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Magnetic vortices and pinning in thin films and superlattices
Thin Solid Films 317 Ž1998. 285–289
Magnetic vortices and pinning in thin films and superlattices J.I. Martın ´ a, M. Velez ´ a, E.M. Gonzalez ´ b, J.L. Vicent b
a,)
a Departamento Fisica de Materiales, Facultad de Fisicas, UniÕersidad Complutense, Madrid 28040, Spain Departamento Propiedades Opticas, Magneticas y de Transporte, Instituto de Ciencia de Materiales, CSIC, Cantoblanco, Madrid 28049, Spain
Abstract Thin films and superlattices of high-temperature superconductors ŽHTS. of the 1:2:3 family are grown by dc magnetron sputtering with different textures. The samples could be grown with the CuO 2 planes parallel to the substrate Žthe so-called c-axis orientation. or with the CuO 2 planes perpendicular to the substrate Žthe so-called a-axis orientation.. The films are superconducting with critical temperatures ŽTc . between 85–90 K and with critical currents Ž Jc . at 77 K in the range of 10 6 Arcm2 and 10 5 Arcm2 for c-axis and a-axis oriented films, respectively. In the case of superlattices of EuBa 2 Cu 3 O 7rPrBa 2 Cu 3 O 7 ŽEBCOrPBCO, superconductingrinsulating., the Tc and Jc change with the modulation lengths. These HTS films show very peculiar magnetic properties in the mixed state. The magnetic properties are linked to the behavior of a very soft magnetic vortex lattice and, in the a-axis oriented superlattices, to the competition between natural and artificial anisotropies. In this case, an enhancement of the critical current density Jc could be obtained when the magnetic field is applied parallel to the substrate. q 1998 Elsevier Science S.A. Keywords: Thin films; Superlattices; Magnetron sputtering
1. Introduction Thin films of the 1:2:3 family of oxide cuprates could be grown by different vacuum deposition techniques, as laser ablation, molecular beam epitaxy, etc.; but, among them, the sputtering method allows us to grow good-quality films and multilayers with different textures. The growing conditions to obtain films of HTS are very extreme, since very high substrate-temperature during deposition and high-oxygen pressure in the chamber are required w1x. Therefore, magnetron sputtering seems to be a useful technique. Laser ablation could produce good quality films too; but in this case, the surface roughness could be a problem if multilayers have to be fabricated. The mixed state behavior of HTS has been one of the most interesting topics in the field w2x. A magnetic field applied to a HTS leads to many new phenomena, most of them due to the combination of the short vortex core size Žsmall coherence length. and the structural anisotropy of these oxide cuprates. Another topic related with basic and applied research is the behavior of the critical current Jc in the vortex state. The pinning mechanisms of the vortices should be understood in a way to enhance the Jc values,
)
Corresponding author.
0040-6090r98r$19.00 q 1998 Elsevier Science S.A. All rights reserved. PII S 0 0 4 0 - 6 0 9 0 Ž 9 7 . 0 0 6 4 2 - 1
which is very important from the technological point of view. In this paper we will present the fabrication of thin films of EuBa 2 Cu 3 O 7 ŽEBCO. and superlattices of E u B a 2 C u 3 O 7 r P rB a 2 C u 3 O 7 Ž su p e rc o n d u c tin g ŽEBCO.rinsulating ŽPBCO.. with different textures. The so-called a-axis oriented films and superlattices allow us to study the interplay between the natural pinning of the magnetic vortices due to the cuprate structure and the artificial pinning due to the PBCO insulating layers.
