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Quantitative analysis of the ZFC magnetization in low magnetic fields in the YBa2Cu3O7-x system
PHYSICA Physica C 233 (1994) 55-60
ELSEVIER
Quantitative analysis of the ZFC magnetization in low magnetic fields in the YBazCu307_xsystem Bokhimi *, A. Morales Institute of Physics, National University of Mexico (UNAM), a.p. 20-364, 01000 M~xico, D.F., Mexico
Received 28 March 1994;revised manuscript received 8 September 1994
Abstract
We present a systematic study of the ZFC magnetization as a function of temperature and magnetic field for polycrystalline superconducting samples of the YBCO system. The study is done in magnetic fields lower than 1560e. We have found that the ZFC magnetization can be quantified using the basic function 1- t 2/~-'~), with t the reduced temperature and a between 0.0 and 1.0 depending on the magnetic field. This quantification allows one to determine the magnetic field at which magnetic flux penetrates into the sample and to follow the temperature dependence of the magnetization produced by the generated vortices. For a given magnetic field the temperature dependence of the ZFC magnetization is similar to that observed in the FC remanent magnetization, suggestingthe possible existence of entities built of local arrangements of superconducting electrons, which are the origin of the diamagnetic response.
1. Introduction
Field-cooling (FC) and zero-field-cooling (ZFC) magnetization as a function of temperature are two of the most measured properties in high-T¢ superconductors [ 1,2 ], which are obtained for a wide range of magnetic field intensities. The potential technological applications of high-T~ superconductors have caused that most of these magnetic properties have been studied at relative high magnetic intensities. However, when the ZFC magnetization is measured at high magnetic fields magnetic flux penetrates into the sample generating flux vortices, that order building domains. In this case the magnetic behavior of the sample is essentially given by the response of these domains to the magnetic field, in a similar way as magnetic domains are responsible for the magnetic behavior in a ferromagnet. If the experiments are * Correspondingauthor.
done in low external magnetic fields, the vortex density will be low and no vortex domains will be generated, so that the measured magnetization will only include information of the magnetic behavior of isolated and interacting single vortices. The magnetic response of the vortices also depends on their interaction with the pinning centers in the sample [ 3 ]. In ceramic polycrystalline samples of high-Tc superconductors with weak links between grains two type of vortices are found, those generated at the contact between the grains (intergrain or Josephson vortices) and those generated in the grain (intragrain or Abrikosov vortices). In ZFC experiments at sufficient low magnetic intensities, lower than the critical fields Hc~ associated to the grains and Hc~j, which is 19 Oe for YBCO samples with a mass density of 88% of the X-ray-calculated mass density [4] and is associated to the weak links, no magnetic flux penetrates the sample. This contrasts with the FC magnetization experiments where magnetic flux is trapped
0921-4534/94/$07.00 © 1994Elsevier ScienceB.V. All rights reserved SSDI0921-4534(94)00587-7
56
BokhimL A. Morales/Physica C 233 (1994) 55-60
including at extremely low external magnetic fields [ 5,6 ]. The generated vortices by flux penetration can he visualized by different techniques, for example, by the Bitter pattern technique which has been used to reveal the static crystalline structure formed by the vortices [ 7 ] or by a new technique based on a Lorentz microscope [ 8 ] which has been recently developed for imaging magnetic flux lines in a superconductor using electron holography. With this last technique it is possible to carry out dynamic studies on the vortex behavior as a function of temperature [ 9 ]. This technique has been successfully applied to study the behavior of vortices in Nb and BSCCO thin films [8,9]. The two above techniques can only be used for low vortex densities obtained in low external magnetic fields. Vortices can he also visualized with an optical microscope combined with an attachment based in the Faraday effect [ 10 ], that can be used in all range of external magnetic fields. The spatial resolution of this technique is insufficient to visualize single vortices, however, the microscope also gives an optical non-magnetic image of the microcrystals and their boundaries, which allows one to observe the local places where magnetic flux penetrates the sample and to know if the generated vortices are inter- or intragrain. Recently, we have reported that DC magnetometry is a complementary technique to study the magnetic properties of FC trapped vortices [ 5 ]; this technique gives information about the magnetic properties of the vortices in all the volume of the sample. In that work we have shown that at low external magnetic fields the magnetic behavior of the vortices as a function of temperature can be quantified using the function 1 - t 2/(l -~), with t the reduced temperature T/ To, and a between 0.0 and 1.0. In the literature the ZFC magnetization of polycrystalline and single-crystal superconducting samples at low external magnetic fields is widely published but hardly quantified, loosing the information involved in such measurements. In the present paper we will show that the quantification of the ZFC magnetization can also be based on the function 1 t 2/(1-~) used to quantify the FC remanent magnetization as a function of temperature.
