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Virgin response of field induced microwave absorption in the high Tc ceramic superconductor BSCCO — RSJ model
Solid State Communications, Vol. 90, No. 12, pp. 809-811, 1994 Elsevier Science Ltd Printed in Great Britain 0038-1098(94)$7.00+.00 0038-1098(94)E0301-Q
Pergamon
VIRGIN RESPONSE OF FIELD INDUCED MICROWAVE ABSORPTION IN THE HIGH Tc CERAMIC SUPERCONDUCTOR BSCCO - RSJ MODEL V. Seshu Bai*, P. V. Patanjali** and S. M. Bhagat Physics Department, University of Maryland, College Park, MD 20770,USA * BOYSCAST Fellow, University of Hyderabad, India ** University of Hyderabad, Hyderabad-500134, India (Received 24 February 1994, accepted for publication 7 April 1994 by A.H.MacDonald)
Field induced microwave absorption is recorded at low fields(<20mT) in a high Tc ceramic superconductor (Bi,Pb)-Sr-CaCu-O, after cooling in zero field to 54, 77 and 90 K at 9.9 GHz and to 77K at 36.4 GHz. The results are discussed in conjunction with the dc magnetization data obtained on the same sample. It is argued that the observed features do not follow the predictions of the flux flow model while they give qualitative evidence in support of the resistively shunted Josephson junction model.
superconductors, there have been, to our knowledge, few attempts to correlate the virgin curve of MMA with a direct determination of the effective field (B) inside the specimen. In fact, not surprisingly, most authors appeal to some variation of the critical state model to obtain B. In this context, it was felt that it would be more appropriate to measure the LFMMA in a bulk ceramic and correlate it, as far as possible, to the field dependence of the dc magnetization in the same sample, in the same configuration. We chose a parellelepiped of (Bi,Pb)-Sr-Ca-Cu-O for this study.
L INTRODUCTION
There have been extensive reports [1-8] on the magnetic field induced microwave absorption (MMA) in high Tc superconductors. However, the mechanism underlying the process that causes absorption on low field ( 20 mT) application is still in debate. One of the models attributes the loss to flux flow resistivity [3,6] according to which the microwave power loss is a function of field(B) inside the sample. This model predicts the power absorbed by the sample to vary as B for B<>Bo, where B0= 8~o)1"1~,2/tp0 and is typically ~10-1 - 10 -2 T. Here, rl is the coefficient of viscous drag, o) the microwave frequency, ~. the penetration depth and tp0 the elementary flux quantum. On the other hand, in earlier work [1] from this laboratory, it was shown that the virgin curve, i.e., the power absorption recorded as a function of applied field, in zero field cooled (ZFC) CuO based superconductors, can be qualitatively understood by invoking a resistively shunted Josephson junction (RSJ) model. In this case, the weak-links are considered to behave like RSJs and the field induced absorption is attributed to the reduction in Jc" Despite the large number of data reported on low field absorption (LFMMA) in high Tc
11. EXPERIMENTAL
The sample has the nominal composition of Bil.2Pb0.aSrl.sCa2CusOy [9]. It is a monophasic superconductor prepared from citrate precursors. The zero resistance temperature was 103 K while the onset of the diamagnetic transition was at 106K. The dc magnetization was measured using Faraday's method, details of which are described elsewhere [10]. Using the techniques described in Ref.[1], the temperature (T) and the field (H) dependences of microwave power loss were measured at 9.9 G Hz and 36.4 G Hz. Essentially, one monitors the power Pe(H,T) reflected at the cavity frequency as T or H is varied. 809
FIELD INDUCED MICROWAVE ABSORPTION
810
Initally one measures the change in zero field absorption as T is varied through Tc, at a given frequency, and this gives
(l)
PN = Pc(O, Tc) " Pc(O, Train)
as a measure of the normal state absorption in the sample. Train is chosen such that Pc is nearly a constant for T-
p ( H ) =ziP/ PN = [Pc(H,T) - Pc(O,T)]/PN
and the virgin curve represents p(H) as a function of H. In the present study, first the zero field absorption was measured at 9.9 G Hz which gave a Tc mw of 104.5 K. That is, Pc(0,T) drops precipitously tbr T
Fig. 1 shows the virgin curve recorded at 77 K. It can be seen that p(H) increases linearly at low H, bends over and eventually saturates for fields ~t0H> 5 mT. This variation is found to be
Vol. 90, No. 12
very well described by the empirical relation [1] (3)
p(H) = AP/P~= a [1/(I+Ho/H)]
