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Flux trapping in high-temperature superconductors determined by microwave absorption
PHYSEA
PhysicaC 201 (1992) 379-385 North-Holland
Flux trapping in high-temperature superconductors determined by microwave absorption B. Czy~ak, J. Stankowski and J. Martinek Institute of Molecular Physics, PolishAcademy of Sciences, Smoluchowskiego 17, 60-179, Poznati, Poland
Received 4 August 1992
Low-field microwaveabsorption has been applied for monitoring magneticflux trapping in a ceramic sample of YBa2Cu306.9 in the presence of a microwavefield. Magnetic field trapping is stronglydependent on the texture of a superconductingsample. On coolingof the sample in a magnetic field, the magnetic flux is observed to reach a saturated value. The observed phenomena are discussed in terms of the model of intergrain Josephsonjunctions where dissipation of energy takes place and is a source of microwave absorption. The proposed method is an important compleme~atto classical methods of magnetization investigation, as it permits studies of the local distribution of magnetic flux trapped in a superconductingsample.
1. Introduction
Recently, many authors involved in high-temperature superconductor investigation have been concerned with the problem of the origin of dissipation processes observed in such superconductors in measurements of magnetization [ 1 ]~ critical current, magnetoresistance [2] and mi~i'owave absorption [ 3,4 ]. The effects of a magnetic field on resistance, as well as on irreversible phenomena observed in measurements of magnetization [5,6 ], were interpreted assuming the model of thermally activated magnetic flux creep. The results of magnetic measurements of YBaCuO thin films were used as the basis for an analytical model of thermally activated flux creep proposed by Hagen et al. [ 7 ]. In th,e work of Zuo et al. [ 8 ] the concept of thermally activated flux creep was discussed and referred to the results of magnetically modulated microwave absorption (MMMA) studies. On the other hand, the properties of granular and single-crystal high-temperature superconductors (HTS) were interpreted in terms of the model proposed by Ambegaokar-Halperin [9 ] where they are treated as a medium of Josephson weak contacts regarded as one effective junction [ 10,11 ]. Tinkham [ 10 ] compared the A - H model predictions with the results of magnetoresistance measurements in single crystals.
Low-field microwave absorption has also been the subject of many works [ 3,4 ]. Its origin, particularly in low magnetic fields, was related to the pinning and depinning of fluxons [ 12,13 ] as well as to fluctuations of superconducting current tunnelling through internal Josephson junctions in ceramic or twinned monocrystal samples. Microwave absorption was also applied fis a method for the detection of the transition to the superconducting state [ 15,16 ], in pressure measurements [ 17 ] and in determination of the local temperature of the Josephson junction system interacting with the microwave field [ 14 ]. Irreversible behaviour of microwave absorption in a magnetic field was commented upon by many authors [ 18,20 ]. Relaxation of microwave absorption (MA) and hysteresis of low-field MA dependent on the rate of magnetic field changes [20] proved difficult to interpret against the results of relaxation of magnetization in strong magnetic fields related to thermally activated flux creep. In low magnetic fields a periodic character of the microwave absorption change was noticed [20], which is also a characteristic behaviour of magnetoresistance and microwave emission changes. Jung et al. proposed the model in which the resistance generated by the flux flow is related to synchronization of internal Josephson junctions induced by the viscous flow of magnetic field vortices [23 ]. How-
0921-4534/92/$05.00 © 1992 Elsevier SciencePublishers B.V. All fights reserved.
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B. Czykak et aL / Flux trapping determined by microwave absorption
ever, the problem of interpreting the dissipative processes observed by different methods in HTS still remains open. Despite the difficulties in referring the results of MA studies to those obtained by other methods and the continuing discussions about the origin of this phenomenon, MA has been widely applied in the investigation of low-field properties of HTS. Recently, Vedeshwar et al. [24 ] reported the application of MA in the investigation of magnetic flux trapping in hafnium-doped YBa2Cu306. 9 ceramics. The results reported by these authors, as well as their conclusions about the inter- and intragrain effects, prompted us to undertake detailed studies of the processes of magnetic flux trapping in a microwave field. Our paper presents the results of experiments in which granular samples of HTS were subjected to cooling in an external magnetic field. The magnetic flux trapping in the presence of a microwave field is discussed in terms of the model in which the trapped flux is monitored by Josephson junctions formed in the ceramics between the superconducting grains. We have confronted our experimental results with those of Vedeshwar et al. [ 24 ] and we have come to the conclusion that they confirm the mechanism of magnetic field trapping in low magnetic field worked out on the basis of classical magnetic measurements.
