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Anomalous Hall effect and vortex pinning in high-Tc superconductors
Physica C 364±365 (2001) 518±521
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Anomalous Hall eect and vortex pinning in high-Tc superconductors W. Lang a,*, W. G ob a, J.D. Pedarnig b, R. R ossler b, D. B auerle b a
Institut fur Materialphysik, Universitat Wien, Kopernikusgasse 15, A-1060 Wien, Austria b Angewandte Physik, Johannes-Kepler-Universitat Linz, A-4040 Linz, Austria
Abstract Pulsed high-current-density measurements of the Hall eect in the mixed state in several high-Tc superconductors allow for a systematical tuning of the balance between Lorentz and pinning forces on the vortices. The characteristic temperatures for the single sign reversal in YBa2 Cu3 O7 d and those for the double sign change of the Hall eect in optimally-doped Bi2 Sr2 CaCu2 Ox are independent of current density. This con®rms that the observed sign changes of the vortex Hall eect are intrinsic properties and are not evoked by vortex pinning. In contrast, underdoped Bi2 Sr2 CaCu2 Ox does not exhibit a sign reversal of the Hall eect but a negative contribution to the Hall conductivity can be detected when pinning is reduced in high-current densities. Ó 2001 Elsevier Science B.V. All rights reserved. Keywords: Hall eect; Flux pinning; Vortex dynamics; High-Tc superconductors
1. Introduction Among many other unusual properties of the high-Tc superconductors (HTS) the behavior of the Hall eect in the mixed state has attracted considerable interest. In particular, a sign reversal of the Hall angle below the critical temperature Tc with respect to the normal state is in contrast to traditional models for the vortex Hall eect. Several theoretical approaches have attempted to explain this phenomenon, but no agreement has been achieved so far. The current discussion is focused on the question, whether the Hall anomaly is an intrinsic electronic property, determined by the
* Corresponding author. Tel.: +431-586-34-08-21; fax: +431586-34-08-13. E-mail address: [email protected] (W. Lang).
trajectory of an individual vortex [1±5], if collective vortex phenomena are essential [6,7], or if vortex pinning is indispensable for the sign reversal [8,9]. Other models are based on the general grounds of the time-dependent Ginzburg±Landau theory [10±13], but only with additional input from a microscopic theory the sign of the vortex Hall eect can be predicted. Recent theoretical works have stressed the in¯uence of strong pinning, eventually leading to an additional reversal of the Hall eect's sign from its polarity in the ¯ux¯ow regime [14,15]. The Hall anomaly in HTS is only observed in moderate magnetic ®elds, becomes more prominent in smaller magnetic ®elds, and attains its maximum within the vortex liquid and thermodynamic ¯uctuation range [16,17]. Above Tc , a rapid drop of the Hall resistivity qyx preceds its sign reversal [18]. It has been claimed that the sign of
0921-4534/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 3 4 ( 0 1 ) 0 0 8 4 1 - 3
W. Lang et al. / Physica C 364±365 (2001) 518±521
the vortex Hall eect has a universal dependence linked to the carrier concentration [19]. Accordingly, the sign reversal should appear in underdoped but not in heavily overdoped cuprates. Other authors, however, report no sign reversal of the vortex Hall eect in underdoped YBa2 Cu3 O7 d (YBCO) [20] in accordance with our observations. In highly anisotropic HTS, like Bi2 Sr2 CaCu2 Ox (Bi-2212), a double sign reversal is observed [21] that is attributed to weak pinning in these cuprates. Recently, it was shown that a double sign reversal could also exist in YBCO in weak magnetic ®elds [22], but, contrary to the Hall anomaly in Bi-2212, it was attributed to strong Bose-glass pinning. Similar conclusions were drawn from measurements on pure YBCO single crystals near the vortex melting transition [23]. The triple sign reversal observed in HgBa2 CaCu2 O6 (Hg-1212) thin ®lms after ion irradiation [24] appears to be also connected with enhanced pinning or proliferated defects. In this paper, we investigate the in¯uence of pinning on the sign reversals of the vortex Hall eect in YBCO and optimally-doped Bi-2212 thin ®lms and the absence of such sign change in underdoped Bi-2212 ®lms. The use of a pulsedcurrent measurement technique allows for a systematical tuning of the balance between Lorentz and pinning forces.
