Topological characterization of magnon-polaron bands and thermal Hall conductivity in a frustrated kagome antiferromagnet

Spin-phonon coupling and its efficacy in inducing multiple topological phase transitions in a frustrated kagome antiferromagnet have been rare in literature. To this end, we study the ramifications of invoking optical phonons in such a system via two different coupling mechanisms, namely, a local and a nonlocal one, which are distinct in their microscopic origin. In case of the local spin-phonon coupling, a single phonon mode affects the magnetic interactions, whereas in the nonlocal case, two neighboring phonon modes are involved in the energy renormalization, and it would be worthwhile to compare and contrast between the two. To tackle these phonons, we propose an analytic approach involving a canonical spin-Peierls transformation applied to magnons. The formalism renders a hybridization between the magnons and the phonon modes, yielding magnon-polaron quasiparticles. In both the coupling regimes, validations for the topological signatures are systematically derived from the bulk and edge spectral properties of the magnon-polaron bands that are characterized by their corresponding Chern numbers. Thereafter, we investigate transitions from one topological phase to another solely via tuning the spin-phonon coupling strength. Moreover, these transitions significantly impact the behavior of the thermal Hall conductivity that aids in discerning distinct topological phases. Additionally, the explicit dependencies on the temperature and the external magnetic field are explored in inducing topological phase transitions associated with the magnon-polaron bands. Thus, our work serves as an ideal platform to probe the interplay of frustrated magnetism and polaronic physics.