2. Experimental Single-phase samples o f YBa2Cu306.9 were studied on an EPR SE/X-2543 Spectrometer, RADIOPAN. Sample no. l was a high-quality orthorhombic ceramic sinter of size: c = 11.67 A, b=3.82 A, a = 3 . 8 9 A, obtained according to a previously described procedure [ 18 ]. Sample no.2 was obtained by grinding the sinter to grains of a mean size of 0.07 m m and then pressing them into a pellet. Both samples were shaped as disks of 0. l cm in radius and 0.2 cm in thickness. The identical shape of both samples eliminated the influence of differences in geometry on the flux trapping. Microwave absorption measurements proved that the temperature of transition to the superconducting state was equal to Tc = 92 K and was the same for both samples. However, it should be remembered that sensitive measurements of microwave absorption can only monitor the properties
of Josephson junctions which are in between the sample grains, so the transport properties of the samples may be different. The sample to be studied was placed in a standard microwave resonator TE~o2 and cooled by liquid nitrogen vapour flowing through a quartz dewar. Its temperature was measured by a copper-constantan thermocouple attached to the sample. All measurements were performed at 77 K. The sample was set in the maximum of the magnetic component of the microwave field and an external magnetic field applied perpendicularly to the direction of this magnetic component was generated by Helmholtz coils put in the place of the spectrometer magnet. Second modulation of the external magnetic field of 100 kHz frequency and a few Gauss amplitude was applied. The residual laboratory magnetic field was compensated for by an additional set of Helmholtz coils. The ZFC procedure of cooling the sample to the superconducting state was carried out in a field lower than 0. l G. While carrying out the FC procedure, the direction of the magnetic field in which the sample was cooled was the same as that of the external field in which the registration was conducted. Each time, after the sample had been cooled to 77 K in a given magnetic field, this field was removed and the registration of the MMMA signal started. The MMMA signal was recorded with the magnetic field swept slowly from zero to positive values and then back to zero and to negative values. The intensity of the trapped field BFc was positive, so its sense was the same as that of the first sweep.
3. Results and discussion The changes in the shape of the MMMA signal of a superconducting sample, versus the magnetic field in which the sample was cooled to the superconducting state, were analyzed. In particular, the measurement of the MMMA signal was performed for the cooling procedure in zero external magnetic field Bo-< 0.1 G, the so called ZFC procedure. Under these conditions the recorded MMMA signal was always symmetric, and took the value of zero for zero magnetic field. Because of the application of 100 kHz modulation of the external magnetic field for high enough modulation amplitude, the MMMA signal is
B. Czy~ak et al. / Flux trapping determined by microwave absorption
a derivative of the microwave absorption signal P with respect to the magnetic field, dP/dB. As follows from ref. [26], in granular superconductors microwave absorption takes nonzero values in a wide range of magnetic field intensity, and only for zero external field does it reveal a characteristic deep minimum. A derivative of this minimum observed as an MMMA signal has the phase inverted relative to the Cu 2+ EPR signal recorded in higher magnetic fields. When a superconducting sample has been cooled in an external magnetic field Brc of a few G in intensity, a clearly marked change in the MMMA line shape is observed (fig. 1 ). The whole signal is shifted with respect to the point corresponding to zero magnetic field in the sense of the external magnetic field applied on cooling the sample. The signal is broadened and the width of the signal measured as the peak to peak distance increases. To describe the MMMA line changes dependent on the value of the field in which the sample was cooled to the superconducting state, we introduced the following parameters characterizing the signal shape (fig. 1 ). ABFc stands for the shift of the
d.d.d~(o rb.u nits )
381
MMMA line with respect to the point corresponding to zero magnetic field. The amplitude and the width of the peak to peak signal, denoted by A/pp and ABpp, respectively, were observed to change significantly with increasing external magnetic field. By BR we denote the limit of the external field sweeping in the sense opposite to that of the field applied in the FC procedure. The signal was also observed to change for the three subsequent runs of an external magnetic field (fig. 2 ). In the first stage, having performed the FC procedure, the field OfBFc= 15 G was removed, and the external magnetic field was slowly swept from zero to B = 8 G. In the next stage, the field was swept in reverse to the value of BR = -- 10 G. In the third run, the field was swept from BR= -- 12 G to B--8 G. Figure 3 illustrates the dependence of the shift ABFc on the trapped magnetic field BFC for two samples: no. 1 - a ceramic sinter of YBaCuO; and no. 2 - a ground YBaCuO sinter pressed and formed into a pellet. For a trapped field intensity higher than 25 G, saturation of the ABFc value was observed for both samples. For sample no. 1 the highest value of ABFc was ABFc~x = 8 G, while for sample no. 2 ABFcm~ = 6 G. This difference suggests that for sample no. 2 the amount of trapped magnetic flux has been reduced. This effect is due to a decrease in the number of trap-
Bm=2O d'~t = 0.2 G/s 15OBm = 2GFC -8
-6
-4
-2
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-8
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l d~ (orb.units)
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~ ~ G )
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~
__I I
I
-8 l
IBR=
r
i
I
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-4
i
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I
(O)
,B(O)
BR -12 Fig. 1. The magnetically modulated microwave absorption signal d P / d B in magnetic field for zero-field cooling and 15 G field cooling. Modulation amplitude Bin---2 G and sweep rate 0.2 G / s have been used. Characteristic parameters of the line-shape are indicated (see text).
I
I
-8
I
-t~
0
~
l
8
B(G)
Fig. 2. Three signals of magnetically modulated microwave absorption for field cooling procedure in a field of 15 G for different sweeps o f magnetic field.
