Spin-orbital–lattice coupling and the phonon Zeeman effect in the Dirac honeycomb magnet CoTiO 3

The entanglement of electronic spin and orbital degrees of freedom is often the precursor to emergent behaviors in condensed matter systems. With considerable spin-orbit coupling strength, the cobalt atom on a honeycomb lattice offers a platform that can make accessible the study of novel magnetic ground states. Using temperature-dependent Raman spectroscopy and high-magnetic-field Raman and IR spectroscopy, we studied the lattice and spin-orbital excitations in ${\mathrm{CoTiO}}₃$, an antiferromagnetic material that exhibits topologically protected magnon Dirac crossings in the Brillouin zone. Under the application of an external magnetic field up to 22 T along the crystalline $c$ axis, we observed the splitting of both the spin-orbital excitations and a phonon nearby in energy. Using density functional theory (DFT), we identify a number of modes that below the antiferromagnetic (AFM) transition become Raman active due to the zone folding of the Brillouin zone caused by the doubling of the magnetic unit cell. The phonon splitting under an applied magnetic field, or the phonon Zeeman effect, is observed in both a zone-centered phonon as well as its zone-folded counterpart. We use a model that includes both the spin and orbital degrees of freedom of the $\mathrm{Co}{}²⁺$ ions to explain the spin-orbital excitation energies and their behavior in an applied field. Our experimental observations along with several deviations from the model behavior point to significant coupling between the spin-orbital and the lattice excitations.