Abstract
By expanding the gauge ππβ‘(π€) for magnon band π in harmonics of momentum π€=(π,π), we demonstrate that the only observable component of the magnon orbital angular momentum ππβ‘(π€) is its angular average over all angles π, denoted by πΉπβ‘(π). Although πΉπβ‘(π) vanishes for antiferromagnetic honeycomb and zigzag (0<π½1<π½2) lattices, it is nonzero for the ferromagnetic (FM) versions of those lattices in the presence of Dzyaloshinskii-Moriya interactions. For a FM zigzag model with equal exchange interactions π½1β’π₯ and π½1β’π¦ along the π₯ and π¦ axes, the magnon bands are degenerate along the boundaries of the Brillouin zone with ππ₯βππ¦=Β±π/π and the Chern numbers πΆπ are not well defined. However, a revised model with π½1β’π¦β π½1β’π₯ lifts those degeneracies and produces well-defined Chern numbers of πΆπ=Β±1 for the two magnon bands. When π½1β’π¦=π½1β’π₯, the thermal conductivity π π₯β’π¦β‘(π) of the FM zigzag lattice is largest for π½2/π½1>6 but is still about four times smaller than that of the FM honeycomb lattice at high temperatures. Due to the removal of band degeneracies, π π₯β’π¦β‘(π) is slightly enhanced when π½1β’π¦β π½1β’π₯.
