Negative curvature of upper critical fields and dimensional cross-over in YBa2Cu3O72d thin films

G.S. Okrama,* , H. Aokia,b, K. Nakamurac

aNational Research Institute for Metals, 1-2-1 Sengen, Tsukuba, Ibaraki 305, JapanbCenter for Low Temperature Science, Tohoku University, Sendai 980-77, Japan

cDepartment of Physics, Zhejiang University, Hangzhou 310027, People’s Republic of China

Received 27 November 1998; accepted 30 December 1998 by C.N.R. Rao

Abstract

The temperature (T) dependence of the upper critical fieldHc2(T) of good quality under-doped YBa2Cu3O72d (YBCO) thinfilms exhibits negative curvature for 90%rn criterion and follows the conventional (12 t), t � T/Tc, dependence far below theTc. A dimensional (3D to 2D) cross-over associated with the negative curvature, not observed earlier, is also found.q 1999Elsevier Science Ltd. All rights reserved.

Keywords:A. High-Tc superconductors; D. Flux pinning and creep

With the advent of high temperature superconduc-tors (HTSC), the area of vortex physics has beenproliferating [1,2]. In isotropic type II superconduc-tors, the core radius of the Abrikosov vortex equalsthe coherence length (j ). This defines the upper criti-cal field Hc2(T) and hence theH–T phase diagram iswell known. In HTSC, the situation differs drasticallybecause of, among others, the high operating tempera-ture, large anisotropy and atomic scale sample inho-mogeneity. They are thus described by either acontinuum anisotropic or a discrete Lawrence–Doniach model [3]. The vortex state, rather intricate,varies with the choice of field orientations [1]. Forfield alongc axis (H'), relatively simpler, it consistsof so-called pancake vortices directed along thec-axis

joined by coreless Josephson vortices running parallelin between two superconducting (SC) planes, whereinintrinsic pinning and creep also play crucial roles[4,5]; for field alongab plane (Hk), only Josephsonvortices exist [1,6–8]. TheirH–T phase diagrams inthe former configuration have delved considerablywell while that for the latter being far less so [1].

The flux-flow resistivity of the SC phase atHc2(T)joins smoothly with normal state resistivity and thesuperconductivity, by definition, nucleates at the criti-cal field and temperature values just below the resis-tive (rn) or diamagnetic transition from the normalstate [9]. This notation has however been often over-looked by choosing the values corresponding to thelower rn values (e.g. Ref. [10]), thereby effectivelydetermining the irreversibility line rather than theusualHc2(T) line (e.g. Ref. [11]). This has seeminglyled to conclude that the positive curvature ofHc2(T) asuniversal (e.g. Refs. [12–15]), contrary to the conven-tional negative curvature as is also observed in someHTSC [16–19]. Consequently, for example, the

Solid State Communications 110 (1999) 327–331

SSC 4620

0038-1098/99/$ - see front matterq 1999 Elsevier Science Ltd. All rights reserved.PII: S0038-1098(99)00060-5

PERGAMON

* Corresponding author. Present address: Carbon TechnologyDivision, National Physical Laboratory, Dr. K.S. Krishnan Road,New Delhi 110012, India. Tel.:191-11-5786086/5786087; Fax:191-11-5752678.

E-mail address:okram@csnpl.ren.nic.in (G.S. Okram)

dimensional cross-over from 3D to 2D has beenunderstood to associate with the positive curvatureof the supposedlyHc2(T) line [20–22]. The presentstudy is therefore aimed at investigating this highlyinteresting aspect of theH–T phase diagram based onthe low Tc phases of YBCO thin films. Our results,consistent with some of the earlier reports, indicatethat most of the previously known to beHc2(T) linesshould correspond to irreversibility lines, and that fornear to appropriate values, the curves exhibit negativecurvatures. More interestingly, the so-called 3D to 2Dcross-over is also found to associate with the negativecurvature. The choice of the lowTc phase materialsjustifies the possible large coverage of theH–T phase

diagram that is otherwise impossible for highTc

counterparts.The lowTc films, ,1500 Athick, were prepared by

ozone-assisted molecular beam epitaxy method onto aMgO substrate (see Ref. [23] for details). Their XRDdata indicated no impurities and perfectc-axis orien-tations. Making the low contact resistance (a fewV)leads, the resistivityr (T) was measured in the stan-dard ac four-probe method with a precision ac resis-tance bridge using,3 A/cm2 and a negligiblemagneto-resistance effect cernox sensor. The maxi-mum appliedH was 17 T. The fine alignment espe-cially of the ab plane along theH direction at aprecision of 0.058 was exercised to obtain nearest tothe desired upper critical fields.

