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Dose effect of heavy-ion irradiation on the critical exponents in YBa2Cu3O7−x thin films
Physica C 412–414 (2004) 497–501 www.elsevier.com/locate/physc
Dose effect of heavy-ion irradiation on the critical exponents in YBa2Cu3O7x thin films T. Sueyoshi a,*, S. Inada a, T. Fujiyoshi a, K. Miyahara a, T. Ikegami a, K. Ebihara a, R. Miyagawa b, Y. Chimi c, N. Ishikawa c, A. Iwase c,1 a
Faculty of Engineering, Kumamoto University, 2-39-1, Kurokami, Kumamoto 860-8555, Japan Kumamoto Industrial Research Institute, 3-11-8, Higashi-machi, Kumamoto 862-0901, Japan c Japan Atomic Energy Research Institute (JAERI), Tokai-mura, Ibaraki 319-1195, Japan
b
Received 29 October 2003; accepted 1 December 2003 Available online 2 July 2004
Abstract We investigated the influence of densities of columnar defects on the critical exponents estimated from the critical scaling analysis of current–voltage characteristics in YBa2 C3 O7x thin films. To avoid the difference of background pinning between samples, the densities of columnar defects were controlled in one sample successively. The dynamic critical exponent z increased with increasing the densities of columnar defects from B/ ¼ 0:5–1.0 T. It was also found that the installed defects led to the appearance of peak in the magnetic field dependence of z, while such peak did not appear before irradiation. These results are explained by the percolation model considering the statistical distribution of the pinning strength rather than the vortex glass–liquid transition model. The various changes of z due to the heavy-ion irradiation are related to the change of the pinning strength distribution due to the introduction of columnar defects, which act as the strong pinning centers. 2004 Elsevier B.V. All rights reserved. PACS: 74.25.Qt; 74.25.Sv; 74.72.Bk Keywords: Columnar defect; Critical current density; Flux pinning; Vortex glass–liquid transition
1. Introduction As a results of worldwide research efforts in recent years, the YBa2 C3 O7x (YBCO) coated conductors with high critical current density have *
Corresponding author. Tel.: +81-96-342-3849; fax: +81-96342-3630. E-mail address: [email protected] (T. Sueyoshi). 1 Present address: Osaka Prefecture University.
been fabricated by developed techniques such as the ion beam assisted deposition (IBAD) [1]. However, the critical current density Jc and the value of n which is defined by the power law of the current (I)–voltage (V ) characteristics, V / I n of such coated conductors still need to be improved and the mechanism limiting them to be explored. Therefore, the mechanism of flux pinning properties in YBCO thin films deposited by the pulsed laser deposition (PLD) method must be precisely comprehended as one of the basic researches for
0921-4534/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2003.12.056
498
T. Sueyoshi et al. / Physica C 412–414 (2004) 497–501
the more developed YBCO coated conductors. Note that the useful method to clarify this problem is comparison with different pinning properties for one sample, which must be achieved by the introduction of pinning centers artificially in a controlled manner. A variety of irradiation-induced defects in highTc superconductors have attracted interest because these defects work as effective flux pinning centers increasing the critical current density Jc and the irreversible temperature Tirr [2–4]. Furthermore, the irradiation with energetic particles (e.g. electrons, protons, neutrons and ions), which enables us to produce the defects artificially in a controlled manner, is a useful method to clarify the complex problems for the flux line dynamics of high-Tc superconductors. Among these, the introduction of columnar defects by the heavy-ion irradiation is the best way for the control of pinning properties. In this study, we investigate the influence of columnar defects on the flux pinning properties in YBCO thin films deposited by the PLD method, where the pinning parameters are Jc and the value of n. Especially, the irradiation effects on the value of n at the vortex glass–liquid transition temperature Tg attracts interest for both physically and technologically. The value of n at Tg is equivalent to the dynamic critical exponent z in the vortex glass–liquid transition model [5], while that also corresponds to the shape factor m of pinning strength distribution in the percolation model [6]. The recent experimental results have supported the latter model [7–10]. In order to clear the mechanism of the value of n in YBCO thin films, we estimate the irradiation effect of the dynamic critical exponent z and the vortex-glass transition temperature Tg by the critical scaling analysis of the current–voltage characteristics for each doses of the irradiation. Note that we controlled the densities of columnar defects in one sample successively in order to avoid the difference of background pinning between samples.
