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Determination of shielding current density in bulk cylindrical samples of high-Tc superconductors from AC susceptibility measurements
#&8olid State Comwnications, +&Printed in Great Britain.
0038-1098188 $3.00 + .OO Pergamon Press plc
Vo1.66,N0.6, pp.645-649, 1988.
DETERMINATION OF SHIELOING CURRENT DENSITY IN BULK CYLINDRICAL SAMPLES HIGH-T, SUPERCONDUCTORS FROM AC SUSCEPTIBILITY WEASUREUENTS F.Giimiky
OF
and P.Lobotka
Electrotechnical Institute, Centre of Electrophysical Research, Slovak Academy of Sciences, 842 39 Bratislava, Czechoslovakia (Received Analyses
of
23 February
temperature
ty measured
on bulk allowed
density
presented
del
it
is
at various
possible
YBaSrCu30,
to
from oxide via
sol-gel
Amongother techniques of superconductor Tc determination,
of
high-Tc
a shielding
paper.
Following
js(T)
this
mo-
from measurements
Data obtained powders
as well
technique
are
for as for reported.
sample B has the composition YBaSrCu30,and
Application
sol-gel
technique was used in its prepara-
on high-T, superconductors is often com-
tionB. More details
plicated
structural
by dependence of both real and
imaginary part on AC field
su-
current
from oxide powders by solid state reaction4,
AC susceptibility
measurement is commonly used’.
AC susceptibili-
samples
in the
amplitudes.
prepared
of
introduce
to determine
AC field
YBa2Cu30x prepared
dependences
cylindrical
perconductors model
1988 by S. Amelinckx)
amplitude2. We
about preparation and
properties
will be given else-
where. The form of samples was cylindrical.
have tried to use this dependence to deter-
Diameter x height were 7.8 x 3.5 for sample
mine density of shielding
A and 8.3 x 2.2 for sanple B - all dimen-
currents at va-
rious temperatures.
sions being in mUmeters.
Experimental arrangement of commontype was utilized3.
Temperature dapendences of AC suscep-
To determine absolute
values of $ and $we used a procedure, ba-
tibility real and imaginary parts measured at 30 Hz on sample A are presented in Fig.1,
sed on assumption that at temperature sub-
and at 7200 Hz on sample B in Fig.2.
stantially
samples did not exhibit
under Tc, where d%/dT
q
0, is
cy dependence of susceptibility
F(T<< Tc) = -1. The active volume with magnetic properties fraction
decrease at low fields
with the
indicates
of sample shielded at low tempe-
rature and low magnetic fields. Normal state resistance
and low temperature
nearly 100 % screening of the of
comparable amplitudes were superimposed
of high-Tc su-
to AC field,
very weak influence
perconductors preserves to exhibitan
ved. As a first
accountable shielding effect,thuswe assume
susceptibility
F(T ‘Tc)
within the
sample volume. WhenDC magnetic fields
The second
point for normalization is the state over TC’
Both frequen-
measurementrange 30 - 7200 Hz and signal
evaluated in the expe-
riment is in this way identified
detectable
= 0.
was obser-
step we assume the AC curves to be DC-amplitude
independent. Crucial for further conside-
As typicalexamples of AC susceptibili-
rations is the coincidence
of $ maxima
ty behaviour two samples have been chosen:
with values of $very
Sample A is YBa2Cu30xcomposition obtained
facts observed on other high-Tc samples 645
near to -l/3.
These
646
HIGH
50
80
70
60
90
fK1
90
100
nK1
Fig.2
Fig.1 AC susceptibility
Vol. 66, No. 6
Tc SUPEBWNDUCTCM FBOMAC SUSCBPTIBILITY WEASUBBNBNTS
curves of sample A
AC susceptibility
curves of sample B
(YBaSrCu30,, sol-gel
(Y8e2Cu30x from oxide powders)
technique)
shape as well,
lead to the
scopic shielding
sama mathematical description
of magneti-
in bulk high-T, samples a role analogous
of cylindrical
zation process as that used for type II superconc&ctor based on critical
state
mode19. In that model, the electric
field
current density,
playing
to that of jc in type II superconductors. Its electrical
field
independence was
checked by measurementsat various fre-
E gives rise to current density of certain
quencies. Experimentally observed weak
(critical)
dependence
value independent on the magni-
&I DC magnetic
field
allows
tude of E and local magnetic field.
to consider js constant in the sample
Lowering E to zero does not change the
portion with nonzero magnetic field.
current density previously
The spatial
results
according
decay of magnetic field
distribution
set.
of magnetic field,
to the 1st Maxwell equation is given as
H(r) =
- js.r
Ho
for r/cHo/js
0.
for rpHo/js
(1)
This
in the proposed linear spatial (1).