2. Experimental 2. I. Sample preparation Appropriate mixtures of high-purity powders of
Y203, BaCO3 and CuO were calcined in air or oxygen at 800°C for 12 h. From these powders, disks and cylinders were prepared at pressures between 27 and 220 MPa and sintered in air or in oxygen at 950°C for 48 h, giving rise to a sample mass density of 85.5 (5)% of the X-ray-calculated mass density for the YBCO superconducting system [4]. After sintering, the samples were annealed in flowing oxygen at 480°C for 48 h. 2. 2. Sample characterization X-ray diffraction and Rietveld refinement of the orthorhombic structure confirms that the samples are single phase. For the magnetic measurements we prepared small cylinders (4 m m in diameter and 6 m m in length) of polycrystalline material. The electromagnet, generating the external magnetic field, was oriented along the earth magnetic field in order to compensate for its horizontal component. The magnetization was measured with a vibrating-sample magnetometer with a He closed-cycle refrigerator, which allows one to vary the sample temperature between 11 and 300 K. The samples were cooled at 3 K/rain in zero magnetic field to a temperature of 11 K, at which the magnetic field was applied. They were maintained under these conditions for several minutes, however, we do not observe any time relaxation of the magnetization for the range of fields reported in the present work 0.0 < H~< 156 Oe. Thereafter the samples were heated to 100 K at a rate of I K/min.
3. Results and discussion In our study of the FC remanent magnetization [ 5 ] we have found that the reduced magnetic induction B/Bo, with B and Bo the magnitude of the magnetic induction at temperatures T and 0 K respectively, has a scale that is independent of the magnetic field. This allows one to distinguish clearly the changes produced by the field generating the vortices. We use a similar function for the analysis of the ZFC magnet-
Bokhimi, A. Morales/Physica C 233 (1994) 55-60
ization, we define the reduced ZFC magnetization as M/Mo, with M and Mo the magnitude of the magnetization at temperatures T and 0 K respectively. Mo is not much different from its value of the lowest sample temperature ( 11 K). This representation of the ZFC magnetization has the advantage that the demagnetizing factor of the sample and the absolute magnetometer calibration are not important; making it very attractive for the analysis of magnetization data obtained with an AC magnetometer. Fig. 1 shows the reduced ZFC magnetization M~ Mo as a function of the reduced temperature t = T/ To, with T the temperature and Tc = 91.2 K, at external magnetic fields of 1, 10 and 100 Oe. We observe that the magnetization is nearly constant for magnetic fields lower than 1.00e and temperatures lower than T¢, which is similar to the behavior observed for the FC remanent magnetization [ 5 ] that is explained by the interaction of the quasi-isolated vortices with the pinning centers. The curves generated at higher fields show that the reduced ZFC magnetization decreases with temperature with a decreasing rate depending on the applied magnetic field. After correcting the effect of the demagnetizing factor due to sample geometry we find that the susceptibility at 0 K is equal to - 1 for external magnetic fields lower than 15 Oe. In order to quantify the ZFC magnetization as a function of temperature we propose for the variation of the reduced ZFC magnetization the same func-
57
tional dependence with reduced temperature as that obtained for the reduced magnetic induction in the FC remanent magnetization experiments [5 ]; then the reduced ZFC magnetization will be given by
M / M o = 1 - t 2/~'-~)
( 1)
Fig. 2 shows the experimental data (open circles) for the reduced ZFC magnetization obtained in an applied magnetic field of 1.00e, and the fitting curve (continuous line) obtained using Eq. (1), with o~= 0.9400 (5). The figure shows that the function given in Eq. ( l ) is a good function to quantify the reduced ZFC magnetization. When the ZFC magnetization is generated at higher magnetic fields but lower than 15 Oe Eq. ( 1 ) is no more sufficient to fit the magnetization data. In this range of fields the fit is only possible using a sum of two functions of the type given in Eq. ( 1 ). M / M o is then given by
M/Mo=(1-tZ/tl-C°)c+(1-tz/(~-c~))d.
(2)
Fig. 3 shows the experimental data for the reduced ZFC magnetization for a magnetic field of 10 Oe and the fit done using Eq. (2). The broken lines correspond to the partial contributions to the total fitting curve, corresponding curve A to a = 0.174 (4) and curve B to a~ = 0.9032 (5); curve C (continuous line) is the sum at each temperature of curves A and B. A tentative explanation of the origin of curves A and B
1.10 t.10
0.86 ~
086
~
1
0e :E :E o
~o 0.62
_
100 0e ~
\ i
~: 0.38 0.14
0.62
H: 10 0e
0.38 0f4
YB02 Cu307-X
x~i
" -0~0
01
p
0.0
Y Bo2 Co3 07-x
0.25
i
i
0.50
0.75
i
1.00
t Fig. 1. Reduced ZFC magnetization as a function of reduced temperature and external magnetic field for a polycrystalline superconducting YBCO sample.
0.0
0'25
0'.50
0175
1'.00
t
Fig. 2. ReducedZFC magnetizationfor an externalmagneticfield of 1 . 0 0 e . Only some of the experimental data are shown (open circles) to avoid hiding the theoretical curve. The continuous line is the fitted curve given by the function ( 1 - t 2/(1-~>) with a=0.94.
BokhimL A. Morales/Physica C 233 (1994) 55-60
58
~i]ii ~
t.10
C ~ 0.86
y Be2 Cu3
15
07_X
Oe
o 0.62
8
o 0.7
0.38
A
0.5
0.'14 -
0.t0
0.0
B ....... C=---
1,t
\
_
..
