Negative curvature of upper critical fields and dimensional cross-over in YBa2Cu3O7−δ thin films

SSC 4620

PERGAMON

Solid State Communications 110 (1999) 327–331

Negative curvature of upper critical fields and dimensional crossover in YBa2Cu3O7⫺d thin films G.S. Okram a,*, H. Aoki a,b, K. Nakamura c a

National Research Institute for Metals, 1-2-1 Sengen, Tsukuba, Ibaraki 305, Japan b Center for Low Temperature Science, Tohoku University, Sendai 980-77, Japan c Department 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 field Hc2(T) of good quality under-doped YBa2Cu3O7⫺d (YBCO) thin films exhibits negative curvature for 90%r n criterion and follows the conventional (1 ⫺ t), t ˆ T/Tc, dependence far below the Tc. A dimensional (3D to 2D) cross-over associated with the negative curvature, not observed earlier, is also found. 䉷 1999 Elsevier Science Ltd. All rights reserved. Keywords: A. High-Tc superconductors; D. Flux pinning and creep

With the advent of high temperature superconductors (HTSC), the area of vortex physics has been proliferating [1,2]. In isotropic type II superconductors, the core radius of the Abrikosov vortex equals the coherence length (j ). This defines the upper critical field Hc2(T) and hence the H–T phase diagram is well known. In HTSC, the situation differs drastically because of, among others, the high operating temperature, large anisotropy and atomic scale sample inhomogeneity. They are thus described by either a continuum anisotropic or a discrete Lawrence– Doniach model [3]. The vortex state, rather intricate, varies with the choice of field orientations [1]. For field along c axis (H⬜), relatively simpler, it consists of so-called pancake vortices directed along the c-axis

* Corresponding author. Present address: Carbon Technology Division, National Physical Laboratory, Dr. K.S. Krishnan Road, New Delhi 110012, India. Tel.: ⫹91-11-5786086/5786087; Fax: ⫹91-11-5752678. E-mail address: [email protected] (G.S. Okram)

joined by coreless Josephson vortices running parallel in between two superconducting (SC) planes, wherein intrinsic pinning and creep also play crucial roles [4,5]; for field along ab plane (Hk), only Josephson vortices exist [1,6–8]. Their H–T phase diagrams in the former configuration have delved considerably well while that for the latter being far less so [1]. The flux-flow resistivity of the SC phase at Hc2(T) joins smoothly with normal state resistivity and the superconductivity, by definition, nucleates at the critical field and temperature values just below the resistive (r n) or diamagnetic transition from the normal state [9]. This notation has however been often overlooked by choosing the values corresponding to the lower r n values (e.g. Ref. [10]), thereby effectively determining the irreversibility line rather than the usual Hc2(T) line (e.g. Ref. [11]). This has seemingly led to conclude that the positive curvature of Hc2(T) as universal (e.g. Refs. [12–15]), contrary to the conventional negative curvature as is also observed in some HTSC [16–19]. Consequently, for example, the

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Fig. 1. The resistivity r (T) of YBa2Cu3O7⫺ d thin film measured at H ˆ 0 T (a) and in magnetic fields 0 ⱕ H ⱕ 17 T parallel Hk (b) and perpendicular H⬜ (c) to ab plane.

dimensional cross-over from 3D to 2D has been understood to associate with the positive curvature of the supposedly Hc2(T) line [20–22]. The present study is therefore aimed at investigating this highly interesting aspect of the H–T phase diagram based on the low Tc phases of YBCO thin films. Our results, consistent with some of the earlier reports, indicate that most of the previously known to be Hc2(T) lines should correspond to irreversibility lines, and that for near to appropriate values, the curves exhibit negative curvatures. More interestingly, the so-called 3D to 2D cross-over is also found to associate with the negative curvature. The choice of the low Tc phase materials justifies the possible large coverage of the H–T phase