519
method, a fast dierential ampli®er, and voltage detection by a boxcar averager [26,27]. The two methods were applied together in moderate current densities to ensure consistency in our data. At the maximum current density (1.5 MA/cm2 ) the temperature rise of the sample relative to the bath was smaller than 3 K and was always corrected using the HTS ®lm as an intrinsic thermometer [28]. 3. Results and discussion Our investigation of the vortex Hall eect in various HTS starts with Fig. 1 that presents the Hall coecient RH of YBCO near Tc as a function of current density. Towards lower temperature RH drops rapidly from its weakly temperaturedependent, positive normal-state value and reverses sign at T 87:5 K. The absence of current dependence demonstrates that pinning does not play an important role in this temperature region and, hence, contradicts models [8,9] that originate the sign reversal on vortex pinning. In contrast, RH is highly nonohmic at the low-temperature side of the anomaly and the onset of ®nite RH shifts to
2. Experimental techniques The typically 100-nm-thick epitaxial ®lms were prepared by pulsed-laser deposition from ceramic YBCO and Bi-2212 targets, respectively, on MgO substrates [25]. A strip-shaped test structure with six voltage probes and dimensions of 250 17 lm2 was patterned into the ®lms by wet chemical etching. The experiments were performed in a closed-cycle cryocooler at a magnetic ®eld B 1 T. To allow for a systematic variation of the Lorentz force on the vortices a broad range of current densities from 200 A/cm2 to 1.5 MA/cm2 was applied. At low-current densities a lock-in technique with 17 Hz ac currents was used. Alternatively, we used 3-ls-long, high-current density pulses with 5 10 4 duty cycle in a four-probe
Fig. 1. Sign reversal of the Hall coecient in a YBCO thin ®lm near Tc at various current densities. The low-temperature part of the anomaly is strongly current dependent.
520
W. Lang et al. / Physica C 364±365 (2001) 518±521
lower T. Such behavior is characteristic for vortex pinning. In low-magnetic ®elds and with small Lorentz force a second sign reversal back to positive RH has been observed in YBCO (not visible in Fig. 1) that is associated with Bose-glass pinning [22]. The various contributions are commonly analyzed in terms of the Hall conductivity rxy qyx = q2xx q2yx , where qyx RH B. The Hall conducS tivity may be decomposed into rxy rN xy rxy P N rxy , where rxy represents a quasiparticle or vortexcore contribution, associated with the normal-state excitations, rSxy a superconducting contribution, resulting from hydrodynamic vortex eects and superconducting ¯uctuations [2,10±13], and rPxy allows for the pinning-dependence of rxy . The sign of rN xy is the same as that of the normal-state Hall eect, but the sign of rSxy depends on details of the Fermi surface [10±12,19]. In Fig. 1 the weakly temperature-dependent, positive part is dominated S by rN xy , the ohmic side of the Hall anomaly by rxy , P and the nonohmic onset region roughly by rxy . Now we compare this outline to the Hall eect in Bi-2212 in Fig. 2, where vortex pinning is rather weak due to the material's high anisotropy and to the decomposition of vortices into `pancakes'. The Hall anomaly is similar to that in YBCO but the
negative dip has a larger amplitude and does not exhibit signi®cant current dependence. A second sign reversal at T 73 K is not shifted at large currents, but the magnitude of the second, positive peak is strongly enhanced by large Lorentz forces on the vortices. Contrary to YBCO, this suggests that the second sign reversal in Bi-2212 is also of intrinsic nature and not caused by pinning. The third sign change observed in ion irradiated Hg-1212 [24] might be evoked by pinning, similar to the second sign reversal in YBCO, in accordance with the theoretical prediction that sgn rPxy 6 sgn rSxy for pinning on line-like defects [14]. Finally, Fig. 3 presents the Hall conductivity of an underdoped Bi-2212 ®lm that does not show a sign reversal of the Hall eect. This observation and similar results on YBCO [20] are in contradiction to recent claims of a universal connection between the sign reversal of RH and the carrier concentration [19]. From the high-current data in Fig. 3 a negative contribution to rxy can be inferred that is overpowered by a steep positive part towards low T before it can become dominant. Such behavior can explain the apparent discrepancies with the presence or absence of a sign reversal of the Hall eect in underdoped HTS on the
Fig. 2. Double sign reversal of the Hall coecient in an optimally-doped Bi-2212 thin ®lm at various current densities. The vortex Hall eect with negative sign is only weakly current dependent.
