Paramagnetic Superconductivity in Extreme Type-II Superconductors

Abstract

Magnetization measurements in applied magnetic fields $0<H\ensuremath{\le}55$ kG and at temperatures $1.2\ensuremath{\le}T\ensuremath{\le}4.2$ \ifmmode^\circ\else\textdegree\fi{}K have been made on some extremely "dirty" (short electron mean free path) type-II superconducting transition-metal alloys with Gor'kov-Goodman-calculated Ginzburg-Landau ${\ensuremath{\kappa}}_{G}$ values in the range 30-100: Ti(16 at.% Mo), V(30 at.% Ti) (10 at.% Cr), Ti(22.5 at.% V), and Ti(25 at.% V). Down to the lowest temperatures of measurement, the data show that the high-field superconducting mixed state of such materials is characterized by (a) reversible paramagnetic magnetization, (b) second-order transitions at upper critical fields ${H}_{u}(T)$ where the paramagnetic superconducting magnetization ${M}_{s}(H)$ becomes equal to the paramagnetic normal-state magnetization ${M}_{n}(H)$, and (c) parameters ${\ensuremath{\kappa}}_{1}(T)\ensuremath{\equiv}\frac{{H}_{u}(T)}{[\sqrt{2}{H}_{c}(T)]}$ (where ${H}_{c}\ensuremath{\equiv}\mathrm{the}\mathrm{thermodynamic}\mathrm{critical}\mathrm{field}$) and ${\ensuremath{\kappa}}_{2}(T)\ensuremath{\propto}{{[\frac{d({M}_{s}\ensuremath{-}{M}_{n})}{\mathrm{dH}}]}_{{H}_{u}}}^{\ensuremath{-}\frac{1}{2}}$ which decrease with decrease of $T$. The second-order nature of the upper-critical-field transition implies a mixed-state Pauli-paramagnetic conduction-electron spin alignment near ${H}_{u}(T)$ which is comparable to that in the high-field normal state. Comparison of the ${H}_{u}(T)$, ${\ensuremath{\kappa}}_{1}(T)$, and ${\ensuremath{\kappa}}_{2}(T)$ data with recent extreme type-II theories of Maki and of Werthamer, Helfand, and Hohenberg suggests that electronic spin-flip scattering induced by spin-orbit coupling effectively acts to decouple superconductive spin pairing and thus enhance mixed-state Pauli paramagnetism.