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Recent theoretical proposals have argued that cobaltates with edge-sharingoctahedral coordination can have significant bond-dependent exchange couplingsthus offering a platform in 3$d$ ions for such physics beyond the much-exploredrealizations in 4$d$ and 5$d$ materials. Here we present high-resolutioninelastic neutron scattering data within the magnetically ordered phase of thestacked honeycomb magnet CoTiO$_3$ revealing the presence of a finite energygap and demonstrate that this implies the presence of bond-dependentanisotropic couplings. We also show through an extensive theoretical analysisthat the gap further implies the existence of a quantum order-by-disordermechanism that, in this material, crucially involves virtual crystal fieldfluctuations. Our data also provide an experimental observation of a universalwinding of the scattering intensity in angular scans around linearband-touching points for both magnons and dispersive spin-orbit excitons, whichis directly related to the non-trivial topology of the quasiparticlewavefunction in momentum space near nodal points.

Order-by-Disorder from Bond-Dependent Exchange and Intensity Signature of Nodal Quasiparticles in a Honeycomb Cobaltate