B. Czy~ak et a L I Flux trapping determined by microwave absorption
382
intergranulor Josephson junction
ABFc(G) 8
sample
I
6
~
trapped flux
/
4 2
0
I
J
i
I
i
5
10
15
20
25
I
BFC(GI
Fig. 3. The ABFc shift of the dP/dB signal, with respect to zero magnetic field as a measure of flux trapping, vs. BFc field applied in the field cooling experiment, for samples no. 1 and no. 2. The experimental results are fitted according to eq. (2).
ping centres. On grinding, the grains are crushed along or at inhomogeneities, so that the areas which in large grain materials are the potential trapping centres, after grinding appear on the surface of smaller grains and lose the properties of pinning centres. The MMMA signal shift, denoted as ABFc, is a consequence of a magnetic flux trapping which takes place on cooling a superconducting sample to a temperature lower then its critical temperature in an external magnetic field BFc. The trapping may occur on any defects of the sample. Local changes in coherence length ~, penetration depth 2, or critical field He, caused by the presence of impurities, grain borders, twinnings and other defects, entail changes in free energy per unit length of the magnetic field flux line. In consequence, certain sites of the fluxon may prove metastable. As a result of freezing a stable magnetic flux at the trapping centres, one can expect a sample of a typeII superconductor to reveal a permanent magnetic field. Because of the mixed structure of vortices in the grains, the lines of this field outside the grains will have approximately the shape of loops (fig. 4). Low-field microwave absorption by superconductors takes place in Josephson junctions being formed on inhomogeneities of the material and on contact points of the grains. In contradistinction to the trapping centre where magnetic flux is permanently frozen, magnetic field in the form of flux quanta may enter or leave a system with Josephson junctions.
~'J ~
pinning
~I
t e n ters
superconducting groin Fig. 4. The lines of magnetic flux frozen in a superconducting granular sample after removal of the magnetic field in which the sample was cooled to the superconducting state. The intergrain Josephson junction monitoring flux trapping is marked.
Microwave absorption of a system with Josephson junctions reveals a deep minimum in zero external magnetic field. When magnetic flux is frozen on, e.g., intragrain inhomogeneities of the studied material, after the removal of the magnetic field applied in the FC procedure, the intergrain system of Josephson junctions monitors the component of the magnetic flux opposite to that of the flux frozen inside grains (fig. 4). In consequence, the sense of the vector of magnetic induction acting on the intergrain Josephson junctions is contrary to that of the trapped field. For a given junction to reach the minimum absorption, the local magnetic field of this junction should be zero. The external magnetic field applied on recording the absorption signal, of the same sense and direction as the trapped field, compensates for the local field experienced by a given junction. This is why the minimum absorption is recorded for the external field described by ABFc. This parameter, whose changes versus the trapped field are shown in fig. 3, corresponds to the mean value of a local magnetic field acting on the system of Josephson junctions and originating from the trapped flux. Thus the material of finer grains contains a lower number of defects acting as trapping centres. The observed effects can be described by the following equation: ~Brc = ~Cm~x
( 1 --e =B~/B~) ,
where
is the maximum value of the mean
z~knFcmax
383
B. Czykak et al. / Flux trapping determined by microwaveabsorption
local field in the sample, and Ba represents the induction'characterizing the pinning centres and is independent of the sample refinement. For sample no. l ABFcmax= 8.0 G, while for sample no. 2 ABFcm,~= 6 G, as with decreasing number of pinning centres the flux frozen ~n a granular sample decreases. Figures 5 and 6 present dependences of the parameters of MMMA line shape versus the field in which sample no. l was cooled to the suPerconducting state. The shape of the microwave absorption signal for a system of Josephson junctions in a magnetic field of intensity B can be described by ( 1 - (sin B / B ) 2). If a magnetic flux is frozen in a material with Josephson junctions, then a strongly inhomogeneous field appears in it. The observed broadening of the MMMA signal illustrated in fig. 5 is related to the fact that by freezing the sample in a greater magnetic field we get a greater distribution of the local field values. In consequence, the signal, which is a superposition of absorption signals from individual groups of Josephson junctions placed in different local magnetic fields, will become more and more broadened. The parameter ABpp can be treated as a measure of inhomogeneities of the magnetic field in the studied material. The broadening of the MMMA line is accompanied by a decrease in intensity of the d P / d B derivative signal A/pp (fig. 6). On the basis of these two parameters, ABpp and A/pp, and employing the expressions describing the intensity of the Lorentzshaped absorption line in terms of the parameters obtained from its derivative, we can estimate the in-
12!_~Bpp(o) .9//
10
/..t7
/0 /
8
/
7
/o / J
4 -° / 2 0
5
10
I
I
I
15
20
25
I
BFC(O)
Fig. 5. The peak-to-peakline-width AB~ of the microwaveabsorption dP/dB signal as a function of BFc field. The dashed line is a guide to the eye only.
~ I pp(arb.units)
-\ \
\
ox ---o-- ~ ..o_ _ D
0
5
10
15 BFc(G)
Fig. 6. The dP/dB signal amplitude vs. the BEcfield. The dashed line is a guide to the eye only.
