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Measurement of in-plane magnetic relaxation in RE-123 coated conductors by use of scanning Hall probe microscopy
Physica C 484 (2013) 139–141
Contents lists available at SciVerse ScienceDirect
Physica C journal homepage: www.elsevier.com/locate/physc
Measurement of in-plane magnetic relaxation in RE-123 coated conductors by use of scanning Hall probe microscopy K. Shiohara a,⇑, K. Higashikawa a, M. Inoue a, T. Kiss a, Y. Iijima b, T. Saitoh b, M. Yoshizumi c, T. Izumi c a
Kyushu University, 744 Motooka, Nishi-ku, Fukuoka City, Fukuoka 819-0395, Japan Fujikura Ltd., Sakura Works 1440 Mutsuzaki, Sakura-shi, Chiba 285-8550, Japan c SRL-ISTEC, 10-13 Shinonome 1-chome, Koto-ku, Tokyo 135-0062, Japan b
a r t i c l e
i n f o
Article history: Accepted 28 March 2012 Available online 5 April 2012 Keywords: Characterization of superconducting materials Visualization of critical current distribution Scanning Hall-probe microscopy Coated conductor
a b s t r a c t We have investigated electric field criterion of in-plane critical current density in a coated conductor characterized by scanning Hall-probe microscopy (SHPM). From remanent field distribution and its relaxation measurements, we could obtain critical current distribution and induced electric field simultaneously by considering the Biot-Savart law and the Faraday’s law, respectively. These results lead us to evaluate a distribution of local critical current density and the corresponding criterion of electric field. As a result, it was found that the electric field criterion for the SHPM analysis was several orders lower than that used in the conventional 4-probe resistive method. However, the data point obtained by the SHPM shows good agreement with E–J curve analytically extended from the measurements by the 4probe method. This means that we could characterize in-plane distribution of critical current density in a coated conductor at an electric field criterion quantitatively by this method in a nondestructive manner. These findings will be very important information since the uniformity of local critical current density in a coated conductor at extremely low electric fields is a key issue (1) especially for DC applications, (2) for quality control of coated conductors, and (3) for the standardization of the characterization of critical current among different methods. Ó 2012 Elsevier B.V. All rights reserved.
1. Introduction Since the discovery of high critical temperature superconductivity, research and development in material science and applications have been carried out extensively. The subject of the enhancement of critical currents and homogeneity in critical current distribution in coated conductors has been always required for practical applications by the optimization of their fabrication process. For a contribution to such efforts, we have been investigating spatial uniformity in a coated conductor by scanning Hall-probe microscopy (SHPM) [1,2]. We reported that this method could characterize in-plane distribution of critical current density in coated conductors in a non-contact and non-destructive manner [2]. From the principle, the characterization results should be quantitative. However, there was some difference between the critical current obtained by SHPM and that by the 4-probe method. We consider that the difference comes from that of electric field criterion. ⇑ Corresponding author. Address: Faculty of Information Science and Electrical Engineering, Kyushu University, #546, West-2 Bldg, Motooka, Nishi, Fukuoka City, Fukuoka 819-0395, Japan. Tel.: +81 92 802 3678; fax: +81 92 802 3677. E-mail address: [email protected] (K. Shiohara). 0921-4534/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.physc.2012.03.067
In this study, we tried to estimate the electric field criterion in the analysis of SHPM. We could estimate such an electric field from the relaxation of magnetic field distribution by use of the Faraday’s law. 2. Experimental 2.1. Sample A piece of coated conductor fabricated by IBAD–PLD processes was selected as the sample of this work. This process is very promising for fabricating long coated conductor with high critical current [3]. The critical current, Ic, at an electric field criterion, Ec, of 104 V/m was measured by the conventional 4-probe method at first. The Ic was estimated to be 612 A for 2.5 lm thick and 10 mm wide GdBCO layer. The corresponding critical current density, Jc, was 2.45 1010 A/m2. 2.2. Measurement by SHPM The SHPM system was used for evaluations of the magnetic field distribution around the sample [1]. The sample was placed on the bore of a coil which was used for the application of external magnetic field to the sample, and was cooled together with the coil by
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K. Shiohara et al. / Physica C 484 (2013) 139–141
