Magnon orbital angular momentum of ferromagnetic honeycomb and zigzag lattice models
By expanding the gauge 𝜆 𝑛 (𝐤) for magnon band 𝑛 in harmonics of momentum 𝐤=(𝑘,𝜙), we demonstrate that the only observable component of the magnon orbital angular momentum 𝑂 𝑛 (𝐤) is its angular average over all angles 𝜙, denoted by 𝐹 𝑛 (𝑘). Although 𝐹 𝑛 (𝑘) vanishes for antiferromagnetic honeycomb and zigzag (0<𝐽 1 <𝐽 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 𝐽 1𝑥 and 𝐽 1𝑦 along the 𝑥 and 𝑦 axes, the magnon bands are degenerate along the boundaries of the Brillouin zone with 𝑘 𝑥 −𝑘 𝑦 =±𝜋/𝑎 and the Chern numbers 𝐶 𝑛 are not well defined. However, a revised model with 𝐽 1𝑦 ≠𝐽 1𝑥 lifts those degeneracies and produces well-defined Chern numbers of 𝐶𝑛=±1 for the two magnon bands. When 𝐽 1𝑦 =𝐽 1𝑥 , the thermal conductivity 𝜅 𝑥𝑦 (𝑇) of the FM zigzag lattice is largest for 𝐽2/𝐽1>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, 𝜅𝑥𝑦(𝑇) is slightly enhanced when 𝐽 1𝑦 ≠𝐽 1𝑥 .