  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.
