AL- +%. , . ELSEVIER Physica C 282-287 (1997) 2085-2086

PHYSICA E

Double-sided decoration on NbSez M. Marchevsky, A. Keurentjes, P. H. Kes, J. Aarts

“Kamerlingh Onnes Laboratory, Leiden University, P.O. Box 9506, 2300 RA Leiden, The Netherlands.

SimultaneouS magnetic decoration of the two sides of a superconducting sample can provide information about dimensionality, longitudinal distortions and elasticity of the vortex lattice. We report double sided deco&on done for a single crystal of NbSes and compare our results with the results reported for the high-T, superconductor BizSrzCaCuzOs_6.We found ratio of the elastic constants cqq/css to be strongly renormalized upwards, which may find its origin in the presence of topological defects.

1. INTRODUCTION

Vortices in superconductors are often modelled as rods that pass straight through a sample. Re alistic models however take into account that vor- tex lines are flexible and can bend in the material. Interplay between 3D elastic and plastic distor- tions due to pinning and thermal fluctuations re- sults in a rich physical picture of the vortex lattice that involves the phenomena of collective pinning, melting and (in the case of strong anisotropy) de coupling transitions. To study these phenomena in more detail it is of importance to probe the development of positional fluctuations in the vor- tex lattice not only in the transverse direction (normal to the field) but also in the longitudinal direction. Recently a novel type of decoration ex- periments was introduced in the work of Z. Yao et al. (11, and later of Yoon et al. [2], who decorated a crystal of the high-T, superconductor BSCCO simultaneously at both sides and found that it is possible to map two vortex patterns onto each other. In this way not only the in-plane distribu- tion of the vortex lines but also their wandering inside the sample was investigated. Below, we show the results of double-sided decoration of a field-cooled vortex lattice in conventional super- conductor NbSez, and compare our results with the results, obtained on BSCCO.

2. EXPERIMENTAL

The double-sided decoration experiment was performed on a single crystal of NbSeg of about 1 mm in diameter. It was cleaved at both sides

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prior to decoration and glued with one side to the copper holder. The final thickness of the cleaved crystal was determined to be about 12.5 pm by electron microscopy. A tiny slit in the edge of the holder plate allowed a small area (- 0.05 mm2) on both crystal sides to be exposed by the magnetic particles in the course of the decoration procedure. The sample was cooled in an exter- nal field of 5.0 mT applied along to the c-axis of the crystal, and decorated at 1.4 K. Heating of the sample during decoration was moderate with temperature rising to about 2.9 K. Electron mi- croscope images of the decoration patterns (see Fig. 1) were obtained from both sides of the crystal, from which the positions of the vortices were determined. The presence of a crystal edge in both original photographs served as a natu- ral reference in the initial attempt to match the patterns. The final accurate matching was car- ried out, however, by using an algorithm [3], in which the root mean square (r.m.s) displacement of the vortex centers as they cross the crystal was sequentially minimized with respect to aspect ra- tio, relative rotation angle and translation vector. The “best match” of the two patterns obtained in course of the procedure is shown in Fig. 2. There are 1644 points in each of the matching parts of the patterns. One sees from that positional shifts of the corresponding points are small and that all the topological defects at both sides match very well with each other. The r.m.s. displacement of the flux line positions (1 r(L) - r(0) 12)li2 cal- culated after all minimizations was found to be about 1% of the lattice parameter a~. In the

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paper of Yao et al. [l] a similar number was found for a BSCCO sample with a thickness of 10 ,um, cooled in a field of 1.2 mT and interpreted as a measure of the wandering of the vortex lines as they pass through the crystal. We think, however,

Side A

Side B (minored)

Figure 1. Decoration patterns obtained on the two sides of the NbSe:! crystal (de 12.5 pm), field cooled, 5.0 mT

that this number should be interpreted with cau- tion. An inaccuracy in finding the vortex centers from the decoration pattern is normally about 5- 10 % of aa and this substantially contributes to the observed value of the r.m.s. displacement.

In order to estimate the con-elated, phys- ically relevant transverse displacement of the

Figure 2. The “best match” of the two pat- terns obtained after sequential minimization of the r.m.s. displacement with respect to rotation and translation.

lattice points, the displacement correlator < u”(r) >=< [u(r, z) - u(r, 0)12 > has to be cal- culated for a part of the lattice free of topologi- cal defects, taken within the single vortex grain. When this type of analysis is performed, the ra- tio of the elastic constants cqq(Ic)/c.as can de esti- mated [4). The number for this ratio found with our data is - 110 times larger then predicted by the elastic theory. We think that this renormal- ization of the elastic distortions might have its origin in the presence of the topological defects in the surrounding vortex lattice. The details of our analysis will be published elsewhere [5].

REFERENCES

1. Z. Yao et al., Nature 371, 777 (1994). 2. S. Yoon et al., Science 270, 270 (1995) 3. M. Cristina Marchetti and D. Nelson, Phys.

Rev. B 52, 7720 (1995). 4. M. Marchevsky, PhD Thesis, Leiden Univer-

sity, 1997. 5. M. Marchevsky, to be published.