  We carried out inelastic neutron scattering to study the spin-orbital (SO)
exciton in a single crystal sample of CoTiO$_3$ as a function of temperature.
CoTiO$_3$ is a honeycomb magnet with dominant XY-type magnetic interaction and
an A-type antiferromagnetic order below $\mathrm{T_N} \approx 38$~K. We found
that the SO exciton becomes softer, but acquires a larger bandwidth in the
paramagnetic phase, compared to that in the magnetically ordered phase.
Moreover, an additional mode is only observed in the intermediate temperature
range, as the sample is warmed up above the lowest accessible temperature below
$\mathrm{T_N}$. Such an unusual temperature dependence observed in this
material suggests that its ground states (an $S_{\mathrm{eff}}=\frac{1}{2}$
doublet) and excited states multiplets are strongly coupled, and therefore
cannot be treated independently, as often done in a pseudo-spin model. Our
observations can be explained by a multi-level theory within random phase
approximation that explicitly takes into account both the ground and excited
multiplets. The success of our theory, which is originally developed to explain
temperature dependence of magnetic excitations in the rare-earth magnets,
highlight the similarity between the magnetic excitations in rare-earth systems
and those in transition metal systems with strong spin orbit coupling.
