Ring-exchange Interaction Effects on Magnons in the Dirac Magnet CoTiO3

The magnetic interactions that determine magnetic order and magnon energiestypically involve only two spins. While rare, multi-spin interactions can alsoappear in quantum magnets and be the driving force in the ground stateselection and in the nature of its excitations. By performing time-domainterahertz and magneto-Raman spectroscopy measurements combined with theoreticalmodeling, we determine the origin of the magnon excitation gap in Diracantiferromagnet CoTiO_3. By adding a ring-exchange interaction in a hexagonalplaquette of the honeycomb lattice to both an XXZ spin model and to a lowenergy spin-orbital flavor wave model, a gap is generated in the magnonspectrum at the Brillouin zone center. With this addition, the flavor wavemodel reproduces a large swath of experimental results including terahertz,Raman, inelastic neutron scattering, and magnetization experiments.