Orbital Angular Momentum of Magnons in Collinear Magnets

We study the orbital angular momentum of magnons for collinear ferromagnet (FM) and antiferromagnetic (AF) systems with nontrivial networks of exchange interactions. The orbital angular momentum of magnons for AF and FM zigzag and honeycomb lattices becomes nonzero when the lattice contains two inequivalent sites and is largest at the avoided-crossing points or extremum of the frequency bands. Hence, the arrangement of exchange interactions may play a more important role at producing the orbital angular momentum of magnons than the spin-orbit coupling energy and the resulting noncollinear arrangement of spins.

Figure 1

FM zigzag. (a) A square lattice with alternating FM exchange interactions $J_1$ and $J_2$ between up spins. (b) Magnon bands for $k_{y}a/2\pi =0.1$. (c) The OAM ${\mathcal{L}}_{zn}(\mathbf{k})/\hslash$ graphed as a function of $\mathbf{k}$ for different values of $r=J_2/J_1$. The dashed line shows $k_{y}a/2\pi =0.1$ (d) Magnons of an $r=2$ FM zigzag material traveling with opposite momenta $\pm \mathbf{k}$ and $\mathrm{OAM}\pm \mathcal{L}$ in a temperature gradient.

Figure 2

AF zigzag. (a) A square lattice with FM exchange $J_2>0$ on zigzag chains with up (closed circles) or down (open circles) spins coupled by AF exchange $J_1<0$. (b) The OAM for upper (top) and lower (bottom) bands versus $\mathbf{k}$ for different values of $J_1$ and $J_2$.

Figure 3

FM honeycomb. (a) A honeycomb lattice with FM exchange $J>0$ between neighboring up spins and DM interaction $D$ between next-nearest neighbors. (b) The OAM for the upper (top) and lower (bottom) bands versus $\mathbf{k}$ for different values of $d=-2D/3J$.

Figure 4

AF honeycomb. (a) A honeycomb lattice with AF exchange $J<0$ between up (closed circles, site 2) and down (open circles, site 1) spins. (b) The OAM of the major (left) and minor (right) bands versus $\mathbf{k}$ for anisotropy $\kappa =0$.