The shielding current density as well as Ho, both driven by the harmonic probing field Hex, are assumed to vary harmonically in time. The symbols appearing in all the expressions denote their amplitudes.
where Ho is the magnetic field
on sample’s
The measured g(T)
and ;c”cT>curves
surface and r is the radial distance from
can be explained in the following
sample’s surface.
Just below the onset of superconductivity,
js is the value of macro-
way:
100
Vol. 66, No. 6
HIGH T C
647
SUPERCONDUCTORS FROM AC SUSCEPTIBILITY MEASUREMENTS
~ble
shielding currents are weak and al:iOw the
Analysis of AC s u s c e p t i b i l i t y curves
magnetic field to reach the sample's centre.
(sample A)
With decreasing temperature (with probing field Hex constant) the shielding current density as well as the losses rise. When
1
/UoHex(lO-4T). To(K) -X~o
~
Js(A/cm2)
the shielding currents begin to screen the
centre of the sample, the losses s t a r t to decrease due to narrowing the zone with nonzero shielding current. Of p a r t i c u l a r i n t e r e s t i s the s i t u a t i o n when at given temperature To magnetic f i e l d j u s t reaches %he centre of sample. Setting sample radius R in expressions (1) we obtain
H(r) : H0 (1
-
0.05
B5
O. 27
0 15
O. 22
0.2
83
0.31
0 17
0.87
0.5
82
O. 32
0 18
2.18 4.55
i
80
0.)3
0 20
2
78
0.55
0 21
8.7
5
72
0.32
0 25
21.8
i0
62
O. 30
0 29
43.5
r/R)
Table 2
(2)
Analysis of AC susceptibility curves
Js(Hex,To) = Ho/R
(sample B) This configuration gives the averaged magnetic field in the sa~le ~ = 2Ho/) (equivalent to ~'= -i/3) and maximum in losses (i.e. ~"= maximum). For various Hex the point ()co
-I/), ~o = max) on AC suscep-
tibility curves is reached at different To.
/UoHex(lO-4T)
To(K)
-~o
0.05
92
0. 32
I
90
0. 32
5
88
0. 30
I0
86
0. 29
In this point we have estimated the rela-
15
82
0. 30
tion between probing field Hex and surface
20
78
0. )2
field H
0
~
Js(A/cm2) 0 2) 0 26 0 0 0 0
0.21 4.21
31 3) 35 35
21 42 63 84
to be
1 " H ° = Hex
-
20/3
I - O
(3)
The main transition of sample A at 87 K is preceded by 2 % decrease in ~ indicating the presence of small amount of better
The estimation has been carried out repla-
component with onset at 94 K. in sample B,
cing the non-uniform magnetization given
the main part of transition beginning at
by (i) by uniform one with the same mean
93 K is caused by better con~onent, but
value in sample cross-section. 0 is de-
the complete shielding at low temperatures
magnetizing factor for cylindrical sampleaS. '
is reached with contribution of a worse com-
Experimental curves from Figs.1 and 2 h a v e been analyzed using the procedure based on r e l a t i o n s (2) and (3). Summary is given in Table 1 for sample A and in Table 2 for sample B. The values of ~o d i f f e r s l i g h t l y from the t h e o r e t i c a l value -0.33. This could indicate nonuniformity
ponent. In sample B the second peak in ~', much lower than the principal one, is observed, one more reason to assume two-co,%oonency. The losses calculated using critical state model for given geometry and field distribution (2) are II Q = 2~nH~/3. i
I
In AC susceptibility measurements the losses are related to ~"as 13 Q = ~ o H2 o ~ ' . I t yields
in the shielding currents. Really, thorough
theoretical value of
inspection of experimentai curves reveals
deviations from this theoreticai value have
~" = 0.21 0
Accountabie
the weakly pronounced two-componency in
been noted in our experiments. Several me-
both samples. That means there exist two
chanisms of loss modification may be con-
types of paths for shielding currents, ~differing at least in critical temperature 14.
sidered, selection of the most appropriate can not be done at this moment.
648
HIGH T
C
SUPEECONDUCTORS
Vol. 66, No. 6
Fl%OM AC SUSCEPTIBILITY MEASUREI~NTS
Determined magnitudes of shielding
!
