Magnetisation study of an optimized single crystal of YBa2Cu3O7−δ

Physica C 235-240 (1994) 1555-1556

PHYSICA

North-Holland

Magnetisation Study of an Optimized Single Crystal of YBa2Cu307.5 C. Baraduc, E. Janod, C. Ayache and J.Y. Henry CEA/D6partement de Recherche Fondamentale sur la Mati~re Condens6e/SPSMS/LCP 38054 Grenoble Codex 9, France A 2D-3D cross-over IS observed on the magnetisation data using an appropriated scaling of the fluctuations under field. The temperature of the cross-over shifts w~th increasing field which is quanutatwely consistent with the decrease of the critical temperature. A crossing point of the M(T)-curves Is also observed.

Magnetic measurements were performed on a large YBaCuO single crystal (150 mg) in wh]ch the oxygen content has been optimized to obtain the maximal critical temperature. The homogeneity of the sample is very well controlled so that the transition width measured by low-field acsusceptibility is e x c e p t i o n n a l y n a r r o w : ~iTc = 0.12 K. The measurements are carried on in a SQUID magnetometer within the reversible region for HIIc. Raw data are compared with specific heat measurements [1 ] by checkmg the Maxwell relatton (dM/dT = dS/dB). Withm experimental error, the agreement between the two sets of data is excellent. 1. F L U C T U A T I O N S A B O V E Tc For analysing the fluctuations of magnetlsation above Te we use a scaling proposed by Prange [2] m which the reduced variables are : x = (T-Ted) / 2(T-Tc(H)) and y = M/H I/2 for a 3D compound or y = M for a 2D one.

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In fig. 1, we plot our data m a 3D-scaling form using Tc(H) values extracted from specific heat measurements [1] The quality of the scahng is surprisingly good, especially considering that such an approach was originally intended only for fluctuations in the normal state. In other words, the scaling was expected to work only for T>Tc(H) i.e. x>-l/2. A poss,ble explanation could be that the thermodynamical hne He2 has a major influence on the physical behav,our, so a very simple scaling law is enough to account for the data. We now discuss in detail the scahng for temperatures a few degrees above T c (fig. 2) For sufflc=ently high temperature, the 2D reduced variables prov,de a better scahng than the 3D ones (the dispersion of the curves at x=2 is AM=4.10 "5 emu m the 2D-scaling and AM=5.8 10 -5 emu m the 3D one). So YBCO seems to behave as a 2D compound at temperatures well above Te and as a 3D one near Tc ; a similar observation was also reported using another scahng form [3]. In fact such a behavlour 1s expected m layered superconductors due to their small coherence length ~co along the caxis. When ~c(T) is smaller than the rater-layer spacing s, the superconductor can be described as 2D, aad near Tc, when ~_c becomes larger than s, it is better described as 3D. The 2D-3D cros,,-f, vc,takes place at Tcr when ~c('I') reaches s By exammmg the dctad of the scahng it is possible to determine the temperature at which the curve for a gr, cn field departs from the others. These cross-over temperatures are indicated with dots in the plot It is worth nottctng that the cross-over temperatures decrease as the field becomes h~gher. When field is appfied parallel to the c-axis, the coherence length along the c-axis diverges at To(H) and dot at Ted. So ~c becamcs of the order of s at

0921-4534~)4/$07 00 © 1994 - l:l¢cv,er Science B V All r, ghts reserved SSDI 0921-4534(94~01344 6

C Baraduc et al /Physica C 235-240 (1994) 1555-1556

1556

lower temperature when the field is increased. More exphcltely the cross-over condition ~c=S is : (Tcr(H)-Tc(H)) / Tc(H) = (~co/S) 2. Let us emphasize that for each field the measured value of Tot(H) leads to exactly the same value for ~cols, corresponding to ~co = 1.8 ~. 1

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Figure 2. Detad of the Prange scahng. The points at which the curves depart from the scahng correspond to the 2D-3D cross-over. 2. F L U C T U A T I O N S OF VORTICES Recent theoretical work [4] on the contribution of vo~ices fluctuauons to the free enegy predict the existence of a crossing point of the M(T)-curves. 0

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T (K) Figure 3. A crosmng point in the magnetlsatton curves M(T) is observed for sufficiently high field.

The magnetisatzon at the crossing M* IS gwen by M* = ks.T*/¢o.S where T* is the temperature at which the crossing occurs. This crossing point is observed in our sample (fig. 3) but our experimental value of M* is much less than the theoretical one. The measured value would correspond to an inter-layer distance of 90 A whereas the unit cell parameter is 12/~. Similar results are observed in many other cuprate superconductors [5-6] : the value of s extracted from the measured M* is always higher than the real inter-layer spacing. Some authors [5] explain this difference by a small fraction of superconducting phase in their sample. This explanation seems unlikely however in our case, as the size of the observed specific heat jump is as large as that for stoechiometric polycnstalline samples. CONCLUSIONS Prange reduced variables prove to be a good method for scaling the magnetisation data and make posmble the observation of a 2D-3D cross-over which shzfis in temperature under field. Quantitative analysis leads to a constant value of the coherence length ~co = 1.8 ~. We also deraonstrate that a crossing point m the M(T)-curves exists m YBCO but is quantitatively inconsistent with the present theories, the inter-layer spacing deduced from the experimental data being 90 A instead of 12 A,.

REFERENCES [I] E. Janod, C. Marcenat, C. Baraduc, A. Junod, R. Calemzcuk, G. Deutscher and JY. Henry, this conference. [2] RE. Prange, Phys. Rev. B 1, 2349 (1970) [3l U. Welp, S. Fleshier, WK. Kwork, RA. Klemm, VM. Vlnokur, J. Downey, B. Veal and GW Crabtree, Phys. Rev. Lett. 67, 3180 (1991) [4] LN. Bulaevskn, M. Ledvij and VG. Kogan, Phys. Rev Lot. 68, 3773 ( 9 9 2 ) ; Z Tesanovtc, L Xlng, L. Bulaevskti, Q LI and M Suenaga, Phys Rev. Lett 69. 3563 (1992) [51 see for example VG. Kogan, M. Ledv U, AY Slmonov, JH Cho and DC. Johnston. Phys. Rex' B 70, 1870 41993) [6] G. Tnscone. AF. Khoder, C. Opaglste, JY. Gcnoud, T Graf. E Janod, T Tsukamoto, A. Junod and J Muller. to be pubhshed in Physlca C