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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 andan A-type antiferromagnetic order below $\mathrm{T_N} \approx 38$~K. We foundthat the SO exciton becomes softer, but acquires a larger bandwidth in theparamagnetic phase, compared to that in the magnetically ordered phase.Moreover, an additional mode is only observed in the intermediate temperaturerange, as the sample is warmed up above the lowest accessible temperature below$\mathrm{T_N}$. Such an unusual temperature dependence observed in thismaterial suggests that its ground states (an $S_{\mathrm{eff}}=\frac{1}{2}$doublet) and excited states multiplets are strongly coupled, and thereforecannot be treated independently, as often done in a pseudo-spin model. Ourobservations can be explained by a multi-level theory within random phaseapproximation that explicitly takes into account both the ground and excitedmultiplets. The success of our theory, which is originally developed to explaintemperature dependence of magnetic excitations in the rare-earth magnets,highlight the similarity between the magnetic excitations in rare-earth systemsand those in transition metal systems with strong spin orbit coupling.

Spin-Orbit Exciton in a Honeycomb Lattice Magnet CoTiO$_3$: Revealing Link Between Rare Earth and Transition Metal Magnetism