The magnetic properties of superconducting alloys. II

Abstract

The lower critical field ${\mathrm{H}}_{\mathrm{c}1}$ is derived from the microscopic theory for superconducting alloys. It is shown that Abrikosov's structure in the field just above ${\mathrm{H}}_{\mathrm{c}1}$ is described by the use of a parameter of which the temperature dependence is obtained. A brief discussion of the gap in the excitation spectrum and the thermodynamical behavior at lower temperatures is given.Next the effect of the Pauli paramagnetism on the magnetic properties of superconducting alloys is investigated in detail. It is shown that Abrikosov's structure is still described completely by the use of two parameters ${\ensuremath{\kappa}}_{1}{}^{*}(\mathrm{T})$ and ${\ensuremath{\kappa}}_{2}{}^{*}(\mathrm{T})$ in the vicinity of the transition point when the phase transition is of the second order. In superconductors having a large Pauli term $\frac{3\ensuremath{\mu}}{e{\ensuremath{\tau}}_{\mathrm{tr}}{\mathrm{v}}^{2}}\ensuremath{\ge}1.475$ where $\ensuremath{\mu}$ is the Bohr magneton, ${\ensuremath{\tau}}_{\mathrm{tr}}$ the transport collision time of an electron and v the fermi velocity, the order of the transition is found to change from the second to the first as temperature decreases.