Magnetoelastic coupling driven magnon gap in a honeycomb antiferromagnet

Cobalt titanate, ${\mathrm{CoTiO}}_3$, is a honeycomb antiferromagnet recently confirmed experimentally to host Dirac magnons, topological spin-orbit excitons, and chiral phonons. Here, we investigate a magnon gap at the zone center which calls for a refined spin Hamiltonian. We propose a microscopic model for the magnon gap and attribute it to a lattice-distortion (phonon)-induced higher-order spin interaction. Strong magnetoelastic coupling in ${\mathrm{CoTiO}}_3$ is also evident in Raman spectra, in which the magnetic order exerts a stronger influence on phonons corresponding to in-plane ionic motions than those with out-of-plane motions. We further examine the evolution of the zone-center magnons in a high magnetic field up to 18.5 T via THz absorption spectroscopy measurements. Based on this field dependence, we propose a spin Hamiltonian that not only agrees with magnon dispersion measured by inelastic neutron scattering but also includes fewer exchange constants and a realistic anisotropy term. Our work highlights the broad implications of magnetoelastic coupling in the study of topologically protected bosonic excitations.