thermal conduction from a liquid nitrogen tank. In this system, a typical temperature was controlled to be 79 K. A Hall probe sensor was fixed on the head of a triaxial stage which was controlled by stepping motors. The active area of the Hall sensor was 50 50 lm, and the spatial resolutions of the stage were 1 lm in xy-plane and 0.25 lm in z-axis. The Hall sensor measured the perpendicular (z) component of magnetic field, Bz, distribution around the sample with a constant lift-off distance from sample surface at a remanent state after the application of sufficiently large external magnetic field. Then, according to the critical state model, the corresponding current density should be critical current density almost all the area of the sample except around the null line [2]. The in-plane distributions of current densities, i.e., sheet current densities, J, were estimated from the corresponding magnetic field distributions, Bz, by considering an inverse problem of the BiotSavart law [4]. Furthermore, if we can obtain the time derivative of magnetic fields, we can obtain the distribution of electric field, E, by the Faraday’s law [5]. In this study, we tried to obtain them from the magnetic relaxation [6] in a remanent state. This is the principle for the estimation of electric field criterion for the characterization of critical current density by SHPM. 3. Results and discussion Fig. 1 shows 2D scanned results for the sample at a remanent state. From the distribution of Bz, the corresponding distribution of J, and those of its components Jx and Jy were obtained as shown in the figure. It took 2 h to take the entire image which has a spatial resolution of 100 lm in x direction and 20 lm in y direction. If the scanning had been started immediately after the magnetization, the image would have been largely influenced by magnetic relaxation. From this point of view, we waited a time comparable to the required time for taking the entire image before we started the scanning. In this way, we could evaluate the in-plane homogeneity in coated conductors. Fig. 2 shows 1D plots for the magnetic field and sheet current density along the width direction across the sample (at the arrow ‘‘"’’ in Fig. 1). The distributions were obtained at two different times with an interval of 300 s. According to the critical state model, the magnitude of sheet current density should correspond to that of critical current density except in the middle part where the direction of the current changes. An objective of this research is to estimate the electric field criterion of the critical current density. The electric field, E, and can be estimated by Faraday’s law using the time differential of magnetic field distribution [5]. As shown in Fig. 1, since the sample has good homogeneity, we can assume that the sheet current flows domi-
nantly in the longitudinal direction at the middle part of the tape sample. Namely, we can assume that the transverse component of electric-field is negligible, then only need to consider longitudinal component, Ex(y). In this condition, we can obtain spatial Fourier transform of Ex(y) from a time derivation of Bz(y) across tape width as follows from Faraday’s law:
~ ~x ðky Þ ¼ i ky ejky jzlift-off @ Bz ðky Þ ; E 2 @t jky j ~x and @ B ~ z =@t are the Fourier transformations of Ex and where E ~ z =@t, respectively. The parameter zlift-off is the distance of the @B measurement point of Bz from the superconducting layer of the sample. The variable ky is the y-component of the wave vector. As mentioned above, we can assume Ey(x) is constant along x-coordinate and equal to zero where, we only need to consider that x-component of the wave vector, kx, is zero, therefore, the absolute value of wave vector can be obtained as |ky|. Fig. 3 shows the results. The time differential of the measured magnetic fields was obtained from the difference between the first and the second measurements with an interval of 300 s. From in~x ðky Þ, we can finally obtain Ex(y). The verse Fourier transform of E electric fields in the sample were approximately within a range of 1 109 to 2 109 V/m. If we calculate the average of them, the value becomes 1.3 109 V/m. It was found that the electric field criterion of the results was almost 5 order smaller than the typical one of 104 V/m. In the result of Fig. 2, the average values of sheet current density were 40.2 A/mm at the first scan and 39.9 A/mm at the second scan. This difference came from the relaxation of the magnetic field as shown in the inset in the plots. If we estimate the critical current by the summation of such sheet current densities, the value becomes 399–402 A at an electric field criterion of 1.3 109 V/m for the 10 mm wide sample at 79 K. The thickness of the superconducting layer was 2.5 lm, and then the corresponding critical current density could be estimated to be 1.6 1010 A/m2. This value is 20% smaller than that of 4-probe measurement at an electric field criterion of 104 V/m. We compared this result with E–J characteristics obtained by the conventional 4-probe transport method. The data point by the SHPM, i.e. the current of 1.6 1010 A/m2 at the electric field of 1.3 109 V/m at 79 K, was plotted in Fig. 4. We obtained this point from an overall average of Fig. 2b and an overall average of Fig. 3b as stated above. The E–J curve at 79 K was analytically described by the percolation model [7] whose parameters were determined from the results by the conventional 4-probe method at 77 K and 83 K. As can be seen in the figure, the SHPM measurement result was consistent with the E–J characteristics estimated
Fig. 1. 2D scanned results for the sample at a remanent state measured by SHPM.
