We theoretically study magnon-phonon hybrid excitations (magnon polarons) in two-dimensional antiferromagnets on a honeycomb lattice. With an in-plane Dzyaloshinskii-Moriya interaction (DMI) allowed from mirror symmetry breaking from phonons, we find nontrivial Berry curvature around the anticrossing rings among the magnon and both optical and acoustic phonon bands, which gives rise to finite Chern numbers. We show that the Chern numbers of the magnon-polaron bands can be manipulated by changing the magnetic field direction or strength. We evaluate the thermal Hall conductivity reflecting the nontrivial Berry curvatures of magnon polarons and propose a valley Hall effect resulting from spin-induced chiral phonons as a possible experimental signature. Our study complements prior work on magnon-phonon hybridized systems without optical phonons and suggests possible applications in spin caloritronics with topological magnons and chiral phonons.

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• Antiferromagnetism
• Bosons
• Magnetoelastic effect
• Thermal Hall effect
• Topological phase transition
• Antiferromagnets
• Honeycomb lattice
• Insulators
• Magnetic insulators
• Bogoliubov-de Gennes equations
• Holstein-Primakoff method
• Spin lattice models
• Tight-binding model