Electron-beam floating-zone refined UCoGe

The interplay between unconventional superconductivity and quantum critical ferromagnetism in the U-Ge compounds represents an open problem in strongly correlated electron systems. Sample quality can have a strong influence on both of these ordered states in the compound UCoGe, as is true for most unconventional superconductors. We report results of a different approach at UCoGe crystal growth using a floating-zone method with potential for improvements of sample quality and size as compared with traditional means such as Czochralski growth. Single crystals of the ferromagnetic superconductor UCoGe were produced using an ultra-high vacuum electron-beam floating-zone refining technique. Annealed single crystals show well-defined signatures of bulk ferromagnetism and superconductivity at $T_c\sim 2.6\mathrm{K}$ and $T_s\sim 0.61\mathrm{K}$, respectively, in the resistivity and heat capacity. Scanning electron microscopy of samples with different surface treatments shows evidence of an off-stoichiometric uranium-rich phase of UCoGe collected in cracks and voids that might be limiting sample quality.

Figure 1

Crystal structure of UCoGe. Uranium atoms: large blue balls; cobalt atoms: light blue balls; germanium atoms: red balls. The lines between U atoms are drawn to emphasize the zig-zag arrangement. The green arrows show the Ising ferromagnetic moments on the uranium sites.

Figure 2

(a) Photograph of the molten floating zone during the growth of UCoGe. The green arrow indicates the fully molten floating zone that was being swept upward. (b) View of the ingot being zone refined showing the circular electron gun filament housed in a water-cooled copper translation stage and the molybdenum grounding plate used to focus the electron-beam held below by two threaded shafts. (c) Picture of the UCoGe sample after three zone refining passes over an $\approx 75\mathrm{mm}$ (3 inches on the ruler) long segment of the sample with the approximate location of S1 and S2 shown by the green and purple stars, respectively. (d) Laue x-ray diffraction image of an aligned piece of the UCoGe zone refined sample. The diffraction pattern shows the sample is aligned close to the [010] ($b$-axis) direction demonstrating the single-crystalline nature of the zone refined sample.

Figure 3

SEM images taken from various zone refined UCoGe samples near the bottom of the ingot at different stages of treatment. (a) SEM image of warm $\mathrm{HCl}+\mathrm{nitric}$ acid etch displaying a large crack. (b) SEM image of the as-grown surface displaying the microstructure of the unknown high-temperature phase observed during the growth process, suspected to be a uranium oxide due to the oxygen detected in EDS on this surface. (c) and (d) SEM image of a surface that was polished to a mirror finish and then annealed at $900{}^{\circ }\mathrm{C}$ for 2 weeks (condition Y). The LTP liquified and collected on the polished surface via either large cracks (c) or small holes (d).

Figure 4

Electrical resistivity $\rho$ vs temperature $T$ of zone refined UCoGe for current parallel to the $a$ axis ($\mathrm{I}\parallel a$ axis) for the two samples S1 while unannealed (X), annealed (Y), and annealed/polished (Z) and S2 while annealed (Y) and annealed/polished (Z) from the bottom and top of ingot, respectively, from 0 to 300 K (a), below 10 K (b), and below 1 K (b). Only annealed (Y) $\rho$ shows deviations that can be ascribed to the LTP. Panel (a) shows the difference that polishing the LTP off the electrical contact surface made in achieving consistent behavior between S1 and S2. The blue arrow shows that $\rho$ for S1 decreased at all temperatures, while the red arrow points out the opposite behavior for S2. Once polished (Z), both samples match quantitatively and qualitatively with the unannealed (X) S1, indicating that the damage from the the LTP is limited to the surface of the sample. Panel (b) shows the ferromagnetic ($T_c$) and superconducting transitions ($T_s$) for the annealed (Y) S1 and S2 and the lack of superconductivity and broadened ferromagnetic transition in unannealed (X) S1. All solid curves are power-law fits to $\rho ={\rho }_0+A{T}^{\frac{5}{3}}$ above $T_c$ or to $\rho ={\rho }_0+A{T}^2$ in the ferromagnetic state. Panel (c) shows that the superconducting transition temperature for both samples remains the same between annealed (Y) and annealed/polished (Z), except afterward the sample with the higher zero-resistance superconducting transition temperature of 0.52 K (S1) now has a lower $\rho \left(T\right)$ than the sample with the lower superconducting transition temperature of 0.44 K (S2).

Figure 5

Heat capacity, plotted as $C/T$ vs $T$, of zone refined UCoGe S1 annealed (Y) and S2 annealed/polished (Z). Anomalies at the ferromagnetic transition $T_c=2.6\mathrm{K}$ and at the superconducting transition at $T_s=0.61\mathrm{K}$ are observed, as indicated by the arrows. The upturn in $C/T$ provides evidence for a bulk superconducting transition.

Figure 6

Magnetization, $M$, vs field, $H$, with an inset focusing on the ferromagnetic hysteresis (a) taken at 2 K with $\mathbf{H}$ parallel to the $c$ axis. $M$ vs $T$ upon cooling in an $H=0.01\mathrm{T}$ parallel to the $c$ axis. Solid lines are fits to $M^2\left(T\right)=M_0^2[1-{(T/T^{*})}^2]$ as described in the text.