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Oscillations in surface resistance with applied magnetic field variation in BSCCO aged superconducting samples
PERGAMON
Solid State Communications 109 (1999) 407–411
Oscillations in surface resistance with applied magnetic field variation in BSCCO aged superconducting samples Pratap Raychaudhuri a,1, V.V. Srinivasu b,2,* a
Department of Physics and Meteorology, Indian Institute of Technology, Kharagpur 721302, India b Solid State Electronics, Tata Institute of Fundamental Research, Bombay 400005, India Received 7 October 1998; accepted 4 November 1998 by H. Akai
Abstract Anomalous oscillations have been observed in surface resistance at 77 K in BSCCO (2212) aged bulk samples in an applied d.c. magnetic field varying from 0 to 1000 Oe. The oscillations show similar behaviour when the surface resistance is measured at different radio frequencies (1.5 and 12 MHz). These oscillations can be explained by considering a mesoscopic network of Josephson Junctions and loops. The observed hysteresis is attributed to flux pinning as well as flux trapping in this network. 䉷 1999 Elsevier Science Ltd. All rights reserved. Keywords: A. High-Tc superconductors; A. Surfaces; A. Magnetic films
1. Introduction Several anomalous behaviours have been reported in radio-frequency and microwave magnetoabsorption in high temperature superconductor (HTS) materials. In all these reports the surface resistance decreased with increasing magnetic field [1–3] instead of increasing. The exact nature of the magnetoabsorption depends critically upon temperature [1], oxygen stoichiometry, history of sample and the superconducting volume fraction, etc. Because of the intrinsic granular nature, HTS oxide ceramic samples can be regarded as a random network of superconducting grains connected by weakly coupled Josephson Junctions. In a single Josephson
* Corresponding author. E-mail: [email protected] 1 Current address: Solid State Electronics, Tata Institute of Fundamental Research, Bombay 400005, India. 2 Current address: Texas Center for Superconductivity, University of Houston, Houston, TX 77204-5932, USA.
Junction the maximum current which can pass through the Junction (Ic(H)) shows a Fraunhofer-like oscillatory pattern with applied d.c. magnetic field. However, in a polycrystalline sample where the number of junctions is very large the overall contribution of currents passing through a network of junctions tend to smear out the oscillatory pattern leaving a gross behaviour characterized by a rapid drop in Ic(H) as a function of magnetic field. However, careful measurements on specially prepared samples revealed such an oscillatory pattern in the transport critical current [4]. These samples were specially prepared to increase the grain size and thus to decrease the number of percolating networks. We report radio-frequency magnetoabsorption measurements on aged BSCCO (2212) bulk samples, which show oscillations in surface resistance [5] as the applied d.c. field is varied from 0 to 1000 Oe. The features in magnetoabsorption which resemble quantum coherence effects in the mesoscopic system are discussed in detail.
0038-1098/99/$ - see front matter 䉷 1999 Elsevier Science Ltd. All rights reserved. PII: S0038-109 8(98)00561-4
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P. Raychaudhuri, V.V. Srinivasu / Solid State Communications 109 (1999) 407–411
Fig. 1. Normalized surface resistance vs magnetic field for freshly prepared BSCCO (2212) samples at 1.5 MHz (at temperature 77 K). The surface resistance increases monotonically with magnetic field.