YBa2Cu307_ x " ' - . ",, H= 100 Oe
~
I
0.25
I
0'50
0.75
t100
t Fig. 3. Reduced ZFC magnetization as a function of the reduced temperature for an external magnetic field of l 0 0 e . Curves A and B are given by equation ( 1 - g2/{1-a)) with c~= 0.174 and 0.9032 respectively. Curve C (continuous line) is generated by adding the respective values of curves A and B at each temperature. In order to avoid hiding the fitted curve, only some of the experimental data are shown (open circles).
will be given at the end of the discussion. The reduced ZFC magnetization generated at fields larger than 15 Oe was also fitted using Eq. (2) but in this case the coefficient d is negative. Because the magnetization at 0 K Mo is negative, a negative value of the coefficient d means that the corresponding contribution to the magnetization is positive. It is known that superconducting YBCO samples with a mass density of 88% of the X-ray-calculated mass density, which is quite similar to the density of our samples, have an Hc u value of 19 Oe [ 4]; therefore, the magnetic field of 15 Oe at which we observe a positive contribution to the magnetization can be assigned to the critical field H~ u of our samples. Consequently, the observed positive magnetization is due to the presence of vortices generated by flux penetration into the sample. As we have reported before [ 5 ], the magnetization due to vortices is well represented by a function similar to that given in Eq. ( 1 ). In Fig. 4 we show the fit to the reduced ZFC magnetization obtained in a magnetic field of 100 Oe; curve A, corresponding to a~--0.829(1), represents the variation of the magnetization due to the vortices, and curve B, corresponding to a = 0.4709 (9), represents the diamagnetic contribution to the magnetization. Curve C (continuous line) is the obtained fitting curve using Eq. (2), which is the sum of curves A and
-0.5
®Q
/-'
- O. 1
A ,
0.0
0.25
, 0.50
,
0.75
,
t .00
t Fig. 4. Reduced ZFC magnetization as a function of the reduced temperature for an external magnetic field of 100 Oe. Curves A and B are given by equation (1 - t 2/{~-~) ) with a = 0 . 8 2 9 and 0.4709 respectively, the coefficient of curve A is negative. Curve C (continuous line ) is generated by adding the respective values of curves A and B at each temperature. In order to avoid hiding the fitted curve, only some of the experimental data are shown (open circles).
B. Table 1 gives the contribution, that increases with the field, of the vortices to the ZFC magnetization for several external magnetic fields. In this table the average vortex density, that would be obtained if they were uniformly distributed in the sample, is also shown. From the table we find that in the ZFC experiments for a given external magnetic field, the vortex density is lower than that obtained when the vortices are generated by cooling the sample in a field, for example, from Table 1 we observe that the vortex density for H = 5 0 . 0 0 e is 0.615 ktm -2, which is also obtained when the vortices are generated by cooling the sample in a magnetic field of l 0 0 e [5]. It is interesting to remark that if at 0 K we take only the diamagnetic magnetization, the corresponding susceptibility will be - 1, within the experimental error. Reports of ZFC magnetization measurements are found in almost all the papers where magnetization curves are published, but hardly one quantifies them when they are done at low magnetic fields. Many people use these curves to determine the transition temperature to the superconducting state To, in some cases giving as Tc the temperature at which the magnetization takes one half of its most negative value. According to our analysis this is wrong, because this temperature depends on the magnetic field in which
59
BokhimL A. Morales/Physica C 233 (1994) 55-60
Table 1 Diamagnetic (M0c) and paramagnetic (Moa) contributions to the ZFC magnetization, and the vortex density (4nMoo/~o); all at 0 K H
Moc
- 4xMo¢/~o
Mod
4xMod/~o
(Oe)
(emu)
(~tm-2)
(emu)
(~tm-2)
1.0 5.0 20.0 50.0 100.0 130.0
-0.00228 -0.01197 -0.03905 -0.10239 -0.21491 -0.29875
0.085 0.447 1.458 3.823 8.025 11.156
0.00299 0.01647 0.05476 0.10261
0.112 0.615 2.045 3.832
the measurement is done. From the fit of the reduced ZFC magnetization with Eqs. ( 1 ) or (2) we have obtained that the temperature for the onset of the superconductivity is a much better value for Tc because it is independent of magnetic field. The above results clearly show the usefulness of Eqs. ( 1 ) and (2) in order to quantify the ZFC magnetization. One frequently speaks about 'good' or 'bad' samples in reference to the form of the ZFC magnetization curve; however, this very qualitative analysis of the magnetic behavior of the samples is not useful to characterize them. In contrast to this, we have shown that quantification of the ZFC magnetization curves generated in low external magnetic fields is possible using the method given in the present paper. This is important because this magnetization is the most easily obtained, and the most commonly measured in high-Tc superconductors. With our quantitative analysis of the ZFC magnetization it is possible to characterize the magnetic behavior of superconducting samples, which could be applied to follow the evolution of any superconducting system with doping and heat treatment. The physical interpretation of the equations reported for the remanent magnetization, corresponding to Eqs. ( 1 ) and (2) in the present paper, generated by trapped vortices [ 5 ], was plausible, because it is well known that flux vortices in superconductors are located in space with a core size of the order of the coherence length [ 11 ] and a vortex size of the order of the penetration length [ 12 ]. There is an interaction between vortices, which together with their size gives rise to the vortex lattice. These two vortex properties are basic in the interpretation of the function 1 t 2/( 1-~) used to fit the FC remanent magnetization. However, in the ZFC experiments for mag--
