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New low-temperature vortex state and flux quantum oscillations at low temperatures in the paramagnetic resonance of high temperature superconductor YBa2Cu3O7−δ
Solid State Communications, Vol. 68, No. 2, pp. 259-262, 1988. Printed in Great Britain.
0038-1098/88 $3.00 + .00 Pergamon Press plc
NEW L O W - T E M P E R A T U R E VORTEX STATE AND FLUX Q U A N T U M OSCILLATIONS AT LOW T E M P E R A T U R E S I N T H E P A R A M A G N E T I C R E S O N A N C E OF H I G H T E M P E R A T U R E S U P E R C O N D U C T O R YBa2Cu307 K.N. Shrivastava School of Physics, University of Hyderabad, P.O. Central University, Hyderabad-500 134, India
(Received 16 June 1988 by S. Amelinckx) We report a microwave signal arising upon excitation of Y B a 2 C u 3 0 7 by microwaves of frequency 9 . 2 G H z which vanishes at a superconducting transition temperature of T, = 92.5K. Near the T, the strength of the signal varies as (T, - T ) 2"7. The exponent of the intensity of the microwave signal indicates that different parts of the sample have different transition temperatures and hence it is concluded that there are clusters in the sample. Using the expression for flux quantization, we find the domain length to be - 0.35 x 10 4 cm at a temperature of 2 0 K which varies with temperature. Below a T,~ _~ 10K a noise like signal appears which indicates a transition in the flux state. In a thin chip, well resolved lines at equal magnetic field spacings B0 = nck/S appear, where n = 0, 1, 2, 3 . . . . . is an integer, ~b is the unit flux hc/2e and S is a typical surfce area depending on the London penetration depth. R E C E N T L Y , IT HAS BEEN possible to identify the temperature at which superconductivity starts in the isolated grains [1]. This onset temperature, T~. ~ 30K, in Ba~La5 xCusOso_y ) was found to be higher than the transition temperatures known in any superconductors at that time. Usually the sample contains grain boundaries and defects but the Cooper pairs tunnel through such boundaries producing a Josephson current. The detection of such a current can be considered as detection of superconductivity, although oxides in the dislocation lines may prevent the resistivity from vanishing at the onset. Worthington et al. [2] have measured the anisotropy o f the coherence length in YBa2Cu307 a which has a T~. of 88.8 K. In a recent paper, we have reported [ 3 ] a paramagnetic resonance study of YBa2fu307 a at 9 . 2 G H z in which a superconducting transition has been identified at T~ "-~ 96 K. We also found the paramagnetic g-values, the concentration of paramagnetic electrons a s a function of temperature, a strong microwave signal interpreted to arise from the Josephson currents due to tunneling across grain boundaries and solved the BCS gap equation numerically which leads to transition temperatures somewhat higher than those given by the BCS expression. In this communication, we describe the microwave signal arising due to the circulation of Josephson currents in Y B a 2 C u 3 0 7 a at a frequency of 9.2 GHz. Since there are domains of varying sizes, there is a
distribution in the intensity of the microwave signal as a function of magnetic fields, we find that the magnetic field at the peak in this distribution corresponds to a domain length of 0.35 × 10 -4 cm which slightly varies with temperature. The intensity of the microwave signal vanishes like the gap at about T, = 92.5 K. F r o m the variation of the intensity, I,. as a function of temperature from 82 to 90K, we find the critical exponent /, ~- (To -- T ) 27. At low temperatures, a noise like signal appears, the intensity of which vanishes at about T,; ~- 10 K which means that there is a phase boundary with different vortex states above and belox~ this second transition temperature. In the case of a 1 m m × 1 m m chip, well resolved lines appear due to flux quantization at about 4 K . These lines in the dg"/dH have a spacing given by B0 = nq~o/S, where n is an integer and S represents a certain surface area. A pallet sample of YBa2Cu3Ov_ 6 is excited by microwaves of frequency 9.2 G H z in an electronparamagnetic resonance spectrometer and the magnetic field is varied. At small fields there is a strong signal as shown in Fig. 1. As Josephson junctions occur at grain boundaries caused by the tetragonal to orthorhombic transformations which nucleates with different orientations, there is a supercurrent which gives rise to a microwave signal. As there is a continuous distribution of domain sizes, those with maximum probability of occurrence give rise to a peak in the signal as the one shown at a field of H = 167G in Fig. 1. Assuming
259
260
HIGH TEMPERATURE
SUPERCONDUCTOR
YBa2Cu307
Vol. 68, No. 2
7
./
6 5 I c - (1 c - T
Inlc
/
2 1 I
i
L
150
250
350
/
/. 3
50
)2.7
i
1
0
4506
tn(Tc-T)
Fig. 1. The microwave signal d z ' / d H as a function o f magnetic field at a temperature o f 2 0 K in YBa2Cu307 ~ showing continuous distribution o f domain sizes with a m a x i m u m corresponding to a field of H = 167G at a frequency o f 9 . 2 G H z .