K. Shiohara et al. / Physica C 484 (2013) 139–141
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Fig. 2. Measured magnetic field, Bz (B\tape) and longitudinal sheet current density, Jx, measured by SHPM. (a) The remanent field, Bz, (b) sheet current, Jx. The insets are partial enlarged view to show the difference between the first and second measurements.
Fig. 3. (a) The time differential calculation of measured magnetic fields and (b) electric field estimated by Faraday’s law.
characterized by scanning Hall-probe microscopy. By a measurement of magnetic relaxation in a remanent state, we could successfully evaluate the electric field criterion by Faraday’s law. The result was consistent with the analytically estimated E–J curve from the conventional 4-probe measurements. This result indicates that the SHPM could characterize the distribution of critical current density at an low electric field which were especially important for DC applications such as magnets using a persistent current mode. Furthermore, the SHPM may predict the value of critical current at the typical electric field criterion by non-destructive manner. This should be discussed as a future work. Acknowledgment Fig. 4. Comparison with E–J characteristics in self magnetic fields by the conventional 4-probe resistive method and the SHPM. Solid lines as well as dotted line are calculation by the percolation transition model [7] based on the 4-probe measurements.
from the conventional 4-probe method. This result indicates that the SHPM could characterize the distribution of critical current density at an extremely low electric field which were especially important for DC applications such as magnets using a persistent current mode. Furthermore, the SHPM may predict the value of critical current at the typical electric field criterion by non-destructive manner. 4. Conclusions In this study, we have investigated electric field criterion of inplane distribution of critical current density in a coated conductor
This work was supported by New Energy and Industrial Technology Development Organization (NEDO) through the ISTEC as the project for Development of Materials and Power Application of Coated Conductors (M-PACC). References [1] M. Inoue, K. Abiru, Y. Honda, T. Kiss, Y. Iijima, K. Kakimoto, T. Saitoh, K. Nakao, Y. Shiohara, IEEE Trans. Appl. Supercond. 19 (2009) 2847. [2] K. Higashikawa, M. Inoue, T. Kawaguchi, K. Shiohara, K. Imamura, T. Kiss, Y. Iijima, K. Kakimoto, T. Saitoh, T. Izumi, Physica C 471 (2011) 1036. [3] M.Igarashi, K. Kakimoto, S. Hanyu, R. Kikutake, Y. Sutoh, R. Suzuki, M. Daibo, H. Fuji, H. Kutami, Y. Iijima, T. Saitoh, EUCAS2011, 2-WT-01. [4] B.J. Roth, N.G. Sepulveda, J.P. Wikswo, J. Appl. Phys. 65 (1989) 361. [5] R.B. Dinner, K.A. Moler, D.M. Feldmann, M.R. Beasley, Phys. Rev. B 75 (2007) 144503. [6] Y. Yeshurun, A.P. Malozemoff, A. Shaulov, Rev. Mod. Phys. 68 (1996) 911. [7] T. Kiss, M. Inoue, S. Egashira, T. Kuga, M. Ishimaru, M. Takeo, T. Matsushita, Y. Iijima, K. Kakimoto, T. Saitoh, S. Awaji, K. Watanabe, Y. Shiohara, IEEE Trans. Appl. Supercond. 13 (2003) 2607.