netic fields lower than the field Hcij = 15 Oe, at which magnetic flux penetration is observed, we do not know about the existence of any interacting local arrangements of superconducting electrons, that might explain the origin of Eqs. (1) and (2), in a similar way as it was done by explaining the vortex magnetic behavior. Because the samples are composed of weaklinked superconducting grains the diamagnetic behavior might be produced by decoupled superconducting grains, however, in order to decouple them they must be exposed to magnetic fields larger than Hc2j that is of the order of 60 Oe for superconducting YBCO samples with a mass density similar to that of our samples [ 4 ]. However, this assumption does not apply to our results because the effect which we are trying to explain is observed at fields lower than 15 Oe. We have done the same type of experiments reported in the present paper in an epitaxially grown YBCO thin film [ 13 ], which has a very high critical current density (10 A/cm2), finding that the similarities of the behavior as a function of temperature between the FC remanent magnetization and the ZFC magnetization persist. The similarity in behavior with temperature of the ZFC magnetization and the FC remanent magnetization of superconducting polycrystalline YBCO samples, suggest the possible existence of entities (for the ZFC experiments), having a finite size, in a similar way as vortices have, built of local arrangements of superconducting electrons, which are the origin of the diamagnetic response of the superconductor, and having a spatial distribution depending on the magnetic field in which they are generated. If we supposed that to each one of these entities is associated a flux quantum qbo, then - 4 n M / ~ o would give the 7
60
BokhimL A. Morales/Physica C 233 (1994) 55-60
average density o f these entities, assuming they were uniformly distributed in the sample, with M their contribution to the magnetization. The values in colu m n three o f Table 1 would correspond to the entity density at 0 K for different values o f the magnetic field. According to this model, curves A and B in Fig. 3 would correspond to two different entity densities coexisting in the sample.
4. Conclusions
We have found that the reduced Z F C magnetization M / M o is a useful function to analyze the changes p r o d u c e d in Z F C m a g n e t i z a t i o n when the external magnetic field used to generate the magnetization is varied. The t e m p e r a t u r e d e p e n d e n c e o f this magnetization is d e t e r m i n e d using the basic function 1 t 2/(1-~), with a between 0.0 and 1.0. This is the same function used to quantify the F C r e m a n e n t magnetization o f polycrystalline superconducting YBCO samples. This quantification o f the Z F C magnetization allows one to obtain the field at which magnetic flux penetrates into the sample, and it could be used to follow the evolution o f the magnetic properties o f a sample when it is d o p e d or thermally treated. The parallelism between the quantification o f the F C r e m a n e n t magnetization and the Z F C magnetization suggests the existence o f entities o f finite size built o f local arrangements o f superconducting electrons, which are the origin o f the diamagnetic response.
Acknowledgement We would like to thank S. Pickart from The University o f R h o d e Island for his comments, a n d A. Aceves for technical assistance.
References [ 1] K.A. Mfiller, M. Takashige and J.G. Bednorz, Phys. Rev. Lett. 58 (1987) 1143. [2] J.G. P6rez-Ramirez, K. Baberschke and W.G. Clark, Solid State Commun. 65 (1988) 845. [ 3 ] A.M. Campbell and J.E. Evetts, Adv. Phys. 21 (1972) 199. [4] B. Schliepe, PhD Thesis, FU-Berlin, Germany, November 1992. [ 5 ] Bokhimi, Proc. 8th World Ceramic Congress and Forum on New Materials, Florence, Italy, June 28-July 4, 1994. [6 ] H. Maletta, A.P. Malozemoff, D.C. Cronemeyer, C.C. Tsuei, R.L. Green, J.G. Bednorz and K.A. Miiller, Solid State Commun. 62 (1987) 323. [7] C.A. Bolle, P.L. Gammel, D.G. Grier, C.A. Murray, D.J. Bishop, D.B. Mitzi and A. Kapitulnik, Phys. Rev. Lett. 66 (1991) 112. [ 8 ] K. Harada, T. Matsuda, J. Bonevich, M. Igarachi, S. Kondo, G. Pozzi, U. Kawabe and A. Tonomura, Nature 360 ( 1992 ) 51. [ 9 ] K. Harada, T. Matsuda, H. Kasai, J.E. Bonevich, T. Yoshida, U. Kawabe and A. Tonomura, Phys. Rev. Lett. 71 (1993) 337. [10]M.R. Koblischka, N. Moser, B. Gegenheimer and H. Kronmiiller, Physica C 166 (1990) 36. [ 11 ] J. Friedel, P.G. De Gennes and J. Matricon, Appl. Phys. Lett. 2 (1962) 119. [12] H.F. Hess, R.B. Robinson, R.C. Dynes, J.M. Valles Jr. and J.V. Waszczak, Phys. Rev. Lett. 62 (1989) 214. [13] Bokhimi, A. Morales and S. Pickart, MRS Fall Meeting, Boston MA, USA, November 20-December 2, 1994, submitted.
