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Temperature dependence of vortex flux pinning in grain-oriented YBa2Cu3O7
Journal of Alloys and Compounds 363 (2004) 75–77
Temperature dependence of vortex flux pinning in grain-oriented YBa2 Cu3O7 M.K. Hasan (Qaseer)∗ Department of Physics, Jordan University of Science and Technology, Irbid 22110, Jordan Received 3 March 2003; received in revised form 14 May 2003; accepted 14 May 2003
Abstract Magnetization measurements were made in grain-oriented YBa2 Cu3 O7 sample over the temperature range from 4.2 K up to TC = 92 K. Within the applicability of Bean-critical state models, the saturated remnant magnetization (MR ), as a detailed function of T, was used as measurable quantity of the average vortex flux pinning. Our results reveal that MR scales according to the empirical relations: MR (emu/cm3 ) = 168t7 +26t1/2 along the c-axis, and MR (emu/cm3 ) = 45t9 +13t1/2 along the a–b plane, where t = 1−T/TC . For T/TC <0.3 the results show that the average pinning forces along the ab-plane are more influenced by temperature than along the c-axis. For T/TC > 0.3 the strength of the pinning forces is twice greater along the c-axis compared to pinning along the ab-plane, with same temperature dependence. © 2003 Elsevier B.V. All rights reserved. Keywords: Rare earth compounds; Superconductors; Magnetic measurements
1. Introduction
2. Experimental results and discussion
The vortex flux pinning is of continuous interest because it is the factor limiting the sustaining of high critical currents. It is known that the high temperature ceramics such as YBa2 Cu3 O7 , Tl2 Ba2 CaCu2 O8 , and Bi2 Sr2 CaCu2 O8 compounds are very anistropic in their magnetic and electrical properties. These anisotropies affect the critical currents sustained by these materials. Long tapes manufactured by inclined substrate deposition exhibit strong anisotropy in the critical currents [1,2]. Moreover, the ion irradiation methods used to enhance the critical currents introduce new anisotropies in these materials [3,4]. Therefore, it is of considerable interest to investigate the average pinning forces in such compounds within the framework of applicability of the Bean critical state model [5,6]. The sample we used in this study is grain-oriented YBa2 Cu3 O7 with specified crystal orientations where the crystal anisotropy and the grain boundaries serve as pinning agents.
Our grain-oriented sample was a circular disk of 5 mm diameter and 1 mm thickness in which small crystallites of YBa2 Cu3 O7 in epoxy matrix had been field oriented such that the c-axis is co-aligned where the other two directions are randomly oriented [7]. The collective c-axis lies in the plane of the sample disk. The DC magnetization M was measured by using vibrating sample magnetometer (VSM). At a fixed temperature, the field He is applied along the c-axis and M vs. He is recorded. The same method applied to measure M vs. He along the ab-plane which is perpendicular to the c-axis. To check the applicability of the Bean critical state model we made a set of measurements of the remnant magnetization from ZFC-states and FC-states. At T = 4.2 K, our results show that for fields above 10 kOe the remnant magnetization saturates at values of ∼168 emu/cm3 along the c-axis, and ∼54 emu/cm3 along the ab-plane. Therefore, if the remanence saturates at temperature of T = 4.2 K by a magnetic field of 10 kOe, then it should saturate even at lower field strength at higher temperatures. In these experiments we cycled the field by ±15 kOe. Therefore, it is not obligatory to use the remanent magnetization as a measurable quantity for the maximum pinning forces of the
∗ Department of Physics, Bahrain University, Isa town, P.O. Box 32038, Kingdom of Bahrain. E-mail address: [email protected] (M.K. Hasan (Qaseer)).
0925-8388/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0925-8388(03)00488-2
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Fig. 1. Major hystresis loops of magnetization M vs. the internal field H at 20 K for grain-oriented YBa2 Cu3 O7 . Closed circles along c-axis and open circles along the ab-plane.