We wish to emphasize that the oscillations observed by Czyzak [6,7] and Blazey et al. [8] in ceramics and single crystals, respectively, are different from ours and are explained in terms of decoupling of Josephson Junctions alone in ceramics and fluxon nucleation in loops in single crystals. 2. Experimental The Bi2Sr2CaCu2O8⫹x superconducting samples used in this study were prepared by the conventional solid state reaction method. These samples were then degraded by keeping in a moist atmosphere for about 60 h. The surface resistance in an applied d.c. magnetic field was measured on both freshly prepared samples as well as the aged ones using a HelwettPackard Q-meter. The bulk samples were cut in the shape of thin rods (diameter ⬃ 3 mm; length ⬃ 1 cm) and placed inside a cylindrical coil. The samples were dipped in liquid nitrogen and the surface resistance (at 77 K) was measured from changes in inductance and quality factor of the coil. Details of the measurement with the Q-meter are published elsewhere [9]. All measurements were carried out in zero field cooled conditions. 3. Results and discussion In our aged samples of BSCCO (2212) we have
observed oscillations in surface resistance with applied d.c. magnetic field which can be attributed to the interference of currents in junctions and loops in the mesoscopic network. However, here the origin of the mesoscopic network is different from the one studied by Kunold and Pereya [4]. Due to ageing a fraction of the superconducting grains can become normal thus reducing the number of percolating paths available for the current to flow. Moreover, the radio-frequency magnetic field can sense only up to a small depth inside the surface of the sample. The radio-frequency loss will thus come from a limited number (mesoscopic) of percolating networks of Josephson Junctions and loops. When the power of the a.c. field is kept constant Dulcic et al. [10] have shown that the surface resistance (Rs) is related to Ic(H) by Rs Rso = 1 ⫹ h; h ho Ic2
1
where ho and Rso are constants for constant a.c. field power. It is thus expected that the oscillations in Ic(H) should be reflected in the surface resistance curve when the applied magnetic field is varied. As we were primarily interested in the change in surface resistance with applied d.c. magnetic field we plotted the quantity Rsn vs. magnetic field, where Rsn {Rs H ⫺ Rs 0}={Rs H Hmax ⫺ Rs 0}: 2 Fig. 1 shows the typical magnetoabsorption curve and hysteresis in the freshly prepared BSCCO sample
P. Raychaudhuri, V.V. Srinivasu / Solid State Communications 109 (1999) 407–411
409
Fig. 2. Normalized surface resistance vs magnetic field for aged samples of BSCCO (2212) at 1.5 MHz (at temperature 77 K). The surface resistance in both increasing and decreasing magnetic fields shows oscillatory patterns.
at 77 K. The curve shows the ususal features [9–14] of magnetoabsorption where the surface resistance monotonically increases with increasing magnetic field. There is a cross-over between the surface resistance curve at increasing and decreasing field. This cross-over behaviour has been described elsewhere [9]. Fig. 2 shows the magnetoabsorption curve and hysteresis of the aged sample at 77 K at 1.5 MHz.
Here the oscillations in the surface resistance can be clearly seen. The oscillations resemble closely the quantum coherence effects. However, the surface inductance vs. magnetic field curve at this frequency shown in Fig. 3 shows a smooth variation with field. Coffey and Clem have theoretically shown that at sufficiently high frequencies the surface resistance and inductance should follow the same behaviour if the loss comes from the motion of vortices alone [15].
Fig. 3. Normalized surface inductance vs magnetic field for aged sample of BSCCO (2212) at 1.5 MHz (at temperature 77 K). The surface inductance curve does not show any oscillatory pattern.
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P. Raychaudhuri, V.V. Srinivasu / Solid State Communications 109 (1999) 407–411
Fig. 4. Calculated surface resistance vs magnetic field curve for a mesoscopic network of Josephson Junctions and loops, using Eqs. (1) and (3). The curve shows an oscillatory pattern.
