a-axis oriented (CuO_2 planes perpendicular to the substrate) films and superlattices grown on cubic substrates show a structure with 90° microdomains. The microdomains are grains with a 90° rotation of the c axis. In the vortex liquid region, this microstructure induces a change from the usual three-dimensional (3D) behavior of the anisotropy toward a 2D behavior, in a temperature range above the usual crossover from 2D to 3D. Moreover, when the thickness of the superconducting part of the multilayers becomes smaller (or of the same order as) than the microdomain size the 3D dimensional anisotropy behavior is recovered

González Casado, J.M.

González Herrera, Elvira María

Vicent López, José Luis

©2000 The American Physical Society.
The authors want to thank I. K. Schuller, F. de la Cruz and G. Crabtree for useful conversations. This work has been supported by Spanish CICYT (MAT99-724).a-axis oriented (CuO_2 planes perpendicular to the substrate) films and superlattices grown on cubic substrates show a structure with 90° microdomains. The microdomains are grains with a 90° rotation of the c axis. In the vortex liquid region, this microstructure induces a change from the usual three-dimensional (3D) behavior of the anisotropy toward a 2D behavior, in a temperature range above the usual crossover from 2D to 3D. Moreover, when the thickness of the superconducting part of the multilayers becomes smaller (or of the same order as) than the microdomain size the 3D dimensional anisotropy behavior is recovered.Spanish CICYTDepto. de Física de MaterialesFac. de Ciencias FísicasTRUEpu