diagram that is otherwise impossible for high Tc counterparts. ˚ thick, were prepared by The low Tc films, ⬃1500 A ozone-assisted molecular beam epitaxy method onto a MgO substrate (see Ref. [23] for details). Their XRD data indicated no impurities and perfect c-axis orientations. Making the low contact resistance (a few V) leads, the resistivity r (T) was measured in the standard ac four-probe method with a precision ac resistance bridge using ⬃3 A/cm 2 and a negligible magneto-resistance effect cernox sensor. The maximum applied H was 17 T. The fine alignment especially of the ab plane along the H direction at a precision of 0.05⬚ was exercised to obtain nearest to the desired upper critical fields. The r (T) behaviours are similar to those reported earlier [23]. The normal states were of high metallic character above 100 K below which small upward curvatures were generally found with Tc(onset) about 60 K and below. The data for a representative film having d ⬇ 0.6, Tc(onset) ⬃ 45 K, Tc(r ˆ 0) ˆ 12.2 K and transition width DTc ˆ 9.5 K are presented here (cf. Fig. 1(a)). A DTc ˆ 9.5 K at H ˆ 0, although broad, is usual for such a low Tc phase and can arise due to a larger gradient in d values which exists in any real sample. The [r (T)]H curves at constant field show interesting features (Fig. 1). Tc decreases and DTc broadens with increasing field with a marked difference in the parallel (Fig. 1(b)) and perpendicular (Fig. 1(c)) to the ab plane orientations (cf. Ref. [24]). The difference lies in particular in the shape of the curves. With increasing Hk, the shift in Tc onset is very slow, perhaps due to coreless Josephson vortices and or strong intrinsic pinning [1,4–8]. For H⬜, the corresponding shifts are much faster suggestive of the presence of the Abrikosov vortices [1,4,5]; the curves systematically bulges up towards r n value and may be because of enhanced fluctuations with H (cf. Refs. [25,26]). Now, to access and also to delve into the situation of finding upper critical field and their behaviours, we consider the r ˆ 10%, 50% and 90%r n criteria, even though the superconductivity may nucleate just below the Tc onset, i.e. Hc2 [9]. The 90%r n criterion may be a reasonably appropriate Hc2 value as there is some uncertainty at Tc onset because of its relatively much smaller suppression (cf. Ref. [27] also). The t ( ˆ T/Tc) dependence of the critical fields, parallel and

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

Fig. 2. The critical fields H(t) perpendicular (solid symbols) and parallel (open symbols) to ab plane of YBa2Cu3O7⫺ d film as determined from the [r (T)]H curves of Fig. 1 using r ˆ 10% (circle), 50% (diamond) and 90%r n (square) criteria. The solid curve is the fit of the H⬜ (t) ˆ a(1 ⫺ t) n for 90%r n criterion; see text for details.

perpendicular to the ab plane, Hk(t) and H⬜ (t), thus determined possess many interesting features (Fig. 2). The curves systematically vary with temperature and hence their slopes at H(t) ˆ 0 can be determined as necessitated to estimate Hc2(0) [28] without ambiguity and hence the coherence lengths. These features contrast with those reported for the 94 K EuBa2Cu3Oy (EBCO) and 92 K YBCO crystals wherein such features are absent [29,30]. However, the slopes at H(t) ˆ 0 clearly vary with the criteria viz. they are (⫺0.27 T/K, ⫺0.42 T/K), (⫺0.44 T/K, ⫺1.25 T/K) and (⫺1 T/K, ⫺15.4 T/K) for the respective (H⬜ (t), Hk (t)) fields. For 90%r n criterion, the present slope of ⫺15.4 T/K for Hk is especially significantly larger than ⫺10.5 T/K that found for the 92 K YBCO crystal [30], suggesting a near to perfect H alignment. Using these slopes and Tc(onset) ˆ 45 K in Hc2 …0† ˆ 0:7Tc 兩dHc2 =dT兩Tc [28], the estimated values of (H⬜(0),Hk(0)) are (9 T,13 T), (14 T,39 T) and (32 T,485 T) and the coherence lengths (j ⬜ (0),j ˚ ˚ ˚ ˚ ˚ ˚ k(0)) are (40 A,62 A), (17 A,49 A) and (2 A,32 A), ˚ respectively. The value of j ⬜(0) ⬇ 2 A is notable as ˚ ) but consistent it is p d, the plane spacing ( ⬇ 8.4 A with that of the 87 K YBCO film [27]. The behaviours of H(t) is worth attention. They exhibit positive curvatures, which otherwise are suggestive of exhibiting the 3D to 2D dimensional cross-over [21,22], for the 10% and 50%r n criteria and conventional-like negative curvatures for the 90%r n criterion, comparing well those observed in some HTSC [16–19]. The observed negative curvature is remarkable as it is contrary to the common