2. Experimental results The films and superlattices have been grown in a commercial dc magnetron sputtering system, using stoichiometric targets and on Ž100. SrTiO 3 substrates. The system is computer-controlled and the substrate holder can be moved in front of each target to grow the multilayers. The substrate–target geometry is on-axis and the technique is the same described in Ref. w3x used to grow c-axis oriented samples. c-axis oriented films ŽCuO 2 planes parallel to the substrate. are the usual texture reported in the literature, a-axis oriented films ŽCuO 2 planes perpendicular to the substrate. need very strict conditions to grow
286
J.I. Martın ´ et al.r Thin Solid Films 317 (1998) 285–289
Fig. 1. Deposition steps for a-axis oriented EuBa 2 Cu 3 O 7 films.
and, as far as we know, very few works have been reported on these films w4x. In brief, the film texture could be modified, at will, changing the substrate temperature and the partial oxygen pressure during deposition w5x. Our c-axis oriented films are grown with the usual conditions reported in the literature. These sputtered films are obtained around 8008C and the sputtering atmosphere being a mixture of Ar and O 2 Ž85% Ar and 15% oxygen up to 300 mTorr total pressure.. After deposition, an in situ annealing process in pure oxygen atmosphere is needed. The a-axis films are grown, in our case, with very low oxygen partial Ž6% O 2 . pressure to improve the normal and superconducting state properties. Concerning the temperature we use the self-template method, no buffer is needed. This means that the film is grown on the substrate without using an intermediate layer of another material. The experimental details are shown in Fig. 1. The total thickness of single films and multilayers is 250 nm. We obtain films with metallic behavior in the normal state and with sharp superconducting transitions Žsee Fig. 2.. Fig. 3 shows the X-ray diffraction scans of c- and a-axis films and the satellites coming from the superstructure in the case of an a-axis oriented superlattice. The films and superlattices were patterned by wet etching, the mask has two parts, one of them with a 50 m m
Fig. 2. Superconductivity resistivity transition for a-axis oriented EuBa 2 Cu 3 O 7 film.
Fig. 3. u y2 u X-ray diffraction scans for: Ža. c-axis oriented EuBa 2 Cu 3 O 7 film; Žb. a-axis oriented EuBa 2 Cu 3 O 7 film; and Žc. a-axis oriented 16 unit cells EuBa 2 Cu 3 O 7 r5 unit cells PrBa 2 Cu 3 O 7 superlattice. The diffraction peaks coming from the substrate are labelled with S.
bridge to measure Jc and a bar of width 500 m m for the resistivity measurements. A commercial cryostat with a 90 kOe superconducting magnet and temperature controller have been used. The experimental method to measure critical current density and magnetotransport effects is the same reported by Colino et al. w6x. In the following, c-axis samples will be only used as a reference and the rest of the paper will deal with the properties of the very unusual a-axis samples. In Fig. 4, the Jc values are shown for c- and a-axis films and a-axis multilayers, at zero applied magnetic field. The critical current Jc in general is one order of magnitude lower in a-axis than in c-axis films. It has been shown in Ref. w7x that this is due to the 908 boundaries that appear in a-axis films grown on cubic substrates. As the SrTiO 3 substrate is cubic, the c axis of the samples can be aligned along two perpendicular directions during the nucleation of the first a-axis oriented cells. This causes the existence of microdomains, with average size of 20 nm. These microdomains are separated by 908 boundaries, see Ref. w5x. It is worth a while to underline that these boundaries do not show any weak link behavior w7x.
J.I. Martın ´ et al.r Thin Solid Films 317 (1998) 285–289
287
Fig. 6. Jc vs. B in a-axis oriented 40 unit cells EuBa 2 Cu 3 O 7 r5 unit cells PrBa 2 Cu 3 O 7 superlattice. Filled symbols: B perpendicular to the substrate; hollow symbols: B parallel to the substrate.
Fig. 4. Ža. Critical current density vs. temperature in c-axis Žfilled symbol. and a-axis Žhollow symbol. oriented EuBa 2 Cu 3 O 7 films. Inset shows Jc vs. T in the whole temperature range for an a-axis oriented film. Žb. Critical current density vs. temperature in an a-axis oriented 20 unit cells EuBa 2 Cu 3 O 7 r5 unit cells PrBa 2 Cu 3 O 7 superlattice.
