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Can the collective pinning approach be applied to YBa2Cu3O7−δ superconductors?
PHYSlCA ELSEVIER
Physica C 341-348 (2000) 1271-1272
www.elsevier.nl/Iocate/physc
Can the collective pinning approach be applied to YBa2Cu3OT_5 superconductors? Franz M. Sauerzopf, M. Zehetmayer, A. KShler*, H. W. Weber Atominstitut, TU Wien, A-1020 Vienna, Austria The widely used collective pinning approach is applied to describe the critical current density Jc of YBa2Cu3Or-8 single crystals. The field dependence of Jc at low temperatures, before and after reactor neutron irradiation and annealing, points to strong pinning. Collective effects are expected at high densities of pinning centers, but the description is not possible in terms of the standard weak pinning model. A comparison of the data of untreated and neutron irradiated crystals indicates that strong pinning also prevails in the as-grown material. Further results on related single crystal samples (RE-123 and Y-124) support the findings.
1. I N T R O D U C T I O N The summation problem, i. e. the calculation of the experimentally accessible macroscopic pinning force P v = Jc x B of a superconductor from the microscopic distribution of elementary pinning forces fp, has been widely discussed for a long time. The early models were based on the assumption of strong pinning, i. e. invoke a strong distortion of the flux line lattice (FLL) by the individual elementary pinning force (cf. [1]). For small distortions, and especially to explain the peak effect in the vicinity of He2, the collective pinning model [2] was developed. Because of the small defect sizes expected in high Tc- superconductors (HTS), the model was very soon successfully applied to these materials (e. g. [3]). Necessary amendments, and a new formulation of the theory [4] led to a large number of papers, which interpreted their data in terms of the collective pinning model. However, a strict test of this and other models was not possible, because the actual effective defect distribution in typical HTS crystals is not directly observable. Also, many authors did not take care to ascertain that the elementary pinning forces involved in their experiments would really fulfil the requirements set by the collective pinning approach, mainly the presence of only small distortions in *This work was supported within the framework of the TMR project SUPERCURRENT
the FLL. In our work we introduce a well characterized defect structure by reactor neutron irradiation and annealing of Y-123 and similar crystals. From the magnetization data of the irradiated (and annealed) samples we can extrapolate backwards to describe the defect structure of the untreated crystals, and compare the measured magnetization to the theoretical model calculations. The results clearly show a failure of the collective pinning approach, but also indicate that present theories for strong pinning are not able to describe the data, especially for higher densities of pinning centers. 2. R E S U L T S A N D D I S C U S S I O N In a first approach [5], one Y-123 single crystal was characterized by Te and magnetization measurements in our SQUID magnetometers. The relevant points of our discussion will be illustrated using the Je-values at low temperatures, where effects due to thermally activated relaxation are small. The data in Figure 1 are extracted from the magnetization data using an extended Bean model, which approximately takes demagnetizing effects into account. These data were obtained on the as-grown crystal, and after irradiation in the central irradiation facility of the TRIGA-reactor Vienna, and after subsequent annealing for eight hours in air at T = 250 °C.
0921-4534/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved. Pll S0921-4534(00)00873-X
EM. Sauerzopf et al./Physica C 341-348 (2000) 1271-1272
1272
E
,< o O
¢1) "10
1 ated 0.8
.o
0.6
magnetic induction (T)
Figure 1. Jc of the Y-123 crystal D1 at T = 5 K, before and after neutron irradiation to various fluences and subsequent annealing.