ELSEVIER
Quantitative analysis of the ZFC magnetization in low magnetic fields in the YBazCu307_xsystem Bokhimi *, A. Morales Institute of Physics, National University of Mexico (UNAM), a.p. 20-364, 01000 M~xico, D.F., Mexico
Received 28 March 1994;revised manuscript received 8 September 1994
Abstract
We present a systematic study of the ZFC magnetization as a function of temperature and magnetic field for polycrystalline superconducting samples of the YBCO system. The study is done in magnetic fields lower than 1560e. We have found that the ZFC magnetization can be quantified using the basic function 1- t 2/~-'~), with t the reduced temperature and a between 0.0 and 1.0 depending on the magnetic field. This quantification allows one to determine the magnetic field at which magnetic flux penetrates into the sample and to follow the temperature dependence of the magnetization produced by the generated vortices. For a given magnetic field the temperature dependence of the ZFC magnetization is similar to that observed in the FC remanent magnetization, suggestingthe possible existence of entities built of local arrangements of superconducting electrons, which are the origin of the diamagnetic response.
1. Introduction
Field-cooling (FC) and zero-field-cooling (ZFC) magnetization as a function of temperature are two of the most measured properties in high-T¢ superconductors [ 1,2 ], which are obtained for a wide range of magnetic field intensities. The potential technological applications of high-T~ superconductors have caused that most of these magnetic properties have been studied at relative high magnetic intensities. However, when the ZFC magnetization is measured at high magnetic fields magnetic flux penetrates into the sample generating flux vortices, that order building domains. In this case the magnetic behavior of the sample is essentially given by the response of these domains to the magnetic field, in a similar way as magnetic domains are responsible for the magnetic behavior in a ferromagnet. If the experiments are * Correspondingauthor.
done in low external magnetic fields, the vortex density will be low and no vortex domains will be generated, so that the measured magnetization will only include information of the magnetic behavior of isolated and interacting single vortices. The magnetic response of the vortices also depends on their interaction with the pinning centers in the sample [ 3 ]. In ceramic polycrystalline samples of high-Tc superconductors with weak links between grains two type of vortices are found, those generated at the contact between the grains (intergrain or Josephson vortices) and those generated in the grain (intragrain or Abrikosov vortices). In ZFC experiments at sufficient low magnetic intensities, lower than the critical fields Hc~ associated to the grains and Hc~j, which is 19 Oe for YBCO samples with a mass density of 88% of the X-ray-calculated mass density [4] and is associated to the weak links, no magnetic flux penetrates the sample. This contrasts with the FC magnetization experiments where magnetic flux is trapped
0921-4534/94/$07.00 © 1994Elsevier ScienceB.V. All rights reserved SSDI0921-4534(94)00587-7
56
BokhimL A. Morales/Physica C 233 (1994) 55-60
including at extremely low external magnetic fields [ 5,6 ]. The generated vortices by flux penetration can he visualized by different techniques, for example, by the Bitter pattern technique which has been used to reveal the static crystalline structure formed by the vortices [ 7 ] or by a new technique based on a Lorentz microscope [ 8 ] which has been recently developed for imaging magnetic flux lines in a superconductor using electron holography. With this last technique it is possible to carry out dynamic studies on the vortex behavior as a function of temperature [ 9 ]. This technique has been successfully applied to study the behavior of vortices in Nb and BSCCO thin films [8,9]. The two above techniques can only be used for low vortex densities obtained in low external magnetic fields. Vortices can he also visualized with an optical microscope combined with an attachment based in the Faraday effect [ 10 ], that can be used in all range of external magnetic fields. The spatial resolution of this technique is insufficient to visualize single vortices, however, the microscope also gives an optical non-magnetic image of the microcrystals and their boundaries, which allows one to observe the local places where magnetic flux penetrates the sample and to know if the generated vortices are inter- or intragrain. Recently, we have reported that DC magnetometry is a complementary technique to study the magnetic properties of FC trapped vortices [ 5 ]; this technique gives information about the magnetic properties of the vortices in all the volume of the sample. In that work we have shown that at low external magnetic fields the magnetic behavior of the vortices as a function of temperature can be quantified using the function 1 - t 2/(l -~), with t the reduced temperature T/ To, and a between 0.0 and 1.0. In the literature the ZFC magnetization of polycrystalline and single-crystal superconducting samples at low external magnetic fields is widely published but hardly quantified, loosing the information involved in such measurements. In the present paper we will show that the quantification of the ZFC magnetization can also be based on the function 1 t 2/(1-~) used to quantify the FC remanent magnetization as a function of temperature.