In c-axis films, the HTS anisotropy shows up very clearly in the critical current density Jc behavior, as can be seen in Ref. w8x. This behavior has been related with different kind of boundaries and defects present in the films and with the intrinsic pinning. That is, the magnetic vortices could be pinned by the defects in the films, and they are also pinned by the weakly superconducting areas between the CuO 2 planes, when the magnetic field is applied parallel to these planes. A better pinning of the
Fig. 5. Jc vs. B in a-axis oriented EuBa 2 Cu 3 O 7 film. Filled symbols indicate B perpendicular to the substrate, and hollow symbols indicate B parallel to the substrate.
vortices leads to higher Jc values. In c-axis films the critical current, Jc , is higher when the magnetic field B is applied parallel to the superconducting planes, Žparallel to the substrate. since a lock-in transition Ždue to the intrinsic pinning. dominates the vortex pinning mechanisms. In the case of a-axis films, the opposite behavior could be expected. Fig. 5 shows the Jc anisotropy behavior observed in these films. Now Jc is higher when the magnetic field is applied perpendicular to the substrate, because then the field again is parallel to the CuO 2 planes and the natural pinning mechanism is acting. The experimental results of the Jc anisotropy in a-axis superlattices are shown in Fig. 6. The data show a Jc anisotropy crossover at a certain magnetic field. So, we have the competition between two effects. The possible explanation of this behavior and more experimental information will be given in Section 3.
3. Discussion In a-axis multilayers, see Fig. 6, the usual behavior of a-axis films is reversed above a certain applied magnetic field. That is, the critical current is larger when the magnetic field is applied parallel to the substrate Žperpendicular to the CuO 2 planes.. In this orientation the lock-in transition is absent, but the insulating PBCO layers could play the same role that in single superconducting films is played by the intrinsic pinning mechanism. Vortices could be pinned by these artificially induced pinning centers. The competition between these two mechanisms would explain the crossover in the Jc anisotropy. The first thing we have to figure out is the meaning of the crossover field. Based on the behavior of the pinning forces w9x, a first approach to this problem could be to consider the Abrikosov vortex lattice. So, if we assume that the vortex lattice parameter a 0 is well defined and it is controlled by the value of the
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J.I. Martın ´ et al.r Thin Solid Films 317 (1998) 285–289
applied magnetic field a 0 s ŽF 0rB .1r2 ŽF 0 being the fluxoid., then the PBCO layers will have the maximum effect as very effective pinning centers when the vortex lattice parameter a0 matches the modulation length of the multilayer L, Ž L being the thickness of the EBCO layer plus the thickness of the PBCO layer.. In this situation, for the superlattice of Fig. 6 Ž40 unit cells of EBCOr5 unit cells PBCO. the maximum effect will appear at Ž a0 s L. a field of BL s 6.5 T. This is not the experimental result reported in Ref. w9x, where a smooth variation of the pinning force could be observed around the value of the matching field. The model of Campbell and Evetts w10x could be an useful tool to explain the pinning mechanism induced by the insulating layers. These authors deal with vortex pinning by a distribution of planar centers. If we evaluate this model in the two possible extreme regime, that is a stiff vortex lattice or a soft vortex lattice, the results are plotted in Fig. 7a. Two very different behaviors of Jc are predicted; in the case of a rigid vortex lattice a maximum in the value of Jc will occur when the applied field is the matching field BL Ž a0 s L.; but in the case of a soft vortex lattice the critical current decreases smoothly from its value at matching field BL. Fig. 7b shows the experimental data of Jc Ž B . for a multilayer of 75 unit cells
Fig. 8. Angular dependence of the resistivity in: Ža. a-axis oriented EuBa 2 Cu 3 O 7 film; and Žb. c-axis oriented EuBa 2 Cu 3 O 7 film.
Fig. 7. Ža. Planar pinning center model ŽRef. w10x. for stiff and soft vortex lattice. Ž BL being the matching field and J0 being Jc when B s BL .. Žb. Jc vs. B measurements of an a-axis 75 unit cells EuBa 2 Cu 3 O 7 r5 unit cells PrBa 2 Cu 3 O 7 superlattice with the magnetic field applied parallel to the substrate.
