Exact Results for the Orbital Angular Momentum of Magnons on Honeycomb Lattices

Abstract: We obtain exact results for the orbital angular momentum (OAM) of magnons at the high symmetry points of ferromagnetic (FM) and antiferromagnetic (AF) honeycomb lattices in the presence of Dzyallonshinskii-Moriya (DM) interactions. For the FM honeycomb lattice in the absence of DM interactions, the values of the OAM at the corners of the Brillouin zone (BZ) (${\bf k}_1^*=(0,2\sqrt{3}/9)2\pi/a $, ${\bf k}_2^*=(1/3,\sqrt{3}/9)2\pi/a ,\ldots $) are alternately $\pm 3\hbar /16$ for both magnon bands. The presence of DM interactions dramatically changes those values by breaking the degeneracy of the two magnon bands. The OAM values are alternately $3\hbar /8$ and 0 for the lower magnon band and $-3\hbar /8$ and 0 for the upper magnon band. For the AF honeycomb lattice, the values of the OAM at the corners of the BZ are $\mp (3\hbar /16)\kappa $ on one of the degenerate magnon bands and $\pm (3\hbar /8) (1+\kappa /2)$ on the other, where $\kappa $ measures the anisotropy and the result is independent of the DM interaction.