Weyl magnons in noncoplanar stacked kagome antiferromagnets

Weyl nodes have been experimentally realized in photonic, electronic, and phononic crystals. However, magnonic Weyl nodes are yet to be seen experimentally. In this paper, we propose Weyl magnon nodes in noncoplanar stacked frustrated kagome antiferromagnets, naturally available in various real materials. Most crucially, the Weyl nodes in the current system occur at the lowest excitation and possess a topological thermal Hall effect, therefore they are experimentally accessible at low temperatures due to the population effect of bosonic quasiparticles. In stark contrast to other magnetic systems, the current Weyl nodes do not rely on time-reversal symmetry breaking by the magnetic order. Rather, they result from explicit macroscopically broken time reversal symmetry by the scalar spin chirality of noncoplanar spin textures and can be generalized to chiral spin liquid states. Moreover, the scalar spin chirality gives a real space Berry curvature which is not available in previously studied magnetic Weyl systems. We show the existence of magnon arc surface states connecting projected Weyl magnon nodes on the surface Brillouin zone. We also uncover the first realization of triply-degenerate nodal magnon point in the noncollinear regime with zero scalar spin chirality.

Figure 1

(a) Top view of unshifted kagome lattice stacked along the (001) direction. The ${120}^{\circ }$ noncollinear spin configuration with a positive vector chirality is indicated (blue arrows). The in-plane unit vectors are ${\mathbf{a}}_1=(1,0,0)$ and ${\mathbf{a}}_2=(1/2,\sqrt{3}/2,0)$. The unit vector along the stacking direction ${\mathbf{a}}_3=(0,0,1)$ is not depicted. The mirror reflection axes (dotted lines) and the direction of DMI (crossed and dotted circles) are indicated. (b) Bulk Brillouin zone (BZ) of stacked hexagonal lattice with indicated high-symmetry points. (c) (010) surface BZ. (d) Scalar spin chirality of three noncoplanar spins on a triangle: ${\chi }_{ijk}={\mathbf{S}}_i·\left({\mathbf{S}}_j\times {\mathbf{S}}_k\right)$ (dashed red arrow).

Figure 2

Magnon bands of stacked kagome antiferromagnets. (a) Magnon band structure of stacked ${120}^{\circ }$ noncollinear spin structure (with zero scalar spin chirality) showing doubly-degenerate nodal-line magnons (red rectangle) and triply-degenerate nodal magnon point (red circle) for $D_z/J=0.2,J_c/J=0.5,H=0$. The flat bulk magnon band along $\mathbf{H}\text{−}\mathbf{A}$ line is a lifted zero energy mode due to the presence of the DMI. It is an artifact of the kagome-lattice structure and can acquire a small dispersion upon the inclusion of an intralayer antiferromagnetic NNN interaction. Inset shows 3D magnon band in the $k_y=0$ plane with nodal magnon rings in the $k_x\text{−}{k}_z$ momentum space. (b) Magnon band structure of stacked noncoplanar spin structure (with nonzero scalar spin chirality) showing Weyl magnon nodes for $D_z/J=0.2,J_c/J=0.5,H=0.3H_s$, where $H_s=6J+2\sqrt{3}{D}_z+4J_c$ is the saturation field. Note that the flat bulk magnon band is now dispersive in the noncoplanar regime, and the doubly-degenerate nodal-line magnons and the triply-degenerate nodal magnon point are lifted with the appearance of WM nodes. Inset shows 3D magnon band in the $k_y=0$ plane for ${\mathrm{W}}_1$ Weyl cones.

Figure 3

Monopole distribution of the lowest magnon band Berry curvature ${\mathrm{\Omega }}_{1,xz}^y\left(\mathbf{k}\right)$ on the $k_y=0$ plane (a) and ${\mathrm{\Omega }}_{1,yz}^x\left(\mathbf{k}\right)$ on the $k_x=2\pi /3$ plane (b), showing the monopole (red dot) and antimonopole (pink dot) distribution of WM nodes. The parameters are the same as Fig. 2.

Figure 4

(a) (010)-projected nodal-line magnons (red and pink dots) with drumhead magnon surface states (red lines) at zero scalar spin chirality with the parameters of Fig. 2. The (010)-projected flat bulk magnon band in the noncollinear regime (i.e., zero scalar spin chirality) is a lifted zero energy mode due to the presence of the DMI. It is an artifact of the kagome-lattice structure and can acquire a small dispersion upon the inclusion of an intralayer antiferromagnetic NNN interaction. (b) (010)-projected Weyl magnon nodes of opposite chirality (red and pink dots) connected by chiral magnon arc surface states (red lines) at nonzero scalar spin chirality with the parameters of Fig. 2.

Figure 5

The density plot of the magnon surface spectral function on the (010) surface BZ. The ${\mathrm{W}}_1$ Weyl nodes form magnon arcs at $E\approx E_{W_1}$. The parameters are the same as Fig. 2.

Figure 6

Topological thermal Hall conductivity. (a) The plot of ${\kappa }_H$ vs $T$ for $D_z/J=0.2,J_c/J=0.5$ and $H=0.3H_s$. (b) The plot of ${\kappa }_H$ vs $H$ for $D_z/J=0.2,J_c/J=0.5$, and $T/J=0.75$.

Figure 7

Bulk Weyl magnon bands of antiferromagnetically coupled stacked kagome antiferromagnets in the noncoplanar regime with nonzero scalar spin chirality. Here $D_z/J=0.2,H=0.3H_s$. (a) $J_c/J=0.05$ (quasi-2D limit). (b) $J_c/J=1.2$ (strong 3D limit). Notice that ${\mathrm{W}}_3$ is type-II WM node.

Figure 8

Bulk magnon bands and surface states of ferromagnetically coupled stacked kagome antiferromagnets in the noncoplanar regime with nonzero scalar spin chirality. (a) Bulk magnon bands along the BZ paths. (b) (010)-projected magnon surface states. The parameters are $D_z/J=0.2,\left|J_c\right|/J=-0.5,H=0.3H_s$.