with t~ =0.19 and l.toH0: 0.7 mT. Clearly, in terms of Eqn.(3), I.toH0 represents the field at which the absorption is 50% of the saturation value and the value of t~ implies that at high fields the MMA is about 19% of the normal state absorption. Virgin curves recorded at 9.9 G Hz at 54 K and 90 K also follow Eqn.(3). While t~ is roughly the same at all the three temperatures, taoH0 is 1.8mT and 0 . 3 m T at 5 4 K a n d 9 0 K , respectively. In Fig.2, we show the field dependence of the dc magnetization (M) measured at 77 K and the induction (B) that represents the effective field inside the sample. These B - H and M - H plots are recorded in the ZFC state of the same sample as was used for the MMA measurements. The sample geometry with respect to dc field was maintained to be the same as in the MMA experiment to ensure that the demagnetization effects, if any, are identical in both cases. It can be seen from Fig.2 that M varies linearly upto g0H---2 mT with a slope of -1, suggesting that the demagnetization factor N--0. Above a field of 2 mT, M increases less rapidly, subsequently saturating at ~t0H > 6 mT. This behaviour is similar to an ideal Bean superconductor [11], a slab for which the full penetration field, H* = 2 Msaturation - 7 mT. For fields below 2 mT, the field (B) inside the sample is effectively zero suggesting that only at fields well above 2 mT will there be a sizeable field penetration inside the sample. 10
'
,
,
,
',
'
B
0.20 m=
•
B
m
v
• ~:~
O oQ
.=.2 0.10
-
M
~m
0.00
i
0
I
i
10
,
!
20
P 0 H(mT)
Fig. 1 Field induced microwave absorption at 9.9 GHz in the ceramic BSCCO zero field cooled to 77 K. The squares show the measured data and the solid line is a fit to Eqn. (3).
m
If
nlum
m
ii
i
_6
0
2
4
6
n
m
i
8
u
n
10
P0 H(mT)
Fig. 2 Field dependence of dc Magnetization (M) and the induction (B) in the ceramic BSCCO, zero field cooled to 77 K.
Vol. 90, No. 12
FIELD INDUCED MICROWAVE ABSORPTION
IV. D I S C U S S I O N
It is interesting to note that the major part of the increase in p(H) (see Fig.l) occurs in the linear region of the M - H curve (Fig.2), where B = 0. This observation clearly supports the contention that the flux flow model [3], which projects p(H) to be a function of B may not be appropriate to account for the large absorption that occurs at low fields. Additionally, at ~ H > 5 mT, p(H) is found to exhibit saturation while the flux flow model predicts a B 1/2 dependence and hence a monotonic rise in p(H) with H. On the other hand, the RSJ model provides a highly satisfactory qualitative picture [1] for the observed virgin curve, i.e. Eqn (3). The fact that B is zero when most of the power absorption occurs indicates that in the LFMMA phenomenon the important physical quantity is the field at the sample surface and the weak-links located therein. Presumably, the 'H' appearing in Eqn.(3) will thus be the applied field modified by any "demagnetization" corrections. It is argued that these modifiers, if any, can be included in the definition of ~0H0. A further check for the appropriateness of the flux flow or RSJ models was sought by observing the virgin curve at a different microwave frequency. It turns out that at 36 GHz and 77 K, l.t0H0~0.5 mT while a= 0.01. Thus the LFMMA reduces drastically with increasing co. As already noted, the flux flow model does not give saturation at large H and hence no direct comparison is possible. However, at large fields
811
it predicts (AP/PN) to be essentially independent of co, contrary to the observed reduction. A single RSJ gives [1], for a set temperature, P(H) = PN/ [1 +(f(H)/ag)]
(4)
where f(H) is a sample dependent parameter that tends to be a constant as H approaches zero and becomes zero at very large H. From this one can write, in order to compare the experimentally seen frequency dependence, for H >>H0 (AP/PN)=[P(H)-P(O)1/PN ~ 1 / [ l + c a j 2 1
(5)
where c is a constant for a given sample at a set temperature. Thus one expects to see a weaker MMA as co is increased, as is indeed the case. In summary, the facts that i) a major part of the low field microwave absorption occurs when measured B=0, ii) the power absorbed exhibits a saturation at fields above 5 mT, instead of a monotonic increase, and iii) a large drop is observed in the power absorption on increasing the frequency - give satisfactory qualitative evidence in support of the RSJ model and suggest that the flux flow model is not entirely appropriate to explain the low field MMA, at least for the present experiments. Acknowledgement - One of the authors (VSB)
is grateful to the Department of Science and Technology, India for the award of BOYSCAST fellowship and to the University of Maryland for hospitality, and PVP gratefully acknowledges University Grants Commission for the fellowship.
