Frequency splitting of chiral phonons from broken time reversal symmetry in CrI$_3$

TL;DR

This paper introduces a first-principles method to accurately calculate chiral phonon frequency splitting in magnetic materials like CrI$_3$, emphasizing the importance of coupled magnon-phonon dynamics due to broken time-reversal symmetry.

Contribution

It develops a novel first-principles approach to include velocity-force coupling, improving the accuracy of lattice dynamics calculations in magnetic systems with broken time-reversal symmetry.

Findings

Velocity-force coupling significantly affects phonon splittings.

Adiabatic separation assumptions can lead to large errors.

Coupled magnon-phonon treatment is essential for accurate results.

Abstract

Conventional approaches for lattice dynamics based on static interatomic forces do not fully account for the effects of time-reversal-symmetry breaking in magnetic systems. Recent approaches to rectify this involve incorporating the first-order change in forces with atomic velocities under the assumption of adiabatic separation of electronic and nuclear degrees of freedom. In this work, we develop a first-principles method to calculate this velocity-force coupling in extended solids, and show via the example of ferromagnetic CrI$_3$ that, due to the slow dynamics of the spins in the system, the assumption of adiabatic separation can result in large errors for splittings of zone-center chiral modes. We demonstrate that an accurate description of the lattice dynamics requires treating magnons and phonons on the same footing.