One of the authors (P.R.) has earlier shown that this is indeed the case at 1.5 MHz when the measurement is carried out on a fresh BSCCO sample [9]. The fact that there are oscillations in surface resistance vs magnetic field curve whereas the inductance vs magnetic field curve is smooth in our aged BSCCO sample is further evidence that the r.f. loss is not coming from the vortices alone. The Rs vs magnetic field curve shows characteristic oscillatory behaviour and also hysteresis. Hysteresis comes from the trapping of fluxons inside the sample. Also in a decreasing field the surface resistance has a higher value than in an increasing field. It can be explained in the framework of one-level critical state models [16,17] and their application to magneto microwave/r.f. absorption [9]. The quantum oscillations arise from a mesoscopic network of loops and branches connected through Josephson Junctions inside the sample. Kunold and Pereya [4] have calculated the value Jc(H) in a mesoscopic network of Josephson Junctions and loops as a function of field using the expression Jc H
X
Jp
p1;nj
⫹
X p1;nl
sin pFp =Fo pFp =Fo Jl
sin pFpl =Fo cos dl ⫹ pFl =Fo pFpl =Fo 3
where Fo is the flux carried by one fluxon, Fp the flux threading the pth junction, Fpl the flux associated with junction p from which current is coming to lth loop, and Fl is the flux associated with the lth loop. Fig. 4 shows the simulated curve of surface resistance as a function of magnetic field using Eqs. (1) and (3), where the values of Jc(H) were taken from Ref. [4]. The curve clearly shows an oscillatory pattern and qualitatively explains the oscillatory pattern of the experimental curve shown in Fig. 2. As the loss in magnetoabsorption coming from the motion of vortices follows a smooth curve the oscillatory pattern can only be attributed to quantum interference effects coming from Josephson Junctions and loops. As the field is increased the amplitude of Josephson oscillations will become smaller. That is why at high field values these oscillations get masked by the contribution coming from the motion of the vortices. Similar calculations using a single Josephson Junction have been carried out by Czyzak [6]. In the freshly prepared bulk samples the surface resistance curve in decreasing field is lower than in increasing field at low field values. This is due to the establishment of a two-level critical state where the sample consists of strongly superconducting grains (with high Jc) separated by weakly but still superconducting grain boundaries (with low Jc) [9,14]. However, in the aged samples it is natural to infer that the grain boundaries will become normal even at very low values of field. Thus the loss coming
P. Raychaudhuri, V.V. Srinivasu / Solid State Communications 109 (1999) 407–411
from the motion of Abrikosov vortices will follow the single level critical state, where the surface resistance in decreasing field is greater than that in increasing field. 4. Conclusion We have shown that quantum interferences can have observable effects in aged bulk samples of BSCCO (2212) and qualitatively explains the anomalous oscillatory pattern in the surface resistance vs magnetic field curve. Preliminary investigations show similar oscillations in pelletized powder samples of BSCCO. To quantitatively analyse these experimental results, one should know the microstructure of the sample to actually estimate the grain size and number of loops, etc. More experiments on the effects of microstructure on magneto microwave/r.f. absorption are in progress. It might also be interesting to investigate the hysteresis curve in these samples at different temperatures as well as at maximum applied field. Acknowledgements One of the authors (P.R.) would like to thank S.K. Ghatak for suggesting the problem and providing constant encouragement. The authors would also like to thank M.S.R. Rao for illuminating discussions.
411
References [1] S.V. Bhat, V.V. Srinivasu, N. Kumar, Phys. Rev. B44 (1990) 873. [2] V.V. Srinivasu, S.V. Bhat, N. Kumar, Solid State Commun. 89 (1994) 375. [3] W. Braunisch, N. Knauf, V. Kataev, S. Neuhausen, A. Gruitz, A. Kock, B. Roden, D. Khomskii, D. Wohlleben, Phys. Rev. Lett. 68 (1992) 1908. [4] A. Kunold, P. Pereya, Physica C245 (1995) 57. [5] P. Raychaudhuri, V.V. Srinivasu, Proceedings of the DAE Solid State Physics Symposium (India), vol. 38C, 1995, p. 289. [6] B. Czyzak, Physica C243 (1995) 327. [7] B. Czyzak, Phys. Rev. (submitted). [8] K.W. Blazey, A.M. Portis, K.A. Muller, J.G. Bednorz, F. Holtzberg, Physica C56 (1988) 153. [9] P. Raychaudhuri, Superconductor Science and Technology 9 (1996) 447. [10] A. Dulcic, B. Rakvin, M. Pozek, Europhys. Lett. 10 (1989) 593. [11] A.M. Portis, K.W. Blazey, K.A. Muller, J.G. Bednortz, Europhys. Lett. 5 (1988) 467. [12] F.J. Owens, Physica C171 (1991) 25. [13] P. Orlandi, A. Rigamonti, Physica C178 (1991) 197. [14] L. Ji, M.S. Rzchowski, N. Anand, M. Tinkham, Phys. Rev. B47 (1993) 470. [15] M.W. Coffey, J.R. Clem, IEEE Transaction on Magnetics 27 (1991) 2136. [16] C.P. Bean, Phys. Rev. Lett. 8 (1962) 250. [17] P.W. Anderson, Y.B. Kim, Rev. Mod. Phys. 36 (1964) 39.
