Non-Local Effects in Magnetization and Torque of Quaternary Borocarbides

Abstract

Importance of the non-local electrodynamics of superconductors was considered decades ago [1] when, in disagreement with the Ginzburg — Landau (GL) theory, the upper critical field H _c2 of cubic niobium was found to be anisotropic: e.g. when the applied field is rotated in one of the principal crystallographic planes, H _c2 shows a four fold symmetric variation. As a consequence, one may expect the magnetization M in superconducting state to vary in a similar manner. However conventional superconducting materials (like Nb) do not provide sufficient room for the studies of non-local effects: these materials typically have a low GL parameter K, i.e. nearly for all fields between H _cl and H _c2 the intervortex spacing is on the order of the coherence length and the spatial variations of the order parameter cannot be neglected. A comprehensible theory for such a complex case does not exist. Although K can be made larger by addition of impurities, in conventional materials this is usually accompanied by a considerable pinning and irreversibility. Another class of materials, high-T _c copper oxide superconductors, possess high values of K that made it possible to successfully describe the behavior of their magnetization at low temperatures within a relatively simple generalization of the London theory which includes non-local corrections [2]. The drawback is that the majority of these materials are so strongly anisotropic, nearly two dimensional, that thermal and quantum fluctuations are an important factor in description of their magnetic properties in the mixed state [3]. Less anisotropic high-T _c superconductors, as YBa₂Cu₃0₇, even in the best quality single crystals have only a narrow region of the H-T phase diagram, near Tc, where the magnetization is reversible.