2. Experimental 2. I. Sample preparation Appropriate mixtures of high-purity powders of
Y203, BaCO3 and CuO were calcined in air or oxygen at 800°C for 12 h. From these powders, disks and cylinders were prepared at pressures between 27 and 220 MPa and sintered in air or in oxygen at 950°C for 48 h, giving rise to a sample mass density of 85.5 (5)% of the X-ray-calculated mass density for the YBCO superconducting system [4]. After sintering, the samples were annealed in flowing oxygen at 480°C for 48 h. 2. 2. Sample characterization X-ray diffraction and Rietveld refinement of the orthorhombic structure confirms that the samples are single phase. For the magnetic measurements we prepared small cylinders (4 m m in diameter and 6 m m in length) of polycrystalline material. The electromagnet, generating the external magnetic field, was oriented along the earth magnetic field in order to compensate for its horizontal component. The magnetization was measured with a vibrating-sample magnetometer with a He closed-cycle refrigerator, which allows one to vary the sample temperature between 11 and 300 K. The samples were cooled at 3 K/rain in zero magnetic field to a temperature of 11 K, at which the magnetic field was applied. They were maintained under these conditions for several minutes, however, we do not observe any time relaxation of the magnetization for the range of fields reported in the present work 0.0 < H~< 156 Oe. Thereafter the samples were heated to 100 K at a rate of I K/min.
3. Results and discussion In our study of the FC remanent magnetization [ 5 ] we have found that the reduced magnetic induction B/Bo, with B and Bo the magnitude of the magnetic induction at temperatures T and 0 K respectively, has a scale that is independent of the magnetic field. This allows one to distinguish clearly the changes produced by the field generating the vortices. We use a similar function for the analysis of the ZFC magnet-
Bokhimi, A. Morales/Physica C 233 (1994) 55-60
ization, we define the reduced ZFC magnetization as M/Mo, with M and Mo the magnitude of the magnetization at temperatures T and 0 K respectively. Mo is not much different from its value of the lowest sample temperature ( 11 K). This representation of the ZFC magnetization has the advantage that the demagnetizing factor of the sample and the absolute magnetometer calibration are not important; making it very attractive for the analysis of magnetization data obtained with an AC magnetometer. Fig. 1 shows the reduced ZFC magnetization M~ Mo as a function of the reduced temperature t = T/ To, with T the temperature and Tc = 91.2 K, at external magnetic fields of 1, 10 and 100 Oe. We observe that the magnetization is nearly constant for magnetic fields lower than 1.00e and temperatures lower than T¢, which is similar to the behavior observed for the FC remanent magnetization [ 5 ] that is explained by the interaction of the quasi-isolated vortices with the pinning centers. The curves generated at higher fields show that the reduced ZFC magnetization decreases with temperature with a decreasing rate depending on the applied magnetic field. After correcting the effect of the demagnetizing factor due to sample geometry we find that the susceptibility at 0 K is equal to - 1 for external magnetic fields lower than 15 Oe. In order to quantify the ZFC magnetization as a function of temperature we propose for the variation of the reduced ZFC magnetization the same func-
57
tional dependence with reduced temperature as that obtained for the reduced magnetic induction in the FC remanent magnetization experiments [5 ]; then the reduced ZFC magnetization will be given by
M / M o = 1 - t 2/~'-~)
( 1)
Fig. 2 shows the experimental data (open circles) for the reduced ZFC magnetization obtained in an applied magnetic field of 1.00e, and the fitting curve (continuous line) obtained using Eq. (1), with o~= 0.9400 (5). The figure shows that the function given in Eq. ( l ) is a good function to quantify the reduced ZFC magnetization. When the ZFC magnetization is generated at higher magnetic fields but lower than 15 Oe Eq. ( 1 ) is no more sufficient to fit the magnetization data. In this range of fields the fit is only possible using a sum of two functions of the type given in Eq. ( 1 ). M / M o is then given by
M/Mo=(1-tZ/tl-C°)c+(1-tz/(~-c~))d.
(2)
Fig. 3 shows the experimental data for the reduced ZFC magnetization for a magnetic field of 10 Oe and the fit done using Eq. (2). The broken lines correspond to the partial contributions to the total fitting curve, corresponding curve A to a = 0.174 (4) and curve B to a~ = 0.9032 (5); curve C (continuous line) is the sum at each temperature of curves A and B. A tentative explanation of the origin of curves A and B
1.10 t.10
0.86 ~
086
~
1
0e :E :E o
~o 0.62
_
100 0e ~
\ i
~: 0.38 0.14
0.62
H: 10 0e
0.38 0f4
YB02 Cu307-X
x~i
" -0~0
01
p
0.0
Y Bo2 Co3 07-x
0.25
i
i
0.50
0.75
i
1.00
t Fig. 1. Reduced ZFC magnetization as a function of reduced temperature and external magnetic field for a polycrystalline superconducting YBCO sample.
0.0
0'25
0'.50
0175
1'.00
t
Fig. 2. ReducedZFC magnetizationfor an externalmagneticfield of 1 . 0 0 e . Only some of the experimental data are shown (open circles) to avoid hiding the theoretical curve. The continuous line is the fitted curve given by the function ( 1 - t 2/(1-~>) with a=0.94.
BokhimL A. Morales/Physica C 233 (1994) 55-60
58
~i]ii ~
t.10
C ~ 0.86
y Be2 Cu3
15
07_X
Oe
o 0.62
8
o 0.7
0.38
A
0.5
0.'14 -
0.t0
0.0
B ....... C=---
1,t
\
_
..