Docta Complutense

idPHYSICAL REVIEW B 1 OCTOBER 2000-IVOLUME 62, NUMBER 13Interplay between the vortex phase coherence and extended disorder defects in the vortex-liquregime of thin films and superlattices of 123 superconductorsE. M. González,1,* J. M. Gonza´lez,2 and J. L. Vicent11Departamento Fı´sica de Materiales, F. Fı´sicas, Universidad Complutense, 28040 Madrid, Spain2Departamento Propiedades Opticas, Magne´ticas y de Transporte, Instituto de Ciencia de Materiales de Madrid (CSIC),28049 Cantoblanco (Madrid), Spain~Received 23 June 2000!a-axis oriented (CuO2 planes perpendicular to the substrate! films and superlattices grown on cubic sub-strates show a structure with 90° microdomains. The microdomains are grains with a 90° rotation of thec axis.In the vortex liquid region, this microstructure induces a change from the usual three-dimensional~3D!behavior of the anisotropy toward a 2D behavior, in a temperature range above the usual crossover from 2D to3D. Moreover, when the thickness of the superconducting part of the multilayers becomes smaller~or of thesame order as! than the microdomain size the 3D dimensional anisotropy behavior is recovered.urye-crtedgleuehhif-inmleexleasraonpylyar-b-raderro-es.thelarionente ofg--0°re-theacesent,eenom-ivitypleOtheen-the-en-n.larA real vortex matter could be studied in high-temperatsuperconductors~HTS’s! with a rich variety and still not wellunderstood vortex phases.1 The associated phenomenolog~vortex glass, Bose glass, splayed glass, vortex liquid, ming, lock-in transition, and so on! reflects a complex interplay among the structural anisotropy, disorder, and smallherence lengths. The high temperature at which the vomatter can be studied is crucial to that phenomenology.Recently, several authors have reported the effects offerent types of defects on the vortex liquid behavior in sincrystals2 and melt textured3 123 cuprates. Lopezet al.2 foundstrongly entangled vortex liquid in single crystals governby pointlike disorder; Puiget al.3 found that randomquenched and correlated disorders compete in the liqphase of melt textured YBa2Cu3O7 composites.In this paper we focus on the effect of the interplay btween extended disorder defects and the vortex phase coence lengths in the anisotropy and dimensionality of tfilms in the vortex liquid regime. We report anisotropy efects in the liquid vortex phase of the 123 superconductcuprates. In general, dimensionality and anisotropy probleare ruled by the interplay between different length scawhich govern the physics of the problem. Therefore, theperimental length scale~for instance, the relevant sampsize! should be comparable to relevant physics length sc~for instance, vortex length!. The behavior reported in thiwork is due to the competition between the microstructudefects and vortex lengths. This interplay leads to a strdeviation from the typical 3D behavior of the anisotroclose to Tc .1,4 The usual 3D anisotropy behavior is onrecovered when artificial HTS superlattices of the adequmodulation lengths are fabricated.The samples used in this work were the so-calleda-axisoriented films and superlattices.5 In these samples, the supeconducting CuO2 planes are grown perpendicular to the sustrate. The samples area-axis EuBa2Cu3O7 films anda-axisEuBa2Cu3O7 /PrBa2Cu3O7 multilayers. They have been obtained by dc magnetron sputtering in the on-axis configution on cubic~100! SrTiO3 substrates and their structural antransport characterization have been reported elsewh6PRB 620163-1829/2000/62~13!/8707~4!/$15.00elt-o-xif-edid-er-ngss-lelgte--e.The most relevant structural characteristic ofa-axis films,grown on cubic substrates, is a microstructure with micdomains of average size around 20 nm with 90° boundari7Therefore, some experimental care has to be taken withgeometry of the experiment. We have followed a simiexperimental geometry that Trisconeet al.8 The films werepatterned with bridges making a 45° angle with the directof the CuO2 planes, and, in our case, the macroscopic currand the magnetic fields are perpendicular to each other~con-stant Lorentz force configuration!. A simple correction has tobe used in the anisotropy expressions to relate the valuthe angleu between the film normal and the applied manetic field H and the anglew, betweenH and the CuO2planes, see Ve´l z et al.6 It is worthwhile to stress that highresolution-transmission electron microscopy in oura-axisfilms and superlattices have shown the typical 9microdomains,9 and that in the case of the superlattices,finement of the structure from x-ray spectra shows thatinterface step disorder is around 1 unit cell and the interfdiffusion is 20 percent,10 values very similar to the valueobtained inc-axis superlattices.11We have to point out that, in-plane-aligneda-axis filmshave been fabricated12 on tetragonal substrates (LaSrGaO4).In this case, the microdomain structure is, of course, absonly antiphase boundaries and stacking faults have bobserved.13The anisotropy of the samples were studied using a cmercial 90 kOe superconducting magnet, standard resistdc technique and a computer controlled rotatable samholder. The valueu50° is with the applied magnetic fieldperpendicular to the film plane, that is parallel to the Cu2planes direction. The raw data we have used to analyzeanisotropic behavior are taken with a constant current dsity of 80 A/cm2, close toTc , in the vortex liquid regime.Variation of the current density around this value andtemperature above 0.85T/Tc do not change the results. Figure 1 shows that the applied magnetic fields and current dsity used in the experiment explore this vortex liquid regioThese (r,J) curves are extracted from current-voltage (I ,V)characteristics, with the applied magnetic field perpendicu8707 ©2000 The American Physical Societyar.thtinevroigcon-ter,thishaseand,ob-u--ch,stingu-cedne-aa-fintsonob-ll,D-ex-thhaore8708 PRB 62BRIEF REPORTSto the substrate~parallel to the CuO2 planes!. Figure 2 shows@r(u),Hi # curves, that is, resistivity vsu ~angle between theapplied magnetic field and the normal to the film! at theconstant fieldHi . From these sets of measurements we eily extract the@r(Hi),u j # curves: at fixed anglesu j ~rangingfrom 0° to 90°), ther value at every measured fieldHi istaken. This last set of curves is used in our analysis lateAmong the HTS families, the 123 cuprates are one ofless anisotropic, following a 3D behavior close toTc .1Therefore the 3D effective-mass model is a good starpoint to analyze the data. In the framework of this modone step further is given by Lawrence and Doniach.14 Thisapproach opens the possibility of a dimensional crossodecreasing the temperature. A clear hint of a crossover fa 3D to a 2D behavior was experimentaly observedintrinsic15 and artificial16 low-temperature superconductinFIG. 1. Resistivity vs the current density, in a double logarimic scale, for ana-axis EuBa2Cu3O7 film at T/Tc50.9. The mag-netic field is perpendicular to the film plane. This figure shows tthe magnetic fields and currents used in the measurements cspond to the linear behavior of the vortices in the liquid phase.FIG. 2. Raw data atT/Tc50.9 for ana-axis EuBa2Cu3O7 filmshowing the resistivity vs the angleu at several constant fields. Thmeasurement current density was 80 A/cm2.s-egl,ermnsuperlattices. TheL-D model, which comes from theGinzburg-Landau equations, investigates layered superducting systems with the superconducting order paramein adjacent layers, coupled by Josephson tunneling. Incase, a loss of the coherence of the order parameter poccurs, and the usual HTS picture of pancake vorticesJosephson vortices could come up easily.1 For these reasonsthe L-D approach seems to be a perfect tool to study prlems of anisotropy and dimensionality in HTS. Unfortnately, the upper critical fieldHc2 is the experimental quantity that is calculated. The use of the scaling approaproposed by Blatteret al.,17 helps to solve this problem. Thiapproach allows us to translate various superconducproperties from isotropic to anisotropic systems. In particlar, the magnetic field at any angle is scaled to a redufield as H red5He(w), where the factore(w) comes fromthe anisotropy models according to the definitione(w)5Hc2(w)/Hc2i (w: angle betweenH and Cu-O planes,Hc2i :upper critical field parallel to the Cu-O planes!. Several au-thors have used this approach to avoid theHc2 problem andto study anisotropy and dimensionality in HTS~see, for in-stance, Ref. 18!. The scaling function, used in the definitioof the reduced field in the 3D model, is given bye(w)5Asin2w1g2cos2w; where the anisotropy parameter is dfined asg5Hc2' /Hc2i andHc2' is the upper critical field per-pendicular to the CuO2 planes. As was pointed out~see Ref.6!, the measurement configuration letw be expressed asfunction of the angleu according to sinw5sinu sinf ~in ourcase,f545°). Therefore, taking into account this last reltion, the anisotropy factore can be written as a function othe angleu,e5e(u), so this is the expression that we usethe graphs.A scaling rule given byH°H f (u) ( f is a factor that onlydepends on the angle! applies successfully in thesea-axisoriented films for sets of resistivity measuremen@r(Hi),u j #, see Fig. 3~a!. In these collapses, thef factors arenot extracted from any anisotropy model. The compariswith the models is presented in Fig. 3~b!, where thee/gvalues vsu are plotted. The same behavior has beenserved at other temperatures aboveT/Tc50.85, also. Theseplots show a clear deviation of the 3D behavior. First of athis means that the anisotropy ina-axis EuBa2Cu3O7 filmson cubic ~100! SrTiO3 substrates does not follow the 3anisotropy behavior ofHc2. However, we were able to fit theexperimental data@see Fig. 3~b!