Superconducting properties of the noncentrosymmetric superconductor ${\mathrm{Re}}_6\mathrm{Hf}$

We report synthesis and detailed characterization of the noncentrosymmetric superconductor ${\mathrm{Re}}_6\mathrm{Hf}$ using powder x-ray diffraction (XRD), magnetization, transport, and thermodynamic measurements. XRD confirmed the noncentrosymmetric, $\alpha$-Mn cubic structure in ${\mathrm{Re}}_6\mathrm{Hf}$ with the cubic cell parameter $a=9.6850\left(3\right)$ Å. Resistivity, DC, and AC magnetization measurements confirmed the type-II superconductivity in ${\mathrm{Re}}_6\mathrm{Hf}$ with the transition temperature $T_c^{\mathrm{onset}}\sim 5.96$ K, having the lower critical field $H_{c1}\left(0\right)5.6$ mT and upper critical field $H_{c2}\left(0\right)12.2$ T. The electronic specific heat data fits well with the single-gap BCS model. The Sommerfeld coefficient $\left(\gamma \right)$ also shows linear relation with the magnetic field. All above results suggest $s$-wave superconductivity in ${\mathrm{Re}}_6\mathrm{Hf}$.

Figure 1

Powder XRD pattern for the ${\mathrm{Re}}_6\mathrm{Hf}$ sample recorded at room temperature using $\mathrm{Cu}{K}_{\alpha }$ radiation. Rietveld refined calculated pattern for cubic noncentrosymmetric $\alpha \text{−}\mathit{Mn}$ (217) structure is shown by a dotted red line.

Figure 2

(a) Temperature dependence of the resistivity for ${\mathrm{Re}}_6\text{Hf}$ shown over the range 1.85 K $\le$ $\mathit{T}$ $\le 300$ K. The inset shows the superconducting transition at $T_c^{\mathrm{onset}}=5.96$ K. (b) Quadratic temperature dependence over the temperature range 10 K $\le$ $\mathit{T}$ $\le 50$ K indicating Fermi-liquid behavior at low temperature.

Figure 3

Temperature dependence of the magnetic moment, collected via zero-field cooled warming (ZFCW) and field cooled cooling (FCC) methods under an applied field of 10 mT.

Figure 4

Temperature dependence of [(a) real and (b) imaginary] AC susceptibility for ${\mathrm{Re}}_6\mathrm{Hf}$.

Figure 5

(a) Low-field magnetization curves for ${\mathrm{Re}}_6\mathrm{Hf}$ at various temperatures (b) Temperature dependence of the lower critical field $H_{c1}$ was fitted using Ginzburg-Landau relation gives $H_{c1}\left(0\right)\sim 5.6$ mT.

Figure 6

Magnetization vs magnetic field variation at $T=1.8$ K. The magnetization is irreversible below a field $H_{Irr}=1.8$ T.

Figure 7

(a) Temperature dependence of specific heat in zero field showing superconducting transition at $T_c=5.96$ K. (b) Field dependence of the specific heat data, showing the suppression of $T_c$ with increasing field.

Figure 8

$C/T$ vs $T^2$ for 36 K $\le T^2\le 100$ K in zero field well described by the equation $\frac{C}{T}={\gamma }_n+{\beta }_3{T}^2+{\beta }_5{T}^4$.

Figure 9

Solid green curve in $C_{el}/{\gamma }_{n}T$ versus $T/T_c$ data show the single-gap BCS model fitting for $\alpha =\mathrm{\Delta }\left(0\right)/k_B{T}_c=1.82$.

Figure 10

$\gamma$ and $\mathit{H}$ were plotted versus each other after normalizing by ${\gamma }_n$(= 27.2 mJ ${\mathrm{mol}}^{-1}$ ${\mathrm{K}}^{-2})$ and $H_{c2}$(0)(= 12.2 T). Solid blue curve in $\gamma /{\gamma }_n$ versus $H/H_{c2}$(0) plot show the linear relation indicating $s$-wave superconductivity in ${\mathrm{Re}}_6\mathrm{Hf}$.

Figure 11

Determination of the upper critical field $H_{c2}$(0) via magnetization and heat capacity measurements. The solid lines are Ginzburg-Landau [Eq. (14)] fits. The inset shows the $\mathit{M}\left(\mathit{T}\right)$ curves for various applied magnetic fields.