!
I
current densities are low compared with those measured on single crystals 6. Here,
B
[ A/cm 2 ]
the same argument could be used as in explainin 9 poor transport current densities: The grains of high-T c superconductor have poor electrical contact. Therefore they seem to be embedded in the component with worse superconducting properties I0. Tempe-
50 A
rature dependence of shielding current densities obtained with the help of procedure described is illustrated in Fig.3.
0 60
The sample 8 with higher values of shielding current density exhibits also dependence closer to linear. It is consistent with the difference in character of AC susceptib i l i t y curves and allows to conclude that in sample A the influence of better compo-
7O
80
go
100
T[K ] Fig.3 ~s(T) determined from AC s u s c e p t i b i l i t y measurements on samples .A and B
nent is weak, whilst in sample B i t dominates. In this time i t is not possible to establish the mechanism of conductivity giving rise to macroscopic shielding currents without doubts. Some facts favour the intergranular transport by Jossphson currents 7. The contribution of other possible mechanisms has been considered recent!y 12. Further theoretical and experimental study is required to solve this problem.
/¢knowled~
- The authors would acknow-
ledge continuous support of ~. 8e~aEka, many valuable discussions with L. Caenak and S. Takdcs and technical assistance of V. Omeste. Kind providing of samples by V. Cernu~o, O. ~ouc, O. Hachajdik, K. Frohl i c h , A. Rceovd (sample A) and by F. Henic, C. Gdlikovd (sample B) is appreciated as well.
REFERENCES
1. C. Lebeau and J. Plnel, J Phys E : Sci Instrum 4, 857, (1971) E. Maxwell and H. Strongin, Phys Rev L e f t lO, 212 (1963) M. Couach, A.F. Khoder, F. Monnier, Cryogenics 25, 695 (1985) 2. T. Ishida, H. Hazaki, Jap Jcur11Appl Phys 26, L1296 (1987) H. Hazaki, M. Takano, R. Kanno, Y. Takeda, Jap Journ Appl Phys 26, L780 (1987) A. Junod, A. Bezioge, D. Cattani, J. Cots, M. Decrous, O. Fischer, P. Genoud, L. Bollmann, 3.-L. Jorda, 3. Muller, E. Walker, to be published in Europhys Lett
3. P. Lobotka and F. C ~ r y , submitted to Physica Status Solidi 4. V. I:ernu~ko, O. ~ouc, O. Mschajd~k, K. FrohIich, A. Rosovd, manuscript in preparation 5. R.B. Goldfarb, J.V. Minervini, Rev 5ci Instrum 55, 761 (1984) 6. G.W. Crabtree, J.Z. Liu, A. Umezawa, W.K. Kwok, D.J. Lain, N.B. Brodsky, 3.W. Oo~r~ey, submitted to Phys Rev Left 7. B. Renker, I. Apfelstedt, H. K{~pfer, C. P o l i t i s , H. Rietechel, W. Schauer, H. Wuhl, U. Gottwick, H. Knieesel, U. Rauchschwalbe, H. Spille, F. Steglich, Z Phys 8 -
V o l . 6 6 , No. 6
HIGH TcSDPERCONDUC~RSI~OM AC SUSCEPTIBILTI~ I ~ U R E I ~ S
Condensed Matter 67, 1 (1987)
3. Garcia, C. Rillo, F. Lera, 3. Bartolome, R. Navarro, D.H.A. Blank, 3. Flokstra, Ooumal of Magnetism and Magnetic Materials 69, L225 (1987) A. Raboutou, D. Peyral, J. Rosenblatt, C. Lebeau, O. Pena, A. Perrin, C. Perrin, M. Sergent, Europhys Lett 4, 1321 (1987) 8. F. Manic, L. G~likov~, manuscript in preparation 9. C.P. Bean, Rev Nod Phys 36, 31 (1964) H. London, Phys Let% 6, 162 (1962)
10. H. Kupfer, I. Apfelstedt, W. Schauer, R. Fl~kiger, R. Maier-Hirmer, H. Wuhl, submltted to Z Phys B 11. M.N. Wilson, Superconducting Magnets, p. 196, Claredon Press, Oxford 1983 12. C.V. Narashima Rao, S.K. Agarwal, B. 3ayaram, A.V. Narlikar, S. Takacs, submitted to Z Matallkunde 13. R.B. Goldfacb and A.F. Clack, IEEE Trans Magn N~-ZI, 3)2 (1985) 14. R.B. Goldfarb, A.F. Clark, A.I. Braginski, A.3. Panson, Cryogenics 27, 475 (1987)
649
0038-1098188 $3.00 + .OO Pergamon Press plc
Vo1.66,N0.6, pp.645-649, 1988.