Fig. 3. Hall conductivity of an underdoped Bi-2212 thin ®lm at various current densities. With reduced pinning in high-current densities a negative contribution to rxy appears.
W. Lang et al. / Physica C 364±365 (2001) 518±521
basis of dierent defect structures and, hence, pinning forces in the materials. In summary, we have investigated the anomalies of the vortex Hall eect near Tc in several HTS and found that high-current density measurements allow to discriminate between intrinsic and pinning-related properties. Acknowledgements We appreciate very helpful correspondence with R. Ikeda and stimulating discussions with Y. Matsuda. This work was supported by the Fonds zur F orderung der wissenschaftlichen Forschung, Austria. References [1] R.A. Ferrell, Phys. Rev. Lett. 68 (1992) 2524. [2] A. van Otterlo, M. Feigel'man, V. Geshkenbein, G. Blatter, Phys. Rev. Lett. 75 (1995) 3736. [3] D.I. Khomskii, A. Freimuth, Phys. Rev. Lett. 75 (1995) 1384. [4] N.B. Kopnin, Phys. Rev. B 54 (1996) 9475. [5] J. Kolacek, P. Vasek, Physica C 336 (2000) 199. [6] P. Ao, J. Phys. Condens. Matter 10 (1998) L677. [7] H.J. Jensen, P. Minnhagen, E. Sonin, H. Weber, Europhys. Lett. 20 (1992) 463. [8] Z.D. Wang, C.S. Ting, Phys. Rev. Lett. 67 (1991) 3618. [9] Z.D. Wang, J.M. Dong, C.S. Ting, Phys. Rev. Lett. 72 (1994) 3875.
521
[10] A.T. Dorsey, Phys. Rev. B 46 (1992) 8376. [11] R.J. Troy, A.T. Dorsey, Phys. Rev. B 47 (1993) 2715. [12] N.B. Kopnin, B.I. Ivlev, V.A. Kalatsky, J. Low Temp. Phys. 90 (1993) 1. [13] T. Nishio, H. Ebisawa, Physica C 290 (1997) 43. [14] R. Ikeda, Physica C 316 (1999) 189. [15] N.B. Kopnin, V.M. Vinokur, Phys. Rev. Lett. 83 (1999) 4864. [16] T.R. Chien, T.W. Jing, N.P. Ong, Z.Z. Wang, Phys. Rev. Lett. 66 (1991) 3075. [17] W. Liu, T.W. Clinton, A.W. Smith, C.J. Lobb, Phys. Rev. B 55 (1997) 11802. [18] W. Lang, G. Heine, P. Schwab, X.Z. Wang, D. Bauerle, Phys. Rev. B 49 (1994) 4209. [19] T. Nagaoka, Y. Matsuda, H. Obara, A. Sawa, T. Terashima, I. Chong, M. Takano, M. Suzuki, Phys. Rev. Lett. 80 (1998) 3594. [20] L. Hofmann, H. Karl, K. Samwer, Z. Phys. B 95 (1994) 173. [21] N.V. Zavaritsky, A.V. Samoilov, A.A. Yurgens, Physica C 180 (1991) 417. [22] W. G ob, W. Liebich, W. Lang, I. Puica, R. Sobolewski, R. R ossler, J.D. Pedarnig, D. Bauerle, Phys. Rev. B 62 (2000) 9780. [23] G. D'Anna, V. Berseth, L. Forro, A. Erb, E. Walker, Phys. Rev. Lett. 81 (1998) 2530. [24] W.N. Kang, B.W. Kang, Q.Y. Chen, J.Z. Wu, Y. Bai, W.K. Chu, D.K. Christen, R. Kerchner, S.I. Lee, Phys. Rev. B 61 (2000) 722. [25] D. Bauerle, Laser Processing and Chemistry, Springer, Berlin, 2000. [26] W. Liebich, P. Gehringer, W. G ob, W. Lang, K. Bierleutgeb, D. Bauerle, Physica C 282 (1997) 2321. [27] W. G ob, W. Lang, J.D. Pedarnig, R. R ossler, D. Bauerle, Physica C 317 (1999) 627. [28] M.N. Kunchur, D.K. Christen, C.E. Klabunde, J.M. Phillips, Phys. Rev. Lett. 72 (1994) 2259.
