Strong electron-phonon coupling in the intermetallic superconductor ${\mathrm{Mo}}_8{\mathrm{Ga}}_{41}$

Crystals of superconducting ${\mathrm{Mo}}_8{\mathrm{Ga}}_{41}$ $\left(T_c=9.8\mathrm{K}\right)$ and ${\mathrm{Mo}}_{8-x}{\mathrm{V}}_x{\mathrm{Ga}}_{41}$ limited solid solution $[x_{\max }=1.9\left(2\right)]$ have been grown from the high-temperature Ga flux and confirmed to have the ${\mathrm{V}}_8{\mathrm{Ga}}_{41}$ type of crystal structure at room temperature. Thermodynamic and transport measurements as well as electronic structure calculations were performed to investigate both normal- and superconducting-state properties of ${\mathrm{Mo}}_8{\mathrm{Ga}}_{41}$. The discontinuity in the heat capacity at $T_c, \mathrm{\Delta }{c}_p/{\gamma }_N{T}_c=2.83$ in zero magnetic field, indicates a much stronger electron-phonon coupling than in the standard BCS limit. From the heat-capacity data, we estimated the electron-phonon coupling constant ${\lambda }_{ep}=0.9$. The upper critical field is ${\mu }_0{H}_{c2}\left(0\right)=8.3\mathrm{T}$, while the lower one is only ${\mu }_0{H}_{c1}\left(0\right)=131\mathrm{Oe}$. The upper critical field of ${\mathrm{Mo}}_8{\mathrm{Ga}}_{41}$ exhibits a clear enhancement with respect to the Werthamer-Helfand-Honenberg prediction, consistent with the strong electron-phonon coupling. The ${\mathrm{Mo}}_{8-x}{\mathrm{V}}_x{\mathrm{Ga}}_{41}$ limited solid solution also exhibits superconducting properties, and the critical temperature $T_c$ is reduced only slightly with increasing $x$.

Figure 1

Experimental (black points) and calculated (red line) XRD patterns of ${\mathrm{Mo}}_8{\mathrm{Ga}}_{41}$. Peak positions are given by black ticks; the difference plot is shown as a black line in the bottom part. The inset shows scanning electron microscope image of a typical ${\mathrm{Mo}}_8{\mathrm{Ga}}_{41}$ crystal, grown from Ga flux.

Figure 2

${\mathrm{Mo}}_8{\mathrm{Ga}}_{41}$ crystal structure: (a) ${\mathrm{MoGa}}_{10}$ polyhedron (orange), (b) the main building block, constructed by ${\mathrm{MoGa}}_{10}$ polyhedra (orange) and ${\mathrm{GaGa}}_{12}$ cuboctahedra (blue), (c) the unit cell content.

Figure 3

Electrical resistivity of ${\mathrm{Mo}}_8{\mathrm{Ga}}_{41}$ in zero magnetic field. The solid curve represents a fit according to the parallel resistance model. The inset shows resistivity at low temperatures in different applied fields.

Figure 4

(a) Normal-state magnetic susceptibility of ${\mathrm{Mo}}_8{\mathrm{Ga}}_{41}$ measured at $H=2\mathrm{T}$; (b) magnetic susceptibility at $H=100\mathrm{Oe}$, measured in zero-field-cooled and field-cooled conditions.

Figure 5

Specific heat $c_p/T$ vs $T$ plot in various magnetic fields for ${\mathrm{Mo}}_8{\mathrm{Ga}}_{41}$.

Figure 6

The specific-heat anomaly in zero magnetic field. The solid curve is a construction to estimate the specific-heat jump at $T=T_c$. The inset shows $c_p/T$ vs $T^2$ plot in $H=11\mathrm{T}$ magnetic field, the solid curve represents the linear fit of the data.

Figure 7

Electronic specific-heat $c_{eS}/T$ vs $T^2$ plot in various magnetic fields together with $\propto T^3$ behavior for $H=0\mathrm{T}$, which is shown by the solid blue line.

Figure 8

Upper critical field ${\mu }_0{H}_{c2}\left(T\right)$ of ${\mathrm{Mo}}_8{\mathrm{Ga}}_{41}$, determined from the magnetization, heat-capacity, and electrical resistivity measurements. The solid lines represent an extrapolation of the data by the second-order polynomial. Lower critical field ${\mu }_0{H}_{c1}\left(T\right)$ is shown in the inset. The solid red line is a fit of the data, as described in the text.

Figure 9

Calculated electronic density of states (DOS) for ${\mathrm{Mo}}_8{\mathrm{Ga}}_{41}$. The Fermi level is indicated by the dashed line.

Figure 10

Electrical resistivity of the ${\mathrm{Mo}}_{8-x}{\mathrm{V}}_x{\mathrm{Ga}}_{41}$ solid solution for $x=0$, 1, and 2 in zero magnetic field.