DETERMINATION OF SHIELOING CURRENT DENSITY IN BULK CYLINDRICAL SAMPLES HIGH-T, SUPERCONDUCTORS FROM AC SUSCEPTIBILITY WEASUREUENTS F.Giimiky
OF
and P.Lobotka
Electrotechnical Institute, Centre of Electrophysical Research, Slovak Academy of Sciences, 842 39 Bratislava, Czechoslovakia (Received Analyses
of
23 February
temperature
ty measured
on bulk allowed
density
presented
del
it
is
at various
possible
YBaSrCu30,
to
from oxide via
sol-gel
Amongother techniques of superconductor Tc determination,
of
high-Tc
a shielding
paper.
Following
js(T)
this
mo-
from measurements
Data obtained powders
as well
technique
are
for as for reported.
sample B has the composition YBaSrCu30,and
Application
sol-gel
technique was used in its prepara-
on high-T, superconductors is often com-
tionB. More details
plicated
structural
by dependence of both real and
imaginary part on AC field
su-
current
from oxide powders by solid state reaction4,
AC susceptibility
measurement is commonly used’.
AC susceptibili-
samples
in the
amplitudes.
prepared
of
introduce
to determine
AC field
YBa2Cu30x prepared
dependences
cylindrical
perconductors model
1988 by S. Amelinckx)
amplitude2. We
about preparation and
properties
will be given else-
where. The form of samples was cylindrical.
have tried to use this dependence to deter-
Diameter x height were 7.8 x 3.5 for sample
mine density of shielding
A and 8.3 x 2.2 for sanple B - all dimen-
currents at va-
rious temperatures.
sions being in mUmeters.
Experimental arrangement of commontype was utilized3.
Temperature dapendences of AC suscep-
To determine absolute
values of $ and $we used a procedure, ba-
tibility real and imaginary parts measured at 30 Hz on sample A are presented in Fig.1,
sed on assumption that at temperature sub-
and at 7200 Hz on sample B in Fig.2.
stantially
samples did not exhibit
under Tc, where d%/dT
q
0, is
cy dependence of susceptibility
F(T<< Tc) = -1. The active volume with magnetic properties fraction
decrease at low fields
with the
indicates
of sample shielded at low tempe-
rature and low magnetic fields. Normal state resistance
and low temperature
nearly 100 % screening of the of
comparable amplitudes were superimposed
of high-Tc su-
to AC field,
very weak influence
perconductors preserves to exhibitan
ved. As a first
accountable shielding effect,thuswe assume
susceptibility
F(T ‘Tc)
within the
sample volume. WhenDC magnetic fields
The second
point for normalization is the state over TC’
Both frequen-
measurementrange 30 - 7200 Hz and signal
evaluated in the expe-
riment is in this way identified
detectable
= 0.
was obser-
step we assume the AC curves to be DC-amplitude
independent. Crucial for further conside-
As typicalexamples of AC susceptibili-
rations is the coincidence
of $ maxima
ty behaviour two samples have been chosen:
with values of $very
Sample A is YBa2Cu30xcomposition obtained
facts observed on other high-Tc samples 645
near to -l/3.
These
646
HIGH
50
80
70
60
90
fK1
90
100
nK1
Fig.2
Fig.1 AC susceptibility
Vol. 66, No. 6
Tc SUPEBWNDUCTCM FBOMAC SUSCBPTIBILITY WEASUBBNBNTS
curves of sample A
AC susceptibility
curves of sample B
(YBaSrCu30,, sol-gel
(Y8e2Cu30x from oxide powders)
technique)
shape as well,
lead to the
scopic shielding
sama mathematical description
of magneti-
in bulk high-T, samples a role analogous
of cylindrical
zation process as that used for type II superconc&ctor based on critical
state
mode19. In that model, the electric
field
current density,
playing
to that of jc in type II superconductors. Its electrical
field
independence was
checked by measurementsat various fre-
E gives rise to current density of certain
quencies. Experimentally observed weak
(critical)
dependence
value independent on the magni-
&I DC magnetic
field
allows
tude of E and local magnetic field.
to consider js constant in the sample
Lowering E to zero does not change the
portion with nonzero magnetic field.
current density previously
The spatial
results
according
decay of magnetic field
distribution
set.
of magnetic field,
to the 1st Maxwell equation is given as
H(r) =
- js.r
Ho
for r/cHo/js
0.
for rpHo/js
(1)
This
in the proposed linear spatial (1).
