PHYSICAL REVIEW B 69, 134505 ~2004! Interface barriers for flux motion in high-temperature superconducting superlattices J. E. Villegas,1 Z. Sefrioui,2 M. Varela,2,* E. M. Gonzalez,1 J. Santamaria,2 and J. L. Vicent1 1Departamento de Fı´sica de Materiales, Facultad CC. Fisicas, Universidad Complutense, 28040 Madrid, Spain 2GFMC, Departamento de Fı´sica Aplicada III, Facultad CC. Fisicas, Universidad Complutense, 28040 Madrid, Spain ~Received 16 September 2003; revised manuscript received 14 January 2004; published 14 April 2004! We study angular dependent magnetoresistance in the vortex-liquid phase of epitaxial YBa2Cu3O7 thin films and YBa2Cu3O7 /PrBa2Cu3O7 superlattices. Superlattices were grown with different PrBa2Cu3O7 thickness in order to tune coupling between YBa2Cu3O7 layers. While dissipation of single film and coupled superlattices is scaled with the anisotropic three-dimensional model in the whole angular range, decoupling through PrBa2Cu3O7 spacer breaks down the scaling and yields strong reduction of the dissipation when the magnetic fields are applied up to620° around the interface direction. Bean-Livingston barriers at the interface are the mechanism which governs this behavior. DOI: 10.1103/PhysRevB.69.134505 PACS number~s!: 74.72.Bk, 74.78.Bz, 74.78.Fk, 74.25.Fy or as la nd ic c ld ce e g. p rt ar te en i ed he e be to b nd tr b tu a s o s s ia r- ter- g d for rried ct- ed ter the he cting It is by lls c. h 2 nce les. ent re ure- he se, nd with is Vortex matter in high-temperature oxide superconduct ~HTCS! has been extensively investigated during the l years. The mixed state properties of HTCS are governed the interplay between the elastic properties of the vortex tice, thermal fluctuations, and the presence of different ki of disorder, yielding a complicated phase diagram wh shows a rich variety of phenomena.1,2 The intrinsically an- isotropic structure of these oxide superconductors indu anisotropic magnetotransport properties. At magnetic fie H applied parallel to Cu-O planes the dissipation is redu with respect to the situation where magnetic fields are p pendicular to them, due to the so-called intrinsic pinnin3 Moreover, it has been recently shown that this anisotro structure stabilizes a vortex smectic phase when the vo lattice matches the periodic layered structure.4 In this con- text, superconducting/insulator YBa2Cu3O7 /PrBa2Cu3O7 ~YBCO/PBCO! superlattices are interesting structures to tificially modify the anisotropic behavior of this HTSC.5 This artificial manipulation yields a number of phenomena rela to low dimensionality and vanishing coupling betwe YBCO layers,6 vortex phase coherence,7 dissipation anisotropy,8 etc. In this paper, we show that vortex pinning is enhanced fully decoupled YBCO layers, when magnetic field is appli parallel to YBCO/PBCO interfaces. We investigate t physical origin of this behavior by studying the angular d pendent dissipation in the liquid state ofc-axis oriented YBCO/PBCO superlattices. We discuss on the interplay tween intrinsic and interface pinning, and we point surfacelike9 barriers at the YBCO/PBCO interface as a pro able origin for the observed behavior. Epitaxial c-axis oriented YBCO/PBCO superlattices a YBCO single film were grown on~100! SrTiO3 substrates using a high-pressure sputtering system, with stoichiome PBCO and YBCO targets. Chamber pressure was 3.4 m of pure oxygen during deposition, and substrate tempera was held at 900 °C. Deposition rate was as low 0.013 nm s21, which accurately allows controlling layer thickness. The structural characterization was made by b low- and high-angle x-Ray-diffraction technique and tran mission Electron microscopy. Both techniques show that perlattices have high structural quality, showing epitax 0163-1829/2004/69~13!/134505~5!