Pauli Spin and Spin-Orbit Effects in the Magnetization of a Superconducting Ti-Mo Alloy

Results are given for some detailed measurements on the upper critical field $H_{c2\mathrm{}}$, and on the relative slope of the magnetization curve ${\chi }_s\equiv {\left[\frac{\partial M-M_s)}{\partial H}\right]}_{H_{c2\mathrm{}}}$ for the high-field (${\kappa }_G\approx 65$) superconductor Ti-16 at.% Mo. The data on the temperature dependence of $H_{c2\mathrm{}}$ and ${\chi }_s$ are shown to be in excellent agreement with recent theories in which Pauli spin paramagnetism and spin-orbit scattering have been included in Gor'kov's equations. It is observed that the $H_{c2\mathrm{}}$ values at $T\ll T_{c0\mathrm{}}$ are smaller than expected for the spin-independent case (no paramagnetic effects) and larger than expected if spin paramagnetism is allowed for but spin-orbit scattering is not. The parameter ${\kappa }_2\propto \chi _s^{}{}_{}{}^{-\frac{1}{2}}$ is found to decrease with decreasing temperature, in contrast to the case of non-"paramagnetically-limited" type-II superconductors, where $\kappa$ is observed to increase with decreasing $T$. When one uses the calculated (from resistivity and specific-heat data) value of 1.75 for the Pauli spin parameter ($\alpha =\frac{3\hslash }{2ml{v}_F}$), the experimental points and the theoretical curves for $H_{c2\mathrm{}}\mathrm{}\left(T\right)\mathrm{}$ are brought into excellent agreement by the proper choice of a single parameter, ${\tau }_{\mathrm{so}}$ the phenomenological spin-orbit scattering time. For the same value of ${\tau }_{\mathrm{so}}$, the agreement for ${\kappa }_2$ is not so good. The critical-field curve cannot be fitted unless spin-orbit coupling is taken into account.