Quantum critical spin-liquid-like behavior in the S=12 quasikagome-lattice compound CeRh1−x…

We present the results of muon spin relaxation ($\ensuremath{\mu}\mathrm{SR}$) and neutron scattering on the Ce-based quasikagome lattice ${\mathrm{CeRh}}_{1\ensuremath{-}x}{\mathrm{Pd}}_{x}\mathrm{Sn}$ ($x=0.1$ to 0.75). Our zero-field (ZF) $\ensuremath{\mu}\mathrm{SR}$ results reveal the absence of both static long-range magnetic order and spin freezing down to 0.05 K in the single-crystal sample of $x=0.1$. The weak temperature-dependent plateaus of the dynamic spin fluctuations below 0.2 K in ZF-$\ensuremath{\mu}\mathrm{SR}$ together with its longitudinal-field (LF) dependence between 0 and 3 kG indicate the presence of dynamic spin fluctuations persisting even at $T=0.05\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ without static magnetic order. On the other hand, the magnetic specific heat divided by temperature ${C}_{\text{4f}}/T$ increases as $\ensuremath{-}\text{log}T$ on cooling below 0.9 K, passes through a broad maximum at 0.13 K, and slightly decreases on further cooling. The ac susceptibility also exhibits a frequency-independent broad peak at 0.16 K, which is prominent with an applied field $H$ along the $c$ direction. We, therefore, argue that such a behavior for $x=0.1$ [namely, a plateau in spin relaxation rate ($\ensuremath{\lambda}$) below 0.2 K and a linear $T$ dependence in ${C}_{\text{4f}}$ below 0.13 K] can be attributed to a metallic spin-liquid-like ground state near the quantum critical point in the frustrated Kondo lattice. The LF-$\ensuremath{\mu}\mathrm{SR}$ study suggests that the out of kagome plane spin fluctuations are responsible for the spin-liquid (SL) behavior. Low-energy inelastic neutron scattering (INS) of $x=0.1$ reveals gapless magnetic excitations, which are also supported by the behavior of ${C}_{\text{4f}}$ proportional to ${T}^{1.1}$ down to 0.06 K. Our high-energy INS study shows very weak and broad scattering in $x=0$ and 0.1, which transforms into well-localized crystal-field excitations with increasing $x$. The ZF-$\ensuremath{\mu}\mathrm{SR}$ results for the $x=0.2$ polycrystalline sample exhibit similar behavior to that of $x=0.1$. A saturation of $\ensuremath{\lambda}$ below 0.2 K suggests a spin-fluctuating SL ground state down to 0.05 K. The ZF-$\ensuremath{\mu}\mathrm{SR}$ results for the $x=0.5$ sample are interpreted as a long-range antiferromagnetic (AFM) ground state below ${T}_{\text{N}}=0.8\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, in which the AFM interaction of the enlarged moments probably overcomes the frustration effect. The long-range AFM ordering is also supported by the evolution of magnetic Bragg peaks in $x=0.75$ sample observed below 5 K in the neutron diffraction data.