www.elsevier.com/locate/physc
Anomalous Hall eect and vortex pinning in high-Tc superconductors W. Lang a,*, W. G ob a, J.D. Pedarnig b, R. R ossler b, D. B auerle b a
Institut fur Materialphysik, Universitat Wien, Kopernikusgasse 15, A-1060 Wien, Austria b Angewandte Physik, Johannes-Kepler-Universitat Linz, A-4040 Linz, Austria
Abstract Pulsed high-current-density measurements of the Hall eect in the mixed state in several high-Tc superconductors allow for a systematical tuning of the balance between Lorentz and pinning forces on the vortices. The characteristic temperatures for the single sign reversal in YBa2 Cu3 O7 d and those for the double sign change of the Hall eect in optimally-doped Bi2 Sr2 CaCu2 Ox are independent of current density. This con®rms that the observed sign changes of the vortex Hall eect are intrinsic properties and are not evoked by vortex pinning. In contrast, underdoped Bi2 Sr2 CaCu2 Ox does not exhibit a sign reversal of the Hall eect but a negative contribution to the Hall conductivity can be detected when pinning is reduced in high-current densities. Ó 2001 Elsevier Science B.V. All rights reserved. Keywords: Hall eect; Flux pinning; Vortex dynamics; High-Tc superconductors
1. Introduction Among many other unusual properties of the high-Tc superconductors (HTS) the behavior of the Hall eect in the mixed state has attracted considerable interest. In particular, a sign reversal of the Hall angle below the critical temperature Tc with respect to the normal state is in contrast to traditional models for the vortex Hall eect. Several theoretical approaches have attempted to explain this phenomenon, but no agreement has been achieved so far. The current discussion is focused on the question, whether the Hall anomaly is an intrinsic electronic property, determined by the
* Corresponding author. Tel.: +431-586-34-08-21; fax: +431586-34-08-13. E-mail address: [email protected] (W. Lang).
trajectory of an individual vortex [1±5], if collective vortex phenomena are essential [6,7], or if vortex pinning is indispensable for the sign reversal [8,9]. Other models are based on the general grounds of the time-dependent Ginzburg±Landau theory [10±13], but only with additional input from a microscopic theory the sign of the vortex Hall eect can be predicted. Recent theoretical works have stressed the in¯uence of strong pinning, eventually leading to an additional reversal of the Hall eect's sign from its polarity in the ¯ux¯ow regime [14,15]. The Hall anomaly in HTS is only observed in moderate magnetic ®elds, becomes more prominent in smaller magnetic ®elds, and attains its maximum within the vortex liquid and thermodynamic ¯uctuation range [16,17]. Above Tc , a rapid drop of the Hall resistivity qyx preceds its sign reversal [18]. It has been claimed that the sign of
0921-4534/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 3 4 ( 0 1 ) 0 0 8 4 1 - 3
W. Lang et al. / Physica C 364±365 (2001) 518±521
the vortex Hall eect has a universal dependence linked to the carrier concentration [19]. Accordingly, the sign reversal should appear in underdoped but not in heavily overdoped cuprates. Other authors, however, report no sign reversal of the vortex Hall eect in underdoped YBa2 Cu3 O7 d (YBCO) [20] in accordance with our observations. In highly anisotropic HTS, like Bi2 Sr2 CaCu2 Ox (Bi-2212), a double sign reversal is observed [21] that is attributed to weak pinning in these cuprates. Recently, it was shown that a double sign reversal could also exist in YBCO in weak magnetic ®elds [22], but, contrary to the Hall anomaly in Bi-2212, it was attributed to strong Bose-glass pinning. Similar conclusions were drawn from measurements on pure YBCO single crystals near the vortex melting transition [23]. The triple sign reversal observed in HgBa2 CaCu2 O6 (Hg-1212) thin ®lms after ion irradiation [24] appears to be also connected with enhanced pinning or proliferated defects. In this paper, we investigate the in¯uence of pinning on the sign reversals of the vortex Hall eect in YBCO and optimally-doped Bi-2212 thin ®lms and the absence of such sign change in underdoped Bi-2212 ®lms. The use of a pulsedcurrent measurement technique allows for a systematical tuning of the balance between Lorentz and pinning forces.