# around the CuO2 planesdirection (0° –20°) using the Yamafujiet al.model19 ~YKI !.In this model,Hc2(w) is calculated by applying a perturbation method to the Ginzburg-Landau equation. The finalpression isHc2~w!Hc2'sin~w!1S Hc2~w!Hc2i cos~w!D 23F123~11A2!S Hc2'Hc2i D 2 Hc2~w!Hc2' sin~w!G51.Actually, the YKI model is a further step in the Tinkhammodel,20 that explores the behavior ofHc2 in superconduct-ing thin films.-tre-il-esiyDctreisrdonoded.thebe-liarththof ae aatheeuresepthea-l..0°heopPRB 62 8709BRIEF REPORTSBefore we begin to analyze these results, it is worthwhto note that recently, Trajanovicet al.21 have studied the anisotropy and dimensionality effects in untwinned in-planaligned a-axis YBa2Cu3O7 films, at a lower temperaturerange than in our case. These authors could fit the dataply by replacingHc2 with Jc in the anisotropy models. Thefound that the critical currentJc follows theHc2(w) anisot-ropy laws in the whole (0° –90°) angular interval, with a 3behavior at high temperatures and a crossover, as expeto 2D ~Tinkham thin-film model! decreasing the temperatubelow T/Tc50.8. However, this expected 3D behaviorabsent in oura-axis films with 90° microdomains. In oucase, the experimental data could only be fitted to a mo~YKI !, related to the Tinkham model, in an angular regiaround the CuO2 superconducting planes.Anisotropy and dimensionality effects are only a mattercomparison between different length scales. Thereby, theFIG. 3. a-axis EuBa2Cu3O7 oriented film~thickness 250 nm! atT/Tc50.90. ~a! Resistivity vs the reduced field variableH f (u)showing the collapse of the experimentalr(H) curves at anglesu:0°, 3°, 5°, 8°, 10°, 15°, 20°, 25°, 30°, 35°, 40°, 50°, 60°, 70°, 8and 90°.~b! Experimental points ofe/g, extracted from Fig. 3~a!,vs theu angle~see text!. The predicted angular dependence of tanisotropy models are also plotted for comparison. The anisotrparameter isg50.185.e-m-ed,elfif-ferent lengths involved in the problem have to be discussOne of them related to the sample characteristics andother to the superconducting properties.The microdomains are the unique structural differencetween the in-plane-aligned films~3D anisotropy! and oursamples~deviation from the expected 3D anisotropy!. Thesample characteristic length could be related to the pecufilm microstructure~20 nm average size microdomains wi90° boundaries!. The superconducting characteristic lengmust be at least of the same order to have the possibilitydimensional crossover. The experimental window could bclue to clarify this point. The measurements are takentemperatures above 0.85T/Tc and with applied magneticfield of the order of 50 kOe. Taking into account that tintervortex distancea0 is given by a051.07 (F0 /B)1/2,where F0 is the fluxoid, the intervortex distance is of thorder of the microdomain size, and, besides, the temperatare close toTc , so the vortices are very soft. The next stshould be to discuss the influence of the microstructure inFIG. 4. Experimental points ofe/g vs u angle for two differentsuperlattices~total thickness 250 nm! at the same reduced temperture T/Tc50.90. The solid line is the prediction of the 3D mode~a! Superlattice of bilayer 50 u.c. EuBa2Cu3O7/5 u.c. PrBa2Cu3O7~u.c. means unit cells!. ~b! Superlattice of bilayer 25 u.cEuBa2Cu3O7/5 u.c. PrBa2Cu3O7.,yrifhedsecoincoagstngoo-oengin;neddtibolshel tngrofseld-e ofofathewsainriestionior; thetheainpyisco-ofer3Dofuzeen8710 PRB 62BRIEF REPORTSentanglement regime. But, before that, we have to clawhich vortex length is ruling this effect. In the 3D case tvortex is well defined along the sample and the flux jumpsnot implicate that the vortex loses its identity. In our cathe dimensionality could be reduced if the vortex phaseherence is lost. The vortex length that should be takenaccount is related to the phase correlation of the superducting order parameter in the direction of the applied mnetic field. That is, the length along the vortex where it exias a phase coherent object. The superconducting lewhich matters is the vortex phase correlation. When the vtex phase correlation is lost, cutting and recombinationvortices take place.22 The dimensionality and anisotropy picture follows, in our case, from the competition of twlengths: the size of the microdomains and the vortex cohence length. At each angle, the phase coherence lewould be given by the vortex length within a microdomawhen that length gets shorter than some other referelength, such as the natural phase coherence length duvortex entanglement, then the angular dependence coulstrongly affected. We assume that the microstructure an90° boundaries could act as barriers cutting and reconnecvortex lines. These films do show vortex cutting inducedcorrelated disorder. This behavior deviates from