Here we present a neutron scattering-based study of magnetic excitations and magnetic order in NaYbO$_2$ under the application of an external magnetic field. The crystal electric field-split $J = 7/2$ multiplet structure is determined, revealing a mixed $|m_z>$ ground state doublet and is consistent with a recent report Ding et al. [1]. Our measurements further suggest signatures of exchange effects in the crystal field spectrum, manifested by a small splitting in energy of the transition into the first excited doublet. The field-dependence of the low-energy magnetic excitations across the transition from the quantum disordered ground state into the fluctuation-driven ordered regime is analyzed. Signs of a first-order phase transition into a noncollinear ordered state are revealed at the upper-field phase boundary of the ordered regime, and higher order magnon scattering, suggestive of strong magnon-magnon interactions, is resolved within the previously reported $up-up-down$ phase. Our results reveal a complex phase diagram of field-induced order and spin excitations within NaYbO$_2$ and demonstrate the dominant role of quantum fluctuations cross a broad range of fields within its interlayer frustrated triangular lattice.
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