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Field-cooling remanent magnetization of polycrystalline samples of the YBCO system in low magnetic fields
Rltlgl PhysieaC234 (1994) 333-338
ELqEVIER
Field-cooling remanent magnetization of polycrystalline samples of the YBCO system in low magnetic fields B o l d a i m i , A. M o r a l e s Institute of Physics, National University of Mexico (UNAM). a. p. 20-264, 01000 Mdxico, D.F., Mexico
Received 15 September 1994
Abstr~t
Field-cooling remanent magnetization of polycrystalline samples of the YBCO system is measured as a function of temperature for vortex-generating external magnetic fields lower than 100 Oe. Using the reduced magnetic induction B/Bo to represent the experimental data allows one to analyze easily the changes produced by the magnetic field in the remanent magnetization with temperature. In this representation we have found the basic function B/Bo= 1 - t 2/¢1-'~) to fit the experimental data, with t the reduced temperature and a a parameter varying between 0.0 and 1.0 and containing information about the difference between the flux pinning force and the vortex-vortex interaction. From the quantitative analysis we find that for magnetic fields between 7.0 and 34.0 two kinds of vortices coexist which can be associated with the intergraln and the intragrain vortices. One of these vortex types that we identify with the intergrain vortices disappears at 34.00e, which we associate with the critical field Hcej. Our quantitative analysis can be used as an alternative technique to analyze the magnetic behavior of inter- and intragrain vortices.
1. Introduction An understanding of the magnetic behavior of flux vortices in high-To superconductors with temperature and magnetic field is basic to their applications; in most of them the involved magnetic fields are high, producing a high vortex density in the superconducting material of the corresponding device. This is why most of the studies of the magnetic properties of superconducting materials are done in high external magnetic fields [ 1 ]. The high vortex density generated in these magnetic fields brings about vortex agglomeration in the form of vortex domains that make the principal contribution of the magnetization in these fields [2,3 ]. These vortex domains creep with temperature producing a time-relaxing magnetization [2,4]. When the vortices are generated in low external
magnetic fields, they will be insulated from each other if the field is sufficient low, or will interact with each other building a vortex lattice [ 1 ]. It is well known that vortices are pinned by interaction with dislocations or impurity atoms in the sample lattice or with voids or non-superconducting phases in the sample, which are known as flux pinning centers [ 5 ]. Therefore, the magnetic properties as functions of temperature and external magnctic field of vortices generated in low magnetic fields are highly determined by their interaction with the pinning centers [ 6 ]. This interaction has an influence on the magnetic properties of the vortex domains as well [ 5 ]. In the regime of low vortex density, at high temperatures or strong vortex-vortcx interactions, the flux pinning force is no longer sufficient to fix the vortices, which start moving. Vortices can be visualized by different methods of
0921-4534/94/$07.00 © 1994 ElsevierScienceB.V. All riots reserved SSD10921-4534 (94)02334-4
334
BokhimL A. Morales / Physica C 234 (1994)333-338
which the Bitter pattern technique is the most used [ 7 ], as it can resolve the static behavior of single vortices. Another technique that resolves single vortices is Tonomura's technique, limited to superconducting thin films and based on a field-emission electron microscope [8], which allows one to obtain the dynamic behavior of vortices as a function of temperature and magnetic field [ 9 ]. High-T¢ superconductors prepared by conventional techniques are ceramics with a low mass density, which produces samples with weak-linking grains that in the superconducting state generate internal Josephson junctions [ 10]. This fact causes two kind of vortices to appear in polycrystalline superconducting samples of high-T¢ materials [ 11 ], those generated at the weak links between the grains, called intergrain or Josephson vortices, and those generated in the grains, called intergrain or Abrikosov vortices. These two kind of vortices are well distinguished in the magnetization as a function of field at a fixed temperature [ 12 ]. They can be visualized with an optical microscope attached with a Faraday-effect sensitive detector [ 13 ], which is sensible to the magnetic induction produced by the vortices emerging at the surface of the sample. This microscope does not resolve single vortices, but it has the advantage that it can simultaneously take magnetic and optical images of the sample, allowing one to correlate both images and to know if the vortices are generated between or in the grains. There are two ways of generating vortices in a superconducting sample: by cooling the sample in a magnetic field (FC) or by applying the magnetic field after cooling it in zero field (ZFC). With this last technique no vortices will be generated in the sample if the external magnetic field is sufficiently low. As the field is increased, flux penetration is observed, generating vortices in the sample initially at the weak links between grains, producing an inhomogeneous vortex distribution in the sample. We are interested in the study of the magnetic properties of vortices as a function of temperature and magnetic field, and the ZFC-generated vortices are inhomogeneously distributed in the sample and cannot be generated at very low external magnetic fields, for the present work vortices were generated by cooling the sample in a magnetic field that is turned off when the sample is at its lowest temperature. Under
these conditions the magnetic response corresponds to the FC remanent magnetization.
