Paramagnetic Superconductivity in Extreme Type-II Superconductors

Abstract

Magnetization measurements in applied magnetic fields $0<H\le 55$ kG and at temperatures $1.2\le T\le 4.2$ °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 ${\kappa }_G$ 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 $H_u\mathrm{}\left(T\right)\mathrm{}$ where the paramagnetic superconducting magnetization $M_s\mathrm{}\left(H\right)\mathrm{}$ becomes equal to the paramagnetic normal-state magnetization $M_n\mathrm{}\left(H\right)\mathrm{}$, and (c) parameters ${\kappa }_1\mathrm{}\left(T\right)\mathrm{}\equiv \frac{H_u\mathrm{}\left(T\right)\mathrm{}}{\left[\sqrt{2}{H}_c\mathrm{}\right(T\left)\right]}$ (where $H_c\equiv \mathrm{the}\mathrm{thermodynamic}\mathrm{critical}\mathrm{field}$) and ${\kappa }_2\mathrm{}\left(T\right)\mathrm{}\propto {{\left[\frac{d(M_s-M_n)}{\mathrm{dH}}\right]}_{H_u}}^{-\frac{1}{2}}$ 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 $H_u\mathrm{}\left(T\right)\mathrm{}$ which is comparable to that in the high-field normal state. Comparison of the $H_u\mathrm{}\left(T\right)\mathrm{}$, ${\kappa }_1\mathrm{}\left(T\right)\mathrm{}$, and ${\kappa }_2\mathrm{}\left(T\right)\mathrm{}$ 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.