Contents lists available at SciVerse ScienceDirect
Physica C journal homepage: www.elsevier.com/locate/physc
Measurement of in-plane magnetic relaxation in RE-123 coated conductors by use of scanning Hall probe microscopy K. Shiohara a,⇑, K. Higashikawa a, M. Inoue a, T. Kiss a, Y. Iijima b, T. Saitoh b, M. Yoshizumi c, T. Izumi c a
Kyushu University, 744 Motooka, Nishi-ku, Fukuoka City, Fukuoka 819-0395, Japan Fujikura Ltd., Sakura Works 1440 Mutsuzaki, Sakura-shi, Chiba 285-8550, Japan c SRL-ISTEC, 10-13 Shinonome 1-chome, Koto-ku, Tokyo 135-0062, Japan b
a r t i c l e
i n f o
Article history: Accepted 28 March 2012 Available online 5 April 2012 Keywords: Characterization of superconducting materials Visualization of critical current distribution Scanning Hall-probe microscopy Coated conductor
a b s t r a c t We have investigated electric field criterion of in-plane critical current density in a coated conductor characterized by scanning Hall-probe microscopy (SHPM). From remanent field distribution and its relaxation measurements, we could obtain critical current distribution and induced electric field simultaneously by considering the Biot-Savart law and the Faraday’s law, respectively. These results lead us to evaluate a distribution of local critical current density and the corresponding criterion of electric field. As a result, it was found that the electric field criterion for the SHPM analysis was several orders lower than that used in the conventional 4-probe resistive method. However, the data point obtained by the SHPM shows good agreement with E–J curve analytically extended from the measurements by the 4probe method. This means that we could characterize in-plane distribution of critical current density in a coated conductor at an electric field criterion quantitatively by this method in a nondestructive manner. These findings will be very important information since the uniformity of local critical current density in a coated conductor at extremely low electric fields is a key issue (1) especially for DC applications, (2) for quality control of coated conductors, and (3) for the standardization of the characterization of critical current among different methods. Ó 2012 Elsevier B.V. All rights reserved.
1. Introduction Since the discovery of high critical temperature superconductivity, research and development in material science and applications have been carried out extensively. The subject of the enhancement of critical currents and homogeneity in critical current distribution in coated conductors has been always required for practical applications by the optimization of their fabrication process. For a contribution to such efforts, we have been investigating spatial uniformity in a coated conductor by scanning Hall-probe microscopy (SHPM) [1,2]. We reported that this method could characterize in-plane distribution of critical current density in coated conductors in a non-contact and non-destructive manner [2]. From the principle, the characterization results should be quantitative. However, there was some difference between the critical current obtained by SHPM and that by the 4-probe method. We consider that the difference comes from that of electric field criterion. ⇑ Corresponding author. Address: Faculty of Information Science and Electrical Engineering, Kyushu University, #546, West-2 Bldg, Motooka, Nishi, Fukuoka City, Fukuoka 819-0395, Japan. Tel.: +81 92 802 3678; fax: +81 92 802 3677. E-mail address: [email protected] (K. Shiohara). 0921-4534/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.physc.2012.03.067
In this study, we tried to estimate the electric field criterion in the analysis of SHPM. We could estimate such an electric field from the relaxation of magnetic field distribution by use of the Faraday’s law. 2. Experimental 2.1. Sample A piece of coated conductor fabricated by IBAD–PLD processes was selected as the sample of this work. This process is very promising for fabricating long coated conductor with high critical current [3]. The critical current, Ic, at an electric field criterion, Ec, of 104 V/m was measured by the conventional 4-probe method at first. The Ic was estimated to be 612 A for 2.5 lm thick and 10 mm wide GdBCO layer. The corresponding critical current density, Jc, was 2.45 1010 A/m2. 2.2. Measurement by SHPM The SHPM system was used for evaluations of the magnetic field distribution around the sample [1]. The sample was placed on the bore of a coil which was used for the application of external magnetic field to the sample, and was cooled together with the coil by
140
K. Shiohara et al. / Physica C 484 (2013) 139–141
