Quantum Griffiths singularity in the stoichiometric heavy-fermion system CeRh$_4$Al$_{15}$

We present a detailed investigation of the stoichiometric CeRh$_4$Al$_{15}$ single crystal compound using the temperature dependence of the heat capacity [$C_{\text{P}}$($T$)], electrical resistivity [$ρ$($T$)], magnetic susceptibility [$χ$($T$)], and magnetization [$M$($H$)] measurements for a magnetic field ($H$) applied in the basal plane and along the $c$-axis. The low temperature power-law behavior of $C$/$T$ $\propto$ $χ$ $\propto$ $T^{-1+α}$, the isotherm magnetization, $M \sim H^α$ with the exponent $α$ = 0.45 - 0.55, and the $T$-linear resistivity $Δρ$ $\sim$ $T^ε$ with $ε\sim$ 1 are found to be consistent with the formation of quantum Griffiths singularities in the non-Fermi-liquid (NFL) regime. We further investigated the spin dynamics of a polycrystalline sample of CeRh$_4$Al$_{15}$, using zero-field (ZF) and longitudinal-field (LF) muon spin relaxation ($μ$SR) measurements. ZF-$μ$SR measurements do not reveal any sign of long-range magnetic ordering down to 70~mK. The electronic relaxation rate ($λ$) below 0.5~K increases rapidly and shows a thermal activation-like characteristic [$T$log($λ$)$\sim$ $T$] over the entire measured temperature range between 70~mK to 4~K, indicating the presence of low energy spin fluctuations in CeRh$_4$Al$_{15}$. LF-$μ$SR measurements show a time-field ($t/H^η$) scaling of the $μ$SR asymmetry indicating a quantum critical behavior of this compound. Furthermore, inelastic neutron scattering study on the polycrystalline sample reveals two crystal field excitations near 19 and 33~meV. These features collectively provide strong evidence of NFL behavior in CeRh$_4$Al$_{15}$ due to the formation of Griffiths phase close to a $T$ $\rightarrow$ 0~K quantum critical point.