519
method, a fast dierential ampli®er, and voltage detection by a boxcar averager [26,27]. The two methods were applied together in moderate current densities to ensure consistency in our data. At the maximum current density (1.5 MA/cm2 ) the temperature rise of the sample relative to the bath was smaller than 3 K and was always corrected using the HTS ®lm as an intrinsic thermometer [28]. 3. Results and discussion Our investigation of the vortex Hall eect in various HTS starts with Fig. 1 that presents the Hall coecient RH of YBCO near Tc as a function of current density. Towards lower temperature RH drops rapidly from its weakly temperaturedependent, positive normal-state value and reverses sign at T 87:5 K. The absence of current dependence demonstrates that pinning does not play an important role in this temperature region and, hence, contradicts models [8,9] that originate the sign reversal on vortex pinning. In contrast, RH is highly nonohmic at the low-temperature side of the anomaly and the onset of ®nite RH shifts to
2. Experimental techniques The typically 100-nm-thick epitaxial ®lms were prepared by pulsed-laser deposition from ceramic YBCO and Bi-2212 targets, respectively, on MgO substrates [25]. A strip-shaped test structure with six voltage probes and dimensions of 250 17 lm2 was patterned into the ®lms by wet chemical etching. The experiments were performed in a closed-cycle cryocooler at a magnetic ®eld B 1 T. To allow for a systematic variation of the Lorentz force on the vortices a broad range of current densities from 200 A/cm2 to 1.5 MA/cm2 was applied. At low-current densities a lock-in technique with 17 Hz ac currents was used. Alternatively, we used 3-ls-long, high-current density pulses with 5 10 4 duty cycle in a four-probe
Fig. 1. Sign reversal of the Hall coecient in a YBCO thin ®lm near Tc at various current densities. The low-temperature part of the anomaly is strongly current dependent.
520
W. Lang et al. / Physica C 364±365 (2001) 518±521
lower T. Such behavior is characteristic for vortex pinning. In low-magnetic ®elds and with small Lorentz force a second sign reversal back to positive RH has been observed in YBCO (not visible in Fig. 1) that is associated with Bose-glass pinning [22]. The various contributions are commonly analyzed in terms of the Hall conductivity rxy qyx = q2xx q2yx , where qyx RH B. The Hall conducS tivity may be decomposed into rxy rN xy rxy P N rxy , where rxy represents a quasiparticle or vortexcore contribution, associated with the normal-state excitations, rSxy a superconducting contribution, resulting from hydrodynamic vortex eects and superconducting ¯uctuations [2,10±13], and rPxy allows for the pinning-dependence of rxy . The sign of rN xy is the same as that of the normal-state Hall eect, but the sign of rSxy depends on details of the Fermi surface [10±12,19]. In Fig. 1 the weakly temperature-dependent, positive part is dominated S by rN xy , the ohmic side of the Hall anomaly by rxy , P and the nonohmic onset region roughly by rxy . Now we compare this outline to the Hall eect in Bi-2212 in Fig. 2, where vortex pinning is rather weak due to the material's high anisotropy and to the decomposition of vortices into `pancakes'. The Hall anomaly is similar to that in YBCO but the
negative dip has a larger amplitude and does not exhibit signi®cant current dependence. A second sign reversal at T 73 K is not shifted at large currents, but the magnitude of the second, positive peak is strongly enhanced by large Lorentz forces on the vortices. Contrary to YBCO, this suggests that the second sign reversal in Bi-2212 is also of intrinsic nature and not caused by pinning. The third sign change observed in ion irradiated Hg-1212 [24] might be evoked by pinning, similar to the second sign reversal in YBCO, in accordance with the theoretical prediction that sgn rPxy 6 sgn rSxy for pinning on line-like defects [14]. Finally, Fig. 3 presents the Hall conductivity of an underdoped Bi-2212 ®lm that does not show a sign reversal of the Hall eect. This observation and similar results on YBCO [20] are in contradiction to recent claims of a universal connection between the sign reversal of RH and the carrier concentration [19]. From the high-current data in Fig. 3 a negative contribution to rxy can be inferred that is overpowered by a steep positive part towards low T before it can become dominant. Such behavior can explain the apparent discrepancies with the presence or absence of a sign reversal of the Hall eect in underdoped HTS on the
Fig. 2. Double sign reversal of the Hall coecient in an optimally-doped Bi-2212 thin ®lm at various current densities. The vortex Hall eect with negative sign is only weakly current dependent.