EBCOr5 unit cells PBCO. A smooth decrease of Jc around BL shows that the vortex lattice in HTS could adjust to the pinning centers, in our case the PBCO insulating layers, and the model of a soft vortex matrix is more likely. The resistivity transition tails could be another experimental technique to observe the interplay between the natural and the artificial anisotropy in a-axis multilayers. The angular dependence of the resistivity should be a good fingerprint of the pinning mechanisms, since they have an angular dependence and they are very effective at the right applied field orientation. In our case, minima in the resistivity mean maxima in the Jc . In Fig. 8 the experimental data of an a-axis oriented film and a c-axis oriented film are shown. The lock-in transition due to the intrinsic pinning by the CuO 2 planes is seen as a minimum in the resistivity when the applied magnetic field is perpendicular to the substrate in the a-axis film ŽFig. 8a. and the minimum occurs when the magnetic field is applied parallel to the substrate in the case of c-axis film ŽFig. 8b.. In Fig. 9 the same type of measurements are shown in the case of superlattices. In c-axis superlattices ŽFig. 9b., both pinning centers are parallel to the substrate, a single minimum is observed, but in the a-axis multilayers both pinning centers are perpendicular to each other. As the intrinsic pinning and the multilayer pinning are present in the
J.I. Martın ´ et al.r Thin Solid Films 317 (1998) 285–289
289
Ža-axis samples. to the substrate, depending on the growing conditions, that is deposition temperature and the oxygen partial pressure. The anisotropic behavior of the magnetic vortices is studied using the critical current densities and the tails of the resistivity transitions. The pinning of the vortices by the weakly superconducting areas between the CuO 2 planes Žintrinsic pinning., enhances the Jc values when the applied field is parallel to the substrate in the case of c-axis samples and when the applied field is perpendicular to the substrate, in the case of a-axis samples. In the latter when multilayers are grown, a new pinning center arises from the insulating layers. This pinning center is effective in a broad range of magnetic fields around the matching field. This is due to the fact that the magnetic vortex lattice is very soft in this system. Finally, the angular dependence of the resistivity show minima Žmaxima in the Jc . when the vortices are either pinned by the intrinsic pinning mechanism or through the insulating layer pinning.
Acknowledgements The authors want to thank the Spanish CICYT Žgrant MAT 96-0904. for financial support. Fig. 9. Angular dependence of the resistivity in: Ža. a-axis 40 unit cells EuBa 2 Cu 3 O 7 r5 unit cells PrBa 2 Cu 3 O 7 superlattice; and Žb. c-axis 16 unit cells EuBa 2 Cu 3 O 7 r2 unit cells PrBa 2 Cu 3 O 7 superlattice.
References samples their relative effectiveness depends on direction of the applied fields.
4. Conclusions Thin films of EuBa 2 Cu 3 O 7 and superlattices of EuBa 2 Cu 3 O 7rPrBa 2 Cu 3 O 7 high-temperature superconductor of the 1:2:3 family cuprates are fabricated by dc magnetron sputtering. Magnetotransport effects, mainly critical current and resistivity, are measured in the mixed state. Thin films and multilayers could be grown with the CuO 2 planes parallel Žc-axis samples. or perpendicular
w1x J. Colino, J.L. Sacedon, J.L. Vicent, Appl. Phys. Lett. 59 Ž1991. 3327. w2x G. Blatter, M.V. Feigel’man, V.B. Geshkenbein, A.I. Larkin, V.M. Vinokur, Rev. Mod. Phys. 66 Ž1994. 1125. w3x O. Nakamura, E.F. Fullerton, J. Guimpel, I.K. Schuller, Appl. Phys. Lett. 60 Ž1992. 120. w4x G.Y. Sung, J.D. Suh, Appl. Phys. Lett. 66 Ž1995. 1145. w5x C.B. Eom, A.F. Marshall, S.S. Laderman, R.D. Jacowitz, T.H. Geballe, Science 249 Ž1990. 1549. w6x J. Colino, M.A. Gonzalez, J.I. Martin, M. Velez, D. Oyola, P. Prieto, J.L. Vicent, Phys. Rev. B 49 Ž1994. 3496. w7x M. Velez, J.I. Martin, J.L. Vicent, Appl. Phys. Lett. 65 Ž1994. 2099. w8x B. Roas, L. Schultz, G. Saemann-Ischenko, Phys. Rev. Lett. 64 Ž1990. 479. w9x J.I. Martin, M. Velez, J.L. Vicent, Phys. Rev. B 52 Ž1995. 3872. w10x A.M. Campbell, J.E. Evetts, Adv. Phys. 21 Ž1972. 199.
