Control of Spin-Wave Refraction Using Arrays of Skyrmions

A periodically patterned and magnetized medium for controlling spin waves is proposed in a magnonic device and presents a clear advantage compared with other metamaterials because of the tunability in reconfiguring its pattern during operation. We study the spin-wave propagation numerically by controlling the arrangement of two magnetic Skyrmion arrays instead of patterned structures. The adjustment the position of each of the Skyrmion arrays could result in distinct spin-wave propagation or refraction depending on the location of the Skyrmions in each array. Control of the arrangement of two Skyrmion arrays can be made by an asymmetric magnetic field generated by a symmetric electrode with different current directions. This simple method of spin-wave manipulation can be applied to the development of magnonic devices consisting of Skyrmions as the building blocks of the magnonic crystals.

Figure 1

Schematic illustration of the sample structure and spin-wave propagations. (a) The area between the white dashed lines represents a reduced region of the simulation structure with the periodic boundary condition. The gray color on the sample denotes the perpendicular magnetization component. The yellow area represents the spin-wave source and the red arrows indicate the spin-wave propagation direction. (b) Spin-wave distribution with $\mathrm{\Delta }y=32\mathrm{nm}$. (c) Spin-wave distribution with $\mathrm{\Delta }y=0\mathrm{nm}$.

Figure 2

Refraction patterns of the spin wave with respect to the arrangements of Skyrmion arrays. (a) Schematic description for spin-wave refraction. The black-shaded and wavy lines represent the spin wave propagating from left to right. The green-shaded and wavy lines represent the scattered spin wave from the Skyrmions. The green arrow shows the propagation direction of the scattered wave. The red (blue) lines denote Skyrmion positions of ${\mathrm{SK}}_B$ for a constructive (destructive) interference of the scattered wave. (b)–(j) Spin-wave distribution with different $\mathrm{\Delta }x$ and $\mathrm{\Delta }y$ values.

Figure 3

Control of the relative position between Skyrmion arrays. (a) Electric current flows over the sample. The directions of the current flow are antiparallel. (b) Magnetic-field distributions on the sample. (c) Gradient field induced by the current flows drive each Skyrmion array into the opposite direction. (d) Reversed current flow reinstates the Skyrmion arrays to their previous positions.

Figure 4

Dispersion of the Skyrmion array.

Figure 5

Periodic defects of perpendicular magnetic anisotropy for trapping the Skyrmion.

Figure 6

Stability of the Skyrmion array with different defect strengths.

Figure 7

Spin-wave propagations with periodic defects. $H=1\mathrm{T}$, $f=100\mathrm{GHz}$, and defect $K_U=0.785\mathrm{MJ}{\mathrm{m}}^{-3}$. (a), (d) Anisotropy distributions and Skyrmion position. (b), (e) Spin-wave distributions. (c), (f) Schematic wave images.

Figure 8

Spin-wave propagations with different frequencies.

Figure 9

Spin-wave propagations with different material parameters. $M_S$ ($650\mathrm{kA}{\mathrm{m}}^{-1}$), $K_U$ ($0.289\mathrm{MJ}/{\mathrm{m}}^{-3}$), $A$ ($10\mathrm{pJ}{\mathrm{m}}^{-1}$), $D$ ($-0.525\mathrm{mJ}{\mathrm{m}}^{-2}$), the damping constant (0.01), the material length (6000 nm), the width (192 nm), the thickness (0.4 nm), and the cell size ($6\mathrm{nm}\times 6\mathrm{nm}\times 0.4\mathrm{nm}$).