Fig. 3. Logarithmic plot o f the intensity o f the microwave signal as a function o f temperature from 82 to 9 0 K showing t h a t / , ~ (T, - T) 27. In
flux quantization within domains, ~ (H n~0, we write HS
=
x
r)" dl
hc n--.
/c 2
(1)
2e
]( I g S
In (T, -
T). It is found that
=
We find that f o r n = l a n d H = 167G, S = 0.124 x l0 8 c m 2, which corresponds to a length o f L = 0.35 x l0 4 cm for S = L 2. The intensity o f the peak at H = 167G varies as shown in Fig. 2, vanishing at T, = 9 2 . 5 K . It is o f interest to determine the exponent o f vanishing o f this microwave signal. Therefore in Fig. 3 we show a logarithmic plot o f the
(f~-
T ) 217,
(2)
In an attempt to understand this exponent, we find that it does not match with any o f the known exponents [4] so that we conclude that the exponent arises due to different transition temperatures at different points. If there are many transition temperatures near the T,, then such an exponent may be observable. We show the height o f the signal as a function o f temperature in another sample in Fig. 4 from which it is quite clear that there are m a n y transition temperatures. In the case of a r a n d o m system the gap depends on the distance, A = A(r). The
i0 L
10
103
tn
1
c
c .d
~
10 2
g g
10-2 10
1o-3
0
25
50
75
lOOK
Temperoture
Fig. 2. The variation o f the intensity o f the microwave signal as a function o f temperature showing that the signal vanishes at the critical temperature o f a b o u t T~-~ 92.5K. The signal also shows a weakening below 10 K.
I X 1 0-/~
I
I
I
10
20
30
I
1
k
40 50 60 Temperature
710
I
80
9
100K
Fig. 4. The height of the microwave signal like that of Fig. 1 as a function o f temperature showing m a n y bumps which may be interpretted as many transition temperatures.
H I G H T E M P E R A T U R E S U P E R C O N D U C T O R YBa2Cu307 6
Vol. 68, No. 2
261
m a x i m u m in the microwave signal may thus be associated with r0. Since the correlation length is larger than the nearest neighbour distance, we may expect to find an expansion function
The Josephson current is given by 0
J
=
J0sin
?,1 - ? ' 2 - ~
A'dl
,
(4)
where ?,~ and 72 are the phase factors, A is the vector potential of the electromagnetic wave and the integral is extended over the width of the Josephson junction so that J
=
2e J0 sin {6(0) - -ff Bw(t + 22)},
(5)
where the amplitude factor is related to the gap and the normal state resistivity Ru of the insulating region of surface area S by the relation, Jo -
ztA 2SRu"
(6)
The m a x i m u m current is given by /m~x =
210 sin (g~bi/qS0) cos (n4~/C~o),
(7)
where ~bj = B(22 + t)w with 2 as the London penetration depth, t the thickness of the normal barrier, w the width, 4) = nh/2e and q50 = h/2e. The height of the signal in Fig. 1 as shown in Fig. 2 is thus predicted to vary as the gap A according to (6).
t
dX Jf dH
Ic
,6o
,~o
~oo~
Magnetic Fietd
Fig. 5. The signal of Fig. 1 at 3 K showing noise when cooled below 10 K. The amplitude of the noise, IN has a T,; of 10 K showing vortex transition whereas I, has a T,. of about 92.5 K.
i
ItO
15
H (6)
Fig. 6. Equally separated multiplet of lines when a 1 m m x 1 m m chip of YBa2Cu307_ 6 is excited by microwaves at ~ 4 K (see also [7, 9]).
As the signal in Fig. 1 is cooled, noise appears as shown in Fig. 5. The amplitude of the noise shows a transition temperature of T," -~ 10K. This may be a transition in the vortex state like that predicted by Nelson [5]. The m a x i m u m of the Josephson current occurs when the argument of the spherical Bessel function (sin x ) / x is zero and the phase difference 6(0) around a closed circuit which encompasses a total magnetic flux q5 is given by 4~ze n hc-c cP°
4ge -~c Bow(t + 22) =
0.