Magnetic vortices and pinning in thin films and superlattices J.I. Martın ´ a, M. Velez ´ a, E.M. Gonzalez ´ b, J.L. Vicent b
a,)
a Departamento Fisica de Materiales, Facultad de Fisicas, UniÕersidad Complutense, Madrid 28040, Spain Departamento Propiedades Opticas, Magneticas y de Transporte, Instituto de Ciencia de Materiales, CSIC, Cantoblanco, Madrid 28049, Spain
Abstract Thin films and superlattices of high-temperature superconductors ŽHTS. of the 1:2:3 family are grown by dc magnetron sputtering with different textures. The samples could be grown with the CuO 2 planes parallel to the substrate Žthe so-called c-axis orientation. or with the CuO 2 planes perpendicular to the substrate Žthe so-called a-axis orientation.. The films are superconducting with critical temperatures ŽTc . between 85–90 K and with critical currents Ž Jc . at 77 K in the range of 10 6 Arcm2 and 10 5 Arcm2 for c-axis and a-axis oriented films, respectively. In the case of superlattices of EuBa 2 Cu 3 O 7rPrBa 2 Cu 3 O 7 ŽEBCOrPBCO, superconductingrinsulating., the Tc and Jc change with the modulation lengths. These HTS films show very peculiar magnetic properties in the mixed state. The magnetic properties are linked to the behavior of a very soft magnetic vortex lattice and, in the a-axis oriented superlattices, to the competition between natural and artificial anisotropies. In this case, an enhancement of the critical current density Jc could be obtained when the magnetic field is applied parallel to the substrate. q 1998 Elsevier Science S.A. Keywords: Thin films; Superlattices; Magnetron sputtering
1. Introduction Thin films of the 1:2:3 family of oxide cuprates could be grown by different vacuum deposition techniques, as laser ablation, molecular beam epitaxy, etc.; but, among them, the sputtering method allows us to grow good-quality films and multilayers with different textures. The growing conditions to obtain films of HTS are very extreme, since very high substrate-temperature during deposition and high-oxygen pressure in the chamber are required w1x. Therefore, magnetron sputtering seems to be a useful technique. Laser ablation could produce good quality films too; but in this case, the surface roughness could be a problem if multilayers have to be fabricated. The mixed state behavior of HTS has been one of the most interesting topics in the field w2x. A magnetic field applied to a HTS leads to many new phenomena, most of them due to the combination of the short vortex core size Žsmall coherence length. and the structural anisotropy of these oxide cuprates. Another topic related with basic and applied research is the behavior of the critical current Jc in the vortex state. The pinning mechanisms of the vortices should be understood in a way to enhance the Jc values,
)
Corresponding author.
0040-6090r98r$19.00 q 1998 Elsevier Science S.A. All rights reserved. PII S 0 0 4 0 - 6 0 9 0 Ž 9 7 . 0 0 6 4 2 - 1
which is very important from the technological point of view. In this paper we will present the fabrication of thin films of EuBa 2 Cu 3 O 7 ŽEBCO. and superlattices of E u B a 2 C u 3 O 7 r P rB a 2 C u 3 O 7 Ž su p e rc o n d u c tin g ŽEBCO.rinsulating ŽPBCO.. with different textures. The so-called a-axis oriented films and superlattices allow us to study the interplay between the natural pinning of the magnetic vortices due to the cuprate structure and the artificial pinning due to the PBCO insulating layers.