2. Experimental 2.1. Sample preparation
Appropriate mixtures of high-purity powders of
Y203, BaCO3, and CuO were calcined in air or in 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 a total of 48 h, with intermediate regrinding and pressing. The sample mass densities were obtained in the range between 40.0(5)% and 85.5(5)% of the ideal YBCO density calculated with the unit cell parameters obtained by X-ray diffraction. After sintering, all samples were annealed in flowing oxygen at 480°C for 48 h. The magnetization curves reported in the figures correspond to three different representative samples of different mass densities. 2.2. Sample characterization
X-ray diffraction and Rietveld refinement of the orthorhombic structure confirmed that the samples were single phase. For the magnetic measurements we prepared small cylinders of the polycrystaUine material with diameters between 1.5 and 4.2 mm and 3 to 6 mm in length. The electromagnet generating the external magnetic field was oriented along the earth's magnetic field in order to compensate its horizontal component. The magnetization was measured with a sample-vibrating magnetometer with a He closedcycle refrigerator, which allows one to vary the sample temperature between 11 and 300 K. Vortices were generated by cooling the sample in the magnetic field of interest from 100 to 11 K at a cooling rate of 1 K / min. Once the sample was at its lowest temperature, the external magnetic field was turned off, causing the diamagnetic contribution to disappear so that the magnetization was the remanence due to the trapped vortices in the sample. After that the sample was heated to its non-superconducting state at a heating rate of 0.5 or 1 K/min.
Bokhimi, A. Morales / Physica C 234 (1994) 333-338
3. Results and discussion
As is known, with each vortex is associated a quantum flux ~o=h/2e, so that the magnetic flux produced by N parallel vortices is N~o =A B, with A the total area perpendicular to them and B the magnitude of the magnetic induction B that they generate, which in our case is equal to 4nM, with M the remanent magnetization. We have found that a good way to see the effect of the vortex-generating magnetic field on the remanent magnetization is to normalize the corresponding magnitude of the magnetic induction to its value at zero kelvin, Bo, which differs little from its value at the lowest sample temperature, using for the normalized magnetic induction B/Bo the name of reduced magnetic induction. Fig. 1 shows this induction for different external magnetic fields as a function of reduced temperature t = T/To, with T the temperature and Tc = 91.2 K the transition temperature to the superconducting state. This figure clearly shows the effect of the field on the temperature variation of the reduced induction that decreases faster with temperature at higher fields, which also depends on sample history. From the figure we also observe that at a magnetic field of 1.00e, where the vortices are nearly insulated from each other, the magnetization is constant for temperatures far away from the transition temperature To; for this magnetic field the vortex density is low and consequently the vortexvortex interaction is negligible. The experiment at a magnetic field of 1.0 Oe was repeated for different t.10
0.86-
heating rates, obtaining the same result, which means that the remanent magnetization, for the range of fields used in the present work, does not depend on the temperature gradients in the sample. This result implies that the variation of the remanent magnetization with temperature for these fields only depends on the flux pinning force, which dominates the weak vortex-vortex interaction. At higher external magnetic fields the reduced magnetic induction decreases with increasing temperature. For these fields a large vortex density is produced, increasing the vortex-vortex interaction. Repeating these experiments at different heating rates, the results are the same, which means that temperature gradients in the sample do not play any role in the observed behavior, at least for the fields used in the present work. Therefore, we conclude that for the fields used in the present work the variation of the FC remanent magnetization is only determined by the competition between the flux pinning force and the vortex-vortex interaction. At much higher magnetic fields and fixed temperature, vortices are no longer static and start to move, producing a time-relaxing magnetization. This only happens in our samples when the field is higher than 250 Oe, which is much higher than the fields used for the reported results in the present work. From the above paragraphs we conclude that the reduced magnetic induction is useful for a qualitative analysis of the remanent magnetization; however, it will be much more interesting if this representation is also useful for a quantitative analysis. Therefore, we have tried to find an analytical function to fit the experimental data, finding at length that the function given by
B/Bo = -o CIC3 C~
0.62 -
0.38-
o.o
I - t 21(l-a) ,
(I )
with 0.0< a < 1.0, fits the experimental data well for
Y B02Cu307-x
0.14
-0.I0
335
0'.25
0'.50
o175
I'.OO
'
÷
Fig. 1. Reduced magnetic induction as a function of temperature for polyerystalline samples of the YBCO system. The vortex-generating external magnetic fields are indicated.
