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Response of the high temperature superconductors to weak AC magnetic field
Physica C 175 ( 1991 ) 634-638 North-Holland
Response of the high temperature superconductors to weak AC magnetic field J u n C h e n ' a n d Lee C h o w Department of Physics, Universityof Central Florida, Orlando, FL 32816, USA
J.Z. L i u Department of Physics, Universityof California, Davis, CA 95616, USA
Received 6 September 1990 Revised manuscript received 19 November 1990
A variation of a magnetic modulated electric resistance technique for the characterization of high-Togranular superconductors is described here. This technique uses a weak AC magnetic field to probe the superconducting sample under a constant DC current bias near the transition temperature. Different high temperature superconducting samples including bulk YBa2Cu30 (YBCO), single crystal YBCO, Bi2Sr2CaICu20 (BSCCO) and Bil.sPbo.2Sr2Ca~Cu20 (BPSCCO) thin films have been characterized with this method. This method not only provides information on the superconducting transition of the sample, it can also be used to distinguish different mechanisms of the high temperature superconductors.
Since the discoveries of high temperature superconductors LalSr2Cu40 [1 ], YBa2Cu30 [2], Bi2Sr2CalCU20 [3] and T12Ba2Ca2Cu30 [4] in the past few years, several widely used techniques have been employed to characterize the superconductors near the superconducting transition region, a m o n g them four probe resistivity measurement has been a very popular technique, because o f the simplicity o f the apparatus and ease of operation. In the four probe resistivity measurements, besides the T¢ determination, the slope o f the normal resistance versus temperature and the shape of the resistance curve near the transition region sometimes can be used as an indicator o f the sample's quality. However, occasionally it is difficult to distinguish between a metal-insulator transition and a superconducting transition, especially in the case o f oxide superconductors where metal-insulator transitions are known to occur. Recently Bohandy et al. [ 5 ] and Kim et al. [6 ] have described a technique based on the detection o f Permanent address: Department of Physics, Nanjing University, Nanjing 210008, People's Republic of China.
magnetic field modulated signal on the DC resistance of superconductors to study the superconducting transition and presence o f weak links in high temperature superconductors. It is a sensitive method to detect the superconducting transition. This technique is an extension o f the magnetic modulated microwave absorption technique developed by Moorjani et al. [ 7 - 9 ] . In this paper, a variation of the above technique to investigate the resistive transition of superconductors with a weak AC magnetic field is presented. We also presented results on various high temperature superconductors including bulk YBCO, single crystal YBCO, BSCCO and BPSCCO thin films obtained with this technique. The experimental apparatus is shown schematically in fig. 1. The superconducting sample is placed under a weak AC magnetic field driven by an oscillator with frequency f = 1 kHz. The sample is biased with a constant current which is perpendicular to the magnetic field. The standard four-probe geometry is employed and a lock-in amplifier is used to detect the 2fsignals from the voltage leads. An external oscillator is used to drive the magnetic coil and also used as the lock-in reference sig-
0921-4534/91/$03.50 © 1991 - Elsevier Science Publishers B.V. (North-Holland)
J. Chen et al. / Response of the high temperature superconductors to weak AC magnetic fieM
/,. ,_/xS'-6~
DC CURRENT SOURCE
OSCIUATOfl
COlt
I J~
-\//-
rs -.15
21
I
6O
o.Q LOCK--IN
635
..
-!/'/
75 .
•
..
90
105
c:
A 0 120
lOO
~:
t~
Fig. 1. Schematic diagram of the experimental set-up, where an oscillator is used to drive a magnetic coil and also provide the reference for the lock-in amplifier.