For clarity, the data prior to annealing are not shown. The dominant defects after neutron irradiation are the defect cascades, which form pinning centers with a diameter of about 6 nm, and a density which varies linearly with the fast neutron fluence, N d = 1022 m - 3 at a fluence of 5 - 1021 m - 2 ( E > 0.1 MeV). After annealing, smaller defect structures are almost completely removed, (cf. the increase in To, [5]), and the stable cascades dominate flux pinning. The Jc over B dependence in Figure 1 follows a power law Jc (x B ~ with a ~ - 0 . 5 for both, the irradiated and the untreated sample. This power law can be considered a fingerprint of the summation of the elementary pinning forces, and may be checked against relevant theories. The equations given in [4] do not agree reasonably with the experimental data. Calculations of a for the various regimes, as given in the reference, lead to significantly larger values, with c~ .~ 3 for the large bundle regime, and constant J c ( B ) in the single vortex region. The slope in the small bundle transition regime may be widely varied, but covers a far too narrow B - r a n g e . Considering the two-dimensional approach, although it may
be questioned for Y-123, results in an exponent a = 1, again much larger than in the experiment. In all models, the results cannot describe even the order of magnitude of the experimental data, when the approximately known values of the pin density and size are used to extract absolute values of the critical current densities. Actually this is not surprising, because the large neutron cascades strongly distort the FLL, violating the basic condition of small distortions in the collective pinning theory. More interesting is the fact, that even the unirradiated crystal shows the same behaviour. This crystal (grown by the self-flux method in a gold crucible, Argonne National Laboratory) is a high quality crystal with Je(0.1 T, 77 K) "~ 2 • 107 Am -2, where one would not hesitate to speak of weak pinning. But the power law with an exponent significantly smaller than one is also observed in the untreated crystal at 77 K. We also find a similar behaviour in many materials, where the power law with exponents close to 0.5 appears at fields well below the second peak in the magnetization. 3. C O N C L U S I O N We have shown that neither the dependence on field nor the order of magnitude of Jc calculated by the collective pinning theory correspond to the experiment on our very clean crystal. Therefore, the uncritical use of the collective pinning theory for Y-123 and maybe other samples will have to be reconsidered in many cases.
REFERENCES 1. E.H. Brandt, Rep. Prog. Phys. 58 (1995) 1465. 2. A.I. Larkin and Y.N. Ovchinnikov, J. Low Temp. Phys. 34 (1979) 409. 3. P.H. Kes and J. van den Berg, in Studies of High Temperature Superconductors Vol. 5 (NOVA Scientific, New York, 1990) pp. 83115. 4. G. Blatter et al., Rev. Mod. Phys. 66 (1994) 1125. 5. F.M. Sauerzopf, Phys. Rev. B 57 (1998) 10959.
Physica C 341-348 (2000) 1271-1272
www.elsevier.nl/Iocate/physc
Can the collective pinning approach be applied to YBa2Cu3OT_5 superconductors? Franz M. Sauerzopf, M. Zehetmayer, A. KShler*, H. W. Weber Atominstitut, TU Wien, A-1020 Vienna, Austria The widely used collective pinning approach is applied to describe the critical current density Jc of YBa2Cu3Or-8 single crystals. The field dependence of Jc at low temperatures, before and after reactor neutron irradiation and annealing, points to strong pinning. Collective effects are expected at high densities of pinning centers, but the description is not possible in terms of the standard weak pinning model. A comparison of the data of untreated and neutron irradiated crystals indicates that strong pinning also prevails in the as-grown material. Further results on related single crystal samples (RE-123 and Y-124) support the findings.
1. I N T R O D U C T I O N The summation problem, i. e. the calculation of the experimentally accessible macroscopic pinning force P v = Jc x B of a superconductor from the microscopic distribution of elementary pinning forces fp, has been widely discussed for a long time. The early models were based on the assumption of strong pinning, i. e. invoke a strong distortion of the flux line lattice (FLL) by the individual elementary pinning force (cf. [1]). For small distortions, and especially to explain the peak effect in the vicinity of He2, the collective pinning model [2] was developed. Because of the small defect sizes expected in high Tc- superconductors (HTS), the model was very soon successfully applied to these materials (e. g. [3]). Necessary amendments, and a new formulation of the theory [4] led to a large number of papers, which interpreted their data in terms of the collective pinning model. However, a strict test of this and other models was not possible, because the actual effective defect distribution in typical HTS crystals is not directly observable. Also, many authors did not take care to ascertain that the elementary pinning forces involved in their experiments would really fulfil the requirements set by the collective pinning approach, mainly the presence of only small distortions in *This work was supported within the framework of the TMR project SUPERCURRENT
the FLL. In our work we introduce a well characterized defect structure by reactor neutron irradiation and annealing of Y-123 and similar crystals. From the magnetization data of the irradiated (and annealed) samples we can extrapolate backwards to describe the defect structure of the untreated crystals, and compare the measured magnetization to the theoretical model calculations. The results clearly show a failure of the collective pinning approach, but also indicate that present theories for strong pinning are not able to describe the data, especially for higher densities of pinning centers. 2. R E S U L T S A N D D I S C U S S I O N In a first approach [5], one Y-123 single crystal was characterized by Te and magnetization measurements in our SQUID magnetometers. The relevant points of our discussion will be illustrated using the Je-values at low temperatures, where effects due to thermally activated relaxation are small. The data in Figure 1 are extracted from the magnetization data using an extended Bean model, which approximately takes demagnetizing effects into account. These data were obtained on the as-grown crystal, and after irradiation in the central irradiation facility of the TRIGA-reactor Vienna, and after subsequent annealing for eight hours in air at T = 250 °C.