Solid State Communications 109 (1999) 407–411
Oscillations in surface resistance with applied magnetic field variation in BSCCO aged superconducting samples Pratap Raychaudhuri a,1, V.V. Srinivasu b,2,* a
Department of Physics and Meteorology, Indian Institute of Technology, Kharagpur 721302, India b Solid State Electronics, Tata Institute of Fundamental Research, Bombay 400005, India Received 7 October 1998; accepted 4 November 1998 by H. Akai
Abstract Anomalous oscillations have been observed in surface resistance at 77 K in BSCCO (2212) aged bulk samples in an applied d.c. magnetic field varying from 0 to 1000 Oe. The oscillations show similar behaviour when the surface resistance is measured at different radio frequencies (1.5 and 12 MHz). These oscillations can be explained by considering a mesoscopic network of Josephson Junctions and loops. The observed hysteresis is attributed to flux pinning as well as flux trapping in this network. 䉷 1999 Elsevier Science Ltd. All rights reserved. Keywords: A. High-Tc superconductors; A. Surfaces; A. Magnetic films
1. Introduction Several anomalous behaviours have been reported in radio-frequency and microwave magnetoabsorption in high temperature superconductor (HTS) materials. In all these reports the surface resistance decreased with increasing magnetic field [1–3] instead of increasing. The exact nature of the magnetoabsorption depends critically upon temperature [1], oxygen stoichiometry, history of sample and the superconducting volume fraction, etc. Because of the intrinsic granular nature, HTS oxide ceramic samples can be regarded as a random network of superconducting grains connected by weakly coupled Josephson Junctions. In a single Josephson
* Corresponding author. E-mail: [email protected] 1 Current address: Solid State Electronics, Tata Institute of Fundamental Research, Bombay 400005, India. 2 Current address: Texas Center for Superconductivity, University of Houston, Houston, TX 77204-5932, USA.
Junction the maximum current which can pass through the Junction (Ic(H)) shows a Fraunhofer-like oscillatory pattern with applied d.c. magnetic field. However, in a polycrystalline sample where the number of junctions is very large the overall contribution of currents passing through a network of junctions tend to smear out the oscillatory pattern leaving a gross behaviour characterized by a rapid drop in Ic(H) as a function of magnetic field. However, careful measurements on specially prepared samples revealed such an oscillatory pattern in the transport critical current [4]. These samples were specially prepared to increase the grain size and thus to decrease the number of percolating networks. We report radio-frequency magnetoabsorption measurements on aged BSCCO (2212) bulk samples, which show oscillations in surface resistance [5] as the applied d.c. field is varied from 0 to 1000 Oe. The features in magnetoabsorption which resemble quantum coherence effects in the mesoscopic system are discussed in detail.
0038-1098/99/$ - see front matter 䉷 1999 Elsevier Science Ltd. All rights reserved. PII: S0038-109 8(98)00561-4
408
P. Raychaudhuri, V.V. Srinivasu / Solid State Communications 109 (1999) 407–411
Fig. 1. Normalized surface resistance vs magnetic field for freshly prepared BSCCO (2212) samples at 1.5 MHz (at temperature 77 K). The surface resistance increases monotonically with magnetic field.
