We have used resonant inelastic x-ray scattering to reveal optical magnons in a honeycomb lattice iridate $alpha$-Li$_{2}$IrO$_{3}$. The spectrum in the energy region 20-25 meV exhibits momentum dependence, of which energy is highest at the location
of the magnetic Bragg peak, ($textit{h}, textit{k}$) = ($pm$0.32, 0), and lowered toward (0, 0) and ($pm$1, 0). We compare our data with a linear spin-wave theory based on a generic nearest-neighbor spin model. We find that a dominant bond-directional Kitaev interaction of order 20 meV is required to explain the energy scale observed in our study. The observed excitations are understood as stemming from optical magnon modes whose intensity is modulated by a structure factor, resulting in the apparent momentum dependence. We also observed diffuse magnetic scattering arising from the short-range magnetic correlation well above $textit{T}_{N}$. In contrast to Na$_{2}$IrO$_{3}$, this diffuse scattering lacks the $C_3$ rotational symmetry of the honeycomb lattice, suggesting that the bond anisotropy is far from negligible in $alpha$-Li$_{2}$IrO$_{3}$.
We report the magnetic structure and electronic properties of the honeycomb antiferromagnet $rm NaNi_2BiO_{5.66}$. We find magnetic order with moments along the $c$ axis for temperatures below $T_{c1}=6.3(1)>{rm K}$ and then in the honeycomb plane fo
r $T < T_{c2}=4.8(1)>{rm K}$ with a counterrotating pattern and an ordering wave vector ${bf q}=(frac{1}{3},> frac{1}{3},> 0.15(1))$. Density functional theory and electron spin resonance indicate this is high-spin Ni$^{3+}$ magnetism near a high to low spin transition. The ordering wave vector, in-plane magnetic correlations, missing entropy, spin state, and superexchange pathways are all consistent with bond-dependent Kitaev-$Gamma$-Heisenberg exchange interactions in $rm NaNi_2BiO_{6-delta}$.