2. Experimental results The films and superlattices have been grown in a commercial dc magnetron sputtering system, using stoichiometric targets and on Ž100. SrTiO 3 substrates. The system is computer-controlled and the substrate holder can be moved in front of each target to grow the multilayers. The substrate–target geometry is on-axis and the technique is the same described in Ref. w3x used to grow c-axis oriented samples. c-axis oriented films ŽCuO 2 planes parallel to the substrate. are the usual texture reported in the literature, a-axis oriented films ŽCuO 2 planes perpendicular to the substrate. need very strict conditions to grow
286
J.I. Martın ´ et al.r Thin Solid Films 317 (1998) 285–289
Fig. 1. Deposition steps for a-axis oriented EuBa 2 Cu 3 O 7 films.
and, as far as we know, very few works have been reported on these films w4x. In brief, the film texture could be modified, at will, changing the substrate temperature and the partial oxygen pressure during deposition w5x. Our c-axis oriented films are grown with the usual conditions reported in the literature. These sputtered films are obtained around 8008C and the sputtering atmosphere being a mixture of Ar and O 2 Ž85% Ar and 15% oxygen up to 300 mTorr total pressure.. After deposition, an in situ annealing process in pure oxygen atmosphere is needed. The a-axis films are grown, in our case, with very low oxygen partial Ž6% O 2 . pressure to improve the normal and superconducting state properties. Concerning the temperature we use the self-template method, no buffer is needed. This means that the film is grown on the substrate without using an intermediate layer of another material. The experimental details are shown in Fig. 1. The total thickness of single films and multilayers is 250 nm. We obtain films with metallic behavior in the normal state and with sharp superconducting transitions Žsee Fig. 2.. Fig. 3 shows the X-ray diffraction scans of c- and a-axis films and the satellites coming from the superstructure in the case of an a-axis oriented superlattice. The films and superlattices were patterned by wet etching, the mask has two parts, one of them with a 50 m m
Fig. 2. Superconductivity resistivity transition for a-axis oriented EuBa 2 Cu 3 O 7 film.
Fig. 3. u y2 u X-ray diffraction scans for: Ža. c-axis oriented EuBa 2 Cu 3 O 7 film; Žb. a-axis oriented EuBa 2 Cu 3 O 7 film; and Žc. a-axis oriented 16 unit cells EuBa 2 Cu 3 O 7 r5 unit cells PrBa 2 Cu 3 O 7 superlattice. The diffraction peaks coming from the substrate are labelled with S.
bridge to measure Jc and a bar of width 500 m m for the resistivity measurements. A commercial cryostat with a 90 kOe superconducting magnet and temperature controller have been used. The experimental method to measure critical current density and magnetotransport effects is the same reported by Colino et al. w6x. In the following, c-axis samples will be only used as a reference and the rest of the paper will deal with the properties of the very unusual a-axis samples. In Fig. 4, the Jc values are shown for c- and a-axis films and a-axis multilayers, at zero applied magnetic field. The critical current Jc in general is one order of magnitude lower in a-axis than in c-axis films. It has been shown in Ref. w7x that this is due to the 908 boundaries that appear in a-axis films grown on cubic substrates. As the SrTiO 3 substrate is cubic, the c axis of the samples can be aligned along two perpendicular directions during the nucleation of the first a-axis oriented cells. This causes the existence of microdomains, with average size of 20 nm. These microdomains are separated by 908 boundaries, see Ref. w5x. It is worth a while to underline that these boundaries do not show any weak link behavior w7x.
J.I. Martın ´ et al.r Thin Solid Films 317 (1998) 285–289
287
Fig. 6. Jc vs. B in a-axis oriented 40 unit cells EuBa 2 Cu 3 O 7 r5 unit cells PrBa 2 Cu 3 O 7 superlattice. Filled symbols: B perpendicular to the substrate; hollow symbols: B parallel to the substrate.