The r(T) behaviours are similar to those reportedearlier [23]. The normal states were of high metalliccharacter above 100 K below which small upwardcurvatures were generally found withTc(onset)about 60 K and below. The data for a representativefilm having d < 0.6, Tc(onset), 45 K, Tc(r � 0) �12.2 K and transition widthDTc� 9.5 K are presentedhere (cf. Fig. 1(a)). ADTc� 9.5 K atH � 0, althoughbroad, is usual for such a lowTc phase and can arisedue to a larger gradient ind values which exists in anyreal sample. The [r(T)]H curves at constant field showinteresting features (Fig. 1).Tc decreases andDTc

broadens with increasing field with a marked differ-ence in the parallel (Fig. 1(b)) and perpendicular (Fig.1(c)) to theab plane orientations (cf. Ref. [24]). Thedifference lies in particular in the shape of the curves.With increasingHk, the shift inTc onset is very slow,perhaps due to coreless Josephson vortices and orstrong intrinsic pinning [1,4–8]. ForH', the corre-sponding shifts are much faster suggestive of thepresence of the Abrikosov vortices [1,4,5]; the curvessystematically bulges up towardsrn value and may bebecause of enhanced fluctuations withH (cf. Refs.[25,26]).

Now, to access and also to delve into the situationof finding upper critical field and their behaviours, weconsider ther � 10%, 50% and 90%rn criteria, eventhough the superconductivity may nucleate just belowtheTc onset, i.e.Hc2 [9]. The 90%rn criterion may be areasonably appropriateHc2 value as there is someuncertainty at Tc onset because of its relativelymuch smaller suppression (cf. Ref. [27] also). Thet(� T/Tc) dependence of the critical fields, parallel and

G.S. Okram et al. / Solid State Communications 110 (1999) 327–331328

Fig. 1. The resistivityr(T) of YBa2Cu3O72 d thin film measured atH� 0 T (a) and in magnetic fields 0# H # 17 T parallelHk (b) andperpendicularH' (c) to ab plane.

perpendicular to theab plane,Hk(t) andH' (t), thusdetermined possess many interesting features (Fig. 2).The curves systematically vary with temperature andhence their slopes atH(t) � 0 can be determined asnecessitated to estimateHc2(0) [28] without ambiguityand hence the coherence lengths. These featurescontrast with those reported for the 94 K EuBa2Cu3Oy

(EBCO) and 92 K YBCO crystals wherein suchfeatures are absent [29,30]. However, the slopes atH(t) � 0 clearly vary with the criteria viz. they are(20.27 T/K, 20.42 T/K), (20.44 T/K, 21.25 T/K)and (21 T/K, 215.4 T/K) for the respective (H' (t),Hk (t)) fields. For 90%rn criterion, the present slope of215.4 T/K for Hk is especially significantly largerthan 210.5 T/K that found for the 92 K YBCOcrystal [30], suggesting a near to perfectH align-ment. Using these slopes andTc(onset)� 45 K inHc2�0� � 0:7TcudHc2=dTuTc[28], the estimated valuesof (H'(0),Hk(0)) are (9 T,13 T), (14 T,39 T) and(32 T,485 T) and the coherence lengths (j' (0),jk(0)) are (40 A,62 A), (17 A,49 A) and (2 A,32 A),respectively. The value ofj'(0) < 2 A is notable asit is p d, the plane spacing (< 8.4 A) but consistentwith that of the 87 K YBCO film [27].

The behaviours ofH(t) is worth attention. Theyexhibit positive curvatures, which otherwise aresuggestive of exhibiting the 3D to 2D dimensionalcross-over [21,22], for the 10% and 50%rn criteriaand conventional-like negative curvatures for the90%rn criterion, comparing well those observed insome HTSC [16–19]. The observed negative curva-ture is remarkable as it is contrary to the common