nal. The effect of the magnetic field on the superconductors near the critical temperature is to destroy the superconductivity, which does not depend on the polarity of the magnetic field. That means, the resistance of a superconductor is an even function of the applied magnetic field. As we demonstrate later on in this paper, this leads to the conclusion that the signals detected at f o r 2fwill give similar information, provided that the modulated magnetic field is of the same order of magnitude as the DC magnetic field. On the other hand, detection at 2f frequency will have the advantage of avoiding the induced noises in the lead wires at the ffrequency. Four different samples were studied using this technique. Sample A is a YBCO ceramic disk, sample B is a BSCCO thin film on LaGaO3, sample C is a BPSCCO thin film on LaGaO3 and sample D is a YBCO single crystal. In fig. 2, the magnetic modulated signal at 2 f a r e plotted as function of temperature for samples A, B and C. In order to make a comparison, the corresponding resistance curves are also plotted on the same figure. The AC magnetic fields used in these samples are about 0.1 to 1 G, while the biased current densities were 1 A / c m 2, 100 A / c m 2 and 200 A / c m 2 for samples A, B and C, respectively. Because of the small magnetic field used, the resistance versus temperature curve under such field cannot be distinguished from the zero magnetic field measurement. From fig. 2, we can see that the magnetically mod-
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Fig. 2. The 2fsignals detected by the lock-in amplifier using the experimental set-up as described in fig. 1 for (a) YBCO pellet, (b) BSCCO thin film on LaGaO3 and (c) BPSCCO thin film on LaGaO3.
ulated 2 f signals showed an absorption-like peak at a temperature slightly higher than the zero resistance temperature of the sample. The width of this peak is roughly proportional to the transition width of each sample. In all measurements, we fixed the lock-in phase near zero at the beginning of each measurement, so the sign of the signal just reflects the relative phase shift between the reference and the signal as the temperature varied. We interpreted the origin of this absorption-like peak as follows: well above To, the sample is in the normal metallic state and the applied magnetic field is too small to induce any magneto-resistance so no signal can be observed. Well
J. Chenet al. / Responseof the high temperaturesuperconductors to weakAC magneticfield
636
below T¢, the critical field is large enough such that the applied magnetic field cannot penetrate into the superconductor deep enough to destroy the superconductivity, so again no signal is observed. In the vicinity of the transition temperature, as the temperature approaches Tc from above, the modulated signal starts to deviate from zero. As mentioned above, the detected resistance R ( H, T) ( = V( H, T) / Ib) is independent of the polarity of the applied magnetic field. So, there are no odd terms in the power expansion series of resistance as function of field. We can write such a series expansion at zero field as follows:
!I , S
R(H, T)=no(0, T)
Fig. 3. Schematic diagrams of R(H, T), R(Hb, T) and AR(H, T), respectively.
+ A ( T ) H 2 + B ( T ) H 4 + C ( T ) H 6 + ...
(1)
|
l
AR(H,T)
/
TM
/ I
---/41/
TEMPERATURE"
where H ( t ) = n b q - H m sin(09t) = H b + S H , and HD is the self-field induced by the DC biased current plus any DC magnetic field, and Hmsin(tot) is the AC modulated component. The difference of resistance between with and without modulated field ~H is evidently temperature dependent.
Because the DC biased current Ib is a constant current, the voltages of both the fundamental ( f ) and the second harmonic ( 2 f ) signals detected by the lock-in amplifier are proportional to Ib, and will have the same order of magnitude, which can be expressed as
AR(H, T ) = R ( H , T ) - R ( H B , T)
Vf=x/~A ( T)HbHmI b
(4a)
V2f= -~2A( T)H~Ib
(4b)
=R(HD + 8H, T) - R ( H b , T)
= [ 2 A ( T ) + 4 B ( T ) H 2 + 6 C ( T ) H 4 + ... ] x n b n m sin (09t)
+ [ A ( T ) + 2 B ( T ) H 2 + 15C(T)H4+ ... ] × H ~ sin2 (tot) + ....
(2)
Figure 3 shows schematically the three parameters R(HD, T), R(H, T) and zXR(H, T), respectively. If both Hb and Hm are small quantities, the higher order terms of Hm and Hb can be neglected, then we obtain
zXR(H, T) = 2A ( T)HDHm sin ( o~t) +A ( T)H2m sin 2 (oJt) =2A(T)HbHm sin (~ot) + A ( T ) H % [ 1 - cos(2tot) 1 / 2 .
(3)
IfHb~H,~, H2m has the same magnitude as Hb/-/m, then both the fundamental or the second harmonic signals will have the same order of magnitude.
However, if both Hb and Hm are large enough, we may need to include the higher order terms. In our experiment, the DC component HD is just resulted from the DC biased current, which can be approximately evaluated as
Hb = I~oIb/ ( 2nl) .
