Investigation of Superconducting Gap Structure in HfIrSi using muon spin relaxation/rotation

Abstract

Appearance of strong spin-orbit coupling (SOC) is apparent in ternary equiatomic compounds with 5$d$-electrons due to the large atomic radii of transition metals. SOC plays a significant role in the emergence of unconventional superconductivity. Here we examined the superconducting state of HfIrSi using magnetization, specific heat, zero and transverse-field (ZF/TF) muon spin relaxation/rotation ($\mu$SR) measurements. Superconductivity is observed at $T_{\mathrm{C}}$ = 3.6 K as revealed by specific heat and magnetization measurements. From the TF$-\mu$SR analysis it is clear that superfluid density well described by an isotropic BCS type $s$-wave gap structure. Furthermore, from TF$-\mu$SR data we have also estimated the superconducting carrier density $n_{\mathrm{s}}$ = 6.6 $\times$10${}^{26}$m${}^{-3}$, London penetration depth ${\lambda }_L(0)$ = 259.59 nm and effective mass $m^{\ast }$ = 1.57 $m_e$. Our zero-field muon spin relaxation data indicate no clear sign of spontaneous internal field below $T_{\mathrm{C}}$, which implies that the time-reversal symmetry is preserved in HfIrSi. Theoretical investigation suggests Hf and Ir atoms hybridize strongly along the $c$-axis of the lattice, which is responsible for the strong three-dimensionality of this system which screens the Coulomb interaction. As a result despite the presence of correlated $d$-electrons in this system, the correlation effect is weakened, promoting electron-phonon coupling to gain importance.

8 pages, 4 figures