Two-Dimensional Twisted Ferromagnetic Domain Wall as a Spin-Wave Diffraction Grating

Abstract

We present a theoretical study of spin-wave scattering by a twisted domain wall (DW) in a two-dimensional ferromagnet with easy-axis anisotropy. While the twisted DW generates an effective gauge field for spin waves, leading to a deflection of their trajectories, our main focus is on a distinct effect that arises when a hard-axis anisotropy is present in addition to the easy-axis anisotropy. In this case, the translational symmetry of the spin-wave Hamiltonian along the DW is broken, resulting in a periodic modulation of the Hamiltonian. This periodicity leads to the formation of multiple diffracted spin wave modes on both sides of the DW, engendering a DW-induced magnonic diffraction pattern. The interplay between the emergent gauge field and the anisotropy-induced periodicity reveals rich spin-wave dynamics and suggests potential applications for manipulating magnon flow in two-dimensional magnetic textures.

Figures (1)

• Figure 1: (a) Reflection coefficients, $|\frac{u_q(x\to-\infty)}{u_0(x\to-\infty)}|^2$ of diffracted wave as a function of $k_x$. (b) Transmission coefficients, $|\frac{u_q(x\to+\infty)}{u_0(x\to+\infty)}|^2$ of diffracted wave as a function of $k_x$. The parameters are $\mathcal{K}_z=0.01$, $k_0=0.1$, $\mathcal{K}_x=0.001$ and $k_y=0$. (c) Schematic illustration of the interaction between a spin wave and a twisted DW. Note the change in the transverse wave vector of the transmitted spin waves caused by the twisting of the DW. (d) Density plot of $|\psi(x,y)|^2$ in the homogeneous region on the right side of the DW, as a function of $x$ and $y$ for $\mathcal{K}=0.001$, $\mathcal{K}_z=0.01$, $k_0=0.1$, $k_x=0.05$ and $k_y=0$.