Upper critical fields and superconducting transition temperatures of some zirconium-base amorphous transition-metal alloys

Abstract

Superconducting upper critical fields ${H}_{c2}(T)$, transition temperatures ${T}_{c}$ and normal-state electrical resistivities ${\ensuremath{\rho}}_{n}$ have been measured in the amorphous transition-metal alloy series ${\mathrm{Zr}}_{1\ensuremath{-}x}{\mathrm{Co}}_{x}$, ${\mathrm{Zr}}_{1\ensuremath{-}x}{\mathrm{Ni}}_{x}$, ${({\mathrm{Zr}}_{1\ensuremath{-}x}{\mathrm{Ti}}_{x})}_{0.78}{\mathrm{Ni}}_{0.22}$, and ${({\mathrm{Zr}}_{1\ensuremath{-}x}{\mathrm{Nb}}_{x})}_{0.78}{\mathrm{Ni}}_{0.22}$. Structural integrity of these melt-spun alloys is indicated by x-ray, density, bend-ductility, normal-state electrical resistivity, superconducting transition width, and mixed-state flux-pinning measurements. The specimens display ${T}_{c}=2.1\ensuremath{-}3.8$ K, ${\ensuremath{\rho}}_{n}=159\ensuremath{-}190$ \ensuremath{\mu}\ensuremath{\Omega} cm, and $|{(\frac{d{H}_{c2}}{\mathrm{dT}})}_{{T}_{c}}|=28\ensuremath{-}36$ kG/K. These imply electron mean free paths $l\ensuremath{\approx}2\ensuremath{-}6$ \AA{}, zero-temperature Ginzburg-Landau coherence distances ${\ensuremath{\xi}}_{G0}\ensuremath{\approx}50\ensuremath{-}70$ \AA{}, penetration depths ${\ensuremath{\lambda}}_{G0}\ensuremath{\approx}(7\ensuremath{-}10)\ifmmode\times\else\texttimes\fi{}{10}^{3}$ \AA{}, and extremely high dirtiness parameters $\frac{{\ensuremath{\xi}}_{0}}{l}\ensuremath{\approx}300\ensuremath{-}1300$. All alloys display ${H}_{c2}(T)$ curves with negative curvature and (with two exceptions) fair agreement with the standard dirty-limit theory of Werthamer, Helfand, Hohenberg, and Maki (WHHM) for physically reasonable values of spin-orbit-coupling induced, electron-spin-flip scattering time ${\ensuremath{\tau}}_{\mathrm{so}}$. This is in contrast to the anomalously elevated ${H}_{c2}(T)$ behavior which is nearly linear in $T$ that is observed by some, and the unphysically low-${\ensuremath{\tau}}_{\mathrm{so}}$ fits to WHHM theory obtained by others, for various amorphous alloys. Current ideas that such anomalies may be due to alloy inhomogeneity are supported by present results on two specimens for which relatively low-${\ensuremath{\tau}}_{\mathrm{so}}$ fits of ${H}_{c2}(T)$ to WHHM theory are coupled with superconductive evidence for inhomogeneity: relatively broad transitions at ${T}_{c}$ and ${H}_{c2}$ current-density-dependent transitions at ${H}_{c2}$ and (in one specimen) a $J$-dependent, high-$H$ ($>{H}_{c2}$), resistive "beak effect." In the ${\mathrm{Zr}}_{1\ensuremath{-}x}{\mathrm{Co}}_{x}$ and ${\mathrm{Zr}}_{1\ensuremath{-}x}{\mathrm{Ni}}_{x}$ series, ${T}_{c}$ decreases linearly with $x$ (and with unfilled-shell average electron-to-atom ratio $〈\frac{e}{a}〉$ in the range $5.05\ensuremath{\le}〈\frac{e}{a}〉\ensuremath{\le}6.40$ in fair agreement with previous results for these systems and contrary to the ${T}_{c}$ vs $〈\frac{e}{a}〉$ behavior of both amorphous and crystalline transition-metal alloys formed between near neighbors in the Periodic Table. Upper-critical-field and normal-state electrical resistivity measurements suggest that the molar electronic specific-heat coefficient ${\ensuremath{\gamma}}_{m}$ decreases with $x$ in parallel with ${T}_{c}$ in the ${\mathrm{Zr}}_{1\ensuremath{-}x}{\mathrm{Co}}_{x}$ and ${\mathrm{Zr}}_{1\ensuremath{-}x}{\mathrm{Ni}}_{x}$ series. In the equal-$〈\frac{e}{a}〉$ ${({\mathrm{Zr}}_{1\ensuremath{-}x}{\mathrm{Ti}}_{x})}_{0.78}{\mathrm{Ni}}_{0.22}$ system, ${T}_{c}$ decreases with $x$; in the ${({\mathrm{Zr}}_{1\ensuremath{-}x}{\mathrm{Nb}}_{x})}_{0.78}{\mathrm{Ni}}_{0.22}$ system, ${T}_{c}$ first increases and then decreases with $x$ (hence with $〈\frac{e}{a}〉$). These diverse $〈\frac{e}{a}〉$ dependencies of ${T}_{c}$ appear consistent with the ultraviolet-photoemission-spectroscopy indicated split-band model of such amorphous transition-metal alloys and the associated idea that the alloying dependence of ${T}_{c}$ cannot be described by general ${T}_{c}$ vs $〈\frac{e}{a}〉$ rules.