Effect of Pauli Paramagnetism on Magnetic Properties of High-Field Superconductors

Abstract

We study the magnetic properties of type-II superconductivity having a large Pauli term. Firstly we restrict ourselves to the case where the spin-orbit scattering is absent. In this case the transition changes at low temperatures from second to first order for $\ensuremath{\alpha}=\frac{3\ensuremath{\mu}}{{\ensuremath{\tau}}_{\mathrm{tr}}{v}^{2}e}\ensuremath{\ge}1$, where $\ensuremath{\mu}$, ${\ensuremath{\tau}}_{\mathrm{tr}}$, and $v$ are the Bohr magneton, the transport collision time, and the Fermi velocity, respectively. This involves a revised calculation of the parameter ${\ensuremath{\kappa}}_{2}(t)$, which appears in the expression for the magnetization. The calculation of ${\ensuremath{\kappa}}_{2}(t)$ in an earlier paper on this subject by the author was incorrect, as was recently point out by de Gennes and co-workers. Secondly, we extend the theory to include the effect of spin-orbit scattering, which may be important in the materials usually considered. In particular, we obtain explicitly expressions for the parameters ${\ensuremath{\kappa}}_{1}(t)$ and ${\ensuremath{\kappa}}_{2}(t)$ in the limit of short spin-orbital mean free path, where ${\ensuremath{\kappa}}_{1}(t)=\frac{{H}_{c2}(t)}{\sqrt{2}{H}_{c}(t)}$, and ${H}_{c2}(t)$, ${H}_{c}(t)$ are the upper critical field and the thermodynamical critical field, respectively. It is shown that in this limit the transition is always second order, independent of temperature.