external magnetic fields lower than 7 . 0 0 e . This function was obtained for the first time by Gorter and Casimier [ 14 ] in their paper from which they later derived their two-fluid model However, for them a takes only the value of 0.5. Because the function given in Eq. ( 1 ) describes the variation of the remanent magnetization with temperature, the parameter ot of this equation must contain information about the competition between the flux pinning force and the vortex-vortex interaction,
Bokhimi, A. Morales I Physica C 234 (1994) 333-338
336
which are the elements responsible for this variation. When the vortices are nearly insulated, they are fixed to the sample by the flux pinning force while the vortex-vortex interaction is negligible; in this case the FC remanent magnetization is constant and a tends to 1.0 according to the results shown in Fig. 2, where the experimental data (circles) and the fitting curve (continuous line) for the reduced magnetic induction are shown as a function of temperature when the vortices are generated in a magnetic field of 0.5 Oe. The data were fitted with the function given by Eq. ( 1 ) using a least squares procedure, obtaining from the fitting an ot value of 0.9497 (3), the standard deviation being obtained from the fitting. As mentioned above, the function given in Eq. ( 1 ) works well for H < 7.0 Oe, where at decreases as the vortex density increases according to Table 1 and Fig. 3. From this table we also observe a correlation between the parameter at and the vortex density at zero kelvin: decreasing at as the vortex density increases. Because for a given sample the flux pinning forces are fixed and do not depend on the external magnetic field, the correlation between parameter at and the vortex density at zero kelvin is an indirect correlation between the vortex density and the difference between the flux pinning force and the vortex-vortex interaction, at changes with external magnetic field, and depends on the preparation and heat treatment 1.10
0
0.62 -
cr~
H (Oe)
ol
0.5 1.0 3.0 5.0 7.0
0.9497(3) 0.9342(4) 0.8854(5) 0.8448(5) 0.817(2)
Bo (gauss)
Bolero
0.00089 0.00173 0.00502 0.00823 0.01146
0.043 0.084 0.243 0.398 0.554
0,tm -2 )
Y 8°2 Cus 07_x 0.8 L/
OO~ v
o
/
0.6i
.
,
~, v
~
/
oo ' O x7
0'4 f 0,2
~
V
°~ ~°
0,0
o
6
1'o'
o i
Y B02 Cu3 07-x H:O.50e
0.38-
0.14-
-0.10 0.25
0.50
o
o4o go H (Oe)
Fig. 3. The parameter or, of the function B/Bo= 1 - t 2/t1-~), as a
function of the vortex-generatingexternal magnetic field, for samples with densities of 72.1 ( 1 )% (filled dots ), 85.5 ( 1 )% (triangles) and 41.8( 1 )% (open circles) of the ideal YBCO mass density.
B/Bo=(1-t2/tl-'~))c+(1-t2/(l-'~l))d, 0.0
o
of the sample (Fig. 3), which is in accordance with the well-known dependence of the vortex distribution and flux pinning forces on the previous history of the sample. For magnetic fields between 7.0 and 34.0 Pc, experimental data are only well fitted by assuming a function generated by the sum of two functions similar to that given in Eq. ( 1 ). B/Bo is then given by
0.86-
co
Table 1 Magnetic induction, average vortex density at zero kelvin and the respective parameter a for vortices generated in external magnetic fields Hlower than or equal to 7 . 0 0 e
0.75
tO0
Fig. 2. Reduced magnetic induction as a function of temperature produced by vortices generated in an external magnetic field of 0.50e. The continuous line is the fitted curve given by the function B/Bo= 1 - t 2/°-'~), with a=0.9497. Only some of the experimental data are shown (open circles) to avoid hiding the theoretical curve.
(2)
with a and a~ between 0.0 and 1.0 and c + d = 1.0. Fig. 4 shows the reduced magnetic induction when vortices are generated in an external magnetic field of 2 0 . 0 0 e . The experimental data were fitted using Eq. (2), and it also shows the partial and total contributions to the reduced magnetic induction. Experimental data are given by the the open circles, show-
Bokhimi, A. Morales / Physica C 234 (1994) 333-338 1,10
CY " - , ~ . 0.86 ~ H
'-'02Cu3 07_x =20.00e
0,62 o
B ............
r-n 0.38-
~.
A
N
.A OO
-0.10
o.o
0:25
0:50
o'.75
i, oo
f Fig. 4. Reduced magnetic induction as a function of reduced
temperature due to vortices generatedin an external magnetic field of 20.00e. Curves A and B are given by the function B~ B0= l - t 2/°-a) with a=0.182 and 0.701, respectively.Curve C (continuousline) is the sum of curvesA and B, with only some of the experimentaldata shown (open circles). ing only some of them in order to make visible the adjusted curve. The contribution (54.7 (6)% at zero kelvin) of the magnetization corresponding to or=0.701 (2) is given by curve B, while the contribution corresponding to a~ (45.3(5)% at zero kelvin) is given by curve A. Curve C (continuous line) represents the adjusted curve to the experimental data, which is the sum of curves A and B. According to the physical interpretation for a given in the above paragraphs, Eq. (2) suggests that for magnetic fields between 7.0 and 3 4 . 0 0 e two types of vortices coexist, which agrees with the well-known fact that polycrystalline samples have two types of vortices, the intergrain or Josephson vortices and the intragrain or Abrikosov vortices identified by magnetization measurements [ 12 ], electron spin resonance [ 15 ] and microwave absorption [ 16 ]. Because in polycrystalline samples of high-T¢ superconductors the grain boundaries between weak-linking grains are good centers for trapping magnetic flux [ 17 ], the intergrain vortex density will be higher than the intragrain vortex density, so that for low fields the vortexvortex interaction between intergrain vortices will be large, dominating the flux pinning forces, which allows the vortices to move producing a change of the magnetization with temperature. This means that at low fields the observed behavior of the magnetization, which is represented by the parameter ot in Eq.