AA
(orb.units)
1 0
I
1
1
5
I0
15
[
2 0 BFC(O)
Fig. 7. The integralarea of the absorptionsignalvs. B field values. tegral intensity of the real absorption signal. We shall use the expression for integral area: zxA--- A/pp(zXBpp) 2 ,
where &dpp is the amplitude of the d P / d B derivative and ABpp is the width of the MMMA signal. The integral area of the absorption curve during the process studied, does not change as a function of BFC (with BFC), ~ (BFc)= const, and the small deviation for low BFC illustrated in fig. 7 is related to the fluctuations appearing for low magnetic fields. The signal whose derivative we observe is a superposition of all absorption signals due to groups of Josephson junctions in different local fields. During our experiment the distribution of the values of local field intensities changes, which entails changes in the line shape, but total absorption remains the same. In the next step we examined the influence of the range of the field swept in the direction opposite to that of the frozen field on the recorded MMMA signal. A change in BR, defined as the maximum field reached in this direction of sweeping, was found to affect the recorded signal. The line was shifted towards the zero-field value, which was described as a change in the value of /~kBFc (fig. 8). At the same time, no essential
384
B. Czykak et al. / Flux trapping determined by microwave absorption
We suggest that a shift of the MMMA signal relative to the zero magnetic field observed after the FC procedure with the field swept in both directions should be a much better measure of magnetic flux trapping.
bBFc(G) 6 ~ O~
2 0
I
I
L
3
6
9
L
12 BR(,G)
Fig. 8. The shift of the dP/dB signal as a function of reversal magnetic field, BR, applied in the experiment. changes in the parameters describing the width and intensity of the MMMA line were observed. As follows from the above, the application of the field of direction opposite to that of the trapped field brings about a decrease in the value of the mean local magnetic field in the sample but does not cause any essential changes in the distribution of the local field values with respect to the mean value. The results reported by Vedeshwar et al. [ 24 ], in particular for very low magnetic fields, raise some doubts because of the experimental technique the authors used. Our experiment was carried out in a magnetic field swept from - B o to +Bo through the zero value, while in experiments reported by Vedeshwar the magnetic field was swept only in one direction. The parameters of the MMMA signal, such as the height of the signal, the peak position, that they report seem to us difficult to interpret without the data from a complete experiment with the field swept in two directions, because of essential changes in the shape of the MMMA signal due to the flux trapping. For example, the increase in the signal height they report for the flux trapping in a field lower than 10 G can be easily explained taking into account their definition of the signal height. For ZFC, when the microwave absorption signal is symmetric with respect to the zero magnetic field, the signal height is half of a peak to peak amplitude. For FC, the height of the signal is difficult to define because of the shift of the MMMA signal relative to the zero magnetic field. The increase in the signal height in fields lower than 10 G may be simply a consequence of the shift relative to the zero field. It is equally difficult to interpret the parameter Vedeshwar uses to describe the area of the loop AA and treats as a measure of flux trapping. Assuming this definition, the amount of the trapped flux diminishes with increasing cooling field.
4. Conclusions In this work we have proposed a new application of microwave absorption as a method for the detection of magnetic flux trapping in granular superconducting samples. This method permits monitoring of the magnetic flux trapping in a low magnetic field in the presence of a microwave field. A decrease in flux trapping has been observed after the sample has been powdered and pressed to form a pellet. The observations we have made allow us to draw the following conclusions: ( 1 ) The shift of the MMMA signal depends on the amount of magnetic flux trapped in the ceramic sample. (2) The nature of the trapping centres does not depend on the refinement of the sample but is an intrinsic property of the material. (3) The shape of the MMMA signal does not depend on the number of trapping centres. A change in the properties of trapping centres, e.g. induced by neutron irradiation, is expected to affect the parameters of the proposed semi-empirical expression describing flux trapping in low magnetic field monitored by microwave absorption. The applied powdering and pressing of the sample did not change the nature of the trapping centres but only decreased their number.
References [ 1] C.P. Poole, T. Datta and H.A. Farach, Copper Oxide Superconductors (John Wiley, New York, 1988) and references therein. [2] K.Y. Chen and Y.J. Qian, PhysicaC 159 (1989 ) 131. [3] R. Durny, I. Hautala, S. Ducharme, B. Lee, O.G. Symko, P.C. Taylor,D.I. Zhengand I.A. Xu, Phys. Rev. B 36 (1987) 2361. [4] J. Stankowki, P.K. Kahol, N.S. Dalai and J.S. Moodera, Phys. Rev. B 36 (1987) 7126. [5]Y. Yeshurun and A.P. Malozemoff, Phys. Rev. Lett. 60 (1988) 2202.
B. Czykak et al. / Flux trapping determined by microwave absorption [6]T.T.M. Palstra, B. Batlogg, L.F. Schneemeyer and J.V. Waszczak, Phys. Rev. Lett. 61 (1988) 1662. [7] C.W. Hagen, R.P. Griessen and E. Salomons, Physica C 157 (1989) 199. [8] F. Zuo, M.B. Salamon, E.D. Bukowski, J.P. Rice and D.M. Ginsberg, Phys. Rev. B 41 (1990) 6600. [9] V. Ambegaokar and B.I. Halperin, Phys. Rev. Lett. 22 (1969) 1364. [10] M. Tinkham, Phys. Rev. Lett. 61 (1988) 1658. [ l 1 ] A.C. Wright, K. Zhang and A. Erbil, Phys. Rev. B 44 ( 1991 ) 809. [ 12] K.W. Blazey, A.M. Portis and J.G. Bednorz, Solid State Commun. 65 (1988) 1153. [ 13 ] M. Warden, M. Stadler, G. Stefanicki, A.M. Portis and F. Waldner, J. Appl. Phys. 64 (1988) 5800. [ 14 ] J. Stankowski, B. Czy~ak and J. Martinek, Phys. Rev. B 42 (1990) 10255. [ 15 ] K. Khachaturyan, E.R. Weber, P. Tejeder, A.M. Stacy and A.M. Portis, Phys. Rev. B 36 (1987) 8309. [ 16 ] B. Czy~,ak, T. Zuk and J. Stankowski, Acta Phys. Polon. A 78 (1990) 769. [ 17 ] J. Stankowski, B. Czy~ak, M. Krupski, J. Baszy6ski and T. Datta (1989).