REFERENCES
1. J. S. Ramachandran, M. X. Huang, S. M. Bhagat, K. Kish and S. Tyagi, Physica C 202,151 (1992). 2. M. X. Huang, S. M. Bhagat, A. T. Findikoglu, T. Venkatesan,M. A. Manheimer and S. Tyagi, Physica C 193, 421 (1992). 3. L. Ji, M. S. Rzchowski and M. Tinkham, Phys. Rev. B 42, 4838 (1990). 4. L. Ji, M. S. Rzchowski, N. Anand and M. Tinkham, Phys. Rev, B 47,470 (1993). 5. M. Mahel, M. Darula and S. Benecka, Supercond. Sci. Technol. 6, 112 (1993).
6. A. M. Portis,K. W. Blazey. K. A. Muller and J. G. Bednorz, Europhys. Lett.5, 467 (1988). 7. E. J. Pakulis, and T. Osada, Phys. Rev. B 37, 5940 (1988). 8. A. Dulcic,B. Ravkin, M. Pozek, Europhys. Lett. 10,593 (1989). 9. V. Seshu Bai, S. Ravi, T. Rajasekharan and R. Gopalan, J1. Appl. Phys. 70,4378 (1991). 10. G. Shaw, S. M. Bhagat, N. D. Spencer, J. E. Crow and S. Tyagi, Phys. C 169, 257 (1990). 11. C. P. Bean, Rev.Mod. Phys. 36,31(1964).
Pergamon
VIRGIN RESPONSE OF FIELD INDUCED MICROWAVE ABSORPTION IN THE HIGH Tc CERAMIC SUPERCONDUCTOR BSCCO - RSJ MODEL V. Seshu Bai*, P. V. Patanjali** and S. M. Bhagat Physics Department, University of Maryland, College Park, MD 20770,USA * BOYSCAST Fellow, University of Hyderabad, India ** University of Hyderabad, Hyderabad-500134, India (Received 24 February 1994, accepted for publication 7 April 1994 by A.H.MacDonald)
Field induced microwave absorption is recorded at low fields(<20mT) in a high Tc ceramic superconductor (Bi,Pb)-Sr-CaCu-O, after cooling in zero field to 54, 77 and 90 K at 9.9 GHz and to 77K at 36.4 GHz. The results are discussed in conjunction with the dc magnetization data obtained on the same sample. It is argued that the observed features do not follow the predictions of the flux flow model while they give qualitative evidence in support of the resistively shunted Josephson junction model.
superconductors, there have been, to our knowledge, few attempts to correlate the virgin curve of MMA with a direct determination of the effective field (B) inside the specimen. In fact, not surprisingly, most authors appeal to some variation of the critical state model to obtain B. In this context, it was felt that it would be more appropriate to measure the LFMMA in a bulk ceramic and correlate it, as far as possible, to the field dependence of the dc magnetization in the same sample, in the same configuration. We chose a parellelepiped of (Bi,Pb)-Sr-Ca-Cu-O for this study.
