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

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 =3{ₓₑv^2e}1, where, ₓₑ, and v are the Bohr magneton, the transport collision time, and the Fermi velocity, respectively. This involves a revised calculation of the parameter ₂ (t), which appears in the expression for the magnetization. The calculation of 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 ₁ (t) and ₂ (t) in the limit of short spin-orbital mean free path, where ₁ (t) =H₂₂ (t) 2{H₂ (t) }, and H₂₂ (t), H₂ (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.