/$22.50 69 1345 s t by t- s h es s d r- ic ex - d n - - - ic ar re s th - u- l growth without significant roughness or interdiffusion. Fu ther details on samples fabrication and structural charac ization are published elsewhere.10,11 Bridges (20mm wide! were patterned by wet etchin technique and the standard four probes setup was use magnetotransport measurements. Measurements were ca out in a commercial liquid He cryostat with a supercondu ing 9 T solenoid. The variable temperature insert allow controlling temperature in the range 1.5–300 K. A compu controlled rotatable sample holder was used, such that direction of the applied magnetic field with respect to t sample could be continuously changed. The studied samples presented sharp supercondu transitions, with critical temperatures of Tc580, 86, 88, and 90 K for samples @YBCO[5 u.c.] /PBCO[5u.c.]#17 (u.c. 5unit cells), @YBCO[8u.c.] /PBCO[5u.c.]#13, @YBCO[17 u.c.] / PBCO[2u.c.]] 9, and YBCO50 nm single film respectively. The total thickness of superlattices is always around 200 nm. important to remark that YBCO layers are fully decoupled the five unit cells thick PBCO spacer12–14 in the YBCO[5 u.c.] /PBCO[5 u.c.] and YBCO[8 u.c.] /PBCO[5 u.c.] su- perlattices, while they are coupled through the two unit ce thick spacer in YBCO[17 u.c.] /PBCO[2 u.c.] . Accordingly, in the following we will refer to superlattices with 5 PBCO u. spacer as the decoupled superlattices and to that wit PBCO u.c. as the coupled one. In Fig. 1 is shown the angular dependence of resista R(u,H) at an injected current densityj 550 A cm22 in ap- plied magnetic fields between 1 and 9 T for the four samp u50 corresponds to field parallel to substrate~i.e., parallel to Cu-O planes and YBCO/PBCO interfaces!. Constant Lor- entz force geometry was kept by injecting electrical curr in theab plane, parallel to the rotation axis. The temperatu T50.99Tc was chosen high enough to ensure that meas ments were performed above the irreversibility line for t three samples, for all fields and angles. With this purpo isothermalI -V characteristics were previously measured, a the temperature for angular measurements was selected the criterion of linear~Ohmic! I -V characteristic at 1 T in field parallel to Cu-O planes (u50) at current level range 25 A cm22, j ,2.5 kA cm22. In Fig. 1, substantially differ- ent behavior of the four samples is observed when field ©2004 The American Physical Society05-1 o on an a r ad en a p a he f t tic r - ip an ge, - g n e- ac- ld d de- ple nce s J. E. VILLEGAS et al. PHYSICAL REVIEW B 69, 134505 ~2004! applied in directions close to YBCO/PBCO interface~or Cu-O planes!, being dissipation highly reduced in the case the decoupled superlattices. We have used the scaling approach for three-dimensi ~3D! anisotropic superconductors proposed by Blatteret al.15 to analyze the anisotropic behavior of the superlattices the YBCO single film. This model gives a scaling rule th allows collapsing angular dependent resistanceR(u,H) curves into a single curve in terms of a reduced fieldR(H«). H« is defined asH«5H«(u), where the scaling facto «(u)5Hc2 (u)/Hc2 a,b , in particular, we use «~u!5Asin2~u!1g22cos2~u! ~1! with the anisotropy parameterg5Hc2 a,b/Hc2 c . It is important to remark that, within this model, no assumptions are m about the dissipation mechanisms, neither on its depend on field, angle, or temperature.7 Following this formalism, we tried to collapseR(u,H) curves depicted in Fig. 1 onto single master curve for each sample, in terms of the sim free parameterg. Results are shown in Fig. 2. Plots are in double logarithmic scale to highlight deviations from t master curve or not-collapsed points. Thus, in the case o YBCO single film, we have obtained good scaling withg ;7, well in the rangeg;5 –10 reported in the literature.16,17 The same behavior is observed for the coupled superlat which is well described within a 3D model with a simila anisotropy parameterg;7. However, in the case of the de coupled superlattices it is not possible to scale down diss tion over the whole angular range, i.e., no value of the FIG. 1. Normalized resistance as a function angle of sam YBCO50 nm ~a! YBCO[17 u.c.] /PBCO[2 u.c.] ~b!, YBCO[8 u.c.]/ PBCO[5 u.c.] ~c!, and YBCO[5 u.c.] /PBCO[5 u.c.] ~d!. Applied fields are m0H51, 3, 5, 7, and 9 T, temperature was in all casesT 50.99Tc and j 550 A cm22. The highlighted areas in~c! and ~d! contain the nonscalable range~see text!. 13450 f al d t e ce le he e, a- - isotropy g allows collapsing points fromR(u,H) curves in the range 20°,u,20° @highlighted area in Figs. 1~c! and 1~d!