(5)
Here, l can be considered as the sample's thickness. For bulk sample, l~ 1 mm, and Ib ~- 100 mA, Hb ~ 0.2 G, for thin film samples, l ~ 1 ~tm, Ib~ 100 ~tA, and HD~ 0.2 G. It has the same order of magnitude as the AC field we used, and it is the same order of magnitude as the earth magnetic field. Because the earth magnetic field is a constant so it can be included in the Hb field. From above, we can conclude that both V/and V2s signals will have the same temperature dependence provided that the Hb and the Hm are both weak enough. In a recent paper Dubson et al. [ 10 ] described the non-ohmic dissipating region in the su-
J. Chen et al. / Response of the high temperature superconductors to weak AC magnetic field
perconducting transition of YBaCuO samples. They found that even a very small magnetic field can alter the I - V characteristic of polycrystalline YBa2Cu3Ox in the transition region. They found that there is an intermediate phase bounded from above by a zeroresistance temperature, Tc~, and from below by a "zero-dissipative" temperature, T¢2. Above Tel, the sample is ohmic, while below TeE, it is in the full superconducting state. However, the sample does not possess a non-zero critical current in the intermediate region, which behaves instead as a non-ohmic resistor with nonlinear current-voltage ( I - V ) characteristics. And they also found that the nature of the intermediate region is strongly influenced by a weak external magnetic field. Even a field of the order of 1 G can destroy the superconductivity. This kind of non-ohmic I - Vbehavior have been observed by other groups [ 1 l - 14 ]. We believe that the temperature region we observed the modulated response signal is corresponding to the intermediate region, A T = T~I - TeE defined by Dubson et al. [ 10], which is just the superconducting transition region. To further test this magnetically modulated technique, we made similar measurements on a single crystal YBCO. In fig. 4, the data on YBCO single crystal is shown. As can be seen the modulated signal has a similar temperature behavior as other high-T~ superconductors shown in fig. 2. However, the width of the peak is much narrower, which is on he order of 0.2 K. Also a side band which is partially resolved can be seen. We believed that this side band in the magnetic modulated signal is probably due to the
18 cl 2
i°
8|
-2
4
637
cross-over of the flux creep to flux flow as described by Malozemoff et al. [ 15 ]. The above described technique although is very similar to the one described by Bohandy [ 7 ] and Kim [8 ], there are several aspects which deviate from their technique. Namely: ( 1 ) we detect the second harmonic signal 2frather than the fundamental signal f t o avoid the induced noise at the fundamental frequency, (2) no DC magnetic field is directly used in our case, (3) the magnetic modulated field we used is extremely small, on the order of 0. I - 1 G, as compared with 2-500 G in refs. [7,8]. In Kim et al. [8], they found that there are two peaks in their magnetic modulated spectrum, one corresponds to the main superconductivity response, and the other corresponds to the response due to the weak links. For large DC magnetic field, only response from the intrinsic grain superconductivity was seen, while in the weak magnetic field, only the weak links response was seen. However, in our case, no peak corresponding to the weak links was observed. However, we found that both the peak amplitude and the peak width of the granular superconductors are influenced by the external field and the bias current density in a quite different way from those of single crystal superconductors. This will be reported elsewhere [16]. Furthermore, from eqs. ( 1 ) and (2), higher order effect can be observed, provided that the applied magnetic field is higher enough. We believe that the coefficients B ( T ) , C ( T ) .... can provide additional information on the mechanism of the resistive transition of high temperature superconductors in the magnetic field. In summary, a magnetic field modulated technique was used to characterize several high-To superconductors. This technique can be used to detect the superconducting transition, in addition, studies of the magnetic field and biased current dependence of the magnetic modulated 2f signals at the transition temperature can provide further information on the physical properties of the high-To superconductors.
-4 93
94
95
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T EMPERA'nJI~E,K
Fig. 4. The magnetic modulated signal as function o f temperature of YBCO single crystals.