337
(1), basically corresponds to that produced by the Josephson vortices; at higher fields the corresponding contribution is given by the parameter ct in Eq. (2). From Fig. 3 we observe that a decreases faster with the magnetic field for the sample with the lowest mass density (41.8% of the ideal mass density), which is the sample richest in weak links and therefore the sample with a higher Josephson vortex density as well. For external magnetic fields between 34.0 and 50.0 Oe the contribution of the first term in Eq. (2) corresponding to the Josephson vortices is zero, which means that the Josephson vortices have disappeared. Consequently, the field of 3 4 . 0 0 e can be identified as the critical field Hc2j, which according to Fig. 3 is independent of the sample. This value for He2j is about one half of the respective value obtained from ZFC magnetization curves of YBCO dense samples [ 12 ]. The field of 50.00e marks the upper limit of the fields for which the type of quantification of the FC remanent magnetization given in the present work can be applied, when the samples belong to the YBCO system and are prepared in a similar way as we did. Above this field it is impossible to fit well the experimental data with Eqs. ( 1 ) or (2). The parameter cq, associated with the intragrain vortices, is nearly independent of the external magnetic field (Table 2), suggesting that the intragrain vortex-vortex interaction does not change significantly for the range of magnetic fields used in the present work.
4. Conclusions Representation of the FC remanent magnetization by the reduced magnetic induction B / B o allows one to see deafly the changes in the magnetization as a function of temperature which are produced at different external magnetic fields. We have found the basic function B / B o = 1 - t 2/(1-'~) to quantify the reduced magnetic induction, with the parameter a related to the competition between the flux pinning force and the vortex-vortex interaction; when this interaction is weak a tends to 1.0, indicating that vortices do not move for temperatures far away from
To. From our quantitative analysis we find that for ex-
338
BokhimL A. Morales/Physica C234 (1994) 333-338
Table 2 Average vortex density at zero kelvin, and the contribution of the two vortex densities to the reduced magnetic induction as a function of the external magnetic field H in which they were generated. According to Eq. (2) each density is characterized by the pairs (ol, c) and (oq, d) H
Bo/Oo
(Oe)
(ttm -2)
1.0 10.0 20.0 30.0 33.0 40.0
0.084 0.643 1.073 1.576 1.644 1.940
a
c
ai
d
0.9342(4) 0.766(2) 0.701(2) 0.693(5) 0.636(9) -
1.0 0.7624(6) 0.547(6) 0.262(8) 0.24(I) -
0.185(2) 0.182(6) 0.185(6) 0.147(8) 0.163(1)
0.234(6) 0.453(5) 0.739(8) 0.76(8) 1.000
ternal magnetic fields between 7.0 and 3 4 . 0 0 e the experimental data can only be well fitted with a sum of two functions of the type mentioned in the above paragraph, which we interpret as the presence of two types of vortices in the sample. This result is in accordance with the well-known fact that for low fields in polycrystalline samples of the YBCO system intergrain and intragrain vortices coexist, showing that the type of analysis of the data described in the present paper can be used as an alternative technique to identify both kinds of vortices. From the quantitative analysis we have also found a magnetic field at which one of the vortex types disappears. This field is sample independent and we associate it with the critical field Hc2j of the intergrain vortices.
Acknowledgement We would like to thank A. Aceves for technical assistance.
References [ 11 D.J. Bishop, P.L. Gamm¢l, D.A. Huse and C.A. Murray, Science 255 (1992) 165.
[2] P.W. Anderson, Phys. Rev. Lett. 9 (1962) 309. [3] Y. Yeshurum and A.P. Malozemoff, Phys. Rev. Lett. 60 (1988) 2202. [4] K.A. Miiller, M. Takashige and J.G. Bednorz, Phys. Rev. Lett. 58 (1987) 1143. [ 5 ] A.M. Campbell and J.E. Evetts, Adv. Phys. 21 ( 1972 ) 199. [6] M. Golosovsky, M. Tsindlekht, H. Chayet and D. Davidov, Phys. Rev. B 50 (1994) July. [7] U. Essman and H. Tfiiuble, Phys. Left. 24A (1967) 526. [ 8 ] K. Harada, T. Matsuda, H. Kasai, J.E. Bonevich, T. Yoshida, U. Kawabe and A. Tonomura, Phys. Rev. Lett. 71 (1993) 337. [9] A. Tonomura, Proc. 4th Int. Conf. on Materials & Mechanism of Superconductivity, High-Temperature Superconductors, MZS-HTSC-IV, Grenoble, France, 5-9 July 1994. [10] S. Senoussi, G. Aguillon and S. Hadjoudj, Physica C 175 (1991) 215. [ 11 ] B. Schultz, B. Schliepe, W. Wisny and K. Bebershke, Solid State Commun. 80 ( 1991 ) 111. [ 12] B. Schliepe, Ph.D. Thesis, FU-Berlin, Germany, November 1992. [13]M.R. Koblischka, N. Moser, B. Gegenheimer and H. Kronmiiller, Physica C 166 (1990) 36. [ 14] C.J. Gorter and H. Casimier, Phys. Z. 35 (1934) 963. [15] H. Muto, K. Matsura and Y. Tai, Physica C 219 (1994) 259. [ 16] B. Czyzak, J. Stankowski and J. Martinek, Physica C 201 (1992) 379. [ 17 ] Videotape and brochure about the Flux Imaging System for Superconducting samples of the Phase Metrix Company, 3987 Sorrento Valley Blvd., San Diego, CA 92121, USA.
