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We present the results of muon spin relaxation ($\mu$SR) and neutronscattering on the Ce-based quasikagome lattice CeRh$_{1-x}$Pd$_{x}$Sn ($x=0.1$to 0.75). Our ZF-$\mu$SR results reveal the absence of static long-rangemagnetic order down to 0.05~K in $x = 0.1$ single crystals. The weaktemperature-dependent plateaus of the dynamic spin fluctuations below 0.2~K inZF-$\mu$SR together with its longitudinal-field (LF) dependence between 0 and3~kG indicate the presence of dynamic spin fluctuations persisting even at $T$= 0.05~K without static magnetic order. On the other hand, $C_{\text{4f}}$/$T$increases as --log $T$ on cooling below 0.9~K, passes through a broad maximumat 0.13~K and slightly decreases on further cooling. The ac-susceptibility alsoexhibits a frequency independent broad peak at 0.16~K, which is prominent withan applied field $H$ along $c$-direction. We, therefore, argue that such abehavior for $x=0.1$ (namely, a plateau in spin relaxation rate ($\lambda$)below 0.2~K and a linear $T$ dependence in $C_{\text{4f}}$ below 0.13~K) can beattributed to a metallic spin-liquid (SL) ground state near the quantumcritical point in the frustrated Kondo lattice. The LF-$\mu$SR study suggeststhat the out of kagome plane spin fluctuations are responsible for the SLbehavior. Low energy inelastic neutron scattering (INS) of $x$ = 0.1 revealsgapless magnetic excitations, which are also supported by the behavior of$C_{\text{4f}}$ proportional to $T^{1.1}$ down to 0.06~K.

physical review. b./physical review. b

Quantum critical spin-liquid-like behavior in S = 1/2 quasikagome  lattice CeRh1-xPdxSn investigated using muon spin relaxation and neutron  scattering