We conducted a comprehensive and comparative muon-spin relaxation and rotation (μSR) investigation on two fcc-lattice metallic compounds, ${\mathrm{HoCdCu}}_4$ $(T_{\mathrm{N}}\approx 8\mathrm{K})$ and ${\mathrm{HoInCu}}_4$ $(T_{\mathrm{N}}\approx 0.76\mathrm{K})$, to elucidate the nature of their magnetic ground states and the role of frustration in stabilizing them. Our μSR results reveal that, in contrast to ${\mathrm{HoCdCu}}_4$, strong magnetic frustration exists in ${\mathrm{HoInCu}}_4$. Notably, in ${\mathrm{HoInCu}}_4$, the majority of the Ho-moments exhibit dynamic correlations and persistent spin dynamics down to 0.3 K, resembling a quantum spin-liquid (QSL) behavior, and the remaining Ho-moments show static correlation. By contrast, in ${\mathrm{HoCdCu}}_4$, all the Ho-moments contribute to the magnetic order below $T_{\mathrm{N}}$. Furthermore, in ${\mathrm{HoInCu}}_4$, the temperature dependence of the relaxation rate indicates the presence of quantum critical fluctuations in the paramagnetic state near $T_{\mathrm{N}}$, suggesting the proximity to a quantum critical point (QCP). These observations suggest that the ground state of ${\mathrm{HoInCu}}_4$ is a proximate quantum spin liquid (PQSL), hitherto unobserved in frustrated metallic systems. Our μSR findings are further corroborated by recent inelastic neutron results on ${\mathrm{HoInCu}}_4$, which show similarities to other insulating PQSL candidates, thus reinforcing our conclusions.

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• Frustrated magnetism
• Quantum spin liquid
• Muon spin relaxation & rotation