Superconductivity at High Magnetic Fields

Abstract

Using pulsed-magnetic-field techniques, we have studied the magnetic-field-induced superconducting transitions of alloys in the systems Ti-V, Ti-Nb, Ti-Ta, Ti-Mo, Zr-Nb, Hf-Nb, Hf-Ta, U-Nb, and U-Mo. For concentrated alloys the low-current-density resistive critical field $H_r(J\lesssim 10 \mathrm{A}/{\mathrm{cm}}^2)$ is nearly independent of the amount of cold working and the relative orientations of magnetic field, current, and anisotropic defect structure. The observed values of $H_r\mathrm{}(J=10\mathrm{})\mathrm{}$ peak up sharply (reaching 145 kG in the Ti-Nb system) in the vicinity of ∼4.5 "valence" electrons per atom, an electron concentration where peaking also typically occurs for such (approximately) defect-independent transition metal alloy parameters as superconducting transition temperature, thermodynamic critical field, and electronic specific heat coefficient. All the above evidence suggests that in these alloys $H_r\mathrm{}(J=10\mathrm{})\mathrm{}$ is determined principally by bulk electronic parameters, rather than by the nature of extended lattice defects. This view is further supported by the observation that, for several Group V-rich, Group IV-Group V transition metal alloys, excellent quantitative agreement is achieved in adjustable-parameter-free comparisons of $H_r\mathrm{}(J=10\mathrm{})\mathrm{}$ with $H_{c2\mathrm{}}$, the "upper critical field" predicted on the basis of bulk electronic parameters by the Ginzburg-Landau-Abrikosov-Gor'kov (GLAG) theory for the case of negative surface energy. For certain ranges of alloy composition, it appears that normal-state paramagnetic free-energy considerations, ignored in the GLAG theory, impose limitations on $H_r\mathrm{}(J=10\mathrm{})\mathrm{}$ in good accord with the theoretical predictions of Clogston. Additional experimental results are reviewed, and it is argued that a comprehensive theoretical understanding of high-field superconductivity in bulk materials may be achieved on the basis of the GLAG theory, modified to include paramagnetic free-energy terms, and extended to consider transport supercurrents stabilized in a manner similar to that suggested by Gorter and Anderson. The a priori assumptions of Mendelssohn's filamentary-mesh model appear, on the other hand, to be inadequate for a suitable description.