2. Experimental We prepared one YBCO thin film deposited on (1 0 0) surface of a SrTiO3 substrate by the PLD
method. The film with the thickness of 300 nm was c-axis oriented. On the thin film, two samples (sample #1 and #2) with the shape of 50 lm wide and 1mm long microbridge were defined by the chemical etching process. Irradiations with 200 MeV 136 Xe14þ ions were performed along the c-axis from a tandem accelerator at JAERI. In the first irradiation, the doses for the sample #1 was 2.5 · 1010 ions/cm2 with corresponding to a matching field B/ ¼ 0:5 T, while the sample #2 was unirradiated. After the measurements of the first irradiation effects, the second irradiation was performed for both samples with the same condition as the first one. The total doses were 5.0 · 1010 ions/cm2 (sample #1) and 2.5 · 1010 ions/cm2 (sample #2), corresponding to the matching fields B/ ¼ 1–0.5 T, respectively. The current–voltage characteristics were measured by the standard four probe method in which the current applied in the direction perpendicular to the applied magnetic field, the c-axis, and the columnar defects. The critical current density Jc was defined by a criterion of 103 V/m electric field. The critical exponents and the vortex glass transition temperature Tg were estimated from the scaling analysis of the current–voltage characteristics under the magnetic field.
3. Results and discussion Fig. 1 shows the comparison of the isothermal sets of the electrical field E versus current density J curves of the sample #1 between the doses of 2.5 · 1010 ions/cm2 (B/ ¼ 0:5 T) and 5.0 · 1010 ions/ cm2 (B/ ¼ 1:0 T) for B ¼ 1:5 T. The E–J curves of the second irradiation are shifted to higher current density region than that of the first one over the all temperatures. This means that the flux pinning force enlarges by the increment of densities of columnar defects. In Fig. 2, we show the typical sets of the temperature dependence of Jc for each dose in the sample #1 and #2 at B ¼ 0:5 and 1.5 T. The temperature is normalized by the critical temperature Tc for each irradiation in order to discuss the irradiation effects on the flux pinning without the influence of the variation of Tc . For the sample #1,
T. Sueyoshi et al. / Physica C 412–414 (2004) 497–501
Fig. 1. Comparison of isothermal E–J characteristics for sample #1 between the first (B/ ¼ 0:5T) and second irradiation (B/ ¼ 1:0 T) at several temperatures for B ¼ 1:5T parallel to the c-axis.
499
force of columnar defects with the small densities and the background pinning force in the as-grown thin films. That is, the critical current density Jc could hardly increase by means of the small dose of irradiation such as 2.5 · 1010 ions/cm2 , because the background pinning force for the as-grown film is too strong, which is well known in YBCO thin films deposited by the PLD method. This is given support by the fact that the values of Jc before and after irradiation for the sample #2 are almost equal to those for the doses of 2.5 · 1010 ions/cm2 for the sample #1, as shown in Fig. 1. In high-Tc superconductors, it is well known that such set of isothermal E–J curves collapses on two master curves above and below the vortexglass transition temperature Tg when plotted as mðz1Þ 2m ðE=J Þ=jT Tg j versus J =jT Tg j , where m and z are the static and dynamic critical exponents, respectively [11]. In Fig. 3, the scaling collapses in the two universal curves estimated from the E–J curves for the sample #1 with the doses of 2.5 · 1010 ions/cm2 in Fig. 1 are shown. Similar scaling behaviors were achieved at all conditions. We compare the dynamic critical exponent z between the dose of 2.5 · 1010 ions/cm2 (B/ ¼ 0:5 T) and 5.0 · 1010 ions/cm2 (B/ ¼ 1:0 T) for the sample #1, as shown in Fig. 4. It is clarified that the values of z increase with the densities of columnar defects. Furthermore, it is interesting that the peak appears
Fig. 2. Temperature dependence of Jc for B ¼ 0:5 T and 1.5 T both the sample #1 (upper) and #2 (lower), where the temperature is normalized by the critical temperature for each irradiation. Open symbols and closed ones represent the first and the second irradiation process, respectively.