(8)
Thus as the value of n varies, different values of B 0 occur for different values of the orientation of the area w(t + 22), thus causing the noise pattern. The microwave signals arising from modulated surface resistance and reactance through processes driven by changing small magnetic fields have also been reported by Portis et al. [6]. In another paper, Blazey et al. [7] report well resolved equally spaced lines in the absorption spectrum of a YBa2Cu307.6 single crystal when excited by microwaves at 4.4 K. The noise pattern in Josephson junction has been found by Jaklevic et al. [8] to arise from flux hopping. In Fig. 6 we show [9] a microwave spectrum with equally separated multiplet of lines caused by B0 =
~'o
i
5
h n'-2eS '
(9)
where S is the area w(t + 22) for different values of the integer n'. The paramagnetic resonance spectrum measures the imaginary part of the response function as a function of magnetic field for a fixed clystron frequency. The appearance of equally spaced lines of (9) can be described by Z" =
6f~ ((.0
--
(3)n) 2 - -
(1~'~)2
•
(10)
262
H I G H T E M P E R A T U R E S U P E R C O N D U C T O R YBa2Cu307 ~
Since the maximum current is given by (6), the corresponding energy is
En = fi~o, = nJo~o,
(11)
which is equivalent to E, = n(aoT~A/(2Ru). Thus equally spaced lines in the spectrum are expected as seen in Fig. 6. However, the line spacings depend on the orientation of the sample with respect to the magnetic field. The Josephson current J = J0 sin (o~t - k . r + 61) with co = 2eV0/h and k = 2~Hd/(Po, is often modulated by a space and time dependent potential V(r, t) = Vo + O(r, t) where the second term is given by O(r, t) = (h/2e)(O/?,t)6~ (r, t). The phase factors in such a case can be analysed in terms of a series.
potential is found to be site dependent and hence it may be concluded that the intersite Hubbard term plays an important role. There is a noisy signal which develops into well resolved lines in small flakes at low temperatures below a second transition temperature at about T[ _~ 10 K while the first transition temperature is at about T, _~ 96 K. Thus we find a transition in the vortex state. As the potential of the electronic configuration of three atoms d - s2p ~ - d is almost flat [10] near the naturally occurring distances, the change in configuration of Cu 2+ to Cu ~ may be an important source of flux transition at 10 K.
REFERENCES I.
where L is the length of the junction. Considering only two terms, we can expect a cosine dependence in the phase factor, ~, ~_ I m { g 0 e~'0~ + g , e ' ..... C O S L } ,
(13)
so that the resonance field (9) becomes, B0 = [(n~0 + 6~)/S] and hence a cosine dependence is expected in (11) and also noted in [7]. This means that the Josephson voltage has a distance and time dependence contribution. In conclusion, we have found that the high temperature superconductor YBa2Cu3Ov ,~describes new resonances in paramagnetic resonance. These resonances are related to flux hopping and Josephson effect in grains. The domain size is of the order of 10 4 cm but it varies with temperature. The gap as well as the
Vol. 68, No. 2
2. 3. 4. 5. 6. 7.
8. 9. 10.
J.G. Bednorz & K.A. Miiller, Z. Phys. B64, 189 (1986). T.K. Worthington, W.J. Gallagher & T.R. Dinger, Phys. Rev. Lett. 89, 1160 (1987). K.N. Shrivastava, J. Phys. C20, L789 (1987). C.J. Lobb, Phys. Rev. B36, 3930 (1987). D.R. Nelson, Phys. Rev. Lett. 60, 1973 (1988). A.M. Portis, K.W. Blazey, K.A. Miiller & J.G. Bednorz, Europhys. Lett. 5, 467 (1988). K.W. Blazey, A.M. Portis, K.A. Mfiller, J.G. Bednorz & F. Haltzberg, Proc. ~#f the high-
temperature superconductivity conference, Interlaken, Switzerland, 1988, Physica C 56, 153 (19883. R.C. Jaklevic, J. Lambe, J.E. Mercereau & A.H. Silver, Phys. Rev. 140~ A1628 (1965). K.N. Shrivastava, Conf on high-temperature superconductivity, University of Bristol, Dec 1415, 1987 (Institute of Physics, London). K.N. Shrivastava, Phys. Rev. B21, 2702 (1980); K.N. Shrivastava & V. Jaccarino, Phys. Rev. BI3, 299 (1976).
