Magnon-Driven Domain-Wall Motion with the Dzyaloshinskii-Moriya Interaction

We study domain-wall (DW) motion induced by spin waves (magnons) in the presence of the Dzyaloshinskii-Moriya interaction (DMI). The DMI exerts a torque on the DW when spin waves pass through the DW, and this torque represents a linear momentum exchange between the spin wave and the DW. Unlike angular momentum exchange between the DW and spin waves, linear momentum exchange leads to a rotation of the DW plane rather than a linear motion. In the presence of an effective easy plane anisotropy, this DMI induced linear momentum transfer mechanism is significantly more efficient than angular momentum transfer in moving the DW.

Figure 1

(a) Illustration of the head-to-head DW in the nanowire using red-blue opaque arrows. The translucent purple arrows represent a spin wave excitation. The DMI exerts a torque to change the DW tilt angle when spin waves pass through the DW. (b) DW profile using Eq. (5) with parameters $A=8.78\times {10}^{-12}\mathrm{J}/\mathrm{m}$, $K=1\times {10}^5\mathrm{J}/{\mathrm{m}}^3$, $D=1.58\times {10}^{-3}\mathrm{J}/{\mathrm{m}}^2$, $K_{\perp }=0$ and $\mathrm{\Phi }=0$. The red dashed line shows the simulation data for $m_z$ with $K_{\perp }^2=6\times {10}^5\mathrm{J}/{\mathrm{m}}^3$: the easy-plane anisotropy favors a reduced $m_z$. (c) The dispersion relations inside and outside the DW.

Figure 2

Simulation results of the DW velocity as a function of spin wave frequency with different DMI constants for the case of $K_{\perp }=0$. The DMI parameters are $D_0=0$ and $D_{\pm }=\pm 1.58\times {10}^{-3}\mathrm{J}/{\mathrm{m}}^2$. The $v_e$ curve is calculated by $v_e=-({\rho }^2/2)V_g$ [11] where $\rho$ at $x=0$ is extracted from the simulation. Inset: Plot of spin wave amplitude decaying characteristic length $\mathrm{\Gamma }$ versus frequency.

Figure 3

The DW velocity as a function of the spin wave frequency with $K_{\perp }=2\times {10}^5\mathrm{J}/{\mathrm{m}}^3$. The DMI constants employed in the simulation are $D_0=0$ and $D_{\pm }=\pm 1.58\times {10}^{-3}\mathrm{J}/{\mathrm{m}}^2$.

Figure 4

(a) Plot of two types of domain walls, ${\mathrm{\Delta }}_c$ is obtained by fitting the simulation data with $\cos \theta =-\tanh (x/{\mathrm{\Delta }}_c)$. (b) The contour plot of the simulated DW velocity (in m/s) for different $K_{\perp }$ and DMI constants, where the frequency of the external ac field is fixed at $f=30\mathrm{GHz}$.