the values of Jc increase with the doses of the irradiation. That is, the columnar defects are effective in increasing the critical current density in the YBCO thin films. However, the irradiation effect scarcely appears on the temperature dependence of Jc for the sample #2 for both B ¼ 0:5 and 1.5 T. This result for the sample #2 would result from the magnitude relation between the pinning
Fig. 3. Scaling collapses of E–J curves for sample #1 with the doses of 2.5 · 1010 ions/cm2 at B ¼ 1:5 T.
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Fig. 4. Comparison of the dynamic critical exponent z between B/ ¼ 0:5 T (M) and B/ ¼ 1:0 T (N) for the sample #1.
in the magnetic field dependences of z near the field B=B/ ¼ 1/3 for the doses of 5.0 · 1010 ions/cm2 . Although it seems that such peak is not seen for the doses of 2.5 · 1010 ions/cm2 where the data for B ¼ 0:1 T were not measured, the abrupt increment of z around B=B/ ¼ 1=3 is observed. In Fig. 5, the comparison of the values of z between before (B/ ¼ 0 T) and after irradiation (B/ ¼ 0:5 T) for the sample #2 is shown. The values of z are almost same between before- and after-irradiation, similar to the temperature dependence of Jc for the sample #2, as shown in Fig. 2. However, the peak is also observed in the magnetic field dependences of z near the field B=B/ ¼ 1=3 after
Fig. 5. Comparison of the dynamic critical exponent z between before-irradiation (M) and B/ ¼ 0:5 T (N) for the sample #2.
irradiation, similar to the sample #1. On the other hand, no peak is exhibited before irradiation. According to the vortex glass–liquid transition model [5], the universality of the critical exponents is predicted. However, our results are incompatible to this prediction. Especially, the appearance of the peak of z near B=B/ ¼ 1=3 could not explained even by the shift from the Bose glass behavior [12] to vortex glass one with increasing magnetic field. According to the percolation model [6], on the other hand, the dynamic critical exponent z is related to the parameter m determining the shape of the local critical current density (Jcl ) distribution. The parameter m increases with the weakening of the relative elastic correlation strength of vortices, which means that the shape of the distribution of Jcl tends to steep [13]. Therefore, one of our results, i.e. the increment of z for the sample #1 is considered to arise from the variation of distribution of Jcl due to the introduction of each different density of the columnar defects. We have already reported results similar to this in the references [8– 10]. The reason why the values of z scarcely make difference between before- and after-irradiation for the sample #2 is that the background pinning force in the as-grown film is too strong to bring the increment of z with small doses of the irradiation. This would be supported by no change of Jc before and after irradiation, as shown in Fig. 1. The peak of z near B=B/ ¼ 1=3 such as shown in Figs. 1 and 2 has been also observed in recent papers [10,14]. In the viewpoint of the percolation model, it is considered that the appearance of such peak of z is corresponding to uniforming the distribution of Jcl due to the matching effect, which would be suggested by the well-known Jc peak near the field of B=B/ ¼ 1=3 [14,15]. That is, every flux lines should be almost trapped in the columnar defects near B/ =B ¼ 1=3 due to the matching effect so that every local domains would possess same value of Jcl with each other. Therefore, the shape of the distribution of the local critical current density Jcl becomes steep and the value of z shows the peak around the B/ =B ¼ 1=3. According to the irradiation effects on the values of z, the scaling collapses of the current–voltage characteristics originate from the percolation network of the unpinned domains in YBCO thin
T. Sueyoshi et al. / Physica C 412–414 (2004) 497–501
films with the pinning strength distribution. So, the value of z, which is equivalent to the value of n at Tg should be governed by the shape of the pinning strength distribution.
501
Acknowledgements The authors would like to thank K. Kawano in the faculty of science in Kumamoto University for his technical supports and advices.
