Damped Topological Magnons in the Kagome-Lattice Ferromagnets

We demonstrate that interactions can substantially undermine the free-particle description of magnons in ferromagnets on geometrically frustrated lattices. The anharmonic coupling, facilitated by the Dzyaloshinskii-Moriya interaction, and a highly degenerate two-magnon continuum yield a strong, nonperturbative damping of the high-energy magnon modes. We provide a detailed account of the effect for the $S=1/2$ ferromagnet on the kagome lattice and propose further experiments.

Figure 1

(a) A ground state of (1) with ${\mathbf{D}}_{ij}=D\widehat{\mathbf{z}}$; arrows on bonds show ordering of ${\mathbf{S}}_i$ and ${\mathbf{S}}_j$ in the DM term with fictitious fluxes indicated. (b) Magnon bands along the $K\mathrm{\Gamma }MK$ path for $D=0$ (solid line) and for $D/J=0.3$ with $\mathbf{M}\parallel \mathbf{D}$ (dashed line).

Figure 2

The LSWT two-magnon DoS (7) for mode 1, $\mathbf{M}\perp \mathbf{D}$. Inset: schematics of a magnon decay from $\mathbf{k}=0$.

Figure 3

Solutions of the iDE (9) for $D/J=0.3$, $S=1/2$ along the $K\mathrm{\Gamma }MK$ path. Inset: the FWHM of spectral lines, ${ϵ}_{\mathbf{k}}\pm {\mathrm{\Gamma }}_{\mathbf{k}}$.

Figure 4

(a) ${\mathrm{\Gamma }}_{1(3),\mathbf{k}=0}$ vs $\theta$. Insets: ${\mathrm{\Gamma }}_{\mu ,\mathbf{k}}$ along the $K\mathrm{\Gamma }M$ path for several $\theta$. (b) The 2D intensity distributions of ${\mathrm{\Gamma }}_{3,\mathbf{k}}$ in $\mathbf{k}$ space for $\pi /2$, $\pi /3$, and $\pi /4$. (c) The $\mathbf{k}-\theta$ intensity maps of ${\mathrm{\Gamma }}_{1(3),\mathbf{k}}$ along the $K\mathrm{\Gamma }M$ path. $D/J=0.3$, $S=1/2$.