the rplays by extended correlated disorder~twin boundaries, co-lumnar defects! which induces vortex correlation for fieldparallel to extended defects.22How do we test this assumption without changing ttemperature~combing the vortices! and the structure of thematerial? Superconducting multilayers are the ideal toodo it. The key could be multilayers with superconductilayer thicknesses of the order or smaller than the micdomain size. Figure 4~a! shows the dimensional behavior oa-axis EuBa2Cu3O7 /PrBa2Cu3O7 ~50/5 u.c.! superlatticegrown on cubic~100! SrTiO3 substrates. This sample followNr-yo,-ton--sthr-fr-thcetobeitsngyeo-a 3D effective mass model behavior when the magnetic fiis applied close to the CuO2 planes, with an anisotropy parameter,g, typical of the 123 cuprates.1 In this multilayer,the thickness of the superconducting layers and the sizthe microdomains are of the same order. If the thicknessthe superconducting layer is reduced even more~25 u.c.!, seeFigure 4~b!, the experimental data follows the 3D model inbroader angular interval than before. In summary, whenmagnetic field is applied close to the CuO2 planes and thesuperconducting layer thickness~vortex length! is of the or-der or smaller than the microdomain size, the system follothe usual 3D anisotropy model. But, when the microdomsize is smaller than the vortex length, the 90° boundacould be seen by the vortices and cutting and recombinacould occur. Then, a deviation of the typical 3D behavhappens. Finally, it has to be noted that in thesea-axis su-perlattices the superconducting layers are not decoupledPBCO layer thickness is only 2 nm, much smaller thandecoupling length estimated by Suzukiet al.23 The superlat-tices are in the strong coupling regime, the microdomboundaries are the main actors in this crossover effect.In conclusion, in the vortex liquid regime, the anisotroof a-axis films grown on cubic substrates follows theHc2(u)behavior given by the YKI model when the magnetic fieldapplied between 0°~parallel to the CuO2 planes! and 20°.This behavior is due to the change of the vortex phaseherence length, which is modified by the microstructurethe film. The 90° microdomains induce correlated disordcutting and recombination of the vortices. The expectedanisotropy behavior is only observed when superlatticesthe appropiate modulation length are fabricated.The authors want to thank I. K. Schuller, F. de la Crand G. Crabtree for useful conversations. This work has bsupported by Spanish CICYT~MAT99-724!.--*Present address: Department of Physics, SUNY, Stony Brook,11794.1G. Blatteret al., Rev. Mod. Phys.66, 1125~1994!; J.M. Trisconeand O. Fisher, Rep. Prog. Phys.60, 1673~1997!; I. Bozovic andJ. N. Eckstein,Physical Properties of High Temperatures Supeconductors V, edited by D.M. Ginsberg~World Scientific, Sin-gapore, 1996!, p. 99.2D. Lopezet al., Phys. Rev. Lett.80, 1070~1998!.3T. Puig et al., Phys. Rev. B60, 13 099~1999!; T. Puig and X.Obradors, Phys. Rev. Lett.84, 1070~2000!.4C.S.L. Chunet al., Phys. Rev. B29, 4915~1984!.5C.B. Eomet al., Science251, 780 ~1991!.6M. Vélez et al., Phys. Rev. B54, 101 ~1996!, and referencestherein.7C.B. Eom et al., Science249, 1549 ~1990!; A.F. Marshall andC.B. Eom, Physica C207, 239 ~1993!.8J.-M. Trisconeet al., J. Alloys Compd.183, 224 ~1992!.9J.I. Martin et al., Thin Solid Films275, 119 ~1996!.10E.M. Gonzalezet al., Stripes and Related Phenomena, edited byY A. Bianconi and N.L. Saini~Kluwer Academic/Plenum Publishers, New York, 2000!, p. 539.11E.E. Fullertonet al., Phys. Rev. Lett.69, 2859~1992!.12K.H. Young and J.Z. Sun, Appl. Phys. Lett.59, 2448~1991!.13Y. Suzukiet al., Phys. Rev. B48, R10 642~1993!.14W.E. Lawrence and S. Doniach,Proceedings of the 12th International Conference on Low Temperature Physics,edited by E.Kanda~Academic Press, Kyoto, 1971!, p. 361.15J.L. Vicentet al., Phys. Rev. Lett.44, 892 ~1980!.16S.T. Ruggieroet al., Phys. Rev. Lett.45, 1299~1980!.17G. Blatteret al., Phys. Rev. Lett.68, 875 ~1992!.18E. Silvaet al., Phys. Rev. B55, 11 115~1997!; H. Iwasakiet al.,Physica C244, 71 ~1995!; C.M. Fuet al., ibid. 205, 111~1993!.19K. Yamafuji et al., Phys. Lett.20, 122 ~1966!.20M. Tinkham, Phys. Lett.9, 217 ~1964!.21Z. Trajanovicet al., Phys. Rev. B56, 925 ~1997!.22D. Lopezet al., Phys. Rev. Lett.76, 4034~1996!.23Y. Suzukiet al., Phys. Rev. Lett.73, 328 ~1994!.

Physical Review B

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Interplay between the vortex phase coherence and extended disorder defects in the vortex-liquid regime of thin films and superlattices of 123 superconductors

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Interplay between the vortex phase coherence and extended disorder defects in the vortex-liquid regime of thin films and superlattices of 123 superconductors

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