Acknowledgements We would like to thank Dr. B. Chai of the Uni-
638
J. Chen et al. / Response of the high temperature superconductors to weak AC magnetic fieM
v e r s i t y o f C e n t r a l F l o r i d a for p r o v i d i n g the L a G a O 3 substrates for the B S C C O t h i n f i l m d e p o s i t i o n . T h i s w o r k is partially s u p p o r t e d by the U.S. D e f e n s e Advanced Research Projects Agency Florida Initiative in A d v a n c e d M i c r o e l e c t r o n i c s a n d M a t e r i a l s P r o g r a m , a n d the U n i v e r s i t y o f C e n t r a l F l o r i d a , D i v i sion o f S p o n s o r e d R e s e a r c h G r a n t N o . 1168-908. W o r k at U C D a v i s was p e r f o r m e d u n d e r t h e auspices o f the U.S. D e p a r t m e n t o f Energy for L a w r e n c e Livermore National Laboratory under contract number W-7405-ENG-48.
References [ 1] J.G. Bednorz and K.A. Miiller, Z. Phys. B 64 (1986) 189. [2] M.K. Wu, J.R. Ashburn, C.J. Torng, P.H. Hor, R.L. Meng, L. Gao, Z.H. Huang, Y.Q. Wang and C.W. Chu, Phys. Rev. Lett. 58 (1987) 908. [ 3 ] H. Maeda, Y. Tanaka, M. Fukutomi and T. Asano, Jpn. J. Appl. Phys. 27 (1988) L209.
[4] Z.Z. Sheng, J.M. Hermann, A. El Ali, C. Almason, J. Estrada, T. Datta and R.J. Matson, Phys. Rev. Lett. 60 (1988) 937. [ 5 ] K. Moorjani, J. Bohandy, F.J. Adrian, B.F. Kim, R.D. ShuU, C.K. Chiang, L.J. Swartzendruber and L.H. Bennett, Phys. Rev. B 36 (1987) 4036. [6] B.F. Kim, J. Bohandy, K. Moorjani and F.J. Adrian, J. Appl. Phys. 63 (1988) 2029. [ 7 ] J. Bohandy, T.E. Phillips, F.J. Adrian, K. Moorjani and B.F. Kim, Mod. Phys. Lett. B 3 (1989) 933. [8] B.F. Kim, J. Bohandy, T.E. Phillips, F.J. Adrian and K. Moorjani, Physica C 161 (1989) 76. [9] K. Moorjani, J. Bohandy, B.F. Kim and F.J. Adrian, Solid State Commun. 74 (1990) 497. [ 10] M.A. Dubson, S.T. Herbert, J.J. Calabrese, D.C. Harris, B.R. Patton and J.C. Garland, Phys. Rev. Lett. 60 ( 1988 ) 1061. [ 11 ] R.H. Hoch, V. Foglietti, W.J. Gallagber, G. Koren, A. Gupta and M.P.A. Fisher, Phys. Rev. Lett. 63 (1989) 1511. [ 12] R. Griessen, Phys. Rev. Lett. 64 (1990) 1674. [ 13 ] N.C. Teh and C.C. Tsuei, Phys. Rev. B 39 ( 1989 ) 9708. [ 14 ] J. Chen and L. Chow, Solid State Commun. 74 (1990) 1095. [ 15 ] A.P. Malozemoff, T.K. Worthington, E. Zeldov, N.C. Yeh, M.W. McElfresh and F. Holtzberg, in: Strong Correlations and Superconductivity, eds. H. Fukuyama, S. Maekawa and A.P. Malozemoff (Springer, Berlin, 1989) p. 349. [ 16] Jun Chen and Lee Chow, to be submitted.
Response of the high temperature superconductors to weak AC magnetic field J u n C h e n ' a n d Lee C h o w Department of Physics, Universityof Central Florida, Orlando, FL 32816, USA
J.Z. L i u Department of Physics, Universityof California, Davis, CA 95616, USA
Received 6 September 1990 Revised manuscript received 19 November 1990
A variation of a magnetic modulated electric resistance technique for the characterization of high-Togranular superconductors is described here. This technique uses a weak AC magnetic field to probe the superconducting sample under a constant DC current bias near the transition temperature. Different high temperature superconducting samples including bulk YBa2Cu30 (YBCO), single crystal YBCO, Bi2Sr2CaICu20 (BSCCO) and Bil.sPbo.2Sr2Ca~Cu20 (BPSCCO) thin films have been characterized with this method. This method not only provides information on the superconducting transition of the sample, it can also be used to distinguish different mechanisms of the high temperature superconductors.
