Magnon orbital angular momentum of ferromagnetic honeycomb and zigzag lattice models
By expanding the gauge π π β‘(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 π π β‘(π€) is its angular average over all angles π, denoted by πΉ π β‘(π). Although πΉ π β‘(π) vanishes for antiferromagnetic honeycomb and zigzag (0<π½ 1 <π½ 2 ) 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 π½ 1β’π₯ and π½ 1β’π¦ along the π₯ and π¦ axes, the magnon bands are degenerate along the boundaries of the Brillouin zone with π π₯ βπ π¦ =Β±π/π and the Chern numbers πΆ π are not well defined. However, a revised model with π½ 1β’π¦ β π½ 1β’π₯ lifts those degeneracies and produces well-defined Chern numbers of πΆπ=Β±1 for the two magnon bands. When π½ 1β’π¦ =π½ 1β’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 π½ 1β’π¦ β π½ 1β’π₯ .