Magneto Raman spectroscopy of magnons in CoTiO₃ at high magnetic fields

CoTiO3 is a Dirac honeycomb antiferromagnet with ferromagnetic layers stacked antiferromagnetically. The Co2+ ions are in a d7 configuration that with spin-orbit coupling and a trigonal lattice distortion, leads to effective spin 1/2 moments. In this approximation, we expect that any Hamiltonian with bilinear interactions will lead to gapless excitations. However, experimentally the gap is ~1 meV is observed at the Brillouin zone center. We demonstrate that multi-spin interactions, in the form of ring-exchange among 6 spins, are responsible for the opening of this gap. We do this by studying the magnetic field dependence of the magnons using magneto Raman spectroscopy in magnetic fields up to 22 T. We use a Hamiltonian with the ring exchange and XXZ interactions that reproduces the details of the magnetic field dependence.