Experimental evidence for anisotropic response of a driven vortex lattice
Introduction
The study of the dynamic behavior of elastic media in the presence of different static potentials has attracted much attention in recent years. Superconducting vortices are almost ideal for studying the phenomenology of these systems because relevant properties such as density, interactions and external force can be easily controlled.
Much work has been done on the problem of moving vortex systems. Depending on the velocity and type of static potential one can expect to have different dynamical phases. Giarmarchi and Le Doussal [1] have predicted the existence of a moving-Bragg-glass phase in a weak disordered static potential for high driving currents. The moving-Bragg-glass phase is free from dislocations, with power law decay of the positional correlations which are anisotropic with respect to flow direction. On the other hand, Balents, Marchetti and Radzihovsky [2] have argued for a smectic phase. In this phase, vortices move along well defined static channels, conserving the correlation perpendicular to the channels, but being uncorrelated along them. A number of experimental reports have presented evidence for the existence of these dynamical phases and their channel-type motion [3], [4], [5], [6]. The case of periodic potentials has been studied by several authors [7], [8], [9]. In particular, Marconi and Domı́nguez [9], [10] have found a transversely pinned vortex lattice with characteristics similar to those found for the disordered pinning case. This transversely pinned phase is distinguished by anisotropic Bragg peaks, quasi-long-range order, transverse superconducting coherence and zero transverse resistivity. One of the most relevant properties of all these moving vortex phases, for both disordered and periodic pinning potentials, is the existence of barriers to a small force transverse to the direction of motion. These barriers could be detected as an effective critical current in the transverse direction [11].
Kinetic inductance techniques have proven to be a valuable tool for measuring superconducting characteristics of two dimensional systems [12], [13], [14]. In this work we use a variation of this technique, which is capable of examining the anisotropic character of dynamical phases. Instead of using circular coils, we use rectangular coils with high aspect-ratio, as sketched in the lower part of Fig. 1. In this geometry, the shielding currents induced in the sample by the primary coil are predominantly parallel to the long side of the coil. Consequently, the voltage generated on the secondary coil is due to shielding currents flowing in one particular direction, specified by the orientation of the coils. Measuring the response as a function of the orientation between the coils and the symmetry axis of a sample we are able to measure its anisotropic properties as, for example, the magnetic penetration depth or resistivity.
We are interested in studying the anisotropic character of vortex dynamical phases driven by externally applied dc currents. The dc current direction will determine the symmetry axis of the dynamical phases. Our experimental setup allows us to apply a dc current to the sample along two directions, parallel and perpendicular to the long dimension of the rectangular coils. Comparing the results of kinetic inductance when applying current in both directions, we should be able to detect any anisotropic character of the vortex dynamical phases.
Section snippets
Experimental details
We performed our measurements in two dimensional Josephson junction arrays. Square arrays of 1000×1000 superconducting Pb islands were patterned on top of a Cu film. The lead was completely removed from the substrate outside the islands. The cross-shaped superconducting islands formed a square lattice with a lattice parameter of 10 μm, and the gap between two adjacent arms was 1 μm. Nearest neighbor Pb islands are coupled through the underlying Cu layer, acting as a
Experimental results
The experiment involves two novel elements: inductive measurements with current in the sample; and the use of rectangular coils. We will first briefly discuss our observations with circular coils on a current-driven sample, as sketched in the upper part of Fig. 1. These coils have a diameter of 1 mm, similar to those used in Ref. [14]. We used a frequency of 8484 Hz for all the measurements reported here. We were careful to take the data well inside the linear regime. Under this condition the
Conclusions
In conclusion, we have used a modified kinetic inductance technique to study diluted vortex lattices on the periodic potential of a Josephson junction array. We have found different superconducting shielding capability in the directions parallel and perpendicular to applied current, providing clear evidence for the anisotropic character of current-driven vortex phases.
The anisotropic kinetic inductance technique which we have developed opens the possibility of investigating anisotropy in
Acknowledgements
We thank S. Candia for providing the samples and useful suggestions on the manuscript. We thank A. Silhanek, B. Maiorov and J. Luzuriaga for a critical reading of the manuscript. This work was partially supported by ANPCyT PICT: 03 5117 and by Fundación Antorchas.
References (19)
- et al.
Phys. Rev. Lett.
(1996) - et al.
Phys. Rev. Lett.
(1997) - et al.
Nature
(1998) - et al.
Phys. Rev. B
(1999) - et al.
Nature
(1999) - et al.
Phys. Rev. Lett.
(1996) - et al.
Phys. Rev. Lett.
(1999) Phys. Rev. B
(2000)- V.I. Marconi, D. Domı́nguez, Phys. Rev. B 63 (2001)...