385
[18]A. Dulcic, B. Rakvin and M. Pozek, Europhys. Lett. 10 (1989) 593. [19]A. Gould, M. Huang, S.M. Bhagat and S. Tyagi, J. Appl. Phys. 69 ( 1991 ) 4880. [20] B. Czy~,ak and J. Stankowski, Phys. Status Solidi B 160 (1991) 219. [ 2 l i P . Erhardt, J.E. Drumheller, B. Senning, S. Mini, L. Fransioli, E. Kaldis, S. Rusiecki and F. Waldner, Proc. Congr. Ampere, Stuttgart 1990, eds. M. Mehring, J.V. von Schutz and H.C. Wolf (Springer, Berlin, 1990) p. 275. [22] J.R. Fraser, T.R. Finlayson and T.F. Smith, Physica C 159 (1989) 70. [ 23 ] G. Jung, J. Konopka and B. Solek, Physica C 180 ( 1991 ) 192. [ 24 ] A.G. Vedeshwar, H.D. Bist, S.K. Agarwal and A.V. Narlikar, Phys. Rev. B 41 (1990) 11294. [25] M.A.-K. Mohammed and J. Jung, Phys. Rev. B 44 ( 1991 ) 4512. [26] A.M. Stewart, Supercond. Sci. Technol. 4 ( 1991 ) 32. [27] T. Xia and D. Stroud, Phys. Rev. B 39 (1989) 4792. [28] L. Krusin-Elbaum, A.P. Malozemoff, Y. Yeshurun, D.C. Cronemeyer and F. Holtzberg, Phys. Rev. B 39 ( 1989 ) 2936.
PhysicaC 201 (1992) 379-385 North-Holland
Flux trapping in high-temperature superconductors determined by microwave absorption B. Czy~ak, J. Stankowski and J. Martinek Institute of Molecular Physics, PolishAcademy of Sciences, Smoluchowskiego 17, 60-179, Poznati, Poland
Received 4 August 1992
Low-field microwaveabsorption has been applied for monitoring magneticflux trapping in a ceramic sample of YBa2Cu306.9 in the presence of a microwavefield. Magnetic field trapping is stronglydependent on the texture of a superconductingsample. On coolingof the sample in a magnetic field, the magnetic flux is observed to reach a saturated value. The observed phenomena are discussed in terms of the model of intergrain Josephsonjunctions where dissipation of energy takes place and is a source of microwave absorption. The proposed method is an important compleme~atto classical methods of magnetization investigation, as it permits studies of the local distribution of magnetic flux trapped in a superconductingsample.
1. Introduction
Recently, many authors involved in high-temperature superconductor investigation have been concerned with the problem of the origin of dissipation processes observed in such superconductors in measurements of magnetization [ 1 ]~ critical current, magnetoresistance [2] and mi~i'owave absorption [ 3,4 ]. The effects of a magnetic field on resistance, as well as on irreversible phenomena observed in measurements of magnetization [5,6 ], were interpreted assuming the model of thermally activated magnetic flux creep. The results of magnetic measurements of YBaCuO thin films were used as the basis for an analytical model of thermally activated flux creep proposed by Hagen et al. [ 7 ]. In th,e work of Zuo et al. [ 8 ] the concept of thermally activated flux creep was discussed and referred to the results of magnetically modulated microwave absorption (MMMA) studies. On the other hand, the properties of granular and single-crystal high-temperature superconductors (HTS) were interpreted in terms of the model proposed by Ambegaokar-Halperin [9 ] where they are treated as a medium of Josephson weak contacts regarded as one effective junction [ 10,11 ]. Tinkham [ 10 ] compared the A - H model predictions with the results of magnetoresistance measurements in single crystals.
Low-field microwave absorption has also been the subject of many works [ 3,4 ]. Its origin, particularly in low magnetic fields, was related to the pinning and depinning of fluxons [ 12,13 ] as well as to fluctuations of superconducting current tunnelling through internal Josephson junctions in ceramic or twinned monocrystal samples. Microwave absorption was also applied fis a method for the detection of the transition to the superconducting state [ 15,16 ], in pressure measurements [ 17 ] and in determination of the local temperature of the Josephson junction system interacting with the microwave field [ 14 ]. Irreversible behaviour of microwave absorption in a magnetic field was commented upon by many authors [ 18,20 ]. Relaxation of microwave absorption (MA) and hysteresis of low-field MA dependent on the rate of magnetic field changes [20] proved difficult to interpret against the results of relaxation of magnetization in strong magnetic fields related to thermally activated flux creep. In low magnetic fields a periodic character of the microwave absorption change was noticed [20], which is also a characteristic behaviour of magnetoresistance and microwave emission changes. Jung et al. proposed the model in which the resistance generated by the flux flow is related to synchronization of internal Josephson junctions induced by the viscous flow of magnetic field vortices [23 ]. How-
0921-4534/92/$05.00 © 1992 Elsevier SciencePublishers B.V. All fights reserved.