We wish to emphasize that the oscillations observed by Czyzak [6,7] and Blazey et al. [8] in ceramics and single crystals, respectively, are different from ours and are explained in terms of decoupling of Josephson Junctions alone in ceramics and fluxon nucleation in loops in single crystals. 2. Experimental The Bi2Sr2CaCu2O8⫹x superconducting samples used in this study were prepared by the conventional solid state reaction method. These samples were then degraded by keeping in a moist atmosphere for about 60 h. The surface resistance in an applied d.c. magnetic field was measured on both freshly prepared samples as well as the aged ones using a HelwettPackard Q-meter. The bulk samples were cut in the shape of thin rods (diameter ⬃ 3 mm; length ⬃ 1 cm) and placed inside a cylindrical coil. The samples were dipped in liquid nitrogen and the surface resistance (at 77 K) was measured from changes in inductance and quality factor of the coil. Details of the measurement with the Q-meter are published elsewhere [9]. All measurements were carried out in zero field cooled conditions. 3. Results and discussion In our aged samples of BSCCO (2212) we have
observed oscillations in surface resistance with applied d.c. magnetic field which can be attributed to the interference of currents in junctions and loops in the mesoscopic network. However, here the origin of the mesoscopic network is different from the one studied by Kunold and Pereya [4]. Due to ageing a fraction of the superconducting grains can become normal thus reducing the number of percolating paths available for the current to flow. Moreover, the radio-frequency magnetic field can sense only up to a small depth inside the surface of the sample. The radio-frequency loss will thus come from a limited number (mesoscopic) of percolating networks of Josephson Junctions and loops. When the power of the a.c. field is kept constant Dulcic et al. [10] have shown that the surface resistance (Rs) is related to Ic(H) by Rs Rso = 1 ⫹ h; h ho Ic2
1
where ho and Rso are constants for constant a.c. field power. It is thus expected that the oscillations in Ic(H) should be reflected in the surface resistance curve when the applied magnetic field is varied. As we were primarily interested in the change in surface resistance with applied d.c. magnetic field we plotted the quantity Rsn vs. magnetic field, where Rsn {Rs H ⫺ Rs 0}={Rs H Hmax ⫺ Rs 0}: 2 Fig. 1 shows the typical magnetoabsorption curve and hysteresis in the freshly prepared BSCCO sample
P. Raychaudhuri, V.V. Srinivasu / Solid State Communications 109 (1999) 407–411
409
Fig. 2. Normalized surface resistance vs magnetic field for aged samples of BSCCO (2212) at 1.5 MHz (at temperature 77 K). The surface resistance in both increasing and decreasing magnetic fields shows oscillatory patterns.
at 77 K. The curve shows the ususal features [9–14] of magnetoabsorption where the surface resistance monotonically increases with increasing magnetic field. There is a cross-over between the surface resistance curve at increasing and decreasing field. This cross-over behaviour has been described elsewhere [9]. Fig. 2 shows the magnetoabsorption curve and hysteresis of the aged sample at 77 K at 1.5 MHz.
Here the oscillations in the surface resistance can be clearly seen. The oscillations resemble closely the quantum coherence effects. However, the surface inductance vs. magnetic field curve at this frequency shown in Fig. 3 shows a smooth variation with field. Coffey and Clem have theoretically shown that at sufficiently high frequencies the surface resistance and inductance should follow the same behaviour if the loss comes from the motion of vortices alone [15].
Fig. 3. Normalized surface inductance vs magnetic field for aged sample of BSCCO (2212) at 1.5 MHz (at temperature 77 K). The surface inductance curve does not show any oscillatory pattern.
410
P. Raychaudhuri, V.V. Srinivasu / Solid State Communications 109 (1999) 407–411
Fig. 4. Calculated surface resistance vs magnetic field curve for a mesoscopic network of Josephson Junctions and loops, using Eqs. (1) and (3). The curve shows an oscillatory pattern.