#. Good scaling is achieved out of this angular ran consistent with an anisotropy parameterg;7. Dissipation in the range 20°,u,20° is lower than expected from the an isotropic (g;7) 3D behavior occurring in the remainin range 20°,u,170°. It is well known that resistivity is thermally activated i the TAFF regime~thermally activated flux flow!,1 r5r0expS 2U~H,T,u! KBT D . ~2! Therefore, to get further insight into this anomalous b havior, we have investigated the field dependence of the tivation energies. Following the 3D anisotropic model, the angular and fie dependent activation energyU(u,H,T) can be described by18,19 U~u,H,T!5U0~u,H !S 12 T Tc D5 b ~H«~u!!aS 12 T Tc D . ~3! Whereb is an energy scale,a gives field dependence, an the anisotropyg is included in«(u) @see Eq.~1!#. Since we got g from the scaling ofR(u,H) curves,b and a can be obtained from fits of ln@R(u,H)# to Eq.~3!. It is worth noting that, onceg is known, the shape of the curveU(u,H) only depends ona. In this way, we have extractedU0(u,H) from the R(u,H) curves shown on Fig. 1, and the results are s FIG. 2. Scaling of the angular dependent normalized resista curves for applied fieldsm0H51, 2, 3, 5, 7, and 9 T, for sample YBCO 50 nm ~a!, YBCO[17 u.c.] /PBCO[2 u.c.] ~b!, YBCO[8 u.c.]/ PBCO[5 u.c.] ~c!, and YBCO[5 u.c.] /PBCO[5 u.c.] ~d!. Note the non- scalable points in~c! and ~d!. 5-2 ce - d a el ta t o e n ie ce a ur ul ti ris in on, d l- of lly as the O as as ss ve , is b- rs in ent ot- n O up- our the in ma- in he per- - d tic nd ipa- le e of ce INTERFACE BARRIERS FOR FLUX MOTION IN HIGH- . . . PHYSICAL REVIEW B 69, 134505 ~2004! picted in Fig. 3. In the case of the YBCO single films, ni fits are obtained yieldinga;1, while for the coupled super lattice we have founda;0.5. In the case of the decouple superlattices, we applied the above analysis only to the gular range where the 3D anisotropic model works, nam 20°,u,170°, and using the valueg;7 obtained from the scaling analysis of Fig. 2, we gota;0.5. This is shown in Figs. 3~c! and 3~d!, where one can see that the experimen values of the activation energy foru50 are almost abou three times higher than expected from the extrapolation the fits to Eq.~3! at u50 ~solid line!. Since, for the decoupled superlattices, the dependenc the activation energy on field~given bya) cannot be inferred from the above procedure when field is applied in directio close to YBCO/PBCO interfaces (220°,u,20°), we mea- suredR(T,H), in both field parallel to Cu-O planes (u50) and field parallel toc-axis (u590). Results foru50 are shown in Fig. 4, in an Arrhenius plot. The activation energ U0(H) ~depicted in the inset of Fig. 4! were obtained from the linear portions of the Arrhenius plots.U0 displays an inverse square-root dependenceU0}H20.5 (a;0.5), for bothu50 andu590, i.e., the activation energy dependen on H does not change with field orientation, excluding this an origin of the dissipation anomaly at low angles. In the case of YBCO single film andc-axis coupled su- perlattice, pinning effects arising from the layered struct dominate over the whole angular range, in a way that ang dependent dissipation can be scaled in terms of an effec field H« by means of the factor«(u). However, forc-axis decoupled superlattices, another pinning mechanism a that overcomes the intrinsic one when field is applied directions in the range220°,u,20° ~close to YBCO/ PBCO interfaces!. This barrier for flux motion is only active FIG. 3. Activation energies as a function of angle for samp YBCO50 nm ~a!, YBCO[17 u.c.] /PBCO[2 u.c.] ~b!, YBCO[8 u.c.] / PBCO[5 u.c.] ~c!, and YBCO[5 u.c.] /PBCO[5 u.c.] ~d!, in applied field m0H59 T. Circles are experimental data, and solid lines are b fits to Eq.~3!. 