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belief that such layered superconductors exhibit positive curvature [10,12–15,20–22,31,32]. To comprehend the negative curvatures more precisely, we carried out the H(t) ˆ a(1 ⫺ t) n fits which yielded a ˆ 1.119 and n ˆ 0.829 for H⬜ (t), and a ˆ 14.236 and n ˆ 0.987 for Hk(t); the fit for H⬜ (t) is shown (Fig. 2). These are, therefore (close to), the conventional linear (1 ⫺ t) dependence, thereby neither the (1 ⫺ t) 1/2 fit reported nor the (1 ⫺ t) 3/2 variation predicted for the HTSC fits the present data [16,26]. We stress here that these features are unexceptional as they are also consistently observed in Tc(r ˆ 0) ˆ 24 K YBCO film [33]. Therefore, choosing near to the conventional values (90%r n criterion), the curvature of Hc2(t) is conventional-like negative for YBCO films as in some cuprates that have determined similarly [17] and using other techniques [18,19]. This consistency may not be accidental and hence the positive curvature reported earlier may be more related to the deviations from the appropriate determination. In almost all the cases, the criterion was made near r ˆ 0 which is consistent with the present observation for smaller %r n criteria. This in turn may be rather the socalled irreversibility line and probably gives rise to the positive curvature [10,11,21–22,34]. Further, the supposed to be Hc2(t) values determined from the r versus H curves seen erroneous [29,31,32], because in this method, the data are collected (well) below the r n i.e. in the (fully) mixed state. Then, the measured r at a fix T (below Tc) gradually decreases with lowering T, thereby the r drops far below 90%r n (e.g. Refs. [29,31,32]). This even compels one to arbitrarily determine the supposedly Hc2 corresponding to a T and H (e.g. Mackenzie et al. [31] and cf. their Ref. [19]). Consequently, the determined H values are then (or close to) the irreversibility fields with a positive curvature (cf. [11,34]). This argument seems undeniably valid because the behaviour of H(t) obtained from our magneto-resistance data (R–H at constant T) on many T1-2201 single crystals and YBCO thin films also exhibits positive curvature in all the cases even when the H(t) are chosen at the same values of %r n suggesting that they always belong to their lower %r n criteria) and may perhaps hold true for similar magnetisation data as well. Therefore, the theoretical explanation for the positive curvature may have to be considered with caution (e.g. Refs. [12–15]). We now turn to the temperature dependence of the

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Fig. 3. The anisotropy, g (t), of YBa2Cu3O7⫺ d film for r ˆ 10%, 50% and 90%r n criteria of finding Hk(t) and H⬜ (t). Inset: expanded view of 90%r n criterion.

anisotropy, g (t) ˆ Hk(t)/H⬜ (t) (Fig. 3). For 10%r n criterion of H(t), g increases almost linearly with decreasing temperature with no sign of saturation and hence suggests no dimensional cross-over match˚ q d [21,22]. The g for 50%r n ing j ⬜(0) ⬇ 40 A criterion grows faster with a marginal saturation-like feature but increases further consistent with j ⬜(0) ⬇ ˚ ⬎ d. Hence in both the cases, dimensional cross17 A over is absent. On the contrary, g (t) for 90%r n criterion increases rapidly to ⬃16 on cooling and drops a little but saturates to ⬃15 below 29 K (Fig. 3, inset). This may be an indication of the dimensional (3D to 2D) cross-over which is also consistent with j ⬜(0) ⬇ ˚ p d. More interestingly, the g saturation value 2A equals g (0) (⬃15) suggesting that the anisotropy remains the same below the dimensional cross-over. Thus, these findings imply that the positive curvature of Hc2(t) does not necessarily lead to the dimensional cross-over. On the contrary, the conventional-like negative curvature are associated with a dimensional cross-over. Interestingly, the g (t) behaviour for 90%r n criterion is similar to those reported for the layered 2H– TaS2 and Nb1⫺xTaxSe2 superconductors [21,22,35]. The present g (t) values are larger than that of the high Tc counterpart (g ⬇ 8) but smaller than the 60 K YBCO (g ˆ 40) [20]. However, g value is not a unique number which tends to vary depending on the choice (%r n) of H(t), not only the temperature dependence (Fig. 3, cf. Ref. [1]). Rather, it may be constant for a temperature range (see Fig. 3 inset, cf.

Ref. [36]). Therefore, g ˆ 15 may be chosen for the present oxygen deficient sample, presuming that the 90%r n criterion of the upper critical field is considerably reliable. In conclusion, the temperature dependence of the upper critical fields for the 90%r n criteria exhibits negative curvature well comparable to the conventional feature. This is associated with a dimensional (3D to 2D) cross-over which is not the case with positive curvatures. The proper understanding of the dimensional cross-over may however require appropriate determination of Hc2(t) for both the orientations as well as their H–T phase diagrams which are lacking now.

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