
o
oT=10 K
o ° O o o o o ~ o T = 2 0 K
O T=30 K T---40 K
0.10
.~T=50 K r3- . --~--. . , ~ . - ~ . ~
.......
.'~*,,~.~.~
~7 " I " - - 6 0 K
E 0.05
. o.
o <~
¢.-ooo
0.00 5.5
....
6.5
'
'
7.5
8.5
9.5
In(t) (t in s e c o n d ) Fig. 4. Magnetic relaxation of T10.sPbo.sSr2Ca0.ssPro.15Cu2Oy at different temperatures after the removal of a magnetic field of 1 T.
0.5
\\
TT'J=I , 3 - ~ T=30
0.3
:3 0.2 0.1
\ \z~---.~~"d ~7-XTT=60 ~
0"00,0
,
~
i
,
r
,
i
0.1 0,2 0.3 0.4 Pr concentration
Fig. 5. Dependence of the magnetic flux-pinning potential on Pr concentration at different temperatures.
high temperatures, it is better to dope the materials at about x = 0.05. References [1] C.P. Bean, Phys. Rev. Lett. 8 (1962) 250; C.P. Bean, Rev. Mod. Phys. 36 (1964) 31. [2] P.G. deGennes, Superconductivity of Metals and Alloys, chapter 3 (Addison-Wesley, Reading, MA, 1989) p. 83. [3] P.W. Anderson and Y.B. Kim, Rev. Mod. Phys. 36 (1964) 39. [4] A.M. Campbell and J.E. Evetts, Adv. Phys. 21 (1972) 199. [5] Q. Hong and J.H. Wang, Physica C 217 (1994) 439. [6] R. Hergt, R. Hiergeist, J. Taubert, H.W. Neumueller and G. Ries, Phys. Rev. B 47 (1993) 5405. [7] Y. Feng, L. Zhou, K.G. Wang, Y.H. Zhang, X. Jin, Y.T. Zhang, J.R. Jin and X.X. Yao, J. Appl. Phys. 74 (1993) 5096. [8] D.-L. Shi and M. Xu, Phys. Rev. B 44 (1991) 4548. [9] M. Balanda, A. Bajorek, A. Szytula and Z. Tomkowicz, Physica C 191 (1992) 515. [10] J. Paasi, M. Polak, M. Lahtinen, V. Plechacek and L. Soderlund, Cryogenics 32 (1992) 1076. [11] G.K. Bichile, K.M. Jadhav, R.L. Raibagkar, L. Hassan, D.G. Kuberkar and R.G. Kulkarni, Supercond. Sci. Techn. 6 (1993) 233. [12] K. Tenya, H. Miyajima, Y. Otani, Y. Ishikawa, S. Kohayashi and S. Yashizawa, J. Phys. Soc. Jpn. 62 (1993) 1006. [13] J. Schwartz and S. Wu, J. Appl. Phys. 3 (1993) 1343. [14] M.A. Kirk, Cryogenics 33 (1993) 235. [15] J.R. Thompson et al., Appl. Phys. Lett. 60 (1992) 2306. [16] A.P. Malozemoff, in: Physical Properties of High Temperatures Superconductors, vol. I, chapter 3, ed. D.M. Ginsberg, (World Scientific, Singapore, 1989) and references therein.