Magnetic properties and critical currents in Tl-based high-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">T</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">c</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>superconducting single crystals

${\mathrm{Tl}}_{2}$${\mathrm{Ca}}_{2}$${\mathrm{Ba}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{10}$ (Tl-2223) and (TlPb)(SrBa${)}_{2}$${\mathrm{Ca}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{8}$ (Tl-1223) single crystals were investigated by superconducting quantum interference device magnetometry in fields up to 8 T (H\ensuremath{\parallel}c axis). The samples were subjected to sequential reactor neutron irradiation up to a fluence of 24\ifmmode\times\else\texttimes\fi{}${10}^{21}$ ${\mathrm{m}}^{\mathrm{\ensuremath{-}}2}$ (E&gt;0.1 MeV). The superconducting transition temperature ${\mathrm{T}}_{\mathrm{c}}$, the magnetization, and the irreversibility lines were measured before and after each irradiation step. Because of the wide range of magnetic fields and temperatures, where the magnetization is totally reversible, especially in Tl-2223, the basic mixed-state parameters, such as the critical magnetic fields and the characteristic lengths, could be evaluated. In the irreversible range, the critical current densities were calculated from the hysteresis loops using an extended Bean model. We find that ${\mathrm{J}}_{\mathrm{c}}$ is strongly enhanced by the radiation-induced defects, e.g., by a factor of 52 in Tl-2223 at 40 K and 1 T. The irreversibility lines are shifted to higher fields and temperatures, but remain always below those of unirradiated Tl-1223, even at the highest neutron fluence. In Tl-1223, the critical current densities are moderately enhanced. The irreversibility line is at the same position or even higher than that of Y-123 and is moderately shifted to higher fields and temperatures after irradiation. The experimental results are discussed in terms of flux pinning and dimensionality.

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