13450 n- y, l f of s s s e ar ve es in this angular range, giving rise to a reduced dissipati while it does not affect vortex motion when field is applie in the range 20°,u,170°, where dissipation becomes sca able with the 3D anisotropic model. The physical origin these interface related barriers inc-axis superlattices is clearly connected with the fact that YBCO layers are fu decoupled by the 5 unit cells PBCO spacer. This point w well established by experiments on the dependence of activation energyU0 on PBCO spacer thickness;12,14; it was found thatU0 saturated with a spacer thickness of 4 PBC unit cells or higher, showing that this PBCO thickness w enough to fully decouple YBCO layers. The same result w obtained from theTc dependence on PBCO spacer thickne n in the c-axis superlattices series YBCO/PBCO[n u.c.] , 13 sinceTc was found independent of PBCO thickness abo four unit cells. Another point, which should be addressed the role played by the PBCO layers. In the case ofa-axis oriented superlattices~Cu-O planes perpendicular to the su strate! the effects of both, intrinsic pinning and PBCO laye pinning, could be easily separated. Velezet al. have shown that, contrary to our observation, vortex pinning at PBCO coupled a-axis superlattices displays an angular depend resistance scaling following a 3D model with a given anis ropy parameterg.20,21 In this case, vortex pinning eve stronger than intrinsic pinning takes place in the PBC spacer, where the order parameter is not completely s pressed, since the superconducting layers are coupled. In case, however, we did not found anyg value that allowed scaling down dissipation in the whole angular range for c-axis decoupled superlattices. Therefore, vortex trapping PBCO layers has to be discarded as the origin of the ano lous reduced dissipation in parallel applied magnetic field decoupled superlattices. In view of the above considerations, we can think of t decoupled superlattices as a stack on thin independent su conducting slabs~YBCO layers! separated by nonsupercon ducting ~insulator! PBCO. When magnetic field is applie close to parallel to the YBCO/PBCO interface, the magne field would enter PBCO layers as magnetic field lines a YBCO layers as vortices. In such situation, reduced diss s st FIG. 4. Superconducting transitions of sample YBCO[8 u.c.] / PBCO[5 u.c.] in applied field ofm0H52, 4, 6, and 8 T parallel to YBCO/PBCO interfaces. Inset: Activation energies as a function applied field, for fields applied parallel to YBCO/PBCO interfa ~upper curve!, and parallel toc axis ~below!. 5-3 rs f d ad th r ts he a in ar ra a ac an n hi ar e a he y s s- O k s e O der e les s the be- gle n- k s to n ved e to g ce the the s l to e- D ices, the o- ults We in T 8, nd N d ok A. R . Y. P. . J. E. VILLEGAS et al. PHYSICAL REVIEW B 69, 134505 ~2004! tion is most likely due to vortex trapping at the YBCO laye instead of at PBCO layers. The mechanism responsible this may be related to the so-called Bean-Livingston~BL! or surface barriers,9 whose importance in the magnetic an electric behavior of HTCS has been experimentally dressed during the last years.22–28 The physical origin of these barriers lies on two contributions: on one hand, vortex-antivortex~mirror image outside the sample! interac- tion, which results in attractive force to the surface~barrier for flux entry!. On the other hand, there is the repulsive Lo entz force on the vortex caused by shielding supercurren presence of applied magnetic field~barrier for flux escape!. When field is applied parallel to YBCO/PBCO interface, t YBCO/PBCO interface behaves as asurface. A similar sce- nario has been theoretically examined by Burlachkovet al.,29 i.e., surface pinning in a HTCS superconducting slab in p allel magnetic field. In that paper, the effects of surface p ning at equilibrium magnetization on transport properties addressed by taking into account the vortex-surface inte tion in addition to the vortex-vortex interaction. This yields characteristic length over which vortices should feel surf influence of the order ofa0.