ELqEVIER
Field-cooling remanent magnetization of polycrystalline samples of the YBCO system in low magnetic fields B o l d a i m i , A. M o r a l e s Institute of Physics, National University of Mexico (UNAM). a. p. 20-264, 01000 Mdxico, D.F., Mexico
Received 15 September 1994
Abstr~t
Field-cooling remanent magnetization of polycrystalline samples of the YBCO system is measured as a function of temperature for vortex-generating external magnetic fields lower than 100 Oe. Using the reduced magnetic induction B/Bo to represent the experimental data allows one to analyze easily the changes produced by the magnetic field in the remanent magnetization with temperature. In this representation we have found the basic function B/Bo= 1 - t 2/¢1-'~) to fit the experimental data, with t the reduced temperature and a a parameter varying between 0.0 and 1.0 and containing information about the difference between the flux pinning force and the vortex-vortex interaction. From the quantitative analysis we find that for magnetic fields between 7.0 and 34.0 two kinds of vortices coexist which can be associated with the intergraln and the intragrain vortices. One of these vortex types that we identify with the intergrain vortices disappears at 34.00e, which we associate with the critical field Hcej. Our quantitative analysis can be used as an alternative technique to analyze the magnetic behavior of inter- and intragrain vortices.
1. Introduction An understanding of the magnetic behavior of flux vortices in high-To superconductors with temperature and magnetic field is basic to their applications; in most of them the involved magnetic fields are high, producing a high vortex density in the superconducting material of the corresponding device. This is why most of the studies of the magnetic properties of superconducting materials are done in high external magnetic fields [ 1 ]. The high vortex density generated in these magnetic fields brings about vortex agglomeration in the form of vortex domains that make the principal contribution of the magnetization in these fields [2,3 ]. These vortex domains creep with temperature producing a time-relaxing magnetization [2,4]. When the vortices are generated in low external
magnetic fields, they will be insulated from each other if the field is sufficient low, or will interact with each other building a vortex lattice [ 1 ]. It is well known that vortices are pinned by interaction with dislocations or impurity atoms in the sample lattice or with voids or non-superconducting phases in the sample, which are known as flux pinning centers [ 5 ]. Therefore, the magnetic properties as functions of temperature and external magnctic field of vortices generated in low magnetic fields are highly determined by their interaction with the pinning centers [ 6 ]. This interaction has an influence on the magnetic properties of the vortex domains as well [ 5 ]. In the regime of low vortex density, at high temperatures or strong vortex-vortcx interactions, the flux pinning force is no longer sufficient to fix the vortices, which start moving. Vortices can be visualized by different methods of
0921-4534/94/$07.00 © 1994 ElsevierScienceB.V. All riots reserved SSD10921-4534 (94)02334-4
334
BokhimL A. Morales / Physica C 234 (1994)333-338
which the Bitter pattern technique is the most used [ 7 ], as it can resolve the static behavior of single vortices. Another technique that resolves single vortices is Tonomura's technique, limited to superconducting thin films and based on a field-emission electron microscope [8], which allows one to obtain the dynamic behavior of vortices as a function of temperature and magnetic field [ 9 ]. High-T¢ superconductors prepared by conventional techniques are ceramics with a low mass density, which produces samples with weak-linking grains that in the superconducting state generate internal Josephson junctions [ 10]. This fact causes two kind of vortices to appear in polycrystalline superconducting samples of high-T¢ materials [ 11 ], those generated at the weak links between the grains, called intergrain or Josephson vortices, and those generated in the grains, called intergrain or Abrikosov vortices. These two kind of vortices are well distinguished in the magnetization as a function of field at a fixed temperature [ 12 ]. They can be visualized with an optical microscope attached with a Faraday-effect sensitive detector [ 13 ], which is sensible to the magnetic induction produced by the vortices emerging at the surface of the sample. This microscope does not resolve single vortices, but it has the advantage that it can simultaneously take magnetic and optical images of the sample, allowing one to correlate both images and to know if the vortices are generated between or in the grains. There are two ways of generating vortices in a superconducting sample: by cooling the sample in a magnetic field (FC) or by applying the magnetic field after cooling it in zero field (ZFC). With this last technique no vortices will be generated in the sample if the external magnetic field is sufficiently low. As the field is increased, flux penetration is observed, generating vortices in the sample initially at the weak links between grains, producing an inhomogeneous vortex distribution in the sample. We are interested in the study of the magnetic properties of vortices as a function of temperature and magnetic field, and the ZFC-generated vortices are inhomogeneously distributed in the sample and cannot be generated at very low external magnetic fields, for the present work vortices were generated by cooling the sample in a magnetic field that is turned off when the sample is at its lowest temperature. Under
these conditions the magnetic response corresponds to the FC remanent magnetization.