One of the authors (P.R.) has earlier shown that this is indeed the case at 1.5 MHz when the measurement is carried out on a fresh BSCCO sample [9]. The fact that there are oscillations in surface resistance vs magnetic field curve whereas the inductance vs magnetic field curve is smooth in our aged BSCCO sample is further evidence that the r.f. loss is not coming from the vortices alone. The Rs vs magnetic field curve shows characteristic oscillatory behaviour and also hysteresis. Hysteresis comes from the trapping of fluxons inside the sample. Also in a decreasing field the surface resistance has a higher value than in an increasing field. It can be explained in the framework of one-level critical state models [16,17] and their application to magneto microwave/r.f. absorption [9]. The quantum oscillations arise from a mesoscopic network of loops and branches connected through Josephson Junctions inside the sample. Kunold and Pereya [4] have calculated the value Jc(H) in a mesoscopic network of Josephson Junctions and loops as a function of field using the expression Jc H
X
Jp
p1;nj
⫹
X p1;nl
sin pFp =Fo pFp =Fo Jl
sin pFpl =Fo cos dl ⫹ pFl =Fo pFpl =Fo 3
where Fo is the flux carried by one fluxon, Fp the flux threading the pth junction, Fpl the flux associated with junction p from which current is coming to lth loop, and Fl is the flux associated with the lth loop. Fig. 4 shows the simulated curve of surface resistance as a function of magnetic field using Eqs. (1) and (3), where the values of Jc(H) were taken from Ref. [4]. The curve clearly shows an oscillatory pattern and qualitatively explains the oscillatory pattern of the experimental curve shown in Fig. 2. As the loss in magnetoabsorption coming from the motion of vortices follows a smooth curve the oscillatory pattern can only be attributed to quantum interference effects coming from Josephson Junctions and loops. As the field is increased the amplitude of Josephson oscillations will become smaller. That is why at high field values these oscillations get masked by the contribution coming from the motion of the vortices. Similar calculations using a single Josephson Junction have been carried out by Czyzak [6]. In the freshly prepared bulk samples the surface resistance curve in decreasing field is lower than in increasing field at low field values. This is due to the establishment of a two-level critical state where the sample consists of strongly superconducting grains (with high Jc) separated by weakly but still superconducting grain boundaries (with low Jc) [9,14]. However, in the aged samples it is natural to infer that the grain boundaries will become normal even at very low values of field. Thus the loss coming
P. Raychaudhuri, V.V. Srinivasu / Solid State Communications 109 (1999) 407–411
from the motion of Abrikosov vortices will follow the single level critical state, where the surface resistance in decreasing field is greater than that in increasing field. 4. Conclusion We have shown that quantum interferences can have observable effects in aged bulk samples of BSCCO (2212) and qualitatively explains the anomalous oscillatory pattern in the surface resistance vs magnetic field curve. Preliminary investigations show similar oscillations in pelletized powder samples of BSCCO. To quantitatively analyse these experimental results, one should know the microstructure of the sample to actually estimate the grain size and number of loops, etc. More experiments on the effects of microstructure on magneto microwave/r.f. absorption are in progress. It might also be interesting to investigate the hysteresis curve in these samples at different temperatures as well as at maximum applied field. Acknowledgements One of the authors (P.R.) would like to thank S.K. Ghatak for suggesting the problem and providing constant encouragement. The authors would also like to thank M.S.R. Rao for illuminating discussions.
411
References [1] S.V. Bhat, V.V. Srinivasu, N. Kumar, Phys. Rev. B44 (1990) 873. [2] V.V. Srinivasu, S.V. Bhat, N. Kumar, Solid State Commun. 89 (1994) 375. [3] W. Braunisch, N. Knauf, V. Kataev, S. Neuhausen, A. Gruitz, A. Kock, B. Roden, D. Khomskii, D. Wohlleben, Phys. Rev. Lett. 68 (1992) 1908. [4] A. Kunold, P. Pereya, Physica C245 (1995) 57. [5] P. Raychaudhuri, V.V. Srinivasu, Proceedings of the DAE Solid State Physics Symposium (India), vol. 38C, 1995, p. 289. [6] B. Czyzak, Physica C243 (1995) 327. [7] B. Czyzak, Phys. Rev. (submitted). [8] K.W. Blazey, A.M. Portis, K.A. Muller, J.G. Bednorz, F. Holtzberg, Physica C56 (1988) 153. [9] P. Raychaudhuri, Superconductor Science and Technology 9 (1996) 447. [10] A. Dulcic, B. Rakvin, M. Pozek, Europhys. Lett. 10 (1989) 593. [11] A.M. Portis, K.W. Blazey, K.A. Muller, J.G. Bednortz, Europhys. Lett. 5 (1988) 467. [12] F.J. Owens, Physica C171 (1991) 25. [13] P. Orlandi, A. Rigamonti, Physica C178 (1991) 197. [14] L. Ji, M.S. Rzchowski, N. Anand, M. Tinkham, Phys. Rev. B47 (1993) 470. [15] M.W. Coffey, J.R. Clem, IEEE Transaction on Magnetics 27 (1991) 2136. [16] C.P. Bean, Phys. Rev. Lett. 8 (1962) 250. [17] P.W. Anderson, Y.B. Kim, Rev. Mod. Phys. 36 (1964) 39.