p
380
B. Czykak et aL / Flux trapping determined by microwave absorption
ever, the problem of interpreting the dissipative processes observed by different methods in HTS still remains open. Despite the difficulties in referring the results of MA studies to those obtained by other methods and the continuing discussions about the origin of this phenomenon, MA has been widely applied in the investigation of low-field properties of HTS. Recently, Vedeshwar et al. [24 ] reported the application of MA in the investigation of magnetic flux trapping in hafnium-doped YBa2Cu306. 9 ceramics. The results reported by these authors, as well as their conclusions about the inter- and intragrain effects, prompted us to undertake detailed studies of the processes of magnetic flux trapping in a microwave field. Our paper presents the results of experiments in which granular samples of HTS were subjected to cooling in an external magnetic field. The magnetic flux trapping in the presence of a microwave field is discussed in terms of the model in which the trapped flux is monitored by Josephson junctions formed in the ceramics between the superconducting grains. We have confronted our experimental results with those of Vedeshwar et al. [ 24 ] and we have come to the conclusion that they confirm the mechanism of magnetic field trapping in low magnetic field worked out on the basis of classical magnetic measurements.
2. Experimental Single-phase samples o f YBa2Cu306.9 were studied on an EPR SE/X-2543 Spectrometer, RADIOPAN. Sample no. l was a high-quality orthorhombic ceramic sinter of size: c = 11.67 A, b=3.82 A, a = 3 . 8 9 A, obtained according to a previously described procedure [ 18 ]. Sample no.2 was obtained by grinding the sinter to grains of a mean size of 0.07 m m and then pressing them into a pellet. Both samples were shaped as disks of 0. l cm in radius and 0.2 cm in thickness. The identical shape of both samples eliminated the influence of differences in geometry on the flux trapping. Microwave absorption measurements proved that the temperature of transition to the superconducting state was equal to Tc = 92 K and was the same for both samples. However, it should be remembered that sensitive measurements of microwave absorption can only monitor the properties
of Josephson junctions which are in between the sample grains, so the transport properties of the samples may be different. The sample to be studied was placed in a standard microwave resonator TE~o2 and cooled by liquid nitrogen vapour flowing through a quartz dewar. Its temperature was measured by a copper-constantan thermocouple attached to the sample. All measurements were performed at 77 K. The sample was set in the maximum of the magnetic component of the microwave field and an external magnetic field applied perpendicularly to the direction of this magnetic component was generated by Helmholtz coils put in the place of the spectrometer magnet. Second modulation of the external magnetic field of 100 kHz frequency and a few Gauss amplitude was applied. The residual laboratory magnetic field was compensated for by an additional set of Helmholtz coils. The ZFC procedure of cooling the sample to the superconducting state was carried out in a field lower than 0. l G. While carrying out the FC procedure, the direction of the magnetic field in which the sample was cooled was the same as that of the external field in which the registration was conducted. Each time, after the sample had been cooled to 77 K in a given magnetic field, this field was removed and the registration of the MMMA signal started. The MMMA signal was recorded with the magnetic field swept slowly from zero to positive values and then back to zero and to negative values. The intensity of the trapped field BFc was positive, so its sense was the same as that of the first sweep.
3. Results and discussion The changes in the shape of the MMMA signal of a superconducting sample, versus the magnetic field in which the sample was cooled to the superconducting state, were analyzed. In particular, the measurement of the MMMA signal was performed for the cooling procedure in zero external magnetic field Bo-< 0.1 G, the so called ZFC procedure. Under these conditions the recorded MMMA signal was always symmetric, and took the value of zero for zero magnetic field. Because of the application of 100 kHz modulation of the external magnetic field for high enough modulation amplitude, the MMMA signal is
B. Czy~ak et al. / Flux trapping determined by microwave absorption
a derivative of the microwave absorption signal P with respect to the magnetic field, dP/dB. As follows from ref. [26], in granular superconductors microwave absorption takes nonzero values in a wide range of magnetic field intensity, and only for zero external field does it reveal a characteristic deep minimum. A derivative of this minimum observed as an MMMA signal has the phase inverted relative to the Cu 2+ EPR signal recorded in higher magnetic fields. When a superconducting sample has been cooled in an external magnetic field Brc of a few G in intensity, a clearly marked change in the MMMA line shape is observed (fig. 1 ). The whole signal is shifted with respect to the point corresponding to zero magnetic field in the sense of the external magnetic field applied on cooling the sample. The signal is broadened and the width of the signal measured as the peak to peak distance increases. To describe the MMMA line changes dependent on the value of the field in which the sample was cooled to the superconducting state, we introduced the following parameters characterizing the signal shape (fig. 1 ). ABFc stands for the shift of the
d.d.d~(o rb.u nits )
381
MMMA line with respect to the point corresponding to zero magnetic field. The amplitude and the width of the peak to peak signal, denoted by A/pp and ABpp, respectively, were observed to change significantly with increasing external magnetic field. By BR we denote the limit of the external field sweeping in the sense opposite to that of the field applied in the FC procedure. The signal was also observed to change for the three subsequent runs of an external magnetic field (fig. 2 ). In the first stage, having performed the FC procedure, the field OfBFc= 15 G was removed, and the external magnetic field was slowly swept from zero to B = 8 G. In the next stage, the field was swept in reverse to the value of BR = -- 10 G. In the third run, the field was swept from BR= -- 12 G to B--8 G. Figure 3 illustrates the dependence of the shift ABFc on the trapped magnetic field BFC for two samples: no. 1 - a ceramic sinter of YBaCuO; and no. 2 - a ground YBaCuO sinter pressed and formed into a pellet. For a trapped field intensity higher than 25 G, saturation of the ABFc value was observed for both samples. For sample no. 1 the highest value of ABFc was ABFc~x = 8 G, while for sample no. 2 ABFcm~ = 6 G. This difference suggests that for sample no. 2 the amount of trapped magnetic flux has been reduced. This effect is due to a decrease in the number of trap-
Bm=2O d'~t = 0.2 G/s 15OBm = 2GFC -8
-6
-4
-2
dd__~(orb.units)
B(G)
dip
I
I
-8
I -4
l d~ (orb.units)
15G FC
0
I 4
~ ~ G )
4
~
__I I
I
-8 l
IBR=
r
i
I
J
-4
i
I
I
I
(O)
,B(O)
BR -12 Fig. 1. The magnetically modulated microwave absorption signal d P / d B in magnetic field for zero-field cooling and 15 G field cooling. Modulation amplitude Bin---2 G and sweep rate 0.2 G / s have been used. Characteristic parameters of the line-shape are indicated (see text).
