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

TL;DR

This paper provides exact calculations of the orbital angular momentum of magnons at high symmetry points in honeycomb lattices, revealing how Dzyaloshinskii-Moriya interactions and anisotropy influence these values.

Contribution

It offers the first exact analytical results for magnon orbital angular momentum in honeycomb lattices, including effects of DM interactions and anisotropy.

Findings

OAM values at BZ corners are alternately ±3ħ/16 without DM interactions.

DM interactions alter OAM values, breaking degeneracy and producing distinct values for magnon bands.

OAM in AF lattices depends on anisotropy, independent of DM interactions.

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.