0038-1098/88 $3.00 + .00 Pergamon Press plc
NEW L O W - T E M P E R A T U R E VORTEX STATE AND FLUX Q U A N T U M OSCILLATIONS AT LOW T E M P E R A T U R E S I N T H E P A R A M A G N E T I C R E S O N A N C E OF H I G H T E M P E R A T U R E S U P E R C O N D U C T O R YBa2Cu307 K.N. Shrivastava School of Physics, University of Hyderabad, P.O. Central University, Hyderabad-500 134, India
(Received 16 June 1988 by S. Amelinckx) We report a microwave signal arising upon excitation of Y B a 2 C u 3 0 7 by microwaves of frequency 9 . 2 G H z which vanishes at a superconducting transition temperature of T, = 92.5K. Near the T, the strength of the signal varies as (T, - T ) 2"7. The exponent of the intensity of the microwave signal indicates that different parts of the sample have different transition temperatures and hence it is concluded that there are clusters in the sample. Using the expression for flux quantization, we find the domain length to be - 0.35 x 10 4 cm at a temperature of 2 0 K which varies with temperature. Below a T,~ _~ 10K a noise like signal appears which indicates a transition in the flux state. In a thin chip, well resolved lines at equal magnetic field spacings B0 = nck/S appear, where n = 0, 1, 2, 3 . . . . . is an integer, ~b is the unit flux hc/2e and S is a typical surfce area depending on the London penetration depth. R E C E N T L Y , IT HAS BEEN possible to identify the temperature at which superconductivity starts in the isolated grains [1]. This onset temperature, T~. ~ 30K, in Ba~La5 xCusOso_y ) was found to be higher than the transition temperatures known in any superconductors at that time. Usually the sample contains grain boundaries and defects but the Cooper pairs tunnel through such boundaries producing a Josephson current. The detection of such a current can be considered as detection of superconductivity, although oxides in the dislocation lines may prevent the resistivity from vanishing at the onset. Worthington et al. [2] have measured the anisotropy o f the coherence length in YBa2Cu307 a which has a T~. of 88.8 K. In a recent paper, we have reported [ 3 ] a paramagnetic resonance study of YBa2fu307 a at 9 . 2 G H z in which a superconducting transition has been identified at T~ "-~ 96 K. We also found the paramagnetic g-values, the concentration of paramagnetic electrons a s a function of temperature, a strong microwave signal interpreted to arise from the Josephson currents due to tunneling across grain boundaries and solved the BCS gap equation numerically which leads to transition temperatures somewhat higher than those given by the BCS expression. In this communication, we describe the microwave signal arising due to the circulation of Josephson currents in Y B a 2 C u 3 0 7 a at a frequency of 9.2 GHz. Since there are domains of varying sizes, there is a
distribution in the intensity of the microwave signal as a function of magnetic fields, we find that the magnetic field at the peak in this distribution corresponds to a domain length of 0.35 × 10 -4 cm which slightly varies with temperature. The intensity of the microwave signal vanishes like the gap at about T, = 92.5 K. F r o m the variation of the intensity, I,. as a function of temperature from 82 to 90K, we find the critical exponent /, ~- (To -- T ) 27. At low temperatures, a noise like signal appears, the intensity of which vanishes at about T,; ~- 10 K which means that there is a phase boundary with different vortex states above and belox~ this second transition temperature. In the case of a 1 m m × 1 m m chip, well resolved lines appear due to flux quantization at about 4 K . These lines in the dg"/dH have a spacing given by B0 = nq~o/S, where n is an integer and S represents a certain surface area. A pallet sample of YBa2Cu3Ov_ 6 is excited by microwaves of frequency 9.2 G H z in an electronparamagnetic resonance spectrometer and the magnetic field is varied. At small fields there is a strong signal as shown in Fig. 1. As Josephson junctions occur at grain boundaries caused by the tetragonal to orthorhombic transformations which nucleates with different orientations, there is a supercurrent which gives rise to a microwave signal. As there is a continuous distribution of domain sizes, those with maximum probability of occurrence give rise to a peak in the signal as the one shown at a field of H = 167G in Fig. 1. Assuming
259
260
HIGH TEMPERATURE
SUPERCONDUCTOR
YBa2Cu307
Vol. 68, No. 2
7
./
6 5 I c - (1 c - T
Inlc
/
2 1 I
i
L
150
250
350
/
/. 3
50
)2.7
i
1
0
4506
tn(Tc-T)
Fig. 1. The microwave signal d z ' / d H as a function o f magnetic field at a temperature o f 2 0 K in YBa2Cu307 ~ showing continuous distribution o f domain sizes with a m a x i m u m corresponding to a field of H = 167G at a frequency o f 9 . 2 G H z .