belief that such layered superconductors exhibit posi-tive curvature [10,12–15,20–22,31,32]. To compre-hend the negative curvatures more precisely, wecarried out theH(t) � a(1 2 t)n fits which yieldeda � 1.119 andn � 0.829 forH' (t), anda � 14.236and n � 0.987 forHk(t); the fit for H' (t) is shown(Fig. 2). These are, therefore (close to), the conven-tional linear (12 t) dependence, thereby neither the(1 2 t)1/2 fit reported nor the (12 t)3/2 variationpredicted for the HTSC fits the present data [16,26].We stress here that these features are unexceptional asthey are also consistently observed inTc(r � 0) �24 K YBCO film [33]. Therefore, choosing near tothe conventional values (90%rn criterion), the curva-ture ofHc2(t) is conventional-like negative for YBCOfilms as in some cuprates that have determined simi-larly [17] and using other techniques [18,19]. Thisconsistency may not be accidental and hence the posi-tive curvature reported earlier may be more related tothe deviations from the appropriate determination. Inalmost all the cases, the criterion was made nearr � 0which is consistent with the present observation forsmaller %rn criteria. This in turn may be rather the so-called irreversibility line and probably gives rise tothe positive curvature [10,11,21–22,34]. Further, thesupposed to beHc2(t) values determined from therversusH curves seen erroneous [29,31,32], because inthis method, the data are collected (well) below thern

i.e. in the (fully) mixed state. Then, the measuredr ata fix T (below Tc) gradually decreases with loweringT, thereby ther drops far below 90%rn (e.g. Refs.[29,31,32]). This even compels one to arbitrarilydetermine the supposedlyHc2 corresponding to aTand H (e.g. Mackenzie et al. [31] and cf. their Ref.[19]). Consequently, the determinedH values are then(or close to) the irreversibility fields with a positivecurvature (cf. [11,34]). This argument seems undeni-ably valid because the behaviour ofH(t) obtainedfrom our magneto-resistance data (R–H at constantT) on many T1-2201 single crystals and YBCO thinfilms also exhibits positive curvature in all the caseseven when theH(t) are chosen at the same values of%rn suggesting that they always belong to their lower%rn criteria) and may perhaps hold true for similarmagnetisation data as well. Therefore, the theoreticalexplanation for the positive curvature may have to beconsidered with caution (e.g. Refs. [12–15]).

We now turn to the temperature dependence of the

G.S. Okram et al. / Solid State Communications 110 (1999) 327–331 329

Fig. 2. The critical fieldsH(t) perpendicular (solid symbols) andparallel (open symbols) toab plane of YBa2Cu3O72 d film as deter-mined from the [r(T)]H curves of Fig. 1 usingr � 10% (circle),50% (diamond) and 90%rn (square) criteria. The solid curve is thefit of theH' (t) � a(1 2 t)n for 90%rn criterion; see text for details.

anisotropy,g(t) � Hk(t)/H' (t) (Fig. 3). For 10%rn

criterion of H(t), g increases almost linearly withdecreasing temperature with no sign of saturationand hence suggests no dimensional cross-over match-ing j'(0) < 40 A q d [21,22]. Theg for 50%rn

criterion grows faster with a marginal saturation-likefeature but increases further consistent withj'(0) <17 A . d. Hence in both the cases, dimensional cross-over is absent. On the contrary,g (t) for 90%rn criter-ion increases rapidly to,16 on cooling and drops alittle but saturates to,15 below 29 K (Fig. 3, inset).This may be an indication of the dimensional (3D to2D) cross-over which is also consistent withj'(0) <2 A p d. More interestingly, theg saturation valueequals g (0) (,15) suggesting that the anisotropyremains the same below the dimensional cross-over.Thus, these findings imply that the positive curvatureof Hc2(t) does not necessarily lead to the dimensionalcross-over. On the contrary, the conventional-likenegative curvature are associated with a dimensionalcross-over.

Interestingly, theg (t) behaviour for 90%rn criter-ion is similar to those reported for the layered 2H–TaS2 and Nb12xTaxSe2 superconductors [21,22,35].The presentg(t) values are larger than that of thehigh Tc counterpart (g < 8) but smaller than the60 K YBCO (g � 40) [20]. However,g value is nota unique number which tends to vary depending onthe choice (%rn) of H(t), not only the temperaturedependence (Fig. 3, cf. Ref. [1]). Rather, it may beconstant for a temperature range (see Fig. 3 inset, cf.

Ref. [36]). Therefore,g � 15 may be chosen for thepresent oxygen deficient sample, presuming that the90%rn criterion of the upper critical field is consider-ably reliable.

In conclusion, the temperature dependence of theupper critical fields for the 90%rn criteria exhibitsnegative curvature well comparable to the conven-tional feature. This is associated with a dimensional(3D to 2D) cross-over which is not the case with posi-tive curvatures. The proper understanding of thedimensional cross-over may however require appro-priate determination ofHc2(t) for both the orientationsas well as theirH–T phase diagrams which are lackingnow.

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