  Very recently we revealed a large family of triangular lattice quantum spin
liquid candidates named rare-earth chalcogenides, which features a
high-symmetry structure without structural/charge disorders and spin
impurities, and may serve as an ideal platform exploring spin liquid physics.
The knowledge of crystalline electric-field (CEF) excitations is an essential
step to explore the fundamental magnetism of rare-earth spin systems. Here we
employed inelastic neutron scattering (INS) and Raman scattering (RS) to carry
out a comprehensive CFE investigation on $NaYbSe_{2}$, a promising
representative of the family. By comparison with its nonmagnetic compound
$NaLuSe_{2}$, we are able to identify the CEF excitations at 15.8, 24.3 and
30.5 meV at 5K. The selected cuts of the INS spectra are well re-produced with
a large anisotropy of $g$ factors ($g_{ab}:g_{c}\sim3:1$). Further, the CEF
excitations are explained well by our calculations based on the point charge
model. Interestingly, $NaYbSe_{2}$ exhibits an unusual CEF shift to higher
energies with increasing temperatures, and the Raman mode close to the first
CEF excitation shows an anomalously large softening with decreasing
temperatures. The absence of the anomalies in $NaLuSe_{2}$ clearly demonstrates
a CEF-phonon coupling not reported in the family. It can be understood in term
of the weaker electronegativity of Se. The fact that the smallest first CEF
excitation in the sub-family of $NaYbCh_{2}$ is $\sim$ 180K (Ch=O, S, Se),
guarantees that the sub-family can be strictly described with an effective
S=1/2 picture at sufficiently low temperatures. Interestingly the CEF-phonon
coupling revealed here may present alternative possibilities to manipulate the
spin systems.
