We explore the moiré magnon bands in twisted bilayer magnets with next-nearest-neighbor Dzyaloshinskii-Moriya interactions, assuming that the out-of-plane collinear magnetic order is preserved under weak interlayer coupling. By calculating the magnonic band structures and the topological Chern numbers for four representative cases, we find that (i) the valley moiré bands are extremely flat over a wide range of continuous twist angles, (ii) the topological Chern numbers of the lowest few flat bands vary significantly with the twist angle, and (iii) the lowest few topological flat bands in bilayer antiferromagnets entail nontrivial thermal spin transport in the transverse direction. These properties make twisted bilayer magnets an ideal platform to study the magnonic counterparts of moiré electrons, where the statistical distinction between magnons and electrons leads to fundamentally new physical behavior.

• Received 1 June 2020
• Accepted 23 August 2020

DOI:https://doi.org/10.1103/PhysRevB.102.094404