Spin Orbitons, Phonons, and the Phonon Zeeman Effect in Dirac Antiferromagnet CoTiO₃

The entanglement of electronic, spin, and orbital degrees of freedom is often the precursor to emergent behaviors in condensed matter systems. With relatively large spin-orbit coupling strength, the octahedrally coordinated cobalt aton on a honeycomb lattice offers a platform to study novel magnetic ground states, including potentially the Kitaev spin liquid. Typically, however, magnetic interactions between the Co atoms tend to result in a regular magnetically ordered ground state, like CoTiO₃, whose ground state symmetries protect a Dirac-like crossing of its magnons. It also provides a clear example where the interplay between these degrees of freedom results in exotic interactions and excitations [1]. Here we explore how the spin-orbital energy levels evolve into their own quasiparticles, that we name spin-orbitons, and interact with phonons using both temperature and magnetic field dependent Raman scattering and Infrared spectroscopy. In both Raman and Infrared spectroscopies the spin-orbitons show the expected Zeeman effect. Surprisingly, we find that the Raman-active phonons hybridize, even at zero magnetic field, with nearby spin-orbitons, resulting in the phonon Zeeman effect: the splitting and linear in field depenence of the phonon frequency. This makes them chiral phonons. On the other hand, the Infrared-active phonons are not hybridized with their nearby spin orbitons. We will discuss potential explanations for these behaviors.

[1] Y. Li, et al. Phys. Rev. B. 109, 184436 (2024).