Microscopic investigation of the superconducting properties of the strongly coupled superconductor IrGe via $\mu \mathrm{SR}$

Exploring superconductors which can possess a pairing mechanism other than the BCS predicted $s$ wave have continually attracted considerable interest. Superconductors with low-lying phonons may exhibit unconventional superconductivity as the coupling of electrons with these low-lying phonons can potentially affect the nature of the superconducting ground state, resulting in strongly coupled superconductivity. In this work, by using magnetization, AC transport, specific heat, and muon spin rotation/relaxation ($\mu \mathrm{SR}$) measurements, we report a detailed investigation on the superconducting ground state of the strongly coupled superconductor, IrGe, that has a transition temperature, $T_C$, at 4.7 K. Specific heat (SH), and transverse field $\mu \mathrm{SR}$ is best described with an isotropic $s$-wave model with strong electron-phonon coupling, indicated by the values of both $\mathrm{\Delta }\left(0\right)/k_B{T}_C=2.3,2.1$ (SH,$\mu \mathrm{SR}$), and $\mathrm{\Delta }{C}_{el}/{\gamma }_n{T}_C=2.7$. Zero-field $\mu \mathrm{SR}$ measurements confirm the presence of time-reversal symmetry in the superconducting state of IrGe.

Figure 1

Room temperature powder XRD pattern of IrGe is shown by yellow circles whereas the blue line represents the Rietveld refinement. Bragg positions are shown by green vertical bars and the red solid line displays the difference between the calculated and observed patterns.

Figure 2

Temperature dependence of resistivity in the temperature range $10\text{K}\le T\le 300$ K. The inset in the top left corner shows the resistivity drop at $T_{C,\mathrm{onset}}=4.7\left(1\right)$ K. The bottom right inset represents the field variation of Hall resistivity up to $+9T$ at $T=100$ K.

Figure 3

(a) The magnetic moment with respect to temperature measured at 1 mT. (b) The lower critical field vs temperature where the inset shows the low-field magnetization curves at various temperatures. (c) The temperature dependence of the upper critical field from various measurements where the inset shows the field and temperature variations of $\rho$.

Figure 4

Temperature dependence of normalized specific heat in zero applied fields where the solid red line is a fit using the isotropic $s$-wave model. Inset (left): Specific heat variation with $T$ which exhibits a sharp jump at $T_C=4.6$ K. Dotted line is a fit using $C={\gamma }_{n}T+{\beta }_3{T}^3$ to calculate the electronic and phononic contributions. Inset (right): Specific heat with respect to temperature at various applied fields starting from 10 mT to 0.5 T.

Figure 5

Time-domain ZF-$\mu \mathrm{SR}$ spectra of IrGe in the superconducting (0.3 K) and normal state (6.0 K). The solid lines are fit using Eq. (8).

Figure 6

(a) TF-$\mu \mathrm{SR}$ asymmetry spectra collected above (6.0 K) and below (0.6 K) $T_C$ shows different relaxation rates. (b) Flux-line lattice contribution to the relaxation rate vs temperature as determined from TF-$\mu \mathrm{SR}$ spectra where the solid line is a fit using the $s$-wave superconducting gap function. Inset: Temperature dependence of internal magnetic field distribution (bottom left) and total depolarization rate (upper right).

Figure 7

Uemura plot representing transition temperature versus Fermi temperature for various superconductors belonging to different classes where the region between two solid blue lines represents the band of unconventionality. IrGe is represented by a hollow red marker.