YBa2Cu307_ x " ' - . ",, H= 100 Oe
~
I
0.25
I
0'50
0.75
t100
t Fig. 3. Reduced ZFC magnetization as a function of the reduced temperature for an external magnetic field of l 0 0 e . Curves A and B are given by equation ( 1 - g2/{1-a)) with c~= 0.174 and 0.9032 respectively. Curve C (continuous line) is generated by adding the respective values of curves A and B at each temperature. In order to avoid hiding the fitted curve, only some of the experimental data are shown (open circles).
will be given at the end of the discussion. The reduced ZFC magnetization generated at fields larger than 15 Oe was also fitted using Eq. (2) but in this case the coefficient d is negative. Because the magnetization at 0 K Mo is negative, a negative value of the coefficient d means that the corresponding contribution to the magnetization is positive. It is known that superconducting YBCO samples with a mass density of 88% of the X-ray-calculated mass density, which is quite similar to the density of our samples, have an Hc u value of 19 Oe [ 4]; therefore, the magnetic field of 15 Oe at which we observe a positive contribution to the magnetization can be assigned to the critical field H~ u of our samples. Consequently, the observed positive magnetization is due to the presence of vortices generated by flux penetration into the sample. As we have reported before [ 5 ], the magnetization due to vortices is well represented by a function similar to that given in Eq. ( 1 ). In Fig. 4 we show the fit to the reduced ZFC magnetization obtained in a magnetic field of 100 Oe; curve A, corresponding to a~--0.829(1), represents the variation of the magnetization due to the vortices, and curve B, corresponding to a = 0.4709 (9), represents the diamagnetic contribution to the magnetization. Curve C (continuous line) is the obtained fitting curve using Eq. (2), which is the sum of curves A and
-0.5
®Q
/-'
- O. 1
A ,
0.0
0.25
, 0.50
,
0.75
,
t .00
t Fig. 4. Reduced ZFC magnetization as a function of the reduced temperature for an external magnetic field of 100 Oe. Curves A and B are given by equation (1 - t 2/{~-~) ) with a = 0 . 8 2 9 and 0.4709 respectively, the coefficient of curve A is negative. Curve C (continuous line ) is generated by adding the respective values of curves A and B at each temperature. In order to avoid hiding the fitted curve, only some of the experimental data are shown (open circles).
B. Table 1 gives the contribution, that increases with the field, of the vortices to the ZFC magnetization for several external magnetic fields. In this table the average vortex density, that would be obtained if they were uniformly distributed in the sample, is also shown. From the table we find that in the ZFC experiments for a given external magnetic field, the vortex density is lower than that obtained when the vortices are generated by cooling the sample in a field, for example, from Table 1 we observe that the vortex density for H = 5 0 . 0 0 e is 0.615 ktm -2, which is also obtained when the vortices are generated by cooling the sample in a magnetic field of l 0 0 e [5]. It is interesting to remark that if at 0 K we take only the diamagnetic magnetization, the corresponding susceptibility will be - 1, within the experimental error. Reports of ZFC magnetization measurements are found in almost all the papers where magnetization curves are published, but hardly one quantifies them when they are done at low magnetic fields. Many people use these curves to determine the transition temperature to the superconducting state To, in some cases giving as Tc the temperature at which the magnetization takes one half of its most negative value. According to our analysis this is wrong, because this temperature depends on the magnetic field in which
59
BokhimL A. Morales/Physica C 233 (1994) 55-60
Table 1 Diamagnetic (M0c) and paramagnetic (Moa) contributions to the ZFC magnetization, and the vortex density (4nMoo/~o); all at 0 K H
Moc
- 4xMo¢/~o
Mod
4xMod/~o
(Oe)
(emu)
(~tm-2)
(emu)
(~tm-2)
1.0 5.0 20.0 50.0 100.0 130.0
-0.00228 -0.01197 -0.03905 -0.10239 -0.21491 -0.29875
0.085 0.447 1.458 3.823 8.025 11.156
0.00299 0.01647 0.05476 0.10261
0.112 0.615 2.045 3.832
the measurement is done. From the fit of the reduced ZFC magnetization with Eqs. ( 1 ) or (2) we have obtained that the temperature for the onset of the superconductivity is a much better value for Tc because it is independent of magnetic field. The above results clearly show the usefulness of Eqs. ( 1 ) and (2) in order to quantify the ZFC magnetization. One frequently speaks about 'good' or 'bad' samples in reference to the form of the ZFC magnetization curve; however, this very qualitative analysis of the magnetic behavior of the samples is not useful to characterize them. In contrast to this, we have shown that quantification of the ZFC magnetization curves generated in low external magnetic fields is possible using the method given in the present paper. This is important because this magnetization is the most easily obtained, and the most commonly measured in high-Tc superconductors. With our quantitative analysis of the ZFC magnetization it is possible to characterize the magnetic behavior of superconducting samples, which could be applied to follow the evolution of any superconducting system with doping and heat treatment. The physical interpretation of the equations reported for the remanent magnetization, corresponding to Eqs. ( 1 ) and (2) in the present paper, generated by trapped vortices [ 5 ], was plausible, because it is well known that flux vortices in superconductors are located in space with a core size of the order of the coherence length [ 11 ] and a vortex size of the order of the penetration length [ 12 ]. There is an interaction between vortices, which together with their size gives rise to the vortex lattice. These two vortex properties are basic in the interpretation of the function 1 t 2/( 1-~) used to fit the FC remanent magnetization. However, in the ZFC experiments for mag--