I
I
-8
I
-t~
0
~
l
8
B(G)
Fig. 2. Three signals of magnetically modulated microwave absorption for field cooling procedure in a field of 15 G for different sweeps o f magnetic field.
B. Czy~ak et a L I Flux trapping determined by microwave absorption
382
intergranulor Josephson junction
ABFc(G) 8
sample
I
6
~
trapped flux
/
4 2
0
I
J
i
I
i
5
10
15
20
25
I
BFC(GI
Fig. 3. The ABFc shift of the dP/dB signal, with respect to zero magnetic field as a measure of flux trapping, vs. BFc field applied in the field cooling experiment, for samples no. 1 and no. 2. The experimental results are fitted according to eq. (2).
ping centres. On grinding, the grains are crushed along or at inhomogeneities, so that the areas which in large grain materials are the potential trapping centres, after grinding appear on the surface of smaller grains and lose the properties of pinning centres. The MMMA signal shift, denoted as ABFc, is a consequence of a magnetic flux trapping which takes place on cooling a superconducting sample to a temperature lower then its critical temperature in an external magnetic field BFc. The trapping may occur on any defects of the sample. Local changes in coherence length ~, penetration depth 2, or critical field He, caused by the presence of impurities, grain borders, twinnings and other defects, entail changes in free energy per unit length of the magnetic field flux line. In consequence, certain sites of the fluxon may prove metastable. As a result of freezing a stable magnetic flux at the trapping centres, one can expect a sample of a typeII superconductor to reveal a permanent magnetic field. Because of the mixed structure of vortices in the grains, the lines of this field outside the grains will have approximately the shape of loops (fig. 4). Low-field microwave absorption by superconductors takes place in Josephson junctions being formed on inhomogeneities of the material and on contact points of the grains. In contradistinction to the trapping centre where magnetic flux is permanently frozen, magnetic field in the form of flux quanta may enter or leave a system with Josephson junctions.
~'J ~
pinning
~I
t e n ters
superconducting groin Fig. 4. The lines of magnetic flux frozen in a superconducting granular sample after removal of the magnetic field in which the sample was cooled to the superconducting state. The intergrain Josephson junction monitoring flux trapping is marked.
Microwave absorption of a system with Josephson junctions reveals a deep minimum in zero external magnetic field. When magnetic flux is frozen on, e.g., intragrain inhomogeneities of the studied material, after the removal of the magnetic field applied in the FC procedure, the intergrain system of Josephson junctions monitors the component of the magnetic flux opposite to that of the flux frozen inside grains (fig. 4). In consequence, the sense of the vector of magnetic induction acting on the intergrain Josephson junctions is contrary to that of the trapped field. For a given junction to reach the minimum absorption, the local magnetic field of this junction should be zero. The external magnetic field applied on recording the absorption signal, of the same sense and direction as the trapped field, compensates for the local field experienced by a given junction. This is why the minimum absorption is recorded for the external field described by ABFc. This parameter, whose changes versus the trapped field are shown in fig. 3, corresponds to the mean value of a local magnetic field acting on the system of Josephson junctions and originating from the trapped flux. Thus the material of finer grains contains a lower number of defects acting as trapping centres. The observed effects can be described by the following equation: ~Brc = ~Cm~x
( 1 --e =B~/B~) ,
where
is the maximum value of the mean
z~knFcmax
383
B. Czykak et al. / Flux trapping determined by microwaveabsorption
local field in the sample, and Ba represents the induction'characterizing the pinning centres and is independent of the sample refinement. For sample no. l ABFcmax= 8.0 G, while for sample no. 2 ABFcm,~= 6 G, as with decreasing number of pinning centres the flux frozen ~n a granular sample decreases. Figures 5 and 6 present dependences of the parameters of MMMA line shape versus the field in which sample no. l was cooled to the suPerconducting state. The shape of the microwave absorption signal for a system of Josephson junctions in a magnetic field of intensity B can be described by ( 1 - (sin B / B ) 2). If a magnetic flux is frozen in a material with Josephson junctions, then a strongly inhomogeneous field appears in it. The observed broadening of the MMMA signal illustrated in fig. 5 is related to the fact that by freezing the sample in a greater magnetic field we get a greater distribution of the local field values. In consequence, the signal, which is a superposition of absorption signals from individual groups of Josephson junctions placed in different local magnetic fields, will become more and more broadened. The parameter ABpp can be treated as a measure of inhomogeneities of the magnetic field in the studied material. The broadening of the MMMA line is accompanied by a decrease in intensity of the d P / d B derivative signal A/pp (fig. 6). On the basis of these two parameters, ABpp and A/pp, and employing the expressions describing the intensity of the Lorentzshaped absorption line in terms of the parameters obtained from its derivative, we can estimate the in-
12!_~Bpp(o) .9//
10
/..t7
/0 /
8
/
7
/o / J
4 -° / 2 0
5
10
I
I
I
15
20
25
I
BFC(O)
Fig. 5. The peak-to-peakline-width AB~ of the microwaveabsorption dP/dB signal as a function of BFc field. The dashed line is a guide to the eye only.