thermal conduction from a liquid nitrogen tank. In this system, a typical temperature was controlled to be 79 K. A Hall probe sensor was fixed on the head of a triaxial stage which was controlled by stepping motors. The active area of the Hall sensor was 50 50 lm, and the spatial resolutions of the stage were 1 lm in xy-plane and 0.25 lm in z-axis. The Hall sensor measured the perpendicular (z) component of magnetic field, Bz, distribution around the sample with a constant lift-off distance from sample surface at a remanent state after the application of sufficiently large external magnetic field. Then, according to the critical state model, the corresponding current density should be critical current density almost all the area of the sample except around the null line [2]. The in-plane distributions of current densities, i.e., sheet current densities, J, were estimated from the corresponding magnetic field distributions, Bz, by considering an inverse problem of the BiotSavart law [4]. Furthermore, if we can obtain the time derivative of magnetic fields, we can obtain the distribution of electric field, E, by the Faraday’s law [5]. In this study, we tried to obtain them from the magnetic relaxation [6] in a remanent state. This is the principle for the estimation of electric field criterion for the characterization of critical current density by SHPM. 3. Results and discussion Fig. 1 shows 2D scanned results for the sample at a remanent state. From the distribution of Bz, the corresponding distribution of J, and those of its components Jx and Jy were obtained as shown in the figure. It took 2 h to take the entire image which has a spatial resolution of 100 lm in x direction and 20 lm in y direction. If the scanning had been started immediately after the magnetization, the image would have been largely influenced by magnetic relaxation. From this point of view, we waited a time comparable to the required time for taking the entire image before we started the scanning. In this way, we could evaluate the in-plane homogeneity in coated conductors. Fig. 2 shows 1D plots for the magnetic field and sheet current density along the width direction across the sample (at the arrow ‘‘"’’ in Fig. 1). The distributions were obtained at two different times with an interval of 300 s. According to the critical state model, the magnitude of sheet current density should correspond to that of critical current density except in the middle part where the direction of the current changes. An objective of this research is to estimate the electric field criterion of the critical current density. The electric field, E, and can be estimated by Faraday’s law using the time differential of magnetic field distribution [5]. As shown in Fig. 1, since the sample has good homogeneity, we can assume that the sheet current flows domi-
nantly in the longitudinal direction at the middle part of the tape sample. Namely, we can assume that the transverse component of electric-field is negligible, then only need to consider longitudinal component, Ex(y). In this condition, we can obtain spatial Fourier transform of Ex(y) from a time derivation of Bz(y) across tape width as follows from Faraday’s law:
~ ~x ðky Þ ¼ i ky ejky jzlift-off @ Bz ðky Þ ; E 2 @t jky j ~x and @ B ~ z =@t are the Fourier transformations of Ex and where E ~ z =@t, respectively. The parameter zlift-off is the distance of the @B measurement point of Bz from the superconducting layer of the sample. The variable ky is the y-component of the wave vector. As mentioned above, we can assume Ey(x) is constant along x-coordinate and equal to zero where, we only need to consider that x-component of the wave vector, kx, is zero, therefore, the absolute value of wave vector can be obtained as |ky|. Fig. 3 shows the results. The time differential of the measured magnetic fields was obtained from the difference between the first and the second measurements with an interval of 300 s. From in~x ðky Þ, we can finally obtain Ex(y). The verse Fourier transform of E electric fields in the sample were approximately within a range of 1 109 to 2 109 V/m. If we calculate the average of them, the value becomes 1.3 109 V/m. It was found that the electric field criterion of the results was almost 5 order smaller than the typical one of 104 V/m. In the result of Fig. 2, the average values of sheet current density were 40.2 A/mm at the first scan and 39.9 A/mm at the second scan. This difference came from the relaxation of the magnetic field as shown in the inset in the plots. If we estimate the critical current by the summation of such sheet current densities, the value becomes 399–402 A at an electric field criterion of 1.3 109 V/m for the 10 mm wide sample at 79 K. The thickness of the superconducting layer was 2.5 lm, and then the corresponding critical current density could be estimated to be 1.6 1010 A/m2. This value is 20% smaller than that of 4-probe measurement at an electric field criterion of 104 V/m. We compared this result with E–J characteristics obtained by the conventional 4-probe transport method. The data point by the SHPM, i.e. the current of 1.6 1010 A/m2 at the electric field of 1.3 109 V/m at 79 K, was plotted in Fig. 4. We obtained this point from an overall average of Fig. 2b and an overall average of Fig. 3b as stated above. The E–J curve at 79 K was analytically described by the percolation model [7] whose parameters were determined from the results by the conventional 4-probe method at 77 K and 83 K. As can be seen in the figure, the SHPM measurement result was consistent with the E–J characteristics estimated
Fig. 1. 2D scanned results for the sample at a remanent state measured by SHPM.