4. Summary References We investigated the influence of densities of columnar defects on the critical exponents estimated from the critical scaling analysis of current– voltage characteristics in YBa2 C3 O7x thin films. The columnar defects were produced by the heavyion irradiation with 200 MeV Xe ions parallel to c-axis. To avoid the difference of background pinning between samples, the densities of columnar defects were controlled in one sample successively. The dynamic critical exponent z increased with increasing the densities of columnar defects from B/ ¼ 0:5–1.0 T. As one of the important results, it was found that the installed defects led to the appearance of peak in the magnetic field dependence of z, while such one did not appear before irradiation. The magnetic field where the value of z has a peak shifts to higher field with increasing the densities of columnar defects and exists near B/ =3. These results are explained by the percolation model considering the distribution of the pinning strength rather than the vortex glass– liquid transition model. The various changes of z due to the heavy-ion irradiation are related to the change of the pinning strength distribution due to the introduction of columnar defects, which act as the strong pinning centers.
[1] Y. Iijima, N. Tanabe, O. Kohno, Y. Ikeno, Appl. Phys. Lett. 60 (1992) 769. [2] M.A. Kirk, Cryogenics 33 (1993) 235. [3] J. Giapintzakis, W.C. Lee, J.P. Rice, D.M. Ginsberg, I.M. Robertson, R. Wheeler, M.A. Kirk, M.-O. Ruault, Phys. Rev. B 45 (1992) 10677. [4] F.M. Sauerzopf, H.P. Wiesinger, H.W. Weber, G.W. Crabtree, Phys. Rev. B 51 (1995) 6002. [5] D.S. Fisher, M.P.A. Fisher, D.A. Huse, Phys. Rev. B 43 (1991) 130. [6] K. Yamafuji, T. Kiss, Physica C 258 (1996) 197. [7] B. Brown, J.M. Roberts, J. Tate, J.W. Farmer, Phys. Rev. B 55 (1997) R8713. [8] T. Sueyoshi, N. Ishikawa, A. Iwase, Y. Chimi, T. Kiss, T. Fujiyoshi, K. Miyahara, Physica C 309 (1998) 79. [9] T. Sueyoshi, N. Ishikawa, A. Iwase, Y. Chimi, T. Kiss, T. Fujiyoshi, K. Miyahara, Adv. Supercond. XI (1999) 79. [10] T. Sueyoshi, H. Yonemura, T. Kisakibaru, T. Fujiyoshi, K. Miyahara, T. Ikegami, K. Ebihara, R. Miyagawa, N. Ishikawa, A. Iwase, Physica C 388–389 (2003) 739. [11] R.H. Koch, V. Foglietti, W.J. Gallagher, G. Koren, A. Gupta, M.P.A. Fisher, Phys. Rev. Lett. 63 (1989) 1511. [12] D.R. Nelson, V.M. Vinokur, Phys. Rev. Lett. 68 (1992) 2398. [13] T. Kiss, T. Nakamura, K. Kuroda, M. Takeo, F. Irie, K. Yamafuji, Czech. J. Phys. 46 (1996) 1791. [14] T. Nojima, J.Z. Liu, T. Nishizaki, S. Okayasu, N. Kobayashi, Physica C 357–360 (2001) 469. [15] N. Chikumoto, M. Konczykowski, T. Terai, M. Murakami, Supercond. Sci. Technol. 13 (2000) 749.