Fig. 4. Ža. Critical current density vs. temperature in c-axis Žfilled symbol. and a-axis Žhollow symbol. oriented EuBa 2 Cu 3 O 7 films. Inset shows Jc vs. T in the whole temperature range for an a-axis oriented film. Žb. Critical current density vs. temperature in an a-axis oriented 20 unit cells EuBa 2 Cu 3 O 7 r5 unit cells PrBa 2 Cu 3 O 7 superlattice.
In c-axis films, the HTS anisotropy shows up very clearly in the critical current density Jc behavior, as can be seen in Ref. w8x. This behavior has been related with different kind of boundaries and defects present in the films and with the intrinsic pinning. That is, the magnetic vortices could be pinned by the defects in the films, and they are also pinned by the weakly superconducting areas between the CuO 2 planes, when the magnetic field is applied parallel to these planes. A better pinning of the
Fig. 5. Jc vs. B in a-axis oriented EuBa 2 Cu 3 O 7 film. Filled symbols indicate B perpendicular to the substrate, and hollow symbols indicate B parallel to the substrate.
vortices leads to higher Jc values. In c-axis films the critical current, Jc , is higher when the magnetic field B is applied parallel to the superconducting planes, Žparallel to the substrate. since a lock-in transition Ždue to the intrinsic pinning. dominates the vortex pinning mechanisms. In the case of a-axis films, the opposite behavior could be expected. Fig. 5 shows the Jc anisotropy behavior observed in these films. Now Jc is higher when the magnetic field is applied perpendicular to the substrate, because then the field again is parallel to the CuO 2 planes and the natural pinning mechanism is acting. The experimental results of the Jc anisotropy in a-axis superlattices are shown in Fig. 6. The data show a Jc anisotropy crossover at a certain magnetic field. So, we have the competition between two effects. The possible explanation of this behavior and more experimental information will be given in Section 3.
3. Discussion In a-axis multilayers, see Fig. 6, the usual behavior of a-axis films is reversed above a certain applied magnetic field. That is, the critical current is larger when the magnetic field is applied parallel to the substrate Žperpendicular to the CuO 2 planes.. In this orientation the lock-in transition is absent, but the insulating PBCO layers could play the same role that in single superconducting films is played by the intrinsic pinning mechanism. Vortices could be pinned by these artificially induced pinning centers. The competition between these two mechanisms would explain the crossover in the Jc anisotropy. The first thing we have to figure out is the meaning of the crossover field. Based on the behavior of the pinning forces w9x, a first approach to this problem could be to consider the Abrikosov vortex lattice. So, if we assume that the vortex lattice parameter a 0 is well defined and it is controlled by the value of the
288
J.I. Martın ´ et al.r Thin Solid Films 317 (1998) 285–289
applied magnetic field a 0 s ŽF 0rB .1r2 ŽF 0 being the fluxoid., then the PBCO layers will have the maximum effect as very effective pinning centers when the vortex lattice parameter a0 matches the modulation length of the multilayer L, Ž L being the thickness of the EBCO layer plus the thickness of the PBCO layer.. In this situation, for the superlattice of Fig. 6 Ž40 unit cells of EBCOr5 unit cells PBCO. the maximum effect will appear at Ž a0 s L. a field of BL s 6.5 T. This is not the experimental result reported in Ref. w9x, where a smooth variation of the pinning force could be observed around the value of the matching field. The model of Campbell and Evetts w10x could be an useful tool to explain the pinning mechanism induced by the insulating layers. These authors deal with vortex pinning by a distribution of planar centers. If we evaluate this model in the two possible extreme regime, that is a stiff vortex lattice or a soft vortex lattice, the results are plotted in Fig. 7a. Two very different behaviors of Jc are predicted; in the case of a rigid vortex lattice a maximum in the value of Jc will occur when the applied field is the matching field BL Ž a0 s L.; but in the case of a soft vortex lattice the critical current decreases smoothly from its value at matching field BL. Fig. 7b shows the experimental data of Jc Ž B . for a multilayer of 75 unit cells
Fig. 8. Angular dependence of the resistivity in: Ža. a-axis oriented EuBa 2 Cu 3 O 7 film; and Žb. c-axis oriented EuBa 2 Cu 3 O 7 film.