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Fig. 2. Measured magnetic field, Bz (B\tape) and longitudinal sheet current density, Jx, measured by SHPM. (a) The remanent field, Bz, (b) sheet current, Jx. The insets are partial enlarged view to show the difference between the first and second measurements.
Fig. 3. (a) The time differential calculation of measured magnetic fields and (b) electric field estimated by Faraday’s law.
characterized by scanning Hall-probe microscopy. By a measurement of magnetic relaxation in a remanent state, we could successfully evaluate the electric field criterion by Faraday’s law. The result was consistent with the analytically estimated E–J curve from the conventional 4-probe measurements. This result indicates that the SHPM could characterize the distribution of critical current density at an low electric field which were especially important for DC applications such as magnets using a persistent current mode. Furthermore, the SHPM may predict the value of critical current at the typical electric field criterion by non-destructive manner. This should be discussed as a future work. Acknowledgment Fig. 4. Comparison with E–J characteristics in self magnetic fields by the conventional 4-probe resistive method and the SHPM. Solid lines as well as dotted line are calculation by the percolation transition model [7] based on the 4-probe measurements.
from the conventional 4-probe method. This result indicates that the SHPM could characterize the distribution of critical current density at an extremely low electric field which were especially important for DC applications such as magnets using a persistent current mode. Furthermore, the SHPM may predict the value of critical current at the typical electric field criterion by non-destructive manner. 4. Conclusions In this study, we have investigated electric field criterion of inplane distribution of critical current density in a coated conductor
This work was supported by New Energy and Industrial Technology Development Organization (NEDO) through the ISTEC as the project for Development of Materials and Power Application of Coated Conductors (M-PACC). References [1] M. Inoue, K. Abiru, Y. Honda, T. Kiss, Y. Iijima, K. Kakimoto, T. Saitoh, K. Nakao, Y. Shiohara, IEEE Trans. Appl. Supercond. 19 (2009) 2847. [2] K. Higashikawa, M. Inoue, T. Kawaguchi, K. Shiohara, K. Imamura, T. Kiss, Y. Iijima, K. Kakimoto, T. Saitoh, T. Izumi, Physica C 471 (2011) 1036. [3] M.Igarashi, K. Kakimoto, S. Hanyu, R. Kikutake, Y. Sutoh, R. Suzuki, M. Daibo, H. Fuji, H. Kutami, Y. Iijima, T. Saitoh, EUCAS2011, 2-WT-01. [4] B.J. Roth, N.G. Sepulveda, J.P. Wikswo, J. Appl. Phys. 65 (1989) 361. [5] R.B. Dinner, K.A. Moler, D.M. Feldmann, M.R. Beasley, Phys. Rev. B 75 (2007) 144503. [6] Y. Yeshurun, A.P. Malozemoff, A. Shaulov, Rev. Mod. Phys. 68 (1996) 911. [7] T. Kiss, M. Inoue, S. Egashira, T. Kuga, M. Ishimaru, M. Takeo, T. Matsushita, Y. Iijima, K. Kakimoto, T. Saitoh, S. Awaji, K. Watanabe, Y. Shiohara, IEEE Trans. Appl. Supercond. 13 (2003) 2607.