Pressure tuning of superconductivity in ${\mathrm{Mo}}_8{\mathrm{Ga}}_{41}$ single crystals

We report on pressure tuning of superconductivity in a strongly coupled superconductor ${\mathrm{Mo}}_8{\mathrm{Ga}}_{41}$ with a critical temperature $T_c\sim 9.8\mathrm{K}$. Resistance measurements show that $T_c$ is suppressed to 3.6 K at 19 GPa followed by a nonmonotonic variation at higher pressures. Synchrotron x-ray diffraction experiments reveal an amorphization taking place at the critical pressure $P_c\sim 19\mathrm{GPa}$. As comparing with $\mathrm{Mg}{\mathrm{B}}_2$, the ${\mathrm{Mo}}_8{\mathrm{Ga}}_{41}$ shows a relative low decreasing rate of $T_c$, which might be attributed to its unique vertex-sharing type of cluster architecture. Survival of superconductivity across the crystalline to amorphous transition indicates that, although long-range structural order of endohedral Ga clusters is destroyed, short-range-ordered intracluster structure still exists and allows for local Cooper pairing. Due to presence of disorders in the amorphous phase, establishment of Cooper pair coherence is shifted to lower temperatures, which causes unusual transport behaviors near $T_c$, e.g., the anomalous resistance peak and dip. The amorphous superconducting phase is able to be retained to ambient pressure and therefore provides an ideal platform to study disorder effects on superconductivity.

Figure 1

(a) Synchrotron x-ray diffraction pattern for powdered ${\mathrm{Mo}}_8{\mathrm{Ga}}_{41}$ single crystals. Red solid line depicts the Rietveld refinement. (b) Temperature dependence of resistivity for a ${\mathrm{Mo}}_8{\mathrm{Ga}}_{41}$ single crystal near $T_c$. Inset: a zoom-out for a whole temperature range. (c) Temperature dependence of magnetization measured in a magnetic field of 10 Oe with zero-field-cooling (ZFC) and field-cooling (FC) conditions. (d) Magnetic field dependence of magnetization measured at $T=2\mathrm{K}$. Inset: Determination of the lower critical field $H_{c1}$ as 190 Oe. (e) Resistive superconducting transition measured in magnetic fields from 0 to 9 T. (f) Upper critical field ${\mu }_0{H}_{\mathrm{c}2}\left(T_c\right)$ as a function of ${T_c}^{\mathrm{onset}}$. Red solid line represents the fitting with Werthamer-Helfand-Hohenberg (WHH) model [11].

Figure 2

Pressure evolution of the resistive superconducting transition for a ${\mathrm{Mo}}_8{\mathrm{Ga}}_{41}$ single crystal: (a) in compression from 0.9 to 22.7 GPa, (b) from 24.2 to 55.8 GPa, and (e) in decompression from 40.6 down to 1.4 GPa. The $R$ units are properly normalized for a clarity purpose. Blue arrows on $R$($T$) curves in (a) and (b) mark the onset superconducting transition temperature ${T_c}^{\mathrm{onset}}$ below which a monotonous decrease of resistance is observed. For $P$ ≥ 22.7 GPa, green arrows mark the characteristic temperature $T^{*}$ which is defined as the onset temperature of the resistance peak or dip. Panel (c) and (d) show the zoom-ins of typical $R$($T$) curves, respectively, for $P=36.1$ and 24.2 GPa to emphasize the anomalous resistance peak and dip.

Figure 3

The magnetic-field evolution of superconducting resistive transition of a ${\mathrm{Mo}}_8{\mathrm{Ga}}_{41}$ single crystal measured under pressures of (a) 0.9 GPa and (b) 12.5 GPa. Insets depict the $T_c$ dependence of the upper critical field ${\mu }_0{H}_{\mathrm{c}2}\left(T\right)$. The $T_c$ here is determined as the temperature where $R$(T) drops to 90% of normal state resistance. Blue solid lines represent the fittings with the WHH model [11].

Figure 4

(a) High-pressure XRD patterns for powdered ${\mathrm{Mo}}_8{\mathrm{Ga}}_{41}$ single crystals under pressures from 0.3 to 55.2 GPa, and then down to ambient pressure (“$d$” means decompression, the diffraction wave length $\lambda =0.6199\AA$). For $P=0.3\mathrm{GPa}$, the red solid line displays a representative Rietveld refinement. (b) Pressure dependence of the refined lattice parameters $a$ and $c$. (c) Pressure dependence of the lattice volume of a unit cell, where the red solid line represents a fit to the data using the Murnaghan equation of states [18].

Figure 5

The T-P phase diagram for superconductivity in ${\mathrm{Mo}}_8{\mathrm{Ga}}_{41}$. Vertical gray line near $P_c\sim 19\mathrm{GPa}$ depicts the phase boundary between crystalline superconducting phase and the amorphous superconducting phase. The ${T_c}^{\mathrm{onset}}$ and $T^{*}$ are determined in Figs. 2 and 2.