Since the discoveries of high temperature superconductors LalSr2Cu40 [1 ], YBa2Cu30 [2], Bi2Sr2CalCU20 [3] and T12Ba2Ca2Cu30 [4] in the past few years, several widely used techniques have been employed to characterize the superconductors near the superconducting transition region, a m o n g them four probe resistivity measurement has been a very popular technique, because o f the simplicity o f the apparatus and ease of operation. In the four probe resistivity measurements, besides the T¢ determination, the slope o f the normal resistance versus temperature and the shape of the resistance curve near the transition region sometimes can be used as an indicator o f the sample's quality. However, occasionally it is difficult to distinguish between a metal-insulator transition and a superconducting transition, especially in the case o f oxide superconductors where metal-insulator transitions are known to occur. Recently Bohandy et al. [ 5 ] and Kim et al. [6 ] have described a technique based on the detection o f Permanent address: Department of Physics, Nanjing University, Nanjing 210008, People's Republic of China.
magnetic field modulated signal on the DC resistance of superconductors to study the superconducting transition and presence o f weak links in high temperature superconductors. It is a sensitive method to detect the superconducting transition. This technique is an extension o f the magnetic modulated microwave absorption technique developed by Moorjani et al. [ 7 - 9 ] . In this paper, a variation of the above technique to investigate the resistive transition of superconductors with a weak AC magnetic field is presented. We also presented results on various high temperature superconductors including bulk YBCO, single crystal YBCO, BSCCO and BPSCCO thin films obtained with this technique. The experimental apparatus is shown schematically in fig. 1. The superconducting sample is placed under a weak AC magnetic field driven by an oscillator with frequency f = 1 kHz. The sample is biased with a constant current which is perpendicular to the magnetic field. The standard four-probe geometry is employed and a lock-in amplifier is used to detect the 2fsignals from the voltage leads. An external oscillator is used to drive the magnetic coil and also used as the lock-in reference sig-
0921-4534/91/$03.50 © 1991 - Elsevier Science Publishers B.V. (North-Holland)
J. Chen et al. / Response of the high temperature superconductors to weak AC magnetic fieM
/,. ,_/xS'-6~
DC CURRENT SOURCE
OSCIUATOfl
COlt
I J~
-\//-
rs -.15
21
I
6O
o.Q LOCK--IN
635
..
-!/'/
75 .
•
..
90
105
c:
A 0 120
lOO
~:
t~
Fig. 1. Schematic diagram of the experimental set-up, where an oscillator is used to drive a magnetic coil and also provide the reference for the lock-in amplifier.
nal. The effect of the magnetic field on the superconductors near the critical temperature is to destroy the superconductivity, which does not depend on the polarity of the magnetic field. That means, the resistance of a superconductor is an even function of the applied magnetic field. As we demonstrate later on in this paper, this leads to the conclusion that the signals detected at f o r 2fwill give similar information, provided that the modulated magnetic field is of the same order of magnitude as the DC magnetic field. On the other hand, detection at 2f frequency will have the advantage of avoiding the induced noises in the lead wires at the ffrequency. Four different samples were studied using this technique. Sample A is a YBCO ceramic disk, sample B is a BSCCO thin film on LaGaO3, sample C is a BPSCCO thin film on LaGaO3 and sample D is a YBCO single crystal. In fig. 2, the magnetic modulated signal at 2 f a r e plotted as function of temperature for samples A, B and C. In order to make a comparison, the corresponding resistance curves are also plotted on the same figure. The AC magnetic fields used in these samples are about 0.1 to 1 G, while the biased current densities were 1 A / c m 2, 100 A / c m 2 and 200 A / c m 2 for samples A, B and C, respectively. Because of the small magnetic field used, the resistance versus temperature curve under such field cannot be distinguished from the zero magnetic field measurement. From fig. 2, we can see that the magnetically mod-
°
~-o~
!