Dose effect of heavy-ion irradiation on the critical exponents in YBa2Cu3O7x thin films T. Sueyoshi a,*, S. Inada a, T. Fujiyoshi a, K. Miyahara a, T. Ikegami a, K. Ebihara a, R. Miyagawa b, Y. Chimi c, N. Ishikawa c, A. Iwase c,1 a
Faculty of Engineering, Kumamoto University, 2-39-1, Kurokami, Kumamoto 860-8555, Japan Kumamoto Industrial Research Institute, 3-11-8, Higashi-machi, Kumamoto 862-0901, Japan c Japan Atomic Energy Research Institute (JAERI), Tokai-mura, Ibaraki 319-1195, Japan
b
Received 29 October 2003; accepted 1 December 2003 Available online 2 July 2004
Abstract We investigated the influence of densities of columnar defects on the critical exponents estimated from the critical scaling analysis of current–voltage characteristics in YBa2 C3 O7x thin films. To avoid the difference of background pinning between samples, the densities of columnar defects were controlled in one sample successively. The dynamic critical exponent z increased with increasing the densities of columnar defects from B/ ¼ 0:5–1.0 T. It was also found that the installed defects led to the appearance of peak in the magnetic field dependence of z, while such peak did not appear before irradiation. These results are explained by the percolation model considering the statistical distribution of the pinning strength rather than the vortex glass–liquid transition model. The various changes of z due to the heavy-ion irradiation are related to the change of the pinning strength distribution due to the introduction of columnar defects, which act as the strong pinning centers. 2004 Elsevier B.V. All rights reserved. PACS: 74.25.Qt; 74.25.Sv; 74.72.Bk Keywords: Columnar defect; Critical current density; Flux pinning; Vortex glass–liquid transition
1. Introduction As a results of worldwide research efforts in recent years, the YBa2 C3 O7x (YBCO) coated conductors with high critical current density have *
Corresponding author. Tel.: +81-96-342-3849; fax: +81-96342-3630. E-mail address: [email protected] (T. Sueyoshi). 1 Present address: Osaka Prefecture University.
been fabricated by developed techniques such as the ion beam assisted deposition (IBAD) [1]. However, the critical current density Jc and the value of n which is defined by the power law of the current (I)–voltage (V ) characteristics, V / I n of such coated conductors still need to be improved and the mechanism limiting them to be explored. Therefore, the mechanism of flux pinning properties in YBCO thin films deposited by the pulsed laser deposition (PLD) method must be precisely comprehended as one of the basic researches for
0921-4534/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2003.12.056
498
T. Sueyoshi et al. / Physica C 412–414 (2004) 497–501
the more developed YBCO coated conductors. Note that the useful method to clarify this problem is comparison with different pinning properties for one sample, which must be achieved by the introduction of pinning centers artificially in a controlled manner. A variety of irradiation-induced defects in highTc superconductors have attracted interest because these defects work as effective flux pinning centers increasing the critical current density Jc and the irreversible temperature Tirr [2–4]. Furthermore, the irradiation with energetic particles (e.g. electrons, protons, neutrons and ions), which enables us to produce the defects artificially in a controlled manner, is a useful method to clarify the complex problems for the flux line dynamics of high-Tc superconductors. Among these, the introduction of columnar defects by the heavy-ion irradiation is the best way for the control of pinning properties. In this study, we investigate the influence of columnar defects on the flux pinning properties in YBCO thin films deposited by the PLD method, where the pinning parameters are Jc and the value of n. Especially, the irradiation effects on the value of n at the vortex glass–liquid transition temperature Tg attracts interest for both physically and technologically. The value of n at Tg is equivalent to the dynamic critical exponent z in the vortex glass–liquid transition model [5], while that also corresponds to the shape factor m of pinning strength distribution in the percolation model [6]. The recent experimental results have supported the latter model [7–10]. In order to clear the mechanism of the value of n in YBCO thin films, we estimate the irradiation effect of the dynamic critical exponent z and the vortex-glass transition temperature Tg by the critical scaling analysis of the current–voltage characteristics for each doses of the irradiation. Note that we controlled the densities of columnar defects in one sample successively in order to avoid the difference of background pinning between samples.
2. Experimental We prepared one YBCO thin film deposited on (1 0 0) surface of a SrTiO3 substrate by the PLD
method. The film with the thickness of 300 nm was c-axis oriented. On the thin film, two samples (sample #1 and #2) with the shape of 50 lm wide and 1mm long microbridge were defined by the chemical etching process. Irradiations with 200 MeV 136 Xe14þ ions were performed along the c-axis from a tandem accelerator at JAERI. In the first irradiation, the doses for the sample #1 was 2.5 · 1010 ions/cm2 with corresponding to a matching field B/ ¼ 0:5 T, while the sample #2 was unirradiated. After the measurements of the first irradiation effects, the second irradiation was performed for both samples with the same condition as the first one. The total doses were 5.0 · 1010 ions/cm2 (sample #1) and 2.5 · 1010 ions/cm2 (sample #2), corresponding to the matching fields B/ ¼ 1–0.5 T, respectively. The current–voltage characteristics were measured by the standard four probe method in which the current applied in the direction perpendicular to the applied magnetic field, the c-axis, and the columnar defects. The critical current density Jc was defined by a criterion of 103 V/m electric field. The critical exponents and the vortex glass transition temperature Tg were estimated from the scaling analysis of the current–voltage characteristics under the magnetic field.