2. Experimental 2.1. Sample preparation
Appropriate mixtures of high-purity powders of
Y203, BaCO3, and CuO were calcined in air or in 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 a total of 48 h, with intermediate regrinding and pressing. The sample mass densities were obtained in the range between 40.0(5)% and 85.5(5)% of the ideal YBCO density calculated with the unit cell parameters obtained by X-ray diffraction. After sintering, all samples were annealed in flowing oxygen at 480°C for 48 h. The magnetization curves reported in the figures correspond to three different representative samples of different mass densities. 2.2. Sample characterization
X-ray diffraction and Rietveld refinement of the orthorhombic structure confirmed that the samples were single phase. For the magnetic measurements we prepared small cylinders of the polycrystaUine material with diameters between 1.5 and 4.2 mm and 3 to 6 mm in length. The electromagnet generating the external magnetic field was oriented along the earth's magnetic field in order to compensate its horizontal component. The magnetization was measured with a sample-vibrating magnetometer with a He closedcycle refrigerator, which allows one to vary the sample temperature between 11 and 300 K. Vortices were generated by cooling the sample in the magnetic field of interest from 100 to 11 K at a cooling rate of 1 K / min. Once the sample was at its lowest temperature, the external magnetic field was turned off, causing the diamagnetic contribution to disappear so that the magnetization was the remanence due to the trapped vortices in the sample. After that the sample was heated to its non-superconducting state at a heating rate of 0.5 or 1 K/min.
Bokhimi, A. Morales / Physica C 234 (1994) 333-338
3. Results and discussion
As is known, with each vortex is associated a quantum flux ~o=h/2e, so that the magnetic flux produced by N parallel vortices is N~o =A B, with A the total area perpendicular to them and B the magnitude of the magnetic induction B that they generate, which in our case is equal to 4nM, with M the remanent magnetization. We have found that a good way to see the effect of the vortex-generating magnetic field on the remanent magnetization is to normalize the corresponding magnitude of the magnetic induction to its value at zero kelvin, Bo, which differs little from its value at the lowest sample temperature, using for the normalized magnetic induction B/Bo the name of reduced magnetic induction. Fig. 1 shows this induction for different external magnetic fields as a function of reduced temperature t = T/To, with T the temperature and Tc = 91.2 K the transition temperature to the superconducting state. This figure clearly shows the effect of the field on the temperature variation of the reduced induction that decreases faster with temperature at higher fields, which also depends on sample history. From the figure we also observe that at a magnetic field of 1.00e, where the vortices are nearly insulated from each other, the magnetization is constant for temperatures far away from the transition temperature To; for this magnetic field the vortex density is low and consequently the vortexvortex interaction is negligible. The experiment at a magnetic field of 1.0 Oe was repeated for different t.10
0.86-
heating rates, obtaining the same result, which means that the remanent magnetization, for the range of fields used in the present work, does not depend on the temperature gradients in the sample. This result implies that the variation of the remanent magnetization with temperature for these fields only depends on the flux pinning force, which dominates the weak vortex-vortex interaction. At higher external magnetic fields the reduced magnetic induction decreases with increasing temperature. For these fields a large vortex density is produced, increasing the vortex-vortex interaction. Repeating these experiments at different heating rates, the results are the same, which means that temperature gradients in the sample do not play any role in the observed behavior, at least for the fields used in the present work. Therefore, we conclude that for the fields used in the present work the variation of the FC remanent magnetization is only determined by the competition between the flux pinning force and the vortex-vortex interaction. At much higher magnetic fields and fixed temperature, vortices are no longer static and start to move, producing a time-relaxing magnetization. This only happens in our samples when the field is higher than 250 Oe, which is much higher than the fields used for the reported results in the present work. From the above paragraphs we conclude that the reduced magnetic induction is useful for a qualitative analysis of the remanent magnetization; however, it will be much more interesting if this representation is also useful for a quantitative analysis. Therefore, we have tried to find an analytical function to fit the experimental data, finding at length that the function given by
B/Bo = -o CIC3 C~
0.62 -
0.38-
o.o
I - t 21(l-a) ,
(I )
with 0.0< a < 1.0, fits the experimental data well for
Y B02Cu307-x
0.14
-0.I0
335
0'.25
0'.50
o175
I'.OO
'
÷
Fig. 1. Reduced magnetic induction as a function of temperature for polyerystalline samples of the YBCO system. The vortex-generating external magnetic fields are indicated.
external magnetic fields lower than 7 . 0 0 e . This function was obtained for the first time by Gorter and Casimier [ 14 ] in their paper from which they later derived their two-fluid model However, for them a takes only the value of 0.5. Because the function given in Eq. ( 1 ) describes the variation of the remanent magnetization with temperature, the parameter ot of this equation must contain information about the competition between the flux pinning force and the vortex-vortex interaction,
Bokhimi, A. Morales I Physica C 234 (1994) 333-338
336
which are the elements responsible for this variation. When the vortices are nearly insulated, they are fixed to the sample by the flux pinning force while the vortex-vortex interaction is negligible; in this case the FC remanent magnetization is constant and a tends to 1.0 according to the results shown in Fig. 2, where the experimental data (circles) and the fitting curve (continuous line) for the reduced magnetic induction are shown as a function of temperature when the vortices are generated in a magnetic field of 0.5 Oe. The data were fitted with the function given by Eq. ( 1 ) using a least squares procedure, obtaining from the fitting an ot value of 0.9497 (3), the standard deviation being obtained from the fitting. As mentioned above, the function given in Eq. ( 1 ) works well for H < 7.0 Oe, where at decreases as the vortex density increases according to Table 1 and Fig. 3. From this table we also observe a correlation between the parameter at and the vortex density at zero kelvin: decreasing at as the vortex density increases. Because for a given sample the flux pinning forces are fixed and do not depend on the external magnetic field, the correlation between parameter at and the vortex density at zero kelvin is an indirect correlation between the vortex density and the difference between the flux pinning force and the vortex-vortex interaction, at changes with external magnetic field, and depends on the preparation and heat treatment 1.10
0
0.62 -
cr~
H (Oe)
ol
0.5 1.0 3.0 5.0 7.0
0.9497(3) 0.9342(4) 0.8854(5) 0.8448(5) 0.817(2)
Bo (gauss)
Bolero
0.00089 0.00173 0.00502 0.00823 0.01146
0.043 0.084 0.243 0.398 0.554
0,tm -2 )
Y 8°2 Cus 07_x 0.8 L/
OO~ v
o
/
0.6i
.