-1C 40D
52~
65,0
7"/.5
8°
.2¢
16
~_ -.lC
8
-'25
4
-.4~55
70
85 TEMP..I(
100
C105 0
Fig. 2. The 2fsignals detected by the lock-in amplifier using the experimental set-up as described in fig. 1 for (a) YBCO pellet, (b) BSCCO thin film on LaGaO3 and (c) BPSCCO thin film on LaGaO3.
ulated 2 f signals showed an absorption-like peak at a temperature slightly higher than the zero resistance temperature of the sample. The width of this peak is roughly proportional to the transition width of each sample. In all measurements, we fixed the lock-in phase near zero at the beginning of each measurement, so the sign of the signal just reflects the relative phase shift between the reference and the signal as the temperature varied. We interpreted the origin of this absorption-like peak as follows: well above To, the sample is in the normal metallic state and the applied magnetic field is too small to induce any magneto-resistance so no signal can be observed. Well
J. Chenet al. / Responseof the high temperaturesuperconductors to weakAC magneticfield
636
below T¢, the critical field is large enough such that the applied magnetic field cannot penetrate into the superconductor deep enough to destroy the superconductivity, so again no signal is observed. In the vicinity of the transition temperature, as the temperature approaches Tc from above, the modulated signal starts to deviate from zero. As mentioned above, the detected resistance R ( H, T) ( = V( H, T) / Ib) is independent of the polarity of the applied magnetic field. So, there are no odd terms in the power expansion series of resistance as function of field. We can write such a series expansion at zero field as follows:
!I , S
R(H, T)=no(0, T)
Fig. 3. Schematic diagrams of R(H, T), R(Hb, T) and AR(H, T), respectively.
+ A ( T ) H 2 + B ( T ) H 4 + C ( T ) H 6 + ...
(1)
|
l
AR(H,T)
/
TM
/ I
---/41/
TEMPERATURE"
where H ( t ) = n b q - H m sin(09t) = H b + S H , and HD is the self-field induced by the DC biased current plus any DC magnetic field, and Hmsin(tot) is the AC modulated component. The difference of resistance between with and without modulated field ~H is evidently temperature dependent.
Because the DC biased current Ib is a constant current, the voltages of both the fundamental ( f ) and the second harmonic ( 2 f ) signals detected by the lock-in amplifier are proportional to Ib, and will have the same order of magnitude, which can be expressed as
AR(H, T ) = R ( H , T ) - R ( H B , T)
Vf=x/~A ( T)HbHmI b
(4a)
V2f= -~2A( T)H~Ib
(4b)
=R(HD + 8H, T) - R ( H b , T)
= [ 2 A ( T ) + 4 B ( T ) H 2 + 6 C ( T ) H 4 + ... ] x n b n m sin (09t)
+ [ A ( T ) + 2 B ( T ) H 2 + 15C(T)H4+ ... ] × H ~ sin2 (tot) + ....
(2)
Figure 3 shows schematically the three parameters R(HD, T), R(H, T) and zXR(H, T), respectively. If both Hb and Hm are small quantities, the higher order terms of Hm and Hb can be neglected, then we obtain
zXR(H, T) = 2A ( T)HDHm sin ( o~t) +A ( T)H2m sin 2 (oJt) =2A(T)HbHm sin (~ot) + A ( T ) H % [ 1 - cos(2tot) 1 / 2 .
(3)
IfHb~H,~, H2m has the same magnitude as Hb/-/m, then both the fundamental or the second harmonic signals will have the same order of magnitude.
However, if both Hb and Hm are large enough, we may need to include the higher order terms. In our experiment, the DC component HD is just resulted from the DC biased current, which can be approximately evaluated as
Hb = I~oIb/ ( 2nl) .