The shielding current density as well as Ho, both driven by the harmonic probing field Hex, are assumed to vary harmonically in time. The symbols appearing in all the expressions denote their amplitudes.
where Ho is the magnetic field
on sample’s
The measured g(T)
and ;c”cT>curves
surface and r is the radial distance from
can be explained in the following
sample’s surface.
Just below the onset of superconductivity,
js is the value of macro-
way:
100
Vol. 66, No. 6
HIGH T C
647
SUPERCONDUCTORS FROM AC SUSCEPTIBILITY MEASUREMENTS
~ble
shielding currents are weak and al:iOw the
Analysis of AC s u s c e p t i b i l i t y curves
magnetic field to reach the sample's centre.
(sample A)
With decreasing temperature (with probing field Hex constant) the shielding current density as well as the losses rise. When
1
/UoHex(lO-4T). To(K) -X~o
~
Js(A/cm2)
the shielding currents begin to screen the
centre of the sample, the losses s t a r t to decrease due to narrowing the zone with nonzero shielding current. Of p a r t i c u l a r i n t e r e s t i s the s i t u a t i o n when at given temperature To magnetic f i e l d j u s t reaches %he centre of sample. Setting sample radius R in expressions (1) we obtain
H(r) : H0 (1
-
0.05
B5
O. 27
0 15
O. 22
0.2
83
0.31
0 17
0.87
0.5
82
O. 32
0 18
2.18 4.55
i
80
0.)3
0 20
2
78
0.55
0 21
8.7
5
72
0.32
0 25
21.8
i0
62
O. 30
0 29
43.5
r/R)
Table 2
(2)
Analysis of AC susceptibility curves
Js(Hex,To) = Ho/R
(sample B) This configuration gives the averaged magnetic field in the sa~le ~ = 2Ho/) (equivalent to ~'= -i/3) and maximum in losses (i.e. ~"= maximum). For various Hex the point ()co
-I/), ~o = max) on AC suscep-
tibility curves is reached at different To.
/UoHex(lO-4T)
To(K)
-~o
0.05
92
0. 32
I
90
0. 32
5
88
0. 30
I0
86
0. 29
In this point we have estimated the rela-
15
82
0. 30
tion between probing field Hex and surface
20
78
0. )2
field H
0
~
Js(A/cm2) 0 2) 0 26 0 0 0 0
0.21 4.21
31 3) 35 35
21 42 63 84
to be
1 " H ° = Hex
-
20/3
I - O
(3)
The main transition of sample A at 87 K is preceded by 2 % decrease in ~ indicating the presence of small amount of better
The estimation has been carried out repla-
component with onset at 94 K. in sample B,
cing the non-uniform magnetization given
the main part of transition beginning at
by (i) by uniform one with the same mean
93 K is caused by better con~onent, but
value in sample cross-section. 0 is de-
the complete shielding at low temperatures
magnetizing factor for cylindrical sampleaS. '
is reached with contribution of a worse com-
Experimental curves from Figs.1 and 2 h a v e been analyzed using the procedure based on r e l a t i o n s (2) and (3). Summary is given in Table 1 for sample A and in Table 2 for sample B. The values of ~o d i f f e r s l i g h t l y from the t h e o r e t i c a l value -0.33. This could indicate nonuniformity
ponent. In sample B the second peak in ~', much lower than the principal one, is observed, one more reason to assume two-co,%oonency. The losses calculated using critical state model for given geometry and field distribution (2) are II Q = 2~nH~/3. i
I
In AC susceptibility measurements the losses are related to ~"as 13 Q = ~ o H2 o ~ ' . I t yields
in the shielding currents. Really, thorough
theoretical value of
inspection of experimentai curves reveals
deviations from this theoreticai value have
~" = 0.21 0
Accountabie
the weakly pronounced two-componency in
been noted in our experiments. Several me-
both samples. That means there exist two
chanisms of loss modification may be con-
types of paths for shielding currents, ~differing at least in critical temperature 14.
sidered, selection of the most appropriate can not be done at this moment.
648
HIGH T
C
SUPEECONDUCTORS
Vol. 66, No. 6
Fl%OM AC SUSCEPTIBILITY MEASUREI~NTS
Determined magnitudes of shielding
!
!
