Topological Magnons and Edge States in Antiferromagnetic Skyrmion Crystals

Antiferromagnetic skyrmion crystals are magnetic phases predicted to exist in antiferromagnets with Dzyaloshinskii-Moriya interactions. Their spatially periodic noncollinear magnetic texture gives rise to topological bulk magnon bands characterized by nonzero Chern numbers. We find topologically protected chiral magnonic edge states over a wide range of magnetic fields and Dzyaloshinskii-Moriya interaction values. Moreover, and of particular importance for experimental realizations, edge states appear at the lowest possible energies, namely, within the first bulk magnon gap. Thus, antiferromagnetic skyrmion crystals show great promise as novel platforms for topological magnonics.

Figure 1

Classical ground-state texture of the AFM-SkX for the model parameters $D/J=0.5$ and $g{\mu }_{B}B/JS=2.5$. The magnetic unit cell, comprised of $7\times 7$ spins enclosed by the white dashed-line loop, has $Q=-1$ topological charge. The color code indicates the out-of-plane component of the spins, showing the noncollinearity of the texture.

Figure 2

Classical phase diagram at zero temperature. Among the magnetic textures are: helical (white dots), AFM-SkX (squares), and vortex crystal (yellow dots). Blue (pink) squares represent AFM-SkX magnons with (without) a global first bulk magnon gap. Absence of plot markers denotes a mixture of various textures. The color code indicates the topological charge density $q=3Q/\mathcal{N}$, with $\mathcal{N}$ the total number of spins.

Figure 3

Bulk magnon band structure of the AFM-SkX along the first BZ loop $\mathrm{\Gamma }\text{−}M\text{−}K\text{−}\mathrm{\Gamma }$ for the same parameters of Fig. 1. Bands are labeled by their Chern numbers (yellow squares). The green rectangle highlights the first bulk magnon gap.

Figure 4

AFM-SkX on a strip of infinite length along the $x$ axis with edges located at the top and bottom of the figure; parameters as in Fig. 1. The magnetic unit cell, comprising $7\times 63$ spins, is enclosed by the white dashed-line loop. (Inset) One-dimensional magnon band structure showing two chiral edge states within the first gap ($G_{\mathrm{s}}=2\pi /7a$). The right- or left-moving edge state is depicted in blue or red, while the color gradients encode the total magnon spin carried by each one.

Figure 5

Real space characterization of the chiral edge states from Fig. 4 inset at $k_x=0.45G_{\mathrm{s}}$. (a) Magnonic contribution of the wave function of the edge states ${\mathrm{\Gamma }}_{L,R}$ over an area spanning 3 times the magnetic unit cell. The right- (left-)moving state, depicted in blue (red), is localized at the top (bottom), as expected of edge states with positive winding. (b) Magnon spin density carried by the edge states.