(5)
Here, l can be considered as the sample's thickness. For bulk sample, l~ 1 mm, and Ib ~- 100 mA, Hb ~ 0.2 G, for thin film samples, l ~ 1 ~tm, Ib~ 100 ~tA, and HD~ 0.2 G. It has the same order of magnitude as the AC field we used, and it is the same order of magnitude as the earth magnetic field. Because the earth magnetic field is a constant so it can be included in the Hb field. From above, we can conclude that both V/and V2s signals will have the same temperature dependence provided that the Hb and the Hm are both weak enough. In a recent paper Dubson et al. [ 10 ] described the non-ohmic dissipating region in the su-
J. Chen et al. / Response of the high temperature superconductors to weak AC magnetic field
perconducting transition of YBaCuO samples. They found that even a very small magnetic field can alter the I - V characteristic of polycrystalline YBa2Cu3Ox in the transition region. They found that there is an intermediate phase bounded from above by a zeroresistance temperature, Tc~, and from below by a "zero-dissipative" temperature, T¢2. Above Tel, the sample is ohmic, while below TeE, it is in the full superconducting state. However, the sample does not possess a non-zero critical current in the intermediate region, which behaves instead as a non-ohmic resistor with nonlinear current-voltage ( I - V ) characteristics. And they also found that the nature of the intermediate region is strongly influenced by a weak external magnetic field. Even a field of the order of 1 G can destroy the superconductivity. This kind of non-ohmic I - Vbehavior have been observed by other groups [ 1 l - 14 ]. We believe that the temperature region we observed the modulated response signal is corresponding to the intermediate region, A T = T~I - TeE defined by Dubson et al. [ 10], which is just the superconducting transition region. To further test this magnetically modulated technique, we made similar measurements on a single crystal YBCO. In fig. 4, the data on YBCO single crystal is shown. As can be seen the modulated signal has a similar temperature behavior as other high-T~ superconductors shown in fig. 2. However, the width of the peak is much narrower, which is on he order of 0.2 K. Also a side band which is partially resolved can be seen. We believed that this side band in the magnetic modulated signal is probably due to the
18 cl 2
i°
8|
-2
4
637
cross-over of the flux creep to flux flow as described by Malozemoff et al. [ 15 ]. The above described technique although is very similar to the one described by Bohandy [ 7 ] and Kim [8 ], there are several aspects which deviate from their technique. Namely: ( 1 ) we detect the second harmonic signal 2frather than the fundamental signal f t o avoid the induced noise at the fundamental frequency, (2) no DC magnetic field is directly used in our case, (3) the magnetic modulated field we used is extremely small, on the order of 0. I - 1 G, as compared with 2-500 G in refs. [7,8]. In Kim et al. [8], they found that there are two peaks in their magnetic modulated spectrum, one corresponds to the main superconductivity response, and the other corresponds to the response due to the weak links. For large DC magnetic field, only response from the intrinsic grain superconductivity was seen, while in the weak magnetic field, only the weak links response was seen. However, in our case, no peak corresponding to the weak links was observed. However, we found that both the peak amplitude and the peak width of the granular superconductors are influenced by the external field and the bias current density in a quite different way from those of single crystal superconductors. This will be reported elsewhere [16]. Furthermore, from eqs. ( 1 ) and (2), higher order effect can be observed, provided that the applied magnetic field is higher enough. We believe that the coefficients B ( T ) , C ( T ) .... can provide additional information on the mechanism of the resistive transition of high temperature superconductors in the magnetic field. In summary, a magnetic field modulated technique was used to characterize several high-To superconductors. This technique can be used to detect the superconducting transition, in addition, studies of the magnetic field and biased current dependence of the magnetic modulated 2f signals at the transition temperature can provide further information on the physical properties of the high-To superconductors.
-4 93
94
95
g6
T EMPERA'nJI~E,K
Fig. 4. The magnetic modulated signal as function o f temperature of YBCO single crystals.
Acknowledgements We would like to thank Dr. B. Chai of the Uni-
638
J. Chen et al. / Response of the high temperature superconductors to weak AC magnetic fieM
v e r s i t y o f C e n t r a l F l o r i d a for p r o v i d i n g the L a G a O 3 substrates for the B S C C O t h i n f i l m d e p o s i t i o n . T h i s w o r k is partially s u p p o r t e d by the U.S. D e f e n s e Advanced Research Projects Agency Florida Initiative in A d v a n c e d M i c r o e l e c t r o n i c s a n d M a t e r i a l s P r o g r a m , a n d the U n i v e r s i t y o f C e n t r a l F l o r i d a , D i v i sion o f S p o n s o r e d R e s e a r c h G r a n t N o . 1168-908. W o r k at U C D a v i s was p e r f o r m e d u n d e r t h e auspices o f the U.S. D e p a r t m e n t o f Energy for L a w r e n c e Livermore National Laboratory under contract number W-7405-ENG-48.
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