Magnon thermal Hall effect in kagome antiferromagnets with Dzyaloshinskii-Moriya interactions

We theoretically study magnetic and topological properties of antiferromagnetic kagome spin systems in the presence of both in- and out-of-plane Dzyaloshinskii-Moriya interactions. In materials such as the iron jarosites, the in-plane interactions stabilize a canted noncollinear “umbrella” magnetic configuration with finite scalar spin chirality. We derive expressions for the canting angle and use the resulting order as a starting point for a spin-wave analysis. We find topological magnon bands, characterized by nonzero Chern numbers. We calculate the magnon thermal Hall conductivity and propose the iron jarosites as a promising candidate system for observing the magnon thermal Hall effect in a noncollinear spin configuration. We also show that the thermal conductivity can be tuned by varying an applied magnetic field or the in-plane Dzyaloshinskii-Moriya strength. In contrast to previous studies of topological magnon bands, the effect is found to be large even in the limit of small canting.

Figure 1

The kagome lattice is a network of corner-sharing triangles. The two lattice vectors ${\mathbf{a}}_1$ and ${\mathbf{a}}_2$ are shown, along with the sublattices $\alpha ,\beta ,\gamma$.

Figure 2

(a) Top and (b) side views of the canted ${120}^{\circ }$ (or “umbrella”) magnetic configuration. The top view also serves as an illustration of the ${120}^{\circ }$ order without canting.

Figure 3

The kagome DM vectors. The in-plane directions are shown by the green arrows, while the out-of-plane component is out of (into) the plane for the triangles pointing up (down).

Figure 4

Spin-wave spectrum for potassium iron jarosite. The full spectrum is shown in (a), and detailed views showing gaps and avoided crossings near the $\mathrm{\Gamma }$ and $K$ points are shown in (b).

Figure 5

Magnon thermal Hall conductivity for potassium iron jarosite in zero magnetic field as a function of temperature, up to the ordering temperature $T_N=65\mathrm{K}$. The dashed vertical line marks $T_0=50\mathrm{K}$.

Figure 6

The magnon thermal Hall conductivity as a function of an applied staggered magnetic field perpendicular to the kagome plane. The magnon thermal Hall signal at $T=T_0$ is shown in blue, and the canting angle (in degrees) is shown in red. The sign change of the conductivity is associated with a sign reversal of all the Chern numbers. We note that the effect does not vanish with the scalar spin chirality as the canting angle approaches zero. The disks correspond to the values for iron jarosites in ambient conditions.

Figure 7

The magnon thermal Hall conductivity as a function of an applied nonstaggered magnetic field perpendicular to the kagome plane. The magnon thermal Hall signal at $T=T_0$ is shown in blue and is obtained by averaging the responses for positive and negative fields in Fig. 6.

Figure 8

The magnon thermal Hall conductivity at $T=T_0$ as a function of the in-plane component of the DM interaction is shown in blue. In red, the canting angle (in degrees) is plotted. Near $|D_p|/J_1=0.25$ there is a topological transition from a situation where all bands are topological to one where the middle band is topologically trivial. The blue disk marks the value obtained in Fig. 5 for the experimental canting angle of $1.9^{\circ }$ (marked by a red disk).

Figure 9

Evolution of the magnon spectrum as the magnetic field strength $B$ is varied.

Figure 10

Top: Evolution of the upper gap as the magnetic field strength $B$ is varied. Bottom: Evolution of the lower gap, the avoided crossing.

Figure 11

Evolution of the magnon spectrum as the in-plane DMI strength $D_p$ is changed.