Fig. 3. Logarithmic plot o f the intensity o f the microwave signal as a function o f temperature from 82 to 9 0 K showing t h a t / , ~ (T, - T) 27. In
flux quantization within domains, ~ (H n~0, we write HS
=
x
r)" dl
hc n--.
/c 2
(1)
2e
]( I g S
In (T, -
T). It is found that
=
We find that f o r n = l a n d H = 167G, S = 0.124 x l0 8 c m 2, which corresponds to a length o f L = 0.35 x l0 4 cm for S = L 2. The intensity o f the peak at H = 167G varies as shown in Fig. 2, vanishing at T, = 9 2 . 5 K . It is o f interest to determine the exponent o f vanishing o f this microwave signal. Therefore in Fig. 3 we show a logarithmic plot o f the
(f~-
T ) 217,
(2)
In an attempt to understand this exponent, we find that it does not match with any o f the known exponents [4] so that we conclude that the exponent arises due to different transition temperatures at different points. If there are many transition temperatures near the T,, then such an exponent may be observable. We show the height o f the signal as a function o f temperature in another sample in Fig. 4 from which it is quite clear that there are m a n y transition temperatures. In the case of a r a n d o m system the gap depends on the distance, A = A(r). The
i0 L
10
103
tn
1
c
c .d
~
10 2
g g
10-2 10
1o-3
0
25
50
75
lOOK
Temperoture
Fig. 2. The variation o f the intensity o f the microwave signal as a function o f temperature showing that the signal vanishes at the critical temperature o f a b o u t T~-~ 92.5K. The signal also shows a weakening below 10 K.
I X 1 0-/~
I
I
I
10
20
30
I
1
k
40 50 60 Temperature
710
I
80
9
100K
Fig. 4. The height of the microwave signal like that of Fig. 1 as a function o f temperature showing m a n y bumps which may be interpretted as many transition temperatures.
H I G H T E M P E R A T U R E S U P E R C O N D U C T O R YBa2Cu307 6
Vol. 68, No. 2
261
m a x i m u m in the microwave signal may thus be associated with r0. Since the correlation length is larger than the nearest neighbour distance, we may expect to find an expansion function
The Josephson current is given by 0
J
=
J0sin
?,1 - ? ' 2 - ~
A'dl
,
(4)
where ?,~ and 72 are the phase factors, A is the vector potential of the electromagnetic wave and the integral is extended over the width of the Josephson junction so that J
=
2e J0 sin {6(0) - -ff Bw(t + 22)},
(5)
where the amplitude factor is related to the gap and the normal state resistivity Ru of the insulating region of surface area S by the relation, Jo -
ztA 2SRu"
(6)
The m a x i m u m current is given by /m~x =
210 sin (g~bi/qS0) cos (n4~/C~o),
(7)
where ~bj = B(22 + t)w with 2 as the London penetration depth, t the thickness of the normal barrier, w the width, 4) = nh/2e and q50 = h/2e. The height of the signal in Fig. 1 as shown in Fig. 2 is thus predicted to vary as the gap A according to (6).
t
dX Jf dH
Ic
,6o
,~o
~oo~
Magnetic Fietd
Fig. 5. The signal of Fig. 1 at 3 K showing noise when cooled below 10 K. The amplitude of the noise, IN has a T,; of 10 K showing vortex transition whereas I, has a T,. of about 92.5 K.
i
ItO
15
H (6)
Fig. 6. Equally separated multiplet of lines when a 1 m m x 1 m m chip of YBa2Cu307_ 6 is excited by microwaves at ~ 4 K (see also [7, 9]).
As the signal in Fig. 1 is cooled, noise appears as shown in Fig. 5. The amplitude of the noise shows a transition temperature of T," -~ 10K. This may be a transition in the vortex state like that predicted by Nelson [5]. The m a x i m u m of the Josephson current occurs when the argument of the spherical Bessel function (sin x ) / x is zero and the phase difference 6(0) around a closed circuit which encompasses a total magnetic flux q5 is given by 4~ze n hc-c cP°
4ge -~c Bow(t + 22) =
0.
