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

Abstract

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 [$\rho$($T$)], magnetic susceptibility [$\chi$($T$)], 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 $C$/$T$ $\propto$ $\chi$ $\propto$ $T^{-1+\alpha }$, the isotherm magnetization, $M\sim H^{\alpha }$ with the exponent $\alpha$ = 0.45 - 0.55, and the $T$-linear resistivity $\Delta \rho$ $\sim$ $T^{\epsilon }$ with $\epsilon \sim$ 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 ($\mu$SR) measurements. ZF-$\mu$SR measurements do not reveal any sign of long-range magnetic ordering down to 70~mK. The electronic relaxation rate ($\lambda$) below 0.5~K increases rapidly and shows a thermal activation-like characteristic [$T$log($\lambda$)$\sim$ $T$] 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-$\mu$SR measurements show a time-field ($t/H^{\eta }$) scaling of the $\mu$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 $T$ $\to$ 0~K quantum critical point.

arXiv comment12 pages, 5 figures

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