  The existence of orbital-dependent electronic correlations has been
recognized as an essential ingredient to describe the physics of iron-based
superconductors. NaFeAs, a parent compound of iron based superconductors,
exhibits a tetragonal-to-orthorhombic lattice distortion below $T_s\approx 60$
K, forming an electronic nematic phase with two 90$^\circ$ rotated (twinned)
domains, and orders antiferromagnetically below $T_N\approx 42$ K. We use
inelastic neutron scattering to study spin waves in uniaxial pressure-detwinned
NaFeAs. By comparing the data with combined density functional theory and
dynamical mean-field theory calculations, we conclude that spin waves up to an
energy scale of $E_\text{crossover} \approx 100$ meV are dominated by
$d_{yz}$-$d_{yz}$ intra-orbital scattering processes, which have the two-fold
($C_2$) rotational symmetry of the underlying lattice. On the other hand, the
spin wave excitations above $E_\text{crossover}$, which have approximately
fourfold ($C_4$) rotational symmetry, arise from the $d_{xy}$-$d_{xy}$
intra-orbital scattering that controls the overall magnetic bandwidth in this
material. In addition, we find that the low-energy ($E\approx 6$ meV) spin
excitations change from approximate $C_4$ to $C_2$ rotational symmetry below a
temperature $T^\ast$ ($>T_s$), while spin excitations at energies above
$E_\text{crossover}$ have approximate $C_4$ rotational symmetry and are weakly
temperature dependent. These results are consistent with angle resolved
photoemission spectroscopy measurements, where the presence of an uniaxial
strain necessary to detwin NaFeAs also raises the onset temperature $T^\ast$ of
observable orbital-dependent band splitting to above $T_s$, thus supporting the
notion of orbital selective spin waves in the nematic phase of iron-based
superconductors.
