Spin-Orbital-Lattice Coupling and the Phonon Zeeman Effect in the Dirac Honeycomb Magnet CoTiO$_3$

TL;DR

This study investigates the spin-orbital-lattice interactions and the phonon Zeeman effect in CoTiO$_3$, revealing how magnetic fields influence excitations and uncovering coupling effects through Raman spectroscopy and theoretical modeling.

Contribution

It provides new insights into the spin-orbital and lattice coupling in CoTiO$_3$, combining experimental spectroscopy with DFT calculations to explain magnetic field effects on excitations.

Findings

Splitting of spin-orbital excitations under magnetic field.

Identification of new Raman-active modes due to zone-folding.

Evidence of significant spin-orbital-lattice coupling.

Abstract

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 infrared (IR) spectroscopy, we studied the lattice and spin-orbital excitations in 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 crystal's $c$-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 new 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. We use a model that includes both the spin and orbital degrees of freedom of the 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.