(f0 /gB)0.5 which, taking into account our experimental data range, is always larger th nm (a0 value for 9 T!, and thus of the order or larger tha YBCO layer thickness in the decoupled superlattices. Wit a0 surface effects should overcome intrinsic ones if BL b riers are higher than intrinsic ones. Always following th work of Burlachkovet al.29 the dissipation in the equilibrium vortex liquid state dominated by surface effects is line ~Ohmic!, yielding an Arrheniuslike resistance law, as in t TAFF @Eq. ~2!#, with an activation energy given b U(H,T)5f0lmeq 3/2/4pAg2H, wheremeq is the equilibrium magnetization andf0 the flux quanta. Using typical value for YBCO, l5l0 /A12(T/Tc) 4 and l05140 nm~penetra- tion depth!, g;7 ~anisotropy parameter! and m0H'B, Burlachkovet al.29 give an estimate forU0'53104/AB K ~with B in T!. Therefore, BL barriers contribution to tran port properties is expected in the case of ultrathin YBC layers in decoupled superlattices with individual layer thic ness of the order ofa0, which points to this mechanism a the responsible for the reduced dissipation observed in th samples in applied magnetic fields parallel to YBCO/PBC *Present address: Condensed Matter Science Div. Oak Ridge tional Laboratory. 1G. Blatter, M.V. Feigel’man, V.B. Geshkenbein, A.I. Larkin, an V.M. Vinokur, Rev. Mod. Phys.66, 1125~1994!. 2F. Bouquet, C. Marcenat, E. Steep, R. Calemczuk, W.K. Kw U. Welp, G.W. Crabtree, R.A. Fisher, N.E. Phillips, and Schilling, Nature~London! 411, 448 ~2001!. 3M. Tachiki and S. Takahashi, Solid State Commun.70, 291 ~1989!. 4S.N. Gordeev, A.A. Zhukov, P.A.J. de Groot, A.G.M. Jansen, Gagnon, and L. Taillefer, Phys. Rev. Lett.85, 4594~2000!. 5For a review, see J.M. Triscone and O” . Fischer, Rep. Prog. Phys 60, 1673~1997!. 6X.G. Qiu, G.X. Chen, B.R. Zhao, V.V. Moshchalkov, and Bruynseraede, Phys. Rev. B68, 024519~2003!. 13450 or - e - in r- - e c- e 6 n - r - se interfaces. Moreover activation energies are within the or of magnitude estimated by Burlachkovet al.29 and exhibit the correct (1/AB) magnetic field dependence. Notic that the behavior of both decoupled samp YBCO[5 u.c.] /PBCO[5 u.c] and YBCO[8 u.c.] /PBCO[5 u.c.] is similar @Figs. 3~c! and 3~d!# despite the number of interface is almost twice in the YBCO[5 u.c.] /PBCO[5 u.c.] superlattice. This can be understood considering that YBCO layers in superlattice are fully decoupled, and thus the observed havior is in fact the same that could be expected for a sin YBCO layer of identical thickness and perfect surfaces. U fortunately in practice YBCO single films five unit cells thic exhibit depressedTc values~60 K! compared to superlattice ~80 K!, resulting from surface imperfections and exposure ambient conditions,30 and thus comparison of the dissipatio properties is meaningless. BL barrier effects are not obser in the coupled superlattice since the relevant length scal compare witha0 is sample thickness~200 nm!. On the other hand, YBCO50 nm single films have rough surfaces resultin from a 3D growth mode for these large thickness. Surfa imperfections~steps, grain boundaries, etc.! with sizes com- parable to coherence lengthj wash out BL barriers.9,29 Ac- cordingly, the absence of BL mechanism contribution to transport properties of the coupled superlattice and YBCO50 nm single film is expected. In summary, decoupledc-axis YBCO/PBCO superlattice show strongly reduced dissipation in applied fields paralle the YBCO/PBCO interfaces, while coupled superlattice b haves similar to single films, following an anisotropic 3 angular dependent dissipation. For decoupled superlatt the fact that YBCO layers thickness are comparable with characteristic length in which BL barriers affect vortices, t gether with the sharpness of YBCO/PBCO interface res in geometry which is suited to strengthen their effects. point to this mechanism as the one governing dissipation applied fields close to parallel to interfaces. We acknowledge financial support from Spanish CICY through Grants Nos. MAT2002-4543 and MAT2000-146 Grant No. CAM 07N/0008/2001, ESF-Vortex Program, a R. Areces Foundation. One of us~E.M.G.! wants to thank Ministerio de Ciencia y Tecnologı´a for a Ramon y Cajal contract. a- , . 7E.M. Gonzalez, J.M. Gonzalez, and J.L. Vicent, Phys. Rev. B62, 8707 ~2000!. 8E.M. Gonzalez, J.E. 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