Fig. 7. Ža. Planar pinning center model ŽRef. w10x. for stiff and soft vortex lattice. Ž BL being the matching field and J0 being Jc when B s BL .. Žb. Jc vs. B measurements of an a-axis 75 unit cells EuBa 2 Cu 3 O 7 r5 unit cells PrBa 2 Cu 3 O 7 superlattice with the magnetic field applied parallel to the substrate.
EBCOr5 unit cells PBCO. A smooth decrease of Jc around BL shows that the vortex lattice in HTS could adjust to the pinning centers, in our case the PBCO insulating layers, and the model of a soft vortex matrix is more likely. The resistivity transition tails could be another experimental technique to observe the interplay between the natural and the artificial anisotropy in a-axis multilayers. The angular dependence of the resistivity should be a good fingerprint of the pinning mechanisms, since they have an angular dependence and they are very effective at the right applied field orientation. In our case, minima in the resistivity mean maxima in the Jc . In Fig. 8 the experimental data of an a-axis oriented film and a c-axis oriented film are shown. The lock-in transition due to the intrinsic pinning by the CuO 2 planes is seen as a minimum in the resistivity when the applied magnetic field is perpendicular to the substrate in the a-axis film ŽFig. 8a. and the minimum occurs when the magnetic field is applied parallel to the substrate in the case of c-axis film ŽFig. 8b.. In Fig. 9 the same type of measurements are shown in the case of superlattices. In c-axis superlattices ŽFig. 9b., both pinning centers are parallel to the substrate, a single minimum is observed, but in the a-axis multilayers both pinning centers are perpendicular to each other. As the intrinsic pinning and the multilayer pinning are present in the
J.I. Martın ´ et al.r Thin Solid Films 317 (1998) 285–289
289
Ža-axis samples. to the substrate, depending on the growing conditions, that is deposition temperature and the oxygen partial pressure. The anisotropic behavior of the magnetic vortices is studied using the critical current densities and the tails of the resistivity transitions. The pinning of the vortices by the weakly superconducting areas between the CuO 2 planes Žintrinsic pinning., enhances the Jc values when the applied field is parallel to the substrate in the case of c-axis samples and when the applied field is perpendicular to the substrate, in the case of a-axis samples. In the latter when multilayers are grown, a new pinning center arises from the insulating layers. This pinning center is effective in a broad range of magnetic fields around the matching field. This is due to the fact that the magnetic vortex lattice is very soft in this system. Finally, the angular dependence of the resistivity show minima Žmaxima in the Jc . when the vortices are either pinned by the intrinsic pinning mechanism or through the insulating layer pinning.
Acknowledgements The authors want to thank the Spanish CICYT Žgrant MAT 96-0904. for financial support. Fig. 9. Angular dependence of the resistivity in: Ža. a-axis 40 unit cells EuBa 2 Cu 3 O 7 r5 unit cells PrBa 2 Cu 3 O 7 superlattice; and Žb. c-axis 16 unit cells EuBa 2 Cu 3 O 7 r2 unit cells PrBa 2 Cu 3 O 7 superlattice.
References samples their relative effectiveness depends on direction of the applied fields.
4. Conclusions Thin films of EuBa 2 Cu 3 O 7 and superlattices of EuBa 2 Cu 3 O 7rPrBa 2 Cu 3 O 7 high-temperature superconductor of the 1:2:3 family cuprates are fabricated by dc magnetron sputtering. Magnetotransport effects, mainly critical current and resistivity, are measured in the mixed state. Thin films and multilayers could be grown with the CuO 2 planes parallel Žc-axis samples. or perpendicular
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