,
~, v
~
/
oo ' O x7
0'4 f 0,2
~
V
°~ ~°
0,0
o
6
1'o'
o i
Y B02 Cu3 07-x H:O.50e
0.38-
0.14-
-0.10 0.25
0.50
o
o4o go H (Oe)
Fig. 3. The parameter or, of the function B/Bo= 1 - t 2/t1-~), as a
function of the vortex-generatingexternal magnetic field, for samples with densities of 72.1 ( 1 )% (filled dots ), 85.5 ( 1 )% (triangles) and 41.8( 1 )% (open circles) of the ideal YBCO mass density.
B/Bo=(1-t2/tl-'~))c+(1-t2/(l-'~l))d, 0.0
o
of the sample (Fig. 3), which is in accordance with the well-known dependence of the vortex distribution and flux pinning forces on the previous history of the sample. For magnetic fields between 7.0 and 34.0 Pc, experimental data are only well fitted by assuming a function generated by the sum of two functions similar to that given in Eq. ( 1 ). B/Bo is then given by
0.86-
co
Table 1 Magnetic induction, average vortex density at zero kelvin and the respective parameter a for vortices generated in external magnetic fields Hlower than or equal to 7 . 0 0 e
0.75
tO0
Fig. 2. Reduced magnetic induction as a function of temperature produced by vortices generated in an external magnetic field of 0.50e. The continuous line is the fitted curve given by the function B/Bo= 1 - t 2/°-'~), with a=0.9497. Only some of the experimental data are shown (open circles) to avoid hiding the theoretical curve.
(2)
with a and a~ between 0.0 and 1.0 and c + d = 1.0. Fig. 4 shows the reduced magnetic induction when vortices are generated in an external magnetic field of 2 0 . 0 0 e . The experimental data were fitted using Eq. (2), and it also shows the partial and total contributions to the reduced magnetic induction. Experimental data are given by the the open circles, show-
Bokhimi, A. Morales / Physica C 234 (1994) 333-338 1,10
CY " - , ~ . 0.86 ~ H
'-'02Cu3 07_x =20.00e
0,62 o
B ............
r-n 0.38-
~.
A
N
.A OO
-0.10
o.o
0:25
0:50
o'.75
i, oo
f Fig. 4. Reduced magnetic induction as a function of reduced
temperature due to vortices generatedin an external magnetic field of 20.00e. Curves A and B are given by the function B~ B0= l - t 2/°-a) with a=0.182 and 0.701, respectively.Curve C (continuousline) is the sum of curvesA and B, with only some of the experimentaldata shown (open circles). ing only some of them in order to make visible the adjusted curve. The contribution (54.7 (6)% at zero kelvin) of the magnetization corresponding to or=0.701 (2) is given by curve B, while the contribution corresponding to a~ (45.3(5)% at zero kelvin) is given by curve A. Curve C (continuous line) represents the adjusted curve to the experimental data, which is the sum of curves A and B. According to the physical interpretation for a given in the above paragraphs, Eq. (2) suggests that for magnetic fields between 7.0 and 3 4 . 0 0 e two types of vortices coexist, which agrees with the well-known fact that polycrystalline samples have two types of vortices, the intergrain or Josephson vortices and the intragrain or Abrikosov vortices identified by magnetization measurements [ 12 ], electron spin resonance [ 15 ] and microwave absorption [ 16 ]. Because in polycrystalline samples of high-T¢ superconductors the grain boundaries between weak-linking grains are good centers for trapping magnetic flux [ 17 ], the intergrain vortex density will be higher than the intragrain vortex density, so that for low fields the vortexvortex interaction between intergrain vortices will be large, dominating the flux pinning forces, which allows the vortices to move producing a change of the magnetization with temperature. This means that at low fields the observed behavior of the magnetization, which is represented by the parameter ot in Eq.
