Nodeless time-reversal symmetry breaking in the centrosymmetric superconductor Sc5Co4Si10 probed by muon-spin spectroscopy

We investigate the superconducting properties of ${\mathrm{Sc}}_{5}{\mathrm{Co}}_{4}{\mathrm{Si}}_{10}$ using low-temperature resistivity, magnetization, heat capacity, and muon-spin rotation and relaxation ($\ensuremath{\mu}\mathrm{SR}$) measurements. We find that ${\mathrm{Sc}}_{5}{\mathrm{Co}}_{4}{\mathrm{Si}}_{10}$ exhibits type-II superconductivity with a superconducting transition temperature ${T}_{\mathrm{C}}=3.5(1)\phantom{\rule{4pt}{0ex}}\mathrm{K}$. The temperature dependence of the superfluid density obtained from transverse-field $\ensuremath{\mu}\mathrm{SR}$ spectra is best modeled using an isotropic Bardeen-Cooper-Schrieffer type $s$-wave gap symmetry with $2\mathrm{\ensuremath{\Delta}}/{k}_{\mathrm{B}}{T}_{\mathrm{C}}=2.84(2)$. However, the zero-field muon-spin relaxation rate reveals the appearance of a spontaneous magnetic field below ${T}_{\mathrm{C}}$, indicating that time-reversal symmetry (TRS) is broken in the superconducting state. Although this behavior is commonly associated with nonunitary or mixed singlet-triplet pairing, our group-theoretical analysis of the Ginzburg-Landau free energy alongside density functional theory calculations indicates that unconventional mechanisms are pretty unlikely. Therefore, we have hypothesized that TRS breaking may occur via a conventional electron-phonon process.