Fig. 3. Hall conductivity of an underdoped Bi-2212 thin ®lm at various current densities. With reduced pinning in high-current densities a negative contribution to rxy appears.
W. Lang et al. / Physica C 364±365 (2001) 518±521
basis of dierent defect structures and, hence, pinning forces in the materials. In summary, we have investigated the anomalies of the vortex Hall eect near Tc in several HTS and found that high-current density measurements allow to discriminate between intrinsic and pinning-related properties. Acknowledgements We appreciate very helpful correspondence with R. Ikeda and stimulating discussions with Y. Matsuda. This work was supported by the Fonds zur F orderung der wissenschaftlichen Forschung, Austria. References [1] R.A. Ferrell, Phys. Rev. Lett. 68 (1992) 2524. [2] A. van Otterlo, M. Feigel'man, V. Geshkenbein, G. Blatter, Phys. Rev. Lett. 75 (1995) 3736. [3] D.I. Khomskii, A. Freimuth, Phys. Rev. Lett. 75 (1995) 1384. [4] N.B. Kopnin, Phys. Rev. B 54 (1996) 9475. [5] J. Kolacek, P. Vasek, Physica C 336 (2000) 199. [6] P. Ao, J. Phys. Condens. Matter 10 (1998) L677. [7] H.J. Jensen, P. Minnhagen, E. Sonin, H. Weber, Europhys. Lett. 20 (1992) 463. [8] Z.D. Wang, C.S. Ting, Phys. Rev. Lett. 67 (1991) 3618. [9] Z.D. Wang, J.M. Dong, C.S. Ting, Phys. Rev. Lett. 72 (1994) 3875.
521
[10] A.T. Dorsey, Phys. Rev. B 46 (1992) 8376. [11] R.J. Troy, A.T. Dorsey, Phys. Rev. B 47 (1993) 2715. [12] N.B. Kopnin, B.I. Ivlev, V.A. Kalatsky, J. Low Temp. Phys. 90 (1993) 1. [13] T. Nishio, H. Ebisawa, Physica C 290 (1997) 43. [14] R. Ikeda, Physica C 316 (1999) 189. [15] N.B. Kopnin, V.M. Vinokur, Phys. Rev. Lett. 83 (1999) 4864. [16] T.R. Chien, T.W. Jing, N.P. Ong, Z.Z. Wang, Phys. Rev. Lett. 66 (1991) 3075. [17] W. Liu, T.W. Clinton, A.W. Smith, C.J. Lobb, Phys. Rev. B 55 (1997) 11802. [18] W. Lang, G. Heine, P. Schwab, X.Z. Wang, D. Bauerle, Phys. Rev. B 49 (1994) 4209. [19] T. Nagaoka, Y. Matsuda, H. Obara, A. Sawa, T. Terashima, I. Chong, M. Takano, M. Suzuki, Phys. Rev. Lett. 80 (1998) 3594. [20] L. Hofmann, H. Karl, K. Samwer, Z. Phys. B 95 (1994) 173. [21] N.V. Zavaritsky, A.V. Samoilov, A.A. Yurgens, Physica C 180 (1991) 417. [22] W. G ob, W. Liebich, W. Lang, I. Puica, R. Sobolewski, R. R ossler, J.D. Pedarnig, D. Bauerle, Phys. Rev. B 62 (2000) 9780. [23] G. D'Anna, V. Berseth, L. Forro, A. Erb, E. Walker, Phys. Rev. Lett. 81 (1998) 2530. [24] W.N. Kang, B.W. Kang, Q.Y. Chen, J.Z. Wu, Y. Bai, W.K. Chu, D.K. Christen, R. Kerchner, S.I. Lee, Phys. Rev. B 61 (2000) 722. [25] D. Bauerle, Laser Processing and Chemistry, Springer, Berlin, 2000. [26] W. Liebich, P. Gehringer, W. G ob, W. Lang, K. Bierleutgeb, D. Bauerle, Physica C 282 (1997) 2321. [27] W. G ob, W. Lang, J.D. Pedarnig, R. R ossler, D. Bauerle, Physica C 317 (1999) 627. [28] M.N. Kunchur, D.K. Christen, C.E. Klabunde, J.M. Phillips, Phys. Rev. Lett. 72 (1994) 2259.