netic fields lower than the field Hcij = 15 Oe, at which magnetic flux penetration is observed, we do not know about the existence of any interacting local arrangements of superconducting electrons, that might explain the origin of Eqs. (1) and (2), in a similar way as it was done by explaining the vortex magnetic behavior. Because the samples are composed of weaklinked superconducting grains the diamagnetic behavior might be produced by decoupled superconducting grains, however, in order to decouple them they must be exposed to magnetic fields larger than Hc2j that is of the order of 60 Oe for superconducting YBCO samples with a mass density similar to that of our samples [ 4 ]. However, this assumption does not apply to our results because the effect which we are trying to explain is observed at fields lower than 15 Oe. We have done the same type of experiments reported in the present paper in an epitaxially grown YBCO thin film [ 13 ], which has a very high critical current density (10 A/cm2), finding that the similarities of the behavior as a function of temperature between the FC remanent magnetization and the ZFC magnetization persist. The similarity in behavior with temperature of the ZFC magnetization and the FC remanent magnetization of superconducting polycrystalline YBCO samples, suggest the possible existence of entities (for the ZFC experiments), having a finite size, in a similar way as vortices have, built of local arrangements of superconducting electrons, which are the origin of the diamagnetic response of the superconductor, and having a spatial distribution depending on the magnetic field in which they are generated. If we supposed that to each one of these entities is associated a flux quantum qbo, then - 4 n M / ~ o would give the 7
60
BokhimL A. Morales/Physica C 233 (1994) 55-60
average density o f these entities, assuming they were uniformly distributed in the sample, with M their contribution to the magnetization. The values in colu m n three o f Table 1 would correspond to the entity density at 0 K for different values o f the magnetic field. According to this model, curves A and B in Fig. 3 would correspond to two different entity densities coexisting in the sample.
4. Conclusions
We have found that the reduced Z F C magnetization M / M o is a useful function to analyze the changes p r o d u c e d in Z F C m a g n e t i z a t i o n when the external magnetic field used to generate the magnetization is varied. The t e m p e r a t u r e d e p e n d e n c e o f this magnetization is d e t e r m i n e d using the basic function 1 t 2/(1-~), with a between 0.0 and 1.0. This is the same function used to quantify the F C r e m a n e n t magnetization o f polycrystalline superconducting YBCO samples. This quantification o f the Z F C magnetization allows one to obtain the field at which magnetic flux penetrates into the sample, and it could be used to follow the evolution o f the magnetic properties o f a sample when it is d o p e d or thermally treated. The parallelism between the quantification o f the F C r e m a n e n t magnetization and the Z F C magnetization suggests the existence o f entities o f finite size built o f local arrangements o f superconducting electrons, which are the origin o f the diamagnetic response.
Acknowledgement We would like to thank S. Pickart from The University o f R h o d e Island for his comments, a n d A. Aceves for technical assistance.
References [ 1] K.A. Mfiller, M. Takashige and J.G. Bednorz, Phys. Rev. Lett. 58 (1987) 1143. [2] J.G. P6rez-Ramirez, K. Baberschke and W.G. Clark, Solid State Commun. 65 (1988) 845. [ 3 ] A.M. Campbell and J.E. Evetts, Adv. Phys. 21 (1972) 199. [4] B. Schliepe, PhD Thesis, FU-Berlin, Germany, November 1992. [ 5 ] Bokhimi, Proc. 8th World Ceramic Congress and Forum on New Materials, Florence, Italy, June 28-July 4, 1994. [6 ] H. Maletta, A.P. Malozemoff, D.C. Cronemeyer, C.C. Tsuei, R.L. Green, J.G. Bednorz and K.A. Miiller, Solid State Commun. 62 (1987) 323. [7] C.A. Bolle, P.L. Gammel, D.G. Grier, C.A. Murray, D.J. Bishop, D.B. Mitzi and A. Kapitulnik, Phys. Rev. Lett. 66 (1991) 112. [ 8 ] K. Harada, T. Matsuda, J. Bonevich, M. Igarachi, S. Kondo, G. Pozzi, U. Kawabe and A. Tonomura, Nature 360 ( 1992 ) 51. [ 9 ] K. Harada, T. Matsuda, H. Kasai, J.E. Bonevich, T. Yoshida, U. Kawabe and A. Tonomura, Phys. Rev. Lett. 71 (1993) 337. [10]M.R. Koblischka, N. Moser, B. Gegenheimer and H. Kronmiiller, Physica C 166 (1990) 36. [ 11 ] J. Friedel, P.G. De Gennes and J. Matricon, Appl. Phys. Lett. 2 (1962) 119. [12] H.F. Hess, R.B. Robinson, R.C. Dynes, J.M. Valles Jr. and J.V. Waszczak, Phys. Rev. Lett. 62 (1989) 214. [13] Bokhimi, A. Morales and S. Pickart, MRS Fall Meeting, Boston MA, USA, November 20-December 2, 1994, submitted.