vortices. It is worth mentioning that the saturation occurs at lower fields when the field is applied along the ab-plane. Typical examples of the major hysteresis loops are shown in Fig. 1. The figure shows the magnetization M vs. the internal field H along both the c-axis and the ab-plane directions at a temperature of T = 20 K. We present the internal filed H instead of the external field He because of the demagnetization effects. The demagnetization factors were determined from the initial slope of M vs. the applied filed He by assuming that the crystallites have identical spheriodal shapes. We found that the demagnetization factor along the c-axis to be DC = 5.84 and along the ab-plane to be Dab = 3.36. The internal field is given by H = He −DM, where D is the magnetization factor along the c-axis or along the ab-plane. The saturated remanent magnetization of the sample at any temperature T is taken from the magnetization M vs. H curve at H = 0. In this way we obtain two values for the remnance where we find the average value and represent it by MR . Therefore, MR is half of the average width of M vs. H curve at H = 0. As mentioned above MR is directly proportional to the average pinning forces holding the vortices (or directly to the critical currents). To explore the temperature variations of MR we repeated this measurement at different fixed temperatures and MR has been deduced at each T. In Fig. 2 we plot MR vs. the normalized temperature T/TC (TC ∼92 K) for fields along the c-axis. The data is fitted empirically by the relation MR (emu/cm3 ) = 168t7 +26t1/2 , where t = T/TC . Fig. 2 shows that MR decreases rapidly for T/TC < 0.3 and then decreases slowly for T/TC > 0.3. In Fig. 3 MR vs. T/TC has been plotted for the fields along the ab-plane. The data is fitted by MR (emu/cm3 ) = 45t9 +13t1/2 . Both expressions for MR show the same general behavior in which the average vortex pinning decreases with T. The exponent factor
Fig. 2. The magnetization remnance MR versus the normalized temperature T/TC for data taken along the c-axis. Solid line is the empirical fitting.
is indicating of the rate of this decrease. At lower temperatures the change in MR along the ab-plane is faster than along the c-axis. Therefore, at low temperatures the pinning forces along the ab-plane are more influenced by T. In both directions this rapid change in MR with temperature occurs for T/TC < 0.3. Above T/TC > 0.3 both curves exhibit the same general behavior but with a difference in the magnitude of the factor in the second term of the expressions for MR . In this regime these factors indicate that the strength of the average pinning forces is twice greater along the c-axis compared to ab-plane. For T/TC < 0.3, if we ignore the exponent factors in the first term of the expressions of MR we conclude that the strength of average pinning is 4-fold greater along the c-axis compared to ab-plane. These
Fig. 3. The magnetization remanence MR versus the normalized temperature T/TC for data taken along the ab-plane. Solid line is the empirical fitting.
M.K. Hasan (Qaseer) / Journal of Alloys and Compounds 363 (2004) 75–77
results indicate that the average pinning forces along the ab-plane is weaker than the pinning forces along the c-axis.
3. Conclusions We have studied the temperature dependence of the vortex flux pinning along two crystallographic directions of grain-oriented YBa2 Cu3 O7 (along the c-axis and along the ab-plane). Using the Bean critical state model the maximum of the average pinning forces was represented by the true remnant magnetization MR . For both directions we found that MR decreases rapidly with temperature for T/TC < 0.3 and then decreases slowly above this value. Our data was fitted empirically by MR = 168t7 +26t1/2 along the c-axis and by MR = 45t9 +13t1/2 along the ab-plane. Similar general behavior was found for both directions for T/TC > 0.3. For T/TC < 0.3 the average pinning forces along ab-plane are more influenced by temperature than along the c-axis. This decrease in the average pinning forces along each direction is purely a thermal effect.
77
Acknowledgements I’m very grateful to Professor J.S. Kouvel and the Physics Department at the University of Illinois at Chicago for the use of the facilities there.
References [1] Y. Sato, S. Hojo, Y. Takahashi, K. Muranaka, K. Fujino, T. Taneda, K. Ohmastu, K. Takei, Physica C 378 (2002) 1118. [2] T. Kiss, M. Inoue, S. Nishimura, T. Kuga, T. Matsushita, Y. Iijima, K. Kakimoto, T. Saitoh, S. Awaji, K. Watanabe, Y. Shiohara, Physica C 378 (2002) 1113. [3] L. Krusin-Elbaum, G. Blatter, J.R. Thompson, J. Ullmann, C.W. Chu, Physica C 355 (2000) 144. [4] J.A. Herbsommer, J. Luzuriaga, L. Civale, G. Nieva, G. Pasquini, H. Lanza, P. Levy, Physica C 304 (1998) 112. [5] C.P. Bean, Phys. Rev. Lett. 8 (1962) 250. [6] C.P. Bean, Phys. Rev. Mod. 36 (1964) 31. [7] M.K. Hasan, S.J. Park, J.S. Kouvel, J. Magn. Magn. Mater. 131 (1994) L1–L4.
