Phonon-magnon band structures in CrI3: Fundamental calculations, band topology, and thermal Hall effect

Phonon and magnon band structures are conventionally calculated by diagonalizing the dynamical matrix and solving the Landau-Lifshitz (or Niu-Kleinman) equation, respectively. However, the exploration of their band structures incorporating phonon-magnon interactions is still in its early stages. In our recent work [1, 2], we developed a method that treats phonons and magnons on an equal footing, initially focusing on zone-center modes. We are now extending this approach to finite momenta, employing both a finite-difference method and a newly developed density-functional perturbation theory approach [3]. In this work, we present the phonon-magnon band structures for bulk and monolayer CrI3, highlighting numerous anticrossing points that give rise to novel quasiparticles called magnon-polarons. We demonstrate the calculation of the Chern number, confirming nontrivial topology in both magnon bands and magnon-polarons. Additionally, our analysis reveals the emergence of multiple Weyl points due to the breaking of time reversal symmetry in phonon-magnon bands, which is not captured by conventional phonon calculations. Finally, we discuss the implications of our method for understanding the thermal Hall effect.