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Polycrystalline samples of NaYbO$_2$ are investigated by bulk magnetizationand specific-heat measurements, as well as by nuclear magnetic resonance (NMR)and electron spin resonance (ESR) as local probes. No signatures of long-rangemagnetic order are found down to 0.3~K, evidencing a highly frustratedspin-liquid-like ground state in zero field. Above 2\,T, signatures of magneticorder are observed in thermodynamic measurements, suggesting the possibility ofa field-induced quantum phase transition. The $^{23}$Na NMR relaxation ratesreveal the absence of magnetic order and persistent fluctuations down to 0.3~Kat very low fields and confirm the bulk magnetic order above 2~T. The $H$-$T$phase diagram is obtained and discussed along with the existing theoreticalconcepts for layered spin-$\frac{1}{2}$ triangular-lattice antiferromagnets

Field-induced instability of the quantum-spin-liquid ground state in the $J_{\rm eff}=\frac{1}{2}$ triangular-lattice compound NaYbO$_2$