Vortex localization in single crystals of Tlb2Bab2CuOb6+[delta] with columnar defects : an empirical model.

Abstract

The peaks and valleys observed by Nowak et al (Phys. Rev. B54, R12725 (1996)) in the local magnetization M(x) and local relaxation rate S(x) in a single crystal of $\rm Tl\sb2Ba\sb2CuO\sb{6+\delta}$ containing columnar defects are well reproduced by an empirical model where the critical current density $j\sb{C}$ is fractionally enhanced in the vicinity of the matching field $B\sb\phi$ and of a multiple of $B\sb\phi$ by superimposing two broad triangular peaks on a continuous dependence of $j\sb{C}$ on the magnetic flux density B. The model fits the variety of M(x) and S(x) data taking $B\sb{S1}$ and $B\sb{S2}$, the flux density at the first and second peaks in $j\sb{C}$, to have a ratio $B\sb{S2}/B\sb{S1}\approx 2.5.$ The model also makes detailed predictions regarding the structure and location of valleys for S(x) versus B(x) descending in magnitude which were not reported in the above article. We demonstrate that a "staircase" type of dependence of $j\sb{C}$ on B proposed by Radzihovsky (Phys. Rev. Letters 74, 4923 (1995)) and exploited by Beauchamp et al, (Phys. Rev. B52, 13025 (1995)) can account for the peak in $\vert M(x)\vert$ adjacent to B = 0 but cannot generate the two peaks encountered when B(x) is ascending in magnitude nor reproduce the two peaks seen at higher fields when B(x) is descending in magnitude. (Abstract shortened by UMI.)