Temperature dependence of vortex flux pinning in grain-oriented YBa2 Cu3O7 M.K. Hasan (Qaseer)∗ Department of Physics, Jordan University of Science and Technology, Irbid 22110, Jordan Received 3 March 2003; received in revised form 14 May 2003; accepted 14 May 2003
Abstract Magnetization measurements were made in grain-oriented YBa2 Cu3 O7 sample over the temperature range from 4.2 K up to TC = 92 K. Within the applicability of Bean-critical state models, the saturated remnant magnetization (MR ), as a detailed function of T, was used as measurable quantity of the average vortex flux pinning. Our results reveal that MR scales according to the empirical relations: MR (emu/cm3 ) = 168t7 +26t1/2 along the c-axis, and MR (emu/cm3 ) = 45t9 +13t1/2 along the a–b plane, where t = 1−T/TC . For T/TC <0.3 the results show that the average pinning forces along the ab-plane are more influenced by temperature than along the c-axis. For T/TC > 0.3 the strength of the pinning forces is twice greater along the c-axis compared to pinning along the ab-plane, with same temperature dependence. © 2003 Elsevier B.V. All rights reserved. Keywords: Rare earth compounds; Superconductors; Magnetic measurements
1. Introduction
2. Experimental results and discussion
The vortex flux pinning is of continuous interest because it is the factor limiting the sustaining of high critical currents. It is known that the high temperature ceramics such as YBa2 Cu3 O7 , Tl2 Ba2 CaCu2 O8 , and Bi2 Sr2 CaCu2 O8 compounds are very anistropic in their magnetic and electrical properties. These anisotropies affect the critical currents sustained by these materials. Long tapes manufactured by inclined substrate deposition exhibit strong anisotropy in the critical currents [1,2]. Moreover, the ion irradiation methods used to enhance the critical currents introduce new anisotropies in these materials [3,4]. Therefore, it is of considerable interest to investigate the average pinning forces in such compounds within the framework of applicability of the Bean critical state model [5,6]. The sample we used in this study is grain-oriented YBa2 Cu3 O7 with specified crystal orientations where the crystal anisotropy and the grain boundaries serve as pinning agents.
Our grain-oriented sample was a circular disk of 5 mm diameter and 1 mm thickness in which small crystallites of YBa2 Cu3 O7 in epoxy matrix had been field oriented such that the c-axis is co-aligned where the other two directions are randomly oriented [7]. The collective c-axis lies in the plane of the sample disk. The DC magnetization M was measured by using vibrating sample magnetometer (VSM). At a fixed temperature, the field He is applied along the c-axis and M vs. He is recorded. The same method applied to measure M vs. He along the ab-plane which is perpendicular to the c-axis. To check the applicability of the Bean critical state model we made a set of measurements of the remnant magnetization from ZFC-states and FC-states. At T = 4.2 K, our results show that for fields above 10 kOe the remnant magnetization saturates at values of ∼168 emu/cm3 along the c-axis, and ∼54 emu/cm3 along the ab-plane. Therefore, if the remanence saturates at temperature of T = 4.2 K by a magnetic field of 10 kOe, then it should saturate even at lower field strength at higher temperatures. In these experiments we cycled the field by ±15 kOe. Therefore, it is not obligatory to use the remanent magnetization as a measurable quantity for the maximum pinning forces of the
∗ Department of Physics, Bahrain University, Isa town, P.O. Box 32038, Kingdom of Bahrain. E-mail address: [email protected] (M.K. Hasan (Qaseer)).
0925-8388/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0925-8388(03)00488-2
76
M.K. Hasan (Qaseer) / Journal of Alloys and Compounds 363 (2004) 75–77
Fig. 1. Major hystresis loops of magnetization M vs. the internal field H at 20 K for grain-oriented YBa2 Cu3 O7 . Closed circles along c-axis and open circles along the ab-plane.