I
current densities are low compared with those measured on single crystals 6. Here,
B
[ A/cm 2 ]
the same argument could be used as in explainin 9 poor transport current densities: The grains of high-T c superconductor have poor electrical contact. Therefore they seem to be embedded in the component with worse superconducting properties I0. Tempe-
50 A
rature dependence of shielding current densities obtained with the help of procedure described is illustrated in Fig.3.
0 60
The sample 8 with higher values of shielding current density exhibits also dependence closer to linear. It is consistent with the difference in character of AC susceptib i l i t y curves and allows to conclude that in sample A the influence of better compo-
7O
80
go
100
T[K ] Fig.3 ~s(T) determined from AC s u s c e p t i b i l i t y measurements on samples .A and B
nent is weak, whilst in sample B i t dominates. In this time i t is not possible to establish the mechanism of conductivity giving rise to macroscopic shielding currents without doubts. Some facts favour the intergranular transport by Jossphson currents 7. The contribution of other possible mechanisms has been considered recent!y 12. Further theoretical and experimental study is required to solve this problem.
/¢knowled~
- The authors would acknow-
ledge continuous support of ~. 8e~aEka, many valuable discussions with L. Caenak and S. Takdcs and technical assistance of V. Omeste. Kind providing of samples by V. Cernu~o, O. ~ouc, O. Hachajdik, K. Frohl i c h , A. Rceovd (sample A) and by F. Henic, C. Gdlikovd (sample B) is appreciated as well.
REFERENCES
1. C. Lebeau and J. Plnel, J Phys E : Sci Instrum 4, 857, (1971) E. Maxwell and H. Strongin, Phys Rev L e f t lO, 212 (1963) M. Couach, A.F. Khoder, F. Monnier, Cryogenics 25, 695 (1985) 2. T. Ishida, H. Hazaki, Jap Jcur11Appl Phys 26, L1296 (1987) H. Hazaki, M. Takano, R. Kanno, Y. Takeda, Jap Journ Appl Phys 26, L780 (1987) A. Junod, A. Bezioge, D. Cattani, J. Cots, M. Decrous, O. Fischer, P. Genoud, L. Bollmann, 3.-L. Jorda, 3. Muller, E. Walker, to be published in Europhys Lett
3. P. Lobotka and F. C ~ r y , submitted to Physica Status Solidi 4. V. I:ernu~ko, O. ~ouc, O. Mschajd~k, K. FrohIich, A. Rosovd, manuscript in preparation 5. R.B. Goldfarb, J.V. Minervini, Rev 5ci Instrum 55, 761 (1984) 6. G.W. Crabtree, J.Z. Liu, A. Umezawa, W.K. Kwok, D.J. Lain, N.B. Brodsky, 3.W. Oo~r~ey, submitted to Phys Rev Left 7. B. Renker, I. Apfelstedt, H. K{~pfer, C. P o l i t i s , H. Rietechel, W. Schauer, H. Wuhl, U. Gottwick, H. Knieesel, U. Rauchschwalbe, H. Spille, F. Steglich, Z Phys 8 -
V o l . 6 6 , No. 6
HIGH TcSDPERCONDUC~RSI~OM AC SUSCEPTIBILTI~ I ~ U R E I ~ S
Condensed Matter 67, 1 (1987)
3. Garcia, C. Rillo, F. Lera, 3. Bartolome, R. Navarro, D.H.A. Blank, 3. Flokstra, Ooumal of Magnetism and Magnetic Materials 69, L225 (1987) A. Raboutou, D. Peyral, J. Rosenblatt, C. Lebeau, O. Pena, A. Perrin, C. Perrin, M. Sergent, Europhys Lett 4, 1321 (1987) 8. F. Manic, L. G~likov~, manuscript in preparation 9. C.P. Bean, Rev Nod Phys 36, 31 (1964) H. London, Phys Let% 6, 162 (1962)
10. H. Kupfer, I. Apfelstedt, W. Schauer, R. Fl~kiger, R. Maier-Hirmer, H. Wuhl, submltted to Z Phys B 11. M.N. Wilson, Superconducting Magnets, p. 196, Claredon Press, Oxford 1983 12. C.V. Narashima Rao, S.K. Agarwal, B. 3ayaram, A.V. Narlikar, S. Takacs, submitted to Z Matallkunde 13. R.B. Goldfacb and A.F. Clack, IEEE Trans Magn N~-ZI, 3)2 (1985) 14. R.B. Goldfarb, A.F. Clark, A.I. Braginski, A.3. Panson, Cryogenics 27, 475 (1987)
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