Superconducting and normal state properties of the noncentrosymmetric superconductor ${\mathrm{NbOs}}_2$ investigated by muon spin relaxation and rotation

Noncentrosymmetric superconductors with $\alpha$-manganese structure has attracted much attention recently, after the discovery of time-reversal symmetry breaking in all the members of the ${\mathrm{Re}}_{6}X$ ($X=\text{Ti}$, Hf, Zr) family. Similar to ${\mathrm{Re}}_{6}X$, ${\mathrm{NbOs}}_2$ also adopts $\alpha \text{−}\text{Mn}$ structure and is found to be superconducting with critical temperature $T_c\simeq 2.7$ K. The results of the resistivity, magnetization, specific heat, and muon spin relaxation/rotation measurements show that ${\mathrm{NbOs}}_2$ is a weakly coupled type-II superconductor. Interestingly, the zero-field muon experiments indicate that the time-reversal symmetry is preserved in the superconducting state. The low-temperature transverse-field muon measurements and the specific-heat data evidence a conventional isotropic fully gapped superconductivity. However, the calculated electronic properties in this material show that the ${\mathrm{NbOs}}_2$ is positioned close to the band of unconventionality of the Uemura plot, indicating that ${\mathrm{NbOs}}_2$ potentially borders an unconventional superconducting ground state.

Figure 1

The powder x-ray diffraction pattern of ${\mathrm{NbOs}}_2$ at room temperature. The line is a Rietveld refinement to the data. The inset shows the crystal structure of ${\mathrm{NbOs}}_2$.

Figure 2

(a) Temperature dependence of resistivity over the range $1.8\text{K}\le T\le 300$ K, with the inset showing a drop in resistivity at the superconducting transition, $T_c^{\text{onset}}=2.7\pm 0.2\mathrm{K}$. The normal state resistivity fitted with the Bloch-$\mathrm{Gr}\ddot{\text{u}}\mathrm{neisen}$ model is shown by solid red line. (b) Temperature dependence of the $\chi \left(T\right)$ is shown over the range of $1.8\text{K}\le T\le 5$ K, displaying strong diamagnetic signal around $T_c^{\text{onset}}=2.7\pm 0.1\mathrm{K}$ in $H=1$ mT.

Figure 3

(a) The $M\left(H\right)$ curves at different fixed temperatures as a function of applied magnetic fields. The lower critical field $H_{c1}$ determined by the GL formula is $2.98\pm 0.11$ mT. (c) Zero-field cooled magnetic isotherms at $T=1.8$ K and $T=4.0$ K. (c) Magnetization vs magnetic field is shown at several fixed temperatures. The inset shows the detailed view of $M\left(H\right)$ curve, where $H_{c2}$ is determined from the discontinuity in the gradient. (d) Upper critical field vs temperature of ${\mathrm{NbOs}}_2$ determined from the high-field $M\left(H\right)$ curves and ac susceptibility data. The black and blue dotted line shows the prediction of $H_{c2}$(0) using Eq. (4). The inset shows the ac susceptibility data measured at different applied magnetic field.

Figure 4

The specific-heat data in superconducting regime fitted for single-gap $s$-wave model [Eq. (15)] for a fitting parameter $\alpha =\mathrm{\Delta }\left(0\right)/k_B{T}_c=1.77\pm 0.01$. Inset: $C/T$ vs $T^2$ data was fitted between $3\text{K}\le T^2\le 100$ K by $C/T={\gamma }_n+{\beta }_3{T}^2+{\beta }_5{T}^4$ to measure electronic and phononic contribution to specific heat.

Figure 5

Zero-field $\mu \mathrm{SR}$ spectra collected below (0.5 K) and above (3 K) the superconducting transition temperature. The solid lines are the fits to Guassian Kubo-Toyabe (KT) function given in Eq. (16).

Figure 6

(a) Representative $\mathrm{TF}\text{−}\mu \mathrm{SR}$ signals collected at 3.0 and 0.4 K in an applied magnetic field of 20 mT. (b) Temperature dependence of the superconducting contribution to depolarization ${\sigma }_{\mathrm{sc}}$ in an applied magnetic field of 20 mT. The inset shows the internal field variation with temperature where a clear diamagnetic signal appears around $T_c$. (c) Temperature dependence of ${\lambda }^{-2}$ follows a single gap $s$-wave model in dirty limit for $\mathrm{\Delta }\left(0\right)=0.43\pm 0.02$.

Figure 7

The Uemura plot showing the superconducting transition temperature $T_c$ vs the Fermi temperature $T_{\text{F}}$, where ${\mathrm{NbOs}}_2$ is shown as a solid red circle just outside the range of band of unconventional superconductors. $T_{\text{B}}$ is the Bose-Einstein condensation temperature. The orange region represents the band of unconventionality, other points with broken TRS such as ${\mathrm{LaNiC}}_2$, ${\mathrm{La}}_7{\mathrm{Ir}}_3$, etc., and Re-based $\alpha \text{−}\text{Mn}$ structure compounds were obtained from Refs. [57, 74, 75, 76].