3. Results and discussion Fig. 1 shows the comparison of the isothermal sets of the electrical field E versus current density J curves of the sample #1 between the doses of 2.5 · 1010 ions/cm2 (B/ ¼ 0:5 T) and 5.0 · 1010 ions/ cm2 (B/ ¼ 1:0 T) for B ¼ 1:5 T. The E–J curves of the second irradiation are shifted to higher current density region than that of the first one over the all temperatures. This means that the flux pinning force enlarges by the increment of densities of columnar defects. In Fig. 2, we show the typical sets of the temperature dependence of Jc for each dose in the sample #1 and #2 at B ¼ 0:5 and 1.5 T. The temperature is normalized by the critical temperature Tc for each irradiation in order to discuss the irradiation effects on the flux pinning without the influence of the variation of Tc . For the sample #1,
T. Sueyoshi et al. / Physica C 412–414 (2004) 497–501
Fig. 1. Comparison of isothermal E–J characteristics for sample #1 between the first (B/ ¼ 0:5T) and second irradiation (B/ ¼ 1:0 T) at several temperatures for B ¼ 1:5T parallel to the c-axis.
499
force of columnar defects with the small densities and the background pinning force in the as-grown thin films. That is, the critical current density Jc could hardly increase by means of the small dose of irradiation such as 2.5 · 1010 ions/cm2 , because the background pinning force for the as-grown film is too strong, which is well known in YBCO thin films deposited by the PLD method. This is given support by the fact that the values of Jc before and after irradiation for the sample #2 are almost equal to those for the doses of 2.5 · 1010 ions/cm2 for the sample #1, as shown in Fig. 1. In high-Tc superconductors, it is well known that such set of isothermal E–J curves collapses on two master curves above and below the vortexglass transition temperature Tg when plotted as mðz1Þ 2m ðE=J Þ=jT Tg j versus J =jT Tg j , where m and z are the static and dynamic critical exponents, respectively [11]. In Fig. 3, the scaling collapses in the two universal curves estimated from the E–J curves for the sample #1 with the doses of 2.5 · 1010 ions/cm2 in Fig. 1 are shown. Similar scaling behaviors were achieved at all conditions. We compare the dynamic critical exponent z between the dose of 2.5 · 1010 ions/cm2 (B/ ¼ 0:5 T) and 5.0 · 1010 ions/cm2 (B/ ¼ 1:0 T) for the sample #1, as shown in Fig. 4. It is clarified that the values of z increase with the densities of columnar defects. Furthermore, it is interesting that the peak appears
Fig. 2. Temperature dependence of Jc for B ¼ 0:5 T and 1.5 T both the sample #1 (upper) and #2 (lower), where the temperature is normalized by the critical temperature for each irradiation. Open symbols and closed ones represent the first and the second irradiation process, respectively.
the values of Jc increase with the doses of the irradiation. That is, the columnar defects are effective in increasing the critical current density in the YBCO thin films. However, the irradiation effect scarcely appears on the temperature dependence of Jc for the sample #2 for both B ¼ 0:5 and 1.5 T. This result for the sample #2 would result from the magnitude relation between the pinning
Fig. 3. Scaling collapses of E–J curves for sample #1 with the doses of 2.5 · 1010 ions/cm2 at B ¼ 1:5 T.
