Spin-orbit exciton in a honeycomb lattice magnet CoTiO 3 : Revealing a link between magnetism in d- and f-electron systems

We carried out inelastic neutron scattering to study the spin-orbit (SO) exciton in a single crystal sample of ${\mathrm{CoTiO}}_{3}$ as a function of temperature. ${\mathrm{CoTiO}}_{3}$ is a honeycomb magnet with dominant $XY$-type magnetic interaction and an $A$-type antiferromagnetic order below ${T}_{N}\ensuremath{\approx}38$ 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 ${T}_{N}$. 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 pseudospin model. Our observations can be explained by a multilevel theory within random phase approximation that explicitly takes into account both the ground and excited multiplets. The success of our theory, originally developed for the rare-earth systems, highlights the similarity between magnetic excitations in $f$- and $d$-electron systems with strong spin-orbit coupling.