(8)
Thus as the value of n varies, different values of B 0 occur for different values of the orientation of the area w(t + 22), thus causing the noise pattern. The microwave signals arising from modulated surface resistance and reactance through processes driven by changing small magnetic fields have also been reported by Portis et al. [6]. In another paper, Blazey et al. [7] report well resolved equally spaced lines in the absorption spectrum of a YBa2Cu307.6 single crystal when excited by microwaves at 4.4 K. The noise pattern in Josephson junction has been found by Jaklevic et al. [8] to arise from flux hopping. In Fig. 6 we show [9] a microwave spectrum with equally separated multiplet of lines caused by B0 =
~'o
i
5
h n'-2eS '
(9)
where S is the area w(t + 22) for different values of the integer n'. The paramagnetic resonance spectrum measures the imaginary part of the response function as a function of magnetic field for a fixed clystron frequency. The appearance of equally spaced lines of (9) can be described by Z" =
6f~ ((.0
--
(3)n) 2 - -
(1~'~)2
•
(10)
262
H I G H T E M P E R A T U R E S U P E R C O N D U C T O R YBa2Cu307 ~
Since the maximum current is given by (6), the corresponding energy is
En = fi~o, = nJo~o,
(11)
which is equivalent to E, = n(aoT~A/(2Ru). Thus equally spaced lines in the spectrum are expected as seen in Fig. 6. However, the line spacings depend on the orientation of the sample with respect to the magnetic field. The Josephson current J = J0 sin (o~t - k . r + 61) with co = 2eV0/h and k = 2~Hd/(Po, is often modulated by a space and time dependent potential V(r, t) = Vo + O(r, t) where the second term is given by O(r, t) = (h/2e)(O/?,t)6~ (r, t). The phase factors in such a case can be analysed in terms of a series.
potential is found to be site dependent and hence it may be concluded that the intersite Hubbard term plays an important role. There is a noisy signal which develops into well resolved lines in small flakes at low temperatures below a second transition temperature at about T[ _~ 10 K while the first transition temperature is at about T, _~ 96 K. Thus we find a transition in the vortex state. As the potential of the electronic configuration of three atoms d - s2p ~ - d is almost flat [10] near the naturally occurring distances, the change in configuration of Cu 2+ to Cu ~ may be an important source of flux transition at 10 K.
REFERENCES I.
where L is the length of the junction. Considering only two terms, we can expect a cosine dependence in the phase factor, ~, ~_ I m { g 0 e~'0~ + g , e ' ..... C O S L } ,
(13)
so that the resonance field (9) becomes, B0 = [(n~0 + 6~)/S] and hence a cosine dependence is expected in (11) and also noted in [7]. This means that the Josephson voltage has a distance and time dependence contribution. In conclusion, we have found that the high temperature superconductor YBa2Cu3Ov ,~describes new resonances in paramagnetic resonance. These resonances are related to flux hopping and Josephson effect in grains. The domain size is of the order of 10 4 cm but it varies with temperature. The gap as well as the
Vol. 68, No. 2
2. 3. 4. 5. 6. 7.
8. 9. 10.
J.G. Bednorz & K.A. Miiller, Z. Phys. B64, 189 (1986). T.K. Worthington, W.J. Gallagher & T.R. Dinger, Phys. Rev. Lett. 89, 1160 (1987). K.N. Shrivastava, J. Phys. C20, L789 (1987). C.J. Lobb, Phys. Rev. B36, 3930 (1987). D.R. Nelson, Phys. Rev. Lett. 60, 1973 (1988). A.M. Portis, K.W. Blazey, K.A. Miiller & J.G. Bednorz, Europhys. Lett. 5, 467 (1988). K.W. Blazey, A.M. Portis, K.A. Mfiller, J.G. Bednorz & F. Haltzberg, Proc. ~#f the high-
temperature superconductivity conference, Interlaken, Switzerland, 1988, Physica C 56, 153 (19883. R.C. Jaklevic, J. Lambe, J.E. Mercereau & A.H. Silver, Phys. Rev. 140~ A1628 (1965). K.N. Shrivastava, Conf on high-temperature superconductivity, University of Bristol, Dec 1415, 1987 (Institute of Physics, London). K.N. Shrivastava, Phys. Rev. B21, 2702 (1980); K.N. Shrivastava & V. Jaccarino, Phys. Rev. BI3, 299 (1976).