  Non-collinear two-dimensional triangular lattice antiferromagnets (2D TLAF)
are currently an area of very active research due to their unique magnetic
properties, which lead to non-trivial quantum effects that experimentally
manifest themselves in the spin excitation spectra. Recent examples of such
insulating 2D TLAF include (Y,Lu)MnO$_3$, LiCrO$_2$, and CuCrO$_2$. Hexagonal
LuFeO3 is a recently synthesized 2D TLAF which exhibits properties of an ideal
multiferroic material, partially because of the high spin ($S=5/2$) and strong
magnetic super-exchange interactions. We report the full range of spin dynamics
in a bulk single crystal of (Lu$_{0.6}$Sc$_{0.4}$)FeO$_3$ (Sc doping to
stabilize the hexagonal structure) measured via time-of-flight inelastic
neutron scattering. Modeling with linear spin wave theory yields a nearest
neighbor exchange coupling of $J$ = 4.0(2) meV (DFT calculations for
$h$-LuFeO$_3$ predicted a value of 6.31 meV) and anisotropy values of $K_D$ =
0.17(1) meV (easy plane) and $K_A$~=~-0.05(1)~meV (local easy axis). It is
observed that the magnon bandwidth of the spin wave spectra is twice as large
for $h$-(Lu,Sc)FeO$_3$ as it is for $h$-LuMnO$_3$.