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Fig. 4. Comparison of the dynamic critical exponent z between B/ ¼ 0:5 T (M) and B/ ¼ 1:0 T (N) for the sample #1.
in the magnetic field dependences of z near the field B=B/ ¼ 1/3 for the doses of 5.0 · 1010 ions/cm2 . Although it seems that such peak is not seen for the doses of 2.5 · 1010 ions/cm2 where the data for B ¼ 0:1 T were not measured, the abrupt increment of z around B=B/ ¼ 1=3 is observed. In Fig. 5, the comparison of the values of z between before (B/ ¼ 0 T) and after irradiation (B/ ¼ 0:5 T) for the sample #2 is shown. The values of z are almost same between before- and after-irradiation, similar to the temperature dependence of Jc for the sample #2, as shown in Fig. 2. However, the peak is also observed in the magnetic field dependences of z near the field B=B/ ¼ 1=3 after
Fig. 5. Comparison of the dynamic critical exponent z between before-irradiation (M) and B/ ¼ 0:5 T (N) for the sample #2.
irradiation, similar to the sample #1. On the other hand, no peak is exhibited before irradiation. According to the vortex glass–liquid transition model [5], the universality of the critical exponents is predicted. However, our results are incompatible to this prediction. Especially, the appearance of the peak of z near B=B/ ¼ 1=3 could not explained even by the shift from the Bose glass behavior [12] to vortex glass one with increasing magnetic field. According to the percolation model [6], on the other hand, the dynamic critical exponent z is related to the parameter m determining the shape of the local critical current density (Jcl ) distribution. The parameter m increases with the weakening of the relative elastic correlation strength of vortices, which means that the shape of the distribution of Jcl tends to steep [13]. Therefore, one of our results, i.e. the increment of z for the sample #1 is considered to arise from the variation of distribution of Jcl due to the introduction of each different density of the columnar defects. We have already reported results similar to this in the references [8– 10]. The reason why the values of z scarcely make difference between before- and after-irradiation for the sample #2 is that the background pinning force in the as-grown film is too strong to bring the increment of z with small doses of the irradiation. This would be supported by no change of Jc before and after irradiation, as shown in Fig. 1. The peak of z near B=B/ ¼ 1=3 such as shown in Figs. 1 and 2 has been also observed in recent papers [10,14]. In the viewpoint of the percolation model, it is considered that the appearance of such peak of z is corresponding to uniforming the distribution of Jcl due to the matching effect, which would be suggested by the well-known Jc peak near the field of B=B/ ¼ 1=3 [14,15]. That is, every flux lines should be almost trapped in the columnar defects near B/ =B ¼ 1=3 due to the matching effect so that every local domains would possess same value of Jcl with each other. Therefore, the shape of the distribution of the local critical current density Jcl becomes steep and the value of z shows the peak around the B/ =B ¼ 1=3. According to the irradiation effects on the values of z, the scaling collapses of the current–voltage characteristics originate from the percolation network of the unpinned domains in YBCO thin
T. Sueyoshi et al. / Physica C 412–414 (2004) 497–501
films with the pinning strength distribution. So, the value of z, which is equivalent to the value of n at Tg should be governed by the shape of the pinning strength distribution.
501
Acknowledgements The authors would like to thank K. Kawano in the faculty of science in Kumamoto University for his technical supports and advices.
4. Summary References We investigated the influence of densities of columnar defects on the critical exponents estimated from the critical scaling analysis of current– voltage characteristics in YBa2 C3 O7x thin films. The columnar defects were produced by the heavyion irradiation with 200 MeV Xe ions parallel to c-axis. To avoid the difference of background pinning between samples, the densities of columnar defects were controlled in one sample successively. The dynamic critical exponent z increased with increasing the densities of columnar defects from B/ ¼ 0:5–1.0 T. As one of the important results, it was found that the installed defects led to the appearance of peak in the magnetic field dependence of z, while such one did not appear before irradiation. The magnetic field where the value of z has a peak shifts to higher field with increasing the densities of columnar defects and exists near B/ =3. These results are explained by the percolation model considering the distribution of the pinning strength rather than the vortex glass– liquid transition model. The various changes of z due to the heavy-ion irradiation are related to the change of the pinning strength distribution due to the introduction of columnar defects, which act as the strong pinning centers.
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