0921-4534/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved. Pll S0921-4534(00)00873-X
EM. Sauerzopf et al./Physica C 341-348 (2000) 1271-1272
1272
E
,< o O
¢1) "10
1 ated 0.8
.o
0.6
magnetic induction (T)
Figure 1. Jc of the Y-123 crystal D1 at T = 5 K, before and after neutron irradiation to various fluences and subsequent annealing.
For clarity, the data prior to annealing are not shown. The dominant defects after neutron irradiation are the defect cascades, which form pinning centers with a diameter of about 6 nm, and a density which varies linearly with the fast neutron fluence, N d = 1022 m - 3 at a fluence of 5 - 1021 m - 2 ( E > 0.1 MeV). After annealing, smaller defect structures are almost completely removed, (cf. the increase in To, [5]), and the stable cascades dominate flux pinning. The Jc over B dependence in Figure 1 follows a power law Jc (x B ~ with a ~ - 0 . 5 for both, the irradiated and the untreated sample. This power law can be considered a fingerprint of the summation of the elementary pinning forces, and may be checked against relevant theories. The equations given in [4] do not agree reasonably with the experimental data. Calculations of a for the various regimes, as given in the reference, lead to significantly larger values, with c~ .~ 3 for the large bundle regime, and constant J c ( B ) in the single vortex region. The slope in the small bundle transition regime may be widely varied, but covers a far too narrow B - r a n g e . Considering the two-dimensional approach, although it may
be questioned for Y-123, results in an exponent a = 1, again much larger than in the experiment. In all models, the results cannot describe even the order of magnitude of the experimental data, when the approximately known values of the pin density and size are used to extract absolute values of the critical current densities. Actually this is not surprising, because the large neutron cascades strongly distort the FLL, violating the basic condition of small distortions in the collective pinning theory. More interesting is the fact, that even the unirradiated crystal shows the same behaviour. This crystal (grown by the self-flux method in a gold crucible, Argonne National Laboratory) is a high quality crystal with Je(0.1 T, 77 K) "~ 2 • 107 Am -2, where one would not hesitate to speak of weak pinning. But the power law with an exponent significantly smaller than one is also observed in the untreated crystal at 77 K. We also find a similar behaviour in many materials, where the power law with exponents close to 0.5 appears at fields well below the second peak in the magnetization. 3. C O N C L U S I O N We have shown that neither the dependence on field nor the order of magnitude of Jc calculated by the collective pinning theory correspond to the experiment on our very clean crystal. Therefore, the uncritical use of the collective pinning theory for Y-123 and maybe other samples will have to be reconsidered in many cases.
REFERENCES 1. E.H. Brandt, Rep. Prog. Phys. 58 (1995) 1465. 2. A.I. Larkin and Y.N. Ovchinnikov, J. Low Temp. Phys. 34 (1979) 409. 3. P.H. Kes and J. van den Berg, in Studies of High Temperature Superconductors Vol. 5 (NOVA Scientific, New York, 1990) pp. 83115. 4. G. Blatter et al., Rev. Mod. Phys. 66 (1994) 1125. 5. F.M. Sauerzopf, Phys. Rev. B 57 (1998) 10959.