L INTRODUCTION
There have been extensive reports [1-8] on the magnetic field induced microwave absorption (MMA) in high Tc superconductors. However, the mechanism underlying the process that causes absorption on low field ( 20 mT) application is still in debate. One of the models attributes the loss to flux flow resistivity [3,6] according to which the microwave power loss is a function of field(B) inside the sample. This model predicts the power absorbed by the sample to vary as B for B<
11. EXPERIMENTAL
The sample has the nominal composition of Bil.2Pb0.aSrl.sCa2CusOy [9]. It is a monophasic superconductor prepared from citrate precursors. The zero resistance temperature was 103 K while the onset of the diamagnetic transition was at 106K. The dc magnetization was measured using Faraday's method, details of which are described elsewhere [10]. Using the techniques described in Ref.[1], the temperature (T) and the field (H) dependences of microwave power loss were measured at 9.9 G Hz and 36.4 G Hz. Essentially, one monitors the power Pe(H,T) reflected at the cavity frequency as T or H is varied. 809
FIELD INDUCED MICROWAVE ABSORPTION
810
Initally one measures the change in zero field absorption as T is varied through Tc, at a given frequency, and this gives
(l)
PN = Pc(O, Tc) " Pc(O, Train)
as a measure of the normal state absorption in the sample. Train is chosen such that Pc is nearly a constant for T-
p ( H ) =ziP/ PN = [Pc(H,T) - Pc(O,T)]/PN
and the virgin curve represents p(H) as a function of H. In the present study, first the zero field absorption was measured at 9.9 G Hz which gave a Tc mw of 104.5 K. That is, Pc(0,T) drops precipitously tbr T
Fig. 1 shows the virgin curve recorded at 77 K. It can be seen that p(H) increases linearly at low H, bends over and eventually saturates for fields ~t0H> 5 mT. This variation is found to be
Vol. 90, No. 12
very well described by the empirical relation [1] (3)
p(H) = AP/P~= a [1/(I+Ho/H)]
with t~ =0.19 and l.toH0: 0.7 mT. Clearly, in terms of Eqn.(3), I.toH0 represents the field at which the absorption is 50% of the saturation value and the value of t~ implies that at high fields the MMA is about 19% of the normal state absorption. Virgin curves recorded at 9.9 G Hz at 54 K and 90 K also follow Eqn.(3). While t~ is roughly the same at all the three temperatures, taoH0 is 1.8mT and 0 . 3 m T at 5 4 K a n d 9 0 K , respectively. In Fig.2, we show the field dependence of the dc magnetization (M) measured at 77 K and the induction (B) that represents the effective field inside the sample. These B - H and M - H plots are recorded in the ZFC state of the same sample as was used for the MMA measurements. The sample geometry with respect to dc field was maintained to be the same as in the MMA experiment to ensure that the demagnetization effects, if any, are identical in both cases. It can be seen from Fig.2 that M varies linearly upto g0H---2 mT with a slope of -1, suggesting that the demagnetization factor N--0. Above a field of 2 mT, M increases less rapidly, subsequently saturating at ~t0H > 6 mT. This behaviour is similar to an ideal Bean superconductor [11], a slab for which the full penetration field, H* = 2 Msaturation - 7 mT. For fields below 2 mT, the field (B) inside the sample is effectively zero suggesting that only at fields well above 2 mT will there be a sizeable field penetration inside the sample. 10
'
,
,
,
',
'
B
0.20 m=
•
B
m
v
• ~:~
O oQ
.=.2 0.10
-
M
~m
0.00
i
0
I
i
10
,
!
20
P 0 H(mT)
Fig. 1 Field induced microwave absorption at 9.9 GHz in the ceramic BSCCO zero field cooled to 77 K. The squares show the measured data and the solid line is a fit to Eqn. (3).
m
If
nlum
m
ii
i
_6
0
2
4
6
n
m
i
8
u
n
10
P0 H(mT)
Fig. 2 Field dependence of dc Magnetization (M) and the induction (B) in the ceramic BSCCO, zero field cooled to 77 K.
