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The study of symmetry-protected topological phases of matter has been extended from fermionic electron systems to various bosonic systems. Bosonic topological magnon phases in magnetic materials have received much attention because of their exotic uncharged topologically protected boundary modes and the potential for dissipationless magnonics and spintronic applications. Here, we establish twisted bilayer honeycomb magnets as a platform for hosting second-order topological magnon insulators (SOTMIs) without fine-tuning. We employ a simple, minimal Heisenberg spin model to describe misaligned bilayer sheets of honeycomb ferromagnetic magnets with a large commensurate twist angle. We found that the higher-order topology in this bilayer system shows a significant dependence on the interlayer exchange coupling. The SOTMI, featuring topologically protected magnon corner states that go beyond the conventional bulk-boundary correspondence, appears for ferromagnetic interlayer couplings, while the twisted bilayer exhibits a nodal phase in the case of antiferromagnetic interlayer coupling. At last, relevance to twisted bilayer CrI₃ is also discussed.
Hua et al. (Thu,) studied this question.