Probing nodeless superconductivity in $\mathrm{La}M\mathrm{Si}$ ($M=\mathrm{Ni}$, Pt) using muon-spin rotation and relaxation

Systems with strong spin-orbit coupling have been a topic of fundamental interest in condensed matter physics due to the exotic topological phases and the unconventional phenomenon they exhibit. In this particular study, we have investigated the superconductivity in the transition-metal ternary noncentrosymmetric compounds $\mathrm{La}M\mathrm{Si}$ ($M=\mathrm{Ni}$, Pt) with different spin-orbit coupling strength, using muon-spin rotation and relaxation measurements. Transverse-field measurements made in the vortex state indicate that the superconductivity in both materials is fully gapped, with a conventional $s$-wave pairing symmetry and BCS-like magnitudes for the zero-temperature gap energies. Zero-field measurements suggest a time-reversal symmetry preserved superconductivity in both the systems, though a small increase in muon depolarization is observed upon decreasing temperature. However, this has been attributed to quasistatic electronic fluctuations.

Figure 1

X-ray diffraction pattern collected at ambient conditions for (a) LaNiSi and (b) LaPtSi refined with noncentrosymmetric $\alpha -{\mathrm{ThSi}}_2$-type structure.

Figure 2

(a) and (b) Magnetization data collected at ZFC-FC mode showing the superconducting transition at 1.25 and 3.45 K, respectively, for LaNiSi and LaPtSi. (c) and (d) $M-H$ curve taken at the superconducting regime showing a type-II behavior by both compounds.

Figure 3

Temperature-dependent electronic specific heat data for both LaNiSi and LaPtSi taken at 0 T. The superconducting region can be well traced by the isotropic BCS $s$-wave model, giving the normalized specific heat jump as 1.64 and 1.6, respectively, for LaNiSi and LaPtSi. The insets show the total specific heat data plotted as $C/T$ vs $T^2$.

Figure 4

Time evolution of the spin polarization of muons implanted under zero-field conditions in (a) LaNiSi and (b) LaPtSi at temperatures above and below $T_c$. The solid lines are the results of fitting the data to Eq. (2). Blue markers show the muon depolarization at a small longitudinal applied field.

Figure 5

Temperature dependence of the electronic relaxation rate in (a) LaNiSi and (b) LaPtSi, collected in ZF. The solid lines are guides to the eye, indicating the exponential decay of $\mathrm{\Lambda }$ in ZF as $T$ is increased. The insets show the constant behavior of nuclear relaxation rate $\sigma$ across the transition temperature.

Figure 6

Transverse-field muon time spectra collected in a magnetic field $H=100$ Oe at 0.1 and 2.0 K for the LaNiSi (top left and bottom left) and in a magnetic field $H=200$ Oe at 0.1 and 4.0 K for the LaPtSi (top right and bottom right).

Figure 7

Temperature dependence of ${\sigma }_{\text{sc}}$ measured at an applied field. The solid line is the dirty limit isotropic $s$-wave fit for the data. The inset shows the internal field variation for the samples.

Figure 8

Uemura plot showing $T_c$ vs the effective Fermi temperature $T_F$. The blue band represents different families of superconductors with unconventional properties. The positions of LaNiSi and LaPtSi indicate a conventional nature of these materials.