Vol. 90, No. 12
FIELD INDUCED MICROWAVE ABSORPTION
IV. D I S C U S S I O N
It is interesting to note that the major part of the increase in p(H) (see Fig.l) occurs in the linear region of the M - H curve (Fig.2), where B = 0. This observation clearly supports the contention that the flux flow model [3], which projects p(H) to be a function of B may not be appropriate to account for the large absorption that occurs at low fields. Additionally, at ~ H > 5 mT, p(H) is found to exhibit saturation while the flux flow model predicts a B 1/2 dependence and hence a monotonic rise in p(H) with H. On the other hand, the RSJ model provides a highly satisfactory qualitative picture [1] for the observed virgin curve, i.e. Eqn (3). The fact that B is zero when most of the power absorption occurs indicates that in the LFMMA phenomenon the important physical quantity is the field at the sample surface and the weak-links located therein. Presumably, the 'H' appearing in Eqn.(3) will thus be the applied field modified by any "demagnetization" corrections. It is argued that these modifiers, if any, can be included in the definition of ~0H0. A further check for the appropriateness of the flux flow or RSJ models was sought by observing the virgin curve at a different microwave frequency. It turns out that at 36 GHz and 77 K, l.t0H0~0.5 mT while a= 0.01. Thus the LFMMA reduces drastically with increasing co. As already noted, the flux flow model does not give saturation at large H and hence no direct comparison is possible. However, at large fields
811
it predicts (AP/PN) to be essentially independent of co, contrary to the observed reduction. A single RSJ gives [1], for a set temperature, P(H) = PN/ [1 +(f(H)/ag)]
(4)
where f(H) is a sample dependent parameter that tends to be a constant as H approaches zero and becomes zero at very large H. From this one can write, in order to compare the experimentally seen frequency dependence, for H >>H0 (AP/PN)=[P(H)-P(O)1/PN ~ 1 / [ l + c a j 2 1
(5)
where c is a constant for a given sample at a set temperature. Thus one expects to see a weaker MMA as co is increased, as is indeed the case. In summary, the facts that i) a major part of the low field microwave absorption occurs when measured B=0, ii) the power absorbed exhibits a saturation at fields above 5 mT, instead of a monotonic increase, and iii) a large drop is observed in the power absorption on increasing the frequency - give satisfactory qualitative evidence in support of the RSJ model and suggest that the flux flow model is not entirely appropriate to explain the low field MMA, at least for the present experiments. Acknowledgement - One of the authors (VSB)
is grateful to the Department of Science and Technology, India for the award of BOYSCAST fellowship and to the University of Maryland for hospitality, and PVP gratefully acknowledges University Grants Commission for the fellowship.
REFERENCES
1. J. S. Ramachandran, M. X. Huang, S. M. Bhagat, K. Kish and S. Tyagi, Physica C 202,151 (1992). 2. M. X. Huang, S. M. Bhagat, A. T. Findikoglu, T. Venkatesan,M. A. Manheimer and S. Tyagi, Physica C 193, 421 (1992). 3. L. Ji, M. S. Rzchowski and M. Tinkham, Phys. Rev. B 42, 4838 (1990). 4. L. Ji, M. S. Rzchowski, N. Anand and M. Tinkham, Phys. Rev, B 47,470 (1993). 5. M. Mahel, M. Darula and S. Benecka, Supercond. Sci. Technol. 6, 112 (1993).
6. A. M. Portis,K. W. Blazey. K. A. Muller and J. G. Bednorz, Europhys. Lett.5, 467 (1988). 7. E. J. Pakulis, and T. Osada, Phys. Rev. B 37, 5940 (1988). 8. A. Dulcic,B. Ravkin, M. Pozek, Europhys. Lett. 10,593 (1989). 9. V. Seshu Bai, S. Ravi, T. Rajasekharan and R. Gopalan, J1. Appl. Phys. 70,4378 (1991). 10. G. Shaw, S. M. Bhagat, N. D. Spencer, J. E. Crow and S. Tyagi, Phys. C 169, 257 (1990). 11. C. P. Bean, Rev.Mod. Phys. 36,31(1964).