337
(1), basically corresponds to that produced by the Josephson vortices; at higher fields the corresponding contribution is given by the parameter ct in Eq. (2). From Fig. 3 we observe that a decreases faster with the magnetic field for the sample with the lowest mass density (41.8% of the ideal mass density), which is the sample richest in weak links and therefore the sample with a higher Josephson vortex density as well. For external magnetic fields between 34.0 and 50.0 Oe the contribution of the first term in Eq. (2) corresponding to the Josephson vortices is zero, which means that the Josephson vortices have disappeared. Consequently, the field of 3 4 . 0 0 e can be identified as the critical field Hc2j, which according to Fig. 3 is independent of the sample. This value for He2j is about one half of the respective value obtained from ZFC magnetization curves of YBCO dense samples [ 12 ]. The field of 50.00e marks the upper limit of the fields for which the type of quantification of the FC remanent magnetization given in the present work can be applied, when the samples belong to the YBCO system and are prepared in a similar way as we did. Above this field it is impossible to fit well the experimental data with Eqs. ( 1 ) or (2). The parameter cq, associated with the intragrain vortices, is nearly independent of the external magnetic field (Table 2), suggesting that the intragrain vortex-vortex interaction does not change significantly for the range of magnetic fields used in the present work.
4. Conclusions Representation of the FC remanent magnetization by the reduced magnetic induction B / B o allows one to see deafly the changes in the magnetization as a function of temperature which are produced at different external magnetic fields. We have found the basic function B / B o = 1 - t 2/(1-'~) to quantify the reduced magnetic induction, with the parameter a related to the competition between the flux pinning force and the vortex-vortex interaction; when this interaction is weak a tends to 1.0, indicating that vortices do not move for temperatures far away from
To. From our quantitative analysis we find that for ex-
338
BokhimL A. Morales/Physica C234 (1994) 333-338
Table 2 Average vortex density at zero kelvin, and the contribution of the two vortex densities to the reduced magnetic induction as a function of the external magnetic field H in which they were generated. According to Eq. (2) each density is characterized by the pairs (ol, c) and (oq, d) H
Bo/Oo
(Oe)
(ttm -2)
1.0 10.0 20.0 30.0 33.0 40.0
0.084 0.643 1.073 1.576 1.644 1.940
a
c
ai
d
0.9342(4) 0.766(2) 0.701(2) 0.693(5) 0.636(9) -
1.0 0.7624(6) 0.547(6) 0.262(8) 0.24(I) -
0.185(2) 0.182(6) 0.185(6) 0.147(8) 0.163(1)
0.234(6) 0.453(5) 0.739(8) 0.76(8) 1.000
ternal magnetic fields between 7.0 and 3 4 . 0 0 e the experimental data can only be well fitted with a sum of two functions of the type mentioned in the above paragraph, which we interpret as the presence of two types of vortices in the sample. This result is in accordance with the well-known fact that for low fields in polycrystalline samples of the YBCO system intergrain and intragrain vortices coexist, showing that the type of analysis of the data described in the present paper can be used as an alternative technique to identify both kinds of vortices. From the quantitative analysis we have also found a magnetic field at which one of the vortex types disappears. This field is sample independent and we associate it with the critical field Hc2j of the intergrain vortices.
Acknowledgement We would like to thank A. Aceves for technical assistance.
References [ 11 D.J. Bishop, P.L. Gamm¢l, D.A. Huse and C.A. Murray, Science 255 (1992) 165.
[2] P.W. Anderson, Phys. Rev. Lett. 9 (1962) 309. [3] Y. Yeshurum and A.P. Malozemoff, Phys. Rev. Lett. 60 (1988) 2202. [4] K.A. Miiller, M. Takashige and J.G. Bednorz, Phys. Rev. Lett. 58 (1987) 1143. [ 5 ] A.M. Campbell and J.E. Evetts, Adv. Phys. 21 ( 1972 ) 199. [6] M. Golosovsky, M. Tsindlekht, H. Chayet and D. Davidov, Phys. Rev. B 50 (1994) July. [7] U. Essman and H. Tfiiuble, Phys. Left. 24A (1967) 526. [ 8 ] K. Harada, T. Matsuda, H. Kasai, J.E. Bonevich, T. Yoshida, U. Kawabe and A. Tonomura, Phys. Rev. Lett. 71 (1993) 337. [9] A. Tonomura, Proc. 4th Int. Conf. on Materials & Mechanism of Superconductivity, High-Temperature Superconductors, MZS-HTSC-IV, Grenoble, France, 5-9 July 1994. [10] S. Senoussi, G. Aguillon and S. Hadjoudj, Physica C 175 (1991) 215. [ 11 ] B. Schultz, B. Schliepe, W. Wisny and K. Bebershke, Solid State Commun. 80 ( 1991 ) 111. [ 12] B. Schliepe, Ph.D. Thesis, FU-Berlin, Germany, November 1992. [13]M.R. Koblischka, N. Moser, B. Gegenheimer and H. Kronmiiller, Physica C 166 (1990) 36. [ 14] C.J. Gorter and H. Casimier, Phys. Z. 35 (1934) 963. [15] H. Muto, K. Matsura and Y. Tai, Physica C 219 (1994) 259. [ 16] B. Czyzak, J. Stankowski and J. Martinek, Physica C 201 (1992) 379. [ 17 ] Videotape and brochure about the Flux Imaging System for Superconducting samples of the Phase Metrix Company, 3987 Sorrento Valley Blvd., San Diego, CA 92121, USA.