A field-induced quantum spin liquid (QSL) state is an extraordinary phenomenon, hitherto unobserved in metallic frustrated compounds. Recent bulk measurements have revealed intriguing field-induced magnetic states in metallic frustrated CePdAl. However, the nature of these field-induced states, potentially including a QSL state, remains unclear due to the lack of detailed microscopic investigation. To elucidate these field-induced states, we employed the transverse-field muon spin relaxation/rotation (TF-$\mu \mathrm{SR}$) technique, applying various magnetic fields parallel to the $c$-axis in single-crystalline CePdAl over a broad temperature range (100 K–100 mK). Our $\mu \mathrm{SR}$ data indicate that field-induced low-temperature states for fields $\mathrm{B}\le B_{c2}(=3.4T)$ exhibit long-range magnetic order, whereas for B > $B_{c2}$ they yield contrasting behavior. Notably, at 3.75 T, the transverse relaxation rate (${\lambda }_T$) diverges following a power-law dependence below 800 mK along with an indication of finite frustration whereas the Knight shift is temperature independent. These observations corroborate the signature of a critical spin liquid (CSL) with antiferromagnetic spin fluctuations. Furthermore, at 4.3 T, a non-Fermi liquid state is observed where frustration is absent. This comprehensive microscopic study strongly suggest the existence of a CSL state in a metallic frustrated system.

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• Frustrated magnetism
• Quantum criticality
• Quantum spin liquid
• Heavy-fermion systems
• Muon spin relaxation & rotation