~ I pp(arb.units)
-\ \
\
ox ---o-- ~ ..o_ _ D
0
5
10
15 BFc(G)
Fig. 6. The dP/dB signal amplitude vs. the BEcfield. The dashed line is a guide to the eye only.
AA
(orb.units)
1 0
I
1
1
5
I0
15
[
2 0 BFC(O)
Fig. 7. The integralarea of the absorptionsignalvs. B field values. tegral intensity of the real absorption signal. We shall use the expression for integral area: zxA--- A/pp(zXBpp) 2 ,
where &dpp is the amplitude of the d P / d B derivative and ABpp is the width of the MMMA signal. The integral area of the absorption curve during the process studied, does not change as a function of BFC (with BFC), ~ (BFc)= const, and the small deviation for low BFC illustrated in fig. 7 is related to the fluctuations appearing for low magnetic fields. The signal whose derivative we observe is a superposition of all absorption signals due to groups of Josephson junctions in different local fields. During our experiment the distribution of the values of local field intensities changes, which entails changes in the line shape, but total absorption remains the same. In the next step we examined the influence of the range of the field swept in the direction opposite to that of the frozen field on the recorded MMMA signal. A change in BR, defined as the maximum field reached in this direction of sweeping, was found to affect the recorded signal. The line was shifted towards the zero-field value, which was described as a change in the value of /~kBFc (fig. 8). At the same time, no essential
384
B. Czykak et al. / Flux trapping determined by microwave absorption
We suggest that a shift of the MMMA signal relative to the zero magnetic field observed after the FC procedure with the field swept in both directions should be a much better measure of magnetic flux trapping.
bBFc(G) 6 ~ O~
2 0
I
I
L
3
6
9
L
12 BR(,G)
Fig. 8. The shift of the dP/dB signal as a function of reversal magnetic field, BR, applied in the experiment. changes in the parameters describing the width and intensity of the MMMA line were observed. As follows from the above, the application of the field of direction opposite to that of the trapped field brings about a decrease in the value of the mean local magnetic field in the sample but does not cause any essential changes in the distribution of the local field values with respect to the mean value. The results reported by Vedeshwar et al. [ 24 ], in particular for very low magnetic fields, raise some doubts because of the experimental technique the authors used. Our experiment was carried out in a magnetic field swept from - B o to +Bo through the zero value, while in experiments reported by Vedeshwar the magnetic field was swept only in one direction. The parameters of the MMMA signal, such as the height of the signal, the peak position, that they report seem to us difficult to interpret without the data from a complete experiment with the field swept in two directions, because of essential changes in the shape of the MMMA signal due to the flux trapping. For example, the increase in the signal height they report for the flux trapping in a field lower than 10 G can be easily explained taking into account their definition of the signal height. For ZFC, when the microwave absorption signal is symmetric with respect to the zero magnetic field, the signal height is half of a peak to peak amplitude. For FC, the height of the signal is difficult to define because of the shift of the MMMA signal relative to the zero magnetic field. The increase in the signal height in fields lower than 10 G may be simply a consequence of the shift relative to the zero field. It is equally difficult to interpret the parameter Vedeshwar uses to describe the area of the loop AA and treats as a measure of flux trapping. Assuming this definition, the amount of the trapped flux diminishes with increasing cooling field.
4. Conclusions In this work we have proposed a new application of microwave absorption as a method for the detection of magnetic flux trapping in granular superconducting samples. This method permits monitoring of the magnetic flux trapping in a low magnetic field in the presence of a microwave field. A decrease in flux trapping has been observed after the sample has been powdered and pressed to form a pellet. The observations we have made allow us to draw the following conclusions: ( 1 ) The shift of the MMMA signal depends on the amount of magnetic flux trapped in the ceramic sample. (2) The nature of the trapping centres does not depend on the refinement of the sample but is an intrinsic property of the material. (3) The shape of the MMMA signal does not depend on the number of trapping centres. A change in the properties of trapping centres, e.g. induced by neutron irradiation, is expected to affect the parameters of the proposed semi-empirical expression describing flux trapping in low magnetic field monitored by microwave absorption. The applied powdering and pressing of the sample did not change the nature of the trapping centres but only decreased their number.
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