vortices. It is worth mentioning that the saturation occurs at lower fields when the field is applied along the ab-plane. Typical examples of the major hysteresis loops are shown in Fig. 1. The figure shows the magnetization M vs. the internal field H along both the c-axis and the ab-plane directions at a temperature of T = 20 K. We present the internal filed H instead of the external field He because of the demagnetization effects. The demagnetization factors were determined from the initial slope of M vs. the applied filed He by assuming that the crystallites have identical spheriodal shapes. We found that the demagnetization factor along the c-axis to be DC = 5.84 and along the ab-plane to be Dab = 3.36. The internal field is given by H = He −DM, where D is the magnetization factor along the c-axis or along the ab-plane. The saturated remanent magnetization of the sample at any temperature T is taken from the magnetization M vs. H curve at H = 0. In this way we obtain two values for the remnance where we find the average value and represent it by MR . Therefore, MR is half of the average width of M vs. H curve at H = 0. As mentioned above MR is directly proportional to the average pinning forces holding the vortices (or directly to the critical currents). To explore the temperature variations of MR we repeated this measurement at different fixed temperatures and MR has been deduced at each T. In Fig. 2 we plot MR vs. the normalized temperature T/TC (TC ∼92 K) for fields along the c-axis. The data is fitted empirically by the relation MR (emu/cm3 ) = 168t7 +26t1/2 , where t = T/TC . Fig. 2 shows that MR decreases rapidly for T/TC < 0.3 and then decreases slowly for T/TC > 0.3. In Fig. 3 MR vs. T/TC has been plotted for the fields along the ab-plane. The data is fitted by MR (emu/cm3 ) = 45t9 +13t1/2 . Both expressions for MR show the same general behavior in which the average vortex pinning decreases with T. The exponent factor
Fig. 2. The magnetization remnance MR versus the normalized temperature T/TC for data taken along the c-axis. Solid line is the empirical fitting.
is indicating of the rate of this decrease. At lower temperatures the change in MR along the ab-plane is faster than along the c-axis. Therefore, at low temperatures the pinning forces along the ab-plane are more influenced by T. In both directions this rapid change in MR with temperature occurs for T/TC < 0.3. Above T/TC > 0.3 both curves exhibit the same general behavior but with a difference in the magnitude of the factor in the second term of the expressions for MR . In this regime these factors indicate that the strength of the average pinning forces is twice greater along the c-axis compared to ab-plane. For T/TC < 0.3, if we ignore the exponent factors in the first term of the expressions of MR we conclude that the strength of average pinning is 4-fold greater along the c-axis compared to ab-plane. These
Fig. 3. The magnetization remanence MR versus the normalized temperature T/TC for data taken along the ab-plane. Solid line is the empirical fitting.
M.K. Hasan (Qaseer) / Journal of Alloys and Compounds 363 (2004) 75–77
results indicate that the average pinning forces along the ab-plane is weaker than the pinning forces along the c-axis.
3. Conclusions We have studied the temperature dependence of the vortex flux pinning along two crystallographic directions of grain-oriented YBa2 Cu3 O7 (along the c-axis and along the ab-plane). Using the Bean critical state model the maximum of the average pinning forces was represented by the true remnant magnetization MR . For both directions we found that MR decreases rapidly with temperature for T/TC < 0.3 and then decreases slowly above this value. Our data was fitted empirically by MR = 168t7 +26t1/2 along the c-axis and by MR = 45t9 +13t1/2 along the ab-plane. Similar general behavior was found for both directions for T/TC > 0.3. For T/TC < 0.3 the average pinning forces along ab-plane are more influenced by temperature than along the c-axis. This decrease in the average pinning forces along each direction is purely a thermal effect.
77
Acknowledgements I’m very grateful to Professor J.S. Kouvel and the Physics Department at the University of Illinois at Chicago for the use of the facilities there.
References [1] Y. Sato, S. Hojo, Y. Takahashi, K. Muranaka, K. Fujino, T. Taneda, K. Ohmastu, K. Takei, Physica C 378 (2002) 1118. [2] T. Kiss, M. Inoue, S. Nishimura, T. Kuga, T. Matsushita, Y. Iijima, K. Kakimoto, T. Saitoh, S. Awaji, K. Watanabe, Y. Shiohara, Physica C 378 (2002) 1113. [3] L. Krusin-Elbaum, G. Blatter, J.R. Thompson, J. Ullmann, C.W. Chu, Physica C 355 (2000) 144. [4] J.A. Herbsommer, J. Luzuriaga, L. Civale, G. Nieva, G. Pasquini, H. Lanza, P. Levy, Physica C 304 (1998) 112. [5] C.P. Bean, Phys. Rev. Lett. 8 (1962) 250. [6] C.P. Bean, Phys. Rev. Mod. 36 (1964) 31. [7] M.K. Hasan